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**Cluster perturbation theory. V : Theoretical foundation for cluster linear target states.** / Pawlowski, Filip; Olsen, Jeppe; Jørgensen, Poul.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Pawlowski, F, Olsen, J & Jørgensen, P 2019, 'Cluster perturbation theory. V: Theoretical foundation for cluster linear target states', *The Journal of Chemical Physics*, vol. 150, no. 13, 134112. https://doi.org/10.1063/1.5053627

Pawlowski, F., Olsen, J., & Jørgensen, P. (2019). Cluster perturbation theory. V: Theoretical foundation for cluster linear target states. *The Journal of Chemical Physics*, *150*(13), [134112]. https://doi.org/10.1063/1.5053627

Pawlowski F, Olsen J, Jørgensen P. 2019. Cluster perturbation theory. V: Theoretical foundation for cluster linear target states. The Journal of Chemical Physics. 150(13):Article 134112. https://doi.org/10.1063/1.5053627

Pawlowski, Filip, Jeppe Olsen, and Poul Jørgensen. "Cluster perturbation theory. V: Theoretical foundation for cluster linear target states". *The Journal of Chemical Physics*. 2019. 150(13). https://doi.org/10.1063/1.5053627

Pawlowski F, Olsen J, Jørgensen P. Cluster perturbation theory. V: Theoretical foundation for cluster linear target states. The Journal of Chemical Physics. 2019;150(13). 134112. https://doi.org/10.1063/1.5053627

Pawlowski, Filip ; Olsen, Jeppe ; Jørgensen, Poul. / **Cluster perturbation theory. V : Theoretical foundation for cluster linear target states**. In: The Journal of Chemical Physics. 2019 ; Vol. 150, No. 13.

@article{66cb10f08fcb4d8d84045741cc1b4c57,

title = "Cluster perturbation theory. V: Theoretical foundation for cluster linear target states",

abstract = "Cluster perturbation (CP) theory was developed in Paper I [F. Paw{\l}owski et al., J. Chem. Phys. 150, 134108 (2019)] for a coupled cluster (CC) target state and is extended in this paper to comprehend a cluster linear (CL) target state, for which the embedding of a CC parent state in the target excitation space is described using a linear parametrization. The theory is developed for determining the energy and molecular properties for a CL state. When CP theory is applied to a CL target state, a series of corrections is determined in orders of the CC parent-state similarity-transformed fluctuation potential, where the zeroth-order term is the energy or molecular property of the CC parent state and where the series formally converges to the energy or molecular property of the CL target state. The determination of energies and molecular properties is simpler for a CL state than for a CC state because the CL state is linearly parametrized. The amplitude equations are quadratic for a CL target state, while quartic for a CC target state, and molecular property expressions for a CL target state have the same simple structure as for a configuration interaction state. The linear parametrization introduces non-size-extensive contributions in the energy and molecular property expressions. However, since the linear parametrization describes the embedding of the CC parent state in the target excitation space, the energy and molecular properties for a CL state are weakly size-extensive. For the energy, weak size-extensivity means that non-size-extensive contributions enter in sixth and higher orders in the CP energy series, whereas for molecular properties, weak size-extensivity means that non-size-extensive contributions enter in second and higher orders. Weak size-extensivity therefore has a little or vanishing effect on calculated energies or molecular properties. The determination of the CP energy and molecular property corrections does not require that amplitude or response equations are solved explicitly for the target state and it becomes computationally tractable to use low-order corrections from these series to obtain energies and molecular properties of CL target state quality. For three simple molecules, HF, N 2 , and CH 2 , the accuracy of the CL approach for ground-state energies is tested using a parent state including single and double excitations (i.e., the CC singles-and-doubles state, CCSD) and a target state that includes triple excitations. It is found that the size-extensive fifth-order CL energies deviate by less than 0.0001 hartree from the energies of a target CC that includes triple excitations (i.e., the CC singles-doubles-and-triples state, CCSDT). CP theory with a CL target state therefore becomes a very attractive replacement of standard CC theory for high-accuracy energy and molecular property calculations, in which triple and higher excitation levels are considered. ",

