scholarly journals Renormalized second-order perturbation theory for the electron correlation energy: Concept, implementation, and benchmarks

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Xinguo Ren ◽  
Patrick Rinke ◽  
Gustavo E. Scuseria ◽  
Matthias Scheffler
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Correlation Energy ◽  
Second Order ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Energy Concept ◽  
Electron Correlation Energy ◽  
Second Order Perturbation Theory

Analytic First-Order Derivatives of Partially Contracted N-Electron Valence State Second-Order Perturbation Theory (PC-NEVPT2)

2019 ◽  
Author(s):  
Yoshio Nishimoto
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Valence State ◽  
Second Order ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Transition Energies ◽  
First Order ◽  
Static Electron ◽  
Second Order Perturbation Theory

A balanced treatment of dynamic and static electron correlation is important in computational chemistry, and multireference perturbation theory (MRPT) is able to do this at a reasonable computational cost. In this paper, analytic first-order derivatives, speci cally gradients and dipole moments, are developed for a particular MRPT method, state-specific partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). Only one linear equation needs to be solved for the derivative calculation if the Z-vector method is employed, which facilitates the practical application of this approach. Comparison of the calculated results with experimental geometrical parameters of O<sub>3</sub> indicates excellent agreement, although the calculated results for O<sub>3</sub><sup>-</sup> are slightly outside the experimental error bars. The 0-0 transition energies of various methylpyrimidines and trans-polyacetylene are calculated by performing geometry optimizations and seminumerical second-order geometrical derivative calculations. In particular, the deviations of 0-0 transition energies of trans-polyacetylene from experimental values are consistently less than 0.1 eV with PC-NEVPT2, indicating the reliability of the method. These results demonstrate the importance of adding dynamic electron correlation on top of methods dominated by static electron correlation and of developing analytic derivatives for highly accurate methods.

scholarly journals Locating Conical Intersections Using the Quasidegenerate Partially and Strongly Contracted NEVPT2 Methods

2020 ◽  
Author(s):  
Yoshio Nishimoto
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Radiative Decay ◽  
Second Order ◽  
Decay Process ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Conical Intersections ◽  
Complete Active Space ◽  
Second Order Perturbation Theory

Conical intersections (CIs) play an important role in photochemistry because they sometimes govern the non-radiative decay process. However, accurate characterizations of CIs are not always straightforward. In this study, analytic gradients and interstate coupling vectors for the quasidegenerate partially and strongly contracted n-electron valence state second-order perturbation theory (QD-PC-NEVPT2 and QD-SC-NEVPT2) were developed and applied to locating CIs of benzene. The pilot application demonstrates that the results of both the methods are similar to the extended multistate complete active space second-order perturbation theory (XMS-CASPT2), while the lack of dynamic electron correlation resulted in a deviation of 0.7 eV.

scholarly journals Locating Conical Intersections Using the Quasidegenerate Partially and Strongly Contracted NEVPT2 Methods

2020 ◽  
Author(s):  
Yoshio Nishimoto
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Radiative Decay ◽  
Second Order ◽  
Decay Process ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Conical Intersections ◽  
Complete Active Space ◽  
Second Order Perturbation Theory

Conical intersections (CIs) play an important role in photochemistry because they sometimes govern the non-radiative decay process. However, accurate characterizations of CIs are not always straightforward. In this study, analytic gradients and interstate coupling vectors for the quasidegenerate partially and strongly contracted n-electron valence state second-order perturbation theory (QD-PC-NEVPT2 and QD-SC-NEVPT2) were developed and applied to locating CIs of benzene. The pilot application demonstrates that the results of both the methods are similar to the extended multistate complete active space second-order perturbation theory (XMS-CASPT2), while the lack of dynamic electron correlation resulted in a deviation of 0.7 eV.

Locating Conical Intersections Using the Quasidegenerate Partially and Strongly Contracted NEVPT2 Methods

2020 ◽  
Author(s):  
Yoshio Nishimoto
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Radiative Decay ◽  
Second Order ◽  
Decay Process ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Conical Intersections ◽  
Complete Active Space ◽  
Second Order Perturbation Theory

Conical intersections (CIs) play an important role in photochemistry because they sometimes govern the non-radiative decay process. However, accurate characterizations of CIs are not always straightforward. In this study, analytic gradients and interstate coupling vectors for the quasidegenerate partially and strongly contracted n-electron valence state second-order perturbation theory (QD-PC-NEVPT2 and QD-SC-NEVPT2) were developed and applied to locating CIs of benzene. The pilot application demonstrates that the results of both the methods are similar to the extended multistate complete active space second-order perturbation theory (XMS-CASPT2), while the lack of dynamic electron correlation resulted in a deviation of 0.7 eV.

scholarly journals Analytic First-Order Derivatives of Partially Contracted N-Electron Valence State Second-Order Perturbation Theory (PC-NEVPT2)

2019 ◽  
Author(s):  
Yoshio Nishimoto
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Valence State ◽  
Second Order ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Transition Energies ◽  
First Order ◽  
Static Electron ◽  
Second Order Perturbation Theory

A balanced treatment of dynamic and static electron correlation is important in computational chemistry, and multireference perturbation theory (MRPT) is able to do this at a reasonable computational cost. In this paper, analytic first-order derivatives, speci cally gradients and dipole moments, are developed for a particular MRPT method, state-specific partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). Only one linear equation needs to be solved for the derivative calculation if the Z-vector method is employed, which facilitates the practical application of this approach. Comparison of the calculated results with experimental geometrical parameters of O<sub>3</sub> indicates excellent agreement, although the calculated results for O<sub>3</sub><sup>-</sup> are slightly outside the experimental error bars. The 0-0 transition energies of various methylpyrimidines and trans-polyacetylene are calculated by performing geometry optimizations and seminumerical second-order geometrical derivative calculations. In particular, the deviations of 0-0 transition energies of trans-polyacetylene from experimental values are consistently less than 0.1 eV with PC-NEVPT2, indicating the reliability of the method. These results demonstrate the importance of adding dynamic electron correlation on top of methods dominated by static electron correlation and of developing analytic derivatives for highly accurate methods.

Analytic First-Order Derivatives of Partially Contracted N-Electron Valence State Second-Order Perturbation Theory (PC-NEVPT2)

2019 ◽  
Author(s):  
Yoshio Nishimoto
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Valence State ◽  
Second Order ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Transition Energies ◽  
First Order ◽  
Static Electron ◽  
Second Order Perturbation Theory

A balanced treatment of dynamic and static electron correlation is important in computational chemistry, and multireference perturbation theory (MRPT) is able to do this at a reasonable computational cost. In this paper, analytic first-order derivatives, speci cally gradients and dipole moments, are developed for a particular MRPT method, partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). Only one linear equation needs to be solved for the derivative calculation if the Z-vector method is employed, which facilitates the practical application of this approach. Comparison of the calculated results with experimental geometrical parameters of O<sub>3</sub> indicates excellent agreement, although the calculated results for O<sub>3</sub><sup>-</sup> are slightly outside the experimental error bars. The 0-0 transition energies of various methylpyrimidines and trans-polyacetylene are calculated by performing geometry optimizations and seminumerical second-order geometrical derivative calculations. In particular, the deviations of 0-0 transition energies of trans-polyacetylene from experimental values are consistently less than 0.1 eV with PC-NEVPT2, indicating the reliability of the method. These results demonstrate the importance of adding dynamic electron correlation on top of methods dominated by static electron correlation and of developing analytic derivatives for highly accurate methods.

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