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

Abstract

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 gradients for restricted active space second-order perturbation theory (RASPT2)

“…which are roughly equivalent to the "orbital Lagrangian" and the "configuration Lagrangian," respectively, in the author's previous studies. 18,40 Once all the Lagrangian multipliers are determined by solving the Z-vector equation, as in the case of the state-averaged RASSCF [Eq. (11) but where L RASSCF is replaced with L RASPT2 ], the derivative of the RASPT2 energy can be evaluated by…”

“…Recent efforts to develop analytic derivatives of MRPTs 15 have made it possible to efficiently compute properties. Earlier studies reported such implementations in MOLPRO, 16 BAGEL, 17 GAMESS-US, 18 and TeraChem 19 for different MRPT methods. However, the size of the active space in these past works was rather limited.…”

“…However, the size of the active space in these past works was rather limited. To the best of our knowledge, the largest active space in terms of the number of determinants [or configuration state functions (CSFs)] applied in analytic derivatives corresponds to 12 electrons in 12 orbitals (12e,12o) 18 or (12e,11o). 20,21 In the former calculation, the number of determinants was 853,776 in GAMESS-US.…”

Analytic Gradients for Restricted Active Space Second-order Perturbation Theory (RASPT2)

“…which are roughly equivalent to the "orbital Lagrangian" and the "configuration Lagrangian," respectively, in the author's previous studies. 18,40 Once all the Lagrangian multipliers are determined by solving the Z-vector equation, as in the case of the state-averaged RASSCF [Eq. (11) but where L RASSCF is replaced with L RASPT2 ], the derivative of the RASPT2 energy can be evaluated by…”

Analytic First-Order Derivatives of (X)MS, XDW, and RMS Variants of the CASPT2 and RASPT2 Methods

“…The most well-known MRPT is probably the CAS second-order PT (CASPT2) method, [8][9][10] but many other versions exist, such as (extended) 11 multiconfiguration quasi-degenerate PT2 [(X)MCQDPT2], 12 n-electron valence state PT2 (NEVPT2), [13][14][15] generalized Van Vleck PT2 (GVVPT2), 16 retaining the excitation degree PT, 17 unitary group adapted state-specific MRPT, 18 and driven similarity renormalization group state-averaged MRPT (SA-DSRG-MRPT2). 19 There is no doubt that analytic derivatives are most convenient to locate minimum energy structures, such that analytic gradient theories and programs have been developed for a variety of MRPTs, namely CASPT2, [20][21][22][23] GVVPT2, 24 NEVPT2, 25,26 (X)MCQDPT2, 27 and (SA-)DSRG-MRPT2. 28,29 Another type of multiconfigurational approach, such as multiconfiguration pair-density functional theory (MC-PDFT), 30 has analytic derivative theories 31 as well.…”