keywords = "CONFIGURATION-INTERACTION, ENERGIES, SPACE",

author = "Filip Pawlowski and Jeppe Olsen and Poul J{\o}rgensen",

year = "2019",

doi = "10.1063/1.5053627",

language = "English",

volume = "150",

journal = "Journal of Chemical Physics",

issn = "0021-9606",

publisher = "AMER INST PHYSICS",

number = "13",

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TY - JOUR

T1 - Cluster perturbation theory. V

T2 - Theoretical foundation for cluster linear target states

AU - Pawlowski, Filip

AU - Olsen, Jeppe

AU - Jørgensen, Poul

PY - 2019

Y1 - 2019

N2 - Cluster perturbation (CP) theory was developed in Paper I [F. Pawłowski et al., J. Chem. Phys. 150, 134108 (2019)] for a coupled cluster (CC) target state and is extended in this paper to comprehend a cluster linear (CL) target state, for which the embedding of a CC parent state in the target excitation space is described using a linear parametrization. The theory is developed for determining the energy and molecular properties for a CL state. When CP theory is applied to a CL target state, a series of corrections is determined in orders of the CC parent-state similarity-transformed fluctuation potential, where the zeroth-order term is the energy or molecular property of the CC parent state and where the series formally converges to the energy or molecular property of the CL target state. The determination of energies and molecular properties is simpler for a CL state than for a CC state because the CL state is linearly parametrized. The amplitude equations are quadratic for a CL target state, while quartic for a CC target state, and molecular property expressions for a CL target state have the same simple structure as for a configuration interaction state. The linear parametrization introduces non-size-extensive contributions in the energy and molecular property expressions. However, since the linear parametrization describes the embedding of the CC parent state in the target excitation space, the energy and molecular properties for a CL state are weakly size-extensive. For the energy, weak size-extensivity means that non-size-extensive contributions enter in sixth and higher orders in the CP energy series, whereas for molecular properties, weak size-extensivity means that non-size-extensive contributions enter in second and higher orders. Weak size-extensivity therefore has a little or vanishing effect on calculated energies or molecular properties. The determination of the CP energy and molecular property corrections does not require that amplitude or response equations are solved explicitly for the target state and it becomes computationally tractable to use low-order corrections from these series to obtain energies and molecular properties of CL target state quality. For three simple molecules, HF, N 2 , and CH 2 , the accuracy of the CL approach for ground-state energies is tested using a parent state including single and double excitations (i.e., the CC singles-and-doubles state, CCSD) and a target state that includes triple excitations. It is found that the size-extensive fifth-order CL energies deviate by less than 0.0001 hartree from the energies of a target CC that includes triple excitations (i.e., the CC singles-doubles-and-triples state, CCSDT). CP theory with a CL target state therefore becomes a very attractive replacement of standard CC theory for high-accuracy energy and molecular property calculations, in which triple and higher excitation levels are considered.

AB - Cluster perturbation (CP) theory was developed in Paper I [F. Pawłowski et al., J. Chem. Phys. 150, 134108 (2019)] for a coupled cluster (CC) target state and is extended in this paper to comprehend a cluster linear (CL) target state, for which the embedding of a CC parent state in the target excitation space is described using a linear parametrization. The theory is developed for determining the energy and molecular properties for a CL state. When CP theory is applied to a CL target state, a series of corrections is determined in orders of the CC parent-state similarity-transformed fluctuation potential, where the zeroth-order term is the energy or molecular property of the CC parent state and where the series formally converges to the energy or molecular property of the CL target state. The determination of energies and molecular properties is simpler for a CL state than for a CC state because the CL state is linearly parametrized. The amplitude equations are quadratic for a CL target state, while quartic for a CC target state, and molecular property expressions for a CL target state have the same simple structure as for a configuration interaction state. The linear parametrization introduces non-size-extensive contributions in the energy and molecular property expressions. However, since the linear parametrization describes the embedding of the CC parent state in the target excitation space, the energy and molecular properties for a CL state are weakly size-extensive. For the energy, weak size-extensivity means that non-size-extensive contributions enter in sixth and higher orders in the CP energy series, whereas for molecular properties, weak size-extensivity means that non-size-extensive contributions enter in second and higher orders. Weak size-extensivity therefore has a little or vanishing effect on calculated energies or molecular properties. The determination of the CP energy and molecular property corrections does not require that amplitude or response equations are solved explicitly for the target state and it becomes computationally tractable to use low-order corrections from these series to obtain energies and molecular properties of CL target state quality. For three simple molecules, HF, N 2 , and CH 2 , the accuracy of the CL approach for ground-state energies is tested using a parent state including single and double excitations (i.e., the CC singles-and-doubles state, CCSD) and a target state that includes triple excitations. It is found that the size-extensive fifth-order CL energies deviate by less than 0.0001 hartree from the energies of a target CC that includes triple excitations (i.e., the CC singles-doubles-and-triples state, CCSDT). CP theory with a CL target state therefore becomes a very attractive replacement of standard CC theory for high-accuracy energy and molecular property calculations, in which triple and higher excitation levels are considered.

KW - CONFIGURATION-INTERACTION

KW - ENERGIES

KW - SPACE

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U2 - 10.1063/1.5053627

DO - 10.1063/1.5053627

M3 - Journal article

C2 - 30954052

VL - 150

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

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ER -