Tunneling dynamics of internal rotation in the nitric acid molecule

Abstract

The Hamiltonian of internal rotation about the 6'., axis in the HNO 3 molecule and its H/D-, OI~/O 16-, and NtS/N14-isotopomers was reconstructed using the results of quantumchemical calculations. The Fermi resonance between the torsional (2v 9) and ONO bending (v5) vibrations is a characteristic feature of the molecule. Tunneling splittings in the ground and excited states were calculated using the perturbative instanton approach. Abnormally large changes in the splittings upon isotope substitution of heavy atoms are predicted.Key words: nitric acid, potential energy surface, internal rotation, tunneling splittings.Intensive experimental studies of internal rotation in the nitric acid molecule were carried out in the 1950--1960s. The structure of the molecule was determined from microwave spectra. 1 Detailed study z of vibrational spectra of its H-, D-, taN-, and 15N-isotopomers showed that hindered internal rotation of the OH group, corresponding to the torsional vibration in planar stable configurations, occurs in the HNO 3 molecule. A salient feature of this molecule is resonance between the torsional and ONO bending vibrations, which is responsible for the fact that tunneling splitting of the ONO bending vibration in the first excited state (35.5 MHz) is comparable with that of the second level of torsional vibration (50:7 MHz) and far (by some orders of magnitude) exceeds the splittings of the zero (-3 kHz) and first (-2 MHz) levels of the latter. 3-7The aim of this work is to carry out a theoretical study of the HNO 3 molecule and its isotopomers. Tunneling splittings found for the ground and lowest excited states are in good agreement with experimental data. Changes in tunneling splittings upon isotope substitution of H (by D) and heavy nuclei are considered and anomalous isotope effects are predicted. A universal approach to description of multidimensional tunneling dynamics, called the perturbative instanton approach (PIA), has been reported earlier, s-t4The PIA considers tunneling dynamics in low-energy potential energy surfaces (PES) of a rather general type. The PES is constructed using 3N -6 generalized reactive coordinates (i.e., a totality of generalized coordinates including the coordinate of transition between stable configurations) and includes (1) a one-dimensional (1 D) potential for the angular-tunneling coordinate 0 and (2) a set of small-amplitude transverse coordinates (coupled with r whose frequencies, equilibrium positions, and anharmonicities depend on 0. Despite the relatively simple structure, such PES provide the possibility of performing calculations with a desired accuracy in the low-energy region.

A hybrid variational-perturbation calculation of the ro-vibrational spectrum of nitric acid

“…From the theoretical perspective, study of the ro-vibrational infrared spectrum of the HNO 3 is difficult because of the relatively large number of the vibrational degrees of freedom, N c = 9, and the large anharmonicity of its vibrations. There are only limited attempts to solve the vibrational and ro-vibrational problems using full-dimensionality [47,[57][58][59][60]. Benderskii and Vetoshkin [57] used a perturbative approach to study the tunneling dynamics of internal rotation.…”

“…There are only limited attempts to solve the vibrational and ro-vibrational problems using full-dimensionality [47,[57][58][59][60]. Benderskii and Vetoshkin [57] used a perturbative approach to study the tunneling dynamics of internal rotation. Lauvergnat and Nauts [58] also concentrated on these levels in both reduced and full dimensionality.…”

Rovibrational energies and spectroscopic constants of the H system in the electronic states 1Sσ, 7iσ, 5fπ, 5gπ, 6iπ, and 6iϕ

“…The Hamilton–Jacobi equation (HJE) has been recently used to describe several problems such as chemical reaction dynamics 1; band edge for periodic potentials 2; bound state of wave functions 3; the WKB approximation 4; the multidimensional wave functions and tunnel splitting in the vibrational spectrum of a nonrigid molecule of H 5, yielding the correct value of the ground state energy 6, and the atomic ground‐state binding energy of the H e atom 7.…”