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Notes: Many biological processes are characterized by an essentially quantum dynamical event, such as electron or proton transfer, in a complex classical environment. To treat such processes properly by computer simulation, allowing nonadiabatic transitions involving excited states, we recently developed a density matrix evolution (DME) method [H. J. C. Berendsen and J. Mavri, J. Phys. Chem, 97, 13464 (1993)] which simulates the dynamics of quantum systems embedded in a classical environment. The formalism of the method is presented and an overview of the applications ranging from collisions of a quantum harmonic oscillator with noble gas atoms to proton tunneling in a double-well hydrogen bond is given. The methodology for treatment of proton-transfer processes with inclusion of excited states is presented. Future application of the method on biologically interesting processes, such as proton transfer in enzymatic reactions, is discussed. © 1996 John Wiley & Sons, Inc.

Notes: For theoretical reasons, and on account of the development of a new interpolation technique, it is useful and important to examine the asymptotic behavior of the solution to the one-dimensional Hubbard model. In this article, it is shown how perturbative expansions for the energy can be developed in the asymptotic region of the relevant coupling for all the relevant excited states of cyclic polyene rings. © 1996 John Wiley & Sons, Inc.

Notes: The simple BSSE-free SCF method (CHA/F) introduced in the previous parts of this series is extended to the case of three subsystems, which may be either three weakly interacting molecules or a bimolecular system described by using bond functions. The CHA/F formalism is formulated in a more transparent manner, indicating also a straightforward way for generalization to the case of an arbitrary number of subsystems. The illustrative calculations show the viability of using the CHA/F scheme for three-component systems. © 1996 John Wiley & Sons, Inc.

Notes: One is often led, in quantum mechanics, to a perturbative solution of an eigenvalue problem, which is defined by a given Hamiltonian. The perturbative series for the energy which results will be a function of a coupling constant which appears in the Hamiltonian. In this article, the perturbative series for the energy of a state of a cyclic polyene ring which are valid for the small and large coupling limit of the model are used to construct algebraic functions. These algebraic functions are defined in terms of polynomials which are given as a function of the energy variable and coupling parameter and can be solved to give the energy as a function of coupling. It is found that relatively small polynomials give very good agreement with the exact values and that the accuracy of the results increases rapidly as the degree of the polynomial increases. The final goal of this and subsequent articles is to study energy levels in PPP models of planar conjugated hydrocarbons. In this article, we test an interpolant technique on the case of the one-dimensional Hubbard model, where an exact solution can be obtained by solving a system of nonlinear equations. In the case of the Hubbard model, the correlation effects are overestimated. Therefore, if the technique works for the Hubbard model, it is reasonable to assume that the technique would work even better for the PPP model. © 1996 John Wiley & Sons, Inc.

Notes: The Ising, small-bipolaron (ISB) theory is a strong-coupling theory of cuprate superconductivity which is based on the negative-U, Hubbard Hamiltonian. Its ground state is composed of (small) bipolarons and (small-bipolaron) holes with a vibronically induced, bipolaron-hole exchange interaction, JBH, between them. The energy gap, Δ(0), is taken to be equal to the dissociation energy of a small bipolaron and which, since it is defined spectroscopically, is not an order parameter. The application of the Ising mean-field theory to the highly degenerate ground-state yields a second-order phase change with kTC/2 = JBH and a real order parameter, Ω(T), which is valid over the entire temperature range from zero to TC. Near TC, the Ising free-energy functional takes the same form as does the Landau. In the presence of an electromagnetic field, the Ising functional is a generalization of the Ginzburg-Landau functional which employs a complex order parameter and which is invariant under the electromagnetic gauge transformation. The breaking of the gauge invariance yields the London theory of superconductivity. © 1996 John Wiley & Sons, Inc.

Notes: The solvent shift of the π* ← n transition of acetone in water, acetonitrile, and tetrachloromethane was calculated in a combined quantum mechanical - classical mechanical approach, using both dielectric continuum and explicit, polarizable molecular solvent models. The explicit modeling of solvent polarizability allows for a separate analysis of electrostatic, induction, and dispersion contributions to the shifts. The calculations confirm the qualitative theories about the mechanisms behind the blue shift in polar solvents and the red shift in nonpolar solvents, the solvation of the ground state due to electrostatic interactions being preferential in the former, and favorable dispersion interaction with the excited state, in the latter case. Good quantitative agreement for the solvent shift between experiment (+1,700, +400, and -350 cm-1 in water, acetonitrile, and tetrachloromethane, respectively) and the explicit solvent model (+1,821, +922, and -381 cm-1) was reached through a modest Monte Carlo sampling of the solvent degrees of freedom. A consistent treatment of the solvent could only be realized in the molecular solvent model. The dielectric-only model needs reparameterization for each solvent. © 1996 John Wiley & Sons, Inc.

Notes: In density functional theory (DFT), a many-electron problem for the electron density in atoms may be reduced, according to the Kohn-Sham scheme, to a one-electron problem. In the present work, a variational model is proposed which leads, within some assumptions, to the set of equations describing the change of the electron density ρ and energy ε during the ionization process. It is shown that the one-electron density contributions are not necessarily spherically symmetric, but assume the symmetry which depends upon the symmetry of the positive field. A few nonspherically symmetric potentials are studied in the present article. The nonlinear differential equation for density r is formulated and solved for Coulombic, Fues-Kratzer, and Hartmann potentials. The solutions and some particular examples are presented. © 1996 John Wiley & Sons, Inc.

Notes: The cycloaddition reaction of FCH(double bond)C(double bond)O and NH2CH(double bond)NH leading to 2-azetidinone was studied theoretically at the level of RHF/6-31G and RHF/6-31G*. Two possible mechanisms via a gauche or trans intermediate were compared. The obtained results show that the reaction proceeds in a gauche manner much easier than in a trans one. © 1996 John Wiley & Sons, Inc.

Notes: The role of the asymptotic behavior of approximating sequences of electron densities ρn(r) in the calculation of one-electron properties is studied. Rigorous mathematical results in the frame of Hilbert spaces are used to prove the following facts: (i) Both the L2 convergence of wave functions ψn and the E convergence of the corresponding energies En guarantee the correctness of the limiting procedure limn→x ∫Ω s((overline)x(/overline)|ψn|2 d(overline)x(/overline) = ∫Ω s((overline)x(/overline))|ψ|2 d(overline)x(/overline) for the most frequently used operators s(x), Ω being any bounded region of the n-particle configuration space R3N; and (ii) the uniform boundedness of the sequence {ρn} together with both the L2 and E convergencies is sufficient to guarantee the correctness of the limiting procedure limn→x ∫∞0 s(r)ρnr2dr = ∫x0 s(r)ρr2 dr for most one-electron operators s(r) including the power moment operators rk which, for large k, are representative of the class of operators not relatively form-bounded by the Hamiltonian. The mathematical concept of uniform boundedness is used to give a characterization of the capability of {ρn} to reproduce the asymptotic behavior of the true electron density ρ and it is shown by means of numerical examples how a sequence {ρn} that does not reproduce the correct asymptotic behavior is not uniformly bounded and can give divergent expectation values of one-electron operators s(r) not relatively form-bounded by the Hamiltonian. © 1996 John Wiley & Sons, Inc.

Notes: We performed electronic ab initio calculations of ion clusters simulating a piece of ionic crystal. Our main interest here is to estimate the (direct) energy band gap from the cluster energy levels. The model consists of a central cation surrounded by four shells of ions, with additional point charges embedding the cluster. We present results for the series of alkali halides with rock-salt structure. © 1996 John Wiley & Sons, Inc.

Notes: In this work, we propose a new orbital set based on density matrices of subsystems. Most of the resultant orbitals are localized in the subsystems and resemble the natural orbitals of the subsystems. Correlation between two electrons, each in a distant localized orbital, should be small and the corresponding configurations can be neglected in a calculation. Test calculations are performed on hexatriene and the usefulness of these orbitals is shown. © 1996 John Wiley & Sons, Inc.

