The probability of non-radiative transitions in photochemical dynamics is determined by the derivative couplings, the couplings between different electronic states through the nuclear degrees of freedom. Efficient and accurate evaluation of the derivative couplings is, therefore, of central importance to realize reliable computer simulations of photochemical reactions. In this work, the derivative couplings for multistate multireference second-order perturbation theory (MS-CASPT2) and its 'extended' variant (XMS-CASPT2) are studied, in which we present an algorithm for their analytical evaluation. The computational costs for evaluating the derivative couplings are essentially the same as those for calculating the nuclear energy gradients. The geometries and energies calculated with XMS-CASPT2 for small molecules at minimum energy conical intersections (MECIs) are in good agreement with those computed by multireference configuration interaction. As numerical examples, MECIs are optimized using XMS-CASPT2 for stilbene and a GFP model chromophore (the 4-para-hydroxybenzylidene-1,2-dimethyl-imidazolin-5-one anion).

We report the development of programs for on-the-fly surface-hopping dynamics simulations in the gas and condensed phases on the potential energy surfaces computed by multistate multireference perturbation theory (XMS-CASPT2) with full internal contraction. On-the-fly nonadiabatic dynamics simulations are made possible by improving the algorithm for XMS-CASPT2 nuclear energy gradient and derivative coupling evaluation. The program is interfaced to a surface-hopping dynamics program, Newton-X, and a classical molecular dynamics package, tinker, to realize such simulations. On-the-fly XMS-CASPT2 surface-hopping dynamics simulations of 9H-adenine and an anionic GFP model chromophore (para-hydroxybenzilideneimidazolin-5-one) in water are presented to demonstrate the applicability of our program to sizable systems. Our program is implemented in the bagel package, which is publicly available under the GNU General Public License.

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.

The green fluorescent protein and its designed variants fluoresce efficiently. Because the isolated chromophore is not fluorescent in a practical sense, it is apparent that the protein environment plays a crucial role in its efficiency. Because of various obstacles in studying excited state dynamics of complex systems, however, the detailed mechanism of this efficiency enhancement is not yet clearly elucidated. Here, by adopting excited state nonadiabatic molecular dynamics simulations together with an interpolated quantum chemical potential model of the chromophore, we find that the strong electric field from the protein matrix contributes dominantly to the motional restriction of the chromophore. The delay in twisting motion subsequently obstructs the nonradiative decay that competes with fluorescence, leading naturally to an enhancement in light-emitting efficiency. Surprisingly, steric constraints make only a minor contribution to these aspects. Through residue specific analyses, we identify a group of key residues that control the excited state behavior. Testing a series of mutant GFPs with different brightnesses also supports the view regarding the importance of protein electrostatics. Our findings may provide a useful guide toward designing new fluorescent chemical systems in the future.

Although photosynthetic pigment-protein complexes are in noisy environments, recent experimental and theoretical results indicate that their excitation energy transfer (EET) can exhibit coherent characteristics for over hundreds of femtoseconds. Despite the almost universal observations of the coherence to some degree, questions still remain regarding the detailed role of the protein and the extent of high-temperature coherence. Here we adopt a theoretical method that incorporates an all-atom description of the photosynthetic complex within a semiclassical framework in order to study EET in the Fenna-Matthews-Olson complex. We observe that the vibrational modes of the chromophore tend to diminish the coherence at the ensemble level, yet much longer-lived coherences may be observed at the single-complex level. We also observe that coherent oscillations in the site populations also commence within tens of femtoseconds even when the system is initially prepared in a non-oscillatory stationary state. We show that the protein acts to maintain the electronic couplings among the system of embedded chromophores. We also investigate the extent to which the protein's electrostatic modulation that disperses the chromophore electronic energies may affect the coherence lifetime. Further, we observe that even though mutation-induced disruptions in the protein structure may change the coupling pattern, a relatively strong level of coupling and associated coherence in the dynamics still remain. Finally, we demonstrate that thermal fluctuations in the chromophore couplings induce some redundancy in the coherent energy-transfer pathway. Our results indicate that a description of both chromophore coupling strengths and their fluctuations is crucial to better understand coherent EET processes in photosynthetic systems.

Structural factors governing the poor emission of dipolar dyes in aqueous media are identified, leading to new acedan derivatives with brighter fluorescence and enhanced two-photon properties.

Analytical nuclear gradient and derivative coupling theories for the quasidegenerate N-electron valence state perturbation theory using stateaveraged orbitals and density matrices are formulated and implemented. In our implementation, the Lagrangian formalism is employed to derive the working expressions. By implementing a direct algorithm for the four-particle reduced density matrix derivatives, large active spaces up to (12e,12o) are routinely tractable. The applicability of the current algorithm is tested for optimizing the minimal energy conical intersections of the representative photochemical systems: ethylene, a retinal protonated Schiff base (penta-2,4-dieniminium cation, PSB3) model, and a green fluorescent protein chromophore (parahydroxybenzilideneimidazolin-5-one, pHBI) model. For ethylene, we show that the optimized geometries reasonably agree with the previous geometries using the (extended) multistate second-order complete active space perturbation theory and the multireference configuration interaction with the singles and doubles method. For PSB3, we investigate the effect of the basis set selections, ranging from cc-pVDZ to cc-pV5Z, and the effect of noninvariance in describing conical intersections. For pHBI, we test two active spaces, (4e,3o) and (12e,11o), and survey the active-space dependence. We also discuss the computational cost, the parallel efficiency, and the future applicability of the current algorithm.

Recently, selected configuration interaction (SCI) methods that enable calculations with several tens of active orbitals have been developed. With the SCI subspace embedded in the mean field, molecular orbitals with an accuracy comparable to that of the complete active space self-consistent field method can be obtained. Here, we implement the analytical gradient theory for the single-state adaptive sampling CI (ASCI) SCF method to enable molecular geometry optimization. The resulting analytical gradient is inherently approximate due to the dependence on the sampled determinants, but its accuracy was sufficient for performing geometry optimizations with large active spaces. To obtain the tight convergence needed for accurate analytical gradients, we combine the augmented Hessian (AH) and Werner–Meyer–Knowles (WMK) second-order orbital optimization methods with the ASCI-SCF method. We test these algorithms for orbital and geometry optimizations, demonstrate applications of the geometry optimizations of polyacenes and periacenes, and discuss the geometric dependence of the characteristics of singlet ASCI wave functions.