### Abstract

The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti, J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend, Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O (N^{4} log N) operations and O (N^{3}) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield μH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung, Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

Original language | English |
---|---|

Article number | 234114 |

Journal | Journal of Chemical Physics |

Volume | 132 |

Issue number | 23 |

DOIs | |

State | Published - 21 Jun 2010 |

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*Journal of Chemical Physics*,

*132*(23), [234114]. https://doi.org/10.1063/1.3442749

}

*Journal of Chemical Physics*, vol. 132, no. 23, 234114. https://doi.org/10.1063/1.3442749

**Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration.** / Eshuis, Hendrik; Yarkony, Julian; Furche, Filipp.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration

AU - Eshuis, Hendrik

AU - Yarkony, Julian

AU - Furche, Filipp

PY - 2010/6/21

Y1 - 2010/6/21

N2 - The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti, J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend, Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O (N4 log N) operations and O (N3) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield μH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung, Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

AB - The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti, J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend, Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O (N4 log N) operations and O (N3) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield μH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung, Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

UR - http://www.scopus.com/inward/record.url?scp=77953864922&partnerID=8YFLogxK

U2 - 10.1063/1.3442749

DO - 10.1063/1.3442749

M3 - Article

VL - 132

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 23

M1 - 234114

ER -