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Notes: A new series of general formulas to evaluate the electron-repulsion integral (ERI) can be derived from modifying the Gauss-Rys quadrature formula. These named as “accompanying coordinate expansion (ACE) formulas” are capable of evaluating very fast ERIs, especially for contracted Gaussian-type orbitals (GTOs). According to the degree of the contraction of GTOs, the optimum formula can be selected among these ACEs. Numerical examples are shown for (ps|ps) and (pp|pp) ERIs as typical examples. It is found that the present ACE algorithm is numerically stable and is most efficient among all algorithms in the literature in the floating-point-operation (FLOP) count for all varieties of the degree of contraction. © 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: Two different approaches were used to explain the distribution of water coordinates in the crystallographically invisible part of the unit cell. Monte Carlo calculations were done starting from different initial water structures. Extended Monte Carlo calculations using equal initial structures were also used to obtain two further water structures. The differences between the Monte Carlo water structures were used to calculate the mean-square displacements of the water molecules. Monte Carlo calculations starting from different structures lead to a mean-square displacement of 0.58 Å2, whereas extended Monte Carlo moves using the same initial structure only show a mean-square displacement of 0.17 Å2. The mean-square displacement of 0.58 Å2 can be used to explain the experimental data. © 1996 John Wiley & Sons, Inc.

Notes: Continuing the search for a broader interpretation of hemeprotein behavior, we give preliminary results showing that there are electric and dynamic couplings between the heme group and amino acid residues within the protein matrix. EPR and X-ray absorption spectroscopy studies on azidometmyoglobin show that both magnetic and geometric properties of Fe—N3 evolve in the same nonlinear way as pH is increased and are tightly correlated to the strains on the helical segments of the protein. Flash photolysis of carbon monoxide hemoglobin, in the presence of ethanol or formamide, allows the study of cosolvent effects on geminate and nongeminate recombinations of the CO ligand trapped within the protein matrix. Data clearly show that cosolvents alter the statistic fluctuations of the protein, as well as the ligand partition between different protein matrix domains. From these studies, it is concluded that alterations occurring at particular sites give way to global protein perturbations. Then, each perturbated protein domain - binding site included - evolves with its own sensitivity to a new metastable state of the protein. The amplification of the initial perturbation which - instead of regressing - progressively propagates through the whole macromolecule is typical of a dissipative structure in the Prigogine sense. Biological properties of hemeproteins largely involve the surrounding solvent, via permanent or temporary exchanges of water molecules, protons, and small ligands. These fluxes along with their entropic corollary are not quite compatible with a conservative system. These works present the current trends developed in our laboratory in association with the European network “The Dynamics of Protein Structure.” In this framework, our laboratory collaborates with Dr. W. Doster and T. Kleinert (Munich, Germany) for the CO recombination studies in hemoglobin and with Dr. J. Hutterman (Homburg, Germany) and Drs. A. Bianconi and S. Della Longa (Rome and L'Aquila, Italy) for the magnetic and geometric properties of the myoglobin iron site. © 1996 John Wiley & Sons, Inc.

Notes: To investigate the backbone dynamics of proteins 15N longitudinal and transverse relaxation experiments combined with {1H, 15N{ NOE measurements together with molecular dynamics simulations were carried out using ribonuclease T1 and the complex of ribonuclease T1 with 2′GMP as a model protein. The intensity decay of individual amide cross peaks in a series of (1H, 15N)HSQC spectra with appropriate relaxation periods was fitted to a single exponential by using a simplex algorithm in order to obtain 15N T1 and T2 relaxation times. The relaxation times were analyzed in terms of the “model-free” approach introduced by Lipari and Szabo. In addition, a nanosecond molecular dynamics (MD) simulation of ribonuclease T1 and its 2′GMP complex in water was carried out. The angular reorientations of the backbone amide groups were classified with several coordinate frames following a transformation of NH vector trajectories. In this study, NH librations and backbone dihedral angle fluctuations were distinguished. The NH bond librations were found to be similar for all amides as characterized by correlation times of librational motions in a subpicosecond scale. The angular amplitudes of these motions were found to be about 10°-12° for out-of-plane displacements and 3°-5° for the in-plane displacement. The contributions from the much slower backbone dihedral angle fluctuations strongly depend on the secondary structure. The dependence of the amplitude of local motion on the residue location in the backbone is in good agreement with the results of NMR relaxation measurements and the X-ray data. The protein dynamics is characterized by a highly restricted local motion of those parts of the backbone with defined secondary structure as well as by a high flexibility in loop regions. Comparison of the MD and NMR data of the free liganded enzyme ribonuclease T1 clearly indicates a restriction of the mobility within certain regions of the backbone upon inhibitor binding. © 1996 John Wiley & Sons, Inc.

Notes: NMR techniques can give insight into a wide variety of motional events that occur in proteins over a range of timescales. In the first section of this article an overview of the results of dynamics studies, using NMR methods, on both small globular and larger multi-domain proteins is presented including the findings from investigations of non-native partly folded states. The second section of the article then concentrates on two topics where NMR can give residue specific quantitative data, namely coupling constant measurements and relaxation studies, including comparisons of these NMR data with results from crystallographic studies and theoretical molecular dynamics simulations. Finally the possible functional significance of the experimentally observed motions in proteins is discussed. © 1996 John Wiley & Sons, Inc.

