Multireference Perturbation Theory Combined with PCM and RISM Solvation Models: A Benchmark Study for Chemical Energetics.

The polarizable continuum model (PCM) has been one of the most widely used approaches to take into account the solvation effect in quantum chemical calculations. In this paper, we performed a series of benchmark calculations to assess the accuracy of the PCM scheme combined with the second-order complete-active-space perturbation theory (CASPT2) for molecular systems in polar solvents. For solute molecules with extensive conjugated π orbitals, exemplified by elongated conjugated arylcarbenes, we have incorporated the ab initio density matrix renormalization group algorithm into the PCM-CASPT2 method. In the previous work, we presented a combination of the DMRG-CASPT2 method with the reference interaction site model (RISM) theory for describing the solvation effect using the radial distribution function and compared its performance to the widely used density-functional approaches (PCM-TD-DFT). The work here allows us to further show a more thorough assessment of the RISM model compared to the PCM with an equal level of the wave function treatment, the (DMRG-)CASPT2 theory, toward a high-accuracy electronic structure calculations for solvated chemical systems. With the exception that the PCM models are not capable of properly describing the hydrogen bondings, accuracy of the PCM-CASPT2 model is in most cases quite comparable to the RISM counterpart.

Improved RISM-CASSCF Optimization via State-Average Treatment and Damping for Characterizing Excited Molecules in Solution with Multireference Perturbation Theory.

Determination of excited states of near-infrared (NIR) bioimaging dyes is a challenging theoretical task because of their energy levels with a small gap and the presence of solvation. In the previous study, we showed that the development of the reference interaction site model coupled with the complete active space second-order perturbation theory, the RISM-CASPT2 method, and its extension with the density matrix renormalization group enabled high accuracy prediction of the photochemical properties of bioimaging-related fluorescent molecules in solution (Shimizu et al., J. Chem. Theory Comput. 2018, 14, 5673-5679). This method, however, has a technical issue in convergence of CASSCF optimization, which was encountered when applying the method to a wider variety of systems; thus, practical applications have been hindered. Here, we present an improved scheme of CASSCF optimization with and without the density matrix renormalization group treatment. Detailed derivations and analysis of the second-order orbital optimization scheme with the inclusion of solvation through RISM revealed the requirement of a correction term to the orbital Hessian matrix. As a practical approach, the state-average RISM-CASPT2 method with damping treatment for solvation is presented for improving the convergence of the calculation under reasonable computational cost. The improved scheme allows for performing accurate and numerically stable theoretical analysis of the bioimaging-related excited state with various types of solvation for a P═O-bridged rhodol derivative, which is recently highlighted as a promising photostable NIR dye molecule.

Electronically Excited Solute Described by RISM Approach Coupled with Multireference Perturbation Theory: Vertical Excitation Energies of Bioimaging Probes.

For theoretically studying molecules with fluorescence in the near-infrared region, high-accuracy determination of state energy level is required for meaningful analyses since the spectra of interest are of very narrow energy range. In particular, these molecules are in many cases handled in solution; therefore, consideration of the solvation effect is essential upon calculation together with the electronic structure of the excited state. Earlier studies showed that they cannot be described with conventional methods such as PCM-TD-DFT, yielding results far from experimental data. Here, we have developed a new method by combining a solvation theory based on statistical mechanics (RISM) and a multireference perturbation theory (CASPT2) with the extension of the density matrix renormalization group reference states for calculating the photochemical properties of near-infrared molecules and have obtained higher-accuracy prediction.