Convergence of the Møller-Plesset perturbation series for the fcc lattices of neon and argon

Complete basis set limit calculations are carried out for the fcc lattices of solid neon and argon, using second- to fourth-order Møller-Plesset theory, MP2–MP4, and coupled-cluster calculations, CCSD(T), to describe electron correlation within a many-body expansion of the interaction potential up to third order. A correct description of the three-body Axilrod-Teller-Muto term for the solid state is only obtained from third order on in the many-body expansion of the correlation energy, correcting the severe underestimation of long-range three-body effects at the MP2 level of theory. MP4 shows good agreement with the CCSD(T) results, and the latter are in good agreement with experimental lattice constants, cohesive energies, and bulk moduli. However, with increasing pressures the convergence of the Møller-Plesset series deteriorates as the electronic band gap decreases, resulting in rather large deviations for the equation of state (pressure-volume dependence). For neon, however, the errors in the MP2 two- and three-body terms almost cancel, i.e., at a volume of $V=3{\text{cm}}^3/\text{mol}$ the MP2 pressure is underestimated by only 1 GPa compared to the pressure of $P=251\text{GPa}$ calculated at the CCSD(T) level of theory. In contrast, for argon this is not the case, and at $V=5.5{\text{cm}}^3/\text{mol}$ the calculated MP2 pressure of 228 GPa deviates substantially from the CCSD(T) result of 252 GPa.

Figure 1

(Color online) Two-body potential curves for ${\text{Ne}}_2$ and ${\text{Ar}}_2$ at various levels of theory from CBS limit calculations.

Figure 2

(Color online) Three-body potential curves for the equilateral triangle of ${\text{Ne}}_3$ and ${\text{Ar}}_3$ at various levels of theory from CBS limit calculations.

Figure 3

(Color online) Basis set dependence of the three-body potential curves for the equilateral triangle of ${\text{Ne}}_3$ (left) and ${\text{Ar}}_3$ (right) from aug-ccPVnZ (abbreviated as aVnZ) MP2 (top) and CCSD(T) (bottom) calculations. Solid lines: including counterpoise correction; dashed lines: without counterpoise correction. Inlets highlight details in important regions.

Figure 4

(Color online) The singlet-triplet gap for ${\text{Ne}}_2$ (upper curves) and ${\text{Ar}}_2$ (lower curves) obtained from separate SCF calculations for the two states at various levels of theory using an aug-ccpVTZ ($+\text{three}$ diffuse $s$ functions) basis set.

Figure 5

(Color online) Deviation of the calculated pressure from the CCSD(T) result, i.e., $\Delta P=P_{\text{CCSD}\left(\text{T}\right)}-P_M$, where $M$ stands for MP2, MP3, MP4, and CCSD.

Figure 6

(Color online) Deviation of the calculated $n$-body contribution to the pressure from our CCSD(T) result, i.e., $\Delta P=P_{\text{CCSD}\left(\text{T}\right)}-P_M$, where $M$ stands for MP2, MP3, MP4, and CCSD.