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Notes: We analyze the theoretical basis of a procedure to determine an unknown normalization factor in discretized wave functions, which we have successfully used in a series of calculations of resonance widths for atomic and molecular systems. By reducing this determination to that of a suitable interpolation function for the energy eigenvalues, the problem is easily solved when atomic basis sets are chosen according to simple rules. Illustrations of our procedure are presented for atomic, molecular, and model systems; renormalized wave functions are compared with the exact ones for these model systems. The resulting method of renormalized continuum wave functions has a wide range of application in the study of long-lived quasibound states (predissociation, autoionization, photoionization, unimolecular reactions, etc.).

Notes: Transmission of vibrational excitation energy conserved in cis-conformation of retinal to the outlet proton channel is considered from the perspective of quantum theory. A distribution of vibrational excitations in the channel is found; it allowed to calculate the magnitude of the directed drift proton current. The differences between velocities of proton movement in active and passive channels are considered. A transition of retinal from cis- to all -trans- conformation with the subsequent capture of proton by Schiff base out of the inlet channel is described. The lack of proton in this channel, i.e., in the H-bonded chain, is eliminated at the expense of the capture of a proton out of the cytoplasmic water enviroment. The correspondence between theoretically established states and spectroscopically identified forms of bacteriorhodopsin (inter-mediates L, M, N, and O) is proposed.

Notes: The generating functional Z(N) of the molecular orbital theory of N electrons has been projected into a subspace of atomic orbitals. By application of the saddle-Point approximataions to the corresponding effective action, a set of equations of motion results. These equations are the classical Roothaan's equations of quantum chemistry.

Notes: The recently developed integral discretization technique for the generator coordinate method is applied to discuss some features of Gaussian expanded wave functions. Using the hydrogen atom ground state, it is shown that the nuclear cusp problem has an interesting relation with the generator coordinator weight function, which allows the production of accurate wave functions by an integration criterion.

Notes: The two-dimensional (2D) band structure of (polyphthalocyaninato)Ni(II), Ni(ppc), has been analyzed by a self-consistent field (SCF) Hartree-Fock (HF) crystal orbital (CO) formalism based on an INDO (intermediate neglect of differential overlap) type Hamiltonian. The calculated HF band gap of Ni(ppc) amounts to 0.24 eV. The highest filled band is a ringlike a1u combination (D4h symmetry label) localized at the carbon sites of the organic fragment. Remarkable hybridization in the valence band leads to the considerable band width Δ∊v of 2.92 eV. This value is close to the Δ∊v numbers which are conventionally encountered in one-dimensional metallomacrocycles. The effective width of the states in Ni(ppc) is 13.8 eV. In graphite a net π interval of 13.0 eV is predicted by the present CO formalism; i.e., the energetic distribution of the π electrons is roughly comparable in both 2D solids. The Ni 3d states in Ni(ppc) are far below the Fermi level which is calculated at -4.9 eV; they are predicted between -12.2 and -16.4 eV in the mean-field approximation. Quasi-particle corrections lead to a significant shift of these strongly metal-centered states. Important electronic structure properties of Ni(ppc) are compared with those of 1D metallomacrocycles with similar molecular stoichiometry. The total density of states distribution of Ni(ppc) has been fragmented into projected (ligand π and σ, Ni 3d) contributions in order to allow for a transparent interpretation of the 2D band structure.

Notes: Conformational preferences of the hypermodified nucleic acid bases N6-(Δ2-isopentenyl) adenine, (i6Ade) and its 2-methylthio derivative (ms2i6Ade) have been investigated theoretically by the quantum chemical perturbative configuration interaction using localized orbitals (PCILO) method.The predicted most stable conformation of i6Ade and ms2i6Ade are such that the isopentenyl substituent is oriented away from the imidazole moiety of the adenine ring. The atoms N(6), C(10), and C(11) remain coplanar with the adenine ring for both molecules. However, in contrast to the predicted cis orientation of the C(10)—C(11) bond with respect to the C(6)—N(6) bond in i6Ade, the trans orientation is favored for ms2i6Ade. The plane of the isopentenyl group is rotated by 120° from that of the purine base in i6Ade, whereas rotation by 60° is favored in ms2i6Ade. The favored orientation of the methylthio group with respect to the C(2)—N(3) bond is trans; however, the alternative cis arrangement is also quite probable. The conformational implications of the methylthiolation of the isopentenyladenine are brought out in the context of the considerably large range of accessible (β,γ) and χ orientations. The compatible roles of i6Ade and ms2i6Ade in tRNA are thus understood, besides their distinguishing features.

Notes: The theory of the Baker-Gammel approximants is applied to the spectral density function associated with the adjacency matrix. As a result, various upper and lower bounds to topological invariants are obtained in a systematic manner. In particular, the (N, M)-type lower bound to the total π-electron energy of benzenoid hydrocarbons is derived for the first time.

Notes: It is shown that the Coulson-Rushbrooke theorem for odd alternant hydrocarbons [15] can be generalized for some classes of nonclassical systems containing heteroatoms. The energy spectrum of such conjugated polymers containing heteroatomic groups, in particular a nitroxide group 〉N—O, is analogous to that studied [1-4] in homonuclear alternant nonclassical polymers, whose ground state is characterized by maximum spin multiplicity. Their band structure is characterized by a wide energy gap, in the middle of which there is a band of degenerate or nearly degenerate quantum states.The presence of a narrow band of degenerate quantum states, the Hund rule, and the alternant character of the polymers of this group determine the maximum multiplicity of their ground state and may give rise to the creation of magnetic order in such compounds, if interchain correlations occur. This is in line with the investigations in Refs. 1-11.

Notes: The quasi-relativistic CNDO/1 method for molecular orbital calculations has been extended to the INDO/1 version where all monocentric repulsion integrals are taken into account. This version has been applied to calculate molecular geometries of MXn-type molecules, with the central atom belonging to from the second to seventh period. Properties of hypothetical superheavy elements (Z = 110-117) have been predicted. Transition metal complexes of the MCl42--type (M = Ni, Pd, Pt, and ePt) have been investigated from the point of view of spin-state and configuration stability.

