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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Notes: The structure and electronic structure of heavy-group V cluster anions (Sbn-, Bin-) are calculated with density functional methods within the local spin density approximation (LSDA). The influence of gradient corrections of the exchange and correlation energy is investigated. The calculated vertical and adiabatic ionization energies are in very good agreement with data from photoelectron spectroscopy (PES) for Sbn-, whereas the relatively large deviations for Bin- can be reduced by the consideration of relativistic effects in a scalar-relativistic manner. Concerning the structures, a strong similarity to the corresponding Pn- clusters was found. In particular, the negatively charged pentamers are planar rings (with similarities to the aromatic [C5H5]- anion) with especially high ionization energies. © 1995 John Wiley & Sons, Inc.

Notes: This article considers two types of 2 × 2, 3 × 3, 4 × 4, and 5 × 5 determinantal inequalities. One type involves Gram determinants, while the other type involves determinants based on a theorem by Pólya and Szegö. The elements of the first type of determinants are 〈rn〉, while the elements of the second type of determinants are c 〈rn〉, where c = 3 + n, and r is the distance from the nucleus of an atom. Both types of determinantal inequalities are used to obtain lower-bound (LB) estimates of 〈1/r〉 for atoms of spherical symmetry. The inequalities involving Gram determinants have been applied previously by the author to atoms of spherically symmetric charge distributions, such as He, Ne, Ar, Kr, Xe; Li, Na, K, Rb; Be, Mg, Ca, Sr. In the resent article, the inequalities involving determinants based on the Pólya and Szegö theorem are applied to the same atoms. It is found that in both cases the LB values of 〈1/r〉, for all atoms considered, appear to converge to the quantum mechanical (QM) values of Boyd, who calculated them with the Roothan-Hartree-Fock wave functions of Clementi and Roetti. It is also found that the LB values of 〈1/r〉, using determinants based on the Pólya-Szegö theorem, converge “faster” to the QM values of 〈1/r〉 than do the LB values of 〈1/r〉 based on Gram determinants. © 1995 John Wiley & Sons, Inc.

Notes: The Shannon information entropies of H2, C2, HF, OH, CH, CN, HOOH, C2H6, MeOH, CH3OCH3, CH3F, CH2O, CH3NH2, and C2H4F2 in both position and momentum space were calculated from HF/6-31G* wavefunctions. The results show that there were definite patterns between the information entropies, molecular geometric changes, and energies. The L1, L2, and 1d, measures were compared as effective measures of distance and with energetic changes. The use of these concepts in describing chemical structure is discussed. © 1995 John Wiley & Sons, Inc.

Notes: We present the results of calculations of the static longitudinal polarizability of model molecular hydrogen chains of increasing length using density functional methods. The study considers the performance of different functionals, different basis sets, and the influence of the degree of bond length alternation. Significant differences in the asymptotic values are obtained in comparison with recent studies which have rigorously assessed the effects of more traditional methods of taking into account electron correlation corrections on coupled Hartree-Fock results. © 1995 John Wiley & Sons, Inc.

Notes: After a short survey of currently available routes for constructing an idempotent firstorder density matrix as a function(al) of its diagonal element, the electron density p(r); recent progress will be surveyed with specific reference to the exchange potential in (a) the Be atom and (b) in the jellium and Bardeen models of a metal surface. In both examples the off-diagonal density matrix is expressed in terms of its diagonal density only. Finally, a brief discussion will be given of the way the exact exchange-correlation potential can be written in terms of higher-order density matrices, the idempotency condition on the first-order density matrix γ now being replaced by the inequality γ2 〈 γ. © 1995 John Wiley & Sons, Inc.

Notes: Using the Bixon-Jortner Hamiltonian as a model of a discrete system, we compare the decay of a prepared state into an infinite, discrete manifold with similar decays into large but finite systems. We find that the differences between these two types of systems are strongly related to the number of manifold states. © 1995 John Wiley & Sons, Inc.

