KEYWORDS:ab initio calculations ¥ chirality ¥ molecular parity violation ¥ NMR spectroscopy Chiral shift reagents and chiral solvents find wide application in NMR spectroscopy for determining the enantiomeric composition of nonracemic mixtures. But even without those external chiral influences and in the absence of aggregation effects that give rise to homo-and heterochiral dimers and oligomers, the NMR spectra of mirror-image compounds differ. This is predicted by the electroweak theory, which is the unified theory of the electromagnetic and the weak interaction, [1±3] and can be attributed to an intrinsic chiral influence caused by the weak force. Although in molecular systems the electromagnetic force prevails by orders of magnitude over the weak force, it is the parity-violating property of the weak force (see discussion in refs. [4 ± 6]) that is expected to give rise to remarkable effects in chiral molecules, for instance, in the form of the intriguing parityviolating energy difference DE pv between enantiomers [4±27] or as parity-violating frequency shifts between the NMR, the microwave, the infrared, the ultraviolet or even Mˆssbauer spectra of the two mirror-image molecules of a chiral compound. [9, 28±36] Therefore, parity violation plays a key role in our modern understanding of the phenomenon chirality.In contrast to molecular physics, where parity nonconservation can give rise to effects in static systems, in atomic physics parity violation is typically only manifested in transition processes (see for instance refs. [37 ± 41]). In the latter field of research, parity nonconservation was already experimentally detected a few decades ago. In molecular systems, however, it still awaits its first successful measurement. Crucial for the preparation and, in particular, for the later interpretation of successful experiments are accurate theoretical calculations of parity-violating effects. Since the computational approaches are presently employed to predict effects from this fundamental symmetry violation, there is a clear need for methods that allow a systematic improvement of the quality of the calculations. This is one major conclusion to be drawn from calculations of parityviolating energy differences DE pv between enantiomers, since current theoretical approaches [4,14,15,19,24, 42,43] often find absolute values of DE pv that are one to two orders of magnitude larger than the values predicted with early methodologies. solutions were mixed and further stirred for 2 h. From this mixture, with a molar composition of TEOS:P123:H 2 O:HCl:EtOH:dye of 1:9.4 Â 10 À3 :5:8.5 Â 10 À3 :10.4:1 Â 10 À4 ± 2 Â 10 À3 , thin films were prepared by dip coating onto glass slides at 10 cm min À1 . Prior to dip coating the glass slides were cleaned by water and isopropanol. X-ray diffraction patterns were measured on a Scintag X2 (Cu,Ka radiation) powder diffractometer. A JEOL 2000FX electron microscope operating at 200 kV was used for the TEM investigations. For TEM measurements the films were removed from the substrate...

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

One promising route towards the first experimental verification of parity violation ͑PV͒ in chiral molecular systems is the detection of line splittings between nuclear magnetic resonance ͑NMR͒ spectra of enantiomers. Those numerical methods which can be systematically refined and allow for an accurate and reliable prediction of molecular PV effects will play a crucial role for the preparation and interpretation of such experiments. In this work the ab initio calculation of isotropic parity-violating NMR-shielding constants ͑ PV ͒ within coupled cluster and multiconfiguration linear response approaches to electroweak quantum chemistry is reported and the results are compared to data obtained at the uncoupled density functional theory level. The PV of the heavy nuclei in hydrogen peroxide, disulfane and diselane ͑H 2 X 2 with X = 17 O, 33 S, 77 Se͒ computed at the coupled cluster singles and doubles level are found to typically deviate from their electron-uncorrelated counterparts by approximately 20%, while in 2-fluorooxirane, electron correlation alters PV of individual nuclei by almost a factor of 2. It is therefore imperative in the accurate prediction of parity-nonconserving phenomena in NMR experiments that systematically improvable electron-correlating electroweak quantum chemical approaches, such as those presented in this study, are employed.

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.