The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase

Abstract

Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute–solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.

Density Functional Theory for Electronic Excited States

“…In recognition of these and other systemic problems exhibited by LR-TDDFT, there has been growing interest in "∆SCF" approaches that attempt to determine excited-state solutions to the Kohn-Sham SCF equation. 338,339 Having found such a solution, the excitation energy is computed simply as the difference relative to the ground-state energy, hence "∆SCF". In contrast to the well-automated machinery of LR-TDDFT, these methods are less "black-box", involving more effort and finesse on the part of the user, because each excited state requires a separate calculation.…”

“…There has also been some preliminary work on the description of conical intersections and nonadiabatic dynamics using ∆SCF methods. 339,393 States with double-excitation character represent another categorical failure of LR-TDDFT within the adiabatic approximation, 99 with the most famous example being the optically-dark S 1 (2 1 A − g ) state in carotenoids, [395][396][397] or the analogous 2 1 A − g state in butadiene and other conjugated polyenes. [398][399][400][401][402] Doublyexcited states can be captured accurately using ∆SCF methods, 338,347,348 as shown for a few examples in Fig.…”

Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting

“…This fact could explain why previous variational calculations with the same functional predict an incorrect CoIn topology and negative energy gaps. This problem highlights the need for algorithms that can selectively converge to physically meaningful excited state solutions in nonadiabatic dynamics simulations based on time-independent approaches. ,, The application of an explicit Perdew–Zunger self-interaction correction improves the relative energy and the ordering of the states as well as the shape of the calculated energy curves. The energy gap between the ground and the doubly excited state is underestimated by 0.6–1.5 eV in calculations with the PBE functional, but it agrees closely with reported results of multireference calculations when PBE-SIC is used.…”

Spin–Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level

“…The delta self-consistent field (ΔSCF) method is an extension of density functional theory (DFT) concepts for the description of any stationary excited electronic state. − As a variational method, unlike its perturbative time-dependent (TD) DFT counterpart, the ΔSCF method optimizes a guess electronic density which approximates an excited electronic state. However, the low computational cost of the ground state energy calculation and the ability to selectively model excited electronic states of interest in a dense manifold of various electronic excitations make the ΔSCF method attractive for simulating NA mechanisms in condensed phase systems. − Because the ΔSCF method just optimizes a guess electron density, it has to be provided, either by an educated guess or, for instance, TD-DFT can provide the initial guess excited electronic state density, , whereas a number of optimization procedures can be chosen for its successful convergence. ,− ,,− In ΔSCF NA-MD, a converged density from a previous step can be used for the guess electron density in the next step. As the method is ignorant to the presence of other electronic states, it is advised to check the ordering and characters of electronic states along the ΔSCF trajectory with another electronic structure method which can directly generate a set of electronic states, for example with TD-DFT, especially when conducting the NA-MD for the first time.…”