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
Dedicated to Professor Duilio Arigoni on the occasion of his 75th birthdayWe present calculations on the parity-conserving and the parity-violating potentials in several MeOH isotopomers for the torsional motion by the newly developed methods of electroweak quantum chemistry from our group. The absolute magnitudes of the parity-violating potentials for MeOH are small compared to H 2 O 2 and C 2 H 4 , but similar to C 2 H 6 , which is explained by the high (threefold) symmetry of the torsional top in MeOH and C 2 H 6 . −Chiral× and −achiral× isotopic substitutions in MeOH lead to small changes only, but vibrational averaging is discussed to be important in all these cases. Simple isotopic sum rules are derived to explain and predict the relationships between parity-violating potentials in various conformations and configurations of the several isotopomers investigated. The parity-violating energy difference D pv E E pv (R) À E pv (S) between the enantiomers of chiral CHDTOH, first synthesized by Arigoni and co-workers, is for two conformers ca. À 3.66 ¥ 10 À17 and for the third one 7.32 ¥ 10 À17 hc cm À1 . Thus, for D pv E, the conformation is more important than the configuration (at the equilibrium geometries, without vibrational averaging). Averaging over torsional tunneling may lead to further cancellation and even smaller values.
Die elektroschwache Quantenchemie führt zur Vorhersage eines neuartigen Isotopeneffekts bei Molekülen, die nur durch Isotopensubstitution chiral sind (siehe Bild). Die durch das Z‐Boson übertragene Elektron‐Nukleon‐Wechselwirkung erzeugt paritätsverletzende Energiedifferenzen ΔpvE zwischen Isotopenantiomeren. Bei der Substitution schwerer Isotope wie 35Cl/37Cl ist ΔpvE fast so groß wie bei gewöhnlichen chiralen Molekülen. Das ist wichtig für spektroskopische Experimente zur Paritätsverletzung.
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