Phenomenological characterization of the isomerization transition state of carbonyl sulfide

TL;DR

This work uses the two-dimensional vibron model to describe the bending spectrum of carbonyl sulfide and to extract the isomerization transition-state barrier. By introducing a modified empirical formula for the effective frequency that accounts for anharmonicity changes in quasilinear molecules, the authors achieve barrier estimates that align well with high-level ab initio results. They fit experimental and predicted bending energies with a four-parameter effective Hamiltonian, identify ESQPT signatures via participation ratios and an order-parameter expectation, and demonstrate that the new formula improves zero-point vibrational energy estimates. The approach provides a computationally efficient route to TS energetics in simple molecules and motivates extending the algebraic treatment to the full vibrational landscape.

Abstract

Signatures of excited-state quantum phase transitions in the bending degree of freedom of triatomic systems that undergo an isomerization reaction have been recently evinced. In this work, we study the carbonyl sulfide bending motion using an effective Hamiltonian within the two-dimensional limit of the vibron model framework, which has been shown to accurately describe critical phenomena in molecular bending spectra within experimental precision. To estimate the transition state energy barrier, we propose an improvement to a phenomenological formula proposed by Baraban et al.[1] , introducing a new term to capture the anharmonicity change that characterizes quasilinear molecules

Figures (4)

• Figure 1: Residuals for Fit I and Fit II calculations versus the experimental and predicted energies in cm$^{-1}$ units. Purple circles show the residuals obtained from Fit I for 51 experimental energies. Red triangles include the predictions of Fit I for the 20 term values in the energy range from 8000cm^-1 to 11000cm^-1 obtained with an effective Hamiltonian GOLEBIOWSKI2014. Green crosses correspond to the residuals for Fit II, including 71 experimental and predicted bending term values.
• Figure 2: Upper panel: Participation ratio (purple dots) and expectation value of the $\hat{n}$ operator (blue triangles) as a function of the computed bending term values for $\ell=0$ states obtained in Fit I. Lower panels: Squared components $|C^{(k)}_{n,\ell}|^2$ as a function of the vibrational quantum number $n$ for $\ell=0$ for three selected eigenstates (I, II, and III) marked in the upper panel with circles.
• Figure 3: Quasilinearity parameter $\gamma_{n,\ell=0}$ as a function of the bending energies calculated using the Hamiltonian (\ref{['eq-hamilt']}) in Fit I.
• Figure 4: Effective frequency as a function of the midpoint bending energy for $\ell=0$ states computed for Fit I results. Green triangles and blue squares are the available experimental and extended energy data. Black circles are the 2DVM results. Purple and orange lines are obtained fitting Eqs. \ref{['TSformula-baraban']} and (\ref{['modified-baraban-formula']}) to Fit I results, respectively.