Second virial coefficients of asymmetric top molecules

A short self-contained derivation is given for the second virial coefficient B2(T) of a gas consisting of identical interacting asymmetric rigid rotors. The resulting expression is correct through variant Planck's over h2. First, the canonical partition function is derived by means of an variant Planck's over h expansion of exp[-H/(k(B)T)] due to Friedmann [Adv. Chem. Phys. 4, 225 (1962)]. The present work applies angular momentum operators and known facts from angular momentum theory. It is considerably more accessible than Friedmann's exposition, which is not based on angular momentum operators, but instead on explicit derivatives with respect to Euler angles. The partition function obtained from the variant Planck's over h expansion is applied to the derivation of an expression for B2(T) that is identical in appearance to the expression for symmetric rotors of T Pack [J. Chem. Phys. 78, 7217 (1983)]. The final equation in this work is valid for rigid rotors of any symmetry.     

Close coupling results for inelastic collisions of NH3 and Ar. A stringent test of a spectroscopic potential

We have calculated state-to-state total cross sections for rotational excitation and inversion of NH3 by collisions with Ar using the close coupling method. The Ar-NH3 interaction potential has been obtained from a fit to the spectrum of this van der Waals molecule. The calculated cross sections agree to within about 30% with the measured values; the estimated error in the latter is 10% to 20%.     

Vibrational predissociation dynamics of methane-Ar: an ab initio approach

We calculated the cross sections for vibrational predissociation of methane-Ar induced by excitation of the methane nu 3 mode with the aid of an ab initio CH4-Ar potential depending explicitly on the nu 3 and nu 1 normal coordinates of the CH4 monomer. We found that dissociation into CH4 fragments excited in the nu 1 mode, a V-->V' process with very low kinetic energy release, strongly dominates over direct dissociation into Ar and ground state CH4, and is responsible for the line broadening observed experimentally. The (observed and calculated) strong variation of the line widths for the Van der Waals levels excited in combination with the nu 3 mode (giving states of A, F and E symmetry) is related to the opening up of appropriate nu 1 dissociation channels and the occurrence of rotational resonances in the nu 1 continuum in the energy range of the quasi-bound nu 3 levels.     

The non-empirical calculation of second-order molecular properties by means of effective states. II. Effective TDCHF spectra for NO+ CO,CO2, and C2H2

Time-dependent coupled Hartree-Fock calculations have been performed in the large bases molecules NO⁺, CO. CO₂ and C₂H₂. Some first- and second-order properties are presented, in particular the isotropic dispersion interaction coefficients C₆⁰⁰⁰, C₈⁰⁰⁰ and C₁₀⁰⁰⁰ for all possible van der Waals dimers consisting of these monometers. These coefficients, and also the corresponding long-range anisotropic interaction coefficients, can be calculated easily for any of these dimers using the effective TDCHF multipole spectra presented in this paper. Formulas to this end are given.     

Ab initio computed diabatic potential energy surfaces of OH-HCl

The two four-dimensional diabatic potential energy surfaces (DPESs) for OH-HCl are computed that correlate with the twofold degenerate (2)Pi ground state of the free OH radical. About 20 000 points on the surface are obtained by the ab initio coupled-cluster and multi-reference configuration interaction methods. Analytic forms for the diabatic potential energy surfaces are derived as expansions in complete sets of orthogonal functions depending on the three intermolecular angles. The numeric computation of the angular expansion coefficients is discussed. The distance-dependence of the angular coefficients is represented by the reproducing kernel Hilbert space method. It is checked that both diabatic potentials converge for large intermolecular separations to the values computed directly from the electrostatic multipole expansion. The final DPESs are discussed and illustrated by some physically meaningful one- and two-dimensional cuts through them.     

