First-order derivative couplings between excited states from adiabatic TDDFT response theory

An efficient approximate algorithm for nonadiabatic molecular dynamics

We propose a modification to the nonadiabatic surface hopping calculation method formulated in a paper by Yu et al. [Phys. Chem. Chem. Phys. 16, 25883 (2014)], which is a multidimensional extension of the Zhu-Nakamura theory with a practical diabatic gradient estimation algorithm. In our modification, their diabatic gradient estimation algorithm, which is based on a simple interpolation of the adiabatic potential energy surfaces, is replaced by an algorithm using the numerical derivatives of the adiabatic gradients. We then apply the algorithm to several models of nonadiabatic dynamics, both analytic and ab initio models, to numerically demonstrate that our method indeed widens the applicability and robustness of their method. We also discuss the validity and limitations of our new nonadiabatic surface hopping method while considering in mind potential applications to excited-state dynamics of biomolecules or unconventional nonadiabatic dynamics such as radiation decay processes in ultraintense X-ray fields.

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born–Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions.

Diabatic States at Construction (DAC) through Generalized Singular Value Decomposition

A procedure, called generalized diabatic-at-construction (GDAC), is presented to transform adiabatic potential energy surfaces into a diabatic representation by generalized singular value decomposition. First, we use a set of localized, valence bond-like configuration state functions, called DAC, as the basis states. Then, the adiabatic ground and relevant excited states are determined using multistate density functional theory (MSDFT). GDAC differs in the opposite direction from traditional approaches based on adiabatic-to-diabatic transformation with certain property restraints. The method is illustrated with applications to a model first-order bond dissociation reaction of CH₃OCH₂Cl polarized by a solvent molecule, the ground- and first-excited-state potential energy surfaces near the minimum conical intersection for the ammonia dimer photodissociation, and the multiple avoided curve crossings in the dissociation of lithium hydride. The GDAC diabatization method may be useful for defining charge-localized states in studies of electron transfer and proton-coupled electron transfer reactions in proteins.

On the applicability of a wavefunction-free, energy-based procedure for generating first-order non-adiabatic couplings around conical intersections

The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Köppel and Schubert [Mol. Phys. 104(5-7), 1069 (2006)]. Such quantities can always be computed in principle for the cost of two numerical Hessians in the worst-case scenario. Analytic-derivative techniques may help in terms of accuracy and efficiency but also raise potential traps due to singularities and ill-defined derivatives at degeneracies. We compare here two approaches, one fully numerical, the other semianalytic, where analytic gradients are available but Hessians are not, and investigate their respective conditions of applicability. Benzene and 3-hydroxychromone are used as illustrative application cases. It is shown that non-adiabatic couplings can thus be estimated with decent accuracy in regions of significant size around conical intersections. This procedure is robust and could be useful in the context of on-the-fly non-adiabatic dynamics or be used for producing model representations of intersecting potential energy surfaces with complete obviation of the electronic wavefunctions.

Approximate DFT-based methods for generating diabatic states and calculating electronic couplings: models of two and more states

Four types of density functional theory (DFT)-based approaches are assessed in this work for the approximate construction of diabatic states and the evaluation of electronic couplings between these states. These approaches include the constrained DFT (CDFT) method, the constrained noninteracting electron (CNE) model to post-process Kohn-Sham operators, the approximate block-diagonalization (BD) of the Kohn-Sham operators, and the generalized Mulliken-Hush method. It is shown that the first three approaches provide a good description for long-distance intermolecular electron transfer (ET) reactions. On the other hand, inconsistent results were found when applying these approaches to intramolecular ET in strongly coupled, mixed-valence systems. Model analysis shows that this discrepancy is caused by the inappropriate use of the two-state model rather than the defects of the approaches themselves. The situation is much improved when more states are included in the model electronic Hamiltonian. The CNE and BD approaches can thus serve as efficient and robust alternatives for building ET models based on DFT calculations.

Relativistic time-dependent density functional theories

The foundations, formalisms, technicalities, and practicalities of relativistic time-dependent density functional theories (R-TD-DFT) for spinor excited states of molecular systems containing heavy elements are critically reviewed.

Charge transfer in time-dependent density functional theory

Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

The role of tachysterol in vitamin D photosynthesis – a non-adiabatic molecular dynamics study

To investigate the role of tachysterol in the regulation of vitamin D photosynthesis, we studied its absorption properties and photodynamics by ab initio methods and non-adiabatic molecular dynamics.

