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  • 1997  (27)
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  • Computational Chemistry and Molecular Modeling
  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 1-11 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Roothaan-Hartree-Fock (RHF) calculations are carried out for the ground states of the atoms from helium to xenon using a minimal basis set of Slater-type functions whose principal quantum numbers are allowed to take variationally optimal noninteger values. The resulting energies are substantially superior to those obtained previously under the usual restriction that principal quantum numbers be positive integers. The energy lowering relative to the single-zeta wave functions of Clementi and co-workers ranges from 0.0066 Eh in He to 11.2 Eh in Xe. Our results are superior to those obtained by Höjer using a minimal basis set of unconventional binomially screened basis functions. Noninteger principal quantum numbers benefit d-orbitals the most; physically realistic negative d-orbital energies are obtained in all cases including those transition-metal atoms for which a conventional single-zeta STF basis leads to positive d-orbital energies. © 1997 John Wiley & Sons, Inc.
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 23-27 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio study on the reaction of the ground state (3D) and the excited state (1D) of Sc+ with methane was performed. Reaction channels on the singlet and triplet potential surface (PES) and the reaction mechanism are examined and discussed. Three regions of the potential surface was studied: the molecular complex, the C(SINGLE BOND)H insertion products, and the transition states for the reaction. Comparisons between singlet and triplet PESs show that the excited state (1D) of Sc+ has more reactivity with methane than does the ground state (3D) due to the spin quantum number conservation with the more stable insertion intermediate. © 1997 John Wiley & Sons, Inc.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 67-76 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The importance of the hybridization displacement charge (HDC) in describing molecular electrostatic potential (MEP) maps was demonstrated by studying six molecules; pyrazine N-oxide, para-nitropyridine, 5-nitropyrimidine, 3-nitropyridazine, N2, and N2O. It is shown that continuously distributed HDC-corrected Löwdin charges reproduce the MEP features of these molecules, most of which have competing electrophilic sites, in agreement with ab initio results. Further, it is found that for homonuclear diatomic molecules MEP minima can be located properly using HDC-corrected Löwdin (or HDC-corrected Mulliken) continuously distributed charges, but these features cannot be obtained using the conventional Löwdin (or Mulliken) charges. It was shown that the order of molecular electric field (MEF) values near the different electrophilic sites becomes changed when one moves away from the molecules. Thus, pyridine-type nitrogen atoms are the preferred binding sites close to the molecules, while at large distances, effects of oxygen atoms of the NO groups become dominant. © 1997 John Wiley & Sons, Inc.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 115-124 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some types of atomic vibrations in a chain of the DNA type constructed of G-C pairs were studied. These are the atomic vibrations of the lateral groups of guanine and N(3)H(1)H(2) of cytosine connected by the hydrogen bond h-b-1 and the vibrations of the centers of masses of bases in the direction parallel to bonds h-b-i, i = 1-3. The vibrations mix partially due to the dependence of the energy of the bond h-b-1 on its length and split into two bands because of the interaction between neighboring base pairs. It was shown that the excitation of the bond h-b-1 results in the splitting off of the two local vibrations and in a small deformation of the chain in the vicinity of the pair with the localized hydrogen bond. The law of the dispersion of band vibrations, values of the split-off frequencies, and degree of poly(dG)-poly(dC) chain deformation were determined. © 1997 John Wiley & Sons, Inc.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 273-278 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical solutions to the Yukawa-like screened Coulomb nuclear attraction and electron repulsion molecular basic integrals, as well as to the basic integrals required to compute the virial coefficient, over Gaussian basis functions, are derived and cast into a practical closed form, suitable to interface with modern codes for the calculation of molecular electronic structure. © 1997 John Wiley & Sons, Inc.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 303-314 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: He I photoelectron (PE) spectra of four carboxylic acids and five esters are measured. Semiempirical and ab initio quantum chemical calculations are used for the interpretation of the spectra. The complex approach which uses empirically established relationships (the dependence of valence electron ionization energies on proton affinities in the gas phase, on the core level ionization energies, and on the structure) was developed. © 1997 John Wiley & Sons, Inc.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 323-328 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Simple molecular orbital calculations are employed in searching electronic parameters which may characterize the chemical carcinogens. Using frontier orbitals, the carcinogen-DNA bond formation is described as an electron transfer from the highest occupied molecular orbital (HOMO) of DNA to the lowest unoccupied molecular orbital (LUMO) of the carcinogen. Analysis of the DNA bases units shows that the electron donation occurs preferentially at the guanine site. The calculated low LUMO energy of several carcinogens indicate correctly the electrophilic character of these compounds. The difference between the carcinogen and the ultimate carcinogen is analyzed. Epoxides, free radicals, alkylating agents, and other metabolite forms are studied. A reasonable correlation is found between the LUMO energy and the carcinogenic function. © 1997 John Wiley & Sons, Inc.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 1107-1122 
    ISSN: 0020-7608
    Keywords: relativistic pseudopotentials ; heavy atoms ; method of molecular calculation ; electronic structure ; Gaussian approximation ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Gaussian expansions of the generalized relativistic effective core potential (GRECP) components are reported for elements Hg through Rn. The accuracy of the analytical GRECPs is estimated by calculations of atomic transition energies with the numerical one-configurational wave functions in comparison with Dirac-Fock calculations. The results of the corresponding calculations with the RECPs of other groups are also given. An “averaged error” in the reproduction of the transition energies without the change of the occupation number of the 5d-shell is an order of magnitude smaller than that for the RECPs of other groups. As is demonstrated for the transitions with the change of the occupation number of the 5d-shell in mercury, the largest absolute error of the GRECP is only 1.5-2 times smaller than that of the energy-adjusted pseudopotential (PP) or the RECP of Ross et al. with the same space of explicitly treated electrons. However, the dispersion of these errors is 19⋅10-4 au for the energy-adjusted PP, 35⋅10-4 au for the RECP of Ross et al. and only 4⋅10-4 au for the GRECP. One-configurational spin-averaged calculations of the molecular properties for HgH and HgH+ are carried out and compared with the corresponding results of Häussermann et al.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1107-1122, 1997
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 1123-1131 
    ISSN: 0020-7608
    Keywords: MD simulations ; liquid surface ; formamide ; molecular orientation ; molecular surface density ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Molecular dynamics simulations of liquid formamide(HCONH2) were carried out using the GROMOS software. The formamide molecule is represented by all of its atoms with all internal degrees of freedom. In contrast to other simulations dealing with bulk properties, this study focuses on the interface liquid-vacuum for the first time. We show that the molecular plane is tilted out of the surface, exposing the HCO group to the vacuum.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1123-1131, 1997
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 29-45 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The H2 interaction with the Pd dimer and trimer were studied using multiconfigurational self-consistent field (MC-SCF) calculations with the relativistic effective core potential (RECP); the correlation energy correction was included in the extended multireference configuration interaction (MRCI), variational and perturbative to second order. Here, we considered the Pd2 first six states: 3Σ+u, 1Σ+g, 3Πg, 3Δxy, 1Σ+u, and 3Σ+g. For them, the four geometrical approaches included were the side-on H2 toward Pd2, for the hydrogen molecule in and out the Pd dimer plane; the perpendicular end-on H2 toward Pd2; and the perpendicular end-on Pd2 to H2. The Pd2 ground state is 3Σ+u, which only captures H2 in the C2v end-on approach, softly relaxing the H(SINGLE BOND)H bond. The closed-shell 1Σ+g captures the H2 molecule in all the approaches considered: The side-on approach of this state presents deep wells and relaxes the H(SINGLE BOND)H bond, and the end-on approach captures H2 with a relatively longer H(SINGLE BOND)H distance and also a deep well. The 3Πg state was the only one which did not capture H2. For the triangular Pd3 clusters, H2 was approached in the C2v symmetry in and out of the Pd3 plane. In the triangular case, H2 was absorbed in both spin states, with deep wells and relaxing the H(SINGLE BOND)H distance. The linear Pd3 singlet and triplet states capture outside of the Pd3 and break the H(SINGLE BOND)H bond. © 1997 John Wiley & Sons, Inc.
