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WIREs Comput Mol Sci
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Different flavors of nonadiabatic molecular dynamics

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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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