Mixed basis functions in molecular quantum mechanics

A series of calculations have been carried out for the linear system of four equidistant hydrogen atoms for an internuclear separation of 1.7 a.u. The configuration interaction technique was used, the orbital basis consisting of a mixed set of 1s Slater and floating spherical Gaussian functions. The results obtained are encouraging although the effects of unoptimized non-linear parameters are noticeable.

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Zusammenfassung Es wurde eine Reihe von Rechnungen für ein lineares System von vier äquidistanten Wasserstoffatomen (Kernabstand jeweils 1.7 a.u.) durchgeführt. Dabei benutzt man die Konfigurationswechselwirkungs-Technik, die Orbitalbasis bestand aus einem gemischten Satz von 1s Slater- und floating sphärischen Gauß-Orbitalen. Die Resultate sind ermutigend, obwohl die Effekte der nicht optimierten nichtlinearen Parameter merklich sind.

     

Molecular mechanics and quantum chemistry study of cobalt-thiazolidinethione complexes

Eigenvalue, eigenvector, and overlap matrix of the cobalt halide complex with thiazolidinethione have been estimated. The theoretically estimated values of ligand field parameters such as Dq, B′, and β are very close to the experimental results. Hence, the theoretical methods based on molecular mechanics calculation can be well relied upon. The eigenvector analysis and population analysis have shown that in bonding only s-and d orbitals are involved both in halides (CoX₂) and their complexes (CoX₂ · 2L). The involvement of p orbitals is negligible. The sd hybridization is accordingly supported. On the basis of these results sd ³ hybridization is supported. The bond angles, total energy, and ligand field parameters estimated theoretically indicate that thiazolidinethione is coordinated to cobalt through its thioamide sulfur. The text was submitted by the authors in English.     

Gaussian expansions of minimal STO basis for calculations in molecular quantum mechanics

By means of minimal basis SCF calculations for HF, H₂O, NH₃ and CH₄ different expansions of Slater orbitals (STO) in terms of Gaussian orbitals (GTO) are tested in order to find an appropriate compromise between sufficient accuracy of the results and reasonable computing times. The least squares fit of the GTO expansion to STO does not appear to have any advantages over the expansion based on a variational procedure. It turns out that for hydrogens an expansion of the 1s orbital in terms of three GTO is quite sufficient, whereas for first row atoms an expansion of the 1s orbital in terms of three to five GTO, of the 2s orbital in terms of two GTO and of the 2p orbitals in terms of three GTO seems to be adequate.

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Zusammenfassung An Hand von SCF-Rechnungen mit minimaler Basis für die Moleküle HF, H₂O, NH₃ und CH₄ wurden verschiedene Entwicklungen von Slater-Orbitalen (STO) nach Gauß-Orbitalen (GTO) getestet, um einen geeigneten Kompromiß zwischen ausreichender Genauigkeit der Ergebnisse und vertretbaren Rechenzeiten zu finden. Es zeigt sich, daß die Entwicklung der STO nach GTO mit Hilfe der Methode der kleinsten Fehlerquadrate keine Vorteile gegenüber der auf einem Variationsverfahren basierenden Entwicklung aufweist. Für H-Atome erweist sich eine Entwicklung des 1s-Orbitals nach drei GTO als ausreichend, für Atome der 1. Periode erscheint eine Entwicklung des 1s-Orbitals nach drei bis fünf GTO, des 2s-Orbitals nach zwei GTO und der 2p-Orbitale nach drei GTO als geeignet.

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Résumé En vue de trouver un compromis approprié entre la précision et la durée des calculs, différents développements des orbitales de Slater (STO) en termes d'orbitales gaussiennes (GTO) sont testés au moyen de calculs SCF en bases minimales pour HF, H₂O, NH₃ et CH₄. L'ajustement par les moindres carrés du développement des STO en GTO ne présente apparemment d'avantages sur le développement fondé sur un procédé variationnel. Il apparaît que pour l'hydrogène un développement de l'orbitale 1s en fonction de trois gaussiennes est largement suffisant, alors que pour les atomes de la première rangée il semble nécessaire de développer l'orbitale 1s en 3 à 5 GTO, l'orbitale 2s en 2 GTO et les orbitales 2p en 3 GTO.

     

Completeness and linear independence of basis sets used in quantum chemistry

Infinite sets of functions in Hilbert space are characterized by their completeness properties and the extent of linear independence. Different measures of linear independence such as orthonormality, Gram's determinant, the special measure of linear independence, and the asymptotic dimension are related to each other and with the degrees of completeness such as overcompleteness, exact completeness, and incompleteness as far as possible.     

Three-body problem in quantum mechanics: hyperspherical elliptic coordinates and harmonic basis sets

Elliptic coordinates within the hyperspherical formalism for three-body problems were proposed some time ago [V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. 85, 1362 (1986)] and recently have also found application, for example, in chemical reaction theory [see O. I. Tolstikhin and H. Nakamura, J. Chem. Phys. 108, 8899 (1998)]. Here we consider their role in providing a smooth transition between the known "symmetric" and "asymmetric" parametrizations, and focus on the corresponding hyperspherical harmonics. These harmonics, which will be called hyperspherical elliptic, involve products of two associated Lame polynomials. We will provide an expansion of these new sets in a finite series of standard hyperspherical harmonics, producing a powerful tool for future applications in the field of scattering and bound-state quantum-mechanical three-body problems.     

