Bibliothek

Notizen: Two MO indices are found to correlate well with the toxicity of 1-substituted silatranes.

Notizen: Rayleigh-Schrödinger perturbation theory for many-electron systems has been rederived by an extension of Löwin's partitioning method in which excited configurations are further partitioned by their orders (two equivalent definitions of the order of a configuration are given). The resulting equations show explicitly how first-, second-, and third-order configurations contribute to the first three orders of perturbative corrections to the ground-state wave function, and the first six orders of corrections to the energy. Because the partitioning is by orders of configurations (rather than level, i.e., single, double, etc., excitations) the formalism is unaffected by the applicability, or nonapplicability, of Brillouin's theorem.

Notizen: Ab initio SCF MO calculations have been carried out on benzene + TCNE (tetracyanoethylene) and naphthalene + TCNE complexes with the STO-3G, STO-3G π-split (STO-3G for π orbitals and a split basis for π orbitals), and 4-31G basis sets. The interaction energy, gross charges, dipole moment, and the electron density in the middle plane of the complexes have also been evaluated. The STO-3G π-split basis set is appropriate for the calculation of large π-π stacking complexes from two points of view, production of reliable results and ease of computations. The approximation scheme based on the semiorthogonalized orgitals is revealed to be very efficient to save CPU time and storage in such calculations. The stable conformation and the charge-transfer interaction of the two complexes are discussed on the basis of the calculated quantities.

Notizen: The electron density and the molecular electrostatic potential of the β-carbolines are studied using ab initio STO-3G wave functions. The analysis was done from the point of view of a previous model built with monoamine oxidase substrates and irreversible inhibitors. The results confirm the usefulness of the model and make it possible to propose new precision to the molecular electrostatic potential patterns needed to have monoamine oxidase inhibitory activity.

Notizen: Generating functions are constructed and recurrence relations are derived for the number of configurations of any number of particles with an arbitrary elementary spin for both fermions and bosons. Similar results are obtained for the number of configurations specified by the total weight and by the degree of excitation.

Notizen: An approximate multireference CI method is presented. By grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory, the number of variational parameters is drastically reduced. The loss of correlation energy is shown to be usually less than 2%, and the timing is less than one ordinary CI iteration. Examples from calculations on some states of the nitrogen atom and nitrogen molecule are given. The basis set convergence for the lowest excitation energy in the atom is very slow. Less than 50% of the correlation effect is obtained at the s, p, d limit. After the inclusion of ƒ functions this value is improved to 83%. The dissociation energies of the molecule also show slow basis set convergence with errors of 0.5 eV even after addition of ƒ functions. The bond distances are, howeever, accurately reproduced with errors of less than 0.005 Å for all the states. A qualitative discussion of predissociation in the a 1Πg and B 3Πgstates caused by spin-orbit interaction with the 5Σg+ state, is finally presented. Rapidly oscillating lifetimes between the different vibrational states are predicted.

Notizen: On the basis of a high-quality LCAO MO SCF calculation, covalency versus ionicity of a Co-F bond in the CoF6(n-) complexes, where n = 4, 3, and 2, is discussed. The overlap and gross atomic populations, delocalization of certain MOS, and the charge densities in the bond region as well as around F's all indicate that the covalency increases as n decreases or the valency of Co increases in these complexes.

Notizen: In an n level quantum system there is a relation between each density operator and an element of su (n) Lie algebra. This relation is also established between Cartan's subalgebras and the complete sets of compatible observables. A scalar product is then defined in this algebra in order to introduce orthonormal bases and to simplify many calculations about expectation values of observables. Therefore simple general rules were established which show how to determine (completely or partly), from linearly independent observables, the density operator of the system.

Notizen: The elastic forward scattering of high-energy electrons from molecules has been studied in the second Born approximation. An integral transformation has been adopted to evaluate the second Born integrals analytically without explicit use of molecular wave functions. In the high-energy limit, the differential cross section for the forward scattering is expressed in terms of electric dipole and quadrupole moments, the second moment of charge distribution with respect to the molecular center, and transition dipole moments. All these quantities are shown to be computable from molecular electron densities in the ground state.

Notizen: The ground states of eight molecules and some of their hole states are calculated. The calculations are performed on a medium-size home-made computer using self-written programs. The basis set used is LEMAO-3G, with scaling factors of the orbitals optimized by means of a method using orthogonal array and finding minima of fitted quadric curves. The conclusions are: (1) The LCAO-MO method is the reflection of the interference effect due to the wave nature of electrons. (2) The mathematical methods of rescaling the orbital exponents is the reflection of the orbital contraction or diffusion occurring during the formation of MO. These conclusions are in agreement with the Virial theorem and the variation principle. They are also strongly supported by the photoelectron spectroscopy data. The calculated values of the energies of the valence orbitals are very near to those obtained by using some extended basis set, which are reported to be very close to the Hartree-Fock limits. From these results and discussions it may be concluded that the nature of the covalent bond should be considered as an interplay and mutual conditioning between the wave nature of the electronic motion on the one hand and the various attractive and repulsive factors on the other hand, among which the kinetic energy should be a very important repulsive factor. The mutual screening effects of the electrons in various MOS, which are different for different molecules, are also very important. This is perhaps one of the main causes of the differences in properties of different molecules.

Notizen: In the study of the ground-state binding energy of atoms, relatively more attention has been paid to the gradient expansion of the kinetic energy term of the Thomas-Fermi-Dirac model than to the gradient expansion of the exchange term of this model. Recently Shih and Shih, Murphy, and Wang have focused on this problem and calculated the first gradient expansion correction to the Dirac exchange term by making use of electron densities constructed from Hartree-Fock wave functions. In previous work, aimed to introduce the shell structure of atoms via a variational procedure using the energy density functional formalism, electron densities have been obtained for the Na atom within the Thomas-Fermi-Dirac model with and without the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term. In this paper we make use of the respective electron densities and calculate the first gradient expansion corrections to the Dirac exchange term. The results show that, for the Na atom, the magnitude of this correction is about 1% of the magnitude of the total binding energy.

Notizen: A scheme for calculating expectation values in coupled-cluster wave functions is given. The unlinked terms originating from the norm of the wave function are eliminated. Hermiticity and trace conditions for the density matrices are exhibited in such a way as to guarantee their conservation in any reasonable truncation scheme.

Notizen: The electron-phonon coupling constants in a cation radical of dibenztetrathiofulvalen (DBTTF.+) have been calculated. To calculate the electronic structure of DBTTF.+ in equilibrium and distorted structures use was made of the unrestricted Hartree-Fock method as π-electron approximation for symmetrical vibrations of DBTTF.+. The results obtained are in good agreement with the experimental data on IR spectra of DBTTF-based cation-radical salts.

