Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

Abstract

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way, and therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field (MCSCF) theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces (PES). This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections, and on-the-fly photodynamics simulations; both depend heavily on the ability of the method to properly explore the PES. Since such applications require the nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly improves the utility of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. To motivate the readers, we first summarize the notable applications of multireference electron correlation methods to mainstream chemistry, including geometry optimizations and on-the-fly dynamics. Subsequently, we review the analytical nuclear gradient and derivative coupling theories for these methods, and the software infrastructure that allows one to make use of these quantities in applications. The future prospects are discussed at the end of this review.

Locating conical intersections using the quasidegenerate partially and strongly contracted NEVPT2 methods

“…Considering the required balance between computational cost and accuracy, MRPT methods are possible solutions. Recent studies [7] on complete active space second-order perturbation theory (CASPT2) [8,9,10] has made it possible to explore CI regions using analytic derivative coupling vectors [11] at the extended multistate (XMS) extension [12,13] of CASPT2 (XMS-CASPT2). Non-adiabatic molecular dynamics simulations can also be performed at the XMS-CASPT2 level of theory [14].…”

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

“…The above equations, particularly Eqs. (14) and (15), were implemented in a local version of OpenMolcas. 43,44 Although these equations are formulated based on the Lagrangian method, the actual implementation closely follows that of the equations derived by direct differentiation, as in Refs.…”

“…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.…”

“…The difference in bond length is also negligible; the maximum deviation is only 2.10 × 10 −4 Å.The number of CSFs (N CSF ) is greatly reduced by employing RAS references. The compu-tational cost for evaluating the partial derivative of the energy with respect to the CI coefficient [t CI ; Eq (15)…”

Intermediate Valence States in Lanthanide Compounds

“…At the time, if the key theoretical milestones of modern theoretical wave‐function‐based methodologies [53, 54] and DFT calculations [55, 56] were known, the large number of electrons in f‐element complexes rendered the task rather difficult. Similarly, when multiconfigurational methods [57, 58] appeared, such as multiconfiguration Hartree–Fock/self‐consistent field (MCHF/SCF), configuration interaction (CI) methods, many‐body perturbation theory (MBPT) and coupled‐clusters (CC), [59–62] only a few studies were attempted with lanthanide complexes. It is only in the late 1980s that Fulde et al.…”