Application of many-body perturbation methods in a discrete orbital basis

The many-body perturbation theory techniques used by Kelly to calculate “pair correlation energies” have been implemented in a discrete orbital basis using a set of coupled non-linear equations. The methodology differs from the usual “independent pair” methods in that the pairs are coupled by “rearrangement” effects. Some numerical results on BH are given to illustrate the utility of the method.     

Response function theory of electron correlation

The full perturbation expansion for the response (or density—density correlation) function is examined in order to provide a useful general theory of excitation energies, oscillator strengths, dynamic polarizabilities, etc., that is more accurate than the random phase approximation. It is first shown how the formal partition of the diagrammatic version of the perturbation expansion into reducible and irreducible diagrams is generally useless as the latter category contains all the difficult terms which have heretofore resisted analysis in all but a haphazard form. It is then shown how the diagram for the response function can be partitioned into “correlated” and “uncorrelated” subsets. Restricting attention to the particle—hole blocks of the full response function, the “uncorrelated” diagrams desecribe the propagation of a particle—hole pair in an N-electron system where the particle and hole are each interacting with the remaining electrons but they are not interacting with each other. The “correlated” diagrams are those containing the hole—particle interactions, and, by defining a new class of reducible and irreducible diagrams, these are all summed to provide a perturbation expansion of the effective two-body hole—particle interaction that appears in the inverse of the response function. The “uncorrelated” diagrams are further partitioned into two sets, one of which is summed to all orders, while the other set is inverted in an order by order fashion. The final result presents a perturbation expansion for the inverse of the response function that is analogous to the Dyson equation for one-electron Green functions. Maintaining the perturbation expansion through first order for the inverse of the response function yields the eigenvalue equation of the familiar random phase approximation, while truncation at second order provides the most advanced theories that have been generated by the equations-of-motion method.     

Electronic correlation studies. II. Self-correlated field method. Application to ground state and first 1P, 3P excited states of two-electron atomic systems

An antisymmetric pair function can be built upon two kinds of monoelectronic functions, the former ones being correlated local functions and the second ones nonlocal functions taking external effects into account. This function, brought into the generalised product function procedure by means of the density matrix formulation, makes possible the study of correlation within N-electronic systems. The results of a first application of this method to the fundamental and to ¹P and ³P excited states of two-electron systems are given.     

Die horizontale Korrelation in π-Elektronensystemen und ihre Beschreibung durch Elektronenpaarfunktionen

Different types of pair functions (geminal products and their linear combinations) are tested with respect to their ability to describe the “horizontal correlation” of the π-electrons of butadiene. The validity of the π-electron approximation is not discussed and “full configuration interaction” within the limited LCAO basis is used as the standard to which the model calculations are referred. An APSG-function (APSG = antisymmetrized product of strongly orthogonal geminals) built up from equivalent (localized) geminals, which contains only one variational parameter is able to account for about 90% of the “horizontal correlation energy”. Both APSG and APIG functions constructed from delocalized geminals, are much less favorable. Criteria of the goodness of an approximate wave function are a) the energy b) comparison of its one- and two-particle density matrices with those obtained from “full CI”. The good results with the localized APSG function are related to the fact that electron correlation between electrons of opposite spin is (in this molecule) essential only within either of the “double bonds” of the “canonical structure”. The pertinent results are quite insensitive to different parametrization of the integrals.     

Polymerization of α,α-disubstituted-β-propiolactones and lactams. 10. Crystalline structure,thermal and mechanical studies of statistical and block copolymers of pivalolactone and α-methyl-α-propyl-β-propiolactone