Notes: The stopping of energetic ions by ultrathin films is of interest, as such films are mesoscopic structures which comprise the delamination limit of crystals, and as they are of practical interest because of their connection to microelectronics. A matter of special interest is the effect of the number of target layers on the stopping. Here we show that the stopping cross-section, S(N, v), of a system of N layers for projectiles with velocity v is a linear function of N-1 for small N. Such behavior would be expected for N → ∞, in which case the constant term would be the bulk crystalline cross section at the specified projectile velocity and the coefficient of the linear term would be the lowest-order surface correction. Surprisingly, the constant coefficient from a small N fit is reasonably consistent (within limits of imprecision) with the crystalline cross section. This linear scaling of S with N-1 for small N tracks the scaling behavior of the cohesive energy of the films. We discuss the physics and provide some illustrations. © 1995 John Wiley & Sons, Inc.

Notes: Using modified MNDO and AM1 semiempirical self-consistent-field molecular orbital methods in the cluster approach, we investigated the environmental influence on the mechanical properties of solids. The computational approach of the chemical reaction coordinate was developed for the study of mechanical deformation. The modeling of different types of deformation was considered. To test the validity of the method, we investigated the mechanical properties of simple hydrocarbon chains and silica systems. Uniaxial deformation and bending were considered for the heptane molecule. Verification of the mechanochemical calculations for polypropylene was fulfilled by analyzing its vibrational spectra. It was found that the influence of active medium particles (water, hydroxonium ion, surfactant) may have caused a sharp decrease of the strength of silica and hydrocarbons. The atom-level mechanism and some qualitative characteristics of these processes were studied. © 1995 John Wiley & Sons, Inc.

Notes: Ab initio calculation of periodically Si-δ-doped GaAs was performed in the regime of high-donor concentration. The electronic confinement exhibit a quasi-2D behavior even for small periods (p = 45 Å). The electronic properties of the clustering SiGa—SAs also was studied. © 1995 John Wiley & Sons, Inc.

Notes: The reaction of the PtSn system with the hydrogen molecule is studied theoretically. The results are compared with experimental reports of commercial-type catalysts and previous theoretical studies of Pt + H2 and Pt2 + H2 reactions. All the calculations were made by the ab initio MC-SCF + MRCI method including relativistic core potentials approximation. We consider two main geometrical approaches of the hydrogen molecule to the SnPt system: parallel and perpendicular. The theoretical and geometrical parameters were taken from our previous studies and from experiments. Many states were studied: Some of them are repulsive and others present weak capture of hydrogen; none scisse the H2 molecule. The main conclusion of this work is that the platinum activity, when Pt and Sn form alloys, is inhibited by the tin, suggesting that the interaction between the two metals occurs through an oxygen atom of the support. © 1995 John Wiley & Sons, Inc.

Notes: The factorization of amplitudes of multiple excitations from those of elementary (single and double) excitations is only reliable when excitation energies are nearly additive. Such deviations from additivity may be important, especially in solid-state physics problems. Instead of introducing many-body operators in the coupled-cluster expansion, one may take into account the effect of these deviations from the additivity of excitation energies by proper energy-dependent corrections to the usual product of amplitudes. Their efficiency is illustrated on several model problems where the traditional approach gives poor results. © 1995 John Wiley & Sons, Inc.

Notes: This communication compares three different approaches to the study of ammonia protonation in acidic chabazite: the cluster model, the supercell model, and the embedded cluster model. In all cases, the Hartree-Fock approximation has been adopted, and a minimal Slater-type orbital basis set has been used. To calculate the interaction energies of ammonia by means of the periodic model, the CRYSTAL92 program has been used. The same program has been employed to generate the Madelung field in which a molecular cluster may be embedded. It also provides the reference solution necessary for the embedded cluster model calculations, which in turn have been performed with the EMBED93 program. All three techniques lead to similar interaction energies; however, the embedded cluster approach allows for the most natural way of performing the present adsorption study. Only those atoms which are chemically involved in the interaction have to be treated explicitly, while the rest of the system, though chemically inert, is treated as a consistently described background acting on the adsorption complex. The present investigation suggests that cooperative interaction between molecules trapped in the cavities of zeolites is of crucial importance for the protonation of ammonia to occur. © 1995 John Wiley & Sons, Inc.

Notes: Schrödinger equations for relativistic atoms and molecules are derived from first principles with the aid of quantum electrodynamics. © 1995 John Wiley & Sons, Inc.

