Vibrational spectra and tripartite entanglement in hydrogen sulfide

Abstract

In this Brief Report an improved u(2) algebraic model is proposed to study both stretching and bending vibrational spectra of a bent triatomic molecule. The model with fewer parameters is used to reproduce the observed spectra of hydrogen sulfide (H 2 S) with better precision than the u(4) algebraic model. Furthermore, the tripartite entanglement dynamics is investigated for vibrationally localized states in H 2 S. It is shown that the entanglement of a highly excited state in the bending mode displays better quasiperiodicity than that in the stretch. Those are useful for molecular vibrations and multipartite quantum entanglement.

Electron–vibration entanglement in the Born–Oppenheimer description of chemical reactions and spectroscopy

“…Indeed, for large cusp diameters great than 1, the BO approximation itself is adequate to describe kinetics, adding the DC correction is 35 required for slightly smaller values, values of order 0.04 < c Q < 0.2 need the full calculation including all correction terms DC+FD+SD, yet even smaller values require just using DC. 40 In Fig. 6 is shown the same dynamics as in Fig.…”

“…In summary, to have significantly entangled adiabatic 40 wavefunctions at the transition state, i.e., significant failure of the Born-Oppenheimer approximation, the energy gap there needs to be small compared to that at the relaxed geometry ( 2 / J λ small, deep cuspy double well) and the vibration frequency has to be significant compared to the electronic energies ( / E ω ∆  not 45 small). This is in accordance with traditional qualitative understandings of BO breakdown but here is presented quantified using a simple model chemical system that shows how groundvibronic-level properties relate.…”

“…The fraction that 35 surface hops quickly hops back, however, and becomes reunited with the directly reflected wavepacket. Using just N=1024 basis functions per state is slightly inadequate for this trajectory, however, as by 2 / t π ω = a near complete reformation of the original wavepacket is actually expected (see the converged 40 propagation in the CA basis shown later in Fig. 6) whereas the displayed function is slightly distorted.…”

“…Hence the entanglement measured in the diabatic basis CA will be different to that measured in the BO basis using FC, whereas other properties such as energies and dipole moments are independent of the choice of the electronic basis. 40 For not just eigenstates but for any general time-dependent wavefunction expressed in one of these forms, the entanglement is calculated by first determining the appropriate reduced electronic density for wavefunction j 1,3 or …”

“…35 Instead of using the BO description to understand the dissociation of the NaCl molecule, an alternative approach is to use diabatic wavefunctions, wavefunctions that are either purely ionic or purely radical with unchanging character as the molecule stretches. These diabatic wavefunctions are mixed in different 40 proportions at each nuclear geometry to make the BO adiabatic wavefunctions. A particularly relevant aspect of the diabatic approach is that it is possible to build spatially localized detectors for the charge or dipole of a molecule as it undergoes dynamics, and these detectors project the quantum wavefunction onto 45 diabatic bases.…”