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Notes: It is shown that configuration interaction calculations, with inclusion of the relativistic corrections, constitute an appropriate approach for the prediction of atomic energy levels and that results of experimental accuracy are possible given the availability of large-scale, fast computers. The results obtained for He through F emphasize both the practical difficulties to be encountered and the possibility of predictions with less than 1% error.

Notes: Through a formalism developed in formr papers, some problems, set by the determination, from experimental data of the evolution equation of an n-states quantum system are considered.

Notes: A many-body diagrammatic perturbation theory of rotation-vibration spectra is elaborated. The present approach is based on two many-body techniques, namely on the second quantization formalism (a rotating-vibrating molecule is formally treated here as a system of interacting vibrons, obeying the Bose-Einstein statistics) and the many-body diagrammatic theory of a model Hamiltonian, initially suggested in the microscopic theory of nuclei and in the last decade very frequently exploited in the accounting for the correlation effects in many electron systems. In the framework of this theory, the rotation-vibration energies are determined as the eigenvalues of a finite-dimensional model eigenproblem.

Notes: A personal and partially anecdotal account is given of the role of the Debye-Waller factor in protein crystallography and protein dynamics.

Notes: Since the overlap integral between two functions in position space is the same as the overlap integral between their counterparts in momentum space, there is an intimate connection between orthonormalization procedures in the two spaces. It is pointed out that in certain cases this situation can be used to simplify the orthogonalization.

Notes: This is the story about how knowledge of the Compton profile led to the technical development of a useful apparatus. It is also the story of interdisciplinary collaboration between condensed matter theorists and medical physicists.

Notes: A quantum system is repeatedly prepared in the same way and then observed in measurement processes. The following problem is stated and solved: Given the results of a series of observations, what is the best guess for a density matrix describing the ensemble of prepared systems? The corresponding classical problem and its solution are obtained as a special case.

Notes: Formulas for the energies and widths of shape resonances, i.e., quasi-stationary levels for a quantal particle moving in a spherically symmetric potential, valid also close to the top of the potential barrier, have been published by Drukarev, Fröman, and Fröman. On the basis of these formulas, in the present paper the potential is explicitly expressed in terms of experimental data on the energies and widths of the quasi-stationary states. The treatment is related to previous treatments by Wheeler and by Cole and Good, Jr., which are in turn related to the Rydberg-Klein-Rees method.

Notes: After a brief review of the historical development of the concept “antiparticle,” some recent theoretical results on CP violation are reviewed.

Notes: The approximation of hyperpolarizabilities through the use of operator inequalities is sketched. Previously applied methods to ordinary polarizabilities are extended. They lead to expressions involving moments of oscillator strength distributions related through sum rules to ground state properties. Systematic applications of new formulae are suggested.

Notes: Light positive particles can be introduced in metallic lattices where they take up interstitial positions. The motion of particles between these sites is usually described as a phonon-assisted tunneling process, which at high temperatures approaches a classical over-barrier jump motion.The present paper reviews briefly the study of such phenomena at very low temperatures where phonon assistance is no longer effective. Experiments on proton transfer between certain sites in niobium metal and on positive muons which diffuse in copper or aluminium lattices show unusual temperature dependencies, which have been explained quantitatively with recent tunneling theories. These approaches take into account the simultaneous dissipation of energy to the electron bath, a phenomenon which was shown by J. Kondo to be determined by the screening electrons following the particle. The temperature dependence is essentially an effect of the Fermi distribution of the conduction electrons. The interaction of the particle with the itinerant electrons will also determine whether the particle wavefunction will be localized or form an extended (Bloch-like) state.

Notes: A microscopic model for nuclear dynamics has been formulated and applied to the collisions between heavy ions. It may be viewed as an extension of the collisionless time-dependent Hartree-Fock (TDHF) method to include nucleon-nucleon collisions. The collision term is written in the form of a time relaxation. The relaxation time is obtained from separate calculations. Some results are shown for the collisions between two 16O nuclei. The computations require a storage of several million words and require a super-computer. Calculations have been done on the John von Neumann Center (JVNC) CYBER-205. Future calculations are planned on the JVNC ETA-10.

Notes: The ground (N) state and the 1B1u(V) excited state of planar ethylene have been studied at the CPF and MR-SDCI levels of theory, using an extended CGTO basis set of the ANO type. The investigation especially addresses the near-degeneracy problem in the ground state and the coupling between the diffuse character of the π* orbital and the amount of correlation included in the wave function of the V state. The MR-SDCI results yield a vertical excitation energy in the range 7.8-8.0 eV, whereas the CPF result is 7.9 eV. The best MR-SDCI result for 〈1π*‖z2‖1π*〉 is 7.8, whereas CPF calculations based on MR-SDCI INOS give the value 6.7. It is clear from the results that these numbers have not converged and that more extended calculations than was possible in the present work would yield an even more compact wave function.

Notes: A generalization of the Gibbs-Bogoliubov inequality F ≤ F0 + 〈H - H0〉0 for the free energy F is studied which leads to a variation principle for this quantity that may be of importance in certain computational applications to quantum systems. This approach is coupled with a study of the perturbation expansion of the free energy for a canonical ensemble with H = H0 + λV in the general case when H0 and V do not commute. The second- and high-order derivatives of the free energy with respect to the perturbation parameter λ are calculated. From the second-order term is finally obtained a second-order correction to the previous variational minimum for the free energy.