Notes: The analysis of the Zeeman effect in diatomic molecules gives rise to parameters that describe small but significant deviations of the molecular electronic g-factor from its free electron counterpart. In order to account for these deviations, correction terms to the standard Zeeman Hamiltonian have been evaluated in first-order perturbation theory. Results obtained from SCF and correlated multi-reference configuration interaction wavefunctions are presented for the molecules NO, O2, and SO. © 1995 John Wiley & Sons, Inc.

Notes: A rational, closed-form Hamiltonian formulation of quantum electrodynamics is presented in a Gaussian basis representation, obtained using a discretized light-cone field quantization method. This approach illustrates the possibility that traditional methods of quantum chemistry may become applicable for the nonperturbative treatment of problems currently accessible only perturbatively if at all, as for example relativistic many-electron interactions in atoms and molecules. © 1995 John Wiley & Sons, Inc.

Notes: The approach of Gross, Oliveira, and Kohn for fractionally occupied states of ensembles is applied to determine ensemble exchange potentials for multiplets. A recently proposed method of the author is used to construct exact ensemble exchange potentials of multiplets. © 1995 John Wiley & Sons, Inc.

Notes: We have used several different methods to solve the one-dimensional, time-dependent Schrödinger equation for a sinusiodally modulated barrier. Analytical solutions are given for the case in which the time-dependent part of the potential has several different forms, but is independent of position. For more general fields, Floquet's theorem is used to write the wavefunction as a summation of components which have different energies as a result of the absorption and emission of modulation quanta. A system of coupled ordinary differential equations is obtained, which is then solved numerically using shooting methods. The examples show a resonance in which the tunneling current is markedly increased. For square barriers, this resonance occurs when the particles absorbing modulation quanta are above the barrier, and the length of the barrier is an integer multiple of one-half the de Broglie wavelength. The existence of the resonance is confirmed by asymptotic solutions for large and small frequencies. Examples suggest that it may be possible to make a microwave power amplifier by illuminating a field emitter array with an amplitude-modulated laser operating near the new resonance. © 1995 John Wiley & Sons, Inc.

Notes: The generalized valence bond method is extended for use in electronic structure calculations of two-atomic molecules made up of the heavy atoms. By applying a purely numerical Hartree-Fock (HF) or Dirac-Hartree-Fock (DHF) basis set, we were able to efficiently produce the potential curves for a large range of the interatomic distances. The configuration interaction and nonorthogonal basis sets are used to obtain an accurate solution for the realistic molecular systems. Adaptation for parallelism allows the simulation to be partitioned and carried out on the coupled multiprocessor network (SP-2) at the NIST. Calculations have been performed for Na2 and In2 quasi-molecules in excited states. © 1995 John Wiley & Sons, Inc.

Notes: We present a formulation of the nonequilibrium solvation problem for the polarizable continuum model (PCM) computational scheme. The solvent is represented by a linear and homogeneous dielectric, characterized by a partition of the medium polarization vector P into a slow and a fast component: P = P8 + Pf. The formalism is expressed in terms of the “direct-BEM” PCM procedure, exploiting the stationarity condition of the free-energy functional of the solute-solvent system in a boundary element method (BEM) computational approach. It parallels a preceding version [Aguilar et al., J. Chem. Phys. 98, 7375 (1993)] based on an iterative PCM procedure. The present version is more convenient for the use of the coupled perturbed Hartree-Fock formalism. The application to the evaluation of the frequency-dependent molecular polarizability is presented as an example. © 1995 John Wiley & Sons, Inc.

Notes: This article presents an object orientated approach to the calculation of quantum chemical quantities, specifically Møller-Plesset second- and third-order energies. Blocking and index symmetry is used to take advantage of the sparsity of the data structures. The two main classes, Arrays and BlockArrays, are presented along with a sample code segment. While this code has been specifically used to calculate quantum chemical quantities, the code has been made general enough to be of use in other computational settings. © 1995 John Wiley & Sons, Inc.

Notes: We describe the design philosophy, structure, and supporting tool kits of the NWChem computational chemistry package. The primary purpose of this effort was to develop efficient parallel algorithms for a broad range of methods commonly used in computational chemistry. To facilitate this, we developed a shared nonuniform access memory model which simplifies parallel programming while at the same time providing for portability across both distributed- and shared-memory machines. In addition to this specific focus on parallelization, a substantial effort has been made to simplify the general problem of large-scale software development, which is common to many research groups. We find that this simplification can be achieved through judicious use of ideas from the computer science field of software engineering in the design and implementation of the program with minimal extra effort on the part of the chemist. © 1995 John Wiley & Sons, Inc.

