A.R. Allnatt

Second order charge overlap effects and damping functions for isotropic atomic and molecular interactions

Abstract Second order charge overlap effects and the related dispersion energy damping functions have been evaluated for the H-(1s)-H(1s) interaction through partial wave indices l a + l b such that ( l a + l b ) ⩽ 13. These results are a substantial improvement on, or addition to, previous literature results and are important since they can be used, following several available scaling approaches, to construct damping functions for other interactions. They also indicate that the “spherical” energies are not an insignificant part of the total second order Coulomb energy until R becomes reasonably large. The various approaches for evaluating the non-expanded second order Coulomb energy are compared and the difficulties associated with the accurate determination of these energies, and the related damping functions, for general interactions are discussed in some detail.

A reliable semi-empirical approach for evaluating the isotropic intermolecular forces between closed-shell systems.

A relatively simple tractable scheme for the evaluation of the isotropic intermolecular potential between two closed-shell systems, which contains one adjustable parameter, is proposed and tested using the He-He, Ne-Ne, Ar-Ar, Kr-Kr, and H2-H2 interactions as models. The approach is based on expressing the potential as a sum of exchange (E x) and coulomb (E c) contributions. A semi-empirical approximation, which is a simple function of the first order coulomb energy (E c (1)), is used to represent E x. The representation for E c is based on E c (1) and a suitably universally damped asymptotic expansion of the second-order coulomb energy through O(R -10). The adjustable parameter formally occurs in the representation for E x and influences the balance between E x and E c in the representation of the potential. The results obtained for the model systems are in excellent agreement with reliable literature potentials, many of which contain several adjustable parameters, and suggest that the scheme proposed he...

On the Ne—Ne potential-energy curve and related properties☆

Abstract The construction of interatomic pair potentials according to the HFD (Hartree—Fock—dispersion) and the XC (exchange—Coulomb) models is reviewed briefly. A new XC potential is constructed for Ne; as in a successful application to Ar, the adjustable parameters in the model are fixed by fitting only second virial coefficient data. The new XC potential, two slight modifications of it, and five literature potentials, are compared with respect to their ability to predict the second virial coefficients and transport properties of dilute Ne gas, the Ne—Ne differential and total scattering cross sections, and the spectroscopic constants of the dimer. A reassessment of the experimental data leads to the conclusion that a literature HFD-C potential is less reliable than previously thought. The new potentials constructed in this paper appear preferable to the other potentials considered; they reproduce essentially all the experimental data used for test purposes to within experimental error.

XC and HFD-B potential energy curves for Xe-Xe and related physical properties

Abstract The XC (exchange-Coulomb) and the HFD (Hartree-Fock-dispersion) potential models for the interaction of two closed shell atoms are reviewed briefly. It is shown that while the original XC potential model (XC-1) does not lead to an optimal potential for the Xe-Xe interaction, two variants, XC-2 and XC-3, do lead to optimal interaction energies for this interaction as a function of the interatomic distance R . The three XC potentials, two HFD-B type potentials, and three other literature potentials are compared with respect to their predictive ability for various microscopic and (dilute gas) macroscopic properties of Xe. One of the HFD-B potentials, developed here, is a modification of the original HFD-B potential for Xe-Xe and this HFD-B2 potential, and the XC-3 potential, are apparently the most reliable representations of the two-body Xe-Xe interaction available. The two-bodypotentials are also used to help discuss the problems associated with the representation of many-body interactions in rare gas systems.

The Kr-Kr potential energy curve and related physical properties; the XC and HFD-B potential models

The construction of pair potentials for closed shell systems following the XC (exchange-Coulomb) and the HFD (Hartree-Fock-dispersion) models is reviewed briefly. New XC potentials for Kr-Kr are constructed. It is shown that, unlike previous applications of the original XC potential model, fixing the adjustable parameter(s) in the model by fitting second virial coefficient data alone does not lead to an optimal Kr-Kr potential; this could be due to inconsistencies in the available experimental second virial data for Kr, but more likely is due to a lack of flexibility in the original XC potential model. Two modifications of the original XC potentials are considered and these lead to optimum Kr-Kr interaction energies. Three XC potentials and two HFD-B type potentials are compared with respect to their ability to predict the second virial coefficient and transport properties of dilute Kr gas, the Kr-Kr differential and total scattering cross sections, the spectroscopic properties of the dimer, and the repul...

