Regularized Perturbation Theory for Ab initio Solids

Abstract

Second-order Moller-Plesset perturbation theory (MP2) for ab initio simulations of solids is often limited by divergence or over-correlation issues, particularly in metallic, narrow-gap, and dispersion-stabilized systems. We develop and assess three regularized second-order perturbation theories: $κ$-MP2, $σ$-MP2, and the size-consistent Brillouin-Wigner approach (BW-s2), across metals, semiconductors, molecular crystals, and rare gas solids. BW-s2 achieves high accuracy for cohesive energies, lattice constants, and bulk moduli in metals, semiconductors, and molecular crystals, rivaling or surpassing coupled-cluster with singles and doubles at lower cost. In rare gas solids, where MP2 already underbinds, $κ$-MP2 does not make the results much worse while BW-s2 struggles. These results illustrate both the potential and the limitations of regularized perturbation theory for efficient and accurate solid-state simulations. While broader testing is warranted, BW-s2($α$ = 2) appears particularly promising, with possible advantages over modern random-phase approximations and coupled-cluster theory.

Figures (8)

• Figure 1: Cohesive energy ($E_0$), equilibrium lattice constant ($a_0$), and bulk modulus ($B_0$) of BCC Li at different regularization strengths for $\kappa$-MP2, $\sigma$-MP2, and BW-s2($\alpha$).
• Figure 2: Cohesive energy ($E_0$), equilibrium lattice constant ($a_0$), and bulk modulus ($B_0$) of lithium calculated with different methods compared with experimental values. $\kappa = 1.1$, $\sigma = 0.7$, and $\alpha = 2.0$ are used for $\kappa$-MP2, $\sigma$-MP2, and BW-s2$(\alpha)$. CCSD result is from Ref. [ ye_periodic_2024], CCSD(T)$_{SR}$ from Ref. [ neufeld_ground-state_2022], and CCSDT from Ref. [ PhysRevLett.131.186402]. VMC result is from Ref. [ PhysRevB.54.8393]. HSE06 result is from Ref. [ zhang_performance_2018]. Experimental result is from Ref. [ schimka_improved_2011] and includes ZPE correction.
• Figure 3: Cohesive energy ($E_0$), equilibrium lattice constant ($a_0$), and bulk modulus ($B_0$) of diamond calculated with different methods compared with experimental values. $\kappa = 1.1$ is used for $\kappa$-MP2, and $\alpha = 2.0$ for BW-s2. dRPA@PBE and dRPA+SOSEX@PBE results are from Ref. [ harl_accurate_2009]. Coupled cluster (CC) results are from Ref. [ ye_periodic_2024]. Auxiliary-field quantum Monte Carlo (AFQMC) result is from Ref. [ malone_accelerating_2020]. HSE06 result is from Ref. [ zhang_performance_2018]. Experimental data is taken from Ref. [ schimka_improved_2011], and includes ZPE correction.
• Figure 4: Cohesive energy (eV) of the benzene crystal calculated with different methods. $\kappa = 1.1$ is used for $\kappa$-MP2, $\alpha = 2.0$ for BW-s2. dRPA+rSE@PBE result is from Ref. [ stein_massively_2024]. CCSD and theoretical best estimate (TBE) value is from Ref. [ yang_ab_2014]. Experimental (Exp.) value from Ref. [ roux_critically_2008] and [ yang_ab_2014].
• Figure 5: Cohesive energy ($E_0$), equilibrium lattice constant ($a_0$), and bulk modulus ($B_0$) of FCC neon crystal calculated with different methods compared with experimental values. $\kappa = 1.1$ is used for $\kappa$-MP2, and $\alpha = 0.5$ for BW-s2. dRPA@PBE result is from Ref. [ harl_cohesive_2008]. Coupled cluster (CC) and experimental results (including ZPE corrections from CCSD(T)) are from Ref. [ schwerdtfeger_convergence_2010].