Vibrational memory in quantum localized states

The rovibrational eigenenergy set of molecular systems is a key feature needed to understand and model elementary chemical reactions. A unique class of molecular systems, represented by an ${}^4{A}^{\prime \prime }$ excited electronic state of the ${\left[\mathrm{H},\mathrm{S},\mathrm{N}\right]}^{-}$ system comprising several distinct dipole-bound isomers, is found to contain both bent and linear minima separated by relatively small barriers. Full-dimensional nuclear-motion computations performed in Jacobi coordinates using three-dimensional potential energy surfaces describing the stable isomers and the related transition states yield rovibrational eigenstates located both below and above the barriers. The rovibrational wave functions are well localized, regardless of whether the state's energy is below or above the barriers. We also show that the states preserve the memory of the isomeric forms they “originate from,” which is signature of a strong vibrational memory effect above isomerization barriers.

Figure 1

Top left: (R)CCSD(T)-F12/aug-cc-pVTZ contour plots of the PES of the $\mathrm{SN}\cdots {\mathrm{H}}^{-}$ quartet electronic state along the Jacobi coordinates $R$ (in units of $a_0$, where $1a_0=1\mathrm{bohrs}=0.5292\AA$) and θ (in units of degrees), where $r$(SN) is fixed at 2.96 bohrs. The step between the contours is $50\mathrm{c}{\mathrm{m}}^{-1}$. The zero energy corresponds to the energy of the $\mathrm{S}{\mathrm{N}}^{-}\left(X^3{\mathrm{\Sigma }}^{-}\right)+\mathrm{H}\left({}^{2}S\right)$ asymptote. Top right: LUMO of $\mathrm{S}{\mathrm{N}}^{-}$ interacting with the $1s$ atomic orbital of hydrogen. Bottom left: (R)CCSD(T)-F12/aug-cc-pVTZ contour plot of the PES of the $\mathrm{SH}\cdots {\mathrm{N}}^{-}$ (${}^4{A}^{\prime \prime }$) electronic state along the Jacobi coordinates $R$ (in units of $a_0$) and θ (in units of degrees), where $r$(SH) is fixed at 2.53 bohrs. Right: HOMO of $\mathrm{S}{\mathrm{H}}^{-}$ interacting with the $2p$ atomic orbital of N. The step between the contours is $50\mathrm{c}{\mathrm{m}}^{-1}$. The zero energy corresponds to the energy of the $\mathrm{S}{\mathrm{H}}^{-}\left(X^1{\mathrm{\Sigma }}^{+}\right)+\mathrm{N}\left({}^{4}S\right)$ asymptote. The red arrows indicate the favorable interactions between the frontier orbitals of $\mathrm{S}{\mathrm{H}}^{-}/\mathrm{S}{\mathrm{N}}^{-}$ and N/H.

Figure 2

Selected rovibrational wave functions from the SM [38] for $\mathrm{SN}\cdots {\mathrm{H}}^{-}$ (top) and $\mathrm{SH}\cdots {\mathrm{N}}^{-}$ (bottom) complexes and their localization in the corresponding potential (blue curve), where $r$ is relaxed. The horizontal black lines indicate the levels appearing when $J$ ⩾ 0, whereas the red horizontal lines represent those appearing only when $J$ ⩾ 1. $R$ is in units of ${\mathrm{a}}_0$ and θ is in units of degrees. $E$ is the energy in units of $\mathrm{c}{\mathrm{m}}^{-1}$.

Figure 3

Selected rovibrational wave functions from the SM [38] for $\mathrm{SN}\cdots {\mathrm{D}}^{-}$ (top) and $\mathrm{SD}\cdots {\mathrm{N}}^{-}$ (bottom) complexes and their localization in the corresponding potential (blue curve), where $r$ is relaxed. The horizontal black lines indicate levels appearing when $J$ ⩾ 0, whereas the red horizontal lines represent those appearing only when $J$ ⩾ 1. $R$ is in units of ${\mathrm{a}}_0$ and θ is in units of degrees. $E$ is the energy in units of $\mathrm{c}{\mathrm{m}}^{-1}$.

Figure 4

Simulated μw-far IR spectra of $\mathrm{SN}\cdots {\mathrm{H}}^{-}$ and of $\mathrm{SH}\cdots {\mathrm{N}}^{-}$, with different isomers used as starting points: (a) linear $\mathrm{H}\cdots \mathrm{S}{\mathrm{N}}^{-}$ (Isomer I); (b) bent $\mathrm{SN}\cdots {\mathrm{H}}^{-}$ (Isomer II); (c) linear $\mathrm{SN}\cdots {\mathrm{H}}^{-}$ (Isomer III); (d) $\mathrm{SH}\cdots {\mathrm{N}}^{-}$. The inset in (d) shows the transitions populating the levels above the potential barrier. The spectra are normalized to the most intense band. They are issued from the corresponding lowest $J=1,\varepsilon =–$ level. The zero energy is taken as the position of the $J=1,\varepsilon =–$ level of $\mathrm{SN}-{\mathrm{H}}^{-}$ (Isomer II) in (a–c) and the $J=1, \varepsilon =–$ level of $\mathrm{SH}-{\mathrm{N}}^{-}$ in (d). Most transitions populate levels located above the potential barriers. ν is the frequency in units of $\mathrm{c}{\mathrm{m}}^{-1}$.