Exchange-Coulomb potential energy curves for He-He, and related physical properties

The investigation of the reliability of the original simple overall damped form of the XC (exchange-Coulomb) potential is extended to the He-He interaction, and a new multidamped version of the XC potential is introduced. New one and two parameter overall damped, and one and two parameter multidamped XC potentials for He-He are constructed. The results obtained from these potentials for the second virial coefficients (1·4 < T < 623 K) and transport properties of dilute He gas, and for integral collision cross-sections for He-He collisions, are compared with experiment and with those obtained with the (reference) HFD-B2 potential. The various XC potentials are explicitly compared, over a wide range of interatomic distances R, with the HFD-B2 potential, with ab initio results and with a very accurate (R ⩽ 3a 0) quantum Monte Carlo potential. While the one parameter versions of the XC potentials generally yield very good results, the two parameter overall and individually damped XC potentials, and the HFD-B2...

A simple reliable approximation for isotropic intermolecular forces. A critical test using HH(3Σu+) as a model

Abstract A simple semi-empirical approximation for the exchange energy ( E x ), coupled with a tractable representation of the Coulomb energy ( E C ), has been found to yield very accurate results for the isotropic part of the interaction energy ( E int = E x + E C ) between two closed shell systems. The expression for E int is based on the knowledge of the first order Coulomb energy and the first three terms in the asymptotic long range expansion of the second order Coulomb energy for the interaction and contains but one adjustable parameter which occurs in E x . The usefulness of this approach for evaluating E int is tested critically by using the non-bonded H(1s)H(1s) ( 3 Σ u + ) interaction as a model (accurate values of the total interaction energy, the exchange energy, and various orders of Coulomb energies, are available for a wide range of R for this system). The results obtained for both E int and (d E int /d R ) are inremarkable agreement with the exact results of Kotos and Wolniewicz for R > 3 a o . Since the law of corresponding states for inert gas pairs holds equally well for the HH( 3 Σ u + ) interaction, our analysis of this simple system yields valuable information on the reliability of the approach for other van der Waals dimers.

A reliable single parameter interatomic potential for argon

A simple semiempirical approximation previously proposed for the isotropic intermolecular forces between two closed shell systems is tested in detail for the argon-argon interaction. The potential is based on the knowledge of the first-order coulomb interaction energy, a suitably damped three term long range asymptotic expansion of the second order coulomb energy, and a semiempirical representation of the exchange interaction energy which contains one adjustable parameter. The single adjustable parameter can be reliably determined by fitting the second virial coefficient for argon in the 130–773 K temperature range with the long range interaction coefficients being constrained within the theoretical bounds specified by Tang, Norbeck and Certain. The reliability of the potential is compared with that of several literature potentials by comparing the theoretical predictions obtained from the potentials with experimental results for the second virial coefficient, viscosity, thermal conductivity and thermal d...

Validity of the multipole results for first-order molecule-molecule interaction energies.

The HF-HF, LiH-LiH and N2-N2 interactions, together with previous work on the H2-H2 interaction, are used as models for discussing how charge overlap effects in the first-order Coulomb energy vary as a function of orientation and intermolecular separation as the nature of the interacting species changes. For interactions such as H2-H2 and HF-HF, where the interacting molecules have positive even permanent multipole moments, charge overlap effects are relatively small and the usual R -1 multipole results for the interaction energy between the permanent moments of the interacting molecules give a remarkably good representation of the first-order Coulomb energy until R becomes quite small. For interactions such as LiH-LiH and N2-N2, where the interacting molecules have negative even permanent moments, charge overlap effects are large as a relative function of R and the multipolar results yield a poor representation of the interaction energy even for moderately large values of R. Some of the problems and erro...

Charge overlap effects and the validity of the multipole results for first-order molecule-molecule interaction energies. Formalism and an application to H2-H2

For the interaction of two molecules, the first-order coulomb energy, E e (1), is expressed as a sum of non-expanded partial wave components which exhibit the orientation dependence of the energy explicitly. By comparing these non-expanded results with the analogous multipolar results for the first-order energy, the effects of charge overlap on the multipole representation of the energy can be investigated as a function of intermolecular separation and orientation, and the validity of the multipole results for E e (1) assessed. The interaction of two ground-state hydrogen molecules is considered as a specific example of this approach for studying the validity of the multipole expansion as a representation of molecular first-order Coulomb energies. All calculations are presented as a function of four molecular wave functions of varying degrees of sophistication in order to assess the sensitivity of (1) the representation of charge overlap effects and (2) the calculated quadrupole and hexadecapole moments o...