Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory

Bozkaya, Uğur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David

doi:10.1063/1.3631129

Cited by 132 publications

(203 citation statements)

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“…Specifically, we use a NewtonRaphson optimizer and a diagonal approximation of the orbital Hessian to obtain the rotated set of orbital expansion coefficients. Our algorithm is analogous to the orbital-optimized coupled cluster approach [35][36][37]. Due to the four-index transformation of the electron repulsion integrals, the computational scaling deteriorates to O K 5 .…”

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confidence: 99%

Efficient description of strongly correlated electrons with mean-field cost

et al. 2014

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We present an efficient approach to the electron correlation problem that is well-suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. The performance of our approach is illustrated for the one-dimensional Hubbard model for different ring lengths, and for the non-relativistic quantum chemical Hamiltonian exploring the symmetric dissociation of the H50 hydrogen chain.The accurate description of the electron-electron interaction at the quantum-mechanical level is a key problem in condensed matter physics and quantum chemistry. Since most of the quantum many-body problems are extraordinarily difficult to solve exactly, different approximation schemes emerged [5][6][7][8][9], among which the density matrix renormalization group (DMRG) algorithm [10][11][12] gained a lot of popularity in both condensed matter physics [11] and quantum chemistry [13][14][15][16][17][18][19][20] over the last decade. Since the DMRG algorithm optimizes a matrix product state wavefunction, it is optimally suited for one-dimensional systems; though DMRG studies on higher-dimensional and compact systems have been reported [14,17,19,21]. Yet, novel theoretical approaches are desirable that can accurately describe strong correlation effects between electrons where the dimension of the Hilbert space exceeds the present-day limit of DMRG or general tensor-network approaches [22] allowing approximately 100 sites or 60 (spatial) orbitals, respectively.Another promising approach, suitable for larger strongly-correlated electronic systems, uses geminals (two-electron basis functions) as building blocks for the wavefunction [23][24][25][26][27][28][29][30]. One of the simplest practical geminal approaches is the antisymmetric product of 1-reference-orbital geminals (AP1roG) [31][32][33]. Unique among geminal methods, AP1roG can be rewritten as a fully general pair-coupled-cluster doubles wavefunc- * ayers@mcmaster.ca † dimitri.vanneck@ugent.be tion [34], i.e.where a † pσ and a pσ (σ = ↓, ↑) are the fermionic creation and annihilation operators, and |Φ 0 is some independent-particle wavefunction (usually the HartreeFock determinant). Indices i and a correspond to virtual and occupied sites (orbitals) with respect to |Φ 0 , P and K denote the number of electron pairs (P = N/2 with N being the total number of electrons) and orbitals, respectively, and {c a i } are the geminal coefficients. This wavefunction ansatz is size-extensive and has mean-field scaling, O P 2 (K − P ) 2 for the projected Schrödinger equation approach [31].To ensure size-consistency, however, it is necessary to optimize the one-electron basis functions [31], where all non-redundant orbital rotations span the occupiedoccupied, occupied-virtual, and virtual-virtual blocks with respect to the reference Slater determinant |Φ 0 . We have implemented a quadratically convergent algorithm: we minimize the energy with respect to the choice of the one-particle basis functions, subject to the constraint that the projected Schrödinger equati...

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Efficient description of strongly correlated electrons with mean-field cost

et al. 2014

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“…11,12 Another way to relax the orbitals is to actually optimize the full Lagrangian with respect to the orbital rotations, [13][14][15] which is still an exact procedure for a doubles-only theory. 16 The advantage of this approach is that the resulting theory is stationary with respect to orbitals, and therefore it is easier to calculate higher order properties.…”

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Communication: The distinguishable cluster approximation. II. The role of orbital relaxation

Kats

2014

The Journal of Chemical Physics

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(2013)] has shown intriguing abilities to accurately describe potential energy surfaces in various notoriously difficult cases. The question that still remained open is to what extend the accuracy and the stability of the method is due to the special choice of orbital-relaxation treatment. In this paper we introduce orbital relaxation in terms of Brueckner orbitals, orbital optimization, and projective singles into the distinguishable cluster approximation and investigate its importance in single-and multireference cases. All three resulting methods are able to cope with many multiple-bond breaking problems, but in some difficult cases where the Hartree-Fock orbitals seem to be entirely inadequate the orbital-optimized version turns out to be superior. © 2014 AIP Publishing LLC. [http://dx

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“…For this reason, many approaches that guarantee second-order convergence have been developed for MC-SCF [10,[107][108][109][110][111][112][113][114][115][116] and DMRG [117][118][119] calculations. While the Lagrangian formulation (equation (6)) is not correct to second order in the orbitals, it has been recently used for a quadratic convergence OO-CC implementation [84]. A similar approach should be feasible for the PPH as well -possibly supplemented by the use of the proxy function approach (freezing the density matrices between orbital update steps) which has been used in the present work.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Analytic gradients and orbital-optimized CC theory have been discussed extensively elsewhere [51,52,84], but a brief overview of the optimization procedure is given below for the sake of completeness. The CC equations are given by…”

Section: Theorymentioning

confidence: 99%

Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes

2017

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We describe the implementation of orbital optimization for the models in the perfect pairing hierarchy [Lehtola et al, J. Chem. Phys. 145, 134110 (2016)]. Orbital optimization, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the π space. While local minima and σ-π symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the π subspace, as well as in the full σπ valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimized orbitals are used. PH is found to yield good agreement with previously published density matrix renormalization group (DMRG) data in the π space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger bases or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.

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Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory

Cited by 132 publications

References 92 publications

Efficient description of strongly correlated electrons with mean-field cost

Efficient description of strongly correlated electrons with mean-field cost

Communication: The distinguishable cluster approximation. II. The role of orbital relaxation

Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes

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