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  • 11
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 89-96 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We presented a calculation of the total and partial decay widths of vibrational predissociation (VP) of the HeI2 molecule for low initial vibrational excitations from the lowest van der Waals (vdW) state with total angular momentum J = 0. A time-dependent golden rule wave-packet method was employed in our numerical calculations for the decay widths. The computed total decay widths, lifetimes, and rates of VP are in fairly good agreement with those extrapolated from the experimental data available. Predicted total decay widths as a function of initial vibrational levels exhibit a highly nonlinear behavior. These results demonstrate that a quantum mechanical decay mode for low vibrational excitation remains as well. The total propagation time needed in the time-dependent golden rule wave-packet calculations is much shorter than is the lifetime of the predissociation of HeI2. It is shown that the final-state interaction between the fragments is important for determining the final rotational-state distribution (partial decay width). We find that the major peak position in the final rotational-state distribution shifts to lower rotational energy levels with increase of the initial vibrational quantum number, which is evidently different from that for higher vibrational levels. This fact can be clearly explained by the dependence of the amount of kinetic energy released to the product degrees of freedom on the initial vibrational state. © 1997 John Wiley & Sons, Inc.
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  • 12
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 1065-1078 
    ISSN: 0020-7608
    Keywords: very precise eigenvalues ; very accurate grid method ; general solution for Schrödinger equations ; rapidly convergent treatment for helium eigenvalues ; superconvergence ; optimization of grids ; treatment of continuum ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An extension to the theory of Schrödinger equations has been made which enables the derivation of eigenvalues from a consideration of a very small part of geometric space. The concomitant unwanted continuum effects have been removed. The theory enables very convergent or “superconvergent” calculations. In the case of the helium ground state, E=-2.90372437703411987 Eh was obtained from 251 terms. The result is comparable to that from the largest variation calculations so far carried out reinforced by extrapolation techniques. The theory is extensible to atoms and molecules irrespectively of the number of electrons or nuclear centers. In these cases, the advantage of “superconvergent” calculations will be more pronounced than in the case of helium.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1065-1078, 1997
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 239-244 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We calculate the resonant and antibound state energies for a Morse potential with a centrifugal barrier using Siegert boundary conditions. Starting with a complex wave number k (purely imaginary for bound and antibound states), we integrate numerically from the origin up to a matching point using Numerov's method. The inward integration is performed using the corresponding (first-order) Riccati equation. The complex eigenvalues are found by matching the two logarithmic derivatives. We find narrow shape resonances within the well, above the dissociation limit, and broad resonances above the centrifugal barrier. Antibound states are found even with J = 0. © 1997 John Wiley & Sons, Inc.
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  • 14
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 265-272 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Numerical experiments with a nonlinear (λχ4) oscillator which has its harmonic frequency changing randomly with time reveal certain interesting features of its dynamics of quantum evolution. When λ = 0, the level populations are seen to oscillate. But, as the nonlinear coupling is switched on (λ 〉 0), a threshold is reached at λ = λc when the evolution is seen to be characterized by an abrupt transition dominantly to the highest available state of the unperturbed (initial) oscillator. It is shown that this transition probability is maximized at a particular value of λ. The time threshold for this transition decreases with increasing nonlinear coupling strength. The numerically obtained structures of the underlying quantum-phase spaces of the linear and nonlinear random oscillators are examined. Possible use of these results in a problem of chemical origin is explored. © 1997 John Wiley & Sons, Inc.
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  • 15
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 279-289 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Testosterone (17β-hydroxy-4-androsten-3-one) was studied by the semiempirical AM1 and PM3 and ab initio STO-3G*, 3-21G*, and 6-31G* methods. The goals were to compare those methods and to know the electronic structure of the hormone. Full geometry optimization was performed, and two crystal conformers (T1 and T2), and experimental dipole moment in solution were used for comparison. One conformer with a dipole moment similar to the solvated conditions was generated. Total energy, entalphies, dipole moments, charges, electrostatic potentials, and highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbital (LUMO) were calculated. Root-mean-square (RMS) index of the theoretical molecules against T1 and T2 showed best results with the 3-21G* and 6-31G* methods, while AM1 gave better energies than PM3. Dipole moments were directed toward the OH group and the botton face of the A ring. The frontier orbitals were located along the C4-C5 π bond, particularly the LUMO was split between C4 and C5, predicting the action of enzymes at C5 yielding to 5α and 5β-reduced androgens. Electrostatic potentials might be also of biological importance since they are coincidental with the dipole-moment orientation. Finally, it is interesting that the solvatedlike conformer, its properties, and the OH group laid between the same group of T1 and T2 and with a total energy between the crystals and the gas phase or in vacuo conditions. This results might also explain the biology of testosterone and use them to model the hormone-receptor interaction. © 1997 John Wiley & Sons, Inc.
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  • 16
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 315-322 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two alternative dehydration reactions C(OH)4 → (HO)2CO + H2O and C(OH)4 + H2O → (HO)2CO + 2H2O are studied by ab initio Becke3LYP/6-311 + G** and MP2/6-31G** methods. Calculated energy and geometry characteristics of intermediates and transition states predict a catalytic effect of one water molecule and the exothermism of the transformations. Relevant HF/6-311 + G**, HF/6-31G**, HF/6-31G, and HF/3-21G calculations were performed for comparison. © 1997 John Wiley & Sons, Inc.