Notes: An alternative approach to secular problems for Hamiltonian matrices H of regular quasi-one-dimensional systems is suggested. The essence of this approach consists of the inverted order of operations against that of the traditional solid-state theory, viz., taking into account the local structure of the system is followed by regarding the translational symmetry of the whole chain. The first step is performed by reducing the initial system of secular equations into an effective N × N-dimensional secular problem, wherein a single equation corresponds to each of N elementary fragments of the initial chain. An implicit form of the dispersion relation and the level density function follow directly from the reduced problem without passing into the delocalized description of the system. The resulting eigenfunctions of the matrix H prove to be expressed as the Bloch sums of N nonorthogonal eigenvalue-dependent local-structure-determined orbitals of algebraic form, each of them corresponding to a definite elementary fragment of the chain. © 1996 John Wiley & Sons, Inc.

Notes: Hypervalent molecules may involve the use of increased-valence structures to provide valence bond descriptions of their electronic structure. For electron-rich molecules with four electrons distributed among three overlapping (nuclear-centered) atomic orbitals, the increased-valence structures are Y(BOND)A·B and Y·A -  - B. Each structure involves a fractional electron-pair bond and a one-electron bond. It is deduced that the Armstrong-Perkins-Stewart valence of the A atom is able to exceed unity in each of these structures when the three bonding electrons occupy nonorthogonal localized molecular orbitals. It is also shown that increased valence for the A atom does not occur when the four electrons occupy localized molecular orbitals to give the valence-bond structure Y - A - B with three overlapping atomic orbitals, and the same number of orbital variational parameters as occurs in the wave functions for either of the increased-valence structures. The results of ab initio valence bond calculations with minimal basis sets are reported for H-3l, CH-5, HF-2, F-3, CIF3, and FF3, and the resulting wave functions for resonance between six canonical Lewis structures are related to those for resonance between the two increased-valence structures. The use of the latter structures to indicate how electronic reorganization proceeds via one-electron delocalizations for SN2 reactions is redescribed, and an elementary argument is presented to deduce that this class of reactions cannot involve the delocalization of a pair of electrons in concert from the nucleophile. Increased-valence wave functions are used to deduce an expression for the avoided crossing for the transition state of the identity SN2 reaction. © 1996 John Wiley & Sons, Inc.

Notes: A number of hydrogen-bond related quantities - geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies - were calculated at the Hartree - Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree - Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree - Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree - Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree - Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree - Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)2 dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.

Notes: We show how to estimate the dissociation energy of CuH using the variational Monte Carlo method. The techniques involved are (i) an all-electron approach, (ii) a diffusion-only Metroplis algorithm which is well-suited for sampling the nodal regions properly, and (iii) a core-valence partitioning scheme such that the dissociation energy is estimated from the valence energies of CuH and Cu only. This approach avoids several of the approximations inherent in pseudopotential methods. Using relatively crude wave functions, we obtain an estimate of the dissociation energy and dipole moment with an accuracy on par with much more elaborate calculations in the literature. © 1996 John Wiley & Sons, Inc.

Notes: Silica sodalite is an ideal model system to establish base-line computer requirements of ab initio periodic Hartree-Fock (PHF) calculations of zeolites. In this article, we investigate the effect of various basis sets on the structural and electronic properties of bulk silica sodalite. We also study the interaction of He, Ne, and Ar with the sodalite cage. Our work shows that basis-set superposition errors (BSSE) in calculations using STO-3G and 6-21G(*) basis sets are as large as the interaction energies, leading to poor confidence in the results. To cure this problem, we present high-quality basis sets for Si, O. He, Ne, and Ar, optimized for use with PHF methods, and demonstrate that the new basis set greatly reduces BSSE. The theoretical barriers for transfer of the rare gases between sodalite cages are 5.6, 13.2, and 62.1 kcal/mol for He, Ne, and Ar. © 1996 John Wiley & Sons, Inc.

Notes: Local coordinate systems are chosen for each quadruple of atoms relative to a four-center integral, in order to avoid linear combinations of orbitals when symmetry operations perform on an orbital. This choice can utilize the complete molecular symmetry to attain the optimal number of symmetry-unique integrals and to construct two-particle matrix elements by multiplying symmetry-unique integrals, called the “standard four-center integrals,” by the corresponding coefficients, called the “C coefficients.” A simple algorithm to use the complete molecular symmetry to reduce calculations of molecular matrix elements is outlined for general highly symmetric molecules. A tetrahedral molecule is analyzed. © 1996 John Wiley & Sons, Inc.

Notes: A recursive method for enumeration of linearly independent and minimal conjugated circuits of benzenoid hydrocarbons had previously been given which is valid for several classes of benzenoid hydrocarbons. In the present article, the properties and constructions of unique minimal conjugated circuits and pairs of minimal conjugated circuits of a ring s in a benzenoid hydrocarbon B are investigated. An analytical expression for the count of LM-conjugated circuits of B is given which is based on the counts of Kekulé structures of selected subgraphs of B. By using the method, the LMC expression of any benzenoid hydrocarbon can be obtained. © 1996 John Wiley & Sons, Inc.

Notes: A spin-free method is presented for evaluating electronic matrix elements over a spin-independent many-electron Hamiltonian. The spin-adapted basis of configuration state functions is obtained using a nonorthogonal spin basis consisting of projected spin eigenfunctions. The general expressions for the matrix elements are given explicitly, and it is demonstrated how the matrix elements may be obtained simply from the knowledge of the irreducible characters of the permutation group ℒN. The presented formulas are very general and may be applied in connection with both spin-coupled valence bond studies and in conventional configuration interaction (CI) methods based on an orthonormal orbital basis. © 1996 John Wiley & Sons, Inc.

Notes: A method of selection of basis functions for the quantum chemical description of atoms and molecules inside spherical and cuboidal cavities is presented. The method consists of two independent steps. First, the appropriate GTO or STO exponents are chosen by fitting the basis functions to cutoff orbitals. The criterion of maximal orbital density inside the cavity is next applied to form the final model orbital space. The method presents the fundamental advantage over many other methods of being trivially applicable in standard quantum chemical progam packages. As an illustration, the method is applied to the hydrogen atom in a spherical box. The use of contracted basis functions is also discussed. © 1996 John Wiley & Sons, Inc.

Notes: The efficiency of modified virtual orbitals (MVO) of ionic type and of approximate orthogonalized natural orbitals (ONO) in the CI-SD calculations was studied for O3 and SO2 molecules and compared with the commonly used canonical virtual orbitals (CVOs). The systems studied represent a class of electron-rich molecules, in which the number of valence electron pairs exceeds substantially the number of formal chemical bonds. We found that the modified orbitals of the types studied appear to be less effective for these systems than in the similar calculations for the AHn type molecules. Physical reasons for this difference were discussed. The evolution of spatial properties of virtual orbitals within the modification process was analyzed. © 1996 John Wiley & Sons, Inc.

Notes: The electronic energy band structures of the La-doped superconductors TlBa1.2 La0.8 CuO5 + δ were calculated. The effect of the oxygen content on their electronic structures was studied. The results show that compared with those for TlBa2CuO5, the La doping at the Ba site results in the moderate change in the band structures and the decrease in the densities of states, but the increase in the oxygen content caused by the La doping results in the great change in the band structures and the densities of states near the Fermi surface. The low oxygen content causes the degree of complexity of the band structures and the densities of states near the Fermi level Ef to increase and the high oxygen content causes them to decrease. The oxygen content plays a dominant role in TlBa1.2La0.8CuO5 + δ. In addition, the Cu-O planes are most sensitive to the increase in the oxygen content. © 1996 John Wiley & Sons, Inc.

Notes: When conventional matrix algebra is used to solve the semiempirical self-consistent field equations for large systems, the time required rises as the third power of the size of the system. A consequence of this is that self-consistent calculations of large systems such as enzymes are impractical. By using localized molecular orbitals instead of matrix methods, the time required for these systems can be made almost proportional to the size of the system. In partial geometry optimizations, the time required depends only upon the size of the fragment being optimized and is almost independent of the size of the whole system. © 1996 John Wiley & Sons, Inc.

