Excitation energies from particle-particle random phase approximation with accurate optimized effective potentials

Jin, Ye; Yang, Yang; Zhang, Du; Peng, Degao; Yang, Weitao

doi:10.1063/1.4994827

Excitation energies from particle-particle random phase approximation with accurate optimized effective potentials

Journal Article · Tue Oct 03 00:00:00 EDT 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4994827· OSTI ID:1511692

^[1]; Yang, Yang ^[2]; Zhang, Du ^[2]; Peng, Degao ^[2]; ^[2]

Duke Univ., Durham, NC (United States); none
Duke Univ., Durham, NC (United States)

The optimized effective potential (OEP) that gives accurate Kohn-Sham (KS) orbitals and orbital energies can be obtained from a given reference electron density. These OEP-KS orbitals and orbital energies are used here for calculating electronic excited states with the particle-particle random phase approximation (pp-RPA). Our calculations allow the examination of pp-RPA excitation energies with the exact KS density functional theory (DFT). Various input densities are investigated. Specifically, the excitation energies using the OEP with the electron densities from the coupled-cluster singles and doubles method display the lowest mean absolute error from the reference data for the low-lying excited states. This study probes into the theoretical limit of the pp-RPA excitation energies with the exact KS-DFT orbitals and orbital energies. We believe that higher-order correlation contributions beyond the pp-RPA bare Coulomb kernel are needed in order to achieve even higher accuracy in excitation energy calculations.

View Accepted Manuscript (DOE)

Research Organization:: Energy Frontier Research Centers (EFRC) (United States). Center for Complex Materials from First Principles (CCM); Temple Univ. of the Commonwealth System of Higher Education, Philadelphia, PA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0012575

OSTI ID:: 1511692

Alternate ID(s):: OSTI ID: 1396313

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 13 Vol. 147; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (41)

