Magnetic susceptibility of the BH molecule

The coupled Hartree-Fock (CHF) perturbation approach and its extension to multiconfiguration wavefunctions (MC CHF scheme) were used to calculate the magnetic susceptibility of the BH molecule. The results obtained for an SCF and two pair-excitation MC SCF functions confirm the paramagnetism of the BH molecule and indicate a rather weak dependence of the computed molecular susceptibility on the correlation effects. Sponsored by the Institute of Low Temperatures and Structure Research, Polish Academy of Sciences.     

Magnetic properties of the BH molecule

Summary The magnetic susceptibility of the BH molecule, as well as the magnetic shielding at the boron nucleus, have been calculated using CASSCF wavefunctions. A variety of active spaces have been employed, thus including more and more dynamical correlation. With very large active spaces, nearly all the valence correlation can be retrieved. The effect of core correlation is discussed in a second series of calculations and found to be small. Final results are +12.5 ppm cgs for the susceptibility and –175 ppm for the magnetic shielding at the boron nucleus.Paper dedicated to Prof. Werner Kutzelnigg on the occasion of his 60th anniversary     

Susceptibility and magnetic shieldings of the BH molecule

Susceptibility and magnetic shieldings of both nuclei of BH are calculated by use of the finite perturbation method and gauge invariant gaussian basis sets. The results provide further evidence for the temperature independent paramagnetism of BH.     

An Aufbau Ansatz for geminal functional theory

We generalize antisymmetric geminal products to more than just one generating geminal using an Aufbau Ansatz similar to the Hartree-Fock theory. Investigation of Li-, Be, B+, LiH, BeH+, and He2 shows a very high recovery of electron-correlation energy using this Aufbau Ansatz. The method is inherently multideterminantal and insensitive to symmetry problems. The computational complexity is en par with configuration interaction of singles and doubles.     

Canonical force field theory in terms of curvilinear internal coordinates: Application to the methane molecule

This Letter generalizes the Kuczera’s theory of the vibrational canonical force field in order to obtain an unambiguous and uniquely defined expression for the anharmonic force field in terms of curvilinear internal coordinates. By using this generalization it has been shown mathematically that the canonical force constants could be transferred between molecules with the same geometrical structure. As illustration, the theory is used to obtain the expressions for the quadratic and cubic canonical force constants of the methane molecule.     

Application of the extended separated pair theory to the π-electrons of trans-butadiene without zero differential overlap approximation

Localized strongly orthogonal geminals are constructed by using the SCF orbitals of Parr and Mulliken. The best geminal product wave function is taken as zeroth order function and second order correction is calculated by the extended separated pair theory. 101.3 % of the total horizontal correlation energy is obtained taking the result of the full CI calculation as standard. It is found that the contribution of terms neglected in the conventional separated pair theory is very important. The results are compared with those obtained by other variants of the Rayleigh-Schrödinger perturbation theory. As has been expected the result of the extended separated pair theory is superior to that of other perturbation theories discussed in the paper.

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Zusammenfassung Lokalisierte stark orthogonale Geminale werden aus den SCF-Orbitalen von Parr und Mulliken konstruiert. Die beste Produktwellenfunktion aus Geminalen wird als Näherungsfunktion nullter Ordnung verwendet, und eine Korrektur zweiter Ordnung wird mit Hilfe der erweiterten Theorie der unabhängigen Elektronenpaare berechnet. 101,3% der gesamten horizontalen Korrelationsenergie wird erhalten, wenn man die volle CI-Rechnung als Standard nimmt. Es wird gefunden, daß der Beitrag von Termen, die in der konventionellen Theorie der unabhängigen Elektronenpaare vernachlässigt werden, sehr wichtig ist. Die Resultate werden mit denjenigen anderer Varianten der Rayleigh-Schrödinger Störungstheorie verglichen. Wie erwartet sind die Resultate der erweiterten Theorie der unabhängigen Elektronenpaare besser als diejenigen anderer hier diskutierter Störungstheorien.

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Résumé Des géminales localisées fortement orthogonales sont construites en utilisant les orbitals SCF de Parr et Mulliken. La meilleure fonction d'onde produit de géminales est prise comme fonction d'ordre zéro et la correction du second ordre est calculée par la théorie des paires séparées étendue. Si l'on prend le résultat de l'I.C. «complète» comme référence, on obtient ainsi 101,3% de l'énergie de corrélation «horizontale». On trouve que la contribution des termes négligés dans la théorie des paires traditionnelle est très importante. Les résultats sont comparés à ceux obtenus à l'aide d'autres variantes de la théorie des perturbations de Rayleigh-Schrödinger. Comme il falleit s'y attendre, la théorie des paires séparées étendue donne un résultat supérieur à celui des autres traitements de perturbation.

     

An extended geminal model calculation of the dissociation energy of the ground state of Li2

The dissociation energy of the ground state of the Li₂ molecule has been calculated by using an extended geminal model. The calculated result is 1.024 eV and the experimental value is 1.048 ± 0.012 eV. the discrepancy can at least partly be attributed to a deficiency in the orbital basis set.     

