Best practices for nonadiabatic molecular dynamics simulations

TL;DR

This Best Practices guide consolidates current knowledge on nonadiabatic molecular dynamics (NAMD), focusing on trajectory-based approaches for gas-phase photodynamics. It integrates fundamental theory (Born-Huang representation, NACs, conical intersections) with practical guidance on electronic-structure method choice (wavefunction- vs density-based), NAM(D) techniques (TSH, AIMS, vMCG, AIMC, FMS), and end-to-end workflow from benchmarking to observable calculation. The document emphasizes rigorous benchmarking in the Franck-Condon region and beyond, careful active-space selection for multireference methods, and prudent initial-condition sampling to faithfully reproduce photoexcitation. It also discusses numerical issues (energy conservation, decoherence, and diabatization strategies) and provides a pragmatic FAQ and a comprehensive checklist to improve reliability and reproducibility of NAMDs. Overall, the guide aims to standardize best practices, enable robust interpretation of NAMD results, and streamline the adoption of NAMD in photochemistry and photophysics research.

Abstract

Nonadiabatic molecular dynamics simulations aim to describe the coupled electron-nuclear dynamics of molecules in excited electronic states. These simulations have been applied to understand a plethora of photochemical and photophysical processes, and, as a result, the number of nonadiabatic dynamics simulations has been growing significantly over the past decade. Yet, the field remains in its infancy, and a potential user may find it difficult to approach this type of simulation, given their complexity and the number of elements that should be considered for a (hopefully) successful nonadiabatic dynamics simulation. Nonadiabatic molecular dynamics relies on several key steps: finding a level of electronic-structure theory to describe the molecule in its Franck-Condon region and beyond, describing the photoexcitation process, selecting a method to perform the nonadiabatic dynamics, and analyzing the final results before calculating observables for a more direct comparison with experiment. This Best Practices guide aims to provide a general guide for the user of nonadiabatic molecular dynamics by (i) discussing the fundamentals of nonadiabatic molecular dynamics and the various trajectory-based methods developed for molecular systems, (ii) introducing the different electronic-structure methods and concepts - adiabatic/diabatic representation, conical intersections - that can be used with nonadiabatic molecular dynamics (or for benchmarking), (iii) providing details on the various steps required to perform a nonadiabatic dynamics simulation and their practical use, as well as guided examples and a discussion on the calculation of observables, (iv) proposing a FAQ with the typical questions a user may have when performing nonadiabatic dynamics, and (v) sketching a checklist for the key practical steps when performing a (trajectory-based) nonadiabatic molecular dynamics.

Figures (19)

• Figure 1: Schematic representation of a photochemical (green) and photophysical (purple) process (center), surrounded by the different key steps necessary to perform a nonadiabatic molecular dynamics simulations and discussed in this Guide. Concepts of electronic-structure theory for excited electronic states (adiabatic/diabatic representation, conical intersections) and various electronic-structure methods are discussed in Section \ref{['elecstructproblem']}, and practical considerations on the selection of an electronic-structure methods can be found in Section \ref{['sec:banchmarkelstr']}. Section \ref{['sec:initconds']} offers a discussion on the generation of initial conditions for nonadiabatic molecular dynamics, namely ground-state sampling and the description of photoexcitation. The fundamental equations of nonadiabatic dynamics are discussed in Section \ref{['setting-the-scene']}, the approximations leading to methods for nonadiabatic molecular dynamics are introduced in Section \ref{['nonadiabaticdynproblem']}, and their practical use is described in Section \ref{['sec:performingNAMD']}. Section \ref{['sec:analysisandobservables']} offers a brief survey on the calculation of experimental observables from nonadiabatic molecular dynamics simulations. The Guide also includes a FAQ (Section \ref{['sec:faq']} and a Checklist for nonadiabatic molecular dynamics (Section \ref{['sec:checklist']}) with its rationale (Section \ref{['sec:rationale']}).
• Figure 2: Schematic representation of potential energy curves in the diabatic (left panel) and adiabatic representation (right panel). Left panel: the electronic energy (expectation value of the electronic Hamiltonian) for two diabatic electronic states, $n\pi^\ast$ (red) and $\pi\pi^\ast$ (blue), is represented along a given nuclear coordinate, together with the diabatic coupling as a dashed green curve. The electronic Hamiltonian matrix in this basis of two diabatic electronic states is given under the panel. Right panel: the adiabatic electronic energy $E_1^{\text{el}}$ and $E_2^{\text{el}}$ (eigenvalues of the electronic Hamiltonian) for two adiabatic electronic states, $\Phi_1$ and $\Phi_2$, are represented along a given nuclear coordinate, together with the NACV as a dashed grey curve. The color code used for the adiabatic electronic energies reflects the underlying character of the electronic state at a specific nuclear configuration (red for $n\pi^\ast$ and blue for $\pi\pi^\ast$, in between when the character is mixed near the avoided crossing). The diagonal electronic Hamiltonian matrix in this basis of two adiabatic electronic states is given under the panel.
• Figure 3: Two different cases for nonadiabatic processes in the diabatic and adiabatic representation. Case I exhibits a system with a weak diabatic coupling, resulting in a strong nonadiabatic coupling in the adiabatic representation. Case II highlights a system with a strong diabatic coupling, meaning a weak nonadiabatic coupling in the adiabatic representation. For both cases, the nuclear dynamics of the system is symbolized by a circle following the arrow.
• Figure 4: Schematic representation of the adiabatic PESs in the branching space (left) and seam space (right) of a two-state CX, where $\mathbf{g}_{IJ}(\mathbf{R})$ and $\mathbf{h}_{IJ}(\mathbf{R})$ are the branching space vectors (expressed in terms of adiabatic states) and $\mathbf{a}_{IJ}(\mathbf{R})$ and $\mathbf{b}_{IJ}(\mathbf{R})$ are two arbitrarily chosen seam space coordinates. Plotting the PESs along one branching space vector (here $\mathbf{g}_{IJ}(\mathbf{R})$) and one seam space coordinate reveals the intersection seam (middle) -- see text for discussion.
• Figure 5: Schematic representation of the adiabatic PESs in the branching space of four two-state CXs characterised by different local topographies: (top left) peaked and single-path ($\delta_{\text{gh}}$ = 0.0949, $\Delta_{\text{gh}}$ = 0.5320, $s_x$ = 0.9550, $s_y$ = 0.0000); (top right) peaked and bifurcating ($\delta_{\text{gh}}$ = 0.1249, $\Delta_{\text{gh}}$ = 0.3402, $s_x$ = 0.0000, $s_y$ = 0.7133); (bottom left) sloped and single-path ($\delta_{\text{gh}}$ = 0.1326, $\Delta_{\text{gh}}$ = 0.2680, $s_x$ = 0.0000, $s_y$ = 2.1588); and (bottom right) sloped and bifurcating ($\delta_{\text{gh}}$ = 0.1399, $\Delta_{\text{gh}}$ = 0.8753, $s_x$ = 0.0000, $s_y$ = 0.4553). The numerical CX branching space topography parameters used to generate the plots in this figure were taken from Ref. fdez_galvan_analytical_2016. We note that, here, in Fig. \ref{['fig:topog_param_schematic']}, and in Fig. \ref{['fig:branch_vs_seam']}, we use the (raw) $\mathbf{g}_{IJ}(\mathbf{R})$ and $\mathbf{h}_{IJ}(\mathbf{R})$ vector notation instead of the $x$ and $y$ (orthonormalized) scalar quantities for schematic simplicity.