Determination of molecular properties by the method of moments. I

The method of moments appears to have some significant advantages over other variational methods of quantum chemistry if complicated molecular systems are investigated and elaborate variational wave functions are applied. The main advantages are (a) the possibility of avoiding the worst difficulties of integration or reducing the number of integrals (b) the possibility of improving the accuracy of the wave function in physically important regions of the configurational space and (c) the possibility of obtaining some random sampling type error estimates. The aim of the series of papers starting with the present one is to collect experience in applying the method of moments to problems of quantum chemistry.

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Zusammenfassung Die Methode der Momente scheint gegenüber den üblichen Variationsmethoden in der Quantenchemie einige bedeutende Vorteile zu besitzen, besonders wenn es sich um Untersuchungen komplizierter molekularer Systeme handelt, die nur mit umfangreichen Variationswellenfunktionen behandelt werden können. Die Hauptvorteile der neuen Methode sind: (a) Die bei der Integration auftretenden großen Schwierigkeiten bzw. die Anzahl der zu berechnenden Integrale können erheblich herabgesetzt werden. (b) In den physikalisch besonders wichtigen Bereichen des Konfigurationsraumes besteht die Möglichkeit, die Wellenfunktionen beträchtlich zu verbessern. (c) Es können Fehlerabschätzungen gemacht werden. Ziel dieser Arbeit ist es, erste Erfahrungen in der Anwendung der neuen Rechenmethode auf quantenchemische Probleme zu sammeln.

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Résumé La méthode des moments parait posséder des avantages nets sur les autres méthodes variationnelles de la chimie quantique si l'on étudie des systèmes moléculaires complexes et si l'on utilise des fonctions d'onde variationnelles perfectionnées. Les avantages principaux sont a) la possibilité d'éviter les difficultés les plus gênantes de l'intégration et de réduire le nombre d'intégrales; b) la possibilité d'améliorer la précision de la fonction d'onde dans les régions de l'espace de configuration les plus importantes pour une observable, et c) la possibilité d'obtenir des évaluations du type «échantillonnage au hasard» des erreurs commises. Le but de la série d'articles qu'inaugure celui-ci est de présenter une information sur l'application de la méthode des moments aux problèmes de la chimie quantique.

     

Determination of molecular properties by the method of moments. II

The wave functions and energies of a number of diatomic molecules have been determined for different nuclear separations by both the method of energy variation and the method of moments. The results obtained by the two methods are compared and indicate definite advantages of the method of moments over the method of energy variation.

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Zusammenfassung Für eine Reihe zweiatomiger Moleküle werden für verschiedene Kernabstände die Wellenfunktionen und Energien nach der Methode der Energievariation und nach der neueren Momentenmethode bestimmt. Der Vergleich der Ergebnisse zeigt, daß die Momentenmethode erhebliche Vorteile besitzt gegenüber der üblichen Methode der Energievariation.

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Résumé Les fonctions d'onde et les énergies de plusieurs molécules diatomiques ont été déterminées à différentes distances internucléaires par la méthode de variation de l'énergie et par la méthode des moments. Les résultats comparés des deux méthodes indiquent de nets avantages de la méthode des moments sur la méthode de variation de l'énergie.

     

Determination of molecular properties by the method of moments

Some precautions needed in the choice of weight functions when calculating wave functions by the method of moments are analysed. It appears that an important criterion for good weight functions is that the difference between the total and the truncated overlaps (both defined in the paper) be high.The method of moments is applied to wave functions involving Hylleraas-type correlation factors using weight functions made up of products of single-particle orbitals. The aim of the calculations is partly to test the criteria for good weight functions, partly a preparation of more extended calculations of a similar type.The new name of the institute is: Computer Application Research and Development Center of the Chemical Industries.     

Determination of molecular properties by the method of moments

The method of moments and the method of least squares is applied to electron scattering on a simple model potential. Some general problems connected with treatment of scattering problems by the method of moments and the method of least squares are discussed. The calculations give an example of the random sampling type error estimates discussed in previous papers of the series, and present a possible way of optimizing nonlinear parameters in the framework of the method of moments and the method of least squares.

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Zusammenfassung Die Momentenmethode und die Methode der kleinsten Quadrate wird auf die Elektronenstreuung an einem einfachen Modellpotential angewandt. Einige allgemeine Probleme bei der Anwendung dieser beiden Methoden auf Streuprobleme wurden diskutiert. Die Berechnungen geben ein Beispiel der Fehlerabschätzung vom Stichproben-Typ, der in vorhergehenden Artikeln dieser Serie untersucht wurde; sie stellen eine Möglichkeit der Optimierung nicht-linearer Parameter bei den genannten zwei Methoden dar.