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 97-113 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Restricted geometry optimizations at the ab initio SCF level with the 3-21G basis set were employed to investigate the conformation space of flavone acetic acid (FAA) and its related compounds. All the conformations are produced from a conformation which is, according to our previous work, probably the active conformation in terms of antitumor activity shown by these compounds. Detailed studies on FAA were carried out while only brief discussions are made on the analogs. The main results obtained are that (1) FAA is a very flexible molecule, e.g., with the energy barrier up to about 3 kcal mol-1 from the reference conformation, the important torsional angle τ1 can change from 27.0° to 117.0°, τ2 from -168.0° to 2.0°, and τ3 from -50.0° to 30.0°; (2) the hydrogen-bonding effect plays an important role in determining lower-energy conformations; (3) among all the FAA conformations considered, some are active and some are inactive; (4) it seems that the analogs will have similar behavior to FAA when the torsional angle τ3 is restricted to the values which are around the equilibrium values; and (5) the hypothesis put forward previously has been further developed in this work. Now, we postulate that efficient charge transfers will lower the energy and that proper charge transfers will activate the molecule. There are mainly two different types of charge transfer corresponding to two different types of conformation, which are specified in this article. © 1997 John Wiley & Sons, Inc.
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  • 18
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 55-65 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We compare geometry configurations, vibrational properties, and electronic structures of (HF)2 in a free state and inside argon atom shells Arn. For the first stage, molecular dynamics calculations for the (HF)2 · Ar62 heterocluster are performed with the help of model potentials HF(SINGLE BOND)HF, Ar(SINGLE BOND)Ar, and Ar(SINGLE BOND)HF. Then, ab initio quantum chemistry analysis is carried out for the smaller systems (HF)2 · Ar15 and (HF)2 · Ar6 when keeping the argon atoms closest to the trapped dimer. We conclude that the hydrogen-bonded complex (HF)2 gains some extra stability inside the argon shells, originating primarily from a decrease of intermolecular distance RFF. Electronic structure calculations are in accord with the changes in dynamical properties, namely, a noticeable increase in the vibrational frequency assigned to the F(SINGLE BOND)F stretching mode (+25 cm-1) and decrease in rms deviations for the corresponding coordinate δFF. In addition to these changes, the argon atoms of the nearest solvent shell donate a small fraction of electron charge which is spent for an increase of population of the antibonding orbital σ*Hf(SINGLE BOND)Ff of the free monomer unit and shift orbital energies primarily of the lone-pair fluorine species. These shifts are greater than the changes due to geometry alterations and the possible inaccuracies of the calculation scheme. © 1997 John Wiley & Sons, Inc.
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  • 19
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 13-21 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis of the anisotropic Heisenberg model is carried out by solving the Bethe ansatz solution of the model numerically as a function of the anisotropy parameter for finite N. A brief introduction to the limit of the infinite chain is presented. The energy for a few special limiting cases of the anisotropy parameter in the Hamiltonian are worked out. Numerical results for finite cycles as well as for the infinite chain are given. Comparison can then be made with the case of finite increasing N. © 1997 John Wiley & Sons, Inc.
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  • 20
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 47-53 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The MELD program is employed to evaluate the Slater average potential v(r) felt by an electron at the point r within an atom. The characteristic radius R of the atom is then defined by the classical turning point equation v(R) = -I, where I denotes the first ionization potential of the atom. The atomic radii defined in this way have a close correlation with the van der Waals atomic radii. © 1997 John Wiley & Sons, Inc.
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  • 21
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 77-88 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Highly accurate upper bounds for several 2Pe states of the Li isoelectronic series obtained by extensive Hylleraas-Cl calculations are given. The best value for the 22Pe state (1s2p2) of Li is -5.21373920 au. The evaluation of the occurring integrals is given explicitly. Additionally, we present some expectation values and isotope energies of the Li isoelectronic series. © 1997 John Wiley & Sons, Inc.
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  • 22
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 245-259 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An efficient expansion method for the evaluation of VB matrix elements is introduced. The overlaps of VB wave functions of N electrons can be treated as algebrants, i.e., generalized determinants, of N × N matrices. An algebrant can be expanded with subalgebrants of lower orders in a successive way. By choosing Rumer spin bases and appropriately arranging the expansion, it is found that the number of unique subalgebrants involved in the expansion increases in a quite moderate way with N. In contrast to the traditional symmetric group approach, which explicitly utilizes all N! representation matrices, the new strategy incorporates the group theoretical factors in a simple way in the successive expansion. As only the unique subalgebrants are further expanded, the computational effort required by the new strategy scales in a very acceptable manner with the increasing number of electrons. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 245-259, 1997
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  • 23
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 261-264 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Characters of irreducible representations (irreps) of the symmetric group corresponding to the two-row Young diagrams, i.e., describing transformation properties of N-electron eigenfunctions of the total spin operators, have been expressed as explicit functions of the number of electrons N and of the total spin quantum number S. The formulas are useful in various areas of theory of many-electron systems, particularly in designing algorithms for evaluation of spectral density moments. © 1997 John Wiley & Sons, Inc.
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  • 24
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 291-296 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The geometries and S-H, S-S, and S-C bond dissociation energies for hydrogen sulfide, hydrogen disulfide, methanethiol, dimethyl disulfide, and dimethyl disulfide were calculated with both ab initio (ROHF and MP2), hybrid (BHandH, BHandHLYP, Becke3LYP and Becke3P86), and nonlocal (BLYP and BP86) density functional theory (DFT) methods. In all studies the 6-31 + G(d) basis set is used. The computed results are compared to the experimentally obtained values, targeting the selection of a suitable ab initio or DFT method for the study of these systems. © 1997 John Wiley & Sons, Inc.
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  • 25
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    International Journal of Quantum Chemistry 62 (1997), S. 297-302 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The mechanism and kinetics for the decomposition of β-hydroxypropaldehyde, primary and secondary β-hydroxyketones, were studied by using ab initio RHF/6-31G and RHF/6-31G* methods. The activation barriers of these reactions were refined to be 39.57, 40.10, and 36.80 kcal mol-1 at the MP2/ /RHF/6-31G* level, respectively. The calculated results show that each decomposition is a concerted process with hydrogen transferring and bond breaking via a six-membered cyclic transition state. The thermal rate constants of the decomposition of primary and secondary β-hydroxyketones were obtained by calculating microcanonical probability fluxes through each transition state. It is theoretically confirmed that methyl substitution at the hydroxyl carbon of β-hydroxyketones causes a small enhancement in rates. The theoretical investigations of the mechanism and the rate constants are in agreement with the experimental results. © 1997 John Wiley & Sons, Inc.
