Pair potential for helium from symmetry-adapted perturbation theory calculations and from supermolecular data

Abstract

Symmetry-adapted perturbation theory (SAPT) was applied to the helium dimer for interatomic separations R from 3 to 12 bohrs. The first-order interaction energy and the bulk of the second-order contribution were obtained using Gaussian geminal basis sets and are converged to about 0.1 mK near the minimum and for larger R. The remaining second-order contributions available in the SAPT suite of codes were computed using very large orbital basis sets, up to septuple-zeta quality, augmented by diffuse and midbond functions. The accuracy reached at this level was better than 1 mK in the same region. All the remaining components of the interaction energy were computed using the full configuration interaction method in bases up to sextuple-zeta quality. The latter components, although contributing only 1% near the minimum, have the largest uncertainty of about 10 mK in this region. The total interaction energy at R=5.6 bohrs is -11.000+/-0.011 K. For R< or =6.5 bohrs, the supermolecular (SM) interaction energies computed by us recently turned out to be slightly more accurate. Therefore, we have combined the SM results for R< or =6.5 bohrs with the SAPT results from 7.0 to 12 bohrs to fit analytic functions for the potential and for its error bars. The potential fit uses the best available van der Waals constants C(6) through C(16), including C(11), C(13), and C(15), and is believed to be the best current representation of the Born-Oppenheimer (BO) potential for helium. Using these fits, we found that the BO potential for the helium dimer exhibits the well depth D(e)=11.006+/-0.004 K, the equilibrium distance R(e)=5.608+/-0.012 bohrs, and supports one bound state for (4)He(2) with the dissociation energy D(0)=1.73+/-0.04 mK, and the average interatomic separation R=45.6+/-0.5 A.

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

“…Data in the literature [16][17][18][19][20] show that the He dimer potential well at 10.9 K and a nuclear equilibrium distance of 2.97 Å only support a single bound rovibrational state with a binding energy of approximately -1.176 mK, 34 which is the weakest bound state ever discovered. Due to this extremely weak interaction, the wave function must be delocalized over a large intermolecular distance.…”

“…[9][10][11][12][13][14][15] The minimum energy value (D = 11.0 K) and the equilibrium distance (R e = 2.965 Å) predicted by the potential used here are in agreement with previous results in the literature. [16][17][18][19][20][21] This proposed potential energy curve is investigated, by comparing the calculated exact quantum second virial coefficient with the experimental results at low temperatures.…”

“…364 Several He-He intermolecular potentials are discussed in the literature. [16][17][18][19][20] The most recent potential has not been tested against thermodynamic and transport property data, 21 such as the quantum second virial coefficients. In the present work, a study of this recent potential was conducted using second virial coefficient data at low temperature.The quantum virial coefficient can be determined by evaluating the quantum ideal gas term, the scattering phase shift dependence on angular momentum [22][23][24][25][26][27][28][29] and the bound states by Levinson's theorem.…”

Quantum Halo States in Helium Tetramers

“…The most sophisticated theoretical model PCKLJS (the authors 22 acronym) was also considered. Jeziorska et al 33 combined supermolecular data and the symmetry-adapted perturbation theory in order to obtain a fitted analytic function for the He-He potential.…”

Parametric sensitivity analysis for the helium dimers on a model potential

“…Helium diatomic has also been studied by perturbation theory. 19 Relativistic effects were also incorporated in this sort of molecule. 20 Although these are very accurate potentials, they are limited to one molecule.…”