Periodic Reporting for period 1 - QDMAP (Quantum dynamics of floppy systems beyond Coulomb interactions: magnetic and parity-violating effects)
Periodo di rendicontazione: 2023-09-01 al 2025-08-31
Small amplitude motions (SAMs) like stretch and bending motions can be described by methods based on harmonic approximation. However, the harmonic approximation cannot describe large-amplitude motion (LAM) such as inversion motion and internal rotation. To analyze these targets, quantum dynamics (QD) methods have been developed, and it is a frontier in theoretical molecular spectroscopy. One of the directions in the theoretical spectroscopic field is to make the calculation faster and available for larger systems, but actually, especially for floppy molecules and complexes, there are two less explored chemical and physical effects that can split the spectrum: hyperfine interactions and parity-violation. Hyperfine interaction is a magnetic interaction, for example, the spin-spin interaction between protons, and the interaction between an external magnetic field and molecular rotation. Parity-violation (PV) interaction is mediated by the Z-boson, which generates the energy difference between enantiomers.
The purpose of this study is to integrate molecular electronic properties such as hyperfine and PV interactions and the QD theory for large-amplitude motion. This study aims to develop a methodology for the coupling between the magnetic properties of molecules and the molecular rotation or vibration of molecules, including LAM.
The PV shift does not appear in 2-3 atomic molecules, and at least 4-5 atomic molecules are required to investigate shift. To investigate the PV effect in five-atomic molecules, a new QD program for methanol is required. The goal of my project is to integrate molecular properties and the QD program as mentioned above, but methanol itself is a very interesting target in astrochemistry and fundamental physics. In astrochemistry, it is used as a probe to measure the external magnetic field from the hyperfine splitting of methanol. In fundamental physics, it has been reported that the time and space dependence of the fundamental constants, such as the proton-to-electron mass ratio, is sensitive in the LAM.
The purpose of this study is to integrate molecular electronic properties such as hyperfine and PV interactions and the QD theory for large-amplitude motion. This study aims to develop a methodology for the coupling between the magnetic properties of molecules and the molecular rotation or vibration of molecules, including LAM.
The PV shift does not appear in 2-3 atomic molecules, and at least 4-5 atomic molecules are required to investigate shift. To investigate the PV effect in five-atomic molecules, a new QD program for methanol is required. The goal of my project is to integrate molecular properties and the QD program as mentioned above, but methanol itself is a very interesting target in astrochemistry and fundamental physics. In astrochemistry, it is used as a probe to measure the external magnetic field from the hyperfine splitting of methanol. In fundamental physics, it has been reported that the time and space dependence of the fundamental constants, such as the proton-to-electron mass ratio, is sensitive in the LAM.
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).
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).
This research highlights the importance and potential of theoretical molecular spectroscopy in verifying the origin of organic molecules and amino acids in space.
Previously, this was done by comparing interstellar spectra obtained with telescopes to known laboratory measurements. However, this approach had limitations: it could not analyze molecular species that cannot be synthesized in the laboratory or spectra in energy bands, which makes spectroscopic experiments difficult.
This research represents a crucial first step toward the ab initio assignment of molecular spectra, including those of LAM, and further progress in this research is anticipated.
Some experimentalists pay attention to the enhancement of PV shift on methanol-like chiral molecules. More expansion of this study is strongly encouraged, e.g. full-dimensional variational vibrational computation and the development of PES for that, as well as a line-list including transition intensity for the transition that is sensitive to the PV search.
The result of the hyperfine interaction of the H3+ molecule is the first step in calculating the hyperfine interactions of bigger molecules, such as methanol. These highly accurate calculations can contribute to the assignment of spectra measured in the universe.
Previously, this was done by comparing interstellar spectra obtained with telescopes to known laboratory measurements. However, this approach had limitations: it could not analyze molecular species that cannot be synthesized in the laboratory or spectra in energy bands, which makes spectroscopic experiments difficult.
This research represents a crucial first step toward the ab initio assignment of molecular spectra, including those of LAM, and further progress in this research is anticipated.
Some experimentalists pay attention to the enhancement of PV shift on methanol-like chiral molecules. More expansion of this study is strongly encouraged, e.g. full-dimensional variational vibrational computation and the development of PES for that, as well as a line-list including transition intensity for the transition that is sensitive to the PV search.
The result of the hyperfine interaction of the H3+ molecule is the first step in calculating the hyperfine interactions of bigger molecules, such as methanol. These highly accurate calculations can contribute to the assignment of spectra measured in the universe.