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  • 26
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    International Journal of Quantum Chemistry 63 (1997), S. 1079-1089 
    ISSN: 0020-7608
    Keywords: large-order perturbation theory ; lie algebra ; three-body problem ; symbolic computations ; helium atom ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of o(4, 2) operator replacements is generalized. As a result, the series whose limiting values when the variable goes to  +∞ should correspond to the two-electron atom energies now have rational coefficients. This generalization allows one also to compute the series for the case of singlet S symmetry, a case which could not be considered in the previous original formulation of the method. Series with rational coefficients for the helium singlet and triplet S ground-state energy are calculated up to order 41 and 45, respectively. Moreover, symbolic computations also allow one to give the first few coefficients of these series for arbitrary values of the nuclear charge Z. Finally, a new method for analytic continuation to the limit  +∞ is presented for the energies of the helium singlet and triplet ground states.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1079-1089, 1997
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  • 27
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    International Journal of Quantum Chemistry 63 (1997), S. 1099-1106 
    ISSN: 0020-7608
    Keywords: metathesis reactions ; bond order ; free valence ; minimum energy path ; nonsynchronization ; Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A few simple atom-transfer reactions (i.e., Ȧ+X-A→A-X+Ȧ) are studied by quantum mechanical ab initio methods. Emphasis is given to the detailed analysis of density matrices rather than to the energetics. Results reveal that during these reactions a small free valence always develops on the migrating atom at the transition state. The barriers in these reactions arise from the greater extent of bond cleavage in the reactant than that of bond formation in the transition state. Analysis of bond orders estimated from bond lengths using Pauling's relation also leads to the fact that the bond-cleavage process is more advanced than is the bond-formation process in these reactions.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1099-1106, 1997
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  • 28
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method proposed recently for the generation of modified Hartree-Fock virtual orbitals has been tested by performing a simple configuration-interaction calculation for the ground state of the He atom. A very compact truncated basis set was constructed by using an a priori criterion based on the probability density within the region of the occupied orbital. The best results were obtained by making the virtual orbital energies more positive.
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  • 29
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    International Journal of Quantum Chemistry 7 (1973), S. 459-473 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper we obtain formulae useful in methods for the direct minimization of the energy functional in the LCAO-MO-MC-SCF approach. The formulae are appropriate for dealing with variations in both the linear and nonlinear parameters. We include formulae for the usual closed- and open-shell problems as special cases.
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  • 30
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    International Journal of Quantum Chemistry 7 (1973), S. 1-13 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The treatment of electrostatic interactions between molecular groups is based on quantum mechanical electron density distributions. A general method is suggested using tesseral harmonic multipole expansions and representing each set of point multipoles by a cluster of discrete charges small with respect to atomic dimensions. The procedure is carried out for the amino group with an electron density derived from the wave function of ammonia. We evaluate the optical rotation of two aminopyrrolidones as a test case. Expansions are compared for several approximate wave functions for ammonia.
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  • 31
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    International Journal of Quantum Chemistry 7 (1973), S. 51-62 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energy terms arising in the water calculation by the FSGO method are analyzed as a function of the bond angle in order to gain insight into the reasons for the particular equilibrium configuration. The analysis is made in terms of symmetrically orthogonalized orbitals so as to exclude three- and four-orbital electron repulsion terms.
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  • 32
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    International Journal of Quantum Chemistry 7 (1973), S. 87-108 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The instabilities of the solutions to the Hartree-Fock equations for the nonalternants in the pentalene, heptalene, etc., series and in the azulene, etc., series are examined. The systems are found to have symmetry-adapted solutions which are unstable for values of the core integral β close to the standard (spectroscopic) value; for example, the pentalene solution is unstable with β equal to 75% of its standard value. The “broken” symmetry solutions although exhibiting only a very slightly lower energy (0.01 eV) may exhibit dramatically different values for other properties, e.g., 30% changes in bond orders. The off-diagonal charge-density wave (CDW) appearing in the “broken” symmetry solutions at the onset of instability is amplified as the cooperative phenomena dominate, until in the “fully correlated” limit, the linked-ethylenic (bond alternating) structure is obtained.
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  • 33
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    International Journal of Quantum Chemistry 7 (1973), S. 133-134 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 34
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    International Journal of Quantum Chemistry 7 (1973) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 35
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    International Journal of Quantum Chemistry 7 (1973), S. 759-777 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electron spin dipole-dipole interaction in CH2 has been calculated as a function of bond angle with configuration-interaction wave functions built from contracted gaussianlobe basis functions. The values D = 0.781 cm-1 and E = 0.050 cm-1 were obtained for the spin dipole-dipole contribution to these parameters for the best CI wave function at the equilibrium geometry. The angular dependence of D shows that the assumption of perfect orbital following is not valid. Based on previous estimates of the spin-orbit contribution to D, the total D is estimated to be 0.9 ± 0.1 cm-1 which is higher than the current experimental value 0.76 ± 0.02 cm-1.
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  • 36
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    International Journal of Quantum Chemistry 7 (1973) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 37
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Expressions are derived for the n-dependent, hydrogen-like relativistic corrections to the magnetic dipole and electric quadrupole radial hyperfine integrals of an arbitrary atomic state.Good agreement has been obtained earlier between these corrections and the relativistic Hartree-Fock results for s1/2 states. The agreement remains good for the p1/2 states. For the p3/2 states in heavier atoms the hydrogenic corrections still reproduce the Hartree-Fock trend. For the higher l values the agreement is poor. Numerical tables are given for 1 ≤ Z ≤ 100 for the s1/2, p1/2, and p3/2 magnetic dipole cases and the p3/2 quadrupole case.
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  • 38
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    International Journal of Quantum Chemistry 7 (1973), S. 27-34 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: SCF-LCAO-MO-CI calculations made on 2- and 4-amino-, and 2,4-diaminopteridines indicate that the most favorable site where the protonation can take place is N-1.
    Additional Material: 3 Ill.
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  • 39
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    International Journal of Quantum Chemistry 7 (1973), S. 15-25 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that gauge terms can be introduced into the Gaussian functions used as the basis functions for an ab initio calculation of the energy of a molecule in the presence of a uniform magnetic field so that all the integrals become independent of the origin of the vector potential. The perturbation treatment of the diamagnetic susceptibility is considered in the molecular orbital approximation. The results show that the susceptibility can be calculated using only the unperturbed orbitals and their first-order corrections. All the integrals that arise can be expressed in terms of known functions.
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  • 40
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    International Journal of Quantum Chemistry 7 (1973), S. 285-300 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Formulae are presented for the evaluation of some definite integrals in which the Laguerre orthogonal functions are contained. In some cases mechanical quadratures are to be preferred, and a scheme is presented for generating such a quadrature as it is needed.
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  • 41
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    International Journal of Quantum Chemistry 7 (1973), S. 345-355 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Upper and lower bounds for the second-order energy in both coupled and uncoupled Hartree-Fock perturbation theories are derived. Using these bounds inequalities are derived for the error in the geometric approximation.
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  • 42
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    International Journal of Quantum Chemistry 7 (1973), S. 521-536 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Alternant molecular orbitals for the lithium metal are constructed in different ways. The corresponding first-order density matrix is calculated for different shapes of the Fermi surface. Numerical methods to calculate the first-order density matrix are described.
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  • 43
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    International Journal of Quantum Chemistry 7 (1973), S. 547-560 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The all-valence electron band structures of the periodic DNA models polyC, polyT, and polyA have been calculated with the aid of the CNDO/2 and MINDO/2 crystal orbital (CO) method.According to the obtained results the valence and conduction bands are always of π type. The widths of the bands are usually larger in the CNDO case, than those obtained for the same systems in the PPP CO approximation. On the other hand the MINDO results show similar widths as the PPP ones. The forbidden bandwidths are by 3-4 eV larger in the CNDO/2 case, than in the PPP one, while the MINDO/2 CO method has resulted in similar gaps like the PPP calculation.
