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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.

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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

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

Notes: The use of effective core potentials in the calculation of the geometrical parameters of the ferrocene molecule and its heavier analogs is reported. It is shown that a critical factor in these calculations is the efective core-core (ECC) potential and, in the absence of ECCs for first-row atoms that are involved in short bonds, calculations of the geometrical parameters are not reliable. Good agreement with experimental geometries may be obtained by using the Los Alamos ECPs for atoms of the second and higher rows of the periodic table at the MP2 level. DFT calculations have been performed and found to give numerical results comparable to MP2 in the same basis. © 1995 John Wiley & Sons, Inc.

Notes: In this article, we report an efficient computational procedure for electron scattering matrix elements in the previously developed cubic-grid Gaussian basis sets. The Green function matrix elements derived for the cubic-grid basis set are simpler and easier to calculate than are those available in the literature for conventional Gaussian basis sets. Special features of the cubic-grid basis sets may also be exploited for a very efficient computation of Coulomb and exchange integrals. Inelastic scattering amplitudes for vibrational excitations may be efficiently calcualted in the harmonic approximation by numerical differention of the T-matrix elements. © 1995 John Wiley & Sons, Inc.

Notes: Previously developed cubic-grid basis sets of various sizes were used for the calculation of cross sections for elastic and inelastic electron scattering by the He and Ne atoms and the H2O molecule by the T-matrix expansion method. The aim was to test the invariance of calculated cross sections with respect to the translation of the target molecule and to examine the effect of basis-set size on the results. We also present a simple procedure for accounting for long-range interactions from the part of space that lies outside the volume that contains the cubic-grid basis set. © 1995 John Wiley & Sons, Inc.

Notes: Atomic charge and momentum densities of 91 atoms (He—U) are classified in terms of their L1, L2, and entropic measures of distance from the densities of the preceding atoms. The relationship between these distances and the first ionization energies is also considered. © 1995 John Wiley & Sons, Inc.

Notes: The subject of this article is the self-consistent-field (SCF) treatment of low-lying molecular vibrations in molecules subject to solvent effects and light atom migration. The analyses use a Cartesian Gaussian basis and Gaussian functional expansions of potential energy operators. The objective of the work was to establish approximate and practical methods of analysis of vibrational degrees of freedom in molecules that build on and compare well with the highly accurate treatments of vibrations in small molecular systems of the past decade. An application to a system in which hydrogen bonding contributes the major anharmonic effect illustrates the method. © 1995 John Wiley & Sons, Inc.

Notes: This article presents methods for computing matrix elements with Cartesian Gaussian wave functions of potential energy operators that depend on functions of the form (r-r0)n exp[-a(r - r0)] as well as matrix elements of the class of polynomial many-body potentials developed by Murrell et al. The matrix elements arise in the analyses of anharmonic vibrations in molecules. © 1995 John Wiley & Sons, Inc.

Notes: The extension of the PPP Hamiltonian for alternant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail. It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of altemant cyclic polyenes (CH)N, (N even) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Möbius) orbitals are used to perform energy extrapolations for N → ∞. © 1995 John Wiley & Sons, Inc.

Notes: General formalism for evaluation of multiparticle integrals involving J̌2 and J̌z operators over explicitly correlated Cartesian Gaussian functions is presented. The integrals are expressed in terms of the general overlap integrals. An explicitly correlated Cartesian Gaussian function is a product of spherical orbital Gaussian functions, powers of the Cartesian coordinates of the particle, and exponential Gaussian factors, which depend on interparticular distances. This development is relevant to both adiabatic and nonadiabatic calculations of energy and properties of multiparticle systems. © 1995 John Wiley & Sons, Inc.

Notes: The molecular g-tensors for the molecules NO2, CO2-, C3H5, H2CO+, and NF3+ are calculated at the unrestricted Hartree-Fock (UHF) level using the Rayleigh-Schrödinger perturbation approach. All one-electron terms have been evaluated, including the relativistic mass correction, the one-electron spin-Zeeman gauge correction, and a second-order term involving the spin-orbit coupling and the orbital-Zeeman interaction. The relative importance of the first-order terms is found to be quite substantial. For first-row molecules, their total contribution is often of the same order of magnitude as of the second-order contribution, in some instances even larger. A study on the basis-set dependence of these g-tensors has been conducted. At this level, the most important basis-set criterion is shown to be a satisfactory description of the valence regions. Finally, the gauge dependence of these g-tensor calculations has been systematically studied. This dependence seems to be substantially reduced for basis sets which include polarization functions. © 1995 John Wiley & Sons, Inc.

Notes: A scaling procedure is used for the force constants generated by the SINDO1 method in internal coordinates to achieve better agreement with experimental frequencies of molecules. The procedure is subsequently used to calculate frequency shifts for adsorbed molecules. The results for CO2 and CO adsorption at NaCl cluster surfaces are in good agreement with experimental data. © 1995 John Wiley & Sons, Inc.

Notes: Ab initio self-consistent-field calculations are reported for electronic states of beryllium clusters comprised of 93, 105, 111, and 123 atoms. The respective clusters correspond to coordination shells 12-15 of a central Be atom with internuclear separations derived from the lattice constants of the bulk metal. Ab initio effective core potentials have been employed to replace the 1 s electrons, thereby reducing the complexity of the calculations. In addition, use of the full D3h point group symmetry of the clusters results in a substantial reduction of the numbers of two-electron integrals that must be computed and processed. Binding energies, orbital energies, electric field gradient, nuclear-electrostatic potential, diamagnetic shielding constant, second moments, and Mulliken populations are calculated for selected electronic states. Calculated binding energies when compared among the different clusters as well as to smaller and larger fragments from earlier studies provide evidence for the onset of convergence to the Hartree-Fock limit of the bulk. Lowest-state ionization potentials are consistently above and agree to within 14% of the experimental workfunction. The net charge on the central beryllium atom decreases toward zero. The variability of observed bulklike behavior for the different properties indicates that the transition between cluster and bulklike behavior is not sharp and depends on the quantity of interest. © 1995 John Wiley & Sons, Inc.

