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A first principles quantum formalism to describe the non-adiabatic dynamicsof electrons and nuclei based on a second quantization representation (SQR) ofthe electronic motion combined with the usual representation of the nuclearcoordinates is introduced. This procedure circumvents the introduction ofpotential energy surfaces and non-adiabatic couplings, providing an alternativeto the Born-Oppenheimer approximation. An important feature of the molecularHamiltonian in the mixed first quantized representation for the nuclei and theSQR representation for the electrons is that all degrees of freedom, nuclearpositions and electronic occupations, are distinguishable. This makes theapproach compatible with various tensor decomposition \emph{ans\"atze} for thepropagation of the nuclear-electronic wavefunction. Here, we describe theapplication of this formalism within the multi-configuration time-dependentHartree (MCTDH) framework and its multilayer generalization, corresponding toTucker and hierarchical Tucker tensor decompositions of the wavefunction,respectively. The approach is applied to the calculation of thephotodissociation cross-section of the HeH$^+$ molecule under extremeultraviolet irradiation, which features non-adiabatic effects and quantuminterferences between the two possible fragmentation channels, He+H$^+$ andHe$^+$+H. These calculations are compared with the usual description based onab \emph{ab initio} potential energy surfaces and non-adiabatic coupling matrixelements, which fully agree. The proof-of-principle calculations serve toillustrate the advantages and drawbacks of this formalism, which are discussedin detail, as well as possible ways to overcome them.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Non-adiabatic quantum dynamics without potential energy surfaces based  on second-quantized electrons: application within the framework of the MCTDH  method