Notes: A explicit expression for the unitary group Clebsch-Gordan coefficients, which couple two fully antisymmetric single-column states into the two-column Gel'fand-Tsetlin states, is given in terms of isoscalar factors for the canonical subgroup chain U(n) ⊃ U(n - 1) ⊃ … ⊃ U(1). The isoscalar factors are expressed through the step numbers labeling canonical basis states and enable a straightforward construction of Gel'fand-Tsetlin states in the Clifford algebra unitary group approach, without the use of the tables for the symmetric group outer-product reduction coefficients.

Notes: The simple semiquantitative approach to the calculation of the energy of surface states, proposed recently by the authors, is applied to high-symmetry surfaces of selected transition metal carbides, nitrides, and oxides. The results are compared with recent experimental and theoretical data. The necessity to include the changes in the potential at the crystal surface is indicated.

Notes: We report here a theoretical formulation of the transport of excitation energy in a three-dimensional molecular crystal containing one impurity. The excitation is assumed to be localized in the jth site at time t, and the expression for the probability of finding the excitation at some other site j′ at a later time t′ is derived. The probability is given by the correlation function \documentclass{article}\pagestyle{empty}\begin{document}$ \left\langle {\hat P_j (t)\hat P_j (0)} \right\rangle $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \left\langle {\hat P_m } \right\rangle $\end{document} represents the site projection operator, |m〉 〈m|. In our derivation we neglect the interaction among excitons of different bands, account for the presence of the impurity by adding a small perturbation term to the pure crystal Hamiltonian, and calculate the exciton solutions through first order. We consider a general impurity; that is, the trap depth is nonvanishing and may even be complex. The exciton-phonon interaction is taken to be linear in lattice displacement vectors; we assume that the short time behavior of \documentclass{article}\pagestyle{empty}\begin{document}$ \left\langle {\hat X} \right\rangle _{{\rm phonon}} $\end{document} gives the dominant contribution to the physical property X being studied and solve the dynamical problem by using a time-dependent effective potential consisting of fluctuations around the equilibrium average exciton-phonon interaction. Several limiting cases are briefly discussed.

Notes: The use of a new time-dependent ket, variationally determined as a linear combination of Slater determinants associated with an electric field variant factor, provides an efficient technique for the calculation of dynamic polarizability tensors. Including electron correlation, the method is applied to the evaluation of the frequency-dependent polarizability of H2O and N2 and can be used even when the photon energy is near the excitation energy. With relatively small basis sets, calculated polarizabilities and resonance frequencies are in good agreement with experimental values for H2O but have to be improved for N2.

Notes: A recently proposed (semiclassical) classical path method for treating reactive scattering is reviewed. This method exploits properties of hyperspherical coordinates which allow a collision coordinate to be defined without reference to the arrangement of the particles. The coordinate space is divided into classical and quantal subspaces such that the description of the “arrangement” is quantal. Selected results are presented for the three-dimensional D + H2 → HD + H reaction.

Notes: In this paper a general method for the evaluation of the matrix elements of spin-dependent operators is proposed to improve the treatment primitively suggesteed by Cooper and Musher. This approach is largely based on the recent results which the present authors have achieved in the representation theory for the inner- and outer-product reduction of the symmetric group. It is shown that the so-called outer-product coupling coefficients (OPCC) can be used to generalize the method for constructing the irreducible tensor operators of group Sn. Together with the use of inner-product coupling coefficients (IPCC), an expression for the matrix elements of spin-dependent operators is presented as the product of a Racah coefficient for Sn and a reduced matrix element which can be expressed in terms of IPCC, OPCC, and the related integrals. The treatment for one- and two-electron spin-dependent operators is discussed in detail.

Notes: Configuration interaction (CI) calculations are carried out for He atom and H2, LiH, and BH molecules in order to obtain the value of the charge density at the nucleus by the use of the Hiller-Sucher-Feinberg (HSF) identity. The HSF density also can be calculated with the double perturbation theory based on the Møller-Plesset-type theory and also on the Epstein-Nesbet type. It is found that each value of the HSF density for these perturbative corrections is very similar to the corresponding value by the CI with single- and double-electron excitations. Especially for the He atom, the HSF density value by the full-CI wave function coincides with the exact value of the charge density in three significant figures. The electron correlation effects are found to be small but cannot be ignored in the HSF density. It can be shown that the superiority of the HSF density over the usual delta-function-type density is excellently confirmed.

Notes: Analytical and numerical studies are performed concerning the exclusion of the basis set superposition error (BSSE) from the SCF calculations of intermolecular interactions. Based on these studies a new procedure is proposed, which consists of the following steps: (1) determine the orbitals by the SCF scheme based on the recent “chemical Hamiltonian approach” (CHA-SCF method), i.e., excluding the delocalization effects caused by BSSE, and then (2) calculate the usual energy expectation value. (This gives results superior to those obtained by the previous nonsymmetric CHA energy formula.) The actual numerical calculations performed for different simple systems (He2, water dimer) by using various basis sets indicate that the CHA/CE (CHA with “conventional energy” formula) potential curves are well-balanced and are close to those obtained by the Boys-Bernardi (BB) method and usually (but not necessarily) go slightly beyond the latter. So our method gives results better than (or close to) those given by the BB method by performing only a single ∼N4 calculation at each geometrical arrangement of the system.