Notes: The discrete variable representation method (DVR) is applied to the calculation of the J = 0 vibrational energy levels of the ground electronic state of nitrogen dioxide, a molecule which shows a large amplitude bending vibration. The Hamiltonian is expressed in Johnson hyperspherical coordinates and developed on a DVR basis set for each coordinate. A successive diagonalization-truncation method is applied which gives accurate values for the energy levels up to ≃ 7000 cm-1. © 1995 John Wiley & Sons, Inc.

Notes: A procedure for finding transition states ( TS) that does not require the evaluation of the second derivatives during the search is proposed. The procedure is based on connecting a series of points representing products Pi and reactants Ri and taking conservative steps along the difference vector from Pi toward Ri and from Ri toward Pi until the two points coalesce. Although the points Po and Ro represent the product and reactant specifically, other Pi and Ri are determined by minimization in hyperplanes perpendicular to Pi -1 and Ri-1. We apply this technique to six well-known potential functions and compare these results with those obtained from other well-known procedures. © 1995 John Wiley & Sons, Inc.

Notes: Potential energy curves for the ground and low-lying excited states of the AH2+ (A = Mg - Ar) dications have been calculated using high-level ab initio methods with large atomic orbital basis sets. Quasi-bound potential energy curves with local minima and deprotonation barriers have been found for most of the dications studied. The energies, tunneling lifetimes, and widths of the quasi-bound states have been calculated by numerical solution of the radial Schrodinger equation using the Numeov method. All these dications except ArH2+ have low-lying states which support quasi-bound vibrational states. The ArH2+ dication has a 2∏i potential energy curve with a minimum so shallow that it does not support any quasi-bound vibrational states. Results of our calculations are compared with previous ab initio calculations and available experimental data. © 1995 John Wiley & Sons, Inc.

Notes: A bond-energy formula deduced by means of the Hellmann-Feynman theorem is applied to selected simple hydrocarbons. The required potentials at the nuclei are calculated with the help of large basis-set expansions including polarization functions. The carbon-carbon bond energy of ethane is evaluated at ∼ 70 kcal mol-1. The CC bond energies of ethane, ethylene, acetylene, benzene, and cyclopropane are approximately in a ratio of 1: 2.0: 3.0: 1.65 1.0. Limitations and possible improvements in future applications of this energy formula are discussed. © 1995 John Wiley & Sons, Inc.

Notes: Ab initio molecular orbital (MO) calculations with the 3-21G and 6-31G basis sets are carried out on a series of complexes of NH3 with Li+, C≡N-, LiCN, and its isomer LiNC. The BSSE-corrected interaction energies, geometrical parameters, internal force constants, and harmonic vibrational frequencies are evaluated for 15 species. Complexes with trifurcated (C3v) structures are calculated to be saddle points on the potential energy surfaces and have one imaginary frequency each. Calculated energies, geometrical parameters, internal force constants, and harmonic vibrational frequencies of the various species considered are discussed in terms of the nature of association of LiCN with ammonia. The vibrational frequencies of the relevant complexed species are compared with the experimental frequencies reported earlier for solutions of lithium cyanide in liquid ammonia. © 1995 John Wiley & Sons, Inc.

Notes: When two electronic potentials present an avoided crossing, the adiabatic approximation breaks down in the energy region near to the crossing. In particular, the correspondence between exact energy levels of the two-state system and the adiabatic levels of the lower and upper adiabatic potentials becomes ambiguous. This implies that the term “nonadiabatic effect,” used for the difference between exact and adiabatic energy eigenvalues, loses its meaning in the crossing regime unless an unambiguous way of assigning an adiabatic to an exact level is defined. This is important in order to investigate where nonadiabatic schemes, such as the generator coordinate approximation, fit in between the adiabatic approximation and quasi-exact approaches. © 1995 John Wiley & Sons, Inc.

Notes: The application of the Σ-separation method to the calculation of multicenter two-electron molecular integrals with Slater-type basis functions is reported. The approach is based on the approximation of a scalar component of the two-center atomic density by a two-center expansion over Slater-type functions. A least-squares fit was used to determine the coefficients of the expansion. The angular multipliers of the atomic density were treated exactly. It is shown that this approach can serve as a sufficiently accurate and fast algorithm for the calculation of multicenter two-electron molecular integrals with Slater-type basis functions. © 1995 John Wiley & Sons, Inc.

Notes: The intersystem crossing (ISC) between the lowest triplet and singlet states occurring in the reaction of atomic oxygen with ethylene was studied. The importance of spin-orbit coupling (SOC) in oxirane biradicals (ĊR′R″ - CRR* - Ȯ) is stressed through calculations where the spin-orbit matrix elements over the full Breit-Pauli SOC operator has been obtained in the singlet-triplet crossing region. The calculations are performed with a multiconfigurational linear response approach, in which the spin-orbit couplings are obtained from triplet response functions using differently correlated singlet-reference-state wave functions. Computational results confirm earlier semiempirical predictions of the spin-orbit coupling as an important mechanism behind the ring opening of oxiranes and addition of oxygen O(3P) atoms to alkenes. © 1995 John Wiley & Sons, Inc.

Notes: We consider a crystal as partitioned into a localized molecular cluster (containing a defect or not) and an embedding region. Within the Hartree-Fock formalism, an expression is derived for an effective potential due to the embedding region of crystal. This potential is part of the cluster Fock operator and requires input from a perfect crystal calculation. Special features of the derivative are rigorous inclusion of cluster-embedding overlap and orthogonality between single-electron states of the embedding region and the function-space manifold of the cluster; physically correct normalization of the Fock eigenstates; and a nontrivial total-energy algorithm. Computational requirements are qualitatively compared with those for an isolated cluster. The method allows for intracluster (and intraembedding) correlation and can be adapted straightforwardly to local density functional approaches. Fundamental aspects of the embedding problem are addressed in a general formulation that is, nevertheless, oriented toward explicit calculations. © 1995 John Wiley & Sons, Inc.

