Calculation of excitation energies from the CC2 linear response theory using Cholesky decomposition

Baudin, Pablo; Marín, J. Sánchez; Cuesta, Inmaculada Garcı́a; Merás, Alfredo M. J. Sánchez de

doi:10.1063/1.4867270

Cited by 11 publications

(14 citation statements)

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“…The LoFEx algorithm as described in Section II has been implemented in a local version of the LSD program. 34,35 The RI-CC2 algorithm used in LoFEx relies on a self-consistent Davidson algorithm 7 where the norm of the residual is converged below τ residual = 10 −4 a.u. and the self-consistent energy threshold is set to τ exc = 10 −4 a.u.…”

Section: A Molecules and Computational Detailsmentioning

confidence: 99%

“…5 The CC2 model has proven to be a good compromise between accuracy and computational cost for a) pablo.baudin@chem.au.dk the calculation of frequency-dependent molecular properties and its reformulation using density fitting techniques (e.g., the resolution of the identity, RI-CC2) has significantly extended the application range of the method. 6,7 To further reduce the cost of the CC2 model, Helmich and Hättig proposed a local version of CC2 for excitation energies where they used orbital-specific virtuals (OSVs) and pair natural orbitals (PNOs) to reduce the dimension of the virtual orbital space. 8 Along the same lines, the local CC implementation of Kats, Korona, and Schütz uses information from the coupled cluster singles (CCS) model to select the relevant occupied LMOs to describe each transition, combined with projected atomic orbitals (PAOs) for the virtual space.…”

Section: Introductionmentioning

confidence: 99%

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LoFEx — A local framework for calculating excitation energies: Illustrations using RI-CC2 linear response theory

Baudin

Kristensen

2016

The Journal of Chemical Physics

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We present a local framework for the calculation of coupled cluster excitation energies of large molecules (LoFEx). The method utilizes time-dependent Hartree-Fock information about the transitions of interest through the concept of natural transition orbitals (NTOs). The NTOs are used in combination with localized occupied and virtual Hartree-Fock orbitals to generate a reduced excitation orbital space (XOS) specific to each transition where a standard coupled cluster calculation is carried out. Each XOS is optimized to ensure that the excitation energies are determined to a predefined precision. We apply LoFEx in combination with the RI-CC2 model to calculate the lowest excitation energies of a set of medium-sized organic molecules. The results demonstrate the black-box nature of the LoFEx approach and show that significant computational savings can be gained without affecting the accuracy of CC2 excitation energies.

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Section: A Molecules and Computational Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

LoFEx — A local framework for calculating excitation energies: Illustrations using RI-CC2 linear response theory

Baudin

Kristensen

2016

The Journal of Chemical Physics

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“…k ∈ R r 3 , the column vectors of U (2) and U (3) , respectively, belong to the coefficients space by means of projection.…”

Section: Appendixmentioning

confidence: 99%

“…⊲ End of the single ALS iteration step. ⊲ Repeat the complete ALS iteration m max times to obtain the optimized Tucker orthogonal side matrices Z (1) , Z (2) , Z (3) , and final projected image U 3 .…”

Section: Appendixmentioning

confidence: 99%

Tensor numerical methods in quantum chemistry: from Hartree–Fock to excitation energies

Khoromskaia

Khoromskij

2015

Phys. Chem. Chem. Phys.

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We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

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“…The efficiency of the approximation was also demonstrated for CC2. [42][43][44] The LT approximation developed by Almlöf and Häser [45][46][47] eliminates the orbital energy denominators appearing in many-body methods like CC2. Together with the DF and further approximations, it can be efficiently used for the scaling reduction of the CC2 method.…”

Section: Introductionmentioning

confidence: 99%

Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions

Mester

Nagy

Kállay

2017

The Journal of Chemical Physics

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A reduced-cost density fitting (DF) linear-response second-order coupled-cluster (CC2) method has been developed for the evaluation of excitation energies. The method is based on the simultaneous truncation of the molecular orbital (MO) basis and the auxiliary basis set used for the DF approximation. For the reduction of the size of the MO basis, state-specific natural orbitals (NOs) are constructed for each excited state using the average of the second-order Møller-Plesset (MP2) and the corresponding configuration interaction singles with perturbative doubles [CIS(D)] density matrices. After removing the NOs of low occupation number, natural auxiliary functions (NAFs) are constructed [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], and the NAF basis is also truncated. Our results show that, for a triple-zeta basis set, about 60% of the virtual MOs can be dropped, while the size of the fitting basis can be reduced by a factor of five. This results in a dramatic reduction of the computational costs of the solution of the CC2 equations, which are in our approach about as expensive as the evaluation of the MP2 and CIS(D) density matrices. All in all, an average speedup of more than an order of magnitude can be achieved at the expense of a mean absolute error of 0.02 eV in the calculated excitation energies compared to the canonical CC2 results. Our benchmark calculations demonstrate that the new approach enables the efficient computation of CC2 excitation energies for excited states of all types of medium-sized molecules composed of up to 100 atoms with triple-zeta quality basis sets.

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Calculation of excitation energies from the CC2 linear response theory using Cholesky decomposition

Cited by 11 publications

References 44 publications

LoFEx — A local framework for calculating excitation energies: Illustrations using RI-CC2 linear response theory

LoFEx — A local framework for calculating excitation energies: Illustrations using RI-CC2 linear response theory

Tensor numerical methods in quantum chemistry: from Hartree–Fock to excitation energies

Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions

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