Notizen: Several approximate analytical formulas for the multidimensional isotropic bounded oscillators and the bounded hydrogen atom are compared. Numerical results show that the coth z method is in both cases better than the Padé approximants method. Perturbational polynomials, necessary in order to build the approximate eigenvalues, are obtained through the hypervirial perturbative method.

Notizen: Using partial minimization of the potential energy function, the determination of the points of the reaction path does not often lead to unambiguous results. The reason is that the subspace of the coordinates where the minimization takes place cannot be arbitrarily chosen.

Notizen: The validity of the Hartree-Fock (HF) approximation in bis(π-pentadienyl)dinickel (1) and in cyclopentadienyl-allyl-cyclobutadiene-dinickel (2) has been investigated by means of the Thouless instability conditions in the computational framework of a variable model Hamiltonian. Singlet, nonsinglet (triplet), and nonreal instabilities in 1 and 2 have been studied as a function of the one-electron resonance integral βμvAB and as a function of the one- and two-center elements of the electron-electron interaction. The one-center integrals of Coulomb (γμvAA) and exchange-type (KμvAA) have been modified by a multiplicative factor; the two-center integrals (γμvAB) have been calculated by means of an exponential interpolation formula with a variable decay amplitude. Additionally the Thouless conditions have been studied for nuclear deformations. The stability domain of the HF solution in the model space spanned by the variable INDO Hamiltonian has been analyzed. The nature of the many-body interactions in the unstable region depends strongly on the parametrization of the model operator. HF instabilities in the high-density region (long-range forces) of 1 have their origin in individual particle-hole fluctuations while negative roots for short-range forces (low-density region) are similar to collective excitations in many-body systems (strong off-diagonal coupling). The opposite behavior is encountered in the Ni complex 2. The physical origin of these different types of correlation processes are analyzed in a simple two-electron two-orbital model. The nature of the HF fluctuations in 1 and 2, the importance of spatial and spin correlation, and the coupling of symmetry breaking of the electronic wave function with nuclear deformations are compared with the nature of phase transitions in solid-state systems.

Notizen: A variant of the interaction energy decomposition scheme proposed by Morokuma which gives more emphasis to polarized MOS is presented and tested on complexes of amines with Li+, BH3, and SO2. A more systematic utilization of polarized MOS (i.e., of orbitals of the interacting molecules computed with the SCF formalism in the Coulombic field of the other molecular components of the system) is adopted, and the connection of this decomposition of the supermolecule interaction energy with perturbation approaches utilizing such polarized MOS is discussed.

Notizen: The bond length alternation problem in cyclic polyene models as described by the Pariser-Parr-Pople Hamiltonian and an empirical quasiharmonic π-core potential is investigated using the one-parameter alternant molecular orbital (AMO) method. It is shown that in contrast to the unrestricted Hartree-Fock (UHF) results, which lead to symmetric equidistant structures, the one-parameter AMO results yield bond length alternating structures similar to those obtained with the restricted HF approach. The correlation energy recovered by the AMO method is examined for the symmetric polyenes in the whole range of coupling constants for both the Pariser-Parr-Pople and Hubbard Hamiltonians and compared with exact full configuration interaction (FCI) results. For the first member of the cyclic polyene series we also compared the FCI and AMO correlation energies for different nuclear framework distortions. This comparison indicates that in contrast to the UHF results the fraction of the correlation energy recovered by the AMO approach is very uniform over the range of nuclear distortions considered. The AMO results thus strongly indicate the dimerization in the polyenic chains.

Notizen: In a previous paper [J. Krechl and J. Kuthan, Int. J. Quantum Chem. 21, 1029 (1982)] the energetically preferred configuration of the supermolecular His 195, Arg 171, NAD+, and lactate system was approximatively calculated. In this paper the EHT, CNDO/2 and INDO methods were used for an analogous reacting complex of lactate dehydrogenase involving His 195, Arg 171, NADH, and pyruvate models. Calculated quantum chemical data for the supermolecule I - II - III - IV are discussed in relation to a possible course of the enzymatic reaction.

Notizen: This paper deals with the perturbation theory of an n-electron Hamiltonian of the general form H = ∑n ƒ(i) + λ∑n g(i, j) = H (f, g; n). In comparison to the Brueckner-Goldstone diagrammatic perturbation theory, we adopt the more general standpoint of admitting, for the construction of an n-particle state, component states of 1, 2, 3, and more particles [O. Sinanoglu, Phys. Rev. 122, 493 (1961) and C. D. H. Chisholm and A. Dalgarno, Proc. R. Soc. (London) Sec. A 292, 264 (1966)]. We show that this leads to the concept of a “partition” of a perturbational eigenstate (or energy) of H. A “partition” is a natural decomposition which: (i) is finite; (ii) relates the eigenvalue problem of the system H = H (f, g; n) to those of certain subsystems H (f, g; n1)(n1 〈 n); (iii) uses “nonseparable” components. We domonstrate (under the preliminary assumption of “strict” nondegeneracy) the second-order energy to possess a “partition.” The components therein are second-order energies of two- and three-particle states. The proof uses an extension of Racah's concept of the fractional-parentage expansion.

Notizen: The nuclear magnetic shielding and magnetizability tensors for the BH molecule are calculated by the coupled-Hartree-Fock method and many-body perturbation theory. As in the case of H2, HF, and F2, the second-order non-CHF diagrams make an inappreciable contribution.

Notizen: Kekulé indices and conjugated circuits are computed for 36 Kekulé structures, together with two VB quantities associated with the corresponding factor graphs (previously called submolecules). These latter quantitites are nonadjacent numbers of Hosoya and the reciprocal of the connectivity indices of Randić. It was found that the index of Hosoya successfully orders a set of Kekulé structures belonging to the same hydrocarbon in a parallel order as their Kekulé indices and branching indices. This substantiates the relation between VB and MO theories. A code is derived by summing contributions of nonadjacent numbers in all Kekulé stuctures of a hydrocarbon. The order of the resulting codes is found to be identical to the order of the molecular properties (resonance energies, π-energies, and eigenvalues) of the hydrocarbons.

Notizen: A reformulation of the Born-Oppenheimer nonadiabatic coupling for diatomic molecules is presented, which clearly demonstrates its hermiticity and allows a computation of the coupling elements using very accurate CI functions for the description of the electronic motion.

Notizen: The concept of atomic valency is looked at as a specific response of an atomic system to an arbitrary environment. It is shown, on the basis of a mathematical result in group actions theory, how valency might be related both to previously found Hartree-Fock deformed states and to the isotropy groups (up to a conjugation) of the extrema of the electronic energy functional.