Notes: The performance of effective core potentials adjusted at the Hartree-Fock level but applied in density functional calculations has been tested in a set of calculations using various basis sets and/or core potentials. Test molecules have been the first-row transition-metal carbonyls Cr(CO)6, Fe(CO)5, and Ni(CO)4 and the second-row carbonyls Mo(CO)6, Ru(CO)5, and Pd(CO)4. Only “small-core” potentials have been used, and these are able to reproduce molecular structures and bond energies from all-electron calculations. Relativistic effects have been estimated for the second-row carbonyls by using quasi-relativistic core potentials. © 1996 John Wiley & Sons, Inc.

Notes: A coherent computational scheme on a very large molecule in which the subsystem that undergoes the most important electronic changes is treated by a semiempirical quantum chemical method, though the rest of the molecule is described by a classical force field, has been proposed recently. The continuity between the two subsystems is obtained by a strictly localized bond orbital, which is assumed to have transferable properties determined on model molecules. The computation of the forces acting on the atoms is now operating, giving rise to a hybrid classical quantum force field (CQFF) which allows full energy minimization and modeling chemical changes in large biomolecules. As an illustrative example, we study the short hydrogen bonds and the proton-exchange process in the histidine-aspartic acid system of the catalytic triad of human neutrophil elastase. The CQFF approach reproduces the crystallographic data quite well, in opposition to a classical force field. The method also offers the possibility of switching off the electrostatic interaction between the quantum and the classical subsystems, allowing us to analyze the various components of the perturbation exerted by the macromolecule in the reactive part. Molecular dynamics confirm a fast proton exchange between the three possible energy wells. The method appears to be quite powerful and applicable to other cases of chemical interest such as surface reactivity of nonmetallic solids. © 1996 John Wiley & Sons, Inc.

Notes: Magnetic and optical properties of transition-metal complexes are governed by the ground state and the low-energy excitation spectrum of the d-shell of the central transition metal ion. These spectra are successfully fit to the crystal field theory. We present here an account of the effective Hamiltonian method recently developed to calculate the ground state and the excitations of the d-shells of transition-metal complexes and report the results of its application to some complexes of particular interest. © 1996 John Wiley & Sons, Inc.

Notes: The problems of semiempirical quantum chemical calculations of (a) spin densities in paramagnetic organometallics, (b) hydrogen bonds, and (c) bond energies and the structure of transition-metal compounds are discussed. Some modifications of the existing semiempirical quantum chemical method are presented. An extended NDDO approximation has been developed. This scheme includes explicit symmetric orthogonalization of the core Hamiltonian and the use of Hellmann's effective core potential for core-electron interaction. © 1996 John Wiley & Sons, Inc.

Notes: A simplified LCAO-DFT-LDA scheme for calculations of structure and electronic structure of large molecules, clusters, and solids is presented. Forces on the atoms are calculated in a semiempirical way considering the electronic states. The small computational effort of this treatment allows one to perform molecular dynamics (MD) simulations of molecules and clusters up to a few hundred atoms as well as corresponding simulations of condensed systems within the Born-Oppenheimer approximation. The accuracy of the method is illustrated by the results of calculations for a series of small molecules and clusters. © 1996 John Wiley & Sons, Inc.

Notes: The application of hybrid quantum mechanical and molecular mechanical (QM/MM) potentials to the study of chemical reactions in enzymes is outlined. The discussion is general and addresses the difficulties encountered in an enzyme QM/MM study. First, general criteria for determining whether a particular enzyme is an appropriate candidate for a QM/MM approach are outlined. Methods for obtaining starting structures are detailed. The importance of choosing appropriate levels of ab initio or semiempirical theory is emphasized. Approaches for interfacing the QM and MM regions are briefly discussed, with greater detail given to describing our CHARMM-GAMESS interface. Techniques for partitioning the system into QM and MM regions are explored. Link atom placement, as distant from reacting atoms as possible within the confines of computational efficiency, is examined in some detail. Methods for determining reaction paths are also discussed. © 1996 John Wiley & Sons, Inc.

Notes: Many quantum mechanical problems are separable in one or several of the standard classifications of general coordinate systems. The associated solution is most conveniently evaluated using expansions in Lamé wave functions. We give here some preliminary numerical results displaying the continuous distortion of an s-, p-, and d-wave spherical harmonic. The results indicate rather surprising features which may be useful in general quantum mechanical contexts. © 1996 John Wiley & Sons, Inc.

Notes: The Feynman path integral method is applied to the many-electron problem. We first give new closure relations in terms of ordinary complex and real numbers, which could be derived from an arbitrary complete set of state vectors. Then, in the path integral form, the partition function of the system and the ensemble average of energy are explicitly expressed in terms of these closure relations. It is impossible to evaluate the path integral by direct numerical integrations because of its huge amount of integration variables. Therefore, we develop an algorithm by the Monte Carlo method with constraints corresponding to the normalization condition of states to calculate the required integral. Finally, the ensemble average of energy for the hydrogen molecule is explicitly evaluated by the quantum Monte Carlo method and results are compared with the result obtained by the ordinary full configuration interaction (CI) method. © 1996 John Wiley & Sons, Inc.

Notes: The mivazerol and three of its methylated derivatives are studied at the ab initio SCF level within the MINI-1 and 6-31G basis sets. This study aimed at determining some probable conformations, either neutral or protonated, that could interact with the α2 adrenoceptors. The solvent effect was also studied within the Onsager's solvent model at the two dielectric constant (ε) values of 4 and 80. The interaction with the environment (either solvent or receptor) is schematically studied by positioning either two water molecules or one formamide or/and one formic acid near the amide and the imidazole for few isomers. The medium polarization, through ε, and the solvation effect, through the interaction with the solvent molecules or the receptor side chains, stabilize the same isomers. Post-SCF calculations are performed at the CISD level, the first excited singlet and triplet states energies are determined, and the question of the wave-function stability is addressed. The results indicate the probability of a spin-orbit coupling with the first excited triplet state, thus opening the question of such a possibility within an enzyme active site. © 1996 John Wiley & Sons, Inc.

Notes: A simple method of calculation of the integrals of the Hylleraas-Ore wave function, used in the description of the four-particle system analogous to the H2 molecule, is presented. The integrals corresponding to the kinetic energies of particles, to the Coulomb energy terms, and to the interparticle distances are given by the appropriate partial derivatives of a functional depending on the wave-function parameters. © 1996 John Wiley & Sons, Inc.

Notes: The geometries and the energies of conformers of PnHn + 2 (n = 2-9) have been studied with PM3 method. To test the quality of the semiempirical results, ab initio calculations have been carried out on P3H5. All results of P2H4 and P3H5 with PM3 are consistent with the experimental and ab initio data. According to the analysis of P3H5 and P4H6 results, it is concluded that gauche interaction between adjacent lone electron pairs and gauche interaction between polar P-H bond with adjacent polar P-P bond are important for predicting the stable conformer of open-chain phosphoanes. The calculations of PnHn + 2 (n 〉 4) give further support to this conclusion. © 1996 John Wiley & Sons, Inc.

Notes: The effective core potential (ECP), using a basis set of different qualities, and ab initio full-electron (FE) calculations were carried out for MoS-24, MoO-24, and MoOCl4 molecules. The topology of - ▿2p(rcp) (the negative Laplacian of the charge density at its critical points) in the atomic valence shell was studied. Results clearly indicate that semicore (ECP2) approaches are able to reproduce, in a qualitative way, the topology of the Laplacian distribution with respect to those obtained by the FE method. Modifications of basis sets, such as introduction of polarization functions on the ligands, affect the electronic charge distribution (number of critical points in MoOCl4) for FE as well as for ECP2 approaches. The ECP2 scheme predicts correctly the order of - ▿2px(rcp) (X = O, S, Cl, Mo) in the valence shell; nevertheless, it fails in the relative magnitudes of - ▿2pMo(rcp) between Mo compounds in respect to FE calculations. A scaling factor consistently improves the values of - ▿2p(rcp) and p(rcp), which are larger than those obtained with FE, particularly the - ▿2p(rc) values. © 1996 John Wiley & Sons, Inc.

