Intermolecular-Potential-Energy Curves—Theory and Calculations on the Helium—Helium Potential

Abstract

Calculation of intermolecular‐potential‐energy curves by the application of the many‐electron theory of atoms and molecules is outlined. The interaction is split into a Hartree—Fock and a correlation part. Both parts are given both in localized and in MO descriptions. Most of the interaction is calculated directly, not by difference of total energies. The correlation part involves only two‐electron variational equations. These results are then used to obtain the many‐electron contributions. To examine the method and estimate the magnitude of the various contributions, the helium—helium interaction is calculated for distances over 4.5 a.u. (experimental minimum about 5.5 a.u.) using a very simple localized molecular wavefunction based on single Slater atomic orbitals. The correlation‐energy contribution is calculated with the Hirschfelder‐Linnett pair function previously used for hydrogen interactions. Many‐electron and distortion effects contribute 29% of the correlation part at the potential minimum (R_e) and 23% at large distances. Like and unlike spin pairs differ in energy by about 6% at R_e. A serious correction for R < R_e is the change in atomic correlation due to distortion. The total potential obtained has the correct behavior [minimum of 4.32°K at 3.04 A. (5.75 a.u.) with a long‐range behavior of −0.853R⁻⁶ in atomic units]. At short distances (R < R_e) the molecular orbital (MO) form of the theory becomes more convenient since the interorbital MO pair correlations are large and have some intra‐atomic correlation character. The MO pair correlations approach ${\text{ε(1σ}}_g^2{\text{)=ε(1σ}}_u^2{\text{)=ε(1σ}}_g{\text{α1σ}}_u\mathrm{\beta )=}\frac{1}{2}\mathrm{\epsilon (}\mathrm{He}\text{)=−0.57\hspace{0.17em}}\mathrm{eV}$ as R → ∞. The LO description is used for R ≳ R_e.