First, I developed a path-following GF method for describing the coupling between vibration and LAM of methanol. In semi-rigid molecules, the curvilinear- (c-) normal coordinates are obtained at the equilibrium structure of the molecule based on the GF method. However, methanol has three equivalent minima due to the internal rotation of the CH3 unit. In our path-following GF method, the c-normal coordinates were obtained along the minimum energy path along the CH3 internal rotation. The coefficient vectors are obtained by taking the average between three equivalent minima. Using the developed code, I have successfully calculated the vibrational states of methanol, to which the coupling between the LAM-SAM contributes [1].
The calculations of the vibrational wavefunctions are successful because the vibrational energies are converged to an error of 1-2 cm-1 with respect to the vibrational basis set size, but a significant deviation from the experiment (20 cm-1) is found in the combination band region. This result encourages me to develop the potential energy surface (PES) of methanol. I developed a new PES by collaborating with Gábor Czakó‘s group (Szeged Univ.). The improvement from the previous PES is that 1) The geometry points are carefully selected with Robosurfer code, 2) The employed basis sets (cc-pVTZ-F12) are larger than the ones employed in the previous work (aug-ccpVDZ-F12), and 3) The numbers of geometry points and fitting coefficients employed for fitting are greater than those in the previous work. Using the new PESs, finally our computation agrees with the experiment within the root-mean-square-error of 2 cm-1 [2]. At the proposal stage of the research, I had planned to stay at the University of Szeged for two months. However, since I was able to acquire the necessary skills during a one-week stay, I shortened the duration and conducted discussions via email if needed.
The code developed for methanol was also applied to the PV search. The CXYZOH (X, Y, Z = H, F, Cl, Br, I) molecules were the target molecules. In addition to the vibrational calculation, I also carried out the relativistic calculation to obtain the parity-violating energy (Epv) using the DIRAC code. According to my calculation, the transition between three wells due to the CXYZ internal rotation is 100 times more sensitive to the PV shift than the conventional stretch mode. In the CHBrIOH molecule, the largest PV shift reaches 3.2 Hz [3].
The integration between the property calculations and floppy molecules was not limited to methanol. The hyperfine interactions, which are magnetic interaction between proton spin and an interaction between the external magnetic fields, and molecular rotation, were first reported for H3+ molecule. The spin-rotation and spin-spin coupling constant of H3+ were calculated for each grid point required for vibrational computations. I first reported the splitting of the molecular spectra of H3+ due to the hyperfine interaction. The result has been published in Phys. Rev. Lett [4].
[1] A. Sunaga, G. Avila, and E. Mátyus, J. Chem. Theory Comput. 20, 8100 (2024).
[2] A. Sunaga, T. Győri, G. Czakó, and E. Mátyus, J. Chem. Phys. 163, 064101 (2025).
[3] A. Sunaga, J. Chem. Phys. 162, 064302 (2025).
[4] G. Avila, A. Sunaga, S. Komorovsky, and E. Mátyus, Phys. Rev. Lett. 135, 043003 (2025).