Notes: An efficient procedure for third-order electron propagator calculations of ionization energies and electron affinities is reported. Diagonal self-energy expressions that are suitable for large molecules are empolyed. The outer-valence Green's function method also is implemented. An integral transformation program for direct and semidirect algorithms is modified to store only nonzero integrals according to Abelian point group symmetry. Contributions to self-energy matrix elements that depend on electron repulsion integrals with four virtual orbital indices are computed in a direct way. Intermediate batches of integrals are created by sort procedures while avoiding storage of transformed integrals in the main memory. This method permits calculation of electron binding energies for C72- with a 231 atomic orbital basis and for Zn(C5H5)2 with a 220 atomic orbital basis on an IBM RISC/6000 Model 550. During these calculations, the CPU is engaged approximately 90% of the time. © 1995 John Wiley & Sons, Inc.

Notes: The intermolecular potentials for the X 2σ and A2Π states of Li… Ar were studied by a variety of multiconfiguration, single-configuration, and perturbation methods (CASPT2). The A 2Π excited state was calculated to have a well depth of 811 cm-1 at an internuclear separation of 2.59 Å, in excellent agreement with the 810 cm-1 derived from experimental data. A smaller well of 77 cm-1 was found for the X 2σ ground state at an intermolecular separation of 4.8 Å. These results are in better agreement with experimental results than were the previously reported pseudopotential calculations. The comparison of CI calculation with the CAPST2 results shows that the latter is able to give good results for interacting metal-rare gas systems. © 1995 John Wiley & Sons, Inc.

Notes: This article is a brief review of the work formalism of electronic structure, its recent developments, and the results of its application to spherically symmetric and nonspherical density atoms. The formalism, which is founded in Schrödinger theory, is derived by physical arguments based on Coulomb's law. The fundamental quantity in the formalism is the pair-correlation density that constitutes the nonlocal quantum-mechanical source charge distribution giving rise to both a local potential representing electron correlations as well as the electron interaction energy. The potential is the work done to move an electron in the force field of the pair-correlation density and the energy the interaction energy between the electronic and pair-correlation densities. (For systems for which the curl of the force field may not vanish, the potential is obtained from the irrotational component of the field, the solenoidal component being neglected). The differential equation governing the system is a Sturm-Liouville equation, and as such, the exact wave function can in principle be obtained as an infinite linear combination of Slater determinants of the self-consistently determined spin-orbitals of the occupied and virtual states. The correctness of the interpretation for the local potential representing electron interaction is evidenced as follows: In the Pauli-correlated and central field approximations, ground-state energies of atoms (2 He -86Rn) lie within 50 ppm of those of Hartree-Fock theory, differing by less than 10 ppm for atoms with Z 〉 35. The densities thus generated clearly exhibit atomic shell structure and also satisfy the Kato-Steiner electron-nucleus cusp condition to 2 ppm. Another attribute of the formalism is that the asymptotic structure of the potential (when both Pauli and Coulomb correlations are considered) is that of the Pauli-correlated approximation. This is rigorously the case as shown for the He atom for which the potential vanishes in the classically forbidden region, the potential there being the exchange potential. As such, it is meaningful to compare the highest occupied eigenvalue of the differential equation in the Pauli-correlated approximation to experiment. A comparison for atoms and atomic ions of this eigenvalue to experimental ionization potentials and electron affinities show them to be consistently superior to the corresponding eigenvalue of Hartree-Fock theory. Transition energies determined from eigenvalue differences are also superior to those obtained from total energy calculations via Hartree-Fock theory when compared to experiment. Further, by considering the carbon atom in one of its degenerate ground states for which the curl of the field due to the Fermi hole does not vanish, it is shown that the solenoidal component of the field is negligible and two orders of magnitude smaller than is the irrotational component. Thus, the approximation of obtaining a path-independent potential for nonspherical density systems from the irrotational component of the field is accurate. Finally, Coulomb correlation effects can be incorporated within the work formalism in practice via the configuration interaction approximation. The self-consistent orbitals thus obtained explicitly incorporate the effects of both Pauli and Coulomb correlations in their structure because the source charge from which they are generated is a pair-correlation density. Furthermore, these orbitals possess the correct asymptotic structure since they are also generated by a potential that is local. The work formalism also provides a physical interpretation for the local potential representing electron correlations of Kohn-Sham density functional theory. Further, the exchange potential of the work formalism satisfies analytically two requisite conditions of the Kohn-Sham theory exchange potential. These are the scaling requirement and the sum rule relating the exchange energy to its functional derivative. The work formalism also leads to a deeper understanding of electron correlations in various approximations within Kohn-Sham theory. For example, it can be rigorously shown that the pair-correlation density in the local density approximation contains a term proportional to the gradient of the density. Thus, in contrast to the Kohn-Sham theory interpretation that electron correlations in this approximation are those of the uniform electron gas assumed valid locally, we learn that the nonuniformity of the electronic density is, in fact, explicitly accounted for by the approximation. This then explains the accuracy of the approximation. © 1995 John Wiley & Sons, Inc.

Notes: The aziridine analogues of the epoxide metabolites of carcinogenic polycyclic aromatic hydrocarbons have greater mutagenic potency than the epoxides. Like their well-studied analogues, the aziridines undergo a pH-dependent decomposition that leads to a reactive carbocation intermediate. In aqueous solution the nucleophile with which the carbocation generally reacts is water. The kinetics of this pH-dependent reaction have been experimentally characterized by others. Although the effect of DNA on this reaction has not been studied, we hypothesize that, like their epoxide analogues, the aziridine derivatives of polycyclic aromatic hydrocarbons undergo a DNA-catalyzed reaction leading through a carbocation to either a DNA-adduct or a hydrolysis product. Using Poisson-Boltzmann calculations in conjunction with Metropolis Monte Carlo simulations and energy-minimized conformations, we predict the DNA-dependence of the acidcatalyzed decomposition of the K-region aziridine, phenanthrene[9,10]imine. © 1995 John Wiley & Sons, Inc.