Notes: The effect of basis set contraction and elimination of primitive Gaussian orbitals on the He2 interaction energy components have been studied within the SCF counterpoise corrected approach supplemented by a dispersion term calculated within the variation-perturbation scheme. Despite elimination of almost half of the primitive Gaussian functions from the saturated sp basis set and complete contraction of the remaining ones, the components of interaction energy in He2 suffer a remarkably small loss of accuracy except for the short range charge transfer contribution.

Notes: We have recently developed a new classification of the amino acid side chains based on doublet acceptor energy levels (DALs). These energy levels, taken as the eigenvalue of the highest occupied molecular orbital in the radical anion, provide insight into the shape of the tunneling barrier in protein electron transfer. We have used this classification to characterize several transfer pathways in myoglobin. We present here a study of the effect of changes in geometry on the doublet acceptor levels. We find that, in general, this influence is rather small for reasonable changes in bond lengths and angles (e.g., those resulting from thermal fluctuations in the protein structure). However, we have found that for serine, threonine and water, changes in geometry that might take place as a result of fluctuations in hydrogen bond geometries lead to rather large changes in DAL. We investigate these correlations in some detail. The relation between protein fluctuations and changes in the shape of the electron tunneling barrier is discussed. Additionally, based on the energetics of changes in the OH bond distance, we discuss aspects of the relation between electron transfer and proton transfer.

Notes: This short communication outlines preliminary work aimed at understanding the recognition of sialylated oligosaccharides by influenza virus haemagglutinin. Initial efforts to model the complex have used the electrostatic interactions between atoms in the binding pocket and (2) as a means of constraining the conformational search in docking these two molecules. Some important features of the lowest energy structure are discussed.

Notes: Ab initio calculations reveal that a cation, in a position equidistant from the two H-bonding oxygen atoms of (HC(OH)O · H · OH2)+, acts to push the proton from HCOOH toward OH2 if the ion is located near the  - OH or C—H group of HCOOH. In contrast, rotation of the cation out of the HCOOH plane, while maintaining its position relative to the two H-bonding atoms, leads to a potential which is little different than that observed in the absence of an ion. These findings are readily explained on the basis of ion-induced internal polarization of the subunit to which the ion is closer. Replacement of OH2 by HCOOH suggests that polarization of the more distant subunit can also be a factor.

Notes: In this work the problem of normal vibrations of a molecule isolated in the argon gas and nitrogen gas matrix is considered. Modification of a valence force field to this problem is described, allowing the use of Lennard-Jones-type pair potentials for molecular-matrix and matrix-matrix interactions. For the selection of molecular-matrix pair potential parameters, the procedures based on combination rules are employed. To obtain the vibrational frequencies a monosubstitutional site in the crystal of an argon gas or a nitrogen gas is chosen as the most probable trapping site for the hydrogen cyanide molecule in the matrix of them. A pseudolattice method is applied to cubic 12 argon or nitrogen crystal fragments in order to eliminate the edge effect; we can obtain good results.

Notes: Since the introduction of dynamical simulated annealing (DSA) by Car and Parrinello in 1985, there has been growing interest in the use of nonlinear optimization to perform electronic structure calculations. We review here the complementary method of steepest descents (SD), a first-order treatment designed for local optimization. Modifications are discussed to adapt SD to a supercell treatment of metallic systems using a plane wave basis. An application to the Zintl phase compound NaTl is presented. The application of separable nonlocal pseudopotentials to improve this momentum space formalism is discussed.

Notes: Structural and energetic results are reported from a series of ab initio calculations on ground state CuCl2-4 in D2d and D4h conformations. All-electron Hartree-Fock calculations including geometry optimization have been carried out with large basis sets reaching triple-zeta valence plus f-function quality. Several ab initio effective core potentials and valence basis sets for Cu and Cl have been tested and evaluated based on comparisons of calculated results obtained at the Hartree-Fock or correlated (Moller-Plesset perturbation theory) levels with the all-electron and experimental data. The optimized structural parameters provided by all-electron or effective core potential methods are very similar, but they differ from averaged experimental data. Thus, the calculated CuCl bond lengths are typically 0.15-0.20 Å too large, and the ClCuCl bond angle (D2d) is 10-15° too small. The square planar (D4h) conformation represents a transition state and not a structural minimum for CuCl2-4. The energy difference between the two conformations (D4h - D2d) is consistently 16-18 kcal/mol at the Hartree-Fock level but approaches 10-12 kcal/mol at the highest levels of theory applied (UMP4(SDTQ)).

Notes: By calculations on CuCl2-4, CuBr2-4, and NiO10-6 clusters it is shown that a first-order configuration interaction (CI) calculation significantly improves the d-d and charge transfer (CT) spectra of ionic transition metal compounds. The first-order CI introduces delocalization (covalency) effects in the dn states, thus increasing the effective ligand-field splitting which is always underestimated at the Hartree-Fock (HF) level. It is demonstrated that this HF + first-order CI treatment is strongly related to a valence bond model. In this model the delocalization is introduced by explicit interactions with relaxed CT states. After account has been taken of the physically very different atomic correlation effects, a very good agreement with experimental d-d spectra is obtained, using only a small cluster. The effect of first-order CI on CT states is to account for hole localization and polarization effects which lead to reductions in the CT excitation energies in the order of 2-3 eV.

Notes: The known bounds on the eigenvalues of 2-Fermion reduced density matrices may be improved by considering unitarily invariant properties of the associated natural geminals and of the system 1-Fermion reduced density matrix. The polynomial invariants are particularly important, since they may be introduced systematically according to the degree of the polynomials.

Notes: We have extended the study of the description of local correlation effects provided by the different partitions of a configuration interaction (CI) wave function to the first excited state of the helium atom. Our analysis makes use of the local mean values of different moments of the interelectronic distance computed with the CI partitions as well as with Hartree-Fock and Hylleraas-type wave functions.

Notes: The resolution of a double determinant into a sum of spin-free orthogonal spin eigenfunctions is presented; its equivalent resolution of a spin function product θM0 is also given. Furthermore, a more general resolution of a Slater determinant into all spin eigenfunctions with S ≥ M is also obtained. Present work has also provided a method to calculate the linear coefficients in the expression of the primitive θMi in terms of the linear combination of spin eigenfunctions X̃NK (S, M).

