Computer generation of Feynman diagrams for perturbation theory I. General algorithm

Paldus, Josef; Wong, Hie Hua

doi:10.1016/0010-4655(73)90016-7

Cited by 58 publications

(29 citation statements)

References 6 publications

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“…(2.174), and writing I l ) = IQ(0)) see that we can calculate the expectation value as 74) we (6) = (Ql6lQ)/(QlQ) = =I (2.175) and similarly for higher order properties. (Cf., e.g., [14,216,320].)…”

Section: F Coupled-cluster Approaches To Propertiesmentioning

confidence: 97%

“…We must emphasize here that although these equations were actually written down only for the most important case of pair (i.e., doubly excited) cluster components (i.e., for the approximation T M T2), referred to originally as coupled-pair many-electron theory (CPMET [72], or CCD in today's terminology), the diagrammatic formulation of Cizek [ 1,2] is completely general, making it straightforward to obtain coupled-cluster equations at any level of approximation. Clearly, the required labor increases with the excitation level at which one truncates the cluster expansion (cf., e.g., [73]), but, should one require a high-order formalism, the procedure can be easily automated (cf., e.g., [74]). However, while it is easy to generate the required equations, it is not at all easy to exploit them computationally in practical applications in view of the rapidly increasing dimensionality of higher order cluster amplitudes.…”

Section: A Historical Outlinementioning

confidence: 98%

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A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

Paldus

1999

Advances in Chemical Physics

337

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Section: F Coupled-cluster Approaches To Propertiesmentioning

confidence: 97%

Section: A Historical Outlinementioning

confidence: 98%

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

Paldus

1999

Advances in Chemical Physics

337

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“…(17), we can expect to obtain identical contributions from distinct MBPT diagrams, namely, from those which can be transformed one into the other by a simple particle-hole (p-h) exchange or by the p-h exchange followed by the time-reversal (hereafter designated as conjugation) [42]. Since both operations are idempotent, we shall denote the corresponding second-order groups formed by these operations as c = { 1, conjugation) and e = { 1, p-h exchange}, where 1 designates the neutral (identity) operation.…”

Section: E(4)=ae(2)+ae(3)+ae(4)mentioning

confidence: 99%

“…The essentially distin$ [42] Hugenholtz diagrams of type (ii) (i-e., containing simultaneously and V, vertices) and their notation are shown in Figure 1. All nonequivalent MBPT diagrams are then obtained from those of Figure 1 In the third order, the canonical particle-particle and hole-hole diagrams [cf., e.g., Fig.…”

Section: E(4)=ae(2)+ae(3)+ae(4)mentioning

confidence: 99%

“…In the third-and fourth-order MBFT [27,[37][38][39][40][41][42] we now distinguish contributions of two types: (i) contributions from diagrams containing only two-body vertices representing q2 [ Since the matrix elements defining the perturbations el and Q2 are real and possess the hole-particle symmetry characterized by Eqs. (17), we can expect to obtain identical contributions from distinct MBPT diagrams, namely, from those which can be transformed one into the other by a simple particle-hole (p-h) exchange or by the p-h exchange followed by the time-reversal (hereafter designated as conjugation) [42].…”

Section: E(4)=ae(2)+ae(3)+ae(4)mentioning

confidence: 99%

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Bond length alternation in cyclic polyenes. V. Local finite‐order perturbation theory approach

Takahashi

Paldus

1984

Int J of Quantum Chemistry

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The finite-order many-body perturbation theory using the localized Wannier orbital basis is applied to the problem of bond length alternation in the Pariser-Parr-Pople model of cyclic polyenes CNHN, N = 4v +2, which may be regarded as a simplified model of polyacetylene. Both the Mbller-Plesset and the Epstein-Nesbet-type partitionings of the model Hamiltonian are employed. The localized orbital basis enables an efficient truncation of the perturbation theory summations over the intermediate states as well as an elimination of energetically unimportant diagrams, thus enabling one to obtain the fourth-order Mbller-Plesset -perturbation energies with a relatively small computational effort even for large polyenes. The results obtained with the second-, third-, and fourth-order Mbller-Plesset and with the third-order Epstein-Nesbet perturbation theories yield very similar bond length distortions (about 0.05 A) and stabilization energies per site (about 0.04 eV) as obtained earlier with the RHF, one-parameter AMO, and delocalized orbital perturbation theories. The effects of truncation and diagram elimination in the fourth-order Mbller-Plesset perturbation theory and the abnormal behavior of the second-order Epstein-Nesbet perturbation theory results in the localized Wannier basis near the instability threshold of the RHF solutions are discussed.

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A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

et al. 2017

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In this work, the automated generator environment for ORCA (ORCA-AGE) is described. It is a powerful toolchain for the automatic implementation of wavefunction-based quantum chemical methods. ORCA-AGE consists of three main modules: (1) generation of "raw" equations from a second quantized Ansatz for the wavefunction, (2) factorization and optimization of equations, and (3) generation of actual computer code. We generate code for the ORCA package, making use of the powerful functionality for wavefunction-based correlation calculations that is already present in the code. The equation generation makes use of the most elementary commutation relations and hence is extremely general. Consequently, code can be generated for single reference as well as multireference approaches and spin-independent as well as spin-dependent operators. The performance of the generated code is demonstrated through comparison with efficient hand-optimized code for some well-understood standard configuration interaction and coupled cluster methods. In general, the speed of the generated code is no more than 30% slower than the hand-optimized code, thus allowing for routine application of canonical ab initio methods to molecules with about 500-1000 basis functions. Using the toolchain, complicated methods, especially those surpassing human ability for handling complexity, can be efficiently and reliably implemented in very short times. This enables the developer to shift the attention from debugging code to the physical content of the chosen wavefunction Ansatz. Automatic code generation also has the desirable property that any improvement in the toolchain immediately applies to all generated code. © 2017 Wiley Periodicals, Inc.

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Computer generation of Feynman diagrams for perturbation theory I. General algorithm

Cited by 58 publications

References 6 publications

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

Bond length alternation in cyclic polyenes. V. Local finite‐order perturbation theory approach

A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

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