Notes: A QSAR analysis of a series of Valproic Acid (vpa) derivatives is given, which shows the importance of hydrophobic and electronic effects as determinants of the anticonvulsivant activity. The statistical analysis allows one to infer that the electron acceptor capability of the carboxylic carbon atom may guide electrostatic interactions of the molecules with the receptor site, in those cases where the lipophilic requirements are satisfied. Both the anticonvulsivant activity and the calculated lipophilic parameters (log P values) are taken from the literature, whereas the electronic descriptors result from Intermediate Neglect of Differential Overlap calculations at the Configuration Interaction level, (INDO/S-CI parametrization), for the most stable conformers of each derivative. The protein environment is modeled as a dielectric continuum in a Self-Consistent Reaction Field approach. The conformational analysis is based on AMI calculations. © 1995 John Wiley & Sons, Inc.

Notes: A new form of second-order multireference perturbation theory coupled with finite-field perturbation theory is applied to evaluate some one-electron molecular properties. Several possible definitions of the zeroth-order Hamiltonian are considered and results tested against bench-mark full CI calculations. © 1995 John Wiley & Sons, Inc.

Notes: The correlation present in the nondegenerate ground state of an interacting Fermi system is discussed in terms of reduced density matrices and their cumulant expansion. By generalizing a result obtained for the interacting uniform electron gas (correlation induced exchange-hole narrowing), possible measures of the correlation strength in terms of natural occupation numbers (the eigenvalues of the true one-particle density matrix) are introduced. These quantities-the v-order nonidempotency and the information entropy of the natural occupation numbers-result from the correlated many-body wave function and characterize the ground-state correlation in addition to the usual correlation energy. The uniform electron gas serves as a first illustrative example. © 1995 John Wiley & Sons, Inc.

Notes: In the present work, we reexamined the gradient expansion of the exchange energy of an electron gas with a slowly varying charge density. We stay within the exchange-only approximation of Sharp, Horton, Talman, and Shadwick but go to second order in the deviation from the homogeneous limit. The coefficient of the lowest-order gradient correction is obtained analytically both for a bare and a screened Coulomb interaction - the former yielding the value previously obtained by Kleinman numerically and by Engel and Vosko analytically. A screened Coulomb interaction gives Sham's coefficient in the limit of infinite screening length. The cause of the difference between the coefficients of Kleinman and Sham is clearly exhibited. The coefficients of the two next highest-order gradient corrections, one of which originates in second-order response theory, is shown to diverge as the screening length becomes large. The bare Coulomb interaction gives finite coefficients of which the one originating from linear response is obtained analytically and differs from the presumably correct result obtained by Engel and Vosko. This discrepancy demonstrates the extreme sensitivity of the analytical expressions to different regularization procedures. We suggest that coefficients should rather be chosen according to the performance of the resulting gradient approximations in weakly perturbed electron gases. © 1995 John Wiley & Sons, Inc.

Notes: The focal point of the present work is the single-particle kinetic energy density tensor in D dimensions. This quantity enters both differential and various integral forms of the virial theorems, which are again set up in D dimensions. Major new results lie in (i) demonstrating that, by one-dimensional quadrature, it is possible to construct the Pauli potential directly from the kinetic energy tensor, without the need for functional differentiation and (ii) generating the gradient expansion for the kinetic energy tensor, in D dimensions. © 1995 John Wiley & Sons, Inc.

Notes: The geometries of the two most important tautomeric forms of adenine and the corresponding methyladenines are investigated by means of quantum chemical calculations at different level of sophistication, ranging from semiempirical methods to correlation corrected ab initio methods at second-order Møller-Plesset perturbation theory level (MP2). The relative stability of the N(7)H ↔ N(9)H tautomeric forms of adenine are investigated with highly correlation corrected methods, MP3 and MP4. The relative stability is also corrected for solvent interactions and compared with experimental information. N(9)H-adenine is predicted to be the most stable tautomer in both vacuum and in solution. The relative stability is predicted to be between 24.5 and 35.0 kJ/mol in vacuum depending on computation method. In water solution N(7)H-adenine is stabilized more by the solvent, and the corresponding relative energies were found to be between 4.9 and 10.2 kJ/mol. We also found that correlation effects are essential to describe the ground state geometry with a high accuracy. The geometries predicted by semiempirical methods and ab initio calculations without correlation correction show large deviations in some parts of the molecule compared to the MP2 results as well as compared with experimental geometries. © 1995 John Wiley & Sons, Inc.

Notes: Ab Initio crystal orbital calculations on three-dimensional crystals/crystallohydrates of a number of diprotonated mononucleotides have been performed using the CRYSTAL92 routine package. The present results help to gain a deeper insight into the physical mechanisms of nucleic acid semiconductivity, as well as into the essence of intermolecular interactions and solvent effects in solid-state samples of nucleic acids. © 1995 John Wiley & Sons, Inc.

Notes: Experimentally measured rates for the oxidation of p-substituted benzyl amines by bovine monoamine oxidase type B (MAO-B) derived from the literature were examined with respect to the effects of molecular (semiempirically (AM1) derived) electronic, steric, and lipophilicity parameters. These properties included vertical and adiabatic ionization potential, LUMO energy, the LUMO-HOMO difference, molecular hardness, absolute electronegativity, calculated log P values, molecular volume, surface area, and ovality. Substrate oxidation rates (log kcat/Km) were found to correlate with molecular ovality and vertical ionization potential while the rate of enzymatic (flavin) reduction associated with substrate oxidation (log kred) was described by a two-parameter model containing an ovality and an absolute electronegativity term. These results are consistent with an initial one-electron substrate oxidation mechanism. In previous work, use of classical Hansch analysis suggested that electronic terms were not important in the enzymatic reactions. This discrepancy may be related to nontransferability inherent in fragment approaches which assume that the substituent of interest behaves similarly in all molecular scaffolds. Analysis of substrate binding (log Kd) to the enzyme was described by a two-parameter model containing a calculated log P term as well as LUMO energy. The significant correlation found with LUMO energy is consistent with studies suggesting that this property is important for drug-receptor interactions. © 1995 John Wiley & Sons, Inc.

