Abstract
Distortions are ubiquitous in nature. Under perturbations such as stresses, fields or other changes, a physical system reconfigures by following a path from one state to another; this path, often a collection of atomic trajectories, describes a distortion. Here we introduce an antisymmetry operation called distortion reversal that reverses a distortion pathway. The symmetry of a distortion pathway is then uniquely defined by a distortion group; it has the same form as a magnetic group that involves time reversal. Given its isomorphism to magnetic groups, distortion groups could have a commensurate impact in the study of distortions, as the magnetic groups have had in the study of magnetic structures. Distortion symmetry has important implications for a range of phenomena such as structural and electronic phase transitions, diffusion, molecular conformational changes, vibrations, reaction pathways and interface dynamics.
Highlights
IntroductionDistortion symmetry has important implications for a range of phenomena such as structural and electronic phase transitions, diffusion, molecular conformational changes, vibrations, reaction pathways and interface dynamics
Why is the concept of distortion-reversal symmetry and distortion groups necessary? It is instructive to look at the history, where a similar question has been posed for over 45 years regarding the need for time-reversal symmetry and magnetic groups versus representation analysis for the study of magnetic structures[25,26]
The irreps of a distortion group classify the ways in which the symmetry can be broken by perturbations of the distortion pathway, potentially leading to lower-energy pathways than would be achieved by only applying nudged elastic band (NEB) or related methods, such as CI-NEB
Summary
Distortion symmetry has important implications for a range of phenomena such as structural and electronic phase transitions, diffusion, molecular conformational changes, vibrations, reaction pathways and interface dynamics. We discovered that a somewhat similar concept was introduced several decades ago in transition-state theory in the limited context of reversing reactants and products in simple molecular reactions[1,2,3]. We show that they can predict the form of tensors that describe any property change of a system as a function of a general distortion parameter We demonstrate that this symmetry framework can be applied to nuclear positions, but to the electronic structure itself, including the Berry phase of a distortion. Double-antisymmetry groups can describe the symmetry of distortions of magnetic molecules and crystals, where both distortion-reversal and time-reversal antisymmetries become relevant
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