K. T. Tang

An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients

Starting from our earlier model [J. Chem. Phys. 66, 1496 (1977)] a simple expression is derived for the radial dependent damping functions for the individual dispersion coefficients C2n for arbitrary even orders 2n. The damping functions are only a function of the Born–Mayer range parameter b and thus can be applied to all systems for which this is known or can be estimated. For H(1S)–H(1S) the results are in almost perfect agreement with the very accurate recent ab initio damping functions of Koide, Meath, and Allnatt. Comparisons with less accurate previous calculations for other systems also show a satisfactory agreement. By adding a Born–Mayer repulsive term [A exp(−bR)] to the damped dispersion potential, a simple universal expression is obtained for the well region of the atom–atom van der Waals potential with only five essential parameters A, b, C6, C8, and C10. The model has been tested for the following representative systems: H2 3Σ, He2, and Ar2 as well as NaK 3Σ and LiHg, which include four che...

Upper and lower bounds of two‐ and three‐body dipole, quadrupole, and octupole van der Waals coefficients for hydrogen, noble gas, and alkali atom interactions

Upper and lower bounds of the multipole van der Waals coefficients C6, C8, and C10 for hydrogen, noble gas, and alkali atoms are established. Nonadditive three‐body coefficients involving dipole, quadrupole, and octupole interactions are also determined. For the dipole polarizabilities a three‐term, two‐point Pade approximant is used to obtain the upper bound and a two‐term Pade approximant is used to obtain the lower bound. For the quadrupole and octupole polarizabilities a one‐term approximation of the dynamic polarizability is used, except for the helium quadrupole polarizability, where extended approximations are possible.

The van der Waals potentials between all the rare gas atoms from He to Rn

The interatomic van der Waals potentials for all the possible 21 homogeneous and heterogeneous pairs of rare gas atoms including radon are determined using the Tang–Toennies potential model and a set of previously derived combining rules. The three dispersion coefficients and the two Born–Mayer parameters needed for calculating the potential curves are listed.

Erratum: A simple theoretical model for the van der Waals potential at intermediate distances. I. Spherically symmetric potentials

A simple potential model is presented, which uses available ab initio calculated short range SCF Born–Mayer parameters and the perturbation theoretical dispersion terms for the long range potential. In the intermediate region two corrections are shown to be necessary to take account of the divergence of the dispersion expansion and the influence of electron overlap. These corrections can be predicted from the known asymptotic parameters and atomic properties. The resulting potential model, which contains only seven potential parameters, is shown to predict the van der Waals potential parameters R0[V (R) =0], Rm (well location), and e (well depth) for six rare gas–rare gas atom combinations and six open shell–rare gas atom combinations. The predicted potential shape for Ar–Ar is in excellent agreement (≲3%) with the best experimental determination. The model is used to predict Born–Mayer parameters from measured values of Rm and e.A simple potential model is presented, which uses available ab initio calculated short range SCF Born–Mayer parameters and the perturbation theoretical dispersion terms for the long range potential. In the intermediate region two corrections are shown to be necessary to take account of the divergence of the dispersion expansion and the influence of electron overlap. These corrections can be predicted from the known asymptotic parameters and atomic properties. The resulting potential model, which contains only seven potential parameters, is shown to predict the van der Waals potential parameters R0[V (R) =0], Rm (well location), and e (well depth) for six rare gas–rare gas atom combinations and six open shell–rare gas atom combinations. The predicted potential shape for Ar–Ar is in excellent agreement (≲3%) with the best experimental determination. The model is used to predict Born–Mayer parameters from measured values of Rm and e.

Interaction potentials for alkali ion–rare gas and halogen ion–rare gas systems

The Tang–Toennies model [J. Chem. Phys. 80, 3725 (1984)] has been modified to predict the potentials for ion–atom systems. First order SCF energies are used to describe the repulsive potential. The long range second order induction and dispersion potential terms up to R−10 are either taken from ab initio calculations or estimated and each term is appropriately damped. The potentials for Li+, Na+, K+, F−, and Cl− interacting with He, Ne, and Ar are found to agree well with both theoretical and experimental data within the expected errors. For comparison with the model new ab initio calculations have been performed for Na+–Ar and the results are in excellent agreement with the model predictions (<10%).

