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The nonadiabatic phenomena, which are characterized by a strong coupling between electronic and nuclear motions, are ubiquitous. The nonadiabatic effect of the studied system can be significantly affected by the surrounding environment, such as solvents, in which such nonadiabatic process takes place. It is essential to develop the theoretical models to simulate these processes while accurately modeling the solvent environment. The time-dependent density functional theory (TDDFT) is currently the most efficient approach to describe the electronic structures and dynamics of complex systems, while the polarizable continuum model (PCM) represents one of the most successful examples among continuum solvation models. Here, we formulate the first-order derivative couplings (DCs) between the ground and excited states as well as between two excited states by utilizing time-independent equation of motion formalism within the framework of both linear response and spin flip formulations of TDDFT/CPCM (the conductor-like PCM), and implement the analytical DCs into the Q-CHEM electronic structure software package. The analytic implementation is validated by the comparison of the analytical and finite-difference results, and reproducing geometric phase effect in the protonated formaldimine test case. Taking 4-(N,N-dimethylamino)benzonitrile and uracil in the gas phase and solution as an example, we demonstrate that the solvent effect is essential not only for the excitation energies of the low-lying excited-states but also for the DCs between these states. Finally, we calculate the internal conversion rate of benzophenone in a solvent with DC being used. The current implementation of analytical DCs together with the existing analytical gradient and Hessian of TDDFT/PCM excited states allows one to study the nonadiabatic effects of relatively large systems in solutions with low computational cost. [ABSTRACT FROM AUTHOR]

A new formulation of the diagonalization step in self-consistent-field (SCF) electronic structure calculations is presented. It exactly replaces the diagonalization of the effective Hamiltonian with the solution of a set of second order nonlinear equations. The density matrix and/or the new set of occupied orbitals can be directly obtained from the resulting solution. This formulation may offer interesting possibilities for new approaches to efficient SCF calculations. The working equations can be derived either from energy minimization with respect to a Cayley-type parametrization of a unitary matrix, or from a similarity transformation approach. [ABSTRACT FROM AUTHOR]

The donor‐acceptor interface plays a critically important role in determining the power conversion efficiency of organic solar cells via controlling charge separation (CS) and recombination (CR) processes. Here, we combine the electronic structure calculations with electron transfer rate theory to clarify the CS and CR processes in ThQs‐C60/PDIxCN2 donor‐acceptor complexes. The results reveal that in ThQs‐PDIxCN2 the CS comes from both the dissociations of photo‐induced singlet exciton and singlet fission‐induced triplet exciton with a high efficiency, whereas in ThQs‐C60 only the singlet exciton dissociation can take place because the triplet exciton lies below the charge‐transfer exciton. However, very high CR rates in ThQs‐PDIxCN2 obliterate the benefit of fast CS, inversely leading to the ThQ‐C60 complex with a better cell efficiency. The present results are consistent with experimental observation and may furnish a possible patten to improve the overall conversion efficiency. © 2018 Wiley Periodicals, Inc. The charge separation (CS) and recombination (CR) processes in the donor‐acceptor interface play a critically important role in the determination of power conversion efficiency of organic solar cells. This work performs a theoretical calculation on CS and CR rates of ThQs‐C60/PDIxCN2 complexes and offers a theoretical explanation to the experimental observation. [ABSTRACT FROM AUTHOR]