Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis

Abstract

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset perturbation theory (MP2). In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, $\mathcal{O}(N^4)$, with respect to the system size $N$ and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 (LTMP2) formulation using plane wave basis sets and Fast Fourier transforms. Analogously, this approach could allow to calculate second order screened exchange (SOSEX) as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

12 pages, 10 figures

References in corpus (2)

• Convergence of many-body wavefunction expansions using a plane wave basis: from the homogeneous electron gas to the solid state
• Analytic Interatomic Forces in the Random Phase Approximation

Cited by in corpus (25)

• Low rank factorization of the Coulomb integrals for periodic coupled cluster theory
• Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
• Properties of the water to boron nitride interaction: from zero to two dimensions with benchmark accuracy
• Local embedding of Coupled Cluster theory into the Random Phase Approximation using plane-waves
• Effective Hamiltonians for the study of real metals using quantum chemical theories
• Surface science using coupled cluster theory via local Wannier functions and in-RPA-embedding: the case of water on graphitic carbon nitride
• Lowering of the complexity of quantum chemistry methods by choice of representation
• On the duality of ring and ladder diagrams and its importance for many-electron perturbation theories
• Efficient and accurate description of adsorption in zeolites
• Cerium Oxides without $U$: The Role of Many-Electron Correlation
• Spectral properties from Matsubara Green's function approach - application to molecules
• RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods
• Focal-point approach with pair-specific cusp correction for coupled-cluster theory
• Integral-direct Hartree-Fock and Møller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal
• Efficient Evaluation of Exact Exchange for Periodic Systems via Concentric Atomic Density Fitting
• Optimized pair natural orbitals for the coupled cluster methods
• Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling
• Inverse Volume Scaling of Finite-Size Error in Periodic Coupled Cluster Theory
• Assessment of random-phase approximation and second order Møller-Plesset perturbation theory for many-body interactions in solid ethane, ethylene, and acetylene
• Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory
• Binding energies of molecular solids from fragment and periodic approaches
• Accurate thermochemistry of covalent and ionic solids from spin-component-scaled MP2
• Regularized Perturbation Theory for Ab initio Solids
• Direct determination of optimal real-space orbitals for correlated electronic structure of molecules
• The binding of atomic hydrogen on graphene from density functional theory and diffusion Monte Carlo calculations