Partial third-order quasiparticle theory: An application to the photoelectron spectrum of S-tetrazine

Ortiz, J. V.

doi:10.1002/(sici)1097-461x(1997)63:2<291::aid-qua2>3.0.co;2-r

Cited by 9 publications

(3 citation statements)

References 30 publications

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“…The same applies to the superoperator algebra ,, and to the Dyson–Gell-Mann–Low time-dependent perturbation theory derivation. , Second, GF theory is based on the Dyson equation (not the Schrödinger equation), and its formulation does not explicitly refer to wave functions, which a determinant-based algorithm stores and manipulates. Whereas two of the authors as well as others implemented partial and full third-order − and partial and full fourth-order self-energies ,− both within the GF and EOM frameworks, higher-order GF methods are yet to be developed and detailed knowledge about convergence is lacking. To obtain these, a general-order implementation, which can generate reliable reference data up to high orders, is paramount in view of the fact that there are many more diagrams in the n th-order GF (GF n ) method than in the n th-order MP (MP n ) method (e.g., 18 Hugenholtz diagrams in GF3 versus three in MP3).…”

Section: Introductionmentioning

confidence: 99%

General-Order Many-Body Green’s Function Method

Hirata

Hermes

Simons

et al. 2015

J. Chem. Theory Comput.

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Electron binding energies are evaluated as differences in total energy between the N- and (N ± 1)-electron systems calculated by the nth-order Møller-Plesset perturbation (MPn) theory using the same set of orbitals. The MPn energies up to n = 30 are, in turn, obtained by the determinant-based method of Knowles et al. (Chem. Phys. Lett. 1985, 113, 8-12). The zeroth- through third-order electron binding energies thus determined agree with those obtained by solving the Dyson equation in the diagonal and frequency-independent approximations of the self-energy. However, as n → ∞, they converge at the exact basis-set solutions from the Dyson equation with the exact self-energy, which is nondiagonal and frequency-dependent. This suggests that the MPn energy differences define an alternative diagrammatic expansion of Koopmans-like electron binding energies, which takes into account the perturbation corrections from the off-diagonal elements and frequency dependence of the irreducible self-energy. Our analysis shows that these corrections are included as semireducible and linked-disconnected diagrams, respectively, which are also found in a perturbation expansion of the electron binding energies of the equation-of-motion coupled-cluster methods. The rate of convergence of the electron binding energies with respect to n and its acceleration by Padé approximants are also discussed.

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Section: Introductionmentioning

confidence: 99%

General-Order Many-Body Green’s Function Method

Hirata

Hermes

Simons

et al. 2015

J. Chem. Theory Comput.

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“…[42][43][44][45] It can be further extended to include frequency dependence [46][47][48] and electron-correlation effects. [49][50][51] What may add to the mysterious appearance of MBGF is the fact that the highest perturbation order of its methods developed so far is only three 15,[52][53][54][55][56][57][58][59][60][61][62][63] or four, 20,54,64,65 the latter case using simplifying approximations. This is in contrast with CI, 66,67 CC, [68][69][70][71][72] or MBPT, 73,74 all of which can be carried out at any arbitrary high order using the determinant-based algorithm of full configuration interaction (FCI).…”

Section: Introductionmentioning

confidence: 99%

One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

Hirata

Doran

Knowles

et al. 2017

The Journal of Chemical Physics

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A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.

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“…Addition of the third-order terms (EP3 and ΔMP3 methods) lead quite often to the opposite trend in results. Thus, in order to obtain qualitatively good predictions, one is forced to use more advanced, but at the same time computationally more demanding, approximations such as the outer valence Green’s function (OVGF) or P3 method . However, to perform calculations for large molecular systems in a reasonable time, it is necessary to use simple and computationally efficient methods, which are at the same time accurate enough to lead to correct predictions (good speed/quality ratio).…”

Section: Introductionmentioning

confidence: 99%

Spin-Component-Scaled ΔMP2 Parametrization: Toward a Simple and Reliable Method for Ionization Energies

Śmiga

Grabowski

2018

J. Chem. Theory Comput.

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A practical, accurate, and cost- and implementation-free method (ΔMP2-SOS(IP)) for the calculation of vertical ionization potentials is proposed. The simple method is based on a single-step, a diagonal, frequency-independent approximation to the second-order self-energy expression combined with the spin-component-scaled technique. The search for an optimal scaling factor is performed for a set of 50 moderately sized molecules, and the quality of the method is additionally assessed for a benchmark set of 24 organic acceptor molecules. The proposed ΔMP2-SOS(IP) method provides the best results of valence ionization energies as compared to the several standard self-consistent variants of the electron propagator methods at the second and higher orders (EP2, SCS-EP2, EP3, OVGF) with almost CCSD(T) or IP-EOM-CCSD accuracy and the cost of only a single opposite-spin ΔMP2-type calculation ( O( N)). For core ionization energies, our new methods outperform the standard ΔMP2 results due to a better balanced treatment of the correlation and relaxation term in the second-order self-energy.

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Partial third-order quasiparticle theory: An application to the photoelectron spectrum of S-tetrazine

Cited by 9 publications

References 30 publications

General-Order Many-Body Green’s Function Method

General-Order Many-Body Green’s Function Method

One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

Spin-Component-Scaled ΔMP2 Parametrization: Toward a Simple and Reliable Method for Ionization Energies

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