Notes: Ab initio molecular orbital methods are employed to study the low-lying states of C3H+, SiC2H+, Si2CH+, and Si3H+. Special attention is paid to a comparative study between C3H+ and Si3H+. In both cases a 3B2 state is found to lie the lowest at the HF level, although inclusion of correlation effects favor a linear structure (1Σ+ state) for C3H+, which lies 25 kcal/mol below the 3B2 state at the MP4 level, and a bent structure (1A′ state) for Si3H+, which lies just 2 kcal/mol below the 3B2 state. The proton affinities of C3, SiC2, Si2C, and Si3 are estimated at different levels of theory. Both protonation at carbon and silicon atoms are considered for SiC2 and Si2C. It is found that C3 comparatively has a low proton affinity. On the other hand, Si3 has a relatively high proton affinity compared with the protonation at silicon atom for both SiC2 and Si2C. These results are discussed on the basis of electronic structure arguments.

Notes: The isotropic (aiso) and dipolar (Adip) hyperfine coupling constants of 19F2- were obtained from MRD-CI wave functions using a variety of basis sets. In series I, increasing numbers of d functions were added to a 5s4p contracted Huzinaga/Dunning basis. In series II, the 5s3p basis set was uncontracted in several steps until 9s5p was reached, to which were added from one to three d-polarization functions. CI parameters (selection thresholds and the number of reference configurations) were also varied. A study of the R dependence of aiso and Adip was performed. The best values obtained at Re are 260 G for aiso and 308 G for Adip, compared with experimental values of about 280 G for aiso and 320 G for Adip.

Notes: Hyperfine coupling constants (HFCC) of the 19F and 35Cl atoms and the 19F2- and 35Cl2- radical anions have been calculated by the unrestricted Hartree-Fock (UHF) method using polarization and diffuse functions with contracted double-zeta as well as uncontracted basis sets. The Adip values are fairly insensitive to changes in the basis set and show good accordance with experimental and other theoretical studies. The isotropic HFCCS aN of 19F, 19F2-, and 35Cl2- show strong dependence on d functions and the state of contraction of the s, p set. Spin-projected UHF wave functions lead to better agreement with experiment.

Notes: The effect of electron correlation on the results of pseudopotential calculations was examined using a simple analytical semiempirical pseudopotential and a correlated floating-type one-center wave function. Investigations were performed for the XH alkali metal hydride molecules (X = Na, K, Rb, Cs). The inclusion of the electron correlation in the ground state proved important for the calculation of the dissociation and ionization energies, but it is less significant for the determination of the equilibrium nuclear distances. The ground state potential energy curves are also determined.

Notes: An empirical potential is introduced that is suitable for calculation of the interaction enegies of biomolecules with thousands of atoms. The potential consists of electrostatic, repulsion, and dispersion energy terms. The approach used for parametrization of the potential is entirely different from that used with other existing potentials. Namely, all the terms were parametrized independently to retain their physical significance. The sum of the electrostatic and repulsion terms mimic the SCF interaction energy calculated using Huzinaga's minimal basis set MINI-1. The dispersion energy is very important and is usually predominant for the interactions of large (polar) molecules in the gas phase as well as in the liquid phase.

Notes: The solitonic models of proton transfer in a molecular hydrogen-bonded chain have been examined with respect to the shape of protonic interaction potential. The kink-like excitations with quadratic, quartic, Morse, and Toda interactions are reported and analyzed.

Notes: Quantum mechanical calculations have been used to study the reaction mechanism of human carbonic anhydrase-catalyzed hydration of CO2. This reaction is responsible for fast metabolism of CO2 in the human body. For each of the reaction steps, possible catalytic effects of active site residues are examined. The pertinent results are as follows. (1) For CO2 binding, the experimentally observed 2.5 cm-1 frequency shift of the asymmetic stretching frequency between measurements taken in the aqueous solution and in the enzyme is reproduced in our theoretical calculations. Our results suggest that CO2 binds to the zinc ion within the hydrophobic pocket. (2) No energy barrier is found for the nucleophilic attack from Zn2+-bound OH- to C of CO2 to form Zn2+-bound HCO3-. (3) For the internal proton transfer within zinc-bound HCO3-, the barrier of 35.6 kcal/mol for the direct internal proton transfer is reduced to 3.5 and 1.4 kcal/mol, respectively, when one or two water molecules are included for proton relay. (4) Displacement of Zn2+-bound HCO3- by H2O is facilitated by the presence of the negatively charged Glu 106-Thr 199 chain and by the association and the subsequent ionization of a fifth water ligand. (5) For the intramolecular proton transfer between Zn2+-bound H2O and His 64, the Zn2+ ion lowers the pKa of Zn2+-bound water and repels the proton. His 64, or a similar proton receptor with a larger proton affinity than H2O, functions as proton receiver; and the active site water molecules visualized by x-ray crystallography are important for the proton relay function. In summary, it is demonstrated that in order to achieve effective catalysis, a sequence of precisely coordinated catalytic events among all participating catalytic elements in the enzyme's active site is essential.

Notes: The pi interaction in complexes of (S)-methyl N-(2-naphthyl)alaninate with (S)- and (R)-N-(3,5-dinitrobenzoyl)leucine n-propylamide was investigated with Hartree-Fock and second-order Møller-Plesset perturbation theory calculations using the STO-3G basis set. For each complex, the geometry of the model of the pi interaction (i.e., naphthalene and 1,3-dinitrobenzene) was derived directly from the complex geometry which was relaxed by the semiempirical quantum-mechanical AM1 method. At the level of treatment used herein, our results are in agreement with our earlier AM1 interaction energy calculations in which the pi interaction, one of the three primary interactions proposed in models of the aforementioned complexes, is attractive and of equal strength (ca. 0.8 kcal/mol) in both complexes.