Notizen: The Hartree-Fock method (standard Roothaan closed-shell HF-LCAO theory) and the Hartree-Fock-Slater method (restricted HFS-LCAO-DV method developed by Baerends and Ros) have been compared with emphasis on the respective one-electron equations and on the matrix elements of the respective Fock operators. Using the same STO basis in the two cases, the matrix elements of the Fock operators and of their separate one-electron, Coulomb, and exchange contributions have been calculated for the same orbitals and density of the ground state of the diatomic molecule ZnO. The effects of methodical (exchange potential) and numerical (DV method, density fit) differences between the HF and HFS methods on the various matrix elements have been analyzed. As expected the methodical effect prevails and is responsible for the higher (less negative) values of the matrix elements of the HFS Fock operator compared to those of the HF Fock operator. Numerical effects are observable also and are caused by the difference in integration procedures (DV method), not by the density fit.

Notizen: In the framework of our theoretical approach of the structure and reactivity of chemical intermediates we have been led to reexamine the concept of stability which is widely used by the experimentalists often without specifying its true meaning. In this work we propose a more general definition of the concept of stabilization energy, namely, \documentclass{article}\pagestyle{empty}\begin{document}$$ SE = \Delta H_a - \Sigma N_{AB} E_{AB} $$\end{document} where ΔHa is the heat of atomization of the species under consideration and the EAB's are standard bond energy terms derived from the heats of atomization of reference compounds. Using experimental heats of formation or semiempirical ones deduced from theoretical heats of reaction of appropriate isodesmic processes, we have calculated the stabilization energies of various types of chemical species: saturated, unsaturated and conjugated molecules, free radicals, carbocations, and carbanions. The results obtained can be rationalized in terms of steric hindrance, angular strain, polar interactions, electron delocalization, and substituent effects. Moreover, we have shown that heats of hydrogenation and bond dissociation energies do not provide accurate information on the thermodynamic stabilization of unsaturated compounds and free radicals, respectively. Among other applications the concept of stabilization energy allowed us to propose a detailed classification of free radicals and to rationalize their reactivity. Considering the particular case of radical recombination reactions we have been able to deduce interesting equations showing the relations between the concept of stabilization energy and other quantities commonly used in chemical physics, namely, the bond cleavage enthalpy [BDE(C—C) if one considers alkane thermolysis], the thermodynamic stability measured by the free enthalpy change of a given reaction, and the kinetic stabilization related to the activation energy of a chosen chemical process \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {{\rm BDE}(R - R) = E(R - R) - 2{\rm SE(R}^ \cdot {\rm)} + {\rm SE(R} - R{\rm),}} \\ {\Delta G^0_r 2{\rm SE(}R^ \cdot {\rm)} - {\rm SE(R} - R{\rm)} - E(R - R) - T\Delta S^0,} \\ {E_a (r) = \alpha [ - {\rm BDE(}R - R{\rm)}] + \beta ({\hbox{Evans - Polanyi relation}}),}\\ {E_a (r) = a[2{\rm SE(R}^ \cdot )} - {\rm SE(}R - R{\rm)] + }b{\rm .} \end{array} $$\end{document} This analysis allowed us to give a new interpretation of the adjectives transient, persistent, and stable introduced by Griller and Ingold and to show that the persistence of a radical may be due to other factors than steric ones. In conclusion, the concept of stabilization energy appears to be a good tool for rationalizing the static and dynamic properties of chemical species.

Notizen: The magnetic susceptibility and screening constant tensors are calculated using an ab initio finite perturbation SCF method, with gauge invariant Gaussian orbitals. The isoelectronic BH BeH-, and CH+ molecules have been studied. The calculated values for BH are relatively different from those obtained by other methods. The CH+ molecule seems to exhibit a stronger temperature independent paramagnetism than BH, while the BeH- molecule would be diamagnetic. The screening constants of the heavy atom of these molecules present a similar variation.

Notizen: Recent progress in multiconfiguration time-dependent Hartree-Fock (MC-TDHF) theory is reviewed. The generality of a formalism first put forward by Moccia [Int. J. Quantum Chemistry 8, 293 (1974)] is emphasized, and illustrative applications are discussed. A calculation of the frequency-dependent electric-dipole polarizability of the helium atom shows that even with a modest amount of CI, it is possible to achieve an accuracy comparable to that obtained by use of Hylleraas-type wave functions.

Notizen: A two-dimensional fully numerical relaxation approach is presented for the electronic Schrödinger equation of linear molecules. The method is tested on the lowest σ, π, δ, and φ states of H2+ and HeH2+. About 10-figure accuracy is obtained for the orbital energies. Seven-point numerical formulas are given for first and second derivatives.

Notizen: Analytical expressions for the square of the spherical average of Fourier transforms of Gaussian type orbitals (GTO's) are given. A direct application of these expressions to the calculation of molecular photoionization cross sections is considered under the generalized sudden (GSA) and dipole (DA) Approximations. Numerical calculations were done on the CO molecule using bound orbitals obtained by ab initio LCAO-MO calculations with Gaussian basis sets. The results are in good agreement with experiments. Those obtained by the GSA method however, suggest a limitation in its use: the GSA method is only applicable when comparing photoionization intensities of neighboring ionization energy orbitals. Applications to other molecules are immediate.

Notizen: Multiple-scattering-Xα (MS-Xα) calculations have been performed on IrCl63-, IrCl62-, and WO66- clusters. Relativistic calculations have been performed by the inclusion of the approximation of Wood and Boring in the MS-Xα method, i.e., mass-velocity and Darwin terms are taken into account self-consistently, while the effects of the spin-orbit operator are estimated by first-order perturbation theory. The strong contraction of s and p orbitals can be seen on selected displays of radial wave functions and significant changes in the energy diagrams between the nonrelativistic and the relativistic calculations can be obtained. The comparison with photoemission spectra clearly shows the necessity of including relativistic corrections in the calculations. The calculated spin-orbit parameters are in agreement with experiment for core levels, while a strong dependence of the spin-orbit parameters on the one electron energies is pointed out; this dependance is unconnected from the atomic contributions to the molecular orbitals.

Notizen: Multiconfiguration (MC) SCF calculations are reported for CO2 for bond angles between 60° and 180°. The ground state configuration is found to be …5a124b22∣b12∣a22 for small bending angles and …6a123b22∣b12∣a22 for large bending angles, the change in ground state character occurring at a bond angle of about 100°. The force constant for bending obtained from the MC-SCF function is about 8.0% lower than the corresponding SCF value, and in considerably better agreement with experiment.

Notizen: Using some properties of the Bessel functions the algebraic representation of the Nakajima-Zwanzig generalized master equation was derived. This representation makes possible the calculation of the memory functions in terms of the probabilities. Using this approach, the formulas for the memory functions giving their dependence on the eigenvalues and eigenvectors of the corresponding stationary Schrödinger equation are given and discussed in detail.

Notizen: A semiempirical SCF MO method has been developed in which the wave function of a composite molecule is written as a linear combination of localized fragment orbitals and which is formulated such that strictly transferable empirical data for the fragments may be introduced into the calculation. Results of FIM calculations in the CNDO/2 approximation for a number of R—X molecules with R = alkyl and X = F, OH, NH2, and CH3 are presented and used to illustrate the possibilities and limitations of the method.