Notes: We measured the νFe-His Raman band of horse heart deoxymyoglobin and human deoxyhemoglobin as a function of temperature between 10 and 300 K. A self-consistent spectral analysis of the deoxymyoglobin Raman band reveals that it is underlied by three different sublines with frequencies at Ο1 = 209 cm-1, Ο2 = 217 cm-1, and Ο3 = 225 cm-1 and an identical half-width of 13 cm-1. All these parameters were found to be independent of temperature. These sublines were attributed to different conformational substates of the Fe2+-His F8 linkage, which comprise different out-off-plane displacements of the heme iron and tilt angles of the Fe2+-Ng(His F8) bond. The intensity ratio I3/I2 exhibits a van't Hoff behavior between 150 and 300 K, bends over in a region between 150 and 80 K, and remains constant at lower temperature. In contrast, I2/I1 shows a maximum at 170 K and approaches a constant value at 80 K. These data can be fitted by a modified van't Hoff expression, which accounts for the freezing into nonequilibrium distributions of substrates in a temperature interval ΔT around a distinct temperature Tf and also for the linear temperature dependence of the protein's specific heat. The fits to the above intensity ratios yield a freezing temperature of Tf = 117 K and a transition region of ΔT = 55 K. The νFe-His Raman band of human deoxyhemoglobin was decomposed into seven sublines with frequencies at 195, 202, 211, 218, 226, 234, and 240 cm-1, with half-widths of 12 cm-1. While the low-frequency sublines are strong at 300 K, the high-frequency sublines dominate the band at cryogenic temperatures. In comparison, we also investigated the temperature dependence of the near-infrared band III at 760 nm. Band III of deoxymyoglobin can be decomposed into two subbands which are 165 cm-1 apart. The ratio of their absorption cross sections shows a temperature dependence which parallels that of the ratio I3/(I2 + I1) of the corresponding Raman sublines. Band III of deoxyhemoglobin was decomposed into three subbands, the absorption cross sections of which also depend on temperature, similar to what has been observed for the νFe-His subbands. These observations provide strong evidence that the frequency positions of the subbands of band III and the νFe-His sublines are governed by the same coordinates. For both proteins investigated, the frequency positions and the half-widths of the band III subbands depend significantly on temperature. This is rationalized in terms of an earlier proposed model (Cupane et al., Eur. Biophys. J. 21; 385 1993) which assumes that the corresponding electronic transition is coupled to a bath of low-frequency modes. Our data indicate that these modes are harmonic below 134 K but become anharmonic above this temperature. This onset of anharmonic motions is interpreted as resulting from conformational transitions within the protein which affect the prostethic group via heme-protein coupling. © 1996 John Wiley & Sons, Inc.

Notes: 131Xe-NMR longitudinal relaxation rates have been measured by the inversion recovery method for xenon in presence of lecithin vesicles or a small protein charybdotoxin. The transverse relaxation rates in the same spectra have been obtained by spectral deconvolution. The results show that xenon in lecithin vesicles is in a rapid exchange between free and bound sites and that averaging of the electric-field gradient at the Xe nucleus is a two-step process. From these results, estimates have been obtained for the parameters entering the 131Xe quadrupolar interaction. © 1996 John Wiley & Sons, Inc.

Notes: The interaction between the R2R3 DNA binding domain of the oncoprotein c-Myb and oligodeoxynucleotides was investigated by 1H-NMR spectroscopy and fluorescence anisotropy assays. Titration of 12 and 16 base-pair DNA fragments containing the TAACGGTC sequence with R2R3 revealed the presence of two complexed forms (in a 40/60 ratio): either two complexes or two conformations in slow exchange at the NMR chemical shift time scale. The largest variations of imino proton chemical shifts were observed for the imino proton of the base pairs 2, 3, 4 and 6 of the DNA sequence, suggesting a direct involvement of these base pairs in the interaction. Using fluorescence anisotropy measurements, a dissociation constant of 5.12 ± 1.49 nM for the specific DNA-R2R3 complex was found, whereas a value of 2.7 ± 0.1 μM was determined for the nonspecific complex. © 1996 John Wiley & Sons, Inc.

Notes: We show that the Ising free-energy functional f(T, X) yields a second-order phase transition. The value of X, a generalized order parameter, which minimizes the functional is the real-order parameter, Ω = tanh[Ω(TC/T)] where Tc = J/(2k) and J is the Ising coupling constant. The Ising theory is applicable to the second-order phase transitions in ferromagnets, ferroelectrics, and superconductors. The constant temperature slices of f(T, X) yields the Ising functional which is valid over the entire range of T and which is identical to the Landau functional for T/TC close to unity. © 1996 John Wiley & Sons, Inc.

Notes: Calculations are reported on the dipole moments, transition energies, and hyperpolarizabilities of 1-amino-4-nitrobutadiene and its four aza-analogs using a semiempirical sum-over-states method. The results obtained suggest that the presence of nitrogen in the unsaturated chain can have a substantial beneficial effect on the molecular hyperpolarizability provided that it is placed in a position which assists charge transfer from the donor to acceptor group on excitation. The values calculated for the 3-azabutadiene are greater than those found for either the simple butadiene or for donor - acceptor aromatics or five-membered heterocycles. The results do not agree with those reported recently using an ab initio approach. © 1996 John Wiley & Sons, Inc.

Notes: In a novel approach to molecular shape representation, molecular electronic density functions are treated as 3D hypersurfaces in a 4D Euclidean space, spanned by the three spatial coordinates and an electronic density threshold variable. The general objects resulting from this approach are topological spheres with handles, modeling the electron density. Based on this model, a new, simple representation of molecular topology of electron density is proposed, using a tree describing the evolution of topological spheres with handles as function of a varying density threshold. The vertices of the tree are characterized by nonnegative integers (the genea of the topological objects). This representation is compared to earlier, detailed 3D topological descriptions of molecular shape as well as to the more conventional molecular network (bond skeleton) representation. A variety of relevant topological equivalence relations of molecules are discussed and a new, global, molecular similarity measure is proposed. © 1996 John Wiley & Sons, Inc.

Notes: An ab initio procedure for the calculation of atomic and molecular electronic wave functions, the Optimized-Basis-Set Multi-Configuration Spin-Coupled (OBS-MCSC) method, is generalized by introducing a separate linear combination of spin functions for each configuration, turning it into the OBS-GMCSC method. The ability to use a second-order minimization procedure in the computation of the wave function is maintained through appropriate generalization of the analytic expressions for the first and second derivatives of the energy with respect to the optimization parameters, as is the optional inclusion among the latter of the basis-function exponential parameters. The generalization, a variational improvement of the wave function, strengthens the connection with classical VB theory, of which the method can now be considered an optimized-orbitals variant, while maintaining the link with single-configuration Spin-Coupled theory, of which it may still be considered a multiconfiguration extension. The method can also be viewed as a nonorthogonal variant of the MCSCF approach. To demonstrate its practical feasibility and usefulness, the OBS-GMCSC method is applied to a study of the electronic structure and electron affinity of boron. © 1996 John Wiley & Sons, Inc.

Notes: Proton affinities (PAs) of a series of phosphorous compounds bearing the phosphoryl function have been calculated using AM1 and PM3, as well as lithium-cation affinities (LCAs) using the recent PM3 lithium parametrization. Sulfonyl derivatives PAs and LCAs have been also calculated using PM3. The Li+ cation can be bonded in a “chelate” form with the two oxygens of the sulfonyl group. Nevertheless, the “linear” adduct, with the lithium-oxygen bond collinear with one of the S=O bonds, is more stable. This is confirmed by ab initio calculations on Me2SO2—Li+ adducts. © 1996 John Wiley & Sons, Inc.

