IMElfremov 10sept2024

CAPT Seminar - Ilia M. EfremovMardi 10 septembre, 9h40 - Amphi IPREM

Le 10 sept. 2024 à 09h40

Ilia M. Efremov
Ph. D. Student, Lomonosov Moscow State University, Chemistry Department

"Ab Initio Direct Vibration-Rotation Problem Solved by the Operator Perturbation Theory. Calculation of Spectroscopic Constants, Transition Intensities and Simulation of Spectra"

(Ilia M. Efremov is Professor Sergey Krasnoshchekov's thesis student, with whom we have been collaborating for several years.)

ABSTRACT
The vibration-rotation spectra of small semi-rigid molecules can be predicted via the variational procedure with exact KEO and ab initio PES with a subsequent small adjustment to fit experimental spectra. A conceptually different inverse approach for deciphering observed line lists is based on a step-by- step procedure of fitting suitable effective Hamiltonians and extrapolation for assigning of rovibrational transitions. The bridge between these theories can be built using the operator Van Vleck perturbation theory CVPT(n) that uses exponential unitary transformations in order to diagonalize rovibrational Hamiltonian providing ab initio spectroscopic constants, parameters of effective dipole moment operators and line lists.

The direct vibration-rotation CVPT can be systematically formulated in operator formalism using the Watson Hamiltonian for a wide range of small and medium sized molecules. The major computational complication of CVPT(n) arises due to the necessity of calculating rotational commutators involving ladder operators of angular momentum (𝐽_z, 𝐽₊, 𝐽_–), but the problem can be efficiently solved using the normal ordering. For calculation of transition intensities, unitary transformations of the dipole moment operator can be made using the normal ordering with the Wigner 𝐷¹_0,ε -functions.

The obtained effective Hamiltonian and dipole moment operators can be further used for calculation of simulated IR spectra for a chosen spectral range and vibrational transitions. Rotational unitary transformations produce centrifugal distortion spectroscopic constants of Watson effective Hamiltonians in A- or S-reductions. A few numerical examples for molecules up to the size of diborane (B₂H₆) is given, demonstrating the efficiency of the developed approach.

Another scientific direction of our research group is the analysis of experimental spectra. As an example, the vibrational-rotational analysis of the mixture of HCFC-22 isotopologues (CHClF₂) enriched in ¹³C is analyzed in the spectral region of 750-850 cm^-1.