Instanton calculations of tunneling splittings in chiral molecules

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

The Interplay between Tunneling and Parity Violation in Chiral Molecules

In this review, the concepts of quantum tunneling and parity violation are introduced in the context of chiral molecules. A particle moving in a double well potential provides a good model to study the behavior of chiral molecules, where the left well and right well represent the L and R enantiomers, respectively. If the model considers the quantum behavior of matter, the concept of quantum tunneling emerges, giving place to stereomutation dynamics between left- and right-handed chiral molecules. Parity-violating interactions, like the electroweak one, can be also considered, making possible the existence of an energy difference between the L and R enantiomers, the so-called parity-violating energy difference (PVED). Here we provide a brief account of some theoretical methods usually employed to calculate this PVED, also commenting on relevant experiments devoted to experimentally detect the aforementioned PVED in chiral molecules. Finally, we comment on some ways of solving the so-called Hund's paradox, with emphasis on mean-field theory and decoherence.

Exact tunneling splittings from symmetrized path integrals

We develop a new simulation technique based on path-integral molecular dynamics for calculating ground-state tunneling splitting patterns from ratios of symmetrized partition functions. In particular, molecular systems are rigorously projected onto their J = 0 rotational state by an "Eckart spring" that connects two adjacent beads in a ring polymer. Using this procedure, the tunneling splitting can be obtained from thermodynamic integration at just one (sufficiently low) temperature. Converged results are formally identical to the values that would have been obtained by solving the full rovibrational Schrödinger equation on a given Born-Oppenheimer potential energy surface. The new approach is showcased with simulations of hydronium and methanol, which are in good agreement with wavefunction-based calculations and experimental measurements. The method will be of particular use for the study of low-barrier methyl rotations and other floppy modes, where instanton theory is not valid.

Proton-Tunneling Dynamics along Low-Barrier Hydrogen Bonds: A Full-Dimensional Instanton Study of 6-Hydroxy-2-formylfulvene

Understanding the dynamics of proton transfer along low-barrier hydrogen bonds remains an outstanding challenge of great fundamental and practical interest, reflecting the central role of quantum effects in reactions of chemical and biological importance. Here, we combine ab initio calculations with the semiclassical ring-polymer instanton method to investigate tunneling processes on the ground electronic state of 6-hydroxy-2-formylfulvene (HFF), a prototypical neutral molecule supporting low-barrier hydrogen-bonding. The results emerging from a full-dimensional ab initio instanton analysis reveal that the tunneling path does not pass through the instantaneous transition-state geometry. Instead, the tunneling process involves a multidimensional reaction coordinate with concerted reorganization of the heavy-atom skeletal framework to substantially reduce the donor-acceptor distance and drive the ensuing intramolecular proton-transfer event. The predicted tunneling-induced splittings for HFF isotopologues are in good agreement with experimental findings, leading to percentage deviations of only 20-40%. Our full-dimensional results allow us to characterize vibrational contributions along the tunneling path, highlighting the intrinsically multidimensional nature of the attendant hydron-migration dynamics.

Heavy-Atom Quantum Tunnelling in Spin Crossovers of Nitrenes

We simulate two recent matrix-isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak-coupling method (based on a linear approximation of the potentials) in describing these deep-tunnelling reactions. The more rigorous approach of semiclassical golden-rule instanton theory in conjunction with double-hybrid density-functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy-atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role at room temperature.

Perspectives on parity violation in chiral molecules: theory, spectroscopic experiment and biomolecular homochirality

The reflection (or ‘mirror’) symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number parity and a fundamental ‘non-observable’ property of space (as defined by an absolute ‘left-handed’ or ‘right-handed’ coordinate system). The discovery of the violation of this symmetry – the non-conservation of parity or ‘parity violation’ – in 1956/1957 had an important influence on the further development of physics. In chemistry the mirror symmetry of space is connected to the existence of enantiomers as isomers of chiral (‘handed’) molecules. These isomers would relate to each other as idealized left or right hand or as image and mirror image and would be energetically exactly equivalent with perfect space inversion symmetry. Parity violation results in an extremely small ‘parity violating’ energy difference between the ground states of the enantiomers which can be theoretically calculated to be about 100 aeV to 1 feV (equivalent to 10⁻¹¹ to 10⁻¹⁰ J mol⁻¹), depending on the molecule, but which has not yet been detected experimentally. Its detection remains one of the great challenges of current physical–chemical stereochemistry, with implications also for fundamental problems in physics. In biochemistry and molecular biology one finds a related fundamental question unanswered for more than 100 years: the evolution of ‘homochirality’, which is the practically exclusive preference of one chiral, enantiomeric form as building blocks in the biopolymers of all known forms of life (the l-amino acids in proteins and d-sugars in DNA, not the reverse d-amino acids or l-sugars). In astrobiology the spectroscopic detection of homochirality could be used as strong evidence for the existence of extraterrestrial life, if any. After a brief conceptual and historical introduction we review the development, current status, and progress along these three lines of research: theory, spectroscopic experiment and the outlook towards an understanding of the evolution of biomolecular homochirality.

The reflection (or ‘mirror’) symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number purity and its violation and has a fundamental relation to stereochemistry and molecular chirality.