Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Abstract

We present a method for performing non-adiabatic, grid-based nuclear quantum dynamics calculations using diabatic potential energy surfaces (PESs) generated "on-the-fly". Gaussian process regression is used to interpolate PESs by using electronic structure energies, calculated at points in configuration space determined by the nuclear dynamics, and diabatising the results using the propagation diabatisation method reported recently [J. Phys. Chem. A, 119, 12457 -12470 (2015)]. To test this new method, the nuclear dynamics on the ground and first electronic excited states of the butatriene cation is studied using a grid-based method. The evolution of diabatic state populations is in very good agreement with those produced using a fitted potential. Overall, our scheme offers a route towards accurate quantum dynamics on diabatic PESs learnt on-the-fly.Keywords: Direct-dynamics, Diabatisation, Grid-based quantum dynamics, Butatriene 2010 MSC: 00-01, 99-00The study of nuclear quantum dynamics of nuclei is of great importance in helping to understand of the time-evolution of molecular systems upon excitation of the electronic degrees-of-freedom (DOFs); such simulations can make direct connections to the states. [6,7] One can model these non-adiabatic transitions using classical mechanics, as in the trajectory surface hopping (TSH) algorithm, [2,[8][9][10] but as the dynamics are inherently quantum mechanical, it is better to use a quantum mechani-25 cal method such as the multi-configuration timedependent Hartree (MCTDH) approach [1, 11,12] where possible.The major bottleneck in performing quantum dynamics calculations is usually not the wavefunc-30 tion time-propagation, but the creation of an appropriate PES on which to run the dynamics. As quantum mechanics is non-local, one needs a PES which is known everywhere in the configuration space of the nuclear motion prior to running the 35 dynamics. For the fully quantum mechanical study of non-adiabatic systems it is usually necessary to convert the PESs from the adiabatic representation to a diabatic representation. The adiabatic representation of the potential is an energy-ordered set 40 of PESs, and corresponds to the energies generated by electronic structure programs. However, at points in configuration space where adiabatic surfaces become degenerate, such as at conical interePreprint submitted to Chemical Physics Letters December 20, 2016 sections (CIs), there is a discontinuity in the gradi-45 ent of the states, such that the adiabatic states are no longer smooth; furthermore, the coupling between the states at these points is also infinite. Neither property of the adiabatic PESs is conducive to performing wavepacket dynamics, so transforma-50 tion to the diabatic representation is performed, resulting in smoothly varying surfaces with finite couplings. Diabatic representations are not unique for a given set of adiabatic states, so an appropriate diabatisation scheme must be chosen before the 55 PES can be used in a dynamics calculation. PESs are usua...

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