Notes: An alternative scheme for ab initio polymer band structure calculations based on a Filon-type quadrature is proposed. This scheme avoids the explicit calculation and the storage of the “troublesome” Fourier transforms of the LCAO density matrix elements and is a first step towards a better control of the convergence of the different lattice sums appearing in the configuration space LCAO-SCF-CO method. The potential of the proposed technique is illustrated by a minimal basis set calculations on an infinite chain of H atoms.

Notes: We describe an efficient new algorithm which extends the range of feasible shell model calculations. This algorithm is applicable to single shell and multiple shell configurations, where two or more quantum numbers (e.g., L and S) are required to label the states within each shell. The algorithm proceeds by factoring the shell model Hilbert space into a product of subspaces, one for each angular momentum. N-particle wave functions are built up recursively from N - 1 particle wave functions. Three kinds of N - 1- to N-particle coefficients are required to carry out the construction of N-particle electron (or fermion) states from N - 1 particle states. These are (1) coefficients of fractional parentage (CFPs) within a single shell, (2) outerproduct isoscalar factors (OISFs) within a single angular momentum subspace, and (3) innerproduct isoscalar factors (IISFs) which describe how multishell states within the complementary angular momentum subspaces are combined to form totally antisymmetric wave functions. All three types of N - 1- to N-particle coefficients are generated recursively using a single powerful and efficient matrix diagonalization algorithm. Matrix elements of single particle creation and annihilation operators are expressed in terms of single particle CFPs, OISFs, and IISFs. We also describe an efficient algorithm for computing matrix elements of products of creation and anihilation operators by inserting and summing over complete sets of intermediate states. This is the Feynman-like sum over path overlaps procedure. Timing benchmarks are presented comparing the new Drexel University shell model (DUSM) code with a state of the art shell model code.

Notes: Experimental works suggest the existence of an oscillating complex in the collisional quenching of Na with N2 molecules. Until now, however, few efforts have been dedicated to the study of these possible complexes. In this work, a diabatic and diabatic-configuration interaction method are proposed in order to investigate the existence of these quasibound levels. The results and their comparison with other available data are presented and discussed.

Notes: Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations based on localized/local orbitals and an “effective” CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. 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 more distant neighbors. 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 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 voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H3C—NO2 bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H3C—NO2 bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H3C—NO2 bond dissociation energies.

Notes: In this article, the Hamiltonian for the scattering of the He + H2 system is given by using the interaction potential V(X, Y, Θ) determined by experiments and the semiclassical method. From this Hamiltonian we find a dynamical algebra h6. The statistical expectation of the energy and the transition probability of H2, Pn→m, are derived; therefore, selection rules have been found easily.

Notes: The magnetooptical properties (B terms) vibronically induced have been calculated for a series of carbonyl compounds in the region of the first absorption band. The rules deduced experimentally for the signs and sizes of the B terms induced by vibrations of different symmetry are generally confirmed by these calculations.

Notes: A short review of the recent development of the stochastic approach to chemical reactions in condensed media is made. The relations of this approach to a general formulation of chemical kinetics are discussed on the basis of a many-frequency oscillator model. It is shown that the classical transition-state theory is not a particular case of the stochastic theory neither in the case of small viscosity nor in the case of large viscosity. The recent quantum generalizations of the stochastic theory are identical to earlier results of a quantum transition-state theory that correspond to the case of large viscosity. Such generalizations based on previous results of a collision theory are made for the case of small viscosity. It is shown that these quantum generalizations of the stochastic theory are possible only in the temperature range of moderate tunneling defined in terms of a characteristic temperature.

Notes: A particularly compact form of the orthogonally spin-adapted coupled-cluster equations involving all singly and doubly excited clusters is derived for the general case of a non-Hartree-Fock closed-shell reference determinant. The diagrammatic approach based on the graphical methods of spin algebras is applied. The relationship of different diagrammatic procedures for spin-adaptation, employing both bare and spin-adapted two-electron interaction vertices, is discussed. A comparison with the results obtained with algebraic spin-adaption approaches is also given.

Notes: It is shown that doubly excited states play an important role in calculations of the optical activity of molecules with well-conjugated electron systems, such as the DNA bases. In some significant cases it is necessary to include a large number of excited states in the configuration interaction (CI) to obtain a reliable, converging result. A new version of the CNDO/OPTIC method, which includes doubly excited states in the CI, is proposed. As an application, the electric transition moments in different pyrimidines are considered. The calculated results agree with experimental data and results obtained from ab initio calculations and INDO calculations using doubly excited states in the CI.

Notes: Electronegativity χ and hardness η for 54 atoms and their positive and negative ions are calculated by means of self-interaction-corrected DFT including correlation terms. The exchange potential energy is treated by local spin density approximation corrected to account for self-interaction effects as suggested by Rae. The highest occupied orbital eigenvalues for ions are identified to the chemical potential μ± for positive and negative charged atoms depending upon the developing charge process. Values of χ±δ and η± for the different ionic species are given for several values of δ. Average values for 〈χ〉 and 〈η〉 in the sense of Mulliken finite formula for neutral atoms are also tabulated and compared with Mulliken values from experimental data. The agreement among them is almost quantitative.

