TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

Ab initio molecular dynamics study of intersystem crossing dynamics for MH2 (M = Si, Ge, Sn, Pb) on spin-pure and spin-mixed potential energy surfaces

Recently, surface-hopping ab initio molecular dynamics (SH-AIMD) simulations have come to be used to discuss the mechanisms and dynamics of excited-state chemical reactions, including internal conversion and intersystem crossing. In dynamics simulations involving intersystem crossing, there are two potential energy surfaces (PESs) governing the motion of nuclei: PES in a spin-pure state and PES in a spin-mixed state. The former gives wrong results for molecular systems with large spin-orbit coupling (SOC), while the latter requires a potential gradient that includes a change in SOC at each point, making the computational cost very high. In this study, we systematically investigate the extent to which the magnitude of SOC affects the results of the spin-pure state-based dynamics simulations for the hydride MH2 (M = Si, Ge, Sn, Pb) by performing SH-AIMD simulations based on spin-pure and spin-mixed states. It is clearly shown that spin-mixed state PESs are indispensable for the dynamics simulation of intersystem crossing in systems containing elements Sn and Pb from the fifth period onward. Furthermore, in addition to the widely used Tully's fewest switches (TFS) algorithm, the Zhu-Nakamura (ZN) global switching algorithm, which is computationally less expensive, is applied to SH for comparison. The results from TFS- and ZN-SH-AIMD methods are in qualitative agreement, suggesting that the less expensive ZN-SH-AIMD can be successfully utilized to investigate the dynamics of photochemical reactions based on quantum chemical calculations.

Highly efficient implementation of analytic nonadiabatic derivative couplings within the pseudospectral method

A pseudospectral implementation of nonadiabatic derivative couplings in the Tamm-Dancoff approximation is reported, and the accuracy and efficiency of the pseudospectral nonadiabatic derivative couplings are studied. Our results demonstrate that the pseudospectral method provides mean absolute errors of 0.2%-1.9%, while providing a significant speedup. Benchmark calculations on fullerenes (Cn, n up to 100) using B3LYP achieved 10- to 15-fold, 8- to 17-fold, and 43- to 75-fold speedups for 6-31G**, 6-31++G**, and cc-pVTZ basis sets, respectively, when compared to the conventional spectral method.

On the circularly polarized luminescence of individual triplet sublevels

We discuss the possibility of using circularly polarized luminescence (CPL) as a tool to probe individual triplet spin sublevels that are populated nonadiabatically following photoexcitation. This study is motivated by a mechanism proposed for chirality-induced spin selectivity in which coupled electronic-nuclear dynamics may lead to a non-statistical population of the three triplet sublevels in chiral systems. We find that low-temperature CPL should aid in quantifying the exact spin state/s populated through coupled electronic-nuclear motion in chiral molecules.

State Interaction Linear Response Time-Dependent Density Functional Theory with Perturbative Spin-Orbit Coupling: Benchmark and Perspectives

Spin-orbit coupling (SOC) is an important driving force in photochemistry. In this work, we develop a perturbative spin-orbit coupling method within the linear response time-dependent density function theory framework (TDDFT-SO). A full state interaction scheme, including singlet-triplet and triplet-triplet coupling, is introduced to describe not only the coupling between the ground and excited states, but also between excited states with all couplings between spin microstates. In addition, expressions to compute spectral oscillator strengths are presented. Scalar relativity is included variationally using the second-order Douglas-Kroll-Hess Hamiltonian, and the TDDFT-SO method is validated against variational SOC relativistic methods for atomic, diatomic, and transition metal complexes to determine the range of applicability and potential limitations. To demonstrate the robustness of TDDFT-SO for large-scale chemical systems, the UV-Vis spectrum of Au₂₅(SR)₁₈ ^- is computed and compared to experiment. Perspectives on the limitation, accuracy, and capability of perturbative TDDFT-SO are presented via analyses of benchmark calculations. Additionally, an open-source Python software package (PyTDDFT-SO) is developed and released to interface with the Gaussian 16 quantum chemistry software package to perform this calculation.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin–orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm–Dancoff approximation to TDDFT, spin–flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine–Ag20 complex), we emphasize that caution is needed to properly account for system–environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

Theoretical Investigation of the Effect of Alkylation and Bromination on Intersystem Crossing in BODIPY-Based Photosensitizers

Halogenated and alkylated BODIPY derivatives are reported as suitable candidates for their use as photosensitizers in photodynamic therapy due to their efficient intersystem crossing (ISC) between states of different spin multiplicities. Spin-orbit couplings (SOCs) are evaluated using an effective one-electron spin-orbit Hamiltonian for brominated and alkylated BODIPY derivatives to investigate the quantitative effect of alkyl and bromine substituents on ISC. BODIPY derivatives containing bromine atoms have been found to have significantly stronger SOCs than alkylated BODIPY derivatives outside the Frank-Condon region while they are nearly the same at local minima. Based on calculated time-dependent density functional theory (TD-DFT) vertical excitation energies and SOCs, excited-state dynamics of three BODIPY derivatives were further explored with TD-DFT surface hopping molecular dynamics employing a simple accelerated approach. Derivatives containing bromine atoms have been found to have very similar lifetimes, which are much shorter than those of the derivatives possessing just the alkyl moieties. However, both bromine atoms and alkyl moieties reduce the HOMO/LUMO gap, thus assisting the derivatives to behave as efficient photosensitizers.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Modeling Spin-Crossover Dynamics

In this article, we review nonadiabatic molecular dynamics (NAMD) methods for modeling spin-crossover transitions. First, we discuss different representations of electronic states employed in the grid-based and direct NAMD simulations. The nature of interstate couplings in different representations is highlighted, with the main focus on nonadiabatic and spin-orbit couplings. Second, we describe three NAMD methods that have been used to simulate spin-crossover dynamics, including trajectory surface hopping, ab initio multiple spawning, and multiconfiguration time-dependent Hartree. Some aspects of employing different electronic structure methods to obtain information about potential energy surfaces and interstate couplings for NAMD simulations are also discussed. Third, representative applications of NAMD to spin crossovers in molecular systems of different sizes and complexities are highlighted. Finally, we pose several fundamental questions related to spin-dependent processes. These questions should be possible to address with future methodological developments in NAMD.

A systematic model study quantifying how conical intersection topography modulates photochemical reactions

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.

Constructing Spin-Adiabatic States for the Modeling of Spin-Crossing Reactions. I. A Shared-Orbital Implementation

In the modeling of spin-crossing reactions, it has become popular to directly explore the spin-adiabatic surfaces. Specifically, through constructing spin-adiabatic states from a two-state Hamiltonian (with spin-orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully-variational spin-adiabatic approach based on Kohn-Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit-Pauli one-electron spin-orbit operator. For three model spin-crossing reactions [predissociation of N₂O, singlet-triplet conversion in CH₂, and CO addition to Fe(CO)₄], the spin-crossing points were obtained. Our results also indicated the Breit-Pauli one-electron spin-orbit coupling can vary significantly along the reaction pathway on the spin-adiabatic energy surface. On the other hand, due to the restriction that low-spin and high-spin states share the same set of molecular orbitals, the acquired spin-adiabatic energy surface shows a cusp (i.e. a first-order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin-adiabatic surfaces.

Reorganization energies and spectral densities for electron transfer problems in charge transport materials

Various contributions to the outer reorganization energy of an electron transfer system and their theoretical and computational aspects have been discussed.