Notes: An adiabatic formalism in the degenerate or quasidegenerate subspaces, which does not depend on the particular form of the switching function g(α, t), is outlined. A general factorization theorem for the dynamic operator Sα(t, t0 | g) is proved. This theorem enables one to formulate the perturbation expansion for the effective Hamiltonian and the wave operator which is free from the adiabatic divergencies.

Notes: A new definition of a canonical set of bonded functions has been introduced. For a given configuration with r singly occupied orbitals and given multiplicity, the set exhibits symmetry properties of a group of order r. It simplifies the evaluation of the energy matrix H as well as the orthogonalization procedure.

Notes: Recently, Perdew and Wang presented an expression for the exchange energy of a many-electron system. This functional has been adapted in the present work in variational density functional calculations of the total atomic binding energy of the Ne atom. For this atom similar calculations have been done earlier using the Dirac expression for the exchange energy. Three different total energy functionals have been considered: (1) the Thomas-Fermi-Perdew-Wang functional, (2) the above functional augmented by (1/9) of the original Weizsäcker correction to the Thomas-Fermi kinetic energy, and (3) the same functional as in 1 augmented by (1/5.3) of the original Weizsäcker correction to the Thomas-Fermi kinetic energy. The electron (number) density of the Ne atom has been constructed from hydrogen-like one-electron wave functions containing three variational parameters. Each of three total energy functionals have been minimized with respect to these parameters. Comparison of the Perdew-Wang and Dirac exchange energies shows that, in each of the three model pairs, the Perdew-Wang exchange energy is larger in magnitude than the Dirac exchange energy. It is also found that the exchange energy obtained by 2, -12.31 a.u., is in excellent agreement with the value of -12.22 a.u. calculated by Perdew and Wang with the Clementi and Roetti near-Hartree-Fock density.

Notes: The distribution of energy levels of an N-identical-particle system among the irreducible representations of the permutation group is examined for a “spin-free” problem. There are calculated the sums of powers of the eigenenergies obtained from the original N!-fold degenerate energy level when the interaction between the particles is switched on. The first-order perturbation theory is applied. Some results of the present approach are shown to be equivalent to the results of the Weyl's theory of the permutation group. The distribution of energy levels is found to be symmetric with respect to the average energy level belonging to a self-conjugate representation. For a special case of the Coulomb interaction the wave function of the highest level is fully symmetric, whereas that of the lowest level is fully antisymmetric with respect to the interchange of the coordinates of any two particles. The average energy and the dispersion of the levels belonging to a given representation are calculated for some N.

Notes: It is shown how the properties of the one-particle Green's function lead naturally to the definition of the so-called natural energy orbitals. These orbitals allow the fully correlated total energy of a system to be written in Hartree-Fock-like fashion and might therefore provide a bridge between sophisticated correlated wave functions and approximate theories of chemical structure and reactivity based on a Hartree-Fock-like energy expression. Moreover these orbitals form the basis for a self-consistent scheme to calculate the one-particle Green's function. The relation between these natural energy orbitals and the extended Koopmans' theorem is considered. Finally it is shown that the exactness of the lowest extended Koopmans' ionization potential implies the linear independence of the corresponding Dyson orbital from all other Dyson orbitals.

Notes: The shape wave u(r) is defined in such a way that the square of its absolute value gives the shape of the electron charge density for a nonrelativistic many-electron system: |u(r)|2 = ρ(r)/∫ρ(r) dr, where ρ(r) is the total electron charge density. The u(r) is treated as the probability amplitude for the shape of the electron charge density in the real three-dimensional space. The secular equation of the u(r) is given as L(r)u(r) = λu(r), where L(r) and λ are a real Hermitean operator and the eigenvalue, respectively. This equation has the form of the spinless one-particle Schrödinger equation. The potential is local and is a functional of ρ(r), and so we need a self-consistent field procedure to solve it. For equilibrium state shape wave u = ueq, which is temperature-dependent, and for stationary state shape wave u = u0, respectively, Leq(r)ueq(r) = λequeq(r) and L0(r)u0(r) = λ0u0(r). For one-electron systems, the latter equation reduces to the Schrödinger equation for a stationary state, with the usual eigenvalue λ0 = E0. In general, λ is identified with the Gibbs chemical potential μG. Boundary conditions such as the cusp condition at a nucleus and exponential decay at an infinitely large distance from the nucleus are easily implemented. In case L(r) allows complex eigenfunctions, u(r) = A(r)eiS(r), the hydrodynamical potential appears in the secular equation for the real amplitude A(r). The real phase S(r) satisfies the equation of continuity. By introducing «apparatus» operators [16], the excited state shape wave is also obtained. Comparisons are made with a recent discussion of Levy, Perdew, and Sahni [3].

Notes: The role of the boundary conditions is emphasized in determining the relation between the counting problem, posed by Coulson and solved by the number theorists, and the physical problem from which it arises. The surface energy term, which Coulson sought, does exist, but only when the periodic boundary conditions, which he used, are replaced by the finite box conditions.

Notes: The graph theory of molecular orbitals including second neighbor interactions (η) is considered here. Graphical methods of getting the characteristic polynomial for the π system of a conjugated molecule are given. It is shown that the characteristic polynomial can be factorized if there are symmetries in the molecule.

Notes: Calculations have been made at the minima of the X1A1 ground state of the ozone molecule. The equilibrium geometries have been obtained by means of CID calculations. The criterion adopted for the choice of configurations gives realistic results. CIPSI calculations at the two minima lead to an estimated gap of 0.92 eV between them.Our results agree with the analysis of previous theoretical works on the relative stability of open and cyclic zone structures, showing that the D3h minimum is stable relative to the ground state dissociation limit.

Notes: The ground state energies of finite Hubbard molecules are calculated by numerically solving the Lieb-Wu equations for a complex Hubbard repulsion parameter U. From the positions of the singular points located in the complex plane, the radii of convergence of the perturbation expansions for the ground state energies are determined.

Notes: A simple procedure has been created for indexing the spin-free configurations of an N-electron system in spin state S. This indexing has been linked to a procedure for generating the matrix representations of the generators of the unitary group U(n) to enable a direct configuration study to be undertaken.