Notes: The reaction of Y+ + NH3 → Y+ NH + H2 was theoretically investigated by ab initio MO methods. Two possible pathways (1-1 H2 loss and 1-2 H2 loss) on the singlet potential energy surface and reaction mechanism were examined and discussed. The singlet and triplet PESs of this reaction system were compared to confirm the correctness of spin conservation concepts. © 1996 John Wiley & Sons, Inc.

Notes: The performance of a number of different local and nonlocal density functional theory (DFT) methods has been investigated for some small titanium - oxygen systems. Equilibrium geometries, ionization potentials, dipole moments, atomization energies, and harmonic vibrational frequencies have been calculated for the TiO, TiO2, and Ti2 molecules, and the results are compared with experimental data and ab initio calculations. It is shown that most DFT methods perform much better than the ab initio Hartree - Fock (HF), second-order perturbation theory (MP2), and configuration interaction including single and double excitations (CISD) treatments. For good agreement with experimental data, gradient corrections to the exchange part of the DFT functional are needed, as well as some type of correction for the errors in the calculated energy splittings between different atomic states of titanium. Hybrid methods including a mixture of HF exchange with DFT exchange correlation do not perform as well as “pure” DFT methods for the studied systems. © 1996 John Wiley & Sons, Inc.

Notes: The Feynman path integral method is applied to the many-electron problem of quantum chemistry. We begin with constructing new closure relations in terms of the linear combination of atomic orbital (LCAO) coefficients and investigate the transition amplitude and the partition function of the system in question; then a “classical path of electrons,” which is described by the time-dependent Hartree-Fock-Roothaan equation, is obtained by minimizing the action integral of the system with respect to the “electron coordinate.” The next order approximation is obtained by evaluating the deviation from this classical path, which is approximately written by a Gaussian integral. The result is expected to be the random-phase approximation. © 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: Formulas are derived for the density matrices belonging to an n-particle wave function built on the basis of single-center explicitly correlated Gaussian basis functions. An explicit formula for the first-order density matrix, P(r1, r′1), is obtained for computing the probability distribution P(r1, r1). Other formulas are derived for matrix elements of the first-order density operator P on a basis of single-particle Gaussian orbitals so that natural orbitals (NOs) can be expressed in such a basis. The method is illustrated for the case of the ground state of the helium atom using the 16-term (geminal) wave function by Singer and Longstaff (E = -2.90233 au) and a set of even-tempered Gaussian orbitals. The resulting natural orbitals compare favorably with natural orbitals from Cl expansions. The method is also applied to our 20 term (trimal) wave function for the ground state of dipositronium (E = -0.51560 au). Analysis is made in this case for pair correlation functions of both the electron-electron and the positron-electron pairs; results include the radial distributions of these pairs and their relative angular momentum. © 1996 John Wiley & Sons, Inc.

Notes: We examine the state of the art of the solvation procedure called the polarizable continuum model (PCM), focusing our attention on the basic properties: energy of the solute, solvation energy, and their derivatives with respect to nuclear coordinates. The PCM method is based on the use of an effective solute Hamiltonian, where the solute-solvent potential is described in terms of continuous response functions with boundary conditions given in terms of the solute cavity surface. This exposition is mainly based on recent progress, a large part of which is still in press. The new procedures are quite effective, at the ab initio quantum mechanical level, but cannot be applied to very large solutes for the limitations of computer hardware. We introduce then other methods, presented here for the first time, which make possible the classical calculation of the solvation energy also for very large solutes (a few thousand atoms). The strategy outlined here regards a new method to define cavity surfaces (supplemented with analytical definitions of its partition in tesserae) and of their derivatives, combined with a fast noniterative method to compute solvation energy. Finally, we discuss the introduction of this procedure in hybrid quantum mechanical/molecular mechanics descriptions of large solutes (enzymes), where the quantum description is limited to the reacting portion of the enzyme. © 1996 John Wiley & Sons, Inc.

Notes: A practical procedure (FUERZA) to obtain internal force constants from Cartesian second derivatives (Hessians) is presented and discussed. It allows a systematic analysis of pair atomic interactions in a molecular system, and it is fully invariant to the choice of internal coordinates of the molecule. Force constants for bonds or for any pair of atoms in general are defined by means of the eigenanalysis of their pair interaction matrix. Force constants for the angles are obtained from their corresponding two-pair interaction matrices of the two bonds or distances forming the angle, and the dihedral force constants are similarly obtained using their corresponding three-pair interaction matrices. © 1996 John Wiley & Sons, Inc.

Notes: We review “Hilbert space basis-set reduction” (BSR) as an approach to reduce the computational effort of accurate correlation calculations for large basis sets. We partition the single-particle basis into a small “internal” and a large “external” set. We use the MRCI method for the calculation for that part of configuration space in which only internal orbitals are occupied and perturbatively correct for the remaining configurations using a method similar to Shavitt's Bk method. The present implementation approximates the MRCI result for the unpartitioned basis set, with a significantly reduced computational effort. To demonstrate the viability of the method, we present results for selected states of small molecules (Be2, CH2, O3). For the examples investigated, we find that relative energy differences can be reproduced to an accuracy of approximately 1 kcal/mol with a significant computational saving. © 1996 John Wiley & Sons, Inc.

Notes: The molecular properties characterizing diammine platinum complexes have by way of example been analyzed and selected because of their role in anticancer activity. The research was done with the use of the nonstandard quantitative method to compare molecular properties resulting from density functional theory (DFT). Among different molecular parameters considered, the multipole moment components were found mainly to have clear correspondence to the trans (anticancer neutral) and cis classes of platinum complexes. The results led to the selection and conjecture of the specific significance of some molecular characteristics contrasted with other assemblies of parameters. © 1996 John Wiley & Sons, Inc.

Notes: The solution of the Schrödinger equation for the d-dimensional hydrogen atom in a d-dependent potential defined by Gauss' law has been studied by the shifted 1/d method and the δ expansion. These methods provide analytical formulas for the eigenvalues and eigenfunctions which have been tested against “exact” numerical values obtained recently. The comparison shows that the results obtained with the analytical expressions are in excellent accord with the numerical ones and, on the other hand, provide a theoretical justification for a proposed empirical expression for the energies of the two-dimensional hydrogen atom with a logarithmic potential energy function. © 1996 John Wiley & Sons, Inc.

Notes: An analysis of the structure of the optimized effective Kohn-Sham exchange potential vx and its gradient approximations is presented. The potential is decomposed into the Slater potential vs and the response of vs to density variations, vresp. The latter exhibits peaks that reflect the atomic shell structure. Kohn - Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of vx with a gradient-dependent Padé approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact vx. © 1996 John Wiley & Sons, Inc.