Notizen: We outline a theory of UV and higher-energy photoemission spectroscopy of chemisorbed atoms, that aims at the accurate calculation of inner electron binding energies and photoabsorption cross sections by including solid state and localized relativistic and correlation effects. It is based on an “atom on (in) solids” approach where one first extracts a surface potential and then uses it in a coupled Hartree-Fock theory to obtain self-consistently the shifts and splittings of atomic levels. A first application of this theoretical program has been carried out on Na on the Al(100) system, by calculating from first principles the binding energies of the Na 1s and 2s electrons. For a coverage of 1.23 × 1014 adatoms/cm2 we find BE(1s) = 1075.2 eV and BE(2s) = 66.2 eV. Also, the Na 2p orbitals are found to split in the cylindrical symmetry by about 0.2 eV.

Notizen: The theory for nuclear shielding including electron correlation effect is derived and applied to the hydrogen fluoride molecule. It is shown that about 20% of the paramagnetic contribution to nuclear shielding at nucleus F is due to electron correlation. Inclusion of electron correlation effect greatly improves the calculated values toward the experimental ones.

Notizen: Following the conjecture of Fröhlich that the Bose condensation of phonons is the dominant biological effect, Wu and Austin derived from the Fröhlich Hamiltonian an expression for the relaxation time which is inversely proportional to the temperature by using the technique of Green's function. In this paper, we have generalized the Wu and Austin expression by improving their approximations with the superconducting canonical transformation and obtained the relaxation time depending exponentially on the inverse temperature. Moreover, we have checked our expression by using a different method based on the “continued fraction expansion” and also employed this technique to derive the dielectric constant for this system.

Notizen: Quantum chemical studies on interaction of p-benzoquinone and mitomycin C with complementary base pairs have been performed. The empirical potential function and semitheoretical algorithm were applied for estimation of intermolecular interaction energy. Non-negligible intercalation of the quinone ring into fragments of nucleic acid seems to be justified. Extensive calculations on the specificity of mitomycin C intercalation were performed using AGNAS/IMNAS algorithm based on an empirical potential function. No clear preference for intercalation into any kind of base pairs was found.

Notizen: Hydration sites of the acetal segment were studied in five of the most stable conformers of 2-methoxy-tetrahydropyran (MTHP) as the first step in the determination of the hydration scheme of glycosides. The intramolecular geometries of a supermolecule formed with MTHP and water were calculated by a PCILO quantum-chemical method. The hydration sites determined can be classified into two groups: (a) individual sites, in which water interacts with one oxygen only, and (b) bridging sites, in which water interacts with both oxygens. The interaction energies of the individual sites are approximately 22 kJ mol-1, and 26 and 29 kJ mol-1 in the bridging sites. An increase of the number of water molecules in the hydration shell of MTHP showed that monohydration of the glycosidic linkage oxygens was most advantageous. Despite of the fact that the hydration shell have various structures in the individual MTHP conformers, the obtained results indicate that the hydration does not operate against the anomeric or exoanomeric effects, i.e., it does not influence the equilibrium of the MTHP conformers in favor of the trans arrangements of a glycosidic bond. Therefore, the experimentally observed stabilization of the trans positions in aqueous solutions should be considered as a result of influence of water being a dielectric continuum.

Notizen: A systematic investigation of momentum densities Π(p), Compton profiles J(q), and internally folded densities B(r) has been made for the ground states of the atoms from H to Kr. The data are presented in reduced form by means of the characteristic momentum p* = q* and length r* = 1/p*, where p* = [J(0)/2πΠ(0)]½. The results indicate that p* and J(0) contain the gross qualitative behavior of the atomic properties in momentum space. They also show that subtle effects over and above the gross scale and size are mostly periodic.

Notizen: The Titchmarsh-Weyl theory for a singular second-order differential equation is presented. The equations, however, are arranged such that the theory is immediately applicable to the multichannel formulation. The mathematical basis of the Titchmarsh-Weyl theory (TWT) is outlined and the Titchmarsh-Weyl m function is presented. Relations to the associated Green's function and the spectral function are given. It is shown how some quantities common in scattering theory can be expressed in terms of the TWT. The method of complex rotation is then applied to the TWT to create a complex rotated analog of the Titchmarsh-Weyl theory. This is then extended as exterior complex scaling is introduced. An outline of a proof for the method of exterior complex scaling is presented and some numerical results of the complete theory are given.

Notizen: A very general form of the hypervirial theorems, which can be applied to several quantum systems of great interest for the theoretical quantum chemists is presented.

Notizen: Use of the general variation method of Weinstein and MacDonald for the relativistic calculation of atoms and molecules is proposed. It is shown from the numerical calculations for hydrogenlike atomic systems that this method is useful in judging an accuracy of energies and wave functions obtained with a relativistic Hamiltonian whose spectra are not bounded. It is also shown that this method can be used to find spurious solutions such as 1p½ or 2d3/2 appearing in atomic systems. Problems in extending the method to many-electron atoms and molecules are discussed.

Notizen: An analytical treatment for a strong crystal field in an octahedral symmetry by using the unitary group approach is given. It shows that the convenience of the unitary group approach is comparable with that of the Racah method.

Notizen: A new method for separating differently transmitted components of spin-spin coupling constants is introduced which is suitable when couplings are calculated using the coupled Hartree-Fock (CHF) approximation via the polarization propagator. Contributions transmitted through different electronic subsystems are found choosing different subsets of orbitals with their corresponding virtual spaces for their description. Examples for two different channels of transmission are given, which are very well known among NMR spectroscopists, namely, components trasmitted via π-electron systems, and “through-space” interactions. In the first case a set of canonical orbitals is chosen, while in the latter noncanonical ones are used. For both cases, numerical results are given within the INDO approximation. These results are compared with others obtained previously by means of the partially restricted molecular orbitals approach. The possibility of using this method of inner projections of the polarization propagator in decomposing other second orther properties is suggested.

Notizen: The negative factor counting method (in its simple and matrix block form) for the determination of the density of states of disordered polymer chains and its applications to different aperiodic organic polymers are reviewed. The problems of the calculation of the correlation energy in large systems like polymers will be discussed. Different ways for the partitioning of an energy band into regions make it possible to perform Møller-Plesset perturbation theoretical calculations on polymers. Applications to hydrogen chains are presented. Finally, possible applications to disordered polymers are also discussed.

Notizen: The quantum dynamical behavior of the Van der Waals molecule (N2)2 and that of the ordered α and γ phases of solid N2 have recently been calculated, starting from the same ab initio N2—N2 potential. By interpreting the results of these calculations we try to improve our understanding of the libration/internal rotation motions of the N2 monomers and the orientational order-disorder (α-β) phase transition. Some new results are presented and further (mean-field and libron-model) calculations are proposed which assess explicitly the intermolecular pair correlation effects caused by the anisotropic interaction potential.