Notes: A perturbation expansion which connects the hydrogenic limit energy density functional to the Thomas-Fermi functional is discussed. This perturbation series, where the Coulomb energy density functional is treated as the perturbation to the hydrogenic limit functional, is, in fact, the q = (N/Z) expansion of Thomas-Fermi theory. A truncated form of the first-order correction to the functional provides further insight into the model which treats the ground state energy as a local functional of the electron density.

Notes: A size-extensive, multireferences coupled-cluster method for studies of quasidegenerate states based on the Jeziorski-Monkhorst [16] ansatz for the cluster operator (Ω = ∑eTjPj, where the sum is extended over the configurations spanning the model space), is presented and applied in pilot calculations. The method is referred to as multireference coupled electron-pair method (MR CEPM), because it is assumed that the individual cluster operators can be approximated by their two-body parts, i.e., Tj ≈ Tj(2). The linear version of this method (MR L-CEPM) is also discussed. Both methods are applied to two simple model systems: (1) a minimum basis set model involving eight hydrogen atoms in various spacial arrangements for which the degree of quasidegeneracy can be continuously varied; (2) a model involving the C2ν insertion of Be into H2. For the first time in multireference coupled-cluster calculations, the nonlinear parts of the equations are completely accounted for. The MR CEPM results are very encouraging for strongly quasidegenerate states. The MR L-CEPM results are slightly below the accurate (FCI) values.

Notes: The interaction of a carbonyl group with two adjacent aromatic units is discussed. The outer valence electronic structure of compounds of general formula Ph—CO—Ar, where Ar is phenyl, substituted phenyl, furyl and thienyl, is determined from their gas phase photoelectron spectra. Particular attention is paid to biologically active derivatives of 2-amino-5-chlorobenzophenone.

Notes: Proteins and other macromolecules may be viewed as shape-based (or tactile) pattern recognizers. Biological cells exploit this inherent capability by transducing macroscopic signal patterns impinging on the external membrane to microscopic patterns at the molecular level, via second messengers. The parallelism inherent in the wave function description of these microscale processes in effect serves to increase the computing power of molecular computing systems as compared to macroscopic analogs. The conversion and recognition process is highly reminiscent of measurement. The linking role of second messengers allows macroscopic signals to set the state of the cell (in analogy to state preparation), while enzymatic readout and control of cellular behavior is an amplification process that corresponds to measurement of the microstate at a later point of time. Since the standard time evolution equations are reversible and unitary, while measurement is not, it is conceivable that the study of molecular computing will lead to new insights into the relation between the microworld and the macroworld. The model presented suggests that projection processes that are masked in ordinary laboratory systems are brought to macroscopic significance by the highly nonlinear chain of amplification events in the biological cell.

Notes: We have developed a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an objective function in search of global minima. We demonstrate the effectiveness of this algorithm by applying it to a model geometry optimization problem. Significant improvements in optimization efficiency are demonstrated, in that our algorithm returns lower minima than conventional line minimization in 79% of the optimization runs we made. The method is orders of magnitude less computationally intensive than simulated annealing, while returning good minima for functions possessing many local minima. The method is simple to program, and requires only two-point gradient calculations for its implementation.

Notes: Toward the goal of efficiently computing field lines for molecular vector fields, where each field-point calculation is computationally intensive, a few appropriate algorithms for calculating vector field lines are presented and compared for various representative applications. Among these algorithms are the first-order tangent-line method (TL), the fourth-order Runge-Kutta method (RK4), the infinite-order Bulirsch-Stoer method (BS), the second-order Taylor's series method (TS2), and the second-order “curvature-following” method (CF). The TL and the RK4 are well known. The TS2 and the CF are new. The RK4, The TS2, and the CF are appropriate for obtaining high accuracy with few field-point calculations. The TL is definitely not appropriate for this purpose, and the BS is so appropriate only at the highest level of required accuracy. The CF uses the value of the vector field and its gradient at the given field point in order to locate the center of curvature of the field line at that point and, thereby, to extrapolate the field line, as an arc of a circle, to the next field point. The TS2 uses the same information, but extrapolates the field line as a segment of a parabola whose vertex is at the field point. The BS is an infinite-order extrapolation on successively finer scale iterations of the lowest-order Runge-Kutta method. All of these methods are compared for the velocity field of a rotating disk, for the vector field of a point dipole, and for electric field of a high-speed orbiting charged particle. For all of these fields, the field lines are exactly expressible in analytic form, so the absolute errors of these different algorithms can be appraised. As several of these methods allow a rather large step size, it was found appropriate to use a continuous-(geometrical)-curvature interpolation scheme to interpolate between the field points on the generated field lines. One prefers this scheme to the use of cubic splines when the physical fields should have their “geometrical pictures” (even under approximation) invariant to an arbitrary change of the coordinate system used in the calculation. These methods have also been used to generate field lines for the approximate and the exact fields of a half-wave antenna. In this case, one sees very large differences in the structure of the field lines of the approximate and the exact fields, in the near-field region, and also sees the manner in which each of these differences diminishes to zero as the field point approaches the far-field region; features that would have been very hard to observe by purely analytical methods. It is hoped that these methods for field line generation might have application for the field lines of the gradient of the molecular density (as in Bader's theory of atoms in molecules) and for the field lines of the electric fields of nucleic acid molecules.

Notes: The results of applying the simulated annealing method to find the lowest energy structure of the decane molecule are analyzed. The algorithm is found to be both efficient and economical. Some preliminary results are presented for a molecule of biochemical interest, Met-enkephalin.