Notes: Analytical exact expressions are obtained for matrix elements of the modified Pöschl-Teller oscillator over different operators including powers of the hyperbolic functions sinh(α x), cosh(α x), and tanh(α x) and the differential operators d/dx and d2/dx2. These expressions are derived using explicitly the Pöschl-Teller eigenfunctions. In addition, several recursion relations connecting different Pöschl-Teller matrix elements are obtained using the factorization and hypervirial techniques. It is shown that these relations can be used to make easier the computation of the matrix elements. © 1996 John Wiley & Sons, Inc.

Notes: The D-dimensional Coulomb system serves as a starting point for generating generalized atomic shells. These shells are ordered according to a generalized Madelung rule in D dimensions. This rule together with an Aufbau Prinzip is applied to produce a D-dimensional periodic table. A model is developed to rationalize the ordering of the shells predicted by the generalized Madelung rule. This model is based on the introduction of a Hamiltonian, invariant under the q-deformed algebra Uq(so(D)), that breaks down the SO(D + 1) dynamical symmetry of the hydrogen atom in D dimensions. The D = 2 case (Flatland) is investigated in some detail. It is shown that the neutral atoms and the (moderately) positive ions correspond to the values q = 0.8 and q = 1, respectively, of the deformation parameter q. © 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: 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: Bond function basis sets combined with the counterpoise procedure are used to calculate the molecular dissociation energies De of 24 diatomic molecules and ions. The calculated values of De are compared to those without bond functions and/or counterpoise corrections. The equilibrium bond lengths re and harmonic frequencies οe are also calculated for a few selected molecules. The calculations at the fourth-order Møller-Plesset approximation (MP4) have consistently recovered about 95-99% of the experimental values for De; compared to as low as 75% without use of bond functions. The calculated values of re are typically 0.01 Å larger than the experimental values, and the calculated values of οe are over 95% of the experimental values. © 1996 John Wiley & Sons, Inc.

Notes: This study demonstrates the use of uneven atomic basis sets for ab initio calculations of NMR shielding in the localized orbital/local origin (LORG) approach with norbornenone as the test case. We distinguish between locally dense sets (extended basis on target atom only) and locally saturated sets (extended bases on target atom and atoms in its first bonding sphere), using 6-311G** and 6-31G sets to describe the high and low level of function sets. It is shown that the use of these uneven sets can simulate high basis set level calculations of shieldings for 1H and for all the 13C nuclei in this molecule and, hence, allows quite accurate ab initio calculations of shielding properties of these nuclei in large molecules using relatively modest computational facilities. The shielding of the double-bonded 17O nucleus is apparently sensitive to basis-set quality beyond the first bonding sphere. © 1996 John Wiley & Sons, Inc.

Notes: The comparison of local nonlocal and hybrid DFT methods with RHF, MP2, CCSD, and CPF ab initio methods in generating geometries and relative energies of cis- and trans-difluorodiazete, SVWN, BLYP, BP86, BECKE3LYP, and BECKE3P86 DFT methods with 6-311 + g(2d) and 6-311 + + g(3df) basis sets. The geometries generated with RHF ab initio models are quite different from experimental values and energy evaluation prefers the wrong isomer. The hybrid methods give superior geometries while energies evaluated with nonlocal DFT methods are better than the one obtained with MP2 or CCDS ab initio methods. The results suggest DFT as the method of choice of studying similar systems. © 1996 John Wiley & Sons, Inc.

Notes: For the first hydrogen bond of the guanine-cytosine (G-C) pair, the potential function V(r, R) is found for the nonequilibrium bond length R. A new form of the semiempirical potential function, Clementi's calculations for V(r, R0) and some experimental data are used. New wave functions and energy levels as a function of the H-bond length for the ground and several excited states are obtained. This allows one to obtain frequencies and amplitudes of some vibrations of the G-C pair side groups involved in the formation of the hydrogen bond when the latter is not excited and when it is excited to the first energy level. © 1996 John Wiley & Sons, Inc.

Notes: The recently introduced set of quadratic ionic and covalent valence indices from changes in the pair-diagonal part of the molecular (Hartree-Fock) two-electron density matrix, ΔΓ(2)(a, b) (orthogonal atomic orbital [OAO] basis set), relative to separated atoms limit (SAL), is extended to cubic valence numbers; they are calculated from the corresponding changes in the three-electron density matrix, ΔΓ(3)(a,b,c). The two- and three-electron indices are given by the corresponding contributions to ΔΓ(2), and ΔΓ(3), which are quadratic and cubic in terms of relevant changes in the one-electron density matrix. The new valence measures are partitioned into one-, two-, and three-center contributions comprising purely ionic (covalent) and mixed ionic-covalent terms. For integral OAO occupations in the SAL, the sum of all three-electron contributions vanishes exactly in the UHF approximation; for fractional occupations, they give rise to a rather small correction to the overall two-electron valence index. The properties of cubic valence numbers are tested on a model three-orbital description of a symmetric (ABA), collinear transition state and on the OQ2 (Q = 1,0, -1) and O2(bond)H+ systems. Preliminary results for B2H6 are also given. © 1996 John Wiley & Sons, Inc.

Notes: The properties of Sturmian basis sets in d-dimensional direct space and d-dimensional momentum space are reviewed, as well as the relationship between hydrogenlike Sturmians and hyperspherical harmonics. The kernel of the reciprocal-space Schrödinger equation is expanded in terms of Strumian basis sets. This expansion allows Shibuya and Wulfman's treatment of many-center Coulomb potentials to be extended to many-center potentials of a general form, and the method is also extended to the calculation of crystal orbitals and band structures. © 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: We applied general quantum mechanical ideas in order to establish the form of the many-electron wave functions suitable for analysis of catalytic processes. This led us to the conclusion that the relevant wave functions for the electrons of the catalytic complexes must be taken as superpositions of the antisymmetrized products of the wave functions of electrons in excited and ionized states of the catalyst and reactants. With use of the trial wave function for the electrons of the catalytic complex in such a form, it becomes possible to construct model potential energy surfaces of catalytic reactions as a superposition of the potential energy surfaces of the reactants in different electronic states. We formulate the criteria which when satisfied make it possible to implement a catalytic version of a desired chemical transformation. We also propose an approach to the explanation of the frequently observed correlations between the catalytic activity and other physical properties of a catalyst. © 1996 John Wiley & Sons, Inc.