Notes: A mathematically well-defined measure of localization is presented based on Mulliken's orbital populations. It is shown that this quantity equals 1 for core- and lone-pair orbitals, 2 for two-atomic bonds, 6 for benzene rings, etc., and it is applicable for delocalized canonical HF orbitals as well. The definition of this quantity is general in the sense that ab initio MOS with overlapping AO expansion, and semiempirical wave functions using the ZDO approximation as well, can be treated. The localization quantity is essentially “intrinsic,” i.e., no subdivision of the molecule is required. For N-electron wave functions, mean delocalization can be defined. This measure is not invariant to unitary transformations of the one-electron orbitals, characterizing in this way the localized or extended representation of the N-electron wave function. It can be proven, however, that for unitary transformed wave functions a maximum delocalization exists which depends only on the physical (N-electron) properties of the molecule. It is shown that inhomogeneous charge distribution can cause strong electron localization in molecular systems. The delocalization of the canonical Hartree-Fock orbitals, the Parr-Chen circulant orbitals, and the optimum delocalized orbitals is studied by numerical calculations in extended systems.

Notes: A graphical approach to the configuration interaction in the basis of pure Slater determinants is presented. The formulation based on the spin-separated two-slope graph (SSTSG), enabling the selection of determinants with the fixed Ms value, has a direct relation to the well-known concept of the group-function product. The commonly used excitation criterion and the spatial (Abelian) symmetry properties are analyzed in terms of the graph's internal structure. The Slater formulae for the Hamiltonian matrix elements between determinants, in the particle-hole formalism and in the spin-separated form, are related to different classes of loops within graphs. Some aspects of implementation within both the matrix-element-driven (ME) and integral driven (ID, direct) CI algorithms are discussed. The presented formulation, of a general complete active space (CAS) CI type, is a basis of the Graphical Determinantal Configuration Interaction (GDCI) computer program.

Notes: The derivative of the electron-electron potential energy Uee with respect to internuclear separation R is studied for light homonuclear diatomic molecules at equilibrium. It is readily related to nuclear-nuclear potential energy Unn, the force constant K, and the electron-nuclear potential energy Uen. An approximate expression, based on the simplest form of density functional theory, is then used to eliminate dUen/dR|Re. The result thus obtained for dUee/dR|Re transcends an earlier proposal of Kryachko by including a term 2/3ReK, with K the force constant. Numerical tests at SCF-RHF level are presented for nine homonuclear diatomic molecules.

Notes: Oxygen clusters of the equilateral ring types On and their negative ions On- are studied by the recently developed pictorial-topological quantum chemistry method, VIF (valency interaction formulas), of this author. The species are found to be of high energy relative to separated oxygen atoms, the cause being evident from the VIF pictures. The odd n rings should be at local minima but are not likely to have observable negative ions. The even n rings have distortional instabilities, yet their negative ions are more likely to be observed as transients in beam experiments.

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: Generalized Padé approximants are used to extrapolate the total energy of polymers described by alternant Hamiltonians to the bulk limit. The method provides an upper bound to the energy. The origin of (quasi) periodic oscillations of the energy per unit cell as the function of the number of unit cells is enlightened through analysis of the moments of the Hamiltonian.

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: Using molecular orbital methods, we propose various models of interactions between GABA or analogs (TACA, muscimol, isomuscimol) and an hypothetical receptor molecular fragment, a methylguanidinium ion. The respective geometries of the GABA-, TACA-, muscimol-, and isomuscimol-methylguanidinium ion complexes are optimized using the semi-empirical MNDO method. Stabilization energies of the complexes obtained by substraction of the heats of formation of the optimized complexes from those of the optimized isolated molecules differentiate the behavior of the anionic heads between the agonist and antagonist compounds. Affinity and stabilization are confirmed by computing ab initio STO-3G ionization potentials and interaction energies taking into account counterpoise corrections. Results show a decrease of the interaction energy from GABA and TACA (-54.9 and -49.4 kcal/mol) to isomuscimol (-35.6 kcal/mol), via muscimol (-46.0 kcal/mol). The low interaction energy of the 5-isoxazolols as isomuscimol compared to the 3-isoxazolols, as muscimol, may explain their antagonist character.

Notes: Whereas localization of orbitals has long been a tool for a semiclassical interpretation of chemical properties, it is in fact electron delocalization that is a fundamental property of quantum mechanical molecules. A mathematically well-defined measure is suggested for the degree of delocalization of molecular orbitals. It is shown that an orbital set of maximum delocalization exists for which the degree of delocalization depends on the charge distribution of the molecule. Hartree-Fock canonical orbitals are definitely more localized than the most uniformaly distributed MO's giving an equivalent description of the molecule. The changes in the geometrical shape of molecular orbitals are studied passing (quasi-) continuously from the strongly localized description towards the most delocalized picture. In the case of charge-inhomogeneities even the most delocalized orbitals remain rather compact. The degree of maximum delocalization may be correlated with chemical properties such as reactivity. The shape distortion of MO's under the perturbing effect of other ions and small molecules is investigated in several examples.

