Molecular chirality and the fundamental symmetries of physics: Influence of parity violation on rovibrational frequencies and thermodynamic properties

Abstract

We introduce the topic of fundamental symmetries of physics in relation to molecular chirality by a brief review of the development and current status of the theory of parity violation in chiral molecules. We then discuss in some detail CHBrClF (bromochlorofluoromethane) as a test case, to which the work of André Collet has contributed importantly. For this molecule and its isotopomers, we report here the first detailed theoretical calculations of the influence of parity violation on statistical thermodynamic properties. High-quality ab initio calculations (RPA, random phase approximation, and CASSCF, complete-active-space self-consistent-field) were performed to determine the small energy difference between R- and S-enantiomers of H and D isotopomers of bromochlorofluoromethane (CHBrClF, CDBrClF), and fluorooxirane ((1)H(3)C(2)OF) introduced by the parity-violating weak interaction. Together with vibrational and rotational frequency shifts caused by parity violation, these were used to determine the statistical thermodynamic quantities from the corresponding partition functions within the separable harmonic and in part also anharmonic adiabatic approximation. Temperature-dependent equilibrium constants for the stereomutation were calculated and are discussed in relation to biochemical homochirality.

Synthetic routes for a variety of halogenated (chiral) acetic acids from diethyl malonate

“…32 and 33) which can be related to the parity violating energy difference, D pv E, between both enantiomers according to D pv E z D r H , thus leading to slightly different absorption spectra of isolated R and S molecules. Attempts to measure these effects have failed until today, [32][33][34] but molecular parity violation is still an active eld of research. The synthesis of these halomethanes usually starts from perhalogenated ethene (see Scheme 1).…”

The Search for Parity Violation in Chiral Molecules

“…Concerning the accurate treatment of the vibrational spectrum of CHFClBr and CDFClBr [181], Rauhut et al [182] used coupled-cluster theory (CCSD(T)) for the total electronic energy and truncated vibrational configuration interaction to produce fundamental frequencies of a few wave number accuracy compared to experiment [183,184]. Similarly, good results were achieved for CHFClI and CDFClI [185].…”

Mode-selective stereomutation tunneling and parity violation in HOClH+ and H2Te2 isotopomers

“…In particular a complete realization of this experiment in the infrared range would be possible, for which our calculations of the corresponding infrared tunneling spectra are of the highest significance. Of course, also the approaches using parity violating frequency shifts (without measuring E pv ) could be used [14,15,[29][30][31]70] and we plan also calculations for such frequency shifts particularly for the D 2 Te 2 isotopomer, where these could be experimentally relevant. Given the particular spectroscopic simplicity of this compound, it may thus serve one day as prototypical for spectroscopic measurements of parity violation as it is prototypical in neutralization-reionization mass spectroscopy [71].…”

“…The recent theoretical discovery that E pv is predicted to be one to two orders of magnitude larger [21][22][23][24] than anticipated from earlier calculations [18] has given new impetus to the field and the present work contributes to the new effort in this field [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. From both an experimental and theoretical point of view, it would be of interest to study particularly simple prototype molecules or ions.…”