Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis

Abstract

A production level implementation of the closed-shell local quadratic configuration interaction and coupled cluster methods with single and double excitations (QCISD and CCSD) based on the concept of pair natural orbitals [local pair natural orbital LPNO-QCISD and LPNO-CCSD) is reported, evaluated, and discussed. This work is an extension of the earlier developed LPNO coupled-electron pair approximation (LNPO-CEPA) method [F. Neese et al., Chem. Phys. 130, 114108 (2009)] and makes extended use of the resolution of the identity (RI) or density fitting (DF) approximation. Two variants of each method are compared. The less accurate approximations (LPNO2-QCISD/LPNO2-CCSD) still recover 98.7%-99.3% of the correlation energy in the given basis and have modest disk space requirements. The more accurate variants (LPNO1-QCISD/LPNO1-CCSD) typically recover 99.75%-99.95% of the correlation energy in the given basis but require the Coulomb and exchange operators with up to two-external indices to be stored on disk. Both variants have comparable computational efficiency. The convergence of the results with respect to the natural orbital truncation parameter (T(CutPNO)) has been studied. Extended numerical tests have been performed on absolute and relative correlation energies as function of basis set size and T(CutPNO) as well as on reaction energies, isomerization energies, and weak intermolecular interactions. The results indicate that the errors of the LPNO methods compared to the canonical QCISD and CCSD methods are below 1 kcal/mol with our default thresholds. Finally, some calculations on larger molecules are reported (ranging from 40-86 atoms) and it is shown that for medium sized molecules the total wall clock time required to complete the LPNO-CCSD calculations is only two to four times that of the preceding self-consistent field (SCF). Thus these methods are highly suitable for large-scale computational chemistry applications. Since there are only three thresholds involved that have been given conservative default values, the methods can be confidentially used in a "black-box" fashion in the same way as their canonical counterparts.

Combined Fragment Molecular Orbital Cluster in Molecule Approach to Massively Parallel Electron Correlation Calculations for Large Systems.

“…Alanine Alpha Helix Test Case. To determine the accuracy and performance of the combined FMO-CIM approach relative to standard CIM and canonical correlation methods, FMO2-CIM/MP2, CIM/MP2, and full MP2 (using GAMESS), were applied to the calculation of the electron correlation energy of a 20-residue polyalanine α helix, Ala 20 (using the FMO2-RHF equilibrium geometry). To study the dependence of the FMO2-CIM/MP2 correlation energy and computational wall time with respect to both the FMO fragment size and the CIM subsystem parameter ζ, calculations were performed using two and four alanine residues per FMO fragment (five-and ten-fragment schemes) while also varying the subsystem size parameter ζ from 0.003 to 0.001 hartree.…”

“…The MP2 subsystem calculations were performed in parallel using one core for each subsystem. The FMO2-CIM/MP2 and CIM/MP2 methods both generated 256 or fewer total subsystems for Ala 20 , except in the case of the ten-fragment, ζ = 0.001 FMO2-CIM/MP2 calculation. (See Table 1.).…”

“…al present an interesting possibility to further improve the efficiency of the CIM algorithm. 44 Table 2 contains the RHF reference and correlation energies (in hartree) for MP2, CIM/MP2, and the four FMO2-CIM/ MP2 combinations of fragment size and subsystem parameter ζ for Ala 20 . The percentage of correlation energy recovered and the absolute error (hartree) of FMO2-CIM/MP2 and CIM-MP2 relative to MP2 is also provided.…”

Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

“…The method is also closely related to PNO methods, except here our special virtual orbitals are labelled by a single occupied index, rather than by a pair of occupied orbitals. This can be expected to confer improved efficiency in integral transformation, even when density fitting is used, 5,6 and also makes extension to odd-order excitations more obvious.…”

“…This can be achieved, however, through the use of pair natural orbitals (PNOs), introduced by Edmiston and Krauss 3 and pioneered as a general method for molecular correlation theories in Meyer's development of the coupled-electronpair approximation. 4 The approach has recently returned to prominence through the work of Neese and co-workers 5,6 and Tew et al have recently demonstrated how the PNO concept can be extended to increase the efficiency of resolution of identity approximations in explicitly correlated F12 theories. 7 An alternative proposed by Pulay and Saebø is the use of fixed domains of projected atomic orbitals (PAOs) for a) Electronic mail: kura@ims.ac.jp.…”