    Additional Material: 3 Ill.
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  • 44
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    International Journal of Quantum Chemistry 7 (1973), S. 187-193 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A theorem is proved which demonstrates the relationship between a product of group functions describing the correlated motion of a particular group of electrons in an N-electron system and a wave function obtained from the exact wave function which describes the correlation of the same group of electrons. By considering such products of group functions as elements in a variational wave function, an expansion for correlated wave functions is suggested, which emphasizes the correlated motion of groups of electrons in the whole system.
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  • 45
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    International Journal of Quantum Chemistry 7 (1973), S. 223-232 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Approximate and ab initio molecular wave functions are obtained using Gaussian expansions of different length for the Slater orbitals. The expectation values of several one-electron operators are obtained and the accuracy of different wave functions discussed.
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  • 46
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    International Journal of Quantum Chemistry 7 (1973), S. 333-344 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Consideration is given to the problem of interactions between molecular systems (magnetic couplings being neglected) by highlighting the fact that the main difficulty of a perturbation theory that takes into account the exchange effects, resides in the differentiated symmetry of the unperturbed state and of the state of interaction (at an overlap other than zero). This difficulty has been overcome by choosing for the Schrödinger equation of the interacting systems a particular representation on the set of unperturbed functions and by reversing the symmetry properties onto the operators. This will lead to a new equation no longer presenting any difficulties for the symmetry interconnection. This equation is used for a double perturbational expansion both in Coulomb and in exchange terms, thus obtaining general perturbation equations. Explicit solutions are provided (up to the second total order) which are briefly discussed.
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  • 47
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    International Journal of Quantum Chemistry 7 (1973), S. 383-404 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: After a discussion of different concepts of anisotropy with reference to the icosahedron, the unusual problems surrounding the construction of icosahedral irreducible tensors are discussed. Tables of these tensors are then presented and applied to orbital problems, molecular polarization phenomena and to the construction of projection operators.
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  • 48
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: A proof of the convergence of the double infinite series form of the radial factor in the bipolar expansion of r12-1 is given. It consists of demonstrating the validity of the required term-by-term integrations.
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  • 49
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    International Journal of Quantum Chemistry 7 (1973), S. 853-867 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A class of reference full density matrices and their reduced density matrices is presented. These density matrices are designed to be of value as references from which to describe and measure the effects of electron correlation in atoms, molecules, and solids. A given reference full density matrix is constructed to contain the least possible information consistent with having the (recognized) symmetry properties of - and reducing to the 1-matrix of - a given “true” full density matrix (which in a typical application is constructed from a correlated variational wave function). Therefore, the reduced density matrices derived from are representable and depend only upon the 1-matrix of and the (recognized) symmetry properties of for their construction. Furthermore, the property of containing the least possible information consistent with the given constraints makes these reference density matrices ideally suitable as references from which to describe the electron correlation contained in the “true” full density matrix .
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  • 50
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    International Journal of Quantum Chemistry 7 (1973), S. 869-876 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of functional iteration applied to orbital optimization is proposed. The main problem, i.e., the most economical parametrization of the rotations of the molecular orbitals, is resolved. First and second derivatives of rotations with respect to the parameters are given. The fact that the orbital space can be decomposed in subspaces such that energy is invariant against transformations of these subspaces into themselves is explicitly taken into consideration.
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  • 51
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    International Journal of Quantum Chemistry 7 (1973), S. 893-903 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio valence bond (VB) method for calculating energies and wave functions for simple electronic systems is described and the results of its application to methylene are given together with extensive comparisons with previous theoretical results.
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  • 52
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    International Journal of Quantum Chemistry 7 (1973), S. 951-958 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Various optimization criteria are compared for the hydrogen atom to find orbitals which improve lower bounds computed from the Weinstein, Temple, and Stevenson-Crawford formulas. Minimization of squared energy deviation, “variance,” is recommended because the resulting lower bound orbitals give excellent lower bounds, converge to the exact wave function, are relatively easy to optimize, and are insensitive to the estimated energy eigenvalue. New linear combinations of Gaussian orbitals which minimize the variance are presented for the 1s, 2s, 2p, 3s, 3p, and 3d orbitals. These orbitals are compared with previous linear combinations with regard to their expectation values and local properties.
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  • 53
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    International Journal of Quantum Chemistry 7 (1973), S. 991-998 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The third-order interaction between two nonpolar molecules due to the instantaneous induced dipole effect of an infinitely long linear molecule is assessed following arguments similar to earlier research on three-body effects. It is found that an attractive force favors small polar angles in approach to the linear molecule; such behavior could be of interest to processes such as those involved in replication of DNA.
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  • 54
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    International Journal of Quantum Chemistry 7 (1973), S. 131-132 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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  • 55
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    International Journal of Quantum Chemistry 7 (1973), S. 139-153 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A theoretical study of the spin-optimized self-consistent field methods is given in a second quantization formalism using the occupation-branching number representation and a biorthogonal basis treatment given by Moshinsky and Seligman. A diagrammatic presentation can then be introduced. Further investigation will be thus facilitated.
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  • 56
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    International Journal of Quantum Chemistry 7 (1973), S. 195-213 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Green functions and Kubo linear-response theory are used to calculate the absorption coefficient of a collection of diatomic molecules embedded in a one-dimensional lattice. The effect of the environment is restricted to the coupling between the molecular internal vibration and lattice vibrations. For the molecular oscillators, both harmonic and anharmonic models are considered. The absorption line shape is expressed in closed form whether the molecular frequency falls outside or within the allowed phonon frequency range. In both cases a frequency shift is found. In the anharmonic case there is a broadening of the absorption lines. Expressions for the shift and line width are given.
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  • 57
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    International Journal of Quantum Chemistry 7 (1973), S. 623-634 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A modified Gaussian function g(u, v, w, a, R) = const s(a, R) is considered where l = u + v + w, s (a, R) is a 1s-type Gaussian function centered at R, a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R. General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.
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  • 58
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    International Journal of Quantum Chemistry 7 (1973), S. 667-674 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A simple, “nearly free electron” model for the dihydrides of Be, Mg, Ca, Sr and Ba is investigated. To zeroth order the valence electrons are assumed to form a free gas. Effects of band structure are included in second-order pseudopotential perturbation theory. The stability of three probable crystal structures is investigated, and lattice parameters are calculated for two different choices of the pseudopotential.
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  • 59
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    International Journal of Quantum Chemistry 7 (1973), S. 647-665 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A computational approach for general Heisenberg spin Hamiltonians for a finite number of interacting doublet species is described. Maximum use of permutation and point group symmetry is incorporated in factorizing the secular equation. Associated problems in the computation of symmetric group characters, related frequencies, and selection of linearly independent kets from a large linearly dependent set are also solved.