Notes: The integrated molecular transform (FTm) is a unitary structure index that has been successfully used for the correlation of 2- and 3-dimensional structure representations with their physicochemical and pharmacological properties. In the present instance the reported pKa values in a series of 30 compounds consisting of five subseries were correlated with their FTm indices. The omission of four outliers gave a moderate correlation across the entire series; within the individual subseries the correlations were considerably improved even with inclusion of the outliers. In general, the logarithmic transform of the pKa did not improve the correlations. This method gives a relatively simple means of estimating pKa in several structure classes. © 1995 John Wiley & Sons, Inc.

Notes: We investigated Raman and infrared spectra of the Watson-Crick type of the guanine cytosine base pair and of the individual guanine and cytosine nucleic acid bases by ab initio Hartree-Fock theory using the 6-31G* basis set. IR and Raman intensities and Raman depolarization ratios were predicted using the double-harmonic approximation. The effects of a polar solvent were modeled by the self-consistent reaction field (SCRF) approximation. Variations in geometries, harmonic force constants, and vibrational spectra of the studied nucleobases due to the specific hydrogen-bonding interactions are discussed. © 1995 John Wiley & Sons, Inc.

Notes: We present here a perturbative analysis of the coupled cluster response method for molecular static properties with Euler and extended coupled cluster functionals under cubic truncation. Comparative analysis is meant to cater to both pedagogical and practical interests. Comprehensive tables for energy-derivative expressions and equations at the stationary point are presented. © 1995 John Wiley & Sons, Inc.

Notes: The ground-state potential energy curve of the F2 molecule as well as spectroscopic constants were calculated by means of the second-order quasi-degenerate many-body perturbation theory within a full (eight) valence orbital space using a DZP basis set. The problem encountered with a large number of valence electrons is avoided by a proper redefinition of the Fermi vacuum. A comparison with other related multireference techniques is also provided. © 1995 John Wiley & Sons, Inc.

Notes: Correlation holes of electrons with the same (Fermi hole) and different (Coulomb hole) spins in the ground (X1Σ+), first (A1Σ+) and second (B1II) excited states of LiH were constructed from full configuration interaction (CI) wave functions. It was found that the shapes of both the Fermi and Coulomb holes in these states are dependent on the location of the reference electron. When the reference electron is chosen to be close to the Li nucleus, the Fermi correlation results in a large negative hole for all three states. However, the A1Σ+ excited state is further characterized by displaying a second hole around the H nucleus, and in the B1II state, the hole is elongated along the molecular axis. Coulomb correlation shows up strongly in the A1Σ+ state and, in addition, there is clearly correlation of electrons at the two nuclei. These features of the correlation holes were compared with those from a two-Slater-determinant model wave function. The Hartree, Fermi, and Coulomb screening potentials in these states were also studied in the light of possible modeling of the correlation functionals for the excited states. © 1995 John Wiley & Sons, Inc.

Notes: The link between a uniform scaling of the electron density and a scaling of the electron-electron interaction is reviewed. The effective potential along the coupling constant path which connects a noninteracting and a fully interacting system with the same electron density is considered. The effective potential for an arbitrary coupling constant is here expressed in terms of the exchange-correlation potential at a coupling constant of unity. The effective potential is then investigated for ionization processes. Use of the fact that the ionization energy is determined by the exponential decay of the electron density allows us to derive new formulas for the ionization energy. Based on the Taylor expansion of the effective potential along the coupling constant path, a density functional perturbation theory is introduced which leads to a formally exact Kohn-Sham KS formalism. To first order, this formalism gives identities for the exchange potential in terms of KS orbitals and orbital eigenvalues. Moreover, higher-order terms give identities for the correlation potential as well as for the exchange potential. These identities are pointwise as well as integrated. Hence, various new requirements for the exchange and correlation functionals are derived. New insight into the optimized effective potential method is gained by discussing it in the light of the results obtained here. © 1995 John Wiley & Sons, Inc.

Notes: Available approximations to Exc[{nσ}], the exchange-correlation energy functional of spin-density-functional theory, do not include self-interaction corrections (SIC). This leads to Kohn-Sham (KS) potentials, Vxcσ, that fail to satisfy some important analytic properties known to be exhibited by the exact potential. To resolve these difficulties, we consider a KS theory for orbital-dependent exchange-correlation energy functionals that explicitly includes SIC. Recent work by Krieger, Li, and lafrate (KLI), which considers the analytic properties of the spin-polarized optimized effective potentials (OEP), Vxcσ0, i.e., the KS potentials corresponding to Exc = Exc[{φiσ,}], is reviewed as well as the properties of VxcσKLI, an easily calculated approximation to the exact result which, unlike Vxcσ0, can be employed for systems of arbitrary symmetry. In addition, we compare the results of the exact and approximate OEP calculation of the properties of the ground state of atoms and singly charged negative ions in the exchange-only case in which Ex = ExHF [{φiσ}] where HF = Hartree-Fock. We conclude that VxσKLI maintains most of the important analytic properties of Vxσ0, and provides an excellent numerical approximation to the exact result. We also give detailed consideration to the calculation of the ionization potential, I, and the electron affinity, A, in the exchange-only approximation for atoms with Z ≤ 20. We find that the KLI results for both I and A are always within 0.1 milli-au of the exact KS results, whereas both the local spin density (LSD) approximation and the Becke exchange only energy functional lead to deviations which on average are two orders of magnitude larger and significantly exceed the criterion for quantum chemistry accuracy. Finally, using the KLI method for orbital dependent Exc, we compare the KS results for I and A for Z ≤ 20 with the experimental values by employing various approximations for Exc[{φiσ] including: (1) HF exchange with LSD correlation with SIC, (2) LSD approximation for exchange and correlation with SIC, (3) the conventional spin density LSD approximation, and (4) the Becke exchange-energy functional with LSD correlation. In addition, we examine how closely the ionization theorem for ∊m, the energy eigenvalue for the highest occupied orbital, is satisfied in these approximations. © 1995 John Wiley & Sons, Inc.