Notes: Recently we derived, implemented, tested, and used successfully a new computational strategy for ab-initio MRD-CI (multireference double excitation - configuration interaction) calculations for molecular decompositions of large molecules and intermolecular reactions of large systems. We carry out the ab-initio SCF for the entire system, then transform the canonical delocalized molecular orbitals to localized orbitals and include explicitly in the MRD-CI only the localized occupied and virtual orbitals in the region of interest, folding the remainder of the occupied localized orbitals into an “effective” CI Hamiltonian. The advantage is that the transformations from integrals over atomic orbitals to integrals over molecular orbitals (the computer time-, computer core-, and external storage- consuming part of the CI calculations) only have to be carried out for the localized orbitals included explicitly in the MRD-CI calculations. The challenge arose to extend our MRD-CI technique based on localized/local orbitals and “effective” CI Hamiltonian to the breaking of a chemical bond in a molecule in a crystal (or other solid environment). This past year we have derived, implemented, and used successfully a procedure for doing this. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of yet more further out surrounding molecules. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are then carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have defects, deformations, dislocations, impurities, dopants, edges, and surfaces, boundaries, etc. We have applied this procedure successfully to the H3C - NO2 bond dissociation of nitromethane with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many further out molecules have to be represented by multipoles. To check the goodness of the model cluster approximation for crystalline nitromethane, we carried out ab-initio crystal orbital (XTLORB) calculations using our POLY-CRYST program. The difference in the XTLORB total energies between the 4 nitromethane molecules/unit cell and the 3 nitromethane molecules/unit cell (Table VIII), ER = E4 - E3 = -48.0609079 a.u., corresponds very closely to the reduced energy per nitromethane molecule, ER = (-;48.0605)9 a.u., calculated from explicit SCF calculations on the model nitromethane cluster in the multipole field of farther out nitromethane molecules for the model cluster. Thus, the multipole approximation for describing the effect of further out molecules on the SCF cluster energies is quite good.

Notes: The electrostatic interaction is a critical component of intermolecular interactions in biological processes. Rapid methods for the computation and characterization of the molecular electrostatic potential (MEP) that segment the molecular charge distribution and replace this continuous function by a series of multipole moments for each segment have been described. There are two sources of error in these techniques: 1( The truncation of the expansion after just a few terms, and 2) the charge in the segmental distribution that is more distant from the expansion center than the observation point. The first may be eliminated by finite expansion methods where truncation is unnecessary or performed in a manner that gives errors that are acceptably small. The second is inherent in the multipole expansion and results from the assumption in performing the expansion that the distance to the observation point is larger than the distance to all points inside the charge distribution. As the basis functions used in molecular wave functions have infinite extent, this will never be the case and the multipole expansion is never strictly valid. In practice this inherent error limits the range of usefulness of all multipole expansion techniques. To expand this range we have introduced a method that uses exact techniques to compute the MEP for the part of the molecular charge distribution described by the gaussians on each atom with the smallest exponential parameter and uses segmental multipole methods for the remainder of the charge. Using pyrrole with an STO-3G wave function as an example, this method significantly improves the potential in the range 1.4-2.0 Å from atoms with only a small increase in computational effort. If other basis sets are used with more diffuse gaussians the convergence of the multipole expansion will be at greater distances from the atoms and this type of correction will be more important.

Notes: Finiteness is usually imposed as a condition for physical admissibility of a wave function. Examination of this condition in both position- and momentum-space shows that finiteness of the wave function at the origin in one space implies “linear” integrability in the reciprocal space, except in some pathological cases. Some implications of this result are discussed.

Notes: The ground state energetics and equilibrium geometries of neutral and positively and negatively charged clusters of Li3, Li2H, Li2Na, Li2Mg, and Na2Li have been obtained from a self-consistent field-linear combination of atomic orbitals-molecular orbital calculations within the Hartree-Fock approximation. The correlation energies are included perturbatively using the Möller-Plesset scheme up to the fourth order. The geometries of all negatively charged clusters are found to be linear with bond lengths that are, in general, larger than their neutral or cationic counterparts. The adiabatic electron affinities and ionization potentials are calculated and compared with earlier theoretical results. The addition of an electron to the neutral cluster is found to stabilize the cluster further against dissociation. The spatial distribution of the electrons in these clusters is studied to determine the extent to which electrons added or taken out are localized in the clusters. Mulliken population analysis is also used to elaborate the charge state of the anionic and cationic clusters.

Notes: A simple proof is given for the thermodynamic inequality F - F0 - 〈H - H0〉0 〈 0 in the case when the two Hamiltonians H and H0 do not commute.

Notes: Electron correlation energies are calculated for a series of small molecules by fourth-order Møller-Plesset perturbation theory (MP4) and by quadratic configuration interaction methods. A method is suggested for partitioning the correlation contributions beyond fourth order that result from single, double, and triple substitutions. Detailed comparison of the results reveals that termination of the MP perturbation series at fourth order is inadequate for some electron-deficient species (inadequate treatment of double substitutions), for triply-bonded molecules (overestimation of the triples effect), and for some unsaturated radicals (poor treatment of single substitutions).

Notes: A completely analytic method for evaluating three-center nuclear attraction integrals for STOS is presented. The method exploits a separation of the STO into an ‘evenly loaded’ solid harmonic and a OS STO. The harmonics are translated to the molecular center of mass in closed finite terms. The OS STO is translated using the Gegenbauer addition theorem; 1s STOS are translated using a single parametric differentiation of the OS formula. Explicit formulas for the integrals are presented for arbitrarily located atoms. A numerical example is given to illustrate the method.

Notes: Two three-dimensional numerical schemes are presented for molecular integrands such as matrix alements of one-electron operators occuring in the Fock operator and expectation values of one-electron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product-Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8-10 digits) may be obtained with obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.

Notes: 4-31G wave functions have been computed for five purines and pyrimidines. The calculated deformation densities have been partitioned into atomic fragments, which were integrated to yield atomic multipole moments. The transferability of atomic fragments between related molecules was verified by constructing model maps for uracil and guanine from appropriate fragments of cytosine and adenine. Model electrostatic potentials calculated from the moments of model atoms are similar to the corresponding 4-31G potentials. Comparison of 4-31G and 4-31G** deformation densities of cytosine provides simple rules for estimating the effects of polarization functions on the atomic multipole moments of most atom types occurring in the purines and pyrimidines. These rules were applied to the other molecules and yielded reasonable approximations for their molecular dipole moments. Substituting CH3 for H has little effect on the deformation density beyond the substitution center.

Notes: We examine a variety of methods for obtaining the stable geometry of molecules and the transition states of simple systems and summarize some of our findings. We find the most efficient methods for optimizing structure to be those based on calculated gradients and estimated second derivative (Hessian) matrices, the later obtained either from the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton update method or from approximations to the coupled perturbed Hartree-Fock method. For uncovering transition states we find particularly useful a variety of the augmented Hessian theory used to uncover regions of the potential energy hypersurface with one and only one negative eigenvalue of the Hessian matrix characterizing the catchment region of the transition state. Once this region is found we minimize the norm of the gradient vector to catch the nearest extreme point of the surface. Examples of these procedures are given.