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: Using ab initio RHF-SCF-MO theory with the 3-21G basis set and geometry optimization with a gradient method, trans pentadienyl lithium and sodium have been shown to have a carbon backbone in which the middle carbon atom falls ca. 40° out of the plane of the other carbon atoms. The free anion was found to be planar. Optimization of the dilithium octateraene complex (C8H10Li2) with C2 symmetry gave a structure where the hydrocarbon backbone is distorted out of plane and folded about the lithium atoms. A partially optimized C8H10Li2 where the C and H atoms are constrained to remain in-plane lies ca. 0.6 eV above the folded structure. The consequences of the distortion are discussed for the applicability to longer polyenes and n-doped polyacetylene. In a vibrational analysis of C5H7Li and C5H7Na and of allyl Li and allyl Na, two very intense bands near 800 cm-1 appear which are not present in the flat, free allyl and pentadienyl anions. The similarity to the broad band at 800 cm-1 which appears in doped polyacetylene is discussed.

Notes: Correlation energies are divided into two parts. One contribution is given by a configuration interaction calculation in the space of the natural orbitals with occupation numbers larger than an arbitrary threshold v. The remaining part is obtained from a v-dependent functional of the electronic density. Representative examples (for which the existing spin-density functionals fail) are (1) the correlation energies in the He and Be series and (2) the contribution of the correlation energy to the dissociation energy of the first-row dimers. It is shown that even for large values of v the errors remain on the order of 0.01 hartree.

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: The need to perform a numerical integration of the exchange-correlation functional because of its non-analyticity severely complicates the accurate application of local-density functional methods to molecules and clusters. The optimal choice of grid points for this integration and the estimation of the error made by the choice are subtle considerations. In particular, because the position and/or weighting of each grid point must change when the nuclear positions change, these errors are most noticeable when different geometries are compared. We have determined a method of grid point selection and weighting that reduces these errors. We have also determined a simple method of estimating the extent of the error made in the particular density of points used for the grid. These results are illustrated for a selection of small molecules.

Notes: The induction of electronic motion by nuclear motion is described for the particular case of the absorption of infrared radiation by chiral molecular systems. The description is in terms of an effective vector potential, which is obtained by averaging over the electronic coordinates. This effective vector potential can be visualized in a number of ways. Nine of these are tabulated and discussed. Strong evidence is presented that the interaction of rings with radiation can be treated in the same way as the interaction with chains. Evidence is also obtained that the bulk of the induced electronic motion can be determined semiclassically.

Notes: All bicyclo[p.q.0] conjugated hydrocarbons are found to fall into ten homolog classes each characterized by the numbers of nonbonding, bonding, and antibonding molecular-orbitals of its first prototype and by the prototype itself. The energy level patterns are obtained by the new “structural covariance” pictorial rules directly from structural formulas. The HOMO-LUMO types, aromaticity or three types of nonaromatic behavior, and reactivities towards nucleophiles or electrophiles thereby also result.

Notes: The COLUMBUS program system is a collection of Fortran programs for performing general multireference single- and double-excitation configuration interaction (MRSDCI) wave function optimization based on the graphical unitary group approach. The program system also includes integral generation, SCF and MCSCF orbital optimization, integral transformation, and wave function analysis programs. The original program system was written in 1980 to 1981. Since that time, it has evolved into one of the most popular MRSDCI program systems used in the computational chemistry community. The discussion of this evolution will include the exploitation of efficient matrix-matrix and matrix-vector product computational kernels, the use of generally contracted symmetry-adapted orbital basis sets, general Hamiltonian diagonalization procedures, energy-based internal walk selection, flexible DRT specification, improved coupling-coefficient evaluation methods, coupled-pair functional and multireference CPF capabilities, and density matrix construction. The numerous versions of the program system that are maintained at different sites and on different computers are now in the process of being merged. The source code for this combined version will be made available to the computational chemistry community. The source code for a specific computer may be generated from the source code for another computer by a single pass through a simple filter utility that is included with the program system. The directly supported computers will initially include various models of VAX, Cray, FPS, IBM, CDC, and ETA machines with the addition of other machines shortly thereafter. The ongoing developments of the COLUMBUS system that are discussed include a new method for computing analytic energy gradients for MRSDCI wave functions. This effective-density-matrix based method avoids the “coupled perturbed MCSCF” solutions for each coordinate direction, avoids the transformation of any derivative-integral quantities from the AO to the MO basis, avoids the transformation of the coupling coefficients from the MO to the AO basis, allows a subset of the MCSCF doubly occupied orbitals to be frozen in the CI wave function, and allows the MRSDCI wave function to be generated from general reference CSFs that are not necessarily related to the MCSCF expansion CSFs.

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: A general technique will be outlined which provides a systematic means for fitting polyatomic potential energy surfaces. Use is made of both ab initio energy and gradient data to fit the surface about an N-dimensional reference curve connecting stationary points. The reference curve may be modified iteratively during the course of the fitting. A particular iteration will specify a new set of points which need to be calculated to improve the accuracy of the surface. An application of this method to a model potential energy surface is discussed.