Notizen: Attempting to explain the differences in the pharmacological profiles of the isomeric monohydroxy-and dihydroxy-2-aminotetralins (DHAT) which are potent dopaminergic agonists we have calculated the conformational energies of 2-aminotetralin and its N,N-dipropyl derivative using the QCFF/Pi and PCILO methods. Molecular electrostatic potential (MEP) maps based on ab initio (STO-3G) wave functions were computed for both dihydroxytetralins. Root-mean-square (rms) deviations from steric congruence between the enantiomeric 5,6- and 6,7-DHAT based either on atomic centers or on the minima in MEP near the putative points of attachment to the receptor are small, but may nevertheless be sufficient to cause differences in activity on subtypes of the dopamine receptor. N,N-dipropyl substitution influences the conformational energies of the skeleton and the preferences in the orientation of the propyl groups in the isomeric DHAT may be important for the interaction with the receptor. The HOMO energies of the isomeric HAT and DHAT do not correlate with their potencies.

Notizen: Doped semiconductors with shallow impurities provide an ideal situation to study a collection of hydrogenlike atoms under controllable experimental conditions. We present the results of recent cluster calculation on the electronic properties of such systems.

Notizen: Collective modes of superfluid 3He B have been studied by means of sound attenuation and sound velocity studies. A new sound attenuation peak has been observed in superfluid 3He B at ħω ≈ Δ(T). This peak has been identified with the real squashing mode. Pulse time of flight methods has been used in these studies. At high sound amplitudes, interesting transient effects have been observed which have been tentatively identified with solitonlike behavior.

Notizen: Møller-Plesset-type perturbation theory is applied to calculate electron correlation effects in infinite, periodic, metallic, and semiconducting polymers. Different possible choices of the zeroth-order Hamiltonian (symmetry adapted Hartree-Fock, spin-, and charge-density waves), the influence of the size of the atomic basis sets, lattice and conduction band sums are investigated. In the case of semiconducting systems a very efficient version of the method using optimally localized Wannier functions has been worked out. Applications include model calculations for infinite atomic hydrogen chains, the investigation of the role of correlation effects in the bond alternation and metal-insulator phase transition in polyene, different one-and many-particle effects contributing to the single-particle gap in polyene, and the calculation of correlated quasiparticle band structures using the electronic polaron model.

Notizen: In a systematic study, the characteristics of triplet oxene models for alkane, alkene, chloroalkane, and aryl oxidations by the cytochrome P450s have been examined using the semiempirical molecular orbital method MNDO and the formalism of statistical mechanics. Specific model substrates chosen were: methane, ethylene, propene, carbon tetrachloride, chloroform, and toluene. It was found that transition state geometries and activation entropies were reliably predicted, but that an empirical factor was necessary to correct overestimation of activation enthalpies. It was determined that both hydroxylations and epoxidation initiated by a O(3P) atom are nonconcerted; and that oxidations of C—Cl bonds (halosylations) occur by a two-step mechanism similar to hydroxylation. It is shown that the radical mechanisms derived from these studies are consistent with a range of observed properties of cytochrome P450 reactions and provide reasonable explanations for secondary deuterium isotope effects and substituent effects in cytochrome P450 epoxidation of styrenes, suicide inactivation of a P450 enzyme by ethylene, and the characteristics of aerobic CCl4 and CHCl3 metabolism. A triplet oxene mechanism for the initial steps of aromatic epoxidation and hydroxylation is also discussed.

Notizen: The molecular electrostatic potential of the triple helix poly(dT)·tpoly(dA)·poly(dT) is calculated, and the results are examined in relation to those obtained for its component double and single helical parts. For the double helix presenting the standard Watson-Crick hydrogen bonds, the deepest potentials are formed on the side of the major groove, a situation similar to that observed in the A-DNA duplex. For the double helix presenting Hoogsteen-type hydrogen bonds the deepest potentials lie in the major groove, on the side of the pyrimidine strand. In the triple helix the deepest potentials are located in the major groove in a narrow zone over the thymine bases of the Watson-Crick pair.

Notizen: An examination of the ground and excited states of magnesium porphine and pheoporphine and their positive and negative ions using the intermediate neglect of differential overlap/spectroscopic method is reported. It is found that rather large changes in the Mg out-of-plane coordinate can be attained at very little cost in energy. These geometric changes alone can be used to explain the large range of spectroscopic shifts observed in the visible band of chlorophyll that are site dependent. These calculations also show a porphyrin to Mg charge transfer excitation at about 20,000 cm-1, which, if populated and allowed to relax, becomes the lowest excited singlet. This suggests that the initial photochemical event in photosynthesis may be excitation to the visible Q band followed by internal conversion to the charge transfer state accompanied by movement of the Mg atom out of the plane of the ring. This movement could result in intermolecular charge transfer, and relaxation of the Mg atom back to the plane of the ring. The nature of the positive and negative ions of these model chlorophylls is discussed in light of their role as the electron donor and their potential role as initial electron acceptor in photosynthesis.

Notizen: Photoreactions on finely divided semiconductors are discussed. Experimental results on photo-oxidation of CO, isobutane, and NH3 over UV-irradiated n-TiO2 (anatase) particles of different size are discussed. The possibility of using size-quantized films for spectroscopy of adsorbates is also considered.

Notizen: The chemical bonding in the interesting class of refractory transition metal compounds is illustrated for TiC, TiN, and TiO. Self-consistent augmented plane wave (APW) calculations are already available for these compounds. Using the respective potentials we have repeated the band calculations on a finer k grid with the linearized APW method to obtain accurate densities of states (DOS). These DOS can be divided into local partial contributions to characterize the bonding. Further information can be obtained from a decomposition of the metal d DOS into t2g and eg symmetry components. These partial local DOS are compared with the LCAO counterpart and give a first picture of the chemical bonding in these compounds. The electron densities corresponding to the occupied valence states are obtained from the LAPW calculations. They provide further insight into characteristic trends in the series from TiC to TiO: around the nonmetal site the density shows increasing localization; around the metal site the deviation from spherical symmetry changes from eg to t2g. These effects can be traced back to the three types of valence bands. Electron density plots of characteristic band states (all energies of a selected k point in the Brillouin zone) will be shown. These plots can describe the different types of bonding occurring in these systems.

Notizen: The Bose-Einstein-like ordering was earlier proposed as an important mechanism of energy handling in the living systems. In this regard two questions arise at once: (1) is such ordering feasible at body temperature and (2) what is the time that may be taken for establishing coherence? In this paper we hope to answer and satisfy these two questions.

