A new ab initio potential energy curve for the helium dimer

The ${\mathrm{He}}_{\mathrm{2}}$ interaction potential has been computed employing augmented correlation-consistent basis sets and several methods beyond those commonly used to recover electron correlation, namely fifth-order Mo/ller–Plesset perturbation theory (MP5), coupled cluster theory with full triple excitations (CCSDT), and full configuration interaction (FCI). Calculations employing the largest basis sets were not feasible for the most sophisticated methods (MP5, CCSDT, and FCI). Nonetheless, because of the rapid convergence of the calculated interaction energy differences with basis set, it was possible to obtain reliable estimates of the complete basis set MP5, CCSDT, and FCI results. The MP5 method is predicted to yield a well depth of $\text{10.67±0.03\hspace{0.05em}}\mathrm{K}$ at the complete basis set (CBS) limit. Thus, the accuracy of the MP5 method is comparable to that of the CCSD(T) method which yields a $D_e$ of $\text{10.68±0.02\hspace{0.05em}}\mathrm{K}.$ The CCSDT method yields an estimated well depth of $\text{10.98±0.03\hspace{0.05em}}\mathrm{K}.$ Thus, the full effect of connected triple excitations on the ${\mathrm{He}}_{\mathrm{2}}$ well depth is 1.74 K (CCSDT-CCSD). Comparing the basis set dependence of the CCSDT and FCI well depths, the effect of connected quadruple excitations on the well depth is estimated to be just 0.015–0.020 K. Thus, the current calculations predict the FCI ${\mathrm{He}}_{\mathrm{2}}$ well depth to be $\text{11.00±0.03\hspace{0.05em}}\mathrm{K},$ in excellent agreement with the recent quantum Monte Carlo calculations of Anderson et al. [J. Chem. Phys. 99, 345 (1993)]. Taking advantage of the rapid convergence of the full triples and quadruples correlation corrections to the CCSD(T) interaction energy with basis set, an estimated FCI/CBS potential energy curve has been constructed for ${\mathrm{He}}_{\mathrm{2}}$ from 3.5 to 15.0 $a_0.$ The resulting curve lies between the HFD-B3-FCI1 and SAPT2 semi-empirical potentials of Aziz et al., being closer to the SAPT2 potential.