A dynamic theory of the transition state in the phase space: Application to isomerization in the LiNC-LiCN molecule

A theoretical method for systematic calculations of all the periodic orbits resulting in isomerization in the LiNC → LiCN system was suggested. Calculations used the property of hyperbolic orbits at the saddle point separating isomers in the configuration space. These orbits formed invariant stable and unstable manifolds in the phase space, which served as guides in fairly entangled and usually chaotic molecular dynamics. Manifold intersections result in the formation of so-called homoclinic orbits, which, in turn, form infinite families of bifurcation orbits constituting the structural framework of the phase space of the system. This approach allows isomerization reactions in the LiNC-LiCN molecular system to be described in terms of a roadmap determining the transfer of classical density from one local minimum to another.     

Application of an extended solvation theory to study on the binding of magnesium ion with myelin basic protein

Binding properties of myelin basic protein (MBP) from bovine central nervous system due to the interaction by divalent magnesium ion (Mg²⁺) was investigated at 27°C in aqueous solution using isothermal titration calorimetry (ITC) technique. An extended solvation model was used to reproduce the enthalpies of Mg²⁺-MBP interaction over the whole Mg²⁺ concentrations. It was found that there is a set of two identical and noninteracting binding sites for Mg²⁺ ions. The dissociation equilibrium constant is K _d=45.5 μM. The molar enthalpy of binding site is identical for both sites; ΔH=−15.24 kJ mol⁻¹. The solvation parameters recovered from the solvation model were attributed to the structural change of MBP due to the metal ion interaction.     

Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor

The recently introduced MP2-R122*A(loc) and LMP2-R122*A(loc) methods are modified to use a short-range correlation factor expanded as a fixed linear combination of Gaussian geminals. Density fitting is used to reduce the effort for integral evaluation, and local approximations are introduced to improve the scaling of the computational resources with molecular size. The MP2-F122*A(loc) correlation energies converge very rapidly with respect to the atomic orbital basis set size. Already with the aug-cc-pVTZ basis the correlation energies computed for a set of 21 small molecules are found to be within 0.5% of the MP2 basis set limit. Furthermore the short-range correlation factor leads to an improved convergence of the resolution of the identity, and eliminates problems with long-range errors in density fitting caused by the linear r12 factor. The DF-LMP2-F122*A(loc) method is applied to compute second-order correlation energies for molecules with up to 49 atoms and more than 1600 basis functions.     

Application of the AMO method to the naphthalene molecule

The alternant molecular orbital (AMO) method was applied to the ground state of naphthalene. Both the single and the many-parameter variants lead to substantial improvement in the energy. Comparison with a limited configurational interaction treatment shows that the AMO method is better in the many-parameter variant.

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Zusammenfassung Die Methode der alternierenden MO (AMO) wurde auf den Grundzustand des Naphthalins angewandt. Beide Varianten der Methode, mit einem sowie mit mehreren Parametern, bringen wesentliche Verbesserung in der Energie. Vergleich mit einer beschrÄnkten Konfigurations-Wechselwirkungs-Methode zeigt, da\ die AMO-Methode besser ist, wenn mehrere Parameter angewandt werden.

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Résumé La méthode des orbitales moléculaires alternantes (AMO) est appliquée a l'état-fondamental du naphthalène. Les variantes a un ou plusieurs parametres de cette methode produisent des améliorations substantielles pour l'énergie. La comparison avec une application de la méthode d'interaction de configurations limitée montre que la méthode AMO est plus efficace dans la variante avec plusieurs parametres.

     

Electron correlation described by extended geminal models: The EXGEM4 and EXGEM5 models

Within the framework of the general extended geminal model, two new approximate models EXGEM 4 and EXGEM 5 are introduced. The models are tested against full CI calculations on the water molecule for three different nuclear configurations and a full CI potential energy curve for the LiH molecule in the ground state. On the basis of these calculations, it is suggested that the models will yield electronic correlation energies with an accuracy of 1–2% of the corresponding full CI result.     

Electron correlation described by extended geminal models: The EXGEM7 and EXRHF3 models

Within the framework of the general extended geminal model, two new approximate models, EXGEM 7 and EXRHF 3, are introduced. Compared with previous models, these new models imply a more sophisticated approximation of the four-electron terms {?_KL}. The models are tested by calculations on the beryllium atom and the HF molecule.     

Electron correlation described by extended geminal models: The EXGEM2 and EXGEM3 models

The general extended geminal model is reviewed and two new approximate models EXGEM 2 and EXGEM 3 are introduced. In a test calculation on water using a double-zeta basis set, the approximate models recover 93.4% of the full CI correlation energy defined within the same basis set. A test calculation on the neon atom demonstrates that the performance of the models in comparison with the full CI , will improve as the basis set is increased. It is suggested that for basis sets of moderate and large size, and which include polarization functions, the extended geminal models are likely to recover 95%–97% of the correlation energy obtainable by the full CI .     

Applicability of multireference many-body perturbation theory to the Ne2+ molecule

The ground state as well as some low-lying excited states of the Ne₂⁺ molecule are calculated by means of the third-order multireference many-body perturbation theory with the “full” eight-orbital valence space using DZP and polarized valence TZ basis sets. The problem encountered with a large number of valence electrons is avoided by a proper definition of the Fermi vacuum. The calculated equilibrium distance of 1.721 Å and chemical dissociation energy D₀ = 1.283 eV are in good agreement with experimental results. A comparison with other ab initio techniques is also provided. © 1997 John Wiley & Sons, Inc.