Conical intersections of free energy surfaces in solution: Effect of electron correlation on a protonated Schiff base in methanol solution

Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids

The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.

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

Crossings between states involve complex electronic structures, making the accurate characterization of the crossing point difficult. In this study, the analytic derivatives of three complete active space second-order perturbation theory (CASPT2) variants as well as an extension of the restricted active space (RASPT2) are developed. These variants are applied to locating minimum energy conical intersections. Our results demonstrate that the three CASPT2 variants predict qualitatively similar results, but a recently developed variant, the rotated multistate CASPT2 (RMS-CASPT2), is least sensitive to the number of states considered in the calculation. We demonstrate that CASPT2 and the reference self-consistent field calculations predict qualitatively different energetics and bond lengths.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

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.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

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 theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

Two-State, Three-Mode Parametrization of the Force Field of a Retinal Chromophore Model

In recent years, the potential energy surfaces of the penta-2,4-dieniminium cation have been investigated using several electronic structure methods. The resulting pool of geometrical, electronic, and energy data provides a suitable basis for the construction of a topographically correct analytical model of the molecule force field and, therefore, for a better understanding of this class of molecules, which includes the chromophore of visual pigments. In the present contribution, we report the construction of such a model for regions of the force field that drive the photochemical and thermal isomerization of the central double bound of the cation. While previous models included only two modes, it is here shown that the proposed three-mode model and corresponding set of parameters are able to reproduce the complex topographical and electronic structure features seen in electronically correlated data obtained at the XMCQDPT2//CASSCF/6-31G* level of theory.

Quantum Mechanical Studies on the Photophysics and the Photochemistry of Nucleic Acids and Nucleobases

The photophysics and photochemistry of DNA is of great importance due to the potential damage of the genetic code by UV light. Quantum mechanical studies have played a key role in interpretating the results of modern time-resolved pump-probe spectroscopy, and in elucidating the main photoactivated reactive paths. This review provides a concise, complete picture of the computational studies carried out, approximately, in the past decade. We start with an overview of the photophysics of the nucleobases in the gas phase and in solution. We discuss the proposed mechanisms for ultrafast decay to the ground state, that involve conical intersections, consider the role of triplet states, and analyze how the solvent modulates the photophysics. Then we move to larger systems, from dinucleotides to single- and double-stranded oligonucleotides. We focus on the possible role of charge transfer and delocalized or excitonic states in the photophysics of these systems and discuss the main photochemical paths. We finish with an outlook on the current challenges in the field and future directions of research.

3D-RISM-MP2 Approach to Hydration Structure of Pt(II) and Pd(II) Complexes: Unusual H-Ahead Mode vs Usual O-Ahead One

Solvation of transition metal complexes with water has been one of the fundamental topics in physical and coordination chemistry. In particular, Pt(II) complexes have recently attracted considerable interest for their relation to anticancer activity in cisplatin and its analogues, yet the interaction of the water molecule and the metal center has been obscured. The challenge from a theoretical perspective remains that both the microscopic solvation effect and the dynamical electron correlation (DEC) effect have to be treated simultaneously in a reasonable manner. In this work we derive the analytical gradient for the three-dimensional reference interaction site model Møller-Plesset second order (3D-RISM-MP2) free energy. On the basis of the three-regions 3D-RISM self-consistent field (SCF) method recently proposed by us, we apply a new layer of the Z-vector method to the CP-RISM equation as well as point-charge approximation to the derivatives with respect to the density matrix elements in the RISM-CPHF equation to remarkably reduce the computational cost. This method is applied to study the interaction of H2O with the d(8) square planar transition metal complexes in aqueous solution, trans-[Pt(II)Cl2(NH3)(glycine)] (1a), [Pt(II)(NH3)4](2+) (1b), [Pt(II)(CN)4](2-) (1c), and their Pd(II) analogues 2a, 2b, and 2c, respectively, to elucidate whether the usual H2O interaction through O atom (O-ahead mode) or unusual one through H atom (H-ahead mode) is stable in these complexes. We find that the interaction energy of the coordinating water and the transition metal complex changes little when switching from gas to aqueous phase, but the solvation free energy differs remarkably between the two interaction modes, thereby affecting the relative stability of the H-ahead and O-ahead modes. Particularly, in contrast to the expectation that the O-ahead mode is preferred due to the presence of positive charges in 1b, the H-ahead mode is also found to be more stable. The O-ahead mode is found to be more stable than the H-ahead one only in 2b. The energy decomposition analysis (EDA) at the 3D-RISM-MP2 level revealed that the O-ahead mode is stabilized by the electrostatic (ES) interaction, whereas the H-ahead one is mainly stabilized by the DEC effect. The ES interaction is also responsible for the difference between the Pd(II) and Pt(II) complexes; because the electrostatic potential is more negative along the z-axis in the Pt(II) complex than in the Pd(II) one, the O-ahead mode prefers the Pd(II) complexes, whereas the H-ahead becomes predominant in the Pt(II) complexes.

