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Convergence of Møller–Plesset perturbation theory for excited reference states. ADVANCES IN QUANTUM CHEMISTRY 2023. [DOI: 10.1016/bs.aiq.2023.01.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/16/2023]
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Battaglia S, Fransén L, Fdez Galván I, Lindh R. Regularized CASPT2: an Intruder-State-Free Approach. J Chem Theory Comput 2022; 18:4814-4825. [PMID: 35876618 PMCID: PMC9367007 DOI: 10.1021/acs.jctc.2c00368] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
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In this work we present a new approach to fix the intruder-state
problem (ISP) in CASPT2 based on σp regularization. The resulting σp-CASPT2 method is compared to previous techniques, namely, the real
and imaginary level shifts, on a theoretical basis and by performing
a series of systematic calculations. The analysis is focused on two
aspects, the effectiveness of σp-CASPT2 in removing the ISP and the sensitivity of the approach with
respect to the input parameter. We found that σp-CASPT2 compares favorably with respect to previous
approaches and that different versions, σ1-CASPT2
and σ2-CASPT2, have different potential application
domains. This analysis also reveals the unsuitability of the real
level shift technique as a general way to avoid the intruder-state
problem.
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Affiliation(s)
- Stefano Battaglia
- Department of Chemistry─BMC, Uppsala University, P. O. Box 576, SE-75123 Uppsala, Sweden
| | - Lina Fransén
- Department of Chemistry─BMC, Uppsala University, P. O. Box 576, SE-75123 Uppsala, Sweden
| | - Ignacio Fdez Galván
- Department of Chemistry─BMC, Uppsala University, P. O. Box 576, SE-75123 Uppsala, Sweden
| | - Roland Lindh
- Department of Chemistry─BMC, Uppsala University, P. O. Box 576, SE-75123 Uppsala, Sweden
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Boggio-Pasqua M, Jacquemin DM, Loos PF. Benchmarking CASPT3 Vertical Excitation Energies. J Chem Phys 2022; 157:014103. [DOI: 10.1063/5.0095887] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on 280 reference vertical transition energies of various natures (singlet, triplet, valence, Rydberg, n → π∗, π → π∗, and double excitations) extracted from the QUEST database, we assess the accuracy of third-order multireference perturbation theory, CASPT3, in the context of molecular excited states. When one applies the disputable ionization- potential-electron-affinity (IPEA) shift, we show that CASPT3 provides a similar accuracy as its second-order counterpart, CASPT2, with the same mean absolute error of 0.11 eV. However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespective of the transition type and system size, with a small reduction of the mean absolute error to 0.09 eV when the IPEA shift is switched off.
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Affiliation(s)
| | - Denis M. Jacquemin
- Chimie Et Interdisciplinarité, Synthèse, Analyse, Modélisation, University of Nantes, France
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Hillers-Bendtsen AE, Høyer NM, Kjeldal FØ, Mikkelsen KV, Olsen J, Jorgensen P. Cluster perturbation theory. VIII. First order properties for a coupled cluster state. J Chem Phys 2022; 157:024108. [DOI: 10.1063/5.0082585] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have extended cluster perturbation (CP) theory to comprehend the calculation of first order properties (FOPs). We have determined CP FOP series where FOPs are determined as a first energy derivative and also where the FOPs are determined as a generalized expectation value of the external perturbation operator over the coupled cluster state and its biorthonormal multiplier state. For S(D) orbital excitation spaces, we find that the CP series for FOPs that are determined as a first derivative in general in second order have errors of a few per cent in the singles and doubles correlation contribution relative to the targeted coupled cluster (CC) results. For a SD(T) orbital excitation space, we find that the CP series for FOPs determined as a generalized expectation value in second order have errors of about ten percent in the triples correlation contribution relative to the targeted CC results. These second order models therefore constitute viable alternatives for determining high quality FOPs.
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Affiliation(s)
| | | | | | - Kurt V. Mikkelsen
- Department of Chemistry, University of Copenhagen Institute of Chemistry, Denmark
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University Department of Chemistry, Denmark
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Olsen J, Hillers-Bendtsen AE, Kjeldal FØ, Høyer NM, Mikkelsen KV, Jorgensen P. Cluster Perturbation Theory. VII. The convergence of Cluster Perturbation Expansions. J Chem Phys 2022; 157:024107. [DOI: 10.1063/5.0082584] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The convergence of the recently developed cluster perturbation CP expansions (Pawlowski et al, J. Chem. Phys. 150 134108(2019)) is analyzed with the double purpose of developing the mathematical tools and concepts needed to describe these expansions at general order and to identify the factors that define the rate of convergence of CP series. To this end, the CP energy, amplitude, and Lagrangian multiplier equations as functions of the perturbation strength are developed. By determining the critical points, defined as the perturbation strengths for which the Jacobian become singular, the rate of convergence as well as the intruder and critical states are determined for five simple molecules: BH, CO, H2O, NH3, and HF. To describe the patterns of convergence for these expansions at orders lower than the high-order asymptotic limit, a model is developed, where the perturbation corrections arise from two critical points. It is shown that this model allows rationalization of the behavior of the perturbation corrections at much lower order than required for the onset of the asymptotic convergence. For the H2O, CO, and HF molecules, the pattern and rate of convergence is defined by critical states where the Fock-operator underestimates the excitation energies, whereas the pattern and rate of convergence for BH is defined by critical states where the Fock-operator overestimates the excitation energy. For the NH3 molecule, both forms of critical points are required to describe the convergence behavior up to at least order 25.