Notes: The application of molecular ab initio methods to investigate the electronic structure of localized impurities in semiconductors requires the study of the convergence of the results with increasing cluster size. Here we compare results for interstitial Ti in silicon, obtained with clusters of increasing size: TiSi10H16, TiSi30H40, and TiSi66H64. These clusters contain one, two, or three shells of silicon atoms, respectively, centered around Ti at a Td interstitial site. The hydrogen atoms serve as saturators of the dangling bonds. The Si core electrons are replaced by an effective potential. The calculations are based on open shell RHF theory and limited CI extensions. The charge distribution in the central part of the three clusters is very similar. In the clusters the partially occupied orbitals are much more delocalized than the 3d orbitals in the free ions. The total impurity-induced electronic charge, however, is quite localized, due to the compensating response of the Si closed shell density. Ionization of the impurity also causes a compensating response of the Si closed shells: only about 10% of the density difference is in the impurity region and the major part is behind the outermost shell of Si atoms. Transition metal associated (3d-like) excitation energies are not very dependent on the cluster size, and the relative ordering of the lowest lying states remains unchanged. Impurity associated ionization energies decrease considerably due to the extra relaxation offered by the additional shells of Si atoms. Our results indicate that a reliable description of interstitial transition metals in silicon can be provided by calculations on reasonably small clusters: Si30H40 is sufficiently large.

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: It is shown by using the Z-1 perturbation expansion in the limit of large nuclear charge, that the leading term in the chemical potential of neutral atoms is given by the summation of two oscillatory terms that have an amplitude proportional to Z-1/3, are periodic in Z1/3, and have slightly different phases. It is further shown that for atoms in the periodic table the position of the point where the derivative of the energy with respect to the number of electrons becomes zero will have a strong influence on the phases of the oscillations but not on their amplitudes.

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: The titled isomerization has been studied at the HF/3-21G level. The changes in thermodynamic functions, equilibrium constant K(T), conversion efficiency C(T), and the rate constant k(T) for the isomerization have been calculated using our energies of the reactant (R), transition state (TS), and product (P), their harmonic vibrational frequencies, and the classical and corrected barrier (by vibrational zero-point energies). In the range of temperature, 300-1200K, ΔH 〈 0, ΔS 〉 0 and ΔG 〈 0; i.e., it is exothermic, increasing in the entropy, and spontaneous reaction. ΔS≠ 〈 0, log A is about 12.0 ±0.15 (s-1), but the k(T) is from 2.627 × 10(-33) to 6.933 × 10(8) (5-1); i.e., it passes through a tight TS, the A factor changes little, but the rate constant varies rapidly with the temperature. These results agree with the fact that the isomerization occurs readily at high temperature. Furthermore, Newman's mechanism, 2SiH2 → (H2SiSiH2)* → (HSiSiH3)* → Si2H2 + H2, is supported. Similarly, the isomerization, HDSiSiH2 → HSiSiDH2, is also studied.

Notes: A complete active space MCSCF (multi-configuration self-consistent field) scheme (CASSCF) using relativistic effective potentials followed by configuration interaction and relativistic CI calculations provides a very good description of the electronic states and potential energy surfaces of transition metal dihydrides. Such calculations are of considerable value not only in our understanding of the transition metal-hydrogen bonding but also in the prediction of the barrier to insert the metal atom into the H2 bond. All-electron CASSCF/CI calculations are carried out on twelve electronic states of CoH2. Comparable RECP-CASSCF/CI calculations are also carried out to show that the RECP-CASSCF/CI calculations provide an accurate method for the investigation of transition metal compounds. The general method of RECP-CASSCF/CI calculations for molecules containing heavy atoms is described. The calculations on CoH2 are compared with similar calculations on ScH2, YH2, PtH2, and PdH2. A critical comparison of all these transition metal hydrides reveals that in general the low-spin excited metal atom inserts into H2 spontaneously while the high spin ground state atom has to surmount a large barrier.

Notes: The Generator Coordinate Approximation (GCA) is the general approximation scheme for molecular systems devised to improve the Adiabatic Approximation (AA). This is achieved by replacing the familiar product-type molecular wave function by a convolution product-like state. One can demonstrate via Born-Oppenheimer perturbation theory that for vibration-rotation levels near potential energy minima the GCA results are bracketted by the exact and adiabatic values, subject to the use of good quality electronic states as input (e.g., the Hellman-Feynman theorem needs to be satisfied accurately). We investigate the relevance of the GCA for energy levels near avoided crossing regions using a system modeled on the EF 1Σ+g state of hydrogen. The results of numerical experiments on this system are very encouraging (80-90%) of the nonadiabatic effects is recovered. This numerical success awaits theoretical explanation.

Notes: Two mapping operators are used to relate the eigenstates of two distorted and displaced oscillators. It is found that these operators satisfy a nonabelian two-dimensional algebra. We exemplify the method by calculating the Franck-Condon integral for the case of two harmonic oscillator wells.

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 problems involved in determining the mechanisms of reactions by quantum mechanical calculations are discussed. Various precautions must be taken if the results of any calculation are to be chemically meaningful. Ab initio studies of reactions must also be carried out at a high level, using large basis sets and allowing for electron correlation. Such calculations are usually restricted to the simplest example of a reaction, which is often untypical. More information can usually be obtained at far less cost through AM1 calculations for a number of examples of a reaction for which experimental data are available. These points are illustrated by recent studies of the Cope rearrangement.

Notes: Visualization techniques have proven extremely valuable for understanding the dictates controlling asymmetric organic reactions. A series of chemical reactivity models has been developed, which provide a convenient connection between the structural and reactivity aspects important in chemical systems. Structural information is conveyed through the use of shading, while reactivity information, evaluated at points located upon the structural model, is displayed coincident with structure using the color dimension hue. The utility of the resulting four-information-dimensional image can be appreciated by the speed at which all the information presented is assimilated and interpreted by the viewer. While having been demonstrated to be useful in understanding the dictates of asymmetric organic reactivity, the visualization techniques discussed here should be applicable to the description of problems in molecular interactions and structure-activity relationships in general.