Notes: First-principles local density functional approximation (LDA) calculations using the linear-response method are more efficient than are traditional supercell or dielectric matrix techniques for determining phonon spectra and dielectric constants. We have implemented this approach using a linearized-augmented-plane-wave (LAPW) basis, which facilitates such calculations for systems containing transition-metal and other atoms with localized orbitals. The accuracy of the method is illustrated with applications to some semiconductors and ferroelectrics. Theoretical work on the perovskite ferroelectrics has focused on the possible roles of disorder and soft-phonon behavior. A complete mapping in the Brillouin zone (BZ) of the ferroelectric instability of KNbO3 has been carried out, revealing a pronounced two-dimensional character. In real space, this instability corresponds to chains oriented along 〈100〉 directions, of displaced Nb atoms. Such instabilities are discussed in relation to the static chain structures in the eight-site order-disorder model introduced by Comes et al. © 1995 John Wiley & Sons, Inc.

Notes: Electrostatic and dispersion contributions of solute-solvent interactions have been considered in the self-consistent reaction field scheme and implemented in the LCGTO-DF (linear combination of Gaussian-type orbitals-density functional) method. Results for the tautomeric equilibrium of formamide-formamidic acid, for the cis-trans energy difference in dichlorodiammineplatinum(II), and for H2O—HF hydrogen-bond systems are in agreement with the available experimental and previous high-level ab initio data. The role of the dispersion energy is discussed for the different studied systems. © 1995 John Wiley & Sons, Inc.

Notes: Local (LSD) and nonlocal (NLSD) spin density calculations using different exchangecorrelation functionals have been performed to determine equilibrium geometries, harmonic vibrational frequencies (ωe), ionization potentials (IP), electron affinities (EA), dipole moments (μ), and singlet-triplet energy gaps (Δ EST) of SiH2, GeH2, and SnH2. Geometrical structures as well as vibrational frequencies are in agreement with the available experimental data and compare favorably with the most sophisticated postHartree-Fock computations performed until now. Both computed IPS (9.15 and 9.25 eV for SiH2 and GeH2, respectively) and EA of SiH2 (1.17 eV) compare favorably with experimental data (9.17, 9.21, and 1.2 eV). Accurate values are obtained also for singlet-triplet energy gaps. We report for the first time the electron affinities of all neutral systems and the spectroscopic constants of the cations and anions. © 1995 John Wiley & Sons, Inc.

Notes: The coupled clusters singles and doubles (CCSD) method for calculations of open-shell systems with the single restricted Hartree-Fock (ROHF) reference determinant is extended by the noniterative triples to give CCSD(T). Our approach profits from the fact that (a) single- and double-excitation amplitudes are spin-adapted, which directly leads to a computationally less demanding algorithm than are nonadapted procedures and produces the spin-adapted CCSD wave function and (b) triple excitations calculated from converged spin-adapted (SA) CCSD amplitudes are also obtained more effectively. Altogether, computer demands of our SA CCSD(T) approach, applicable to high-spin open-shell cases which are well represented by a single-determinant reference is comparable to that for closed-shell systems. Our approach is not based on semicanonical orbitals, applied by Bartlett's group. However, we compare some other possible choices of ROHF orbitals to this “standard.” Numerical results for a series of atoms and molecules demonstrate little sensitivity to this selection. © 1995 John Wiley & Sons, Inc.

Notes: Ab initio accurate all-electron relativistic molecular orbital Dirac-Fock self-consistent field calculations are reported for the linear symmetric XeF2 molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree-Fock calculations were also performed for XeF2 at various internuclear distances. The relativistic correction to the electronic energy of XeF2 was calculated as ∼ -215 hartrees (-5850 eV) by using the Dirac-Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac-Fock-Breit self-consistent field and perturbation methods. The calculated Breit correction is ∼6.5 hartrees (177 eV) for XeF2. The relativistic Dirac-Fock as well as the nonrelativistic HF wave functions predict XeF2 to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF2 by using various ab initio post Hartree-Fock methods. The calculated dissociation energy obtained using the MP2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ∼ -2 hartrees (-54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe - F distance of 1.979 Å in XeF2. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (De) close to experimental value for XeF2. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF2. © 1995 John Wiley & Sons, Inc.

Notes: Based on the EHMO approach, the band structures for the Y—Ba—Cu—O superconductors doped by La were calculated. The influence of the partial substitutions of La for Y and Ba in YBa2CU3Oy on its electronic structures was investigated. The results demonstrate that the La doping at the Ba site has a great effect on the electronic structures of the Y—Ba—Cu—O superconductors, whereas the change in the band structures caused by the La doping at the Y site is very small. The increase in the oxygen content caused by the La doping results in an increase in the densities of states at Ef, N(Ef), for La1+x Ba2-xCu3Oy, but the increase in N(Ef) cannot compensate the decrease caused by the La doping at the Ba site. In addition, the 2D Cu—O planes are much more sensitive to the change in N(Ef) than are the 1D Cu—O ribbons, which implies an important role of the 2D Cu—0 planes in the Y—Ba—Cu—O superconducting system, regardless of whether La substitutes for Y or for Ba. © 1995 John Wiley & Sons, Inc.