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  • 60
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    International Journal of Quantum Chemistry 7 (1973), S. 725-737 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio self-consistent computation has been performed on the permanganate ion (MnO4-) in a large basis set of contracted gaussian functions. The ground state description as well as those of the first two excited states are discussed and compared with those obtained experimentally from photoelectron spectroscopy, ESCA, optical spectroscopy and magnetic circular dichroism.
    Additional Material: 11 Tab.
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  • 61
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    International Journal of Quantum Chemistry 7 (1973), S. i 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 62
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    International Journal of Quantum Chemistry 7 (1973), S. 63-73 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The exchange polarization energy and higher-order exchange corrections arising in the second order of the Murrell-Shaw and Musher-Amos (MS-MA) theory are evaluated analytically for the hydrogen molecule ion. At large internuclear distances the second-order exchange energy predicted by MS-MA theory behaves like \documentclass{article}\pagestyle{empty}\begin{document}$- \frac{1}{{18}}Re^{ - R}$\end{document}. It represents only 80% of the difference between the exact result of Holstein and the asymptotic value of the first-order exchange energy. The same result holds for the case of Hirschfelder-van der Avoird (HAV) and Hirschfelder-Silbey (HS) theories.
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  • 63
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    International Journal of Quantum Chemistry 7 (1973), S. 127-130 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 64
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    International Journal of Quantum Chemistry 7 (1973), S. 569-581 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Applying an extended form of the Mulliken approximation and a monopole approximation for the Coulomb integrals the Hartree-Fock nonorthogonal energy expression is decoupled. Thus, the total energy splits into a sum of one-electron increments. The increments are minimized directly with respect to the linear coefficients and orbital exponents. Further, the ZDO approximation is used in the decoupled energy expression to avoid difficulties arising in connection with the evaluation of multicenter integrals. “Rigid core” calculations were carried out for the valence electrons of first-row diatomics. In case of nonpolar molecules good results are obtained for equilibrium distances and force constants. The method fails for molecules with atoms having very different nuclear charges.
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  • 65
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    International Journal of Quantum Chemistry 7 (1973), S. 609-622 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Various molecular properties have been calculated for pyridine and pyrazine from Gaussian lobe ab initio SCF molecular wave functions. Values are compared with available experimental data. In general, agreement is satisfactory with the exception of the rather sensitive asymmetry parameter of the quadrupole coupling tensor. The distributions of total electronic charge, and of selected molecular orbitals have been displayed as plots of the charge density contours in two dimensions.
    Additional Material: 8 Ill.
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  • 66
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    International Journal of Quantum Chemistry 7 (1973), S. 641-646 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For an estimation of the pair correlation the interelectronic distance r12 in geminal ψk(12) is introduced. The calculations are carried out by the local energy method [1, 2]. The influence of other electrons are taken into consideration with the help of the one- and two-electron integrals depending upon r1 and r2 as parameters. If the strong orthogonality condition is satisfied all two-electron integrals and most of the one-electron integrals vanish. All atomic orbitals are expressed in terms of Gaussian functions. A trial calculation is made for the beryllium atom.POUR tenir compte de la corrélation, on introduit la distance interélectronique r12 dans la géminale ψk(12). Le calcul est réalisé par une méthode des énergies locales [1, 2]. L'influence des autres électrons est décrite par des intégrales à un et deux electrons, dépendantes de r1 et r2 comme paramètres. Dans les conditions de l'orthogonalité forte, toutes les intégrales à un électron et la plupart des intégrales à deux électrons disparaissent. Pour simplifier l'algorithme du problème, toutes les orbitales sont exprimées par les fonctions de Gauss. Le calcul est réalisé sur le modèle de l'atome Be.Für Berechnung der Korrelation wird der Interelektronenabstand r12 in Geminal ψk(12) eingeführt. Die Berechnung wird mit der Lokalenenergiemethode durchgeführt [1, 2]. Die Einwirkung der anderen Elektronen wird durch 1- und 2-Elektronenintegrale berücksichtigt, die von Parametern r1 und r2 abhängen. Bei Erfüllung der starken Orthogonalitätsbedingung verschwinden alle 2-Elektronen- und die Mehrzahl der 1-Elektronenintegrale. Alle Orbitale werden durch Gaussfunktionen ausgedrückt. Eine Berechnung für das Atom Be wird durchgeführt.
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  • 67
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    International Journal of Quantum Chemistry 7 (1973), S. 675-686 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: As until now proposed in the literature, in the local energy calculations we can distinguish “few-points” procedures, in which the number M of configurational points is strictly related to the number N of trial functions used, and statistical “many-points” procedures, in which the number M of points can be arbitrarily increased. In this paper we demonstrate that the energy errors resulting from a “many-points” calculation M points/N functions (M 〉 N) can be connected in a simple way with the errors of the (MN) partial calculations N points/N functions.This suggests a possible approach for the problem of the choice of the configurational points to be introduced in the calculation, and leads to a simple interpretation of the numerical meaning of the error associated with the ordinary Ritz energy. Numerical examples on the hydrogen atom are reported.
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  • 68
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    International Journal of Quantum Chemistry 7 (1973), S. 717-723 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown how to obtain pseudonatural orbitals directly from the equations of motion. A sample calculation on the ground state of the Be atom is given.
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  • 69
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    International Journal of Quantum Chemistry 7 (1973), S. 155-171 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Exchange perturbation theory of the Rayleigh-Schrödinger type is applied, in first and second orders, to the problem of bonding in rare-gas halides. The basic model is that of a four-electron, three-center system with one effective electron replacing the unpaired electrons of a halogen atom, and two spin-paired electrons representing the closed shells of the rare-gas atom. On the basis of exchange perturbation theory, the model verifies a direct parallelism between bonding in rare-gas compounds and the phenomenon of super-exchange in ionic solids with paramagnetic cations. It is found that the observed stability and specific geometric configuration of the xenon and krypton fluorides are readily reproduced by the model. In addition, the model explains why other dihalides cannot exist. The two principal components of the interaction energy are found to be indirect exchange between halogen atoms via the rare-gas atoms (attractive in the stable configurations) and, in compounds with coordination higher than two, simultaneous interactions between three halogen atoms (always repulsive). The observed approximate constancy of the binding energy per bond in xenon fluorides with increasing coordination is accounted for.
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  • 70
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Slater orbital r12-1 integrals are calculated with a numerical Fourier-transform method based on a formulation first given by Bonham, Peacher and Cox. Spherical wave expansions are introduced that decouple the Feynman integrations for the charge distribution Fourier transforms. The Feynman integrals are evaluated semianalytically, and their properties are analyzed in detail. The final computational step involves a numerical integration over charge distribution quantities. Results for (coplanar) multicenter exchange integrals over 1s orbitals are given. As long as the charge distributions are overlapping considerably, the method gives good results, even when these distributions are highly asymmetric. The method as presently implemented fails when highly disconnected charge distributions are involved.