Notes: Numerical experiments were carried out to determine the timewise self-consistency of different physical processes involved in the energy transfer in green plant photosynthetic units. A 6 × 6 × 6 array of chlorophyll-a with cubic lattice constants a = b = c = 20 Å was chosen as a model of the thylakoid disc. Another model aggregate was obtained by substituting chlorophyll-b molecules for some of the chlorophyll-a molecules. In both models, a reaction center occupied a central site in the last xy plane. Two extreme arrangements were considered for the orientation of molecules. In one, the transition moments of all molecules were directed along the y-axis. The other had chlorophyll molecules randomly oriented. The four resulting model systems were used in our investigation on exciton generation, transport, decay by fluorescence, and trapping. All excitons were assumed to be generated by a 20 ms exposure to sunlight at high altitudes. The general trends noticed from these computations are as follows: The number of excitons generated is influenced by lattice disorders. Disorders also increase the time for the establishment of an equilibrium distribution. The decay of excitons by fluorescence is always a monotonic function of time. The energy transfer is adversely affected by a lower degree of orientation in the crystal: The trapping time increases with disorder. The number of trappings decreases with the onset of fluorescence of the host molecules and the trap. From these investigations, we also made three specific observations: (1) The efficiency of exciton utilization varies from 12% for a completely random arrangement of transition dipoles to 46% for a perfectly ordered arrangement. This agrees with the experimental efficiency, about 20%. (2) The number of excitons trapped varies from one to six. This tallies with the time scale of electron transfer along the Z-scheme that requires at least two excitons trapped in about 20 ms. Thus, the photon density and the exciton transfer rate are consistent with the rates of electron transfers. (3) The trapping rate also indicates that the thylakoid disc must resemble a considerably ordered system. © 1996 John Wiley & Sons, Inc.

Notes: The direct reaction field (DRF) force field gives a classical description of intermolecular interactions based on ab initio quantum-chemical descriptions of matter. The parameters of the DRF force field model molecular electrostatic and response properties, which are represented by distributed charges and dipole polarizabilities. The advantage of the DRF force field is that it can be combined transparently with quantum-chemical descriptions of a part of a large system, such as a molecule in solution or an active site in a protein. In this study, the theoretical basis for the derivation of the parameters is reviewed, paying special attention to the four interaction components: electrostatic, induction, dispersion, and repulsion. The ability of the force field to provide reliable intermolecular interactions is assessed, both in its mixed quantum-chemical-classical and fully classical usage. Specifically, the description of the water dimer and the solvation of water in water is scrutinized and seen to perform well. The force field is also applied to systems of a very different nature, viz. the benzene dimer and substituted-benzene dimers, as well as the acetonitrile and tetrachloromethane dimers. Finally, the solvation of a number of polar solutes in water is investigated. It is found that as far as the interaction energy is concerned, the DRF force field provides a reliable embedding scheme for molecular environments. The calculation of thermodynamic properties, such as solvation energy, requires better sampling of phase space than applied here. © 1996 John Wiley & Sons, Inc.

Notes: The lattice constant, cohesive energy, bulk modulus, and band gap for Si were calculated with the linear combinations of Gaussian-type orbitals-fitting function (LCGTO-FF) technique using three distinct types of charge density and exchange-correlation fitting function basis sets: (l) site-centered s-type GTOs only; (2) site- and bond-centered s-type GTOs; and (3) site-centered s-and f-type GTOs. All three basis sets produce good results for the lattice constant and bulk modulus of Si, but only the two larger basis sets determine the cohesive energy and LDA band gap accurately. The numerical results obtained with the two larger basis sets are in good quantitative agreement with each other and with results from other techniques. © 1996 John Wiley & Sons, Inc.

Notes: The interaction of two iron atoms with molecular nitrogen was studied by means of density functional techniques. Calculations were of the all-electron type, and both conventional local and gradient-dependent approximate (GDA) models were used. A ground state (GS) of linear structure was found for Fe2-N2 with 2S + 1 = 7; whereas a distorted tetrahedral structure, being also a septuplet, was located at 4.0 and 14.3 kcal/mol above the GS, at the local and GDA levels of theory, respectively. The N-N bond is moderately perturbed in the GS, but it is strongly activated in the tetrahedral mode: It has bond orders of 2.6 and 1.5, vibrational frequencies of 2148 and 1496 cm-1, and equilibrium bond lengths of 1.14 and 1.24 Å, for the linear and tetrahedral geometries, respectively. These values are 3.0, 2359 cm-1, and 1.095 Å, for free N2. At GDA level of theory, the Fe2-N2 binding energy is 15 kcal/mol, which is bigger than that of Fe-N2 (9 kcal/mol). The π-back donation, in the linear GS, is of 0.31 electrons, but the total charge transfer, from Fe2 to N2, is only 0.05 units. This is relevant in comparison with the tetrahedral mode, where the Fe2 to N2 total charge transfer is of 0.45 electrons, yielding a stronger activated N2 moiety. © 1996 John Wiley & Sons, Inc.

Notes: With a view to elucidate and develop a model for the mechanism of conduction in doped transpolyacetylene (t-PA), we have carried out an ab initio study of the ground and excited state of transoctatetraene in the presence of an iodine atom. While the ground state is calculated as characterized by a slightly distorted alternating bond geometry, with iodine remaining largely neutral on top of the plane of the polyene near roughly the midpoint of the chain axis, the excited state has the geometry characterized by a solitonic distortion with the octatetraene carrying a net positive charge close to 0.7e. The bandgap [highest occupied to lowest unoccupied molecular orbital (HOMO(SINGLEBOND)LUMO) gap] is computed to be nearly 0.8 eV. Moreover, the excited-state energy appears very insensitive to the position of iodine along the axis of the octatetraene chain. As an extension of an earlier calculation on the transport of charge by a charged soliton, a similar calculation is performed on a C8H10 +“kink” traveling along the backbone of C12H14+, yielding very similar results. A computer code has been developed to compute the transport velocity of charge based on the above model and can be used in conjunction with the GAMESS program package. © 1996 John Wiley & Sons, Inc.

Notes: Self-consistent electronic structure calculations of δ-doped quantum wells (QW) in the presence of in-plane magnetic fields B up to 20 Tesla are carried out within the frameworks of the effective mass and the local density approximations. QWs composed of two layers of Ga1-xA1xAs, separated by a layer of GaAs with a donor δ-doped sheet in the center, are considered. The width of the GaAs layer was varied from 100 to 400 Å. It is shown that the diamagnetic shift increases with the increasing of the GaAs QW width. The magnetic field induces remarkable changes in the energy dispersions of electrons and holes, along an in-plane direction perpendicular to B. The most striking effect occurs in the nature of the band gap of these systems. We found that the valence band displays a double-maximum character instead of a single maximum at the center of the Brillouin zone. © 1996 John Wiley & Sons, Inc.

Notes: The interaction on and the rotation of C60 in akali-doped C60 solids, AXA′3-XC60 (X = 1, 2, 3; A, A′ = alkali), have been calculated with Buckingham potential model. The results show that the total interaction on C60 changes dramatically when the pure C60 solid is alkali-doped into K3C60. The interaction on C60 in K3C60 is about 20 times greater than that in pure C60. And the main component in the former, occupying 〉 90% is electrostatic, while in the latter, the main components, occupying 〉 90%, are dispersive and repulsive. The results also show that in contrast to the whole-region free rapid rotation of C60 molecule in its pure solid, the rotation of C60 in K3C60 is mostly forbidden due to a 10 times increase (reaching about 300 kJ/mol) in potential barrier, except for the region from 0° to 50° where a broad, smooth, and shallow potential well exists. Calculations for alkali-doped complexes other than K3C60, i.e., AXA′3-XC60 (X = 1, 2, 3; A, A′ = K, Rb, Cs), come to the same conclusion. Finally, an interesting and meaningful result is that the superconducting transition temperatures of AXA′3-XC60 (X = 1, 2, 3; A, A′ = K, Rb, Cs) change inversely with the total interactions on C60. © 1995 John Wiley & Sons, Inc.