Notes: γ-Aminobutyric acid (GABA) is an inhibitory transmitter used by interneurons in the central nervous system (CNS). In aqueous solution GABA exists as a zwitterion, but in the gas phase the stable form of GABA is a nonzwitterion. Since zwitterions are difficult to transport into the CNS, details of the mechanism for the transformation between nonzwitterionic and zwitterion forms of GABA provide potentially important suggestions for enhancing transport of GABA and GABA analogues into the CNS. A mechanism for the conversion of GABA into the zwitterion form upon aqueous solvation is suggested as a multistage process by simple quantum chemical simulation. Initially, hydrogen bonding at the carbonyl oxygen is followed by attack of water at the carbonyl carbon and results in the formation of a triol. Hydrogen bond bridging, through solvent, from the triol end of the molecule to the amino terminus, facilitates N-protonation from the solvent. The latter appears to trigger rearrangement of the hydrogen bonding at the triol function, thus giving the anionic precursor to the zwitterion. This mechanism is based upon full INDO calculations using a supermolecule composed of GABA and 14 water molecules and resembles part of one of the mechanisms for the hydrolysis of esters as well as a process for the hydration of aldehydes.

Notes: The kinetics of gas-phase electron transfer reactions for a variety of metal-containing reactants have been studied by using Fourier transform ion cyclotron resonance mass spectrometry. Classes of ion/molecule processes studied include both self-exchange (thermoneutral) and exoergic cross reactions. The molecules investigated include metallocenes and octahedral coordination complexes of the transition elements. In a few cases, direct comparisons of condensed-phase and gas-phase reactivities can be made. The experiments with octahedral coordination complexes are the first studies of Werner-type metal complexes in electron-transfer reactions in the gas phase. Simple theoretical models involving unimolecular rate theory, classical reorganization barriers, and quantum mechanical approaches are used to rationalize the dependence of the overall rates of these reactions on the molecular properties of the reactants. In particular, the role of Franck-Condon factors in charge-transfer reactions is examined, and theoretically estimated factors are compared with experiment for a typical metallocene, ferrocene.

Notes: Vibrational frequencies and IR band intensities for 18 isotopomers of uracil, including deuterated 15N and 18O species, have been calculated using the scaled ab initio force field of Ref. 1. The results obtained are compared with available experimental data, and a number of refinements in former assignments are proposed. The good agreement between the calculated and experimental frequencies confirms the reliability of the scaled quantum mechanical-force field.

Notes: The reaction field (RF) model of solvent effects, implemented within the SCF-CNDO/2 scheme of calculation, has been applied to analyze the proton transfer in the NH3…HCOOH system in the presence of several polarizable media. The aim of such a study was to characterize the tatutomeric equilibrium between the neutral and zwiterionic forms of H-bonded amino acids in aprotic solvents. Qualitative results concerning the energetics of this equilbrium show the stabilization of two different H-bonded complexes, corresponding to two separate minima in the free energy surface. These well known double minima potentials are found to be dependent on both the intermolecular N—O distance and the strength of the reaction field. The behavior of this model is qualitatively consistent with experimental observations of nitrogen-substituted amino acids in solution: both show, for low values of the dielectric constant, tautomeric equilibria where the H-bonded complexes appear to be more stable than the corresponding monomeric forms. The charge transfer process associated with the proton migration along the H-bond is also discussed. It is found that the amount of charge transferred increases with the N—O distance and with the RF strength, In order to test the general approach and compare it with previous work, calculations on the real monomeric systems glycine, β-alanine, and γ-amino butyric acid was also performed.

Notes: The quasirelativistic CNDO/1 method has been in investigating the geometry, electronic structure, and redox stability of metal complexes. The systems of [Co(NH3)6]q and [MCl4]q, M being Ni, Pd, and Pt, have been studied. A modified Germer model of solvation has been implemented into the method. This yields reliable results on the redox stability of complexes in aqueous solutions. The calculated excitation energies resemble the electronic spectra of [MCl4]2- complexes.

Notes: The energy of an infinite, homogeneous electron gas is examined by second order perturbation theory using a Hartee-Fock rather than a noninteracting particle unperturbed state. The second order energy still diverges for small promotions k, albert than as ln|ln k| rather than as In k.

Notes: A Hartree-Fock (HF) self-consistent field (SCF) crystal orbital (CO) formalism for two- and three-dimensional (2D/3D) solids on the basis of semiempirical CNDO/INDO (complete neglect of differential overlap; intermediate neglect of differential overlap) Hamiltonians is presented. The employed SCF variants allow for the treatment of atomic species up to bromine under the inclusion of the first (i.e., 3d) transition metal series. Band structure investigations of 2D and 3D materials containing more than 30 atoms per unit cell are feasible by the present SCF HF CO formalism. The theoretical background of the computational scheme is given in this contribution. Special emphasis is placed on physically reliable truncation criteria for the lattice sums, the adaptation of the crystal symmetry in k space, as well as the suitable choice of domains in Brillouin zone (BZ) integrations required in the determination of charge-density matrices. The capability and limitations of the semiempirical SCF HF CO approach is demonstrated for some simpler solids by comparing the present computational results with those of ab initio CO schemes as well as conventional numerical methods in soid-state theory. The employed model solids are graphite and BN (2D and 3D networks for both solids) as well as diamond, silicon, germanium, and TiS2.

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: 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.