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Affiliation(s)
- Jeppe Olsen
- Department of Chemistry, Aarhus University Department of Chemistry, Denmark
| | | | | | | | - Kurt V. Mikkelsen
- Department of Chemistry, University of Copenhagen Institute of Chemistry, Denmark
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Høyer NM, Kjeldal FØ, Hillers-Bendtsen AE, Mikkelsen KV, Olsen J, Jorgensen P. Cluster perturbation theory. VI. Ground-state energy series using the Lagrangian. J Chem Phys 2022; 157:024106. [DOI: 10.1063/5.0082583] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we derive alternative cluster perturbation series to the energy cluster perturbation (ECP) series of Paper I. The ECP series were derived using the standard coupled cluster energy framework. Here, we use the coupled cluster Lagrangian framework to derive the Lagrangian cluster perturbation (LCP) series and show that a slightly modified order concept means that the ECP and the LCP series become identical. Using the Lagrangian, we also derive a perturbation series where total cluster amplitudes and multipliers are determined through the same orders as dictated by the 2n+1/2n+2 rule, the VCP series. The VCP energies have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. The convergence of the test calculations can be divided into two groups. The first group contains molecules that exhibit a slow monotonic geometric convergence pattern in both orbital spaces. The second group, containing the rest of the molecules, exhibits a fast low order convergence. For the S(D) calculations, the deviations in fourth order from the coupled cluster singles and doubles energy are below 1.3 per cent for the LCP series and 0.3 per cent for the VCP series, respectively. For the SD(T) calculations, the second group hardly shows any difference between the low order convergence of the three series ECP, LCP, and LCP and at fourth order the deviations from the triples correlation energy are less than 1 per cent.
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Affiliation(s)
| | | | | | - Kurt V. Mikkelsen
- Department of Chemistry, University of Copenhagen Institute of Chemistry, Denmark
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University Department of Chemistry, Denmark
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Surjan PR, Kőhalmi D, Szabados A. A Note on Perturbation-Adapted Perturbation Theory. J Chem Phys 2022; 156:116102. [DOI: 10.1063/5.0085350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The partitioning introduced recently by Knowles(J. Chem. Phys., 156:011101, 2022) is analyzed and itsconnections with the Adams partitioning and the Davidson-Kapuy partitioning arediscussed. Davidson's partitioning is reformulated usingsecond quantized formalism. A relation is pointed outbetween Knowles' conditionfor the MBPT zero order Hamiltonian and the CEPA0 equations.
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Affiliation(s)
- Peter R Surjan
- Faculty of Science, Intitute of Chemistry, Laboratory of Theoretical Chemistry, Eötvös Loránd Tudományegyetem, Hungary
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Abstract
A new general approach is introduced for defining an optimum zero-order Hamiltonian for Rayleigh-Schrödinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the exact Hamiltonian within any desired functional form. When applied to many-body perturbation theory for electrons, strongly improved convergence is observed in cases where the conventional Fock Hamiltonian leads to divergence or slow convergence.
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Affiliation(s)
- Peter J Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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Marie A, Burton HGA, Loos PF. Perturbation theory in the complex plane: exceptional points and where to find them. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:283001. [PMID: 33601362 DOI: 10.1088/1361-648x/abe795] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 02/18/2021] [Indexed: 05/24/2023]
Abstract
We explore the non-Hermitian extension of quantum chemistry in the complex plane and its link with perturbation theory. We observe that the physics of a quantum system is intimately connected to the position of complex-valued energy singularities, known as exceptional points. After presenting the fundamental concepts of non-Hermitian quantum chemistry in the complex plane, including the mean-field Hartree-Fock approximation and Rayleigh-Schrödinger perturbation theory, we provide a historical overview of the various research activities that have been performed on the physics of singularities. In particular, we highlight seminal work on the convergence behaviour of perturbative series obtained within Møller-Plesset perturbation theory, and its links with quantum phase transitions. We also discuss several resummation techniques (such as Padé and quadratic approximants) that can improve the overall accuracy of the Møller-Plesset perturbative series in both convergent and divergent cases. Each of these points is illustrated using the Hubbard dimer at half filling, which proves to be a versatile model for understanding the subtlety of analytically-continued perturbation theory in the complex plane.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France
| | - Hugh G A Burton
- Physical and Theoretical Chemical Laboratory, Department of Chemistry, University of Oxford, Oxford, OX1 3QZ, United Kingdom
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France
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Abstract
We present a Perspective on what the future holds for full configuration interaction (FCI) theory, with an emphasis on conceptual rather than technical details. Upon revisiting the early history of FCI, a number of its key contemporary approximations are compared on as equal a footing as possible, using a recent blind challenge on the benzene molecule as a testbed [Eriksen et al., J. Phys. Chem. Lett., 2020 11, 8922]. In the process, we review the scope of applications for which FCI continues to prove indispensable, and the required traits in terms of robustness, efficacy, and reliability its modern approximations must satisfy are discussed. We close by conveying a number of general observations on the merits offered by the state-of-the-art alongside some of the challenges still faced to this day. While the field has altogether seen immense progress over the years-the past decade, in particular-it remains clear that our community as a whole has a substantial way to go in enhancing the overall applicability of near-exact electronic structure theory for systems of general composition and increasing size.
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Affiliation(s)
- Janus J Eriksen
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
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