Linear-scaling atomic orbital-based second-order Møller–Plesset perturbation theory by rigorous integral screening criteria

Abstract

A Laplace-transformed second-order Moller-Plesset perturbation theory (MP2) method is presented, which allows to achieve linear scaling of the computational effort with molecular size for electronically local structures. Also for systems with a delocalized electronic structure, a cubic or even quadratic scaling behavior is achieved. Numerically significant contributions to the atomic orbital (AO)-MP2 energy are preselected using the so-called multipole-based integral estimates (MBIE) introduced earlier by us [J. Chem. Phys. 123, 184102 (2005)]. Since MBIE provides rigorous upper bounds, numerical accuracy is fully controlled and the exact MP2 result is attained. While the choice of thresholds for a specific accuracy is only weakly dependent upon the molecular system, our AO-MP2 scheme offers the possibility for incremental thresholding: for only little additional computational expense, the numerical accuracy can be systematically converged. We illustrate this dependence upon numerical thresholds for the calculation of intermolecular interaction energies for the S22 test set. The efficiency and accuracy of our AO-MP2 method is demonstrated for linear alkanes, stacked DNA base pairs, and carbon nanotubes: e.g., for DNA systems the crossover toward conventional MP2 schemes occurs between one and two base pairs. In this way, it is for the first time possible to compute wave function-based correlation energies for systems containing more than 1000 atoms with 10 000 basis functions as illustrated for a 16 base pair DNA system on a single-core computer, where no empirical restrictions are introduced and numerical accuracy is fully preserved.

Third-order corrections to random-phase approximation correlation energies

“…25 and 26 for singular value decomposition approaches in coupled-cluster theory), the transformation into local basis functions, 14,15,[27][28][29][30][31][32][33][34][35][36][37][38] or the exploitation of parallel computer architectures 18,[39][40][41][42] has lead to an increase of the feasibility of standard ab initio methods also for extended molecular systems so that electron correlation effects can nowadays also accurately be accounted for quite large systems that formally could be described only on the density functional theory level. However, though in contrast to DFT common ab initio correlation methods have a) Electronic mail: andreas.hesselmann@chemie.uni-erlangen.…”

Laplace-transformed atomic orbital-based Møller–Plesset perturbation theory for relativistic two-component Hamiltonians

“…(35) -(37), reduced-or even linear-scaling implementations can be designed as for NR AO-based MP2. 8,9,12 Like for HTIs in Fig. 1 and for the contributions to the exchange interaction energy in Fig.…”

“…8,12 First, this distance behavior is investigated by means of the contributions to the interaction energy of Ba 2 in Fig. 2.…”

“…By employing estimates for integral screening, low-order scaling implementations were proposed by Häser 6 and Ayala and Scuseria. 7 Ochsenfeld and his co-workers showed how to achieve linear scaling of all computationally demanding steps by accounting for the distance-dependent decay of integrals, 8,11,12 and their implementation currently allows for calculations on molecules with 1000 atoms and more on a single core. 12 The same authors have also presented a promising computational performance for large AO basis sets that include high angular momentum and / or diffuse basis functions when the LT AO-based approach is combined with Cholesky decomposition of two-electron integrals.…”

“…To overcome this computational bottleneck, several reduced scaling approaches were proposed for MP2 over the years. [5][6][7][8][9] One of the most successful approaches originates from Almlöf 5,10 and Häser 6 where the MP2 correlation energy is formulated purely in the AO basis by means of a numerical Laplace transformation (LT) of orbital-energy denominators. By employing estimates for integral screening, low-order scaling implementations were proposed by Häser 6 and Ayala and Scuseria.…”