Notes: Molecular Orbital (MO) calculations by the MINDO/3 method on tumor-inhinbitory nitrosoureas is reported. Electronic structures for 18 chlorethyl nitrosoureas and 30 cyclohexyl nitrosoureas (CCNUS) are related to biological activity in the form of toxicity, therapeutic activity, and increase in life span and chemical reactivity in the form of alkylating and carbamoylating activity. Hydrophobicity, as measured by the logarithm of the partition coefficient (octan-1-o1/water), shows a parallelism with calculated bulk molecular properties. Mechanisms of alkylation and other reactions related to biological action are proposed and discussed.

Notes: The path of proton motion in protein bacteriorhodopsin is constructed: Tyr 43 → Tyr 26 → Asp 212 → Tyr 83 → Tyr 57 → Tyr 79 → Glu 204 → Tyr 64 → Glu 74. From the position of quantum theory the light-induced isomerization of retinal, the process carrying out the proton and throw-over from the inlet H-bond chain (Tyr 43 → Tyr 26 → Lys 216) to the outlet one (Lys 216 → Asp 212 → … → Glu 74) are investigated. The kinetics of the transition of the excitation from the π-electron subsystem to the vibrational one is studied; the function of the nonequilibrial excitation distribution of the collective intramolecular retinal vibrations is found. The mechanism of deprotonation of Schiff base (transmission of proton to the outlet channel) is considered. The correspondence between the theoretically estimated states and spectroscopically identified forms of bacteriorhodosin (initial form bR, intermediates J, K) is proposed.

Notes: A formalism is developed for the construction of relativistic symmetry-adapted molecular basis functions under consideration of time reversal invariance. The theory is applicable to the finite double point groups Cn, Cnh, Sn, Cnv, Dn, Dnd, Dnh, T, Th, Td, O, and Oh. It is based on the LCAO method. A projection operator technique is employed to construct molecular symmetry orbitals from atomic orbitals. The search for linearly independent basis function is simplified by means of group theoretical considerations.

Notes: For the Hartree-Fock ground state of atomic two-electron systems, the variational function of Wilson and Silverstone, φ(r) = (a + kr)-1 exp(-kr) / (4π)1/2, can be optimized in two complementary ways. For small values of the atomic number Z, all intergrals have been calculated numerically and optimization can be performed accurately. However, as Z increases, loss of significant figures is increasingly detrimental to the optimization process. For sufficiently large values of Z, the integrals may be replaced by asymptotic expansions in terms of (2a)-. As a result of optimization, the parameters and expectation values can be given as expansions in terms of (32Z)-1/2. Both methods yield good results for Z ≈ 25, so that the whole range of Z can be treated accurately. The results have been compared with those derived from other analytical two-parameter functions. It is found that φ(r) is indeed the outstanding two-parameter function, at least for small and intermediate values of Z.

Notes: Extended Hückel molecular orbital calculations have been made for the silver adatom-pyridine complex in order to reveal the very chemical nature of the surface-enhanced Raman scattering. The variation of the behaviors of the bond orders and charge densities as functions of the Ag—N distance and the net charge on the Ag atom, which is applied voltage dependent, is demonstrated. The calculated optical transition of the system can accommodate the experimental observation that as the wavelength of the exciting line shifts from 4880 to 6328 Å, the surface-enhanced Raman signal is enhanced more. Most interesting is the fact that the calculations reproduce well the experimental observation that there is an applied voltage on the electrode at which the surface-enhanced Raman signal is a maximum. The calculations show that the charge transfer enhanced mechanism is mostly due to the transfer of electrons from the silver atom to the pyridine molecule. Several useful overlap integrals involving d orbitals not available in the literature before are listed in the appendices for convenient reference.

Notes: A new and very simple one-range expansion of the 0s function is derived and employed as the starting point of three recurrence relations which allow the expansion of arbitrary Slater functions over displaced centers. Convergence of the expansions, both pointwise and in norm, are analyzed, and three-center nuclear attraction integrals are chosen for a further test of the formal developments and the numerical behavior of these expansions.

Notes: Two molecular charge similarity index (CSI) methods are further evaluated for practical application: one method based on a simple CNDO-type approximation to the electron density function and the other based on an ab initio pseudo total charge density function. The test system consists of isosteric analogues of dimethyl ether and methoxy acetic acid. The effects of differences in skeletal structure on the CSI measure of electron density similarity about corresponding atoms is estimated, and two new developments are presented for application of the ab initio-based method: (1) an INDO-type approximation which improves the efficiency of the CSI calculation; and (2) a FOCUS feature which enables comparisons of local molecule regions.

Notes: The dynamics of a model triatomic hydrogen bond are analyzed through classical mechanics. The approximate separability of the equations of motion induces the existence of an adiabatic invariant for the intramolecular mode motion. This mode is governed by a Mathieu equation, a feature already present for the antisymmetric mode in symmetric triatomics. The corresponding spectrum readily obtained as the Fourier transform of a classical trajectory shows that the fundamental frequency is shifted to lower values owing to the anharmonicity of the potential. We observe also a substructure of combination lines generated by a nonlinear resonance with the intermolecular mode. These properties are consistent with experimental observation. In a four-atoms model, the lines are split when intramolecular Fermi resonance occurs. When the intermolecular mode becomes chaotic there is no vibrational heating of the intramolecular neighboring mode which tends to behave like a local isolated oscillator.

Notes: We have analyzed the ability of a tertiary amide group to activate an ortho position on aromatic system toward an electrophilic attack using an ab initio SCF molecular orbital method. The molecular electrostatic potential was used to analyze the electronic nature of the ortho-lithiated intermediate complex and possible sites for electrophilic attack.

Notes: It is demonstrated that the total π-electron energy calculated within the “variable β” Hückel method is almost entirely determined by the total π-electron energy computed within the ordinary (topological) Hückel method and the number of the carbon-carbon bonds. This explains the fact that the topological Hückel method is capable of predicting relative stabilities of various molecules, even if they possess different bond lengths.

