Ab initio study of the ground and first excited state of LiAr

The intermolecular potentials for the X ²σ and A²Π states of Li… Ar were studied by a variety of multiconfiguration, single-configuration, and perturbation methods (CASPT 2). The A ²Π excited state was calculated to have a well depth of 811 cm^?1 at an internuclear separation of 2.59 Å, in excellent agreement with the 810 cm^?1 derived from experimental data. A smaller well of 77 cm^?1 was found for the X ²σ ground state at an intermolecular separation of 4.8 Å. These results are in better agreement with experimental results than were the previously reported pseudopotential calculations. The comparison of CI calculation with the CAPST 2 results shows that the latter is able to give good results for interacting metal–rare gas systems. © 1995 John Wiley & Sons, Inc.     

Finite-field many-body perturbation theory II. SD-MBPT study of the nuclear charge dependence of the electron correlation contribution to the dipole polarizability of 10-electron atomic systems

The finite-field many-body perturbation theory limited to intermediate states involving single and double substitutions in the reference HF determinant is applied to the calculation of dipole polarizabilities of 10-electron atomic systems. The nuclear charge dependence of the convergence of the SD-MBPT series for correlation corrections to the dipole polarizability is investigated. It is concluded that the fourth-order SD-MBPT scheme is quite appropriate for neutral and positively charged species. For negatively charged systems the convergence of the SD-MBPT series becomes much poorer and including higher-order substitutions may be necessary. The role of the renormalization contributions to the SD-CI polarizability results is also considered. It follows that the corresponding data need to be corrected for the erratic treatment of unlinked clusters. The size inconsistency effects make quite important contributions to the SD-CI values of the correlation corrections to dipole polarizabilities.     

Coupled multiconfiguration self-consistent field (MC SCF) perturbation theory

The analytical form of the perturbation theory for the MC SCF method of Veillard and Clementi is presented. The appropriate second-order energy functional which takes into account the self-consistency requirements, leads to a set of coupled first-order perturbed equations determining the perturbed configuration coefficients and orbitals. The second-order energy formula derived from this functional can be given a clear physical interpretation. The present analytical approach is compared with the finite perturbation MC SCF scheme. The possibility of the approximate solution of the coupled MC SCF perturbation equations is also discussed and the so-called uncoupled procedures are devised. In the limit of the single determinant wave function the present formulae are shown to be equivalent to the appropriate Hartree-Fock perturbation results. The differences between the one-configuration SCF and the MC SCF approach are illustrated by the calculation of the electric dipole polarizability of. HZ in the CNDO/2 approximation. It is shown that the one-configuration SCF approaches cannot account for the correct asymptotic properties of the second-order energy for large internuclear distances. This feature of the SCF perturbation theories does not depend on the specific approximations of the CNDO/2 scheme and is corrected by using the MC SCF perturbation theory.     

A quantum chemical study of the hydrogen bonding in the CO2⋯HF and N2O⋯HF complexes

Summary Quantum chemical ab initio calculations have been performed for the complex CO₂HF and N₂OHF. The interaction energies were computed through fourth order MBPT and were corrected for basis set superposition errors. Extended polarized basis sets were used which are constructed to give accurate values for electric moments and polarizabilities. The complex NNOHF was found to be bent, while OCOHF is linear, in agreement with experiment. The MBPT calculations give evidence for a second linear isomeric structure FHNNO, a possibility which has also been suggested by recent experimental data. The computed binding energies are: 2.5 kcal/mol for OCOHF, 2.4 kcal/mol for NNOHF, and 3.0 kcal/mol for FHNNO. At the SCF level, the FHNNO complex is less stable than NNOHF, but correlation has a large effect on the geometry and energetics of the latter complex. The NNOHF complex seems to be a system where the positive intramolecular correlation correction prevails over the negative intermolecular component.     

Proton magnetic shielding in the water molecule

The variation-perturbation uncoupled Hartree-Fock procedure of Karplus and Kolker is employed for the calculation of the second-order properties of the water molecule. The SCF MO LCGO ground state wave function was chosen and the first-order perturbed orbitals were approximated in the multiplicative form. The convergence of the method as well as the violation of the gauge independence are studied. For the preferred gauge origin at the electronic centroid the calculated proton shielding constant is 28.30 ppm and compares favourably with the experimental data (30.20, 30.03 ±0.60 ppm).The results for the magnetic susceptibility of the water molecule are also in reasonable agreement with experimental values.

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Zusammenfassung Die ungekoppelte Hartree-Fock Variationsstörungsrechnung von Karplus u. Kolker wird für die Berechnung von Eigenschaften 2. Ordnung des Wassermoleküls verwendet. Für die Berechnung wird die SCF MO SCGO-Wellenfunktion des Grundzustandes gewählt, und die gestörten Orbitale 1. Ordnung werden in der multiplikativen Form approximiert. Die Konvergenz der Methode und die Frage, ob die Eichinvarianz verletzt wird, werden untersucht. Für den gewählten Potential-Nullpunkt im Zentrum der negativen Ladungsverteilung beträgt die errechnete Protonenabschirmungskonstante 28,30 ppm in guter Übereinstimmung mit den experimentellen Werten (30.20, 30.03 + 0.60 ppm). Die Ergebnisse für die magnetische Suszeptibilität des Wassermoleküls sind gleichfalls in vernünftiger Übereinstimmung mit dem Experiment.

     

Analytic techniques for the coupled multiconfiguration SCF perturbation theory

The perturbation theory based on the paired excitation multiconfiguration self-consistent field approach of Clementi and Veillard is considered. The coupled first-order perturbed orbital equations are analysed and an appropriate computational scheme for their solution is discussed. The proposed computational scheme is analogous to the technique employed for the solution of the coupled Hartree–Fock equations in the one-configuration approximation. However, because of the presence ofnondiagonal Lagrangian multipliers and the use of different one-electron operators for different orbitals, the present scheme raises some new computational problems. In this context a new technique for the solution of the unperturbed multiconfiguration self-consistent field equations is proposed. A simple illustration of the superiority of the multiconfiguration perturbation approach with respect to the ordinary coupled Hartree–Fock scheme is given. Also the validity of the variation formulation of the presented scheme and its relation to the finite-field approach are discussed.     

Correlation effects in externally perturbed many-electron systems

Different methods for the calculation of the electron correlation contribution to atomic and molecular properties are analyzed and evaluated. The methods based on the self-consistent solution of the external perturbation problem are shown to offer several formal and computational advantages. The analysis of the correlation perturbation series for properties of many-electron systems indicates the importance of the appropriate treatment of unlinked diagrammatic contributions. In particular, the standard limited configuration interaction scheme based on single and double substitutions in the reference function may significantly suffer from the erratic treatment of unlinked clusters and needs to be corrected appropriately. The basis set choice for the calculation of highly accurate values of properties is also discussed. In order to circumvent the dimensionality problem the use of basis sets with explicit dependence on the external perturbation strength is recommended and methods for their choice and optimization are presented. A particular attention is paid to the many-body perturbation theory involving singly and doubly substituted intermediate states and based on the coupled Hartree–Fock solution for the one-electron perturbation problem. Different computational aspects of this method are discussed and compared with other techniques currently in use.