AB and ABA block copolyesters based on racemic poly(α-methyl-α-n propyl-α-propiolactone) (PMPPL) as a “soft” or elastomeric segment and polypivalolactone (PPL) as a “hard” or crystallizable segment have been synthesized and compared with random copolymers of the same composition. X-ray studies show the coexistence of polymorphic crystal forms for a given polymer in a given sample. Thermal and dynamic mechanical properties give clear evidence of heterophase structure corresponding to segregation of PPL and PMPPL. The crystalline phase clearly provides thermally reversible crosslinking in the ABA block copolymers. On stretching, the planar zigzag form of PMPPL is observed. Because of the domain structure, moduli of ABA samples are higher than those of PMPPL and their tensile strengths are similar to those of comparable styrene-butadiene block copolymers. The polymer synthesis was achieved by sequential monomer addition with tetrahexyl ammonium benzoate as initiator. For the ABA polymers the diammonium salt of sebacic acid provided a di-functional initiator. The agreement between calculated and observed molecular weights testify to the “living” character of this polymerization reaction.     

Study of pair correlation in three-electron atoms

Pair correlation in the ground state of the Li isoelectronic sequence is studied through four approximate wave functions which incorporate inter- and intrashell pair correlation. Of these functions, two possess symmetry appropriate to a three-electron system, while two do not. The functions are not variational functions in the usual sense. They are instead fixed linear combinations of products of orbitals and pair functions for the appropriate states of two-electron atoms. They are considered here as zero-order approximations to the exact wave functions, and the corresponding zero-order Hamiltonians are obtained. The simplest of these functions is improved by the introduction of a screening parameter for the “outer” electron. This latter function is found to be a satisfactory compromise between accuracy and simplicity and is proposed for study via higher-order perturbation theory.     

On the quantum momentum method for the exact solution of separale multiple well bound state and scattering problems

A simple method is suggested for the convenient application of Milne's method of solution of the one-dimensional Schrödinger equation to multiple well potentials. The method involves the introduction of “quantum momentum” functions which resemble the classical momentum over each “well”. The wavefunction is matched at intermediate point between the “wells”, and the quantization requirements are determined. The double oscillator and scattering by spherically symmetric potentials are cited as applications.     

A BSSE-free SCF algorithm for intermolecular interactions. II. Sample calculations on hydrogen-bonded complexes

The usefulness and reliability of the recent BSSE -free SCF algorithm based on the “chemical Hamiltonian approach” (CHA /F ) is demonstrated by calculating potential curves for several hydrogen-bonded complexes with 4-31G , 6-31G , and 6-31G ** basis sets. It is concluded that the CHA /F scheme gives results that are numerically close to those of the Boys–Bernardi a posteriori correction scheme but are free from the “overcompensation” characteristic of the latter at smaller distances and given basis sets. © 1992 John Wiley & Sons, Inc.     

A minimum principle for atomic systems allowing the use of discontinuous wave functions

In this paper a variational principle proposed by Hall [1] is shown to be a minimum principle for coulombic systems. Into this principle it is possible to admit a larger class of trial wave functions than is possible in the conventional variational treatment, including wave functions with discontinuities. It is further shown that the upper bounds given by this treatment are always at least as good as that given by the Rayleigh–Ritz method. The theory is then applied to the hydrogen atom and upper bounds to the energy are calculated for various “cutoff” wave functions. It is usually possible to define an optimum “cut off” distance which minimizes the upper bound.     

微芯片上Ag2S电化学纳米开关的构筑及电学测量的初步研究

初步探索了利用电化学方法“自下而上”地构筑了Au/Ag/Ag2S-Au固体电化学纳米开关, 并确定了较适宜的开关工作条件. 小于1 nm的Ag2S-Au间隔是Ag2S开关器件的关键结构, 以保证电子的量子遂穿和间隔中Ag凸起的生长与收缩. 测量结果表明, Ag2S开关转换具有较好的可逆性和稳定性, 开关转换电流相差3个数量级以上.     

