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.