Ab Initio Transient Vibrational Spectral Analysis

Pump probe spectroscopy techniques have enabled the direct observation of a variety of transient molecular species in both ground and excited electronic states. Time-resolved vibrational spectroscopy is becoming an indispensable tool for investigating photoinduced nuclear dynamics of chemical systems of all kinds. On the other hand, a complete picture of the chemical dynamics encoded in these spectra cannot be achieved without a full temporal description of the structural relaxation, including the explicit time-dependence of vibrational coordinates that are substantially displaced from equilibrium by electronic excitation. Here we present a transient vibrational analysis protocol combining ab initio direct molecular dynamics and time-integrated normal modes introduced in this work, relying on the recent development of analytic time-dependent density functional theory (TDDFT) second derivatives for excited states. Prototypical molecules will be used as test cases, showing the evolution of the vibrational signatures that follow electronic excitation. This protocol provides a direct route to assigning the vibrations implicated in the (photo)dynamics of several (photoactive) systems.

That Little Extra Kick: Nonadiabatic Effects in Acetaldehyde Photodissociation

The effect of nonadiabatic transitions on branching ratios, kinetic and internal energy distribution of fragments, and reaction mechanisms observed in acetaldehyde photodissociation is investigated by nonadiabatic molecular dynamics (NAMD) simulations using time-dependent hybrid density functional theory and Tully surface hopping. Homolytic bond breaking is approximately captured by allowing spin symmetry to break. The NAMD simulations reveal that nonadiabatic transitions selectively enhance the kinetic energy of certain internal degrees of freedom within approximately 50 fs. Branching ratios from NAMD and conventional "hot" Born-Oppenheimer molecular dynamics (BOMD) are similar and qualitatively agree with experiment. However, as opposed to the BOMD simulations, NAMD captures the high-energy tail of the experimental kinetic energy distribution. The extra "kick" of the nuclei in the direction of the nonadiabatic coupling vector results from nonadiabatic transitions close to conical intersections. From a mechanistic perspective, the nonadiabatic effects favor asynchronous over synchronous fragmentation and tend to suppress roaming.

Fast Numerical Evaluation of Time-Derivative Nonadiabatic Couplings for Mixed Quantum-Classical Methods

We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the time-derivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.

Proton-Coupled Electron Transfer: Moving Together and Charging Forward

Proton-coupled electron transfer (PCET) is ubiquitous throughout chemistry and biology. This Perspective discusses recent advances and current challenges in the field of PCET, with an emphasis on the role of theory and computation. The fundamental theoretical concepts are summarized, and expressions for rate constants and kinetic isotope effects are provided. Computational methods for calculating reduction potentials and pKa's for molecular electrocatalysts, as well as insights into linear correlations and non-innocent ligands, are also described. In addition, computational methods for simulating the nonadiabatic dynamics of photoexcited PCET are discussed. Representative applications to PCET in solution, proteins, electrochemistry, and photoinduced processes are presented, highlighting the interplay between theoretical and experimental studies. The current challenges and suggested future directions are outlined for each type of application, concluding with an overall view to the future.

The requisite electronic structure theory to describe photoexcited nonadiabatic dynamics: nonadiabatic derivative couplings and diabatic electronic couplings

Electronically photoexcited dynamics are complicated because there are so many different relaxation pathways: fluorescence, phosphorescence, radiationless decay, electon transfer, etc. In practice, to model photoexcited systems is a very difficult enterprise, requiring accurate and very efficient tools in both electronic structure theory and nonadiabatic chemical dynamics. Moreover, these theoretical tools are not traditional tools. On the one hand, the electronic structure tools involve couplings between electonic states (rather than typical single state energies and gradients). On the other hand, the dynamics tools involve propagating nuclei on multiple potential energy surfaces (rather than the usual ground state dynamics). In this Account, we review recent developments in electronic structure theory as directly applicable for modeling photoexcited systems. In particular, we focus on how one may evaluate the couplings between two different electronic states. These couplings come in two flavors. If we order states energetically, the resulting adiabatic states are coupled via derivative couplings. Derivative couplings capture how electronic wave functions change as a function of nuclear geometry and can usually be calculated with straightforward tools from analytic gradient theory. One nuance arises, however, in the context of time-dependent density functional theory (TD-DFT): how do we evaluate derivative couplings between TD-DFT excited states (which are tricky, because no wave function is available)? This conundrum was recently solved, and we review the solution below. We also discuss the solution to a second, pesky problem of origin dependence, whereby the derivative couplings do not (strictly) satisfy translation variance, which can lead to a lack of momentum conservation. Apart from adiabatic states, if we order states according to their electronic character, the resulting diabatic states are coupled via electronic or diabatic couplings. The couplings between diabatic states |ΞA⟩ and |ΞB⟩ are just the simple matrix elements, ⟨ΞA|H|ΞB⟩. A difficulty arises, however, because constructing exactly diabatic states is formally impossible and constructing quasi-diabatic states is not unique. To that end, we review recent advances in localized diabatization, which is one approach for generating adiabatic-to-diabatic (ATD) transformations. We also highlight outstanding questions in the arena of diabatization, especially how to generate multiple globally stable diabatic surfaces.