Notes: The sampling of the exact solution of the Schrödinger equation by quantum Monte Carlo methods allows one to solve the problem of the optimization of linear and nonlinear parameters of a trial wave function by minimization of the distance to the exact wave function in Hilbert space even for those systems whose exact wave function is unknown. The overlap integrals between the basis functions and the exact wave function can be easily estimated within the quantum Monte Carlo formalism. Several observables of the helium atom ground state, computed both within the orbital approximation and by an explicitly correlated basis set, evidence the overall goodness of the wave function optimized according to this criterion. © 1996 John Wiley & Sons, Inc.

Notes: Ultrafast dissipative dynamics of vibrational degrees of freedom in molecular systems in the condensed phase are studied here. Assuming that the total system is separable into a relevant part and a reservoir, the dynamics of the relevant part can be described by means of a reduced statistical density operator. For a weak or intermediate coupling between the relevant part and the reservoir, it is possible to derive a second-order master equation for this operator. Using a representation of the reduced statistical operator in an appropriate molecular basis set, vibrational dynamics in a variety of potential energy surfaces can be studied. In the numerical calculations, we focus on the dissipative dynamics under the influence of external laser fields. In the first example, vibrational wave-packet dynamics and time-resolved pump-probe spectroscopy of molecular systems with nonadiabatically coupled excited-state potential energy surfaces is presented. In the second part, we show how an intense laser field modifies the wave-packet motion onto two radiatively coupled potential energy surfaces. Finally, the controlled preparation of definite vibrational states in a triatomic molecule with infrared laser pulses is considered taking relaxation and dephasing processes into account. © 1996 John Wiley & Sons, Inc.

Notes: The idea of dilation, or dilatation, analyticity with respect to complex scaling of the interparticle distances for nonrelativistic atomic or molecular electronic Hamiltonians is now over 20 years old and the first major reviews are just over 10. The method continues to be a fruitful source of new theoretical and computational results. Under the scale transformation r → reiθ, the usual “spectrum” of bound states is exactly preserved, and scattering continua are “rotated” off the real axis by an angle of -2Re(θ) about their respective thresholds. Useful features of this transformation are (1) that resonances are exposed, and, thus, (complex) resonance eigenvalues are easily calculated as the wave functions are L2, and standard results of Kato-type perturbation theory can thus be applied to them; (2) that utilization of this technique to study atoms in ac and dc fields was an early, and still evolving extension of the original theory; and (3) the fact that the “continua” are rotated off the real energy axis allows scattering information to be extracted from computations carried out entirely L2 in bases as the usual resolvents of scattering theory are no longer singular on the real axis. After a brief survey of the technique and its applications, these ideas are illustrated by discussion of positive energy-bound states and resonances, the extension of the theory to include the dc Stark effect, and a review of the resolution of the initially perplexing problem of atomic and molecular bound states in continua. These theoretical results are followed by a discussion of some very recent computational results, allowing computation of atomic partial photoionization cross sections with no specific coordinate space enforcement of boundary conditions, a highly advantageous situation for calculation of the partial cross section for three-body breakup, as in the process ℏ ω + He → He2+ + e- + e-. © 1996 John Wiley & Sons, Inc.

Notes: Generalized overlap amplitudes (GOAS) are calculated between the lithium atom and several states of Li+. An examination of the long-range behavior of the GOAS indicates that they are coupled, appearing to have the same exponential decay at large r. At intermediate distances from the nucleus, the GOAS decay with their unique exponential rate and the decay rates only merge at large r. Although many of the GOAS appear to be similar, their distinctness indicates that they may, in fact, be linearly independent. © 1996 John Wiley & Sons, Inc.

Notes: The orthogonal group function approach, as based on the Huzinaga equation, is extensively applied in reduced basis frozen-core calculations. Although the theory is developed for orthogonal electronic groups, the use of reduced basis sets prevents strict orthogonality and the formalism is complemented to take, partially, into account nonorthogonality (projection factors, projection energy). In the present article, an alternative to this approach, based on the nonorthogonal formalism, is proposed. An orbital equation is derived from the Adams-Gilbert equation and the energy is evaluated according to a recent proposal based on the power-series expansion of the overlap energy. A comparative overview of the orthogonal and nonorthogonal formalisms is presented and the results of reduced basis frozen-core calculations as obtained with the two methods are compared. It is found that the nonorthogonal formulation predicts equilibrium geometrical parameters in some cases similarly and, in other cases, slightly better than does the orthogonal one. Based on this observation and on the fact that the nonorthogonal formulation is exempt from empirical parameters (projection factors), it is concluded that the nonorthogonal formalism represents an appealing alternative in reduced basis frozen-core calculations. © 1996 John Wiley & Sons, Inc.

Notes: We sketch the procedure that we are using to optimize a spin-coupled wave function built with partially orthogonalized orbitals. It is shown how it is possible to parametrize the orbitals in order to deal with independent variables while maintaining the partial orthogonalization and how to calculate first- and second-order derivatives with respect to these variables. A test calculation on CH4 molecule is shown. © 1996 John Wiley & Sons, Inc.

Notes: The goal of obtaining accurate potential energy surfaces for the study of intermolecular forces is of fundamental importance. In this article, we propose a new method to generate a set of virtual orbitals optimized in such a way to give very compact valence bond (VB) wave functions with the same accuracy of very large VB calculations. These optimized virtual orbitals, completely free from BSSE, are developed in the framework of spin coupled theory. Test calculations on the He ··· LiH system are presented together with a comparison with previous studies. © 1996 John Wiley & Sons, Inc.

Notes: A novel procedure for calculating magnetic susceptibilities and nuclear magnetic shieldings in molecules is outlined, based on formal annihilation of transverse paramagnetic contribution to quantum mechanical current density induced within the electron cloud by an external homogeneous, static magnetic field. Within this method all the components of nuclear magnetic shielding are independent of a gauge translation, in any calculation relying on the algebraic approximation, irrespective of size and quality of the gaugeless basis set adopted; magnetic susceptibilities are invariant for center-symmetric molecules (virtual invariance is actually observed for molecules of arbitrary symmetry). Large basis set calculations of near-Hartree-Fock magnetic properties and maps describing a current density field of acetylene molecule carried out via the new procedure are compared with corresponding ones adopting the common origin-coupled Hartree-Fock approach and methods formally annihilating the diamagnetic contribution to the current density. © 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: The photoionization cross sections and asymmetry parameters of the three main valence ionization processes in HI, corresponding to the formation of, respectively, 6π, 11σ, and 10σ holes, were calculated in the random-phase approximation (RPA). Our particular computational procedure, based on solving the integral equation for the half on the shell K-matrix upon a grid of points supplied by an L2 basis set calculation, affords recovery of the electronic continuum degeneracy of the final states. This makes it possible to compute the differential ionization cross section at any energy up to the fourth ionization threshold, allowing for the interaction of the three channels considered. The total cross section obtained by applying the Stieltjes imaging procedure to the discrete spectrum yielded by the RPA is also reported. © 1996 John Wiley & Sons, Inc.

