Assessment of the Density-Fitted Second-Order Quasidegenerate Perturbation Theory for Transition Energies: Accurate Computations of Singlet–Triplet Gaps for Charge-Transfer Compounds

2020 ◽  
Vol 124 (34) ◽  
pp. 6889-6898
Author(s):  
Süleyman Aykut Servan ◽  
Aslı Ünal ◽  
Büşra Hamarat ◽  
Uğur Bozkaya
Keyword(s):  
Perturbation Theory ◽  
Charge Transfer ◽  
Second Order ◽  
Transition Energies ◽  
Accurate Computations

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.

Quantum theory of bridge group assisted charge transfer between ions in solution

1969 ◽  
Vol 22 (4) ◽  
pp. 673 ◽  
Author(s):  
PP Schmidt
Keyword(s):  
Perturbation Theory ◽  
Quantum Theory ◽  
Charge Transfer ◽  
Second Order ◽  
Time Dependent ◽  
Transfer Theory ◽  
Bridge Group

By means of the second-order time-dependent perturbation theory we present a synthesis of the charge transfer theory of Levich and Dogonadze and the model of bridge assisted transfer proposed by Halpern and Orgel.

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.

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules

2019 ◽  
Author(s):  
Brian Nguyen ◽  
Guo P Chen ◽  
Matthew M. Agee ◽  
Asbjörn M. Burow ◽  
Matthew Tang ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
System Size ◽  
State Density ◽  
Second Order ◽  
Binding Energies ◽  
Basis Set ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Relative Errors ◽  
Ground State Density

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order Møller–Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFA), and the post-Kohn–Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5-10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 1‰ per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed which uses monomers at full coupling whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation–dissipation theorem, we obtain a nonperturbative “screened second-order” expression for the dispersion energy in terms of monomer quantities which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. Whereas the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series within MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete “electrodynamic” screening of the Coulomb interaction due to induced particle–hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust non-perturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.<br>

scholarly journals Continuum limit of the conformal sector at second order in perturbation theory

2021 ◽  
Vol 103 (8) ◽  
Author(s):  
Tim R. Morris
Keyword(s):  
Perturbation Theory ◽  
Continuum Limit ◽  
Second Order

scholarly journals A scaled explicitly correlated F12 correction to second-order Møller–Plesset perturbation theory

2021 ◽  
Vol 154 (4) ◽  
pp. 044101
Author(s):  
L. Urban ◽  
T. H. Thompson ◽  
C. Ochsenfeld
Keyword(s):  
Perturbation Theory ◽  
Second Order ◽  
Explicitly Correlated ◽  
Moller Plesset ◽  
Plesset Perturbation Theory

Semiclassical Perturbation Theory of Molecular Collisions. I. First and Second Order

1970 ◽  
Vol 53 (5) ◽  
pp. 1815-1831 ◽  
Author(s):  
Herschel A. Rabitz ◽  
Roy G. Gordon
Keyword(s):  
Perturbation Theory ◽  
Second Order ◽  
Molecular Collisions

The dehydrogenation of 1,4-dihydronaphthalene by tetrachloro-p-benzoquinone

1976 ◽  
Vol 54 (14) ◽  
pp. 2261-2265 ◽  
Author(s):  
Z. M. Hashish ◽  
I. M. Hoodless
Keyword(s):  
Electron Transfer ◽  
Charge Transfer ◽  
Reaction Rate ◽  
Second Order ◽  
Charge Transfer Complexes ◽  
Ion Transfer ◽  
Hydride Ion ◽  
Rate Determining Step ◽  
Hydride Ion Transfer

The dehydrogenation of 1,4-dihydronaphthalene by tetrachloro-p-benzoquinone in phenetole solution has been investigated. The present work does not fully confirm earlier studies which report that the reaction follows second-order kinetics and that the hydride ion transfer is rate determining. In the investigations described in this paper second-order kinetics are only observed in the later stages of the reaction and a 1:1 stoichiometry of the reactants in the process is not obtained. Substitution of tritium in the 1,4-positions of the hydrocarbon appears to not significantly affect the reaction rate. The present results indicate that charge-transfer complexes are formed in the reaction and it is suggested that electron transfer within these complexes could be the rate-determining step in the dehydrogenation.

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