A new statistical thermodynamic theory for substoichiometric fluorite structure compounds and its application: I. An order-disorder model theory for the thermodynamic functions of substoichiometric fluorite structure compounds

In this work an attempt is made of constructing the (G, T, x) curves for the case of substoichiometric oxides of the fluorite structure on the basis of a statistical model. Considering the fluorite structure as a repitition of oxygen ions tetrahedrically coordinated, the hypothesis is made of a local bond between the reduced cations and the oxygen vacancy in the tetrahedron (“tetrahedral defect”).This “tetrahedral defect” constitutes the building block of the low temperature sub-phases often encountered in these systems; at higher temperatures its packing in the lattice gives rise to “residual structures”.One can express all thermodynamic functions, at given oxygen/metal ratio, as a function of an “ordering parameter” p, representing larger and larger packings of the tetrahedral defects, in such a way making this model a typical order-disorder treatment.Introducing the formalism of chemical equilibria in the equilibria between the various defect species it is also possible to obtain thermodynamic functions by the solution of a system of pseudo-chemical equilibrium equations, when probability functions f are employed in place of the activities of the defects species.     

A united-residue force field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data

A two-stage procedure for the determination of a united-residue potential designed for protein simulations is outlined. In the first stage, the long-range and local-interaction energy terms of the total energy of a polypeptide chain are determined by analyzing protein-crystal data and averaging the all-atom energy surfaces. In the second stage (described in the accompanying article), the relative weights of the energy terms are optimized so as to locate the native structures of selected test proteins as the lowest energy structures. The goal of the work in the present study is to parameterize physically reasonable functional forms of the potentials of mean force for side-chain interactions. The potentials are of both radial and anisotropic type. Radial potentials include the Lennard-Jones and the shifted Lennard-Jones potential (with the shift parameter independent of orientation). To treat the angular dependence of side-chain interactions, three functional forms of the potential that were designed previously to describe anisotropic systems are evaluated: Berne-Pechukas (dilated Lennard-Jones); Gay-Berne (shifted Lennard-Jones with orientation-dependent shift parameters); and Gay-Berne-Vorobjev (the same as the preceding one, but with one more set of variable parameters). These functional forms were used to parameterize, within a short-distance range, the potentials of mean force for side-chain pair interactions that are related by the Boltzmann principle to the pair correlation functions determined from protein-crystal data. Parameter determination was formulated as a generalized nonlinear least-squares problem with the target function being the weighted sum of squares of the differences between calculated and “experimental” (i.e., estimated from protein-crystal data) angular, radial-angular, and radial pair correlation functions, as well as contact free energies. A set of 195 high-resolution nonhomologous structures from the Protein Data Bank was used to calculate the “experimental” values. The contact free energies were scaled by the slope of the correlation line between side-chain hydrophobicities, calculated from the contact free energies, and those determined by Fauchere and Pliška from the partition coefficients of amino acids between water and n-octanol. The methylene group served to define the reference contact free energy corresponding to that between the glycine methylene groups of backbone residues. Statistical analysis of the goodness of fit revealed that the Gay-Berne-Vorobjev anisotropic potential fits best to the experimental radial and angular correlation functions and contact free energies and therefore represents the free-energy surface of side-chain-side-chain interactions most accurately. Thus, its choice for simulations of protein structure is probably the most appropriate. However, the use of simpler functional forms is recommended, if the speed of computations is an issue. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 849–873, 1997     

Molecular weight distributions in radiation-induced polymerization. VII. γ-ray-induced polymerization of “wet” styrene in the solid state

In the present paper kinetic and molecular weight distribution results are reported for the γ-ray-initiated polymerization of styrene in the solid state. “In-source” polymerization over the temperature range ?35°C to ?55°C and post-polymerization at ?35°C have been investigated for “wet” styrene samples (water concentration ≈ 10^?3 mole/l.). An interesting feature of the solid-state polymerization of styrene is the bimodal nature of the molecular weight distribution. On a qualitative basis the results resemble those obtained previously for the polymerization of rigorously dried (“dry”) styrene. However, there are noticeable differences on a quantitative basis resulting from the considerable difference in the water content between wet and dry samples. On the basis of these studies, the kinetic and molecular weight distribution data have been interpreted as being indicative of polymerization occurring simultaneously via free-radical and cationic mechanisms.     