Notizen: Similarities and differences between mitochondrial monoamine oxidase (MAO) substrates and inhibitors (both A and B types) are considered, studying quantitatively two molecular properties: electron density and molecular electrostatic potential (MEP). The following molecules are considered: substrates: PHEA, BZA, tele-N-methyl-histamine, phenylethanolamine, phenylpropylamine, tryptamine, dopamine, phenoxylethylamine, noradrenaline, serotonin, and p-nitro-phenylethanolamine; inhibitors: Deprenil, Clorgyline, and Lilly 51641 (only the moiety involved in the A-B differentiation is considered). The wave functions needed to calculate the analyzed properties are of ab initio quality, and have been calculated in analogous conformations, all near the energetic minima. Electron densities distributions are qualitatively compared by means of a correlation coefficient defined over the whole space. Otherwise, patterns of the possible zones of electrostatic interactions are described by means of the distances and angles between minima, in order to differentiate MAO-A and MAO-B substrates. The results reproduce efficiently the experimental classification and enable us to predict the type of enzymatic action of molecules not yet experimentally classified.

Notizen: The semiempirical self-consistent field MO (CNDO/2) calculations have been undertaken for 13 compounds involving 3-methyl-fentanyl and its analogs. Various quantum chemical indices were obtained. The relationships between the biological activity and quantum chemical indices of molecules of these compounds were investigated and it was found that there are remarkable relationships between the activity and some important quantum chemical indices such as the α-electron density of β substituent and the electron density of piperidyl nitrogen. The nature of interaction between the analgesics' molecule and the receptor was discussed on the basis of the relationships between the activity and quantum chemical indices and it was proposed that the β-substituent functions not only as a hydrophobic group, but also its electronic property has important effect on the activity. It may act as an electron acceptor and form acceptor-donor complex with receptor through the charge transfer process. The piperidyl nitrogen interacts with receptor forming quaternary ammonium ion and acting as positive charge center, and its electron density also has an important effect on the activity. The amide oxygen and nitrogen may be other active centers which function as donors when they interact with the receptor. The influence on activity through introduction of the hydroxyl group to the β-position of the 1-substituent of the piperdyl ring has also been discussed.

Notizen: A number of trimers of water molecules have been computed with an extended basis set in the Hartree-Fock and in the direct CI approximations. It has been verified that the three-body interaction energy can be calculated within the Hartree-Fock method. Therefore, the correlation corrections to the Hartree-Fock level are essentially additive and do not contribute significantly to three-body effects.

Notizen: The definition of the cyclic polynomial of conjugated hydrocarbons is offered. The combinatorial characteristics of this polynomial are investigated. The most important property of the cyclic polynomial is that it can be used for enumeration of conjugated circuits.

Notizen: Vertical ionization potentials for core orbitals of HF, H2O, and CO are calculated with the ab initio transition operator method. The results are improved by third-order Rayleigh-Schrödinger perturbation theory. The effect of basis sets is also investigated. The computed core-electron binding energies are compared with the experimental values and with those obtained by other theoretical methods. The comparison shows that the present approach leads to reliable core ionization energies, the average absolute deviation from experiment being only 0.4 eV for the cases studied.

Notizen: An attempt to classify various types of avoided surface crossings originally discussed by Salem and co-workers is presented. From the present scheme, an order-of-forbiddenness criterion regarding reactivity is established from a consideration of electron and orbital counting. Since the new classification is qualitatively related to the energy gap created in the avoided crossing, the classification appears to be more systematic and informative. Energy transfer processes involved in electronically excited states may also be rationalized by such an application. Three major mechanistic types are distinguished: concerted two-electron process, concerted one-electron process, and stepwise one-electron process involving an ionic-pair intermediate.

Notizen: A procedure for generating basis sets for diatomic molecule electronic structure calculations is described. In essence, this procedure maps the results of nearly exact numerical Hartree-Fock calculations into basis set form. Two applications of the procedure are proposed: (a) generation of very high accuracy basis sets, and (b) investigation of basis sets for unusual systems. The latter application is illustrated by some results for diatomic anions.

Notizen: Analytical properties of hydrogen-like atomic orbitals (HAO) that are used in the MOLCAO approach to the quantum theory of molecules have been studied. Addition and expansion theorems for HAO have been proved, both in coordinate and momentum representations. A close relation has been established between HAO and the reduced Bessel functions of half-integer indices. New methods are suggested to calculate integrals for atomic and molecular form factors, and multicenter integrals, for the HAO basis in the MO LCAO theory.

Notizen: A method for nonadiabatic many-particle quantum-mechanical calculations is described and illustrated for the special case of three particles. The method uses a basis of explicitly correlated Singer-type exponential quadratic function (polymals) of the internal degrees of freedom. Rigorous symmetry states are projected from the basis: linear momentum of the center of mass, total angular momentum, and permutational symmetry under interchange of indistinguishable particles. The nonadiabatic wave functions are interpreted via purely quantum-mechanical criteria of interparticle correlation as measured by average values of powers of interparticle distances and angles. The illustrations are made on H2+ which is easily treated in the Born-Oppenheimer and adiabatic approximations, on helium, muonic helium, and on (e+, e-, e+) which are poorly described in adiabatic methods. The ground and lowest bound excited states of these systems are studied with up to 256 tempered Singer polymals for which we find energies too high by 0.0011 a.u. in H2+, 0.0017 a.u. in muonic helium, 0.0009 a.u. in 4He, and 0.0002 a.u. in (e+, e-, e+); the corresponding relative errors are 1800, 4, 300, and 200 ppm, respectively.

Notizen: The Gel'fand-Levitan theory is applied to obtain the exact potential function for an atomic or a molecular system when the solution of the Schrödinger equation with a reference potential which is close to the actual potential is known. With this method one can construct bound state equivalent local potentials, or potentials which, for large quantum numbers, have spectra similar to that of the reference potential. In one-dimensional problems the resulting potentials are not generally symmetric about the origin, even if one starts with symmetric reference potentials. This lack of symmetry is due to the presence of additional terms in the Hamiltonian which are of purely quantal origin, and therefore in any semiclassical treatment become negligible. This observation leads one to investigate the relationship between the spectrum of a given system and the symmetry of the underlying Hamiltonian. Examples are given to show that the dynamical symmetries usually associated with the spectral properties do not necessarily follow from the Gel'fand-Levitan inverse theory, but can be imposed as constraints on the solution. Additional constraints on the form of the two-body wave function also arise from the observable transition rates for atom-molecule collisions and for the interaction of the charged particles in the system with an external electromagnetic field.

Notizen: The equilibrium Co—F bond distance and the a1g vibrational frequency of CoF6n- complexes (n = 4, 3, and 2) in crystals were investigated from a theoretical point of view. Ab initio SCF MO calculations were performed for the isolated CoF6n- complexes in order to obtain the potential energy curves against the Co—F distance. These potential energy curves were improved by considering the effect of the surrounding ions. It is shown that the effects of the next-nearest neighbors (eight K+ ions) and the next-next-nearest neighbors (six Co2+ ions) are very important in determining these properties for “ionic” KCoF3 crystal. On the other hand, for Cs2CoF6 crystal, in which the Co—F bond has considerable degree of covalency, the shape of the potential energy curve is almost completely determined by the nonelectrostatic component of the intramolecular interaction of the isolated CoF62- unit.

