Table 1. MP2 Correlation Energies E_c^MP2 Obtained from a Conventional MP2 Calculation and the Stochastic Approach, MPs2^a.

system		EcMP2 [a.u.]	EcMPs2 [a.u.]	ΔEMPs2MP2 [a.u.]	ΔE/e– [a.u.]	Nijab	psNijab
ethylene	crystal	–0.78054	–0.78056	2 × 10–5	8 × 10–7	5.06 × 109	3.26 × 108
benzene	crystal	–4.69164	–4.69149	–1.5 × 10–4	–1 × 10–6	1.30 × 1011	3.50 × 109
	monomer	–1.05681	–1.05695	1.4 × 10–4	5 × 10–6	8.62 × 109	6.26 × 108
	dimer	–2.12780	–2.12777	–3 × 10–5	–5 × 10–7	3.33 × 1010	8.78 × 109
	binding	–0.01417	–0.01387	–3 × 10–4	–5 × 10–6

^aΔE_MPs2^MP2 and ΔE/e^– denote absolute and per-electron energy differences between stochastic sampling and conventional calculations, respectively. N_ijab denotes the number of matrix elements (ijab-tuples) sampled in a conventional calculation, and p_sN_ijab is the number of effectively sampled matrix elements in a stochastic MPs2 calculation, with both numbers rounded to three digits. The threshold for stochastic sampling expressed with respect to the HOMO was identical for all systems, ε_c = ε_c – ε_HOMO = 120 eV. The same holds for N_MC = 12,000, the number of terms sampled per virtual contribution η_c(a), as described in eq 7. For details on the systems used, cf. the Supporting Information.