Notes: An extended geminal model has been applied to determine the interatomic potential for the X1Σ+g state Be2. By adopting a [11s, 9p, 6d, 4f, 2g] contracted Gaussian-type basis, the following potential minimum parameters are obtained: Re = 4.67 a.u. (4.63 a.u.) and De = 3.70 mH (3.82 ± 0.05 mH), experimental values in parentheses. A calculation with a nuclei-centered [9s, 7p, 4d, 2f, 1g] GTO basis plus two sets of bond-type function, each set comprising diffuse (2s, 2p, 2d, 2f, 1g) GTOs, yielded -3.79 mH as the value of the potential at R = 4.63 a.u. On the basis of an error analysis the best theoretical estimate of the binding energy is determined to be 3.83 ± 0.08 mH. The calculated value for the fundamental vibrational frequency is v0→1 = 224.7 cm-1 (exp. = 224 ± 3 cm). © 1996 John Wiley & Sons, Inc.

Notes: Electron delocalization between the reagent and reactant molecules is the principal driving force of chemical reactions. It brings about the formation of new bonds and the cleavage of old bonds. By taking the aromatic substitution reaction as an example, we have shown the orbitals participating in electron delocalization. The interacting orbitals obtained are localized around the reaction sites, showing the chemical bonds that should be generated and broken transiently along the reaction path. By projecting a reference orbital function that has been chosen to specify the bond being formed on to the MOs of the reactant molecules, the reactive orbitals that are very similar to the interacting orbital have been obtained. The local potential of the reaction site for electron donation estimated for substituted benzene molecules by using these projected orbitals shows a fair correlation with the experimental scale of the electron-donating and -withdrawing strength of substituent groups. The reactivity is shown to be governed by local electronegativity and local chemical hardness and also by the localizability of interaction on the reaction site. © 1996 John Wiley & Sons, Inc.

Notes: The two lower-lying electronic states (3Σ- and 5Σ-) of the BeC, MgC, and CaC molecules were investigated using restricted Hartree-Fock (RHF), generalized valence bond (GVB), and configuration interaction (CI) calculations to establish the relative ordering of those states as a function of the size of the alkaline-earth element. It is shown that as a result of the competition between bonding effects, which predominate for the 3Σ- states, and exchange effects, which stabilize the 5Σ- states, the ordering of these states can be reversed as we move from the Be to the Ca atom. For both the BeC and MgC molecules, the ground state was found to be a triplet X3Σ- state, but for the CaC molecule, the high-spin X5Σ- becomes more stable. © 1996 John Wiley & Sons, Inc.

Notes: On the example of several atomic and small molecular systems, the regular behavior of nodal patterns in the electronic one-particle reduced Wigner function is demonstrated. An expression found earlier relates the nodal pattern solely to the dot-product of the position and the momentum vector, if both arguments are large. An argument analogous to the “bond-oscillatory principle” for momentum densities links the nuclear framework in a molecule to an additional oscillatory term in momenta parallel to bonds. It is shown that these are visible in the Wigner function in terms of characteristic nodes. © 1996 John Wiley & Sons, Inc.

Notes: Generalized oscillator strengths for a number of singlet transitions of the NH3 molecule, evaluated according to the random-phase approximation approach, are presented and discussed so as to provide characterization of some portions of the Bethe surface of the molecule. © 1996 John Wiley & Sons, Inc.

Notes: The problem of bond length alternation in linear extended φ-electron systems with conjugated double bonds is examined using the valence bond theory applied to a simple model of cyclic polyenes CNHN with N = 4v and N = 4v + 2 sites as described by the Pariser-Parr-Pople Hamiltonian. Overlap enhanced atomic orbitals are employed in order to achieve the optimal treatment with only two Kekulé structures. The predicted bond length alternation and its magnitude are in good agreement with earlier molecular orbital based calculations and with experiment. Special attention is given to the discussion of the origin of bond length alternation in long polyenic chains and to the role of the resonance energy leading to stabilization of undistorted, symmetric structures for small aromatic (N = 4v + 2) cycles. © 1996 John Wiley & Sons, Inc.

Notes: The exchange-correlation potential associated with excited-state density functional theory is studied numerically using accurate electron densities for ground and excited states of He, Be, Ne, Mg, and Ar. The long-range and short-range behaviors of this potential are discussed. First-excitation energies are estimated using various prescriptions. © 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: Several modelings of exchange and correlation forces which can be carried out using density functional theory (DFT) methods have been analyzed to study their efficiency and reliability when evaluating possible competing structures of helium ionic clusters of increasing size. This study examines Hen+systems with n from 1 to 7 and compares the present calculations with earlier evaluations that used more conventional, and more computationally intensive, methods with configuration interaction (CI) approaches. The present results indicate that it is indeed possible to strike a fruitful balance between reduction of computational times and quality of the ensuing structural information. © 1996 John Wiley & Sons, Inc.

Notes: A general formula has been established for the overlap integrals with the same screening parameters of Slater-type orbitals in terms of bionomial coefficients. The final results are especially useful for the calculation of these integrals for large quantum numbers, which occur in the multicenter integrals. © 1996 John Wiley & Sons, Inc.

Notes: The application of the frozen-core approximation to the calculation of the shielding tensor of nuclear magnetic resonance (NMR) spectroscopy is discussed and an implementation is presented. A complete formulation of the shielding calculation within the frozen-core approximation is given, both in general terms and for the special case of density functional theory (DFT) and “gauge including atomic orbitals” (GIAOs). The practical implementation is validated by a detailed discussion of the consequences of the approximation. The general conclusion is drawn that the frozen-core approximation is a useful tool for shielding calculations - if the valence space is increased to contain at least the ns, np, (n - 1)p, (n - 1)d (fourth period and higher) shells, where n is the number of the given period in the periodic table of elements. The new method is applied to 77Se shieldings and chemical shifts for a small number of compounds. The agreement between theory and experiment is good for relative shifts, whereas calculated absolute shieldings are generally too small by about 300-400 ppm. This difference is attributed to the relativistic contraction of the core density at the selenium atom that had been explicitly incorporated into the experimental absolute shielding scale. © 1996 John Wiley & Sons, Inc.

