Isotopic Chirality and Molecular Parity Violation

Abstract

Dedicated to Richard N. Zare on the occasion of his 65th birthday Studies of isotope effects have a long tradition in providing fundamental insights into molecular spectroscopy and reaction dynamics, [1,2] usually dealt with theoretically on the basis of the electromagnetic interaction that is parity conserving, i.e. remains unchanged under space inversion at the origin. [3][4][5] Isotope effects are frequently caused by mass differences of the isotopes. There are also isotope effects due to the different nuclear spins of the isotopes, [6] and, in principle, isotope effects can arise independent of mass and spin because of symmetry restrictions on the molecular wavefunction leading to different symmetry selection rules for different isotopomers.[7] Here we report the first quantitative investigations of a new isotope effect, which leads to a ground-state energy difference D pv E % D pv H 0 0 /N A for the enantiomers of molecules that are isotopically chiral, i.e. chiral only by isotopic substitution (Figure 1). This parity-violating isotope effect arises from the electroweak interaction between electrons and nucleons, mediated by the Z-boson, and thus depends upon nucleonic composition. Our calculations are of interest in relation to efforts of measuring D pv E in enantiomers, [5,8] and they are also important for the fundamental understanding of isotope effects and molecular chirality. The present work opens a new avenue in this field by providing quantitative calculations on such chiral isotopomers in the framework of electroweak quantum chemistry [9] including the weak nuclear force. Since recent theoretical approaches predict absolute values of D pv E that can be orders of magnitude larger [9][10][11][12] than anticipated on the basis of earlier calculations, [14,15] there is new hope that accurate measurements and calculations, particularly for molecules with light atoms, will provide additional insights into the standard model of high-energy physics. [5,16] We refer here to recent articles with extensive further references. [4,5,10,12] In this context we address and answer the following questions: 1. How large is D pv E in isotopically chiral systems compared to "ordinary" enantiomers? 2. Is D pv E dominated here by the parity-violating potential at the equilibrium geometry or by vibrationally averaging the parity-violating potential? 3. How does vibrational excitation change D pv E (i.e. D pv E*) in such systems compared to "ordinary" enantiomers where this question was addressed previously? [17] The answers to these questions will help in planning future experiments possibly including isotopic enantiomers. We study the phosphane derivatives PHDX (X = F, 35 Cl, 37 Cl, 79 Br, 81 Br) and P 35 Cl 37 ClY (Y = F,H,D) with these goals in mind. While isotopic chirality has been considered for some time, [3,[18][19][20] as an isotope effect through variation of

Polyatomic Candidates for Cooling of Molecules with Lasers from Simple Theoretical Concepts

“…Using the scheme from the above paragraphs it is also possible to identify chiral molecular structures having a quasidiagonal FC matrix. One way is isotopic substitution to a known molecule [29,31]. The chiral methyl group CHDT is well established in chemistry (see review [32] for general aspects as well as ref.…”

High‐Resolution Fourier Transform Infrared Spectroscopy

“…The chiral isotopomer CH 35 Cl 37 ClF is of potential importance for general aspects of isotopic chirality and parity violation (Quack 1989b, Berger et al 2005, Albert and Quack 2007a. In particular, the rovibrational analysis of the 2ν 3 mode of CH 35 Cl 37 ClF can make it possible to carry out quasiresonant two-photon transitions with a CO 2 laser based on the assignments of the 2ν 3 band (Albert et al 2007).…”

The Search for Parity Violation in Chiral Molecules

“…They pointed out that even the coupling terms in the cubic force field between different normal modes are important, which are usually neglected. Isotope effects in chiral phosphorus compounds of the form PXYZ (XYZ ¼ H, F, Cl, and Br with different isotopes) have been studied by Quack and coworkers [189]. These molecules are all good test cases for theoretical investigations, but have not yet been prepared, and as such may be thermodynamically unstable.…”