Single-Reference ab initio Methods for the Calculation of Excited States of Large Molecules Dreuw, Andreas; Head-Gordon, Martin ChemInform, Vol. 37, Issue 5 https://doi.org/10.1002/chin.200605293	journal	January 2006
Calculation of the electron affinity and 1A1-3B1T0 value of methylene using the ab initio MRD CI method for a large AO basis Shih, Shing-Kuo; Peyerimhoff, Sigrid D.; Buenker, Robert J. Chemical Physics Letters, Vol. 55, Issue 2 https://doi.org/10.1016/0009-2614(78)87003-1	journal	April 1978
Variational collapse of the optimized effective potential method with an orbital-dependent exchange-correlation functional based on second order perturbation theory Rohr, Daniel; Gritsenko, Oleg; Baerends, Evert Jan Chemical Physics Letters, Vol. 432, Issue 1-3 https://doi.org/10.1016/j.cplett.2006.10.021	journal	December 2006
Geometry and singlet-triplet energy gap in methylene: a critical review of experimental and theoretical determinations Shavitt, Isaiah Tetrahedron, Vol. 41, Issue 8 https://doi.org/10.1016/s0040-4020(01)96393-8	journal	January 1985
Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules Dreuw, Andreas; Head-Gordon, Martin Chemical Reviews, Vol. 105, Issue 11 https://doi.org/10.1021/cr0505627	journal	November 2005
Physical Meaning of Virtual Kohn–Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations van Meer, R.; Gritsenko, O. V.; Baerends, E. J. Journal of Chemical Theory and Computation, Vol. 10, Issue 10 https://doi.org/10.1021/ct500727c	journal	September 2014
Singlet−Triplet Energy Gaps for Diradicals from Fractional-Spin Density-Functional Theory Ess, Daniel H.; Johnson, Erin R.; Hu, Xiangqian The Journal of Physical Chemistry A, Vol. 115, Issue 1 https://doi.org/10.1021/jp109280y	journal	January 2011
Singlet–Triplet Energy Gaps for Diradicals from Particle–Particle Random Phase Approximation Yang, Yang; Peng, Degao; Davidson, Ernest R. The Journal of Physical Chemistry A, Vol. 119, Issue 20 https://doi.org/10.1021/jp512727a	journal	April 2015
Does Unrestricted Møller−Plesset Perturbation Theory for Low Spin Converge When the System Has a Triplet Ground State? Jarzȩcki, Andrzej A.; Davidson, Ernest R. The Journal of Physical Chemistry A, Vol. 102, Issue 24 https://doi.org/10.1021/jp981290x	journal	June 1998
Spectrum and Structure of the Free Methylene Radical Herzberg, G.; Shoosmith, J. Nature, Vol. 183, Issue 4678 https://doi.org/10.1038/1831801a0	journal	June 1959
The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies Baerends, E. J.; Gritsenko, O. V.; van Meer, R. Physical Chemistry Chemical Physics, Vol. 15, Issue 39 https://doi.org/10.1039/c3cp52547c	journal	January 2013
Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study Slipchenko, Lyudmila V.; Krylov, Anna I. The Journal of Chemical Physics, Vol. 117, Issue 10 https://doi.org/10.1063/1.1498819	journal	September 2002
A direct optimization method for calculating density functionals and exchange–correlation potentials from electron densities Wu, Qin; Yang, Weitao The Journal of Chemical Physics, Vol. 118, Issue 6 https://doi.org/10.1063/1.1535422	journal	January 2003
Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3 Schreiber, Marko; Silva-Junior, Mario R.; Sauer, Stephan P. A. The Journal of Chemical Physics, Vol. 128, Issue 13 https://doi.org/10.1063/1.2889385	journal	April 2008
The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties Stanton, John F.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 98, Issue 9 https://doi.org/10.1063/1.464746	journal	May 1993
Density‐functional thermochemistry. III. The role of exact exchange Becke, Axel D. The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652 https://doi.org/10.1063/1.464913	journal	April 1993
General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: Theory, implementation, and benchmarks Bernard, Yves A.; Shao, Yihan; Krylov, Anna I. The Journal of Chemical Physics, Vol. 136, Issue 20 https://doi.org/10.1063/1.4714499	journal	May 2012
Improving virtual Kohn–Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities Tozer, David J.; Handy, Nicholas C. The Journal of Chemical Physics, Vol. 109, Issue 23 https://doi.org/10.1063/1.477711	journal	December 1998
Benchmark tests and spin adaptation for the particle-particle random phase approximation Yang, Yang; van Aggelen, Helen; Steinmann, Stephan N. The Journal of Chemical Physics, Vol. 139, Issue 17 https://doi.org/10.1063/1.4828728	journal	November 2013
Double, Rydberg and charge transfer excitations from pairing matrix fluctuation and particle-particle random phase approximation Yang, Yang; van Aggelen, Helen; Yang, Weitao The Journal of Chemical Physics, Vol. 139, Issue 22 https://doi.org/10.1063/1.4834875	journal	December 2013
Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation van Aggelen, Helen; Yang, Yang; Yang, Weitao The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4865816	journal	May 2014
Linear-response time-dependent density-functional theory with pairing fields Peng, Degao; van Aggelen, Helen; Yang, Yang The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4867540	journal	May 2014
Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies Yang, Yang; Peng, Degao; Lu, Jianfeng The Journal of Chemical Physics, Vol. 141, Issue 12 https://doi.org/10.1063/1.4895792	journal	September 2014
Charge transfer excitations from particle-particle random phase approximation—Opportunities and challenges arising from two-electron deficient systems Yang, Yang; Dominguez, Adriel; Zhang, Du The Journal of Chemical Physics, Vol. 146, Issue 12 https://doi.org/10.1063/1.4977928	journal	March 2017
Nature of ground and electronic excited states of higher acenes Yang, Yang; Davidson, Ernest R.; Yang, Weitao Proceedings of the National Academy of Sciences, Vol. 113, Issue 35 https://doi.org/10.1073/pnas.1606021113	journal	August 2016
Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem Levy, M. Proceedings of the National Academy of Sciences, Vol. 76, Issue 12 https://doi.org/10.1073/pnas.76.12.6062	journal	December 1979
Excitation energies from time-dependent density functional theory with accurate exchange-correlation potentials Wu, Qin; Cohen, Aron J.; Yang *, Weitao Molecular Physics, Vol. 103, Issue 6-8 https://doi.org/10.1080/0026897051234267	journal	March 2005
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/physrev.140.a1133	journal	November 1965
Optimized effective atomic central potential Talman, James D.; Shadwick, William F. Physical Review A, Vol. 14, Issue 1 https://doi.org/10.1103/physreva.14.36	journal	July 1976
Density-functional theory for time-dependent systems Dhara, Asish K.; Ghosh, Swapan K. Physical Review A, Vol. 35, Issue 1 https://doi.org/10.1103/physreva.35.442	journal	January 1987
Systematic approximations to the optimized effective potential: Application to orbital-density-functional theory Krieger, J. B.; Li, Yan; Iafrate, G. J. Physical Review A, Vol. 46, Issue 9 https://doi.org/10.1103/physreva.46.5453	journal	November 1992
From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies Zhao, Qingsheng; Morrison, Robert C.; Parr, Robert G. Physical Review A, Vol. 50, Issue 3 https://doi.org/10.1103/physreva.50.2138	journal	September 1994
Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation van Aggelen, Helen; Yang, Yang; Yang, Weitao Physical Review A, Vol. 88, Issue 3 https://doi.org/10.1103/physreva.88.030501	journal	September 2013
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density Lee, Chengteh; Yang, Weitao; Parr, Robert G. Physical Review B, Vol. 37, Issue 2 https://doi.org/10.1103/physrevb.37.785	journal	January 1988
Optimized effective potential made simple: Orbital functionals, orbital shifts, and the exact Kohn-Sham exchange potential Kümmel, Stephan; Perdew, John P. Physical Review B, Vol. 68, Issue 3 https://doi.org/10.1103/physrevb.68.035103	journal	July 2003
Density-Functional Theory for Time-Dependent Systems Runge, Erich; Gross, E. K. U. Physical Review Letters, Vol. 52, Issue 12 https://doi.org/10.1103/physrevlett.52.997	journal	March 1984
Excitation Energies from Time-Dependent Density-Functional Theory Petersilka, M.; Gossmann, U. J.; Gross, E. K. U. Physical Review Letters, Vol. 76, Issue 8 https://doi.org/10.1103/physrevlett.76.1212	journal	February 1996
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/physrevlett.77.3865	journal	October 1996
Direct Method for Optimized Effective Potentials in Density-Functional Theory Yang, Weitao; Wu, Qin Physical Review Letters, Vol. 89, Issue 14 https://doi.org/10.1103/physrevlett.89.143002	journal	September 2002
Equations-of-Motion Method and the Extended Shell Model Rowe, D. J. Reviews of Modern Physics, Vol. 40, Issue 1 https://doi.org/10.1103/revmodphys.40.153	journal	January 1968
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density Robert, Parr,; Chengteh, Lee,; Weitao, Yang, The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/zrp0-ry04	text	January 1988