Notizen: Computations are performed on the interaction specificities of tetramethylammonium (TMA) for double-stranded oligonucleotides held in the B conformation. The effects of base sequence and chain length are investigated. In the short oligomers (helices formed from dinucleoside monophosphates and trinucleoside diphosphates), the interaction energies of TMA are larger in the major groove of (dG)n · (dC)n than in the minor groove of either (dA)n · (dT)n or (dA - dT)n. Upon lengthening the oligomers, and owing to the gradual shaping of the grooves of the helix and cumulative effect of the phosphates, TMA is shown to increasingly favor the minor groove of (dA)n · (dT)n with respect to the major groove of (dG)n · (dC)n, with a sizeable energy difference computed at the pentanucleoside hexaphosphate level. The binding of TMA in the minor groove of (dA)n · (dT)n involves stabilizing contacts with several sites, on the bases and on the deoxyriboses. Configurations locating the cation closer to the thymine strand are slightly preferred over configurations locating it closer to the adenine strand.

Notizen: This paper reports a study on which behavior of the Hamiltonian gives rise to violation of the noncrossing rule. In principle, the noncrossing rule may be violated when a special symmetry other than spatial and spin symmetries is present or there exists the so-called alternance, which corresponds to a Hamiltonian in a real vector space anticommuting with a Hermitian operator. In the HMO models for pericyclic reactions, violations due to special symmetry or alternance have been found. The [m,n] supra-antara cycloadditions have no symmetry in the traditional sense, but have special symmetry leading to the existence of crossings in the correlation diagram. Alternance results in one crossing in the middle of the correlation diagram of a forbidden pericyclic reaction with intermediate states in the form of even alternant hydrocarbon. For the reactions with intermediate states in the form of odd alternant hydrocarbon such as [2,4]-cycloaddition of an allyl cation or an allyl anion to butadiene, there should be no crossing in the correlation diagrams, and both the supra-supra and the supra-antara processes are predicted to be allowed. Such a prediction is beyond the Woodward-Hoffmann rule.

Notizen: The expectation values 〈rk〉 (-2 ≤ k ≤ 4, k = 10), values of the charge density ρ(r) at selected points, and coefficients in the MacLaurin expansion of ρ(r) are used to test the quality of 71 orbital basis sets used for the atomic helium Hartree-Fock problem. These tests in position space are complementary to the momentum space tests previously carried out [Int. J. Quantum Chem. 21, 419 (1982)]. Information theoretic measures with respect to either or both position and momentum space properties are subsequently defined and the orbitals are ranked accordingly. These measures indicate that, for a given orbital, momentum space properties are more poorly predicted than position space ones. Moreover an improvement in the virial ratio does not necessarily lead to a more balanced orbital with respect to position and momentum space properties. Basis sets containing Slater-type orbitals are again found to be rather accurate. The exponentially damped rational function is confirmed to be the outstanding two-parameter unconventional orbital.

Notizen: A new Tamm-Dancoff method for the ground and excited states of molecular electronic systems is developed. The method begins with a number-projected BCS (PBCS) wave function and is generated by excitations of particle pairs from the degenerate geminals in the PBCS wave function. A direct optimization of the PBCS wave function is accomplished with successive Bogoliubov transformations so that one-pair excitation terms in the Tamm-Dancoff expansion of the ground state vanish (the generalized Brillouin theorem). The spin-symmetry adapted first- and second-order Tamm-Dancoff bases and matrix elements are calculated by means of the CI expansion of the PBCS wave function with natural orbitals that diagonalize the BCS geminal matrix. Numerical calculations are presented for the H4 system with D2h and D4h conformations and for methylene. The PBCS wave function is not a very good approximation for the ground state, accounting for only about half of the correlation energy. The second-order Tamm-Dancoff correction improves the result as much as the double excitation CI. The Tamm-Dancoff terms consisting of two triplet pairs coupled to a singlet, and those relaxing the constraint imposed on the pairwise excitations in the PBCS wave function are important.

Notizen: Quasi-Wannier functions for the ammonia crystal have been determined from optimized ab initio calculations of the heptamer (NH3)7, thus accounting for all the first neighbor interactions. The calculated geometry and binding energy are in good agreement with their experimental counterparts.

Notizen: The energetics of rotation about the N—C′(ω); N—Cα(ϕ), and Cα—C′(φ) bonds of the peptide unit have been investigated in the pseudo-FSGO fragment scheme on model compounds formamide and N-methylacetamide. The results indicated that the position of the minimum in ω is in the near vicinity of 0°, i.e., the planar arrangement of the peptide unit. The minimum in ϕ (C′—N—Cα—H) has been found to be 180° and in ψ(H—Cα—C′—N) to be 60°, in good agreement with PCILO and Gaussian-70 results.

Notizen: A new density-functional equation is suggested for the direct calculation of electron density ρ(r) in many-electron systems. This employs a kinetic energy functional T2 + f(r)T0, where T2 is the original Weizsäcker correction, T0 is the Thomas-Fermi term, and f(r) is a correction factor that depends on both r and the number of electrons N. Using the Hartree-Fock relation between the kinetic and the exchange energy density, and a nonlocal approximation to the latter, the kinetic energy-density functional is written (in a.u.) \documentclass{article}\pagestyle{empty}\begin{document}$$ t[\rho] = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$4$}}\nabla ^2 \rho + {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 8}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$8$}}(\nabla \rho \cdot \nabla \rho)/\rho + C_k f({\bf r})\rho ^{5/3}, $$\end{document} where \documentclass{article}\pagestyle{empty}\begin{document}$ C_k = {\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 {10}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${10}$}}(3\pi ^2)^{2/3} $\end{document}. Incorporating the above expression in the total energy density functional and minimizing the latter subject to N representability conditions for ρ(r) result in an Euler-Lagrange nonlinear second-order differential equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \left[{ - {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}\nabla ^2 + v_{{\rm nuc}} ({\bf r}) + v_{{\rm cou}} ({\bf r}) + v_{XC} ({\bf r}) + {\raise0.7ex\hbox{$5$} \!\mathord{\left/ {\vphantom {5 3}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$3$}}C_k g({\bf r})\rho ^{2/3}} \right]\phi ({\bf r}) = \mu \phi ({\bf r}) $$\end{document} where μ is the chemical potential, we have ρ(r) = |φ(r)|2, and g(r) is related to f(r). Numerical solutions of the above equation for Ne, Ar, Kr, and Xe, by modeling f(r) and g(r) as simple sums over Gaussians, show excellent agreement with the corresponding Hartree-Fock ground-state densities and energies, indicating that this is likely to be a promising method for calculating fairly accurate electron densities in atoms and molecules.