Assessment of Approximate Coupled-Cluster and Algebraic-Diagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model

As a minimal model of the chromophore of rhodopsin proteins, the penta-2,4-dieniminium cation (PSB3) poses a challenging test system for the assessment of electronic-structure methods for the exploration of ground- and excited-state potential-energy surfaces, the topography of conical intersections, and the dimensionality (topology) of the branching space. Herein, we report on the performance of the approximate linear-response coupled-cluster method of second order (CC2) and the algebraic-diagrammatic-construction scheme of the polarization propagator of second and third orders (ADC(2) and ADC(3)). For the ADC(2) method, we considered both the strict and extended variants (ADC(2)-s and ADC(2)-x). For both CC2 and ADC methods, we also tested the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) variants. We have explored several ground- and excited-state reaction paths, a circular path centered around the S1/S0 surface crossing, and a 2D scan of the potential-energy surfaces along the branching space. We find that the CC2 and ADC methods yield a different dimensionality of the intersection space. While the ADC methods yield a linear intersection topology, we find a conical intersection topology for the CC2 method. We present computational evidence showing that the linear-response CC2 method yields a surface crossing between the reference state and the first response state featuring characteristics that are expected for a true conical intersection. Finally, we test the performance of these methods for the approximate geometry optimization of the S1/S0 minimum-energy conical intersection and compare the geometries with available data from multireference methods. The present study provides new insight into the performance of linear-response CC2 and polarization-propagator ADC methods for molecular electronic spectroscopy and applications in computational photochemistry.

Excited-state free energy surfaces in solution: time-dependent density functional theory∕reference interaction site model self-consistent field method

Constructing free energy surfaces for electronically excited states is a first step toward the understanding of photochemical processes in solution. For that purpose, the analytic free energy gradient is derived and implemented for the linear-response time-dependent density functional theory combined with the reference interaction site model self-consistent field method. The proposed method is applied to study (1) the fluorescence spectra of aqueous acetone and (2) the excited-state intramolecular proton transfer reaction of ortho-hydroxybenzaldehyde in an acetonitrile solution.

Nonadiabatic photodynamics of a retinal model in polar and nonpolar environment

The nonadiabatic photodynamics of the all-trans-2,4-pentadiene-iminium cation (protonated Schiff base 3, PSB3) and the all-trans-3-methyl-2,4-pentadiene-iminium cation (MePSB3) were investigated in the gas phase and in polar (aqueous) and nonpolar (n-hexane) solutions by means of surface hopping using a multireference configuration-interaction (MRCI) quantum mechanical/molecular mechanics (QM/MM) level. Spectra, lifetimes for radiationless deactivation to the ground state, and structural and electronic parameters are compared. A strong influence of the polar solvent on the location of the crossing seam, in particular in the bond length alternation (BLA) coordinate, is found. Additionally, inclusion of the polar solvent changes the orientation of the intersection cone from sloped in the gas phase to peaked, thus enhancing considerably its efficiency for deactivation of the molecular system to the ground state. These factors cause, especially for MePSB3, a substantial decrease in the lifetime of the excited state despite the steric inhibition by the solvent.

Conical intersections in solution: formulation, algorithm, and implementation with combined quantum mechanics/molecular mechanics method

The significance of conical intersections in photophysics, photochemistry, and photodissociation of polyatomic molecules in gas phase has been demonstrated by numerous experimental and theoretical studies. Optimization of conical intersections of small- and medium-size molecules in gas phase has currently become a routine optimization process, as it has been implemented in many electronic structure packages. However, optimization of conical intersections of small- and medium-size molecules in solution or macromolecules remains inefficient, even poorly defined, due to large number of degrees of freedom and costly evaluations of gradient difference and nonadiabatic coupling vectors. In this work, based on the sequential quantum mechanics and molecular mechanics (QM/MM) and QM/MM-minimum free energy path methods, we have designed two conical intersection optimization methods for small- and medium-size molecules in solution or macromolecules. The first one is sequential QM conical intersection optimization and MM minimization for potential energy surfaces; the second one is sequential QM conical intersection optimization and MM sampling for potential of mean force surfaces, i.e., free energy surfaces. In such methods, the region where electronic structures change remarkably is placed into the QM subsystem, while the rest of the system is placed into the MM subsystem; thus, dimensionalities of gradient difference and nonadiabatic coupling vectors are decreased due to the relatively small QM subsystem. Furthermore, in comparison with the concurrent optimization scheme, sequential QM conical intersection optimization and MM minimization or sampling reduce the number of evaluations of gradient difference and nonadiabatic coupling vectors because these vectors need to be calculated only when the QM subsystem moves, independent of the MM minimization or sampling. Taken together, costly evaluations of gradient difference and nonadiabatic coupling vectors in solution or macromolecules can be reduced significantly. Test optimizations of conical intersections of cyclopropanone and acetaldehyde in aqueous solution have been carried out successfully.