Vibrational partition functions for atomâ€diatom and atomâ€triatom van der Waals systems (original) (raw)
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Physical Chemistry Chemical Physics, 2000
The vibrational partition function of and ArÉ É ÉCN systems is calculated within the framework of H 2 O quantum and classical statistical mechanics. The phase space integral arising in the classical picture is solved adopting an efficient Monte Carlo technique. The temperature dependence of the partition function for the two molecules is exploited with a view to study the range of applicability of classical statistical mechanics. For the case of ArÉ É ÉCN van der Waals complex the role played by freezing the CN bond is also analyzed.
Monte Carlo Simulation Approach to Internal Partition Functions for van der Waals Molecules
The Journal of Physical Chemistry A, 1999
Classical Monte Carlo simulation methods have been used to evaluate the internal partition function of diatomic and triatomic van der Waals molecules. All simulation methods are simple to implement and are shown to yield very accurate results for Ar‚‚‚O, Ar‚‚‚O 2 , and Ar‚‚‚CN when compared with the corresponding exact quantum mechanical results. Their efficiencies are also examined.
Chemical Physics Letters, 2008
A detailed application of the Gaussian-weighted trajectory method to the photodissociation of the Rg� � �Br 2 (Rg = He, Ne, Ar) van der Waals triatomics is presented. In agreement with previous applications on molecular collisions, the approach significantly enhances the quasi-classical predictions of product state distributions with respect to those obtained with the Standard Binning procedure, especially near a vibrational channel closing. The different molecules studied shed light on the sort of improvement to expect for various densities of vibrational quantum-states involved in the fragmentation process. Extension to larger polyatomic molecules, its possible difficulties and solutions are briefly sketched.
Journal of Molecular Structure: THEOCHEM, 1985
This paper is concerned with recent theoretical progresses on the determination of potentials for use in spectroscopic and gas phase scattering calculations. Emphasis is placed on the global representation of the potential surface by using the many-body expansion of the molecular potential energy. Novel developments which allow further flexibility and reliability to this method while conveying generality both for chemically stable and van der Waals molecules are described. The essential feature of the new method is to separate the (extended-) Hartree-Fock and correlation energy components of the terms of the manybody expansion. In this double many-body expansion of the molecular energy the Hartree-Fock components are, in principle, obtained from accurate SCF ralculations while the correlation components are obtained semiempirically from the dispersion energy coefficients for the various separate and united aton limits and those also known for the equilibrium geometries of the subsystems. Examples are given to illustrate the method. IWTRODUCI'ION Theoretical research on molecular potential energy functions has been active for the past few years at the Chemistry Department of the University of Coimbra. The object of current interest is therefore the functional representation of the molecular potential energy and its subsequent application to the study of the spectroscopy and dynamics of reactive and non-reactive molecular collisions on small polyatomic systems. Since the concept of potential energy surface is an outcome from the Born-Oppenheimer (ref.11 approximation for the decoupling of the electronic and nuclear motions, each point on that surface, E AB...N@) can be calculated using standard quantum chemical methods for solving the electronic Schr&inger equation HyAB ___N(&;R)=E (R)y (r;R)-AB...N-AB_..N-(1) and represents the total energy of the n-atom, AB.. .N, system with the nuclei clamped at a given geometrical arrangement defined by its 3n-6 independent internal coordinates E (5 represents the complete set of the electronic coordinates). Hence, EAB represents the potential which controls the dynamics .I. N(E) of the nuclei on the AB. ..N system in studies which include the rates of chemica 016&1280/8S/$O3.30 01986 ElsevierSciencePublishersB.V. reactions, molecular beam cross sections, transport cross sections, and vibrational and rotational spectroscopy. _ The solution of equation (1) with sufficient accuracy for physical needs is not yet feasible at present for most systems of interest, hence the need for adopting semiempirical metlods in determining the interaction energy as a function of the nuclear coordinates. In addition to imposing the surface some of the essential attributes needed for the dynamics studies, those methods have the further advantage of giving the potential in analytic@ form which is of central importance for studying the molecular dynamics. Thus, even if electronic structure calculations are to be used to produce a surface it is essential to have a model capable of reproducing the ab initio energies and use it to extend the surface to regions of the molecule conriguration space accessible to the nuclei which may not have been explored by the ab initio methods. In this regard, we guote a recent sentence by H-F. Schaeffer (ref.2): "we have been convinced for about five years that ab initio electronic structure calculations should not even attempt (except for the very simplest systems) to predict the entire potential energy surface". This situation has not been changed in the more recent years and is iikely to persist in the iorthcoming years. Thus, along with Schaeffer, we advocate a judicious synthesis of theory and experiment (i.e., a semiempirical approach) to arrive at a complete working potential surface. This article is mainly concerned with recent studies on diatomic and triatomic potentials using what we refer for brievity as the double many-body expansion (DMRE). Such systems not only reveal the essential features of the problem but may also open the way for the development of a systematic approach to larger ones. Selected examples will be considered for illustration and the guality of the potentials judged, whenever possible, on the basis of available spectroscopic and dynamical calculations. Comprehensive reviews on nonbonding interactions include, e.g., the articles by Stoles (ref. 3) and Jesiorski and Kolos (ref.41, and the books by Maitland et al (ref.51 and Hobsa and Zahradnik (ref.61, while recent reviews on potential energy surfaces for reactive scatteking calculations can be found in various articles , particularly those in the books edited by Bernstein (ref-2) and Truhlar (ref.7). A monograph on molecular potential energy functions which provides a comprehensive coverage of the work published over the past ten years, and gives particular emphasis to the global representation of the potential energy .using the many-body expansion (MBE), has also recently appeared by Murrell et al (ref_E). Although some overlap with this monograph is clearly unavoidable in the present article, emphasis will be placed here on newer topics which have not been treated there in detail. A DODBIJ3 MANY-BODY EXPANSION OF TBB MOLECULAR ENERGY Without SIIy loss Of generality, E~~___N(g)can be writzten in a formof a In summary, existing evidence on tetra-atomic systems (ref.81 suggests that
Atom—atom potential parameters for van der Waals complexes of aromatics and rare-gas atoms
Chemical Physics Letters, 1990
The structure of the dispersion terms in the interaction for van der Waals complexes of aromatics and we-gas atoms is examined and found to contain important three-body terms. Using calculations for benzene with a sequence of rare gases, the errors in approximating the three-body lr-electron dispersion energy by atom-atom terms are found to be generally s&o&ant, but small for certain symmetrical positions (including the equilibrium position). For these positions, the total interaction coefficients are compared with empixically determined values using a Lennard-Jones model. Agreement is good after waling to allow for higherorder terms.
Van der Waals coefficients of atoms and molecules from a simple approximation for the polarizability
Physical Review B, 2009
A simple and computationally efficient scheme to calculate approximate imaginary-frequency dependent polarizability, hence asymptotic van der Waals coefficient, within density functional theory is proposed. The dynamical dipolar polarizabilities of atoms and molecules are calculated starting from the Thomas-Fermi-von Weizsäcker (TFvW) approximation for the independent-electron kinetic energy functional. The van der Waals coefficients for a number of closed-shell ions and a few molecules are hence calculated and compared with available values obtained by fully first-principles calculations. The success in these test cases shows the potential of the proposed TFvW approximate response function in capturing the essence of long range correlations and may give useful information for constructing a functional which naturally includes van der Waals interactions.