Propagation with distributed Gaussians as a sparse, adaptive basis for higher-dimensional quantum dynamics

A simple quantum wavepacket propagation algorithm is presented, designed to produce a very compact, non-direct product representation in higher-dimensional cases. Instead of moving basis functions around, localized basis functions at pre-defined centers are added to and deleted from the representation, generating an active basis function set strictly localized to the region where the moving wavepacket has significantly non-zero values. Simple one-dimensional examples prove this property, as well as the ability of the algorithm to accommodate splitting and rejoining of an arbitrary number of wavefunction pieces, and tunnelling through potential energy barriers. It is argued that future applications to higher-dimensional examples will be less expensive than with traditional direct-product bases, since making the basis adaptive has a lower scaling than the elementary steps necessary for any propagation algorithm itself.     

Search for a density-based alternative quantum mechanics of many-electron systems

There are three reasons for seeking an alternative density-based quantum mechanics of many-electron systems, incorporating both interpretive and basic quantum mechanical aspects: (i) failure of popularad hoc chemical concepts underab initio scrutiny; (ii) failure ofab initio calculations to provide simple concepts; and (iii) highly attractive concepts and pictures generated by the electron density in three-dimensional space. At present the three interlinked pillars for such a density mechanics (in contrast to wave mechanics) are: (a) density functional theory; (b) quantum fluid dynamics; and (c) property densities in three-dimensional space. This article describes several studies dealing with these aspects. Although a density mechanics may well be an impossible ideal to realize, the search for it is indeed rejuvenating the whole of quantum chemistry.     

Haptic quantum chemistry

We present an implementation designed to physically experience quantum mechanical forces between reactants in chemical reactions. This allows one to screen the profile of potential energy surfaces for the study of reaction mechanisms. For this, we have developed a interface between the user and a virtual laboratory by means of a force‐feedback haptic device. Potential energy surfaces of chemical reactions can be explored efficiently by rendering in the haptic device the gradients calculated with first‐principles methods. The underlying potential energy surface is accurately fitted on the fly by the interpolating moving least‐squares (IMLS) scheme to a grid of quantum chemical electronic energies (and geometric gradients). In addition, we introduce a new IMLS‐based method to locate minimum‐energy paths between two points on a potential energy surface. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Numerical integration techniques for quantum chemistry

Korobov theory for multidimensional numerical integration is used to evaluate electronic integrals. This paper shows the important role played by periodization techniques. Singularity (r ₁₂ ^?1 ) in the bielectronic six-dimensional integrals is removed through a twofold three-dimensional integration. Results are presented for atomic integrals involving Slater type atomic orbitals.     

Energetics of xylose decomposition as determined using quantum mechanics modeling

The decomposition of xylose has been studied using quantum mechanical calculations supported by NMR data. Proposed mechanisms for the decomposition of xylose have been investigated by obtaining the structures and energies of transition states and products. The intent of this study was to understand the experimentally observed formation of furfural and formic acid that occurs during the decomposition of xylose in mildly hot acidic solutions. A mechanism of furfural formation involving the opening of the pyranose ring and subsequent dehydration of the aldose was compared to a direct intramolecular rearrangement of the protonated pyranose. Energies were determined using CBS-QB3, and it was shown that the barriers for dehydration of the aldose were high compared to intramolecular rearrangement. This result suggests that the latter mechanism is a more likely mechanism for furfural formation. The intramolecular rearrangement step results from protonation of xylose at the O2 hydroxyl group. In addition, it has been shown that formic acid formation is a likely result of the protonation of xylose at the O3 hydroxyl group. Finally, solvation of xylose decomposition was studied by calculating energy barriers for xylose in selected water clusters. The mechanisms proposed here were supported in part by 13C-labeling studies using NMR.     

Independent-cluster methods as mappings of quantum theory into classical mechanics

Summary The algebraic structures of theconfiguration interaction, normal coupled cluster, andextended coupled cluster methods are reviewed and developed. These methods are pointed out to perform a mapping of the quantum mechanical problem into a classical phase space, where in each case the classical canonical coordinates have characteristically different cluster and locality properties. Special focus is given to the extended coupled cluster method (ECCM), which alone is based on an entirely additively separable coordinate system. The general principles are formulated for systems with both bosonic and fermionic degrees of freedom, allowing both commutative and anticommutative (Grassmann) cluster amplitudes. The properties of the classical images are briefly discussed. It is proposed that phase spaces may exist which are fixed points of quantization.Based on a talk given at theWorkshop on Coupled-Cluster Theory at the Interface of Atomic Physics and Quantum Chemistry, Harvard-Smithsonian Institute for Theoretical Atomic and Molecular Physics, Cambridge, MA, August 7–11, 1990     

Co9S8 as a catalyst for electroreduction of O2: quantum chemistry predictions

The slab band quantum computational approach in the Vienna ab initio simulation package (VASP) is used to calculate the adsorption energies of reactants, reaction intermediates, and products in O2 reduction and in water oxidation in acid on three crystallographic surfaces of pentlandite structure Co9S8. Reversible potentials for the reaction steps involving electron and proton transfer are determined by using the energies in a linear Gibbs free energy relationship. On the basis of these results, we find that the partially OH-covered (202) surface is active toward O2 reduction and should have overpotential behavior similar to that observed for platinum electrodes. One structure in the predicted four-electron reduction mechanism is novel: S2- provides an adsorption site for O following O-O bond scission, which, unlike the case of platinum electrodes, takes place prior to the first reduction step.     

Towards a new interpretation of quantum mechanics?

Quantum mechanics is a remarkable formalism for studying problems in the microscopic domain, and nobody has reasonably contested its power. Nevertheless, in spite of the many interpretations which have been proposed, its true meaning is far from being clear. The aim of this preliminary paper is to show that it is possible to conceive within a classical framework an interpretation of quantum mechanics and to make its limits of validity precise.     

Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By separating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described.