Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states

Abstract

The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear configurations. The electron-nucleus Hamiltonian is block-diagonalized up to $\mathcal{O}({\epsilon }^{n+1})$ through a unitary transformation of the electronic subspace and the corresponding $n$th-order effective Hamiltonian is derived for the quantum nuclear motion. Explicit but general formulae are given for the second- and the third-order corrections. As a special case, the second-order Hamiltonian corresponding to an isolated electronic state is recovered which contains the coordinate-dependent mass-correction terms in the nuclear kinetic energy operator. For a multi-dimensional, explicitly coupled electronic band, the second-order Hamiltonian contains the usual BO terms and non-adiabatic corrections but generalized mass-correction terms appear as well. These, earlier neglected terms, perturbatively account for the outlying (discrete and continuous) electronic states not included in the explicitly coupled electronic subspace.

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Cited by in corpus (14)

• Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\mathrm{u}}^{+}$)
• Precise computation of rovibronic resonances of molecular hydrogen: $EF{}^1{\Sigma }_{\mathrm{g}}^{+}$ inner-well rotational states
• Non-adiabatic mass correction for excited states of molecular hydrogen: improvement for the outer-well $H\bar{H}{}^1{\Sigma }_{\mathrm{g}}^{+}$ term values
• H${}_3^{+}$ as a five-body problem described with explicitly correlated Gaussian basis sets
• Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ ${}^1{\Sigma }_{\text{g}}^{+}$ manifold of molecular hydrogen
• Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen
• Variational Vibrational States of Methanol (12D)
• Benchmark potential energy curve for collinear H${}_3$
• High-Precision Quantum Dynamics of He${}_2$ over the b ${}^3{\Pi }_{\mathrm{g}}$-c ${}^3{\Sigma }_{\mathrm{g}}^{+}$ Electronic Subspace by including Non-adiabatic, Relativistic and QED Corrections and Couplings
• The Moving Born-Oppenheimer Approximation
• Exactly factorized molecular Kohn-Sham density functional theory
• Rovibrational computations for He${}_2^{+}$ X ${\Sigma }_{\mathrm{u}}^{+}$ including non-adiabatic, relativistic and QED corrections
• Rovibrational computations for the He${}_2$ a ${}^3{\Sigma }_{\mathrm{u}}^{+}$ state including non-adiabatic, relativistic, and QED corrections
• Rovibrational computation of H${}_3^{+}$ with permutationally invariant Pekeris coordinates