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Title: A low-cost approach to electronic excitation energies based on the driven similarity renormalization group

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1]; ORCiD logo [1]
  1. Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1375254
Grant/Contract Number:
SC0016004
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 7; Related Information: CHORUS Timestamp: 2018-02-15 02:24:26; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

Citation Formats

Li, Chenyang, Verma, Prakash, Hannon, Kevin P., and Evangelista, Francesco A.. A low-cost approach to electronic excitation energies based on the driven similarity renormalization group. United States: N. p., 2017. Web. doi:10.1063/1.4997480.
Li, Chenyang, Verma, Prakash, Hannon, Kevin P., & Evangelista, Francesco A.. A low-cost approach to electronic excitation energies based on the driven similarity renormalization group. United States. doi:10.1063/1.4997480.
Li, Chenyang, Verma, Prakash, Hannon, Kevin P., and Evangelista, Francesco A.. 2017. "A low-cost approach to electronic excitation energies based on the driven similarity renormalization group". United States. doi:10.1063/1.4997480.
@article{osti_1375254,
title = {A low-cost approach to electronic excitation energies based on the driven similarity renormalization group},
author = {Li, Chenyang and Verma, Prakash and Hannon, Kevin P. and Evangelista, Francesco A.},
abstractNote = {},
doi = {10.1063/1.4997480},
journal = {Journal of Chemical Physics},
number = 7,
volume = 147,
place = {United States},
year = 2017,
month = 8
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on August 16, 2018
Publisher's Accepted Manuscript

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  • Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994) and S. D. Głazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron correlation are considered. In addition to presenting a production-level implementation of the SRG based on a single-reference formalism, a novel integral version of the SRG is reported, in which the flow of the Hamiltonian is driven by a source operator. It is shown that this driven SRG (DSRG) produces a Hamiltonian flow that is analogous to that of the SRG. Compared tomore » the SRG, which requires propagating a set of ordinary differential equations, the DSRG is computationally advantageous since it consists of a set of polynomial equations. The equilibrium distances, harmonic vibrational frequencies, and vibrational anharmonicities of a series of diatomic molecules computed with the SRG and DSRG approximated with one- and two-body normal ordered operators are in good agreement with benchmark values from coupled cluster with singles, doubles, and perturbative triples. Particularly surprising results are found when the SRG and DSRG methods are applied to C{sub 2} and F{sub 2}. In the former case, both methods fail to converge, while in the latter case an unbound potential energy curve is obtained. A modified commutator approximation is shown to correct these problems in the case of the DSRG method.« less
  • Here, a third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2, H 2O 2, C 2H 6, and N 2 along the F–F, O–O, C–C, and N–N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbationmore » theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST = E T–E S) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol –1, a value that is within 0.1 kcal mol –1 from multireference coupled cluster results.« less
  • We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller–Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (Δ{sub ST}) of the naphthyne isomers strongly depend onmore » the equilibrium structures. For a consistent set of geometries, the Δ{sub ST} values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.« less
  • Research Highlights: > We study the similarity renormalization group evolution of chiral NN potentials. > We evolve an effective potential derived using a subtractive renormalization scheme. > Unitarity of the SRG evolution is verified within the subtractive scheme. > High- and low-momentum components decouple for the SRG evolved potential. - Abstract: Methods based on Wilson's renormalization group have been successfully applied in the context of nuclear physics to analyze the scale dependence of effective nucleon-nucleon (NN) potentials, as well as to consistently integrate out the high-momentum components of phenomenological high-precision NN potentials in order to derive phase-shift equivalent softer forms,more » the so called V{sub low-k} potentials. An alternative renormalization group approach that has been applied in this context is the similarity renormalization group (SRG), which is based on a series of continuous unitary transformations that evolve hamiltonians with a cutoff on energy differences. In this work we study the SRG evolution of a leading order (LO) chiral effective NN potential in the {sup 1}S{sub 0} channel derived within the framework of the subtracted kernel method (SKM), a renormalization scheme based on a subtracted scattering equation.« less
  • In this paper we discuss the performance of the several simplified variants of equation-of-motion coupled cluster method (EOMCC) with iterative inclusion of singles, doubles and active-space triples (EOMCCSDt). In particular, we explore simplified EOMCCSDt approaches which enable one to generate the triply excited amplitudes in on-the-fly manner. The original EOMCCSDt formulation has already demonstrated a great success in encapsulating the most important excited-state correlation effects due to triples. In analogy to the original EOMCCSDT formulation, the proposed approach can by-pass the typical bottlenecks associated with the need for storing triply-excited amplitudes. In this paper, we illustrate the performance of severalmore » approximate EOMCCSDt methods, named EOMCCSDt-3 and EOMCCSdt-3x, on typical benchmark systems including C2, N2, and the ozone molecules. These new methods yield excitation energies close to the EOMCCSDt ones. The extrapolation of excitation energies for basis sets ranging from cc-pVDZ to cc-pV6Z for N2 and C2 shows very good convergence to the experimental results for states dominated by single excitations.« less