High resolution TDL spectroscopy of the Ar-CH4 complex

The spectrum of the weakly bound complex Ar-CH4 in the 7 microm region was discovered, analysed, and compared with a spectrum, predicted from ab initio calculations. The measurements were made by probing a supersonic gas expansion with a tunable diode laser (TDL). Several bands of Ar-CH4 associated with different ro-vibrational transitions of the v4 vibration of CH4 were recorded and analysed in a spectral region from 1295 to 1330 cm(-1). In particular the following transitions were studied: j = 1 <-- 0 (at 1311 cm(-1)) reported in Pak et al. [Z. Naturforsch. 53 (1998) 725], j = 0 <-- 1 (at 1301 cm(-1)), j = 2 <-- 1 (at 1316 cm(-1)), and j = 3 <-- 2 transitions (at 1322 cm(-1)). Here, j denotes the angular momentum of the methane unit inside the complex. Analysis of the recently recorded j = 1 <-- 1 transitions at about 1306 cm(-1) in the region of methane Q(1) is in progress. The experimental results are compared with ab initio calculations. The close agreement between observed and ab initio spectra is convincingly demonstrated with respect to the gross spectral features, including many details of the spectra.     

Configuration interaction matrix elements. III. Spin functions relating the unitary and symmetric group approaches

Spin functions that are compatible with orbital ordering and geminal antisymmetry conditions are investigated. It is shown that two widely used classes of spin functions, namely, the spin-bonded functions and Yamanouchi–Kotani (or, equivalently, Gelfand–Tsetlin) functions possess these properties. The relationship of the latter with Young–Yamanouchi spin functions is also outlined using graphical techniques of spin algebras. These techniques are also used to rederive the Hamiltonian matrix elements between spin-bonded functions and to show the relationship among the various schemes used in this case.     

The TCNE-benzene complex: A CNDO approach

CNDO/2 calculations on the TCNE-benzene complex are reported. A stable complex is found which exhibits a relatively large stabilization energy (0.2 a.u.) at a short interplanar separation (1.75 Å); the binding apparently arises solely through charge transfer. Mulliken population analyses were performed by reinterpreting the CNDO orbitals as Löwdin orbitals. Sample calculations on small organic molecules and first row diatomics indicate the procedure to be satisfactory. It is shown that generally only overlap populations that are summed over the orbitals of the atoms in question reflect the symmetry of the molecule.

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Zusammenfassung Die Ergebnisse von CNDO/2-Rechnungen an Tetracyanaoäthylen-Benzol-Komplexen werden mitgeteilt. Es wird ein stabiler Komplex gefunden, der eine relativ große Stabilisierungsenergie (0,2 A.E.) bei geringem Abstand (1,75 Å) der Molekülebenen besitzt; die Bindung entsteht anscheinend nur durch Ladungsübertragung. Eine Populationsanalyse nach Mulliken wurde mit Hilfe der Interpretation der CNDO-Orbitale als Löwdin-Orbitale durchgeführt. Berechnungen an Beispielen wie kleinen organischen Molekülen und zweiatomigen Molekülen aus Elementen der ersten Reihe zeigen, daß die Methode befriedigende Ergebnisse liefert. Es wird gezeigt, daß im allgemeinen nur die Überlappungs-Populationen, die über die Orbitale der betrachteten Atome summiert werden, die Symmetrie des Moleküls widerspiegeln.

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Résumé Calculs CNDO/2 sur le complexe TCNE-benzène. Un complexe stable apparaît pour une séparation interplan courte (1,75 Å) avec une énergie de stabilisation relativement forte (0,2 u.a); la liaison provient apparemment du seul transfert de charge. Une analyse de population de Mulliken a été effectuée en réinterprétant les orbitales CNDO comme orbitales de Löwdin. Des calculs échantillonés sur de petites molécules organiques et des molécules diatomiques de la première ligne montrent que le procédé s'avère satisfaisant. On montre qu'en général, seules les populations de recouvrement sommées sur les orbitales des atomes en question reflètent la symétrie de la molécule.

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Supported in part by NASA University Sustaining Grant NGR 34-001-005 and National Science Foundation Grant GP-8298.     

Ab-initio valence bond calculations on the He-He potential curve using small bases

In studying methods for the ab-initio calculation of Van der Waals interactions which can be extended to larger molecules, we have tested the Valence Bond scheme on the He₂ system. This method looks promising, as it appears to yield in one consistent formalism both the attractive dipole—dipole terms and the repulsive exchange terms with reasonable accuracy, using only a simple orbital basis and a very small number of VB structures.