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  • 71
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    International Journal of Quantum Chemistry 7 (1973), S. 253-284 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Tensorial sets adapted to sequences of finite subgroups are applied to the crystal field problem, and a general method for generating sequence-adapted molecular tensors using finite group algebra is formulated. All subgroup sequences of the abstract finite group G(24), isomorphic to the octahedral, O, tetrahedral, Td, and symmetric, S(4), groups are tabulated with explicit isomorphisms provided. The sequences fall into eight equivalence classes. A catalog of irreducible representations of G(24) adapted to a member of each of the eight sequence classes is given together with the transformations which generate representations adapted to all other sequences. With this data it is possible to systematically generate tensorial sets adapted to any sequence of a realization of G(24). Unitary transformations which adapt conventional forms of first- and second-rank irreducible tensorial sets of the rotation group to the eight sequences of the octahedral group are provided. Forms suitable for use with magnetic fields are included. The problem of a d1 ion in a trigonal crystal field is treated with sequence-adapted molecular tensors, and the utility of different sequences for descent in symmetry is discussed.
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  • 72
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    International Journal of Quantum Chemistry 7 (1973), S. 1051-1061 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The coarse structure magnetic theory presented here is a reformulation of conventional magnetic theory which emphasizes the spin-free (i.e., the coulombic) nature of the electron-electron interaction. We show that the magnetic properties of a system for which fine and hyperfine structure can be neglected depend only on the energy spectrum of a spin-free Hamiltonian. As an example, we treat the Heisenberg linear chain.
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    International Journal of Quantum Chemistry 7 (1973), S. 1077-1090 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The infinite interaction range model (IIRM) for ferromagnetic systems is presented in its spin-free formulation. In this formulation the states are labelled by partitions which provide a natural variable for thermodynamic computation. We have extended the calculations of Kittel and Shore by computing to a practical thermodynamic limit (N ∼ 100,000). The heat capacity, magnetic susceptibility and the magnetization of the first two functions exhibit a critical temperature while the magnetization is zero at zero field for all temperatures. Spontaneous magnetization is obtained by linear extrapolation from high field or equivalently by a polarized partition function. Relationships are explored among IIRM, the Heisenberg model and the mean field model. Application to IIRM of the Yang-Lee condition for a phase transition yields a critical temperature identical to that obtained by the direct calculation.
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  • 74
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    International Journal of Quantum Chemistry 7 (1973), S. 1175-1182 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Theoretical electronic wave functions, potential curves, and expectation values of some one-electron properties are given for the c3IIu state of the hydrogen molecule. The calculations are carried out by the matrix Hartree-Fock method and use a 2-center basis of Slater-type orbitals. A total energy of -0.7292 a.u. is obtained in the best calculation. Our potential curve is reasonably consistent with that calculated by Browne, but we have examined the region of small internuclear distances (those at and below Re for the ground state) more extensively than any previous calculation. At R ≦ 1.6 a.u. our calculated potential curve is in excellent agreement with experiment.
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    International Journal of Quantum Chemistry 7 (1973), S. 1203-1220 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The expressions for matrix elements of spin-independent operators F and G with the use of Young operators are obtained in the case of arbitrary nonorthogonalized orbital configuration, including both singly and doubly filled orbitals and corresponding to the definite value of total spin. The formulas obtained do not require a preliminary construction of linear combinations of determinants and turn into known Löwdin formulas in the particular case of fully antisymmetric spatial states.
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  • 76
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    International Journal of Quantum Chemistry 7 (1973), S. 1227-1228 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 77
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    International Journal of Quantum Chemistry 7 (1973), S. 637-637 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 78
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    International Journal of Quantum Chemistry 7 (1973), S. 699-705 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A discussion of Hartree damping in closed-shell Hartree-Fock theory is given indicating when the method might force convergence of intrinsically divergent cases. An alternative, but closely related principle, “level shifting” is described, and the advantages of the latter procedure discussed.
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  • 79
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    International Journal of Quantum Chemistry 7 (1973), S. 687-698 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The half-projected Hartree-Fock function (HPHF) for singlet states is defined as a linear combination of two Slater determinants, which contains only spin eigenfunctions with even quantum number. Using a self-consistent procedure based on the generalized Brillouin's theorem, the RHF, HPHF and PHF functions are deduced for the ground states of the Li-, Be, B+, and C2+ systems, in a limited basis set. It is found that the HPHF function yields better energy values than the RHF function, very close to that of the PHF one. The HPHF scheme seems thus to be useful as a substitute for the PHF model, specially in the case of large electronic systems in which the latter method becomes unmanageable.
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  • 80
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A procedure for the use of the plethysm operation for classification of the permitted electronic terms of impurity complexes in a crystal is presented. The cases of polyatomic symmetrical complexes are discussed as examples.
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  • 81
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    International Journal of Quantum Chemistry 7 (1973) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 82
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    International Journal of Quantum Chemistry 7 (1973), S. 561-568 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A quadratically convergent process using a continued fraction method for finding the square root of the overlap matrix used in Löwdin orthogonalization is presented. The continued fraction method is compared to several other methods for finding the square root of a matrix. The method is found to be more efficient than the other methods when high accuracy is desired.
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  • 83
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    International Journal of Quantum Chemistry 7 (1973), S. 635-636 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
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  • 84
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    International Journal of Quantum Chemistry 7 (1973) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 85
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    International Journal of Quantum Chemistry 7 (1973), S. 707-715 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A core model approach to the calculation of deuteron quadrupole coupling constants is investigated using NH3 as an example. First the deuteron quadrupole coupling constant is calculated from a CNDO wave function. This result is subsequently improved by recomputing the N - D bond orbital by means of a variational calculation using the CNDO function to construct a core potential for the bond Hamiltonian. In order to simplify integrations a single-center basis is chosen to represent the variational wave function. A projection operator formalism is used as a computational scheme to maintain orthogonality of the bond orbital to core orbitals. Excellent agreement with experiment is obtained. The procedure is applicable to more complicated molecules.
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    International Journal of Quantum Chemistry 7 (1973), S. 779-783 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The time-dependent variational principle due to Frenkel is derived from Hamilton's principle using a suitable general expression for the variational wave function. The connections with a recent comment of P. O. Löwdin and P. K. Mukherjee on the same subject are discussed.
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  • 87
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    International Journal of Quantum Chemistry 7 (1973), S. 807-817 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By performing calculations on H2 O similar to the calculations of Dunning and McKoy on C2H4 and HCHO [1a], it is shown that the singlet excited states of the water molecule cannot be adequately represented by an ab initio calculation (no semiempirical elements) using a valence-like basis set (either minimum basis or double zeta) of Slater-type orbitals. The triplets which are the lowest states of their symmetry appear to be described more accurately than the other states, and the lowest four triplet excitation energies are calculated to be 8.1, 8.4, 9.5, and 10.3 eV. The implications for the applicability of simple molecular orbital theory of the type commonly applied are discussed.