Notes: We present the results of ab initio calculations on the first-, second-, and third-order molecular polarizabilities of urea. An efficacious general finite field perturbation approach, previously applied in the case of paranitroaniline, is extended to the evaluation of axial and nonaxial components of the nonlinear responses. The validity of our numerical procedure is examined at the Hartree-Fock level of theory by comparison with analytical derivative results. The impact of electron correlation is analyzed, by calculating the optical nonlinearities at the Moller-Plesset perturbation theory level. The second-order Moller-Plesset electron correlation correction is shown: (i) to enhance the third-order polarizability y by almost a factor of 2 and (ii) to include the major correlation effects as consideration of the fourth-order correction further improves the y components by less than 20%. We also discuss the frequency-dependence of the nonlinear optical properties of urea by presenting calculations of the dynamic components at the noncorrelated level of theory for different optical processes. © 1995 John Wiley & Sons, Inc.

Notes: Semiempirical-FF calculations were performed for the second-order hyperpolarizabilities 〈γ〉 of a series of polycyclic aromatics to examine the structure-optical-propertyrelationship. First, 〈γ〉 of the unsubstituted PAHs were presented. For linear polyacenes, 〈γ〉 and total resonance energy were found to be increased while the HOMO-LUMO gap and resonance energy per electron decreased as the number of six-membered rings increased. For nonlinear PAHs, the chain topology should be taken into consideration. An empirical formula was given to relate the computed 〈γ〉 and linear polarizabilities 〈α〉. 〈γ〉 of mono- and di-substituted PAHs were then presented to examine the substituent effects on 〈γ〉. © 1995 John Wiley & Sons, Inc.

Notes: A theoretical study was performed to design a method for predicting the intercalation behavior of lithium ion and aromatic organic cations into a graphite lattice. The purpose of these predictive capabilities is to provide fundamental information on the molecular interactions in graphite intercalates for optimization of electrodes in rechargeable batteries. The graphite sheet system was modeled on a workstation using MOPAC 93 to observe possible structural changes in the graphite following an intercalation process as well as any molecular orbital interactions between the graphite and the cation. Initial modeling of the graphite sheets used lithium intercalated graphite (LIG) as a benchmark. The results indicate that a complex graphite system can be modeled simply and effectively using semiempirical methods for the study of the intercalation-deintercalation behavior of ions. © 1995 John Wiley & Sons, Inc.

Notes: A modified derivation of the free energy perturbation (FEP) equation leads to a more general interpretation of the procedures for generating the geometry of a perturbed molecule from the reference one in FEP simulations of flexible systems. Using this form of the equation, it is possible to implement a wide variety of procedures which heretofore would have been considered impossible. A new method, generalized alteration of structure and parameters (GASP), has been implemented in the BOSS program and has been found to be more efficient for perturbations of harmonic degrees of freedom than the commonly adopted procedure. Additionally, an extreme example for which the new procedure proves less satisfactory is presented, and a more efficient method which is also derived from the new form of the FEP equation is devised and tested. It is concluded that the key to a convergent FEP method is efficient sampling of low-energy configurations of the perturbed state; the new form of the equation suggests ways of generating such configurations. © 1995 by John Wiley & Sons, Inc.

Notes: We present a robust and efficient numerical method for solution of the nonlinear Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact-Newton method, combined with linear multilevel techniques we have described in an article appearing previously in this journal. A detailed analysis of the resulting method is presented, with comparisons to other methods that have been proposed in the literature, including the classical nonlinear multigrid method, the nonlinear conjugate gradient method, and nonlinear relaxation methods such as successive overrelaxation. Both theoretical and numerical evidence suggests that this method will converge in the case of molecules for which many of the existing methods will not. In addition, for problems which the other methods are able to solve, numerical experiments show that the new method is substantially more efficient, and the superiority of this method grows with the problem size. The method is easy to implement once a linear multilevel solver is available and can also easily be used in conjunction with linear methods other than multigrid. © 1995 by John Wiley & Sons, Inc.