Configuration interaction matrix elements. I. Algebraic approach to the relationship between unitary group generators and permutations

Matrix elements of unitary group generators between spin-adapted antisymmetric states are shown to be proportional to spin matrix elements of so-called “line-up” permutations. The proportionality factor is given explicitly as a simple function of the orbital occupation numbers. If one bases the theory on ordered orbital products, the line-up permutations are given a priori. The final formulas have a very simple structure; this is a direct consequence of the fact that the spin functions have been taken to be geminally antisymmetric.     

A new look at correlations in atomic and molecular systems. I. Application of fermion monte carlo variational method

We are engaged in research directed toward the development of compact and accurate correlation functions for many-electron systems. Our computational tool is the variational method in which the many-electron integrals are calculated by Monte Carlo using the fermion Metropolis sampling algorithm. That is, a many-fermion system is simulated by sampling the square of a correlated antisymmetric wave function. The principal advantage of the method is that interelectronic distance r_ij may be included directly in the wave function without adding significant computational complexity. In addition, other quantities of physical and theoretical interest such as electron correlation functions and representations of Coulomb and Fermi “holes” are very easily obtained. Preliminary results are reported for He, H₂, and Li₂.     

Correlation effects in the low–lying excited states of the PPP models of alternant hydrocarbons. I. Qualitative rules for the effect of limited configuration interaction

Simple rules for an estimate of the correlation effects in the low-lying states of alternant hydrocarbons, as described by the Pariser–Parr–Pople Hamiltonian, are formulated. These rules are based on the alternancy and spin symmetry classification of states in both strongly and weakly correlated limits and on the valence bond characteristics of those states in the fully correlated limit. It is shown that the largest effect of the electron correlation will be found for the singlet “minus” states (using Pariser's classification of the alternancy symmetry species), a smaller effect for the triplet “plus” states, and a much smaller effect for the remaining states. These rules are exemplified by limited CI calculations including all monoexcited and all mono- and bi-excited configurations, respectively, for a number of π-electronic systems. In view of these rules the success of the PPP model in the monoexcited CI approximation may be understood.     

Highly correlated particle densities and idempotent one-densities

The problem of determining idempotent one-densities which integrate to the exact or to a highly correlated particle density is considered. A method for obtaining the minimum energy idempotent one-density integrating to a given correlated particle density within a finite basis is described. The implications of this are twofold. First, Hartree–Fock accuracy can be exceeded in describing the electron density with an idempotent one-density; this is particularly relevant to the problem of constructing orbitals from experimental x-ray scattering data. Second, electron densities from analytic CI or MCSCF wave functions can be made available in a form as compact as the Hartree–Fock density by reporting the orbitals which define the correlated density via an idempotent one-density. A numerical example of the new method is given in which an accurate correlated density for He is “fitted” by an idempotent one-density represented in a finite (near Hartree–Fock) basis. Considering the deficiencies of the basis for this purpose, a technique is suggested for constructing basis sets optimized for prediction of one-electron properties rather than for energy.     

Spatial correlations of interatomic voids in molecular liquids studied using Delaunay simplices

Pair correlation functions are calculated for interatomic voids determined using Delaunay simplices. Various modifications of these functions are suggested in relation to the problem formulated. In the simplest case, this correlator is a conventional radial distribution function g(r), but its calculation employs the centers of voids, but not the centers of atoms. For analysis of nonuniform systems, it is suggested that a “weighted” radial distribution function be used, where pair distances are taken with weights that depend on the volume of the voids. To study structural differences between molecular liquids (e.g., alkane isomers) we use the partial radial distribution functions that take into account only relatively “wide” voids. The ion-void distance distribution functions define voids in the hydration shells of ions an aqueous salts.     

The Coulomb hole in the 23S state of the helium isoelectronic sequence

The pair distribution functions evaluated for the 2³S state of the helium isoelectronic sequence from the Hart and Herzberg correlated wave functions and those corresponding to the Hartree-Fock approximation are used to determine the shape of the corresponding Coulomb holes. As a consequence of a discontinuity in the Hartree-Fock solution between He and Li⁺, the Coulomb hole has a different shape for He than for Li⁺ and the other isoelectronic ions.