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Résumé La méthode des moments et la méthode des moindres carrés sont appliquées à l'étude de la diffusion électronique sur un potentiel modèle simple. Discussion de certains problèmes généraux liés à l'emploi de ces méthodes à l'étude de la diffusion. Les calculs donnet un exemple de l'estimation d'erreur par échantillonage discutée dans les articles précédents, et présentent une méthode pour optimiser des paramètres non linéaires dans le cadre des méthodes des moments et des moindres carrés.

     

Determination of molecular properties by the method of moments

Basic principles of a possibility of simplifying the unrestricted spin-projected Hartree-Fock equations by means of the method of moments are outlined.     

Calculation of molecular electric polarizabilities and dipole moments. III. BH molecule

We use a previously proposed variation-perturbation method to calculate the electric polarizabilities and the electric dipole moment at equilibrium nuclear distance of the BH molecule. We obtain 3.56 × 10^?24 cm³ for the perpendicular polarizability α_xx and 3.22 × 10^?24 cm³ for the parallel polarizability α_zz. Our result for the electric dipole moment μ₀ is 1.734 debye units; there is no reliable experimental result to compare it with.     

Determination of dipole moments and stability constants for molecular complexex

Conclusions Dipole moments and stability constants have been determined for various molecular complexes through measurements of the dielectric constants over a single series of solution concentrations, following the proposed method of equivalent concentrations. The results obtained for a series of 11 complexes have been checked against the theory.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2283–2287, October, 1978.The authors wish to thank A. A. Kryuchkov for his help in carrying out the spectrophotometric measurements.     

Evaluation of molecular moments by three methods

The three evaluative methods of the moment by means of the coefficient a_k of the HMO characteristic polynomial, the tree graph, and walk graph have been studied. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 237–244, 2000     

Determination of the molecular weight of polysaccharides by the light-scattering method

Conclusions We made a comparative study of the molecular weights of certain polysaccharides isolated from natural sources, using the light-scattering method and determination of the reductive terminal groups by periodate oxidation of the compounds investigated.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2815–2816, December, 1969.     

On the representation of molecular quadrupole moments in terms of atomic moments

The magnitude and algebraic sign of the molecular quadrupole moments of the homonuclear diatomic molecules N2, O2, F2, P2, S2 and Cl2 are analyzed by expressing them as a sum of the quadrupole moments of the free atoms and an induced molecular quadrupole due to bond formation. This induced molecular quadrupole is further analyzed in terms of in situ atomic dipole and quadrupole moments constructed following the electron partitioning method suggested by Hirshfeld. These in situ moments are interpreted in terms of the sigma and pi character of the chemical bonds and are compared with those predicted by the DMA method of Stone (The Theory of Intermolecular Forces; Clarendon: Oxford, 1996).     

On the calculation of molecular dipole moments

The approximation made in the calculation of molecular dipole moments by including only the point charges and the atomic dipoles is evaluated in different all-valence (or all)-electrons MO procedures. In the CNDO method, the use of the exact formula after retransformation of the atomic basis into Slater orbitals gives poorer values than the Pople-Segal's procedure.     

Bond length alternation in cyclic polyenes. III. Alternant molecular orbital method

The bond length alternation problem in cyclic polyene models as described by the Pariser–Parr–Pople Hamiltonian and an empirical quasiharmonic π-core potential is investigated using the one-parameter alternant molecular orbital (AMO) method. It is shown that in contrast to the unrestricted Hartree–Fock (UHF) results, which lead to symmetric equidistant structures, the one-parameter AMO results yield bond length alternating structures similar to those obtained with the restricted HF approach. The correlation energy recovered by the AMO method is examined for the symmetric polyenes in the whole range of coupling constants for both the Pariser–Parr–Pople and Hubbard Hamiltonians and compared with exact full configuration interaction (FCI) results. For the first member of the cyclic polyene series we also compared the FCI and AMO correlation energies for different nuclear framework distortions. This comparison indicates that in contrast to the UHF results the fraction of the correlation energy recovered by the AMO approach is very uniform over the range of nuclear distortions considered. The AMO results thus strongly indicate the dimerization in the polyenic chains.     

Environmental effects of the determination of molecular dipole moments by stark spectroscopy

From the orientational Stark splitting in the absorption spectra of parafluoroaniline, the apparent change in dipole moment between the ground state and the first excited singlet state of this molecule isolated in a durene host crystal was found to be about 100% larger than the value reported for the vapor phase. Possible reasons for this difference are given.