Notes: An approach which considers both nuclear and electronic motions for molecular systems is derived using algebraic techniques within the vector model. The dynamical symmetries of the Hamiltonian thus derived are examined and shown to account for the analytic diagonalizability of the LEPS level potential function for molecular systems. The initial application is to the H3 collision system, demonstrating the ability of the model to treat systems without bound states. Extensions to more complicated systems are also considered, and these efforts allow for the determination of the algebraic source of the coupling in the “diatomics in molecules” (DIM) potential surface. In general, these terms in the DIM approach preclude analytical diagonalization of the Hamiltonian, which may also be understood in terms of the dynamic symmetry of the corresponding algebraic description.

Notes: The quantity ∊ = (Φ||(H - E)Φ|) gives a measure of the error in the approximate solution, Φ (with corresponding energy expectation value E), to an eigenfunction of the Hamiltonian operator H of the system under consideration; this quantity vanishes for the exact function ψ. In a percentage scale (with 0% error for the exact function and 100% for a reference, approximate function), the error of Φ may be expressed as 100(∊/∊r), where ∊r corresponds to the reference function (e.g., obtained with a minimal basis set). This approach eliminates the need of knowing beforehand the exact solution in order to have an estimate of the error of an approximate solution.

Notes: Interaction energies between an alanine zwitterion and a water molecule at 150 different positions and orientations have been calculated using the ab initio method with the minimal basis set and employing the counterpoise method to eliminate the basis set superposition error. Dispersion energies are estimated using the Slater-Kirkwood formula. Out of a total of 150 computed interaction energies, 140 whose SCF interaction energies are below 5 kcal/mol have been fitted with a summation of atom-atom pair potentials in the form of the Lennard-Jones potential plus an electrostatic term. The standard deviation for this fitting is 0.49 kcal/mol.A sampling scheme regarding geometrical configurations is presented. Twenty rays are uniformly drawn from the origin of coordinates, a floatable division with equal ratios is made along each ray, and one of 60 orientations is randomly taken as the orientation of a water molecule. A nonlinear fitting method is used with a restriction on the sign change of fitting coefficients.

Notes: In reexamining the thermodynamic parameters of the protein refolding of ribonuclease systems over the temperature range of 220-360° K, based on the Nernst heat theorem, we found that at the temperature 〈Ts〉, the thermodynamic quantities ΔG0〈Ts〉 and ΔH0〈Ts〉 are of the same magnitude, while TΔS0〈Ts〉 approaches zero. Based on the Planck-Benzinger thermal work function, ΔW0(T) = ΔH0(T0) - ΔG0(T). Therefore, ΔH0(T0) = ΔW0〈Ts〉 + ΔG0〈Ts〉 at 〈Ts〉. Within the limits of statistical error, plotted values for ΔH0(T0) at 0° K and 〈Ts〉 are equivalent for each of the three ribonuclease systems we examined. Error-minimizing statistical simulation suggests that a reasonable a priori estimation of ΔH0(T0) can be made at 〈Ts〉, provided that the expansion coefficient of the Planck-Benzinger thermal work function is accurately determined. Values for ΔH0(T0) at 〈Ts〉 were determined to be 34.05 ± 1.30 and 19.49 ±0.42 kcal/mol in 20-S1 [I] and 14-S1 [II] systems, respectively. The value for ΔH0〈T0〉 at 〈Ts〉 in the ribonuclease A conformational transition as a function of pH was determined to be 59.0 kcal/mol. The magnitude of ΔH0(T0) values for 20-S1 [I] and 14-S1 [II] is an effective measure of the ease with which these molecules can be refolded to resemble the native protein structure, with greatest ease of folding at the lowest chemical bond energy. The Planck-Benzinger thermal work function, ΔW0(T), is an effective measure of the energy potentially available for any interaction to take place. ΔH0(T0), a temperature-invariant quantity, is a primary source of the chemical bond energy essential for any reaction to proceed in a biological system, and is indispensable in any consideration of macromolecular interaction. Certainly this function has yet to receive sufficient recognition in the field of thermodynamics. After applying it in studies of ribonuclease refolding and protein-protein interaction, we predict that this new state function will eventually supplant the Gibbs-Helmholtz expression in thermodynamic analysis.

Notes: We have investigated the impurity states in direct gap doped semiconductors via the alternant molecular orbital method with application to n-CdS. Good agreement compared with available experimental data and other calculations for resistivity and metal-nonmetal transition critical point are found. For spin susceptibility we have done an extensive calculation with and without correlation or disorder effects. Such calculation suggests experiments on concentration-dependent susceptibility in n-CdS.

Notes: The possibility of obtaining itinerant antiferromagnetism in the new high Tc superconductors is explored by means of self-consistent spin-polarized calculations for the nonsuperconductor YBa2Cu3O6, which is related to the 90K superconductor YBa2Cu3O7-δ and for models of doped copper oxide planes. Investigation of both the ferromagnetic and antiferromagnetic ground states reveals the former to be unstable and the latter to be stable. Our calculations show that for metastable antiferromagnetic ordering of copper magnetic moments in the CuO2 plane, there is a Peirels-type antiferromagnetic gap around the Fermi energy, and YBa2Cu3O6, in particular, is semiconducting as observed experimentally. Comparison is made with recent neutron diffraction studies.

Notes: An approximate relation between the static-density response function and the fukui function is used to develop a perturbation approach within the framework of density functional theory. It is shown that the approximate relation describes correctly the equivalence between the representation of the energy in terms of the electronic density and the external potential, and the representation in terms of the number of electrons and the external potential. The perturbation scheme is applied to calculate the first and second order corrections to the energy of a two-electron atom. The results show that the present approach incorporates part of the correlation energy.

Notes: Two possible mechanisms have been suggested for the formation of soot in fuel-rich flames. The first of these involves reactions of small radicals, the second of small ions. We examine the latter possibility in this paper. Reactions between C3H3+ ions and acetylene were studied by quantum mechanical methods. The results suggest that the linear propargylium cation reacts without barrier. Cyclic C3H3+ does not readily react with acetylene. These observations are in agreement with FT-ICR experiments that suggest one inactive form of the C3H3+ cation. The properties of five different products of the reactions were studied for possible identifications in experiments on flames and on model flames.