New Combining Rules for Well Parameters and Shapes of the van der Waals Potential of Mixed Rare Gas Systems

New combining rules are presented for calculating the van der Waals well parametersε andσ as well asC6,C8 andC10 for the mixed rare gas systems from the corresponding values of the homogeneous dimers. The combining rules forε andσ are tested by comparison with the recent compilation of Aziz and found to be superior to the best previous combining rules selected by Aziz. Effective Born-Mayer repulsive potential parameters are determined from the model potential of Tang and Toennies and make possible the calculations of accurate potential curves for all combinations of rare gas atoms.

The anisotropic potentials of He–N2, Ne–N2, and Ar–N2

The anisotropic potentials of He–N2, Ne–N2, and Ar–N2 are predicted using the Tang–Toennies potential model. This model damps the long‐range ab initio dispersion terms individually using a universal damping function and adds to this a simple Born–Mayer repulsive term. The Born–Mayer parameters for the three systems were derived from SCF calculations. The dispersion coefficients were estimated from established combining rules using an effective multipole spectrum for the N2 molecule computed by Visser and Wormer from the time‐dependent coupled Hartree–Fock approximation. The resulting potentials were used to predict the second interaction virial coefficients for each system, and they are found to be in excellent agreement with experiment. It is concluded that the spherical symmetric potentials are within 2%–3% of the true potentials. Some discrepancies with recent molecular beam experiments appear to be present, however, for the anisotropies especially in the case of He–N2. Finally, it is found that the la...

A simple theoretical model for the van der Waals potential at intermediate distances. III. Anisotropic potentials of Ar–H2, Kr–H2, and Xe–H2

A simple model proposed in an earlier paper [J. Chem. Phys. 66, 1496 (1977)] is applied to the prediction of the radial V0(R) and anisotropic parts v2(R) of the van der Waals potentials, V (R,γ) =v0(R)+v2(R) P2 (cosγ), where R is the distance between centers of mass and γ is the angle between R and the molecular axis, for He–H2 and Ne–H2. All the parameters used in the model are derived either from ab initio SCF data on the repulsive potential calculated by Hariharan and Kutzelnigg or from perturbation calculations of Meyer of the long range dispersion terms and their angular dependence. The predicted v0 and v2 radial dependences for He–H2 are compared with several of the latest ab initio CI‐type calculations. For Ne–H2, for which ab initio potentials are not available in the potential well region the results are compared with the most reliable experiments. In addition the predicted potentials are used to calculate the orientation dependence of total integral cross sections for direct comparison with meas...

MULTIPOLAR POLARIZABILITIES AND TWO- AND THREE-BODY DISPERSION COEFFICIENTS FOR ALKALI ISOELECTRONIC SEQUENCES

Using simple wave functions based on the asymptotic behavior and on the binding energies of the valence electron, we have evaluated multipolar matrix elements. They allow us to obtain polarizabilities up to α12 of Li, Na, K, Rb, Cs, Be+, Mg+, Ca+, Sr+, Ba+, and dispersion coefficients of homonuclear and heteronuclear interactions from c6 to c24. Comparisons with previously determined low order quantities show that this approach is capable of yielding quite useful values for these quantities.

A combining rule calculation of the van der Waals potentials of the rare-gas hydrides

Abstract The van der Waals potentials of the rare-gas hydrides are obtained from potential parameters of the homogeneous rare gas and the H atom interactions in 3 Σ H 2 with the aid of combining rules. With one simple modification, the combining rules of Nyeland and Toennies are used to estimate the Born-Mayer [ A exp(- bR )] short-range repulsive potential parameters of the rare-gas hydrides. These parameters, together with the dispersion coefficients obtained from the well established combining rules, are used in the Tang-Toennies model to yield the full potential energy curves of the mixed systems. The predicted well parameters for H-Ne, H-Ar, HKr and HXe are in excellent agreement with experiment, but the predicted well depth of HHe seems to be in error by about 10%. The present results show that the reduced potential curves for the five rare-gas hydrides are almost identical to each other and that they have a somewhat wider potential bowl than that of either 3 Σ H 2 or the rare-gas dimers.