Notes: Multireference configuration interaction wave functions with single and double excitations were calculated for the 1Σ+g ground state of the C2 molecule and the excited states of C+2 with symmetries 2Σ+g, 2Σ-u, 2Πu, and 2Πg. The corresponding σg, σu, πu, and πg valence Dyson orbitals were calculated. Most of the density due to the valence electrons is accounted for by three σg, one σu, and one degenerate pair of πu Dyson orbitals. Electron correlation plays an important role in the bond strength of C2 by increasing the occupation of the σg valence orbitals and decreasing the occupation of the σu and πu valence orbitals. © 1996 John Wiley & Sons, Inc.

Notes: For formaldehyde, the C — O stretch potential of 1(π, π*) crosses all 1A1 Rydberg potentials, such as n, 3py, n, 3dyz, etc., thereby transferring the intensity of the unassigned 1(π, π*) ← X??? system to these Rydberg states. For thioformaldehyde, the situation is similar but a shift in the potentials allows for direct observation of 1(π, π*). In its 1(π, π*) state, H2CO is planar, having a low barrier of about 0.2 eV toward the nonplanar 1(σ, π*) state. For H2CS, the planar conformation of 1(π, π*) is a saddle point, with 1(π, π*) being the global minimum on the 21A′ surface. The triplet π, π* states of H2CO and H2CS are nonplanar, having inversion barriers of 0.1 and 0.05 eV, respectively. For both H2CO and H2CS, the π, π* configuration also crosses the ground-state configuration, which explains predissociation and radiationless transitions of some Rydberg states. © 1996 John Wiley & Sons, Inc.

Notes: We carried out variational model calculations for the assessment of the combined effect of the nonparabolicity of the electron effective mass and the screening of the donor ion by the valence electrons of GaAs for a donor placed at the center of a spherical quantum dot. We considered finite confining potentials between the GaAs QD and the surrounding Ga1-xAlxAs matrix. We found that the combined effect becomes more pronounced as the radius of the quantum dot decreases. © 1996 John Wiley & Sons, Inc. Int J Quant Chem 60: 507-510, 1996

Notes: An ab initio conformational analysis of 4-chloroindole-3-acetic acid was performed at the RHF/6-311G * * level. The mirror symmetrical conformer (in which the indole ring is coplanar with the COOH group) is most stable; next in energy are the two conformers with the C - COOH fragment perpendicular to the indole ring with relative energies of 2.72 and 6.69 kJ/mol. H(SINGLEBOND)Cl hydrogen bonding results in only a minor stabilization. The results are combined with those obtained earlier for indole-3-acetic acid and recent biological data regarding auxin (growth hormone) activity. From this, assumptions concerning the biologically active conformation are drawn. © 1996 John Wiley & Sons, Inc.

Notes: A theoretical analysis based upon large-scale self-consistent Hartree-Fock calculations at a semiempirical quantum theory level (CNDO/S) is performed to investigate long-range electron transfer in a donor-DNA-acceptor molecule, where the donor and acceptor moieties are tethered to the DNA. The π-stacked base pairs are found to dominate the long-range electronic coupling. Despite the π-electron mediated coupling, the exponential distance decay constant of the electron transfer rate is ∼ 1.2-1.6 Å-1, values typical of electron transfer proteins. The calculated long-range electron transfer rate of the order of 106 s-1 for a metal-to-metal distance of 21 Å is found to be in agreement with kinetic measurements by Meade and Kayyem. Based on the current analysis, the π-electrons dominate the long-range electronic coupling interactions in DNA, but they do not lead to one-dimensional molecular wire-like properties. © 1996 John Wiley & Sons, Inc.

Notes: Estimation of brain uptake of solutes and drugs would be useful in designing novel therapeutic agents. Given the problems associated with fragment-based models, including the need for strict additivity, we used AM1-derived molecular parameters in attempting to generate an equation for predicting the log of the brain-to-blood concentration ratios (log B:B) for a collection of compounds. Sequential fitting of the data using 10 AM1-derived variables indicated that dipole generated the most predictive one-term equation, dipole and log P, the best two-parameter system, dipole, log P, and molecular weight produced the optimal three-term model, and dipole, log P, molecular weight, and HOMO energy resulted in the best four-parameter paradigm. These systems were statistically similar to those generated using general solvation equations, but with the use of fewer parameters. An expanded parameter set may generated models of even better predictability. © 1996 John Wiley & Sons, Inc.

Notes: In this work, we evaluated structural and electronic similarities between a new class of acylhydrazones, recently presented as effective inhibitors of a Plasmodium falciparum cysteine protease, and a series of pyrazole arylacylhydrazones with analgesic and antiaggregating (antithrombotic) properties, using AM1. The calculated results suggest that at least one of the pyrazole compounds is similar enough to the active compounds to be considered as a candidate for a future antimalarial series. © 1996 John Wiley & Sons, Inc.

Notes: The problem of excitons in interaction with phonons in a molecular crystal has been reinvestigated as a continuation of our earlier work. The exciton-phonon interaction has been taken to be linear in lattice displacements. The external medium, the phonon assembly, has been considered to be in thermal equilibrium. Following Simons, we have incorporated the effects of the medium on the exciton dynamics into a time-dependent effective potential that contains the equilibrium average exciton-phonon interaction as well as terms arising from the fluctuations in the medium's coordinates about their equilibrium values. A correlation function that represents the probability of exciton transfer has been given in the interaction picture. The time evolution of this correlation function has been determined by following Kubo's technique of cumulant expansion. The zeroth-, second-, and fourth-order contributions to the correlation function have been calculated in this way. The second- and fourth-order contributions have been diagrammatically represented. The second-order contribution has been explicitly calculated in different physical limits, namely, the slow exciton and the slow phonon limits at high and low temperatures and for very large and very small time. A few simple formulas for the transfer probability of a bare exciton in a molecular crystal of cubic symmetry have been derived from the Debye approximation for the dispersion of phonons. It has been specifically shown that the sum over phonon modes in the large time dynamics leads to a fully destructive interference in second order at a very low temperature and gives rise to a diffusive transport at a high enough temperature. A natural way of clothing the excitons has been considered and the clothed exciton has been represented diagrammatically. The dressing requires the correlation function to be redefined in terms of the clothed states and the clothed operators. The clothed exciton correlation function that represents the probability of transfer of excitons fully clothed by the phonons in thermal equilibrium turns out to be identical with the bare exciton correlation function. This attaches a novel interpretation to the correlation function which was originally defined by Simons. Transfer probabilities for a clothed exciton in a cubic crystal has been explicitly worked out for different physical limits under the Debye model of phonon dispersion. From these results a few expressions for the macroscopic diffusion coefficient of the clothed exciton have been obtained. A few critical comments have been incorporated. © 1996 John Wiley & Sons, Inc.

Notes: A simple formalism of real irreducible tensorial sets of real bases is proposed. The definition of the real bases, the coupling of the real bases, and the transformation of the real bases in a group chain including the three-dimensional rotation group and the molecular point groups are studied. The double coset technique is used to derive the close formulas for generating the coupling coefficients and the transformation coefficients. © 1996 John Wiley & Sons, Inc.

Notes: The energy eigenvalues of coupled oscillators in two dimensions with quartic and sextic couplings have been calculated to a high accuracy. For this purpose, unbounded domain of the wave function has been truncated and various combination of trigonometric functions are employed as the basis sets in a Rayleigh-Ritz variational method. The method is applicable to the multiwell oscillators as well. © 1996 John Wiley & Sons, Inc.

Notes: An improved scheme to accelerate the convergence in the calculations of N-electron atoms, which is based on the exact method we proposed before in hyperspherical coordinates, is presented. The factors influencing the rate of convergence in both parts of expansions in wave function with the hyperspherical harmonics (HHs) of hyperangles and the generalized Laguerre polynomials (GLPs) of hyperradius were investigated. A reselected asymptotic term was introduced by including more structural features in it to accelerate the convergence in the expansion part with the HHs, and a transformation of the hyperradius was used to keep the convergence going properly in the expansion part with the GLPs. Calculations with this scheme for the helium atom were given and compared with some other ones. More accurate results were obtained by considering a simple cusp parameter. © 1996 John Wiley & Sons, Inc.