Notes: We consider the question of long-range propagation of informational signals in biosystems. This is done for the case of a modeled biosystem of the type considered by H. Fröhlich and A. S. Davydov but under general nonequilibrium thermodynamic conditions. For that purpose we resort to the so-called informational statistical thermodynamics. It is shown that Fröhlich's effect may follow in this system. It consists in the emergence of a self-organized dissipative homogeneous and stationary structure (in Prigogine's sense), resembling a nonequilibrium Bose-Einstein condensation in the low-lying-in-frequency modes of polar vibrations. It follows once a critical level of pumping of metabolic energy is achieved. Furthermore, it is shown that signals in this system propagate in the form of Davydov solitons, which are strongly thermally damped in near equilibrium at physiological conditions. However, the situation drastically changes in nonequilibrium conditions, leading to Fröhlich's condensation, when the lifetime of a Davydov-like soliton is enormously enhanced, allowing for very long range propagation of signals. © 1996 John Wiley & Sons, Inc.

Notes: Secular polynomials (SPs) have been constructed and studied for the adjacency matrices A(GaCh) and A(GbCh) corresponding to chemical graphs of alkanes in terms of atoms (GaCh) and in terms of bonds (GbCh). The three second-class Chebyshev polynomials Up(Q), Up - 1(Q), and Up - 2(Q), with respect to the variable Q proportional to the SP of an isolated CH2-like subgraph, have been shown to appear within both SPs P[A(GaCh)] and P[A(GbCh)] and to play the role of algebraic analogues of a (CH2)p-like subgraph. Common noncanonical algebraic expressions for both SPs reflecting the regular internal structure of alkanes have been constructed on this basis. Spectral properties of both graphs GaCh and GbCh have been shown to be determined by those of Up(Q), e.g., the band limits of spectra proved to be related to the orthogonality interval Q = [-1;1] for polynomials Up(Q). Since the adjacency matrices (AMs) A(GbCh), but not A(GaCh), are proportional to definite model Hamiltonian matrices, the obtained results serve to interpret the one-electron spectra of alkanes in terms of peculiarities of usual chemical structure. © 1996 John Wiley & Sons, Inc.

Notes: A computational study of substituent effects on methane activation and elimination by high-valent zirconium complexes is reported. Substituent (Z) effects (in a structural, electronic, and enthalpic sense) are substantially less important for the imido (LnZr(DOUBLE BOND)NZ) and imidolike TS than the amido (LnM(SINGLE BOND)NHZ). For the microscopic reverse reaction, methane CH activation, it suggests that tailoring imido reactivity through electronic modification of nitrogen substituents will be difficult. Analysis of the earliest part of the reaction coordinate for methane elimination entails structural deformation of the Zr - amido to assume an appropriate geometry for elimination, which, in some cases, is directly reflected in substantially higher elimination barriers. Lower elimination barriers correlate with stronger agostic bonding, providing further support for the crucial importance of agostic bonding in facilitating alpha-elimination processes for high-valent transition-metal complexes. © 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 discussion is presented for possible diamond-lattice-based structures containing holes that can be filled with metal atoms or ions. To allow the formation of coordinative bonds to the metal, some carbon atoms should be replaced by heteroatoms (with nitrogen preferred, but in some cases oxygen or other heteroatoms may be considered). Two types of holes that may lead to the formation of coordinative bonds are discussed in detail: tetrahedral holes for four such bonds and quasi-octahedral holes for six such bonds. In turn, when suitably arranged in a translationally symmetric manner, these holes may resemble open or closed pores in foams; when they are open, the “channels” may lead to interesting properties with regard to metallic conductivity or superconductivity. © 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: The valence isomerization of the 1,2-dithiete parent compound to the open-chain dithial was studied by CASSCF multiconfiguration methods including the CASPT2 perturbational treatment. The isomerization energy remains small at the highest level of theory. In agreement with Jonas and Frenking, the cyclic structure is only then preferred over the acyclic ones if f-functions on the sulfur atoms are considered. If they are included, the 1,2-dithiete is more stable by 3.8 kcal/mol and the barrier amounts to 24.9 kcal/mol at the CASPT2(8,8)/6-31G(2df)//MP2/6-31G* level of theory. According to MP2/6-31G* geometry optimizations, substitution of H by NH2 and CH3 reduces the stability of the 1,2-dithiete ring structures relative to the open-chain dithiocarbonyl structures, whereas the inverse holds for acceptor substitution by CN and CF3. A higher stability of benzodithiete relative to ortho-dithiobenzoquinone is predicted at all employed levels of theory. This is in good agreement with conclusions drawn from experimental results. Whereas the experimental microwave geometry of 1,2-dithiete is well reproduced theoretically, the experimental electron diffraction geometry of 3,4-bis-(trifluoromethyl)-1,2-dithiete differs from the calculated one. © 1996 John Wiley & Sons, Inc.

Notes: We previously studied the first stable conformations of flavone acetic acid and related compounds. In this article, a similar investigation was carried out on the second stable conformation of the same compounds. Emphasis is on the conformation dependence of the hydrogen-bonding effects, the molecular electrostatic potential (MEP), and the antitumor activity shown by these compounds. The results show that the second conformation is about 7.0 kcal mol-1 higher in energy and possibly is an inactive conformation as no correlation has been found between the antitumor activity and the MEP features. In addition, a detailed comparison with the first conformation, which is probably the active conformation, has been made of the geometry, the total energy, the Mulliken charges on some important atoms, hydrogen-bonding effects, and the MEP minima and isosurfaces. The role of the hydrogen-bonding effects, which was unclear in our previous work, is clarified in this work. The possible molecular basis of the antitumor activity is suggested. © 1996 John Wiley & Sons, Inc.

Notes: The calculation of group electronegativity and hardness for amino acid “functional groups,” considered as a biradical taken out of their protein environment, is performed for both the α-helix and β-sheet geometry of these amino acids. Group electronegativity and hardness are then used to interpret the experimental gas-phase proton affinity sequence of the amino acids. Group hardness was found to play the dominant role, whereas group electronegativity only had a minor influence on the sequence, thereby stressing the importance of the charged form in the acid-base equilibrium. An explanation for the deviations, seen for some of the amino acids, from the correlation between these group properties and the proton affinity was sought. © 1996 John Wiley & Sons, Inc.

