State-specific multireference perturbation theory: development and present status

Knowles Partitioning at the Multireference Level

A multireference generalization of the partitioning introduced recently by Knowles (J. Chem. Phys. 2022 156, 011101) is presented with the aim to study electronic systems at a medium level of correlation. The multireference formalism applied is the general framework of multiconfiguration perturbation theory (MCPT).

Description of the Methylene Amidogene Radical and Its Anion with an Economical Treatment of Correlation Effects Using Density Functional Theory Orbitals

The ground and low-lying excited state electronic structural properties (such as equilibrium geometries, harmonic frequencies, excitation energies, barrier energy, and so on) of the methylene amidogene radical (H₂CN) and its anion (H₂CN^-) have been studied using the CASCI (complete active space configuration interaction) and SSMRPT (state-specific multireference Møller-Plesset perturbation theory) methods with density function theory (DFT) orbitals. Here, the span of the active orbitals have been obtained from Kohn-Sham DFT using B3LYP exchange-correlation functionals in the CASCI (DFT-CASCI) approximation to describe nondynamic correlation associated with electronic degeneracies. The DFT-SSMRPT protocol provides an attractive way to deal with both dynamical and nondynamical correlation effects in strongly correlated systems such as H₂CN and H₂CN^-. The present work clearly indicates that the electronic absorption band near 35,050 cm^-1 corresponds to the B̃²A₁ ← X̃²B₂ transition. DFT-SSMRPT findings are in close agreement with high-level theoretical estimates. It is concluded that the transition at 1725 cm^-1 could be due to the CN stretching of the trans-HCNH isomer which is originally assigned to the CN stretch of H₂CN in the experiment. The present results confirm most of the previous vibrational assignments. It is not possible to definitively assign a transition to the 35,600 cm^-1 band with the present estimations, suggesting further experiment is urgently called for.

Single-Root Multireference Brillouin-Wigner Perturbative Approach to Excitation Energies

The state-specific Brillouin-Wigner multireference perturbation theory [which employs Jeziorski-Monkhorst parametrization of the wave function] using improved virtual orbitals, denoted as IVO-BWMRPT, is applied to calculate excitation energies (EEs) for methylene, ethylene, trimethylenemethane, and benzyne systems exhibiting various degrees of diradical character. In IVO-BWMRPT, all of the parameters appearing in the wave function ansatz are optimized for a specific electronic state. For these systems, the IVO-BWMRPT method provides EEs that are in close agreement with the benchmark results and experiments, where available, indicating that the method does not introduce imbalance in the target-specific treatment of closed- and open-shell states involved. The good performance of the present methodology is primarily related to structural compactness of the formalism. Overall, present findings are encouraging for both further development of the approach and chemical applications on the energy differences of strongly correlated systems.

Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method

We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N⁵) operations, while the rest of the calculations can be computed with O(N³) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N⁴) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.

Quantum Trajectory Mean-Field Method for Nonadiabatic Dynamics in Photochemistry

The mixed quantum-classical dynamical approaches have been widely used to study nonadiabatic phenomena in photochemistry and photobiology, in which the time evolutions of the electronic and nuclear subsystems are treated based on quantum and classical mechanics, respectively. The key issue is how to deal with coherence and decoherence during the propagation of the two subsystems, which has been the subject of numerous investigations for a few decades. A brief description on Ehrenfest mean-field and surface-hopping (SH) methods is first provided, and then different algorithms for treatment of quantum decoherence are reviewed in the present paper. More attentions were paid to quantum trajectory mean-field (QTMF) method under the picture of quantum measurements, which is able to overcome the overcoherence problem. Furthermore, the combined QTMF and SH algorithm is proposed in the present work, which takes advantages of the QTMF and SH methods. The potential to extend the applicability of the QTMF method was briefly discussed, such as the generalization to other type of nonadiabatic transitions, the combination with multiscale computational models, and possible improvements on its accuracy and efficiency by using machine-learning techniques.

