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WIREs Comput Mol Sci
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Different flavors of nonadiabatic molecular dynamics

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The Born‐Oppenheimer approximation constitutes a cornerstone of our understanding of molecules and their reactivity, partly because it introduces a somewhat simplified representation of the molecular wavefunction. However, when a molecule absorbs light containing enough energy to trigger an electronic transition, the simplistic nature of the molecular wavefunction offered by the Born‐Oppenheimer approximation breaks down as a result of the now non‐negligible coupling between nuclear and electronic motion, often coined nonadiabatic couplings. Hence, the description of nonadiabatic processes implies a change in our representation of the molecular wavefunction, leading eventually to the design of new theoretical tools to describe the fate of an electronically‐excited molecule. This Overview focuses on this quantity—the total molecular wavefunction—and the different approaches proposed to describe theoretically this complicated object in non‐Born‐Oppenheimer conditions, namely the Born‐Huang and Exact‐Factorization representations. The way each representation depicts the appearance of nonadiabatic effects is then revealed by using a model of a coupled proton–electron transfer reaction. Applying approximations to the formally exact equations of motion obtained within each representation leads to the derivation, or proposition, of different strategies to simulate the nonadiabatic dynamics of molecules. Approaches like quantum dynamics with fixed and time‐dependent grids, traveling basis functions, or mixed quantum/classical like surface hopping, Ehrenfest dynamics, or coupled‐trajectory schemes are described in this Overview. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Software > Simulation Methods Theoretical and Physical Chemistry > Spectroscopy
Schematic representation of a one‐dimensional (1D) model for a coupled proton–electron transfer reaction. Two positive charges are fixed (gray) at a position Rfixed,1 = −10 bohr and Rfixed,2 = 10 bohr, giving a fixed distance L = 20 bohr. A moving proton (red circle) and electron (e) can evolve along the axis defined by the two fixed charges. Their respective position is characterized by R (proton) and r (electron). This model is strictly one‐dimensional
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Schematic representation of the nonadiabatic dynamics presented in Figure b in the framework of the exact factorization. Classical trajectories (filled circles, at times t0 (blue), t1 (orange) and t2 (red)) propagated according to the CT‐MQC algorithm follow the TDPEC (colored plain lines), and are localized in the regions where the nuclear density (colored dashed lines) is large. The trajectories are coupled, and the coupling is indicated as the green area around each circle. The thin dotted lines are the adiabatic PECs shown as reference
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Schematic representation of the nonadiabatic dynamics presented in Figure b using trajectory surface hopping dynamics. A swarm of independent classical trajectories (circles) are initiated in S0 at time t0 (blue circles) and follow the adiabatic ground electronic state until the region of strong nonadiabaticity is reached (t1, orange circles, and t2, red circles) where hops between surfaces can be observed. The nuclear amplitudes (dashed and dotted lines) and adiabatic PECs (thick plain lines) are given for references
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Schematic representation of the nonadiabatic dynamics presented in Figure b using a method based on trajectory basis functions (here, full multiple spawning). The nuclear wavefunctions (thin dashed lines) at three different times (t0 = blue, t1 = orange, and t2 = red) are expressed on a basis of coupled TBFs (Gaussians with center indicated by a dot). New TBFs can be created in region of strong nonadiabatic couplings, and amplitude can be exchanged between the TBFs
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Schematic representation of a grid‐based quantum dynamics version of the nonadiabatic dynamics presented in Figure b. The PECs as well as the nuclear wavefunctions at three different times (t0 = blue, t1 = orange, and t2 = red) are represented on a fixed grid (dots)
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Exact‐factorization representation of the molecular quantum dynamics described in Figure , for the two cases (a) and (b). For each case, the gauge‐independent (GI) part of the TDPEC (ɛGI(R, t)) is plotted on the upper panels and compared to the PECs of the corresponding model, along with the nuclear density. From left to right, snapshots along the dynamics for times t0 (blue curves), t1 (orange curves), and t2 (red curves) are shown. The modulus of the conditional electronic wavefunction is showed in the lower panels. The white dashed boxes highlight the regions of non‐negligible nuclear amplitude, where the exact‐factorization quantities are computed
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Born‐Huang representation of the molecular quantum dynamics described in Figure , for the two cases (a) and (b). Upper panels show the PECs (ground‐state PEC in green, first excited‐state PEC in palatinate), as well as the squared‐modulus of the time‐dependent nuclear amplitudes at the three different times t0 (blue), t1 (orange), and t2 (red). The middle and lower panels corresponds to the modulus of the S1 and S0 time‐independent electronic wavefunctions, respectively
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Snapshots of the modulus of the total molecular wavefunction, |Ψ(r, R, t)|, at three different times during the quantum molecular dynamics of the coupled proton‐electron transfer model. The upper and lower panel give the snapshots for two different dynamics: dynamics with a strong (a) or a weak (b) interaction between the moving proton and electron. The top of each panel proposes a schematic representation of the studied dynamics. The white horizontal dashed line gives the expectation value of the position of the moving proton
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Software > Simulation Methods
Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics
Theoretical and Physical Chemistry > Spectroscopy

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