Notes: The proof of Parr and Chattaraj for the Principle of Maximum Chemical Hardness is very general and can be applied to many more observables. The case of the physical, or mechanical, hardness of a solid is taken as an example. It is shown that this also should be a maximum in an equilibrium system. Assuming the validity of the argument leads to new information about the compressibility of solids. A simple expression is also given for the Gruneisen constant. These maximum principles are necessary consequences of the equilibrium conditions of quantum mechanics and thermodynamics. © 1995 John Wiley & Sons, Inc.

Notes: The field theoretical background of relativistic density functional theory is emphasized and its consequences for relativistic Kohn-Sham equations are shown. The local density approximation for the exchange energy functional is reviewed and the importance of relativistic corrections for an accurate representation of the exchange functional is demonstrated. © 1995 John Wiley & Sons, Inc.

Notes: The dynamics of Jahn-Teller systems has recently been discussed in terms of generalized electronic charge and current densities in nuclear-coordinate space. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, was a crucial component of this formulation. Here, a densitybased treatment of Born couplings is derived from first-principles quantum mechanics beyond the Born-Oppenheimer approximation. Because of the degenerate electronic configuration of a Jahn-Teller molecule, there are an infinite number of ways in which the charge distribution can be oriented for the same energy, leading to a vanishing bond hardness for the molecule in the symmetric nuclear configuration. Further, the moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, leading to unhindered rotation of the charge cloud. This leads to the dynamical Jahn-Teller problem, namely, the coupling of electronic and nuclear motions through the Born coupling terms. Applications to superconductivity theory are discussed. © 1995 John Wiley & Sons, Inc.

Notes: It is possible to reformulate the reaction field (RF) model of continuum solvent effects, by considering an approximate expression describing the energy changes from one ground state to another, in the frame of density functional theory (DFT). The energy functional for an arbitrary electronic system coupled to a spin-independent electrostatic external perturbation is used to derive the well-known Born expression giving the electrostatic component of the solvation energy of an atomic ion. The approximate RF-DFT model is illustrated for a series of representative singly positive and negatively charged atomic ions. A Kohn-Sham (KS)-like formalism is then proposed to compute solvation energies within a self-consistent field scheme. The extension of the RF-DFT model to molecular systems is also outlined. © 1995 John Wiley & Sons, Inc.

Notes: Recent reactivity concepts formulated within charge analysis (CSA) are outlined. The charge stability criteria of equilibrium states in open and closed systems are conveniently characterized in terms of the condensed reactant hardness quantities of reactants; their implications for catatytic systems are examined. A use of characteristics associated with selected collective charge displacement modes, including the populational normal modes and minimum-energy coordinates, as diagnostic tools in the theory of chemical reactivity is proposed. The importance of the mapping relations between modes defined in the electron population and nuclear position spaces, respectively, as the unifying concept linking the conjugate charge and geometry displacements, is commented upon. Recent results for model catalytic clusters are used to illustrate some of the concepts introduced. Finally, the relevant contributions to the quadratic interaction energy between reactants are reexamined and expressed in terms of relevant charge sensitivities. © 1995 John Wiley & Sons, Inc.

Notes: The Boltzmann-Shannon (BS) information entropy Sρ = ∫ ρ(r)log ρ(r)dr measures the spread or extent of the one-electron density ρ(r), which is the basic variable of the density function theory of the many electron systems. This quantity cannot be analytically computed, not even for simple quantum mechanical systems such as, e.g., the harmonic oscillator (HO) and the hydrogen atom (HA) in arbitrary excited states. Here, we first review (i) the present knowledge and open problems in the analytical determination of the BS entropies for the HO and HA systems in both position and momentum spaces and (ii) the known rigorous lower and upper bounds to the position and momentum BS entropies of many-electron systems in terms of the radial expectation values in the corresponding space. Then, we find general inequalities which relate the BS entropies and various density functionals. Particular cases of these results are rigorous relationships of the BS entropies and some relevant density functionals (e.g., the Thomas-Fermi kinetic energy, the Dirac-Slater exchange energy, the average electron density) for finite many-electron systems. © 1995 John Wiley & Sons, Inc.

Notes: The local density approximation (LDA) to exchange and correlation effects has well-known limitations. The nonlocal weighted density approximation (WDA) corrects some of those defects. This is illustrated here by applications to free atoms and small atomic clusters. The WDA also induces a nonlocal kinetic energy functional that is tested for atoms. © 1995 John Wiley & Sons, Inc.

Notes: We present a density functional scheme for calculating the frequency-dependent linear response of superconductors. The central result is a set of integral equations determining the linear response of the normal and anomalous densities to external perturbations. Analytic solutions of these integral equations are obtained for homogeneous systems with separable effective interactions. For inhomogeneous superconductors, the formalism leads to a scheme for calculating the critical temperature without explicitly solving the gap equation. © 1995 John Wiley & Sons, Inc.

Notes: The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM) as well as the problem of reconstruction of the N-particle system density matrices (N-DM) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators Θλk are represented using particular values (at specially chosen ) of the Radon transform of the N-DM spatial parts (or their sums) DNλ(x′ | x″) (here, is a d-plane in the n-space ∝n of x = (x′, x″)), with n = 6N, d = 3 (N - k), x′ ≡ (r′1,⃛, r′N), x′ ≡ (r1″,⃛, r″N ()). In this way, the problem is reduced to investigation of the properties of the functions . For a normalizable N - DM, it is proved that are bounded functions. The properties of implied by the N-DM permutational symmetry, Hermiticity, and positive definiteness are found. A formal procedure of reconstruction of all N-DM corresponding to a given k-RDM is proposed. © 1995 John Wiley & Sons, Inc.

Notes: The π-allylic organonickel compounds are considered to be key structures in the catalytic reactions of butadiene. Bis(η3-allyl)nickel, bis(η3-methallyl)nickel, and the syn-crotyl-cyclooctadiene-nickel cation have been calculated with DZ and TZ basis sets in all-electron and pseudopotential (ECP) Hartree-Fock (HF) methods and compared with experimental structures. In the second part, we report a systematic investigation of these compounds by density functional theory (DFT). The DFT-optimized structures are generally in better agreement with experimental data than are the HF results. © 1995 John Wiley & Sons, Inc.