Notes: All the possible rotamers of 2-aminoethanol and 2-amino-ethanethiol were fully optimized at the ab initio level using the 6-31G** basis with correlation energy inclusion and zero-point energy evaluation. Thirteen local minima for the former and 14 for the latter compound were found. In both molecules, the gauche′-gauche-gauche′ (g′Gg′) is the prevailing conformation, but in the sulfurated compound, it is accompanied by relevant percentages of other conformers, owing to the very low ΔE values. The stability of the g′Gg′ accommodation derives mainly from the presence of weak hydrogen bridges (O(SINGLE BOND)H···N and S(SINGLE BOND)H···N, respectively). The rotation barriers around the C(SINGLE BOND)C and C(SINGLE BOND)N bonds are higher than those around the C(SINGLE BOND)O and C(SINGLE BOND)S ones. © 1996 John Wiley & Sons, Inc.

Notes: That the bound energy eigenstates of one-dimensional quantum systems can be degenerate in the presence of specific singular or supersingular potentials is demonstrated by choosing a family of bistable and other oscillators. Relevance of our study to spectroscopic observations is noted. Quasi-degeneracy is found even in the absence of any singularity in the potential and the importance of tunneling is highlighted in this context to analyze the general nature of such potentials leading to double degeneracy. Additionally, the case of spiked oscillators is discussed with particular reference to the “Klauder phenomenon,” revealing clearly that the mere presence of singularity in the potential is not a sufficient criterion for the occurrence of degeneracy. © 1996 John Wiley & Sons, Inc.

Notes: We employ a dynamical configuration interaction approach to study the transport of charge along the polyacetylene chain axis when placed in an external electric field. The steady-state wave function in this approach is constructed as a linear combination of solitonic wave functions weighted by nuclear vibrational functions. We retain the Born-Oppenheimer approximation, i.e., we neglect the terms involving the differentiation of the electronic configurations with respect to the nuclear coordinates. We also use basis functions that follow the nuclei. A solution of the time-dependent Schrödinger equation in terms of the wave functions of the above kind is obtained, leading to a closed formula for estimating mobilities of the soliton transport. © 1996 John Wiley & Sons, Inc.

Notes: The impact of the choices of the complete model space (CMS) and of the orbital basis set on the existence, attainability, and properties of the nonstandard solutions of the valence-universal coupled-cluster (VU-CC) methods has been studied for the case of nonlinear equations corresponding to the atomically oriented form of these methods accounting for one- and two-electron excitations (VU-CCSD/R method) and applied to the Be atom. The results for five 1S states are discussed. In addition to the previously applied CMS defined by the orbital set (2s, 2p) and (2s, 3s), we have employed the CMSs defined by the (2s, 2p, 3s) set. For each of the CMSs several nonstandard solutions are documented. It is found that the energies of the individual states corresponding to standard and nonstandard solutions differ very little. These energies are also almost independent on the choice of CMS. On the other hand, the energies of excited states disclose a strong dependence on the radial structure of the orbital basis set. It is also demonstrated that the magnitudes of the cluster amplitudes representing a set of states depend both on the choice of the CMS and whether they correspond to the standard or nonstandard solutions. © 1996 John Wiley & Sons, Inc.

Notes: Configuration interaction (CI) spaces obtained from the full CI space by imposing arbitrary restrictions on the occupancies of molecular orbital (MO) groups are studied. It is proved that such restricted spaces are in a certain sense “closed.” Namely, in the course of the Hamiltonian matrix construction the excitations out of the chosen restricted CI space may be easily replaced by the excitations within this space. © 1996 John Wiley & Sons, Inc.

Notes: A variable-step method has been developed for the numerical solution of the eigenvalue Schrödinger equation. The eigenvalues are computed directly as roots of a function known in transmission line theory as the impedance. The novel numerical algorithm is based also on the piecewise perturbation analysis. The new variable-step method is based on two methods, one with first-order perturbative corrections and the other with second-order perturbative corrections. © 1996 John Wiley & Sons, Inc.

Notes: No abstract.

Notes: One- and two-dimensional cellular automata (CA) simulations of neutral “atoms,” viewed as “complex” distributions of electron density around a central nucleus, are performed in order to explore CA-based discretized and connectionist approaches to the synthesis and structure-dynamics problems of many-electron systems. A link between CA and the quantum mechanics of atoms is made by taking the Thomas-Fermi theory as an illustrative example. Starting from a nonstationary distribution, the stationary distribution of electron density around a nucleus arises out of a natural stability criterion described through CA rules. © 1996 John Wiley & Sons, Inc.

Notes: The body-fixed Hamiltonian developed here is expressed in terms of the atom's distance from and orientation with respect to the plane defined by the triatomic. © 1996 John Wiley & Sons, Inc.

Notes: Ionization energies below 20 eV of 10 molecules calculated with electron propagator techniques employing Hartree-Fock orbitals and multiconfigurational self-consistent field orbitals are compared. Diagonal and nondiagonal self-energy approximations are used in the perturbative formalism. Three diagonal methods based on second- and third-order self-energy terms, all known as the outer valence Green's function, are discussed. A procedure for selecting the most reliable of these three versions for a given calculation is tested. Results with a polarized, triple ζ basis produce root mean square errors with respect to experiment of approximately 0.3 eV. Use of the selection procedure has a slight influence on the quality of the results. A related, nondiagonal method, known as ADC(3), performs infinite-order summations on several types of self-energy contributions, is complete through third-order, and produces similar accuracy. These results are compared to ionization energies calculated with the multiconfigurational spin-tensor electron propagator method. Complete active space wave functions or close approximations constitute the reference states. Simple field operators and transfer operators pertaining to the active space define the operator manifold. With the same basis sets, these methods produce ionization energies with accuracy that is comparable to that of the perturbative techniques. © 1996 John Wiley & Sons, Inc.

Notes: A particular formulation of the distributed Gaussian basis-set approach, the extended Gaussian cell model, is applied to the simplest polycentric molecule, the linear H32+ ion. Calculations of the total energy using two extensions of the original Gaussian cell model are described and results are reported for the ground state and the first excited state. A comparison with recently reported finite element calculations is made for a number of nuclear geometries. © 1996 John Wiley & Sons, Inc.

Notes: Using a mixture of classical and quantum mechanics, Drude model formulas for the polarizability and magnetic susceptibility of an atom or molecule and the dispersion coefficient for intermolecular forces between atoms and molecules are obtained both when the same frequency of oscillation is used for all the electrons and when different frequencies are used. The latter case allows us to discuss bond properties. The frequencies involved can be determined in a nonempirical way when it is recognized that the Frost model can be regarded as giving an ab initio quantitative justification for the Drude model. © 1996 John Wiley & Sons, Inc.

Notes: We study the intensity and polarization of light emitted during slow ion-atom collisions. We describe the nuclei as moving along classical trajectories while the electronic rearrangement is treated using time-dependent molecular orbitals. The intensity of emitted light is calculated from the diatomic time-dependent dipole. We evaluate the diatomic dipole matrix elements involving 1s, 2s, and 2p traveling atomic orbitals suitable for time-dependent collision studies. We calculate the intensity and the polarization of light emitted in p + H(1s) collisions at kinetic energies from 10 to 1000 eV, for several impact parameters, changing over time. The emitted intensity goes through a maximum as the collision energy increases and lasts between 10 and 1 fs; the polarized light components parallel and perpendicular to the incoming beam direction show pronounced dependences on impact parameters and time. © 1996 John Wiley & Sons, Inc.