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  • 88
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Several schemes are discussed for partitioning the second-order reduced density matrix Γ into two parts, Γ0 and Γ′.The Γ0s are based on the independent particle model and the Γ′s are corrections due to electron correlation. The difficulties of choosing a Γ0 that will serve as a suitable reference point for studying electron correlation are discussed.In order to compare alternative partitioning schemes, an atomic wave function for the 1S ground state of the Be atom in the configuration-interaction approximation was selected. A fifty-two configuration wave function was computed and contour graphs were made of the total pair density Γ(1 2) and of the “correlation pair density” Γ′(1 2) for several choices of the reference Γ0.
    Additional Material: 14 Ill.
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  • 89
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    International Journal of Quantum Chemistry 7 (1973), S. 927-944 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An interpretation of degenerate symmetry spaces associated with a given atomic or molecular configuration is presented, and the theory necessary for atomic applications is discussed in detail. Löwdin's symmetric projection operator for spin and orbital angular momentum is applied on a well-defined sequence of Slater determinants. In this way a degenerate LS space is divided into orthogonal invariant subspaces which can be classified according to internal couplings of angular momentum. A procedure is found which permits expression of each of these LS eigenfunctions as the smallest possible number of successively orthogonalized projected Slater determinants. In particular, minimum size Hartree-Fock interacting spaces (important in rapidly convergent correlation energy calculations) are obtained in their most compact form. An optimum partition of degenerate spaces of three and four excited (atomic or molecular) configurations is obtained in general. Interpretations, simplifications, and systematizations in atomic configuration interaction calculations are discussed in light of present results.
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  • 90
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    International Journal of Quantum Chemistry 7 (1973), S. 971-984 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The 1P and 3P states arising from the configuration (1s)2(2s)(2p) of the Be isoelectronic sequence are investigated. In the single configuration approximation, the energies of the two states are expressed as E0 + K2s2p and E0 - K2s2p, respectively. K2s2p is the exchange integral between the 2s and 2p electrons and E0 is the energy of a model in which K2s2p is deleted. First we calculate the 2s- and 2p-orbitals in this model. Second, by taking account of K2s2p in this model, effects of this term on the 2p-orbitals in the 1,3P states are investigated. In this manner, an explanation is given for the following facts which are obtained from a minimal Slater-type orbital set; (1) for Be and B+, the 2p-orbital of the 1P state is broader than that of the 3P state; (2) for C2+, the extension of the 2p-orbital in the two states is almost the same; (3) for O4+ and Ne6+, in contrast to Be and B+, the 2p-orbital of the 1P state is tighter than that of the 3P state.
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    International Journal of Quantum Chemistry 7 (1973), S. 999-1019 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electron spin dipole-dipole contribution to the zero field splitting has been evaluated for the 3A2 (n → π*) and 3A1 (π → π*) states of formaldehyde using a CI wave function constructed from contracted Gaussian-lobe functions. The values D = 0.539 cm-1 and E = 0.031 cm-1 were obtained for the 3A2(n → π*) state and D = -0.588 cm-1 and E = 0.058 cm-1 were obtained for the 3A1 (π → π*) state using the CI wave function constructed from SCF orbitals of the respective parent configurations. An analysis of the effect of CI on the parameters is given for the 3A2 (n n → π*) state of formaldehyde and the 3B1 ground state of methylene. Numerical results are given which show that internally consistent self-consistent field orbitals (ICSCF) are superior to canonical SCF orbitals as a starting point for a CI calculation. Our CI wave function for the 1A1 ground state gave an energy of -114.13658 hartrees which is significantly lower than any previously reported energy calculation. This wave function gives a dipole moment of 2.22 Debye (C+O-) in good agreement with the experimental value of 2.33 ± 0.02 Debye.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 92
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 1039-1043 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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  • 93
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 1063-1075 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have obtained the Bloch spin wave dispersion formula using the methods of spin-free quantum chemistry. The spin-free eigenvectors are waves in spin-free space. This development makes the point that Bloch spin waves are dynamically spin-free. The neutron diffraction transition moment for spin waves is calculated employing the antisymmetrized projections of vector products of spin-free eigenkets and spin kets and is found to be agreement with results of Moorhouse.
    Additional Material: 1 Tab.
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  • 94
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 1099-1116 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The importance sampling method of point selection has been used in the local energy framework to obtain least-squares solutions of the Schrödinger equation for a variety of H2 functions. It is shown that good results are obtainable with relatively small samples, and that the method is rather insensitive within broad limits to the nature of the weighting function employed. Expectation values for a number of operators besides the energy are examined. The energy variances are likewise scrutinized and attempts are made to rationalize their behavior in terms of how and to what extent sample points are chosen.
    Additional Material: 7 Tab.
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  • 95
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 35-49 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: One-center core integrals for valence orbitals are determined from the experimental average energies of neutral atomic configurations from Li through Zn. These values are compared with those estimated from CNDO/1, “INDO/1”, CNDO/2, “INDO/2” and with theoretical values calculated from a pseudo-potential method. The agreement is good between values obtained from neutral atoms and from the psuedo-potential calculation except for the 3d orbitals of the transition elements where the theoretically calculated integrals over single ξ functions are not realistic. These two methods reproduce both term and average configuration energies for the first two rows of atoms; the semiempirical method reliably reproduces them for the third row. The CNDO/1 and INDO/1 methods underestimate atomic energies, while the CNDO/2 and INDO/2 procedures fail rather poorly.The propriety of using core integrals estimated semiempirically in molecular orbital calculations is discussed.
    Additional Material: 10 Tab.
    Type of Medium: Electronic Resource
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  • 96
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 109-125 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method of direct treatment of valence electrons is proposed for the various 2S, 2P,2D, 2F states of the lithium, sodium, and potassium atoms and the corresponding isoelectronic ions. The function describing the outer electron, which is orthogonal to the wave functions of the electrons in the core, is given as a linear combination of generalized Laguerre functions, with effective charges Q = 1, 2 … equal to the charges of the core.A simpler analytical STO function, with non-integer principal quantum number n is then proposed.
    Additional Material: 11 Tab.
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  • 97
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 135-135 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 173-186 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The equation for the screened potential in the RPA has been derived by using the method of functional differentiation of Martin and Schwinger. The contribution of the “oyster” diagram has been contained in this equation.
    Type of Medium: Electronic Resource
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  • 99
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 501-520 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The total electronic energy per atom in the lithium metal has been calculated for three different Fermi surfaces as a function of the internuclear distance. In each case the optimized AMO energy as well as the total energy corresponding to doubly filled molecular orbitals (MO) has been calculated. For densities around the equilibrium density the spherical Fermi surface yields the lowest energy whereas a cubic Fermi surface is preferred for low densities. For densities around the equilibrium there is no band splitting: the AMO energy coincides with the MO energy. The computations have been carried out within an LCAO approximation with overlap and multicenter-integrals calculated accurately.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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