1. Introduction
Isotopes, homo-electronic nuclei, showing distinct properties due to the different nuclear spins1,2, are omnipresent in the universe3. Traditionally, different properties have been associated with the mass difference and observed for instance in the variation of rate or equilibrium constant of two reactions (i.e. kinetic isotope effect or a thermodynamic isotope effect4. In principle, isotopes can occur independent of mass and spin because of symmetry restrictions on the molecular wavefunction leading to different symmetry selection rules for different isotopomers5. In this work we refer to the isotopic effect as a change of any property between molecules with distinct isotopic components (isotopomers). Nevertheless, the isotopic effects related to the lightest elements are most pronounced. The natural abundance of atomic isotopes is then reflected in the isotopic composition of molecules, but the artificial isotopic substitution– mainly of hydrogen (H) to deuterium (D) has been used in many applications. One group of applications is related to the identification of species, or elucidation of molecular structures, by enhancing the amount of available experimental data (in mass spectrometry, optical spectroscopies, nuclear magnetic resonance (NMR) spectroscopy)6–8. Alternatively, isotopic labeling allows one to mark and distinguish between specific parts of molecular systems, for instance in biomolecular chemistry and deuterium labeling for reaction analysis9–15. Among the isotopic substitutions of particular interest are those which change formally achiral molecules into chiral ones. Such newly created species can then be recognized by chiroptical spectroscopies, while Quack and co-workers reported the first quantitative investigations of a ground-state energy difference for the enantiomers of molecules that are chiral only by isotopic substitution16.
The origins of chiral molecules in space and its relation with the chiral asymmetry of life on the Earth still remains a mystery17. So far the only chiral molecule detected in the interstellar medium (ISM) is methyl-oxirane, however as it was identified by means of achiral (rotational) signals its enantiomeric composition is unknown18. D and L forms of amino acids have been found in meteorites and comets, but L-enantiomeric excesses have been also established 17. As the star-planet formation regions are characterized by very high D/H ratio, contributing significantly to the formation of heavier molecules19, isotopically induced chirality maybe highly relevant in an astrochemical context. Oba et. al . reported experimental evidence of chiral glycine formation by the surface reaction of normal glycine in solid form with deuterium atoms at conditions simulating interstellar molecular clouds20. Chiral glycine is a known chiral trigger for amplifying an enantiomeric excess under certain conditions21: these results add to the long standing debate on the origin of homochirality. The investigation of Kawasakiet. al . discovered that achiral meteoritic amino acids that included glycine with hydrogen isotope (D/H) chirality were the source of chirality in asymmetric autocatalysis with amplification of enantiomeric excess to enable the creation of highly enantioenriched 5-pyrimidyl alkanols21. Kawasaki et. al found that the chirality of the S and R enantiomers was mainly attributable to the very small difference between the C-D and C-H bond-lengths associated with the alpha carbon of glycine21–23. The development of a highly sensitive method for the detection of isotopic chirality in meteoritic organic compounds such as amino acids24 with an achiral framework and isotopic enrichment therefore remains a challenging subject25.
The unknown chirality-helicity equivalence, that associates chirality with a helical characteristic, was recently located although not quantified by some of the current authors26 and was used to distinguish the S and R stereoisomers of lactic acid in agreement with the naming schemes from optical experiments. Some of the current authors have very recently published the derivation of the chirality-helicity equivalence that quantifies the chiral character in formally achiral species27. Consistency with our work was found from experiments by Beaulieu et al. on neutral molecules28 that utilize coherent helical motion of bound electrons. Abstract chirality measures for non-rigid objects have been used to associate optical rotation with the structure of a molecule29.
Within the Born-Oppenheimer (B.O.) approximation the electronic spectra of isotopomers are identical because the electronic Hamiltonian\({\hat{H}}_{e}\) in the BO approximation is not dependent on nuclear masses despite differences in their nuclei dynamics. Therefore isotope sensitivity is typically achieved via nuclear dynamics, for example by considering vibrational spectra. In this contribution we explore the effect of non-adiabatic coupling corrections and find that despite subtle differences that they induce in geometries those differences are sufficient to be reliably captured by non-scalar QTAIM quantities.