Notes: The vibrational frequencies of NaN clusters (2 ≤ N ≤ 72) are calculated by direct diagonalization of the dynamical matrix. Density functional theory with a spherically averaged pseudopotential is used to compute the total energy. The geometry is optimized by the simulated annealing technique. Contributions to the Hessian matrix due to electron relaxation following the ionic displacements are calculated in linear response theory. The frequencies are in the range 0-220 cm-1 and the electron relaxation strongly modifies those of the modes dominated by radial oscillations, particularly the breathing mode frequencies that are proportional to N-1/3. The filling of atomic shells produces a stepwise behavior of the highest frequencies. The giant dipole resonance energies are obtained as a byproduct of the calculation. © 1995 John Wiley & Sons, Inc.

Notes: The Weizsäcker functional TW is a necessary element to explain basic physical and chemical phenomena of atomic and molecular systems in the general density functional theory initiated by Hohenberg and Kohn. Here, rigorous inequalities which involve the functional TW and two arbitrary power-type density functionals ωα ≔ ∫ ρα(r)dr are found by the successive applications of Sobolev and Hölder inequalities. Particular cases of these inequalities give lower bounds to the Weizsacker functional of an N-electron system in terms of a fundamental and/or experimentally measurable quantity such as, e.g., the Thomas-Fermi kinetic energy T0, the Dirac-Slater exchange energy K0 and the average electronic density 〈ρ〉 in doing so, some known relationships appear. A numerical Hartree-Fock study of the accuracy of some resulting lower bounds is carried out. Finally, rigorous relationships between the Weizsäcker functional and the Boltzmann-Shannon information entropy of the system under consideration are given. © 1995 John Wiley & Sons, Inc.

Notes: Over the past 7 years, the enediyne anticancer antibiotics have been widely studied due to their DNA cleaving ability. The focus of these antibiotics, represented by kedarcidin chromophore, neocarzinostatin chromophore, calicheamicin, esperamicin A, and dynemicin A, is on the enediyne moiety contained within each of these antibiotics. In its inactive form, the moiety is benign to its environment. Upon suitable activation, the system undergoes a Bergman cycloaromatization proceeding through a 1,4-dehydrobenzene diradical intermediate. It is this diradical intermediate that is thought to cleave double-stranded DNA through hydrogen atom abstraction. Semiempirical, semiempirical CI, Hartree-Fock ab initio, and MP2 electron correlation methods have been used to investigate the inactive hex-3-ene-1,5-diyne reactant, the 1,4-dehydrobenzene diradical, and a transition state structure of the Bergman reaction. Geometries calculated with different basis sets and by semiempirical methods have been used for single-point calculations using electron correlation methods. These results are compared with the best experimental and theoretical results reported in the literature. Implications of these results for computational studies of the enediyne anticancer antibiotics are discussed. © 1995 John Wiley & Sons, Inc.

Notes: The potential energy surface for the first step of the alkaline hydrolysis of methyl acetate was explored by a variety of methods. The conformational search routine within SPARTAN was used to determine the lowest energy AM1 and PM3 structures for the anionic tetrahedral intermediate. Ab initio single point and geometry optimization calculations were performed to determine the lowest energy conformer, and the linear synchronous transition (LST) method was used to provide an initial structure for transition state optimization. Transition states were obtained at the AM1, PM3, 3-21G, and 3-21 + G levels of theory. These transition states were compared with the anionic tetrahedral intermediates to examine the assumption that the intermediate is a good model for the transition state. In addition, the Cramer/Truhlar SM3 solvation model was used at the semiempirical level to compare gas phase and aqueous alkaline hydrolysis of methyl acetate. © 1995 John Wiley & Sons, Inc.

Notes: We present nonlocal density-functional calculations for a model of the [Fe4S4]3+ cluster found in high potential iron proteins, which consists formally of a ferric pair Fe 3+Fe3+ and a mixed-valence pair Fe 2.5+—Fe2.5+. Three Spin Hamiltonian parameters, J (the interlayer Heisenberg interaction), B (a resonance delocalization term) and ΔJ12 (associated with the ferric pair) have been estimated using density-functional energies of a high-spin state as well as two different broken symmetry states. We obtain J=673 cm-1, B=878 cm-1, and Δ J12=160 cm-1. These results are discussed in the light of experimental work on a model compound in the same oxidation state, in which the temperature dependence of the magnetic susceptibility was analyzed with this sort of spin Hamiltonian. Good overall agreement between theory and experiment (J=652 cm-1, B=592 cm-1), and ΔJ12=145 cm-1 is found. In particular, the antiferromagnetic spin coupling constant for the ferric pair exceeds in magnitude all other Heisenberg-type interactions (ΔJ12 〉 0) as expected from previous theoretical and experimental work; this is the first time that the broken symmetry method has been used to analyze a spin Hamiltonian with multiple coupling constants in an Fe4S4 cluster. © 1995 John Wiley & Sons, Inc.

Notes: In this article, some applications of lower bounds to density-dependent functionals in terms of radial expectation values are performed. These diverse applications include accurate upper bounds to the exact kinetic energy and to conjecture a wide set of relationships among radial and momentum expectation values. Some open questions for the improvement of these results are remarked upon. © 1995 John Wiley & Sons, Inc.

Notes: Two transition-metal oxide diatomic cations, VO+ and MoO+ are considered in this article. Ground- and excited-state properties of the cations are derived from spin-polarized DF calculations, including spectroscopic constants and metal-oxygen bonding features. A set of ionization potentials are calculated and, for vanadium oxide, compared with photoelectron spectroscopy data and a few available ab initio calculations. All calculated properties are close to experiment, the agreement being much better than for other traditional quantum chemical calculations. Present results together with our earlier findings for neutral molecules provide an excellent confirmation of the good performance of DFT in the case of transition-metal systems. © 1995 John Wiley & Sons, Inc.