Notizen: The use of the antisymmetrized geminal power (AGP) consistent reference state for RPA polarization propagator calculations is explored. Illustrative applications to the three lowest electronic states (3B1, 1A1, and 1B1) of the methylene radical are reported with comparisons to other theoretical methods and experiment.

Notizen: A method has been developed to analyzed the bond and current correlation structures of a molecular many-electron wave function. It is shown that the second order density matrix contains information about the bond and current correlations in its off-diagonal components with respect to the indices of orbital basis functions. We break down the off-diagonal correlation functions into five kinds: charge, spin scalar, spin quadrupole, charge spin, and spin polar correlation functions. For a real wave function, the four correlation functions, except for the spin polar one, have only symmetric-symmetric and antisymmetric-antisymmetric components. The former components give site-bond and bond-bond correlations of charges and spins, while the latter components give current-current correlations of charges and spins. The spin polar correlation function has only symmetric-antisymmetric components that give site-current and bond-current correlations of spins. The five off-diagonal correlation functions are expressed in terms of the off-diagonal components of the second order density matrix. The linked off-diagonal correlation functions are defined in that they give dynamical bond and current correlations. The method is applied to the analyses of the bond and current correlations in the low lying exact eigenstates of the PPP Hamiltonian of benzene.

Notizen: This work amalgamates some basic elements defined in the first paper of this series and in related papers with the theory of coupling coefficients for an arbitrary group with the view of generating the Clebsch-Gordan coefficients and V symbols for point symmetry groups. The connection between Clebsch-Gordan coefficients and V symbols is established for an arbitrary group in a form that reduces to the one known for the chain SU(2) ⊃ U(1). The Clebsch-Gordan coefficients and V symbols of any point symmetry group G are shown to be obtainable from Clebsch-Gordan coefficients and \documentclass{article}\pagestyle{empty}\begin{document}$ {\bar f} $\end{document} symbols of the chain SU(2) ⊃ G through the resolving of a system of nonlinear equations.

Notizen: A new concept of the “stability” of the quantum mechanical state is presented. This concept is closely related to the hydrodynamical theory of quantum mechanics. For charged particles, the “stability” against the application of the external electromagnetic field is examined. Under a nonlinear interaction, a new type of the solitonlike phenomenon is shown as a novel, illustrative example of the “stable” state. An extension for the relativistic treatment is also examined.

Notizen: Unitary transformations are performed with respect to three Lie group chains in quasispin schemes that are involved in the study of three different calculation schemes in ligand field theory. The unitary transformations hold true for either molecular or atomic orbitals being taken as the starting point. As a result, unitary transformations with respect to matrix elements are accomplished as well.

Notizen: The probability distribution of the interparticle distance is obtained for the N-body boson problem where the potential is an attractive delta function. This is done for both the exact wave function and the Hartree wave function allowing the calculation of the correlation hole.

Notizen: Two-dimensional fully numerical solutions of the Hartree-Fock problem are reported for the singlet ground states of H-, He, H2, and HeH+. The H2 energy at R = 1.4 a.u. is -1.13362957 a.u.

Notizen: An analysis of the LCAO Hamiltonian is performed in terms of a “mixed” formulation of the second quantization for nonorthogonal orbitals, compressing the different interactions to one- and two-center terms as far as possible by performing appropriate projections. For this purpose an operator of atomic charge is also introduced, the expectation values of which are the Mulliken gross atomic populations on the individual atoms. The LCAO Hamiltonian is decomposed into terms having different physical meaning and significance: (i) sum of effective atomic Hamiltonians; (ii) the electrostatic interactions in the point-charge approximation; (iii) the electrostatic effects connected with the deviation of the actual charge distribution from the pointlike one; (iv) two-center overlap effects; (v) finite basis (“counterpoise”) correction terms related to the individual atoms; and (vi) similar finite basis correction terms with respect to the two-center interactions. Only terms of types (i) to (iv), containing no three- or four-center integrals, are considered as having physical significance. Based on the analysis of the Hamiltonian, an energy partitioning scheme is developed, and explicit expressions are given for one- and two-center (and basis extension) components of the SCF energy. The approach is also applied to the problem of intermolecular interactions, and an explicit formula is given permitting calculation of the “counterpoise” part of the supermolecule energy by properly taking into account that it depends not only on the extension of the basis, but also on the occupation of the additional orbitals in the intervening molecule - a factor completely overlooked in the usual scheme of calculations.

Notizen: Quantum mechanics is a remarkable formalism for studying problems in the microscopic domain, and nobody has reasonably contested its power. Nevertheless, in spite of the many interpretations which have been proposed, its true meaning is far from being clear. The aim of this preliminary paper is to show that it is possible to conceive within a classical framework an interpretation of quantum mechanics and to make its limits of validity precise.

Notizen: Theoretical potential energy curves are computed for the X 2Σ+ and A 2Π states of CsO using a relativistic effective core potential and a large valence Gaussian basis set. Seventeen electrons are correlated by a CI(SD) calculation from each HF reference. We find the X 2Σ+ state lower by 497 and 726 cm-1 at the HF and CI(SD) levels. Our calculated ωe of 312 cm-1 for the X 2Σ+ state agrees well with experimental values deduced from studies in matrices.

Notizen: A self-consistent field approximation allowing for a change of coordinates is applied to a model of two coupled oscillators considered by Davis and Heller [J. Chem. Phys. 75, 246 (1981)]. The model accounts well for the unsymmetrical nonstationary states involved in the quantum dynamical tunneling phenomenon.

Notizen: The application of the charge-transfer concept on core electron ionization in donor-acceptor molecules is analyzed. A single excitation picture, involving the highest occupied and lowest unoccupied molecular orbitals is compared with a full π-valence orbital active space model. The connections between the notion of charge transfer in donor-acceptor species with the shake-up picture used for core photoelectron spectra of small molecules and with the dynamical screening concept applied on surface-adsorbate spectra are discussed.

Notizen: The reaction activity is analyzed in terms of an electronic factor and a Franck-Condon factor, in analogy to that in problems of spectroscopy. A scheme for codifying a number of physical and chemical processes based on magnitude of the two factors is proposed. The electronic factor not only determines the topological feature of the potential surfaces, but also is capable of revealing certain clues leading to the mechanistic understanding from the type of operator involved. Based on such an analysis, it is concluded that all processes involving a one-electron operator, either concerted or stepwise, may compete favorably with processes involving two-electron operators. A forbidden reaction with a two-electron process may therefore become a more efficient one-electron process by either choosing a nonleast motion pathway, by carrying out the overall transformation stepwise, or by changing the occupation number of certain orbitals in the ionic form. The mechanisms of energy transfer in the excited state is also briefly discussed in terms of one-electron and two-electron processes.