A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

Paldus, Josef; Li, Xiangzhu

doi:10.1002/9780470141694.ch1

Cited by 337 publications

(88 citation statements)

References 515 publications

(515 reference statements)

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“…Developing efficient algorithms for this problem is among the most heroic endeavors in computational science and has achieved remarkable successes. An incomplete list of the major methodologies developed so far includes the Hartree-Fock (HF) based methods [3,4], configuration interaction (CI) based methods [5][6][7][8], coupled cluster (CC) based schemes [9][10][11][12], Monte Carlobased approaches [13][14][15][16][17][18][19][20], and the more recently developed density matrix renormalization group (DMRG) theory [21][22][23][24][25] and density matrix embedding theory (DMET) [26][27][28]. We refer to Refs.…”

Section: Introductionmentioning

confidence: 99%

Solving many-electron Schrödinger equation using deep neural networks

Han

Zhang

Weinan

2019

Journal of Computational Physics

189

131

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We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schrödinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical. The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons. The algorithm does not make use of any prior knowledge such as atomic orbitals. Yet it is able to represent accurately the groundstates of the tested systems, including He, H 2 , Be, B, LiH, and a chain of 10 hydrogen atoms. This opens up new possibilities for solving large-scale many-electron Schrödinger equation.

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Section: Introductionmentioning

confidence: 99%

Solving many-electron Schrödinger equation using deep neural networks

Han

Zhang

Weinan

2019

Journal of Computational Physics

189

131

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“…Consequently, much effort has been devoted to finding suitable extensions of coupled cluster theory to treat residual dynamic correlation in multireference problems. 19 We have been implementing a program of research to tackle the aforementioned twin challenges of static and dynamic correlation in the multireference quantum chemistry of larger molecules. For the static correlation problem, we have been exploring the density matrix renormalization group ͑DMRG͒.…”

Section: Introductionmentioning

confidence: 99%

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory

Yanai

Kurashige

Neuscamman

et al. 2010

The Journal of Chemical Physics

166

208

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We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, ͑i͒ total correlation energies in long polyenes and ͑ii͒ the isomerization curve of the ͓Cu 2 O 2 ͔ 2+ core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a ͑24e ,24o͒ active space and 268 atomic orbitals in the polyenes and a ͑28e ,32o͒ active space and 278 atomic orbitals in ͓Cu 2 O 2 ͔ 2+ .

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“…Canonical transformation ͑CT͒ theory [26][27][28] is designed to model dynamic correlation in large multireference systems while meeting three important criteria: rigorous sizeextensivity, a cost scaling equivalent to CCSD, and accuracy for multireference systems comparable to what CCSD provides for single-reference systems. CT theory uses a unitary exponential ansatz, which is also used in unitary CC theory, [29][30][31][32][33][34][35] some multireference CC theories, 36,37 van Vleck-type perturbation theories as explored by Freed 38 and Kirtman, 39 and White's 40 earlier canonical diagonalization theory. The central object in CT theory is the effective Hamiltonian ͑as in canonical diagonalization theory͒ which is Hermitian as a result of using the unitary exponential.…”

Section: Introductionmentioning

confidence: 99%

Quadratic canonical transformation theory and higher order density matrices

Neuscamman

Yanai

Chan

2009

The Journal of Chemical Physics

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Canonical transformation ͑CT͒ theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating ͑i͒ a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and ͑ii͒ incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H 2 O and N 2 binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction ͑MRCI+ Q͒, averaged coupled pair functional, and averaged quadratic coupled cluster theories.

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A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

Cited by 337 publications

References 515 publications

Solving many-electron Schrödinger equation using deep neural networks

Solving many-electron Schrödinger equation using deep neural networks

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory

Quadratic canonical transformation theory and higher order density matrices

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