Notes: For intermolecular perturbation theories in which it is assumed that the unperturbed wave function of the composite system is a product of the unperturbed wave functions of its components, and which satisfy one general constraint, we derive two renormalized interaction energy expressions which are more accurate than the perturbation expansions, when all are evaluated to comparable order. This is accomplished by focusing on the parameter λ in terms of which the perturbation expansions are derived rather than on the potential of interaction between components. In the derivation of each renormalized energy formula, we discard zeroth- through infinite-order terms which do not contribute to the interaction energy when the interaction is turned on fully, i.e., when λ = 1. The first renormalized interaction energy when λ = 1 is identical in form to the interaction energy in the symmetrized Rayleigh-Schrödinger (SRS) theory, but not in interpretation. The wave function appearing in the renormalized energy cannot generally be that assumed in the SRS theory, and the renormalized energy to zeroth order in λ is not zero. The latter is not surprising because we discarded a zeroth-order term in the derivation. The second renormalized interaction energy formula is derived from the first by using the same set of assumptions and arguments that were used in deriving the first. We expect it to be more accurate than the first, which is expected to be more accurate than the sum of the perturbation energies, all evaluated to comparable order. These expectations are supported by the results of calculations on LiH using two perturbation theories, the polarization approximation and the Amos-Musher theory. The first-order wave functions for both were calculated in the configuration interaction (CI) approximation; then the interaction energies were calculated by summing the perturbation energies through third order and by evaluating the renormalized energy expressions. The perturbation results are compared to interaction energies calculated by full CI with the same basis set. As important as the formulas is the light our analysis throws on the meaning of order in intermolecular perturbation theory. © 1996 John Wiley & Sons, Inc.

Notes: Reaction energetics of the highly strained tetrahedrane molecule, as well as some smaller hydrocarbons, were computed at the ab initio MP4, QCISD (T), G1, and G2 levels and also by several density functional (DF) approaches: VWN(LDA), PW86, BLYP, and B3LYP. A variety of basis sets were used in the DF calculations. For atomization processes, nonlocal DF procedures are superior to MP4 and QCI. For the other reactions, B3LYP is the most reliable DF approach and is overall competitive with MP4 and QCISD (T), although the MP4/6-311G(2df, p) results are generally the closest to the experimental and/or the G2 values. There is no consistent correlation between the accuracy of the DF results and the size of the basis set. © 1996 John Wiley & Sons, Inc.

Notes: The π-allyl insertion mechanism of the 1,4-cis polymerization of butadiene by means of allyl-nickel catalysts has been studied theoretically by density functional theory (DFT) for the ligand free cationic butenyl nickel(II) complexes [Ni(C3H5)(C4H6)]+, I, [Ni(C3H5)(C4H6)(C2H4)]+, II, and [Ni(C7H11)(C4H6)]+, III. DFT energy profiles have been determined for the insertion of s-cis-butadiene into the anti-η3-butenyl nickel(II) bond in the supine and prone orientation of the reacting ligands. One of the objectives of the study was to support the proposed π-allyl insertion mechanism. With increasing size of the model compound there is better agreement between the calculated reaction and activation energies in relation to the known experimental behavior. Among the different arrangements (anti- or syn-butenyl) of the allylic end of the growing polymer chain and the relative orientation (supine or prone) of cisoid butadiene at the catalytic site, the anti-butenyl/prone reacts in compound III with a small activation barrier (8.2 kcal/mol) to the product (-5.7 kcal/mol). The stabilizing effect of the coordination of an additional double bond of the growing polymer chain for the correct description of the geometrical and energetical aspects of the insertion reaction was demonstrated by II. The results support the s-cis-butadiene insertion into the anti-η3-butenyl nickel(II) bond according to the proposed π-allyl mechanism. © 1996 John Wiley & Sons, Inc.

Notes: Many applications involve the use of macromolecules at interfaces, including adhesion, lubrication, and the manufacture of surfaces resistant to wear. Modeling these systems requires an understanding of how the dominant conformational features of a macromolecule are modified by the presence of a boundary. In this work, we are interested in monitoring the shape changes that accompany the configurational rearrangements of a single polymer chain near a hard plane. We provide a detailed characterization of essential molecular shape features of compressed grafted chains. These chains are modeled by three-dimensional (off-lattice) walks with excluded-volume interaction, anchored to a flat surface by a terminal point. Compression is induced by confining the chains between two parallel walls. For these systems, we have studied how shape descriptors depend on polymer size and the separation between walls. We show that compression causes a number of nontrivial changes in shape (shape transitions). In particular, we show that the most compact chains found during compression are neither spheroidal nor maximally self-entangled. Maximal entanglements are found in chains that are already mostly “flattened” toward the surface. The present results provide new insights that can be useful in the design of interfaces with targeted properties. © 1996 John Wiley & Sons, Inc.

Notes: We present electronic and structural parameters for bulk rutile (TiO2) determined by means of different theoretical methods, namely, the periodic Hartree-Fock approach, subsequent post-Hartree-Fock density functional correlation correction, and a linear-combination-of-atomic-orbitals approach based entirely on density functionals. Differences between the use of effective core potentials, a frozen-core treatment, and all-electron calculations are investigated. © 1996 John Wiley & Sons, Inc.

Notes: The distinction between a finite system - however large - and an extended one is emphasized. The implications of the very different types of boundary conditions imposed on wave functions for such systems are discussed as well as the role of the long-range Coulomb potential in the two types of systems. © 1996 John Wiley & Sons, Inc.

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Notes: The Ghosh-Berkowitz-Parr macroscopic thermodynamic description of an electronic ground state is reviewed. The information entropy defined in this theory is calculated for several atoms using Hartree-Fock and double-zeta wave functions. It is shown that the information entropy is a measure of wave function quality provided that a particularly preferred definition of the local kinetic energy density is implied. © 1996 John Wiley & Sons, Inc.

Notes: The size consistency property of a general algebraic propagator method referred to as intermediate-state representation (ISR) is discussed. In this method intermediate states |Ψj constructed by a specific orthonormalization procedure from the set of “correlated excited states” Ĉj|ΨnN are used to represent the Hamiltonian Ĥ. Here Ĉj denotes a physical excitation operator and |ΨnN is the N-electron ground state. The ISR secular equations are shown to be separable, that is, they decouple into independent (local) sets of equations for a system consisting of noninteracting (separate) fragments. This result follows from a general factorization theorem for the intermediate states. Separability is a sufficient condition for size consistency. © 1996 John Wiley & Sons, Inc.