Notes: A hybrid quantum/classical model is developed for the photodissociation and recombination dynamics of an I2 molecule in low-temperature rare-gas (Rg) matrices. The simplified model consists of an I2 molecule embedded in a linear chain of Rg atoms. The aggregate is partitioned into a quantum system and a classical bath, which are self-consistently coupled. Two partitioning schemes are used. The first treats the I-I coordinate quantum mechanically and the Rg coordinates classically. The second and more reliable scheme includes in the quantum system both the I-I mode and the symmetric motion of the two nearest Rg atoms. Both models show substantial energy transfer from the dissociating I2 to the solvent, followed by coherent vibrational motion of the recombined I2. It is found that the one-dimensional quantum/classical scheme is consistent with its higher dimensional counterpart, although the latter shows much faster dephasing. © 1996 John Wiley & Sons, Inc.

Notes: We present an assessment on the accuracy of a dielectric continuum solvation model, the generalized conductor-like screening model (GCOSMO), for predicting hydration free energies, tautomeric equilibria, and reaction profiles in solution. © 1996 John Wiley & Sons, Inc.

Notes: Aspects of the influence of a strong Debye plasma environment on the negative hydrogen ion and the neutral helium atom have been studied. Contrary to earlier work, in the present calculation all interactions have been screened. This increases the stability of the systems to the extent that neither the H- ion nor the ground state of helium will lose an electron by pressure ionization. It has been found that the charge distribution of H- remains remarkably constant over a vast range of values of the Debye parameter D. © 1996 John Wiley & Sons, Inc.

Notes: Despite their importance in the characterization of molecular magnetism, electronic g-tensors have received rather little theoretical attention. In this work, however, the ground-state g-tensor of MgF is computed at both the ROHF and multireference CI levels. The calculations are expanded complete to second order in appropriate Breit-Pauli terms and the contributions of all important magnetically coupled excited states are accounted for. Both the CI- and ROHF-level Δg∥-values (-59 and -55 ppm, respectively) are in agreement with experiment (-319 ± 500 ppm) within the range of experimental uncertainty. For Δg⊥, however, the ROHF treatment yields a value (-659 ppm) in substantial disagreement with experiment (-1319 ± 500 ppm). Fortunately, this discrepancy is alleviated by CI level treatment (Δg⊥ = -1447 ppm). © 1996 John Wiley & Sons, Inc.

Notes: Electron orbits having a definite angular momentum in a static magnetic field are calculated with the aid of the Bohr-Sommerfeld quantization rules. The quantization gives that orbits are arranged along a straight line but the distance between the centers of two neighboring orbits decreases with increase of the absolute value of the angular momentum. With the energy correction equal to the zero-point energy of the harmonic oscillator, the distribution of orbits becomes identical to that obtained recently with the aid of a mixed semiclassical and quantum mechanical theory.   © 1996 John Wiley & Sons, Inc.

Notes: A new version of solutions in the form of an exponentially weighted power series is constructed for the two-dimensional circularly symmetric quartic oscillators, which reflects successfully the desired properties of the exact wave function. The regular series part is shown to be the solution of a transformed equation. The transformed equation is applicable to the one-dimensional problem as well. Moreover, the exact closed-form eigenfunctions of the harmonic oscillator can be reproduced as a special case of the present wave function. © 1996 John Wiley & Sons, Inc.

Notes: The potential barriers for the internal rotation of silole dimers are studied theoretically using the ab initio molecular orbital method at the RHF/6-31G** level of calculations. In 2,2′-bisilole, it is found that the anti-conformation is the most stable structure in the ground state and that the potential barrier height for rotation over the perpendicular conformation is 3.3 kcal/mol. © 1996 John Wiley & Sons, Inc.

Notes: The transition electric dipole moments between low-lying valence states of NH+ are calculated by an ab initio effective valence-shell Hamiltonian (Hv) method. The Hv calculated transition moments are found to be in good agreement with those by other accurate ab initio methods. The spontaneous emission probabilities for the A2- → X2Π, B2Δ → X2Π, and C2-+ → X2Π transitions of NH+ are computed. Also, radiative lifetimes for A2∑-, B2Δ, and C2∑+ states are all theoretically determined using the potential energy functions by Hv. Also, the Hv results are well compared with those computed using the Morse potentials and the rkr potentials which are obtained from experimental data. © 1996 John Wiley & Sons, Inc.

Notes: The chemisorption of atomic hydrogen and oxygen on a cobalt surface has been studied on a five-atom cluster model using one-electron effective core potential (1e-ECP) and all-electron calculations at the ab initio SCF and MCPF levels. Also, density functional calculations have been carried out. The different approaches are evaluated. The 1e-ECP has been compared to similar ECPS for nickel and copper. Our results indicate that this approach is valid also for cobalt. Different contributions to the cluster-adsorbate bonding energy are discussed. © 1996 John Wiley & Sons, Inc.

Notes: A kinetic energy analysis of total energy differences in 115 atomic multiplet states is presented. We show by numerical restricted Hartree - Fock calculations that there is a reasonably accurate linear relationship between the kinetic energy of the electrons in open subshells and the total energy within a manifold of states arising from the same spn or s2pn (n = 2,3,4) electron configuration in main-group atoms. © 1996 John Wiley & Sons, Inc.

Notes: The non-Bloch LCAO wave functions for cubic crystals are discussed and applied to the calculation of the matrix elements for electron transitions in an external electric field. The sum of transitions between non-Bloch electron states is compared with the matrix element for a conventional nearly free electron transition. © 1996 John Wiley & Sons, Inc.

Notes: This article presents a treatment scheme of the tunneling of hydrogen between two molecular centers (Cl…Cl). The purpose is to calculate the tunneling probabilities of hydrogen atom transfer from the initial (the proceeding complex) to the final-state energy minima (the succeeding complex) in two anharmonic vibrational states (0 → 0 and 1 → 1) in terms of the time-dependent perturbation theory expression and to see whether spectroscopic signatures of tunneling persist in the form of splittings of the vibrational modes. The analysis uses the realistic potential energy function calculated at the HF/6-31 + G** self-consistent-field basis-set level for the interaction between transferred hydrogen and its molecular skeleton (Cl…H…Cl). This potential energy surface is calibrated by comparing its properties with those from sf-POLCI and the LEPS potential-energy surfaces. The anharmonic vibrational state is characterized by the corrected vibrational energy levels and a set of linear combination coefficients obtained via perturbation theory. The tunneling probabilities for two transitions (0 → 0 and 1 → 1) were calculated and compared with those from Gamow's equation. Applicability of the time-dependent perturbation theory expression and Gamow's equation to the [Cl BOND H…Cl] system is discussed. The vibrational splitting energies are obtained, and a spectroscopic signature caused by tunneling is expected and should be observable. © 1996 John Wiley & Sons, Inc.

Notes: The kinetic and the exchange energy functionals are expressed in the form T[ρ] = CTF∫ drρ5/3(r)ft(s) and K[ρ] = CD∫ drρ4/3(r)fK(s), where CTF = (3/10)(3π2)2/3 and CD = -(3/4)(3/π)4/3 are the Thomas-Fermi and the Dirac coefficients, respectively, and s = |∇ρ(r)|/Csρ4/3(r), with Cs = 2(3π2)1/3. These expressions are used to perform a comparison of fT(s) and fK(s) in terms of their generalized gradient expansion approximations. It is shown that fκ(s) and is congruent to fT(s) in the range characteristic of the interior regions of atoms and many solids and that the second-order gradient expansion of the kinetic energy provides a rather reasonable approximation to the generalized gradient expansion approximation of both the kinetic and the exchange energy functionals. © 1996 John Wiley & Sons, Inc.

Notes: General system partitioning in the many-electron correlation problem for atomic and molecular systems is addressed within the spinshift formalism. The conventional method of the unitary group subduction coefficient expansion is reconsidered in the latter framework and an orbital-level factorization of the coefficients is obtained. “Group-spinshifts” are introduced and exploited to propose an alternative method of generating states adapted to arbitrary subduction chains. © 1996 John Wiley & Sons, Inc.