Notes: Ab initio molecular orbital calculations were performed on a series of phosphazene trimer molecules to elucidate the electronic structure of these systems. The role of the d orbitals was analyzed from comparison of the molecular orbital contour calculations performed both with and without d orbitals in a split valence basis set description. The results indicate that, although the major geometric aspects of these systems can be described without invoking the use of d orbitals, these orbitals are essential to properly describe the electronic structure. The d orbital involvement in out-of-plane π bonding contains elements of both the classical Craig, Paddock, and Mitchell [1-3] and Dewar et al. [4] bonding schemes; the d orbital effects on in-plane bonding modes are also substantial. The charge distribution in these systems is best described as a zwitterionic form, because a significant amount of charge accumulates on the ring nitrogens.

Notes: We report the results of ab initio calculations on a model Cu4O12 cluster. The spectrum of the undoped cluster is most appropriately described in a localized valence bond framework. The ground state and low lying excitations can be fit quite well to a Heisenberg Hamiltonian with an anti-ferromagnetic coupling constant between nearest-neighbor Cu3d spins. For a doping level x = 0.25, the electronic states are most easily interpreted in a molecular orbital (Fermi liquid) framework. In addition, doping introduces low-lying Cu ↔ O charge transfer excitations. Our best calculations to date associate the ground state with a hole in the Cu3d anti-bonding band (Cu3+O2-), but the state in which the hole is associated with the O2p band (Cu2+O1-) is nearly degenerate.

Notes: A modified cluster approach for modeling local chemisorption phenomena is suggested on the basis of the linear combination of Gaussian-type orbitals (LCGTO) Xα method. Contractions of the fitting bases are employed to take into account the reduced polarizability of a surface cluster and to access larger cluster sizes. Furthermore, embedding of a cluster in the surface is mimicked by Gaussian broadening of the one-electron levels leading to fractional occupation numbers via a self-consistently determined Fermi energy of the cluster. As a first application results are presented for the clusters NinNa (n = 5, 9, 17) modeling the low coverage limit of the chemisorption system Ni(100)/Na. Calculated bond length, binding energy, and induced “surface” dipole moment show fair agreement with experimental values, indicating a substantial covalent character of alkali bonding on transition metal surfaces even in the zero coverage limit.

Notes: The spectra and characteristic polynomials of polyhedral cluster graphs containing 4-120 vertices are obtained. Some of the polyhedral graphs considered such as icosahedron, Archimedene etc., are models for some interesting clusters such as C120. For the Archimedene the spectra and delocalization energies are obtained with and without bond alternations. The characteristic polynomials and spectra of all the polyhedral clusters considered in this investigation are unique.

Notes: The experimental and theoretical effort in the Chemistry Division of the Naval Research Laboratory in the area of clusters is briefly reviewed. We have focused on the effects of structural isomers and “magic number” structures on distributions of cluster sizes and, more recently, on the role of isomers in chemical reactions. The focus of this work is on whether or not the existence of a magic cluster size precludes there being more than one isomer of that size. Various theoretical methods have been used to study the sometimes magic 9-atom alkali-halide cluster ions. It is possible, but not compelling, that isomers of this cluster size are produced in sputtering sources of clusters. Under certain experimental conditions the relative intensity of the 60-carbon-atom ion appears so great as to suggest that no isomer other than the proposed icosahedral structure can be present. The geometry of this unique structure has been optimized using two local density functionals to predict some of its special properties. For the case of the magic C+7 ion, theoretically the two lowest-lying isomers are clearly linear and monocyclic. Experimentally, both forms are observed with cyclic form predominant.

Notes: Square planar transition metal cluster compounds are uncommon, there is only one good example, [Os4(CO)16], and it is an unstable molecule, with longer than expected metal-metal bonds. Force field calculations of ligand packing show that the molecule has no particular steric problem. A qualitative molecular orbital analysis shows an orbital symmetry problem that allows the formation of no more than two in-plane metal-metal bonds. This symmetry restriction is due to the nodal patterns of the occupied d orbitals and should apply to other square transition metal clusters as well.

Notes: This article presents a variational approach for calculation of the dynamic third-order susceptibility χ(3). The susceptibility is obtained directly through a solution of two sets of inhomogeneous linear equations.

Notes: A polarization propagator method based upon an approximate coupled cluster doubles (ACCD) wavefunction is presented and applied to CH+ and Be in calculations of excitation energies and radiative lifetimes. It is found that in these cases the computational results are nearly identical to results obtained using a similar method based on the full coupled cluster doubles (CCD) reference state. Since ACCD is far less time-consuming than CCD the approximate coupled cluster doubles polarization propagator approximatior (ACCDPPA) should be an effective method for large scale computations preserving the quantitative reliability of CCDPPA.

Notes: Given the invariance of an N-body system under discrete operations of reflection, inversion, a rotation by 2π/n, and the corresponding relations among the derivatives of energy, we have constructed through an invertible transformation a set of active and redundant coordinates. Movement along the active coordinates preserves all symmetry relations. We show that algorithms for locating stationary points or for calculating reaction paths are exactly separable in these active and redundant coordinates. We further show that this formalism is equally applicable when equations of constraints among coordinates are specified for the movement of particles. This includes geometrical constraints on bond lengths, angles, substituent group internal rotations, etc. This formalism enhances the efficiency since (laborious) cartesian derivatives need to be calculated only for the active variables and that the problem is reduced in term of m(≤3N) variables. We apply this procedure to obtain the equilibrium geometry of H2O molecule within the subspace of C2v symmetry configurations ab initio derivatives.

Notes: This paper analyzes the use of electric-field-variant (EFV) atomic orbitals in calculations of molecular polarizabilities using the finite field approximation. It is shown that, in the absence of an external electric field, the optimal positions of the orbital centers which minimize the total energy are already shifted with respect to the atomic sites and that these optimal positions constitute a better starting point to compute molecular polarizabilities by the finite field method. The technique is applied to the hydrogen molecule and to the alkane series CnH2n+2, n = 1, 2, 3, 4, 5, 6 in the framework of a floating spherical gaussian orbital-EFV basis.