Calculation of the dispersion contribution to the interaction energy of two hydrogen molecules at large but finite distances

An attempt to calculate the dispersion energy between two hydrogen molecules by a perturbative procedure and from a simple product of the individual molecular Hartree-Fock wavefunctions (ab initio, using small basis sets) has been made. The results are very much smaller than the semi-empirical calculations but, qualitatively, it has been found that the main contribution is due to the first virtual orbital, that seems to justify the semi-empirical ideas. Our values, though still small, increase strongly if we use the expectation values of the respective hamiltonian for the energy denominator instead of the energy eigenvalues of the Hartree-Fock hamiltonians.     

Electric properties of the water molecule in 1A1, 1B1, and 3B1 electronic states: Refined CASSCF and CASPT2 calculations

Summary The dipole moments and dipole polarizabilities of the ¹A₁, ¹B₁, and ³B₁ electronic states of the water molecule have been calculated by using the CASSCF approach followed by the evaluation of the dynamic electron correlation contribution by the second-order perturbation scheme CASPT2. All calculations have been carried out in a specifically extended ANO basis set which accounts for the Rydberg character of the two excited states. In order to estimate the correctness and accuracy of the present data a scan over a variety of different active spaces for the CASSCF wave function has been made. The present results are superior to earlier CASSCF calculations, although their qualitative features remain essentially the same. The dipole moments in ¹B₁ and ³B₁ states are predicted to be about 0.49 a.u. and 0.33 a.u., respectively, and have the opposite orientation with respect to the ground state dipole moment. The dipole polarizability tensors of the excited states are characterized by high anisotropy and are dominated by the in-plane component perpendicular to the symmetry axis. All their components are found to be about an order of magnitude larger than those of the ground state polarizability tensor. The excitation energy dependence on the choice of the active orbital space in the CASSCF reference function is also considered and the analysis of the present data concludes in the concept of what is called the mutually compatible active spaces for the two states involved in excitation. All CASPT2 results are in good agreement with the results of recent calculations carried out in the framework of the open-shell coupled cluster formalism. This agreement confirms the high efficiency of the CASSCF/CASPT2 approach to the treatment of the electron correlation effects.     

Calcul par double perturbation de l'interaction dipolaire spin-spin dans les molécules

Résumé Les paramètres D et E de molécules dans l'état triplet sont calculés par double perturbation au premier ordre par rapport à l'hamiltonien de corrélation de P. S. Epstein, et à l'hamiltonien d'interaction dipolaire spin-spin. On montre que les seules configurations diexcitées triplets fournissant une contribution non nulle sont celles où les orbitales occupées par un seul électron dans le plus bas triplet deviennent vides ou doublement occupées. On trouve ainsi pour le naphtalène D= 0,090 cm^–1, E=–0,014 cm^–1 (exp = D=0,100 cm^–1, E=–0,014 cm^–1). La polarisation de spin seule donne D=0,113 cm^–1, E= –0,027 cm^–1. La contribution du 2ème ordre par rapport à la perturbation due à la corrélation est évaluée à 10% de D total.

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Calculation of the dipolar spin-spin interaction by double perturbation theory in moleculesApplication to the triplet states of hydrocarbons

A double perturbation calculation of D and E parameters of molecular triplet states is performed in first order with respect both to correlation (as defined by P. S. Epstein) and dipolar spin-spin interaction. A non zero contribution is obtained from diexcited triplet configurations only if the singly occupied orbitals of the lowest triplet configuration become either empty or doubly occupied. Results are for Naphtalene: D=0.090 cm^–1, E=–0.014 cm^–1 (exp: D=0.100 cm^–1, E=–0.014 cm^–1). Spin polarization alone yields D=0.113 cm^–1, E=–0.027 cm^–1. The correlation second order contribution for D is estimated to 10% of the over-all value.

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Zusammenfassung Es wird eine Berechnung des D- und E-Parameters molekularer Triplettzustände im Rahmen einer zweifachen Störungsrechnung bis zur ersten Ordnung durchgeführt, und zwar sowohl in bezug auf die Korrelation (wie definiert von P. S. Epstein) als auch die dipolare Spin-Spin-Wechselwirkung. Der Beitrag zweifach angeregter Triplettkonfigurationen ist nur dann von Null verschieden, wenn die beiden in der Grundkonfiguration einfach besetzten Orbitale entweder gar nicht oder doppelt besetzt sind. Die Ergebnisse für Naphthalin sind: D=0,090 cm^–1, E=–0,014 cm^–1 (exp.: D=0,100 cm^–1, E=–0,014 cm^–1), während die Spinpolarisation allein D=0,113 cm^–1, E=–0,027 cm^–1 liefert. Der Beitrag der Korrelation zu D in zweiter Ordnung wird auf 10% des Gesamtwertes geschätzt.

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Travail effectué dans les cadres de la Convention N-67-34217-00-480-75-01 de la Direction des Recherches et Moyens d'Essais (Responsable: Prof. B. Pullman).     

Non-empirical interpretation of nitrogen 14 nuclear quadrupole coupling constants

The ¹⁴N nuclear quadrupolar coupling constants have been calculated for a series of nitrogen containing molecules from ab initio SCF-LCAO-MO wavefunctions built on basis sets of Gaussian type atomic functions. The various nuclear and electronic (from MO's, atoms, basis functions) contributions to the total field gradient have been analyzed and their relation to molecular and electronic structure is discussed.The effect of the nature of the basis set on the accuracy of the computed field gradients has also been studied.

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Zusammenfassung Die ¹⁴N-Kernquadrupol-Kopplungskonstanten sind für eine Reihe von N-haltigen Verbindungen aus ab initio-Wellenfunktionen, die auf Gauß-Orbitalen basieren, berechnet worden. Die einzelnen Kern- und Elektronenbeiträge zum Feldgradienten wurden untersucht und diskutiert, desgleichen der Einfluß des Typus der Basis auf die Genauigkeit der Resultate.

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Résumé Les constantes de couplage quadrupolaire nucléaire de ¹⁴N ont été calculées pour une série de composés azotés à partir de fonctions d'onde ab initio SCF-LCAO-MO (Hartree-Fock) construites sur une base de fonctions atomiques gaussiennes. Les diverses contributions nucléaires et électroniques (provenant des orbitales moléculaires, des atomes, des fonctions atomique de base) au gradient de champ total ont été analysées et reliées aux caractéristiques structurales des molécules considérées.L'effet de la nature de la base de fonctions atomiques sur la précision des gradients de champs calculés a aussi été étudié.

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We thank Drs. H. Basch, J. L. Calais, J. F. Harrison and P. Pyykkö for sending us test calculations for checking our program and Drs. H. Basch and G. Berthier for communicating to us the molecular wavefunctions of some of the nitrogen containing heterocycles.     

Ab initio intermolecular energies between Li+ and H2 near the van der waals minimum: comparison between a perturbative procedure and an SCF supermolecule treatment

The electrostatic, exchange, polarization, and dispersion energies are computed without using the multipole expansion. It is seen that the overlap between the orbitals of the interacting molecules must be taken into account to describe qualitatively the first order term. The neglect of overlap in the polarization term overestimates the attractive energy around the van der Waals minimum. An interpretation of the polarization phenomena in terms of molecular orbitals is proposed. The results are compared with SCF calculations and the use of small basis sets is considered.