Notes: We explain that the symmetrized Rayleigh-Schrödinger (SRS) perturbation theory formula for intermolecular interaction energies cannot be derived under assumptions which are generally true, and that the formula must generally become indeterminate when the perturbation expansion is carried to infinite order. Although one can use a limiting procedure to calculate the interaction energy to infinite order, there is no unique value for this limit when the perturbation expansion is divergent, which is generally the case. The exact ground-state interaction energy is among the possible limits, but there is no known prescription for reaching that limit. For LiH we present numerical results for one of the possible limits, showing that the SRS energy formula can give very inaccurate results over a range of nuclear separations, its accuracy decreasing rapidly with increasing separation. We review reasons for believing that the SRS theory can, however, give results of useful accuracy when truncated to second order in the energy. Because this study completes our demonstration that the simplest intermolecular perturbation theories are generally invalid when carried to infinite order, we review the alternative theories that promise to be valid. © 1996 John Wiley & Sons, Inc.

Notes: Extended Fokker-Planck (FP) equations are generalized stochastic equations which describe the evolution of a set of coordinates, loosely referred to as solute, coupled with a relevant set of solvent variables. They are useful for the analysis of molecular dynamics in liquids, when a time-scale separation between probe motions and relaxation times of interactions with surroundings particles cannot be performed, because of persistence of slowly fluctuating components. In this article, we focus attention on a model system, made up of an angular coordinate and its conjugate momentum, submitted to a bistable potential, and coupled to a dissipative harmonic mode, to investigate the influence of polar solvents on reactive dynamics. The results are appropriate to describe dielectric effects, solvent-controlled conformational changes involving charge transfer which occur in photophysical processes, and the dynamic Stokes shifts observed in time-resolved fluorescence experiments. © 1996 John Wiley & Sons, Inc.

Notes: The formulation of the time-dependent Frenkel variational principle for Hamiltonians containing a term depending on the wave function is here considered. Starting from the basic principles, it is shown that it requires the introduction of a related functional, G, which, for the systems we are considering, has the status of a free energy. An explicit use of functional G as starting point to obtain variational wave functions makes it easier to implement computational methods for a variety of physical and chemical problems in solution, the first one among them being the calculation of frequency-dependent nonlinear optical properties of components of the liquid phase. A concise overview of applications of this approach which are presently being worked out in our laboratory is also given. © 1996 John Wiley & Sons, Inc.

Notes: The bona fide method of classical dynamics on a manifold of quantum chemical variational parameters such as, for instance, linear combination of atomic orbital (LCAO) and configuration interaction (CI) coefficients, exponents, and centers of the basis-set atomic orbitals (AO) that mimics quantum propagation of a state vector is elaborated toward understanding the physics which underlies this dynamics. © 1996 John Wiley & Sons, Inc.

Notes: In this article, we present a study of the localization and properties of the molecular orbitals (MOs) of polyatomic systems by using a comprehensive version of the G1 model. In this version, the wave function is written as a DODS product of univocally determined spin orbitals (MOs), “projected” on the singlet ground state. A procedure for determining the MOs is given and applied to the BeH2 ground state. Equivalent split shell and localized MOs are found. The Be orbitals are seen to exhibit sp hybridization and the localized valence MOs are found to produce - 13.7 kcal/mol localization energy. Multistructural calculations are carried out and show that the present approach is able to describe localized and well-oriented bonds whenever the molecule under study presents only a single well-defined nonresonant chemical structure. © 1996 John Wiley & Sons, Inc.

Notes: The 13C shielding of the isotopomers CH3Cl, CH2 DCl, CHD2Cl, and CD3Cl has been calculated for a range of temperatures from an self-consistent field (SCF) shielding surface computed by Buckingham and Olegario. It is found that each successive deuterium substitution increases the shielding by about 0.19 ppm and that a very slight nonadditivity occurs. The principal factor which governs the nuclear motion correction for each isotopomer is the stretching of the bonds with both first- and second-order terms being significant. Angle bending contributions are very small at first order but quite substantial at second order. Not only should the 13C-isotope shifts in this experimentally uninvestigated series be easily measured but the temperature dependence of the shielding in any one isotopomer should be observable provided that careful measurements are made. The 13C-shielding difference between CH3 35Cl and CH3 37Cl has also been calculated and is found to agree well with experiment. © 1996 John Wiley & Sons, Inc.

Notes: Complete geometry optimizations using ab initio SCF/3-21G* calculations were performed on silatrane and azasilatrane, on their fluoro derivatives, and on methylsilatrane. By comparison with optimized geometries obtained for a series of model systems, the predicted transannular internuclear distances were interpreted in terms of the combined effects of electronegative substituents on Si and the anomeric interaction in the silatranes. The predicted geometries indicate that there is a weak transannular interaction in silatrane and a more significant one in azasilatrane, the predicted equilibrium distances being 2.66 and 2.15 Å, respectively. © 1996 John Wiley & Sons, Inc.

Notes: The ground state of benzocyclobutadiene, a bicyclic molecule with 8π electrons containing a benzene and a cyclobutadiene ring, is studied by means of modern valence bond (VB) theory in its spin-coupled (SC) form and the complete-active-space self-consistent field (CAS SCF) approach. The CAS SCF wave function is used to optimize the geometry, and SC theory - to obtain a well-correlated and easy to visualize and understand model of the active space hosting the π electrons. It is shown that the π system of the ground state of benzocyclobutadiene can be described with sufficient accuracy as a combination of the π systems of a distorted benzene ring and an isolated double bond. Each of the eight SC orbitals is found to be well-localized about one carbon atom only, with small distortions toward its nearest neighbors. The analysis of the optimal active-space spin-coupling pattern within the SC wave function for benzocyclobutadiene shows unambiguously that this molecule inherits neither the aromatic nor the antiaromatic character of its cyclic components, and it is most appropriate to regard it as nonaromatic. © 1996 John Wiley & Sons, Inc.

Notes: Trigonometric basis sets are used in a Rayleigh-Ritz variational method for computing two-sided eigenvalue bounds of the Schrödinger equation in one dimension. The method is based on truncating the infinite interval and solving an eigenvalue problem which obeys the von Neumann and the Dirichlet boundary conditions, respectively. Highly accurate numerical results are presented for the asymmetrical two-well oscillators. © 1996 John Wiley & Sons, Inc.

Notes: In the previous article we introduced a method to obtain an ensemble density describing a molecule in a crystal from diffraction experiment structure factors. Here the method is applied to the CoCl42- molecular ion in a Cs3CoCl5 crystal for which accurate magnetic structure factors are known. First, the approximations involved in the interpretation of polarized neutron experiment are reviewed with special emphasis on the collinearity approximation which has been avoided in this work. Second, the derivation of magnetic structure factors corresponding to theoretical ensemble densities is explained (the spin and the exact orbital contributions have been included). Third, the fitting procedure is presented and results at different levels of approximation are discussed. The main conclusions are: (1) A density built by using several molecular wave functions can give a very good agreement with the experimental data. (2) The ensemble representability constraint is necessary to retrieve physical information from the optimized parameters. (3) Taking into account the proper paramagnetic contribution to the magnetization improves significantly the agreement between theory and experiment. (4) Neglecting the diamagnetic contribution and the fact that the magnetization may be locally noncollinear to the applied external field is fully justified for the system under study. © 1996 John Wiley & Sons, Inc.

Notes: Electrostatic potential maps of certain biologically important molecules (guanine, adenine, cytosine, thymine, and two conformers of glycine) were studied employing a “hybridization displacement charge (HDC)” correction to Löwdin charge distributions and using the conventional Mulliken charge distributions of the molecules. In these calculations, the magnitude of each of the point charges was distributed in 3-dimension in a spherically symmetric manner. The method of computing HDC using MNDO wave functions was optimized by introducing two adjustable parameters. It has been clearly demonstrated that HDC-corrected Löwdin charge distributions of the molecules mentioned above are able to reproduce most of the important features of their ab initio MEP maps, while the conventional Mulliken charge distributions fail in many respects. Thus, HDC-corrected Löwdin charge distributions are shown to be quite reliable for the study of molecular electrostatic properties, particularly for molecules with more than one competing electrophilic site. © 1996 John Wiley & Sons, Inc.