REMP: A hybrid perturbation theory providing improved electronic wavefunctions and properties

We propose a new perturbation theoretical approach to the electron correlation energy by choosing the zeroth order Hamiltonian as a linear combination of the corresponding "Retaining the Excitation degree" (RE) and the Møller-Plesset (MP) operators. In order to fulfill Kato cusp conditions, the RE and MP contributions are chosen to sum up to one. 15% ± 5% MP contribution is deduced to be in an optimal range from a fit of the first order REMP wavefunction to near full configuration interaction reference data. For closed shell systems, the same range of MP weights shows best performance for equilibrium bond distances and vibrational wavenumbers of diatomic molecules, the reaction energies in the spin component scaled MP2 fit set, the transition energies of the BHPERI test set, and the parameterized coupled cluster with singles and doubles (pCCSD) fit set. For these properties, REMP outperforms all other tested perturbation theories at second order and shows equal performance as the best coupled pair approaches or pCCSD methods as well as the best double hybrid density functionals. Furthermore, REMP is shown to fulfill all required fundamental boundary conditions of proper wavefunction based quantum chemical methods (unitary invariance and size consistency).

Ab Initio Probing of the Ground State of Tetraradicals: Breakdown of Hund's Multiplicity Rule

The electronic structure of organic σ-type polyradical including 2,4,6-tridehydropyridine radical cation (246-TDHP) and three isomers of tetradehydrobenzene (TDHB) have been studied using a computationally robust and cost-effective second-order multireference perturbative model which provides a balanced treatment of nondynamic and dynamic contributions to the electron correlation problem in the ground or excited electronic states which are imperative for predicting structural properties (e.g., ground state multiplicity, energy gaps between high-spin and low-spin states, etc.) of polyradicals. Energy gaps are useful to capture insight into the degree of interaction between the radical sites. An important finding of this study is that the tetraradicals considered here possess singlet ground states, contrary to Hund's rule. Present findings are in close agreement with the available high-level ab initio estimates at attainable cost implying that a perturbative description of the systems is adequate. The impact of N⁺ on the nature of ground state for the 246-TDHP have also analyzed. The singlet-triplet energy gaps for 1245- and 1234-TDHB are smaller than for o-benzyne mainly due to the ring strain. 1235-TDHB is 14.42 and 11.05 kcal/mol lower in energy than 1245- and 1234-isomers, respectively. IVO-SSMRPT predicts ¹A₁-³B₂ and ¹A₁-⁵B₂ gaps of 25.84 and 105.15 kcal/mol, respectively for the 246-TDHP cation.

Four-Component Relativistic State-Specific Multireference Perturbation Theory with a Simplified Treatment of Static Correlation

The relativistic multireference (MR) perturbative approach is one of the most successful tools for the description of computationally demanding molecular systems of heavy elements. We present here the ground state dissociation energy surfaces, equilibrium bond lengths, harmonic frequencies, and dissociation energies of Ag₂, Cu₂, Au₂, and I₂ computed using the four-component (4c) relativistic spinors based state-specific MR perturbation theory (SSMRPT) with improved virtual orbital complete active space configuration interaction (IVO-CASCI) functions. The IVO-CASCI method is a simple, robust, useful and lower cost alternative to the complete active space self-consistent field approach for treating quasidegenerate situations. The redeeming features of the resulting method, termed as 4c-IVO-SSMRPT, lies in (i) manifestly size-extensivity, (ii) exemption from intruder problems, (iii) the freedom of convenient multipartitionings of the Hamiltonian, (iv) flexibility of the relaxed and unrelaxed descriptions of the reference coefficients, and (v) manageable cost/accuracy ratio. The present method delivers accurate descriptions of dissociation processes of heavy element systems. Close agreement with reference values has been found for the calculated molecular constants indicating that our 4c-IVOSSMRPT provides a robust and economic protocol for determining the structural properties for the ground state of heavy element molecules with eloquent MR character as it treats correlation and relativity on equal footing.