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Related Experiment Video

Updated: May 12, 2026

A Protocol for Real-time 3D Single Particle Tracking

A Protocol for Real-time 3D Single Particle Tracking

Published on: January 3, 2018

First-order Dyson coordinates and geometry.

Matthew R Hermes¹, So Hirata

¹Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA.

The Journal of Physical Chemistry. A

|April 13, 2013

Summary

This summary is machine-generated.

New Dyson coordinates and geometry simplify vibrational analysis in chemistry and physics. These mathematical tools unify theories like VSCF and self-consistent phonon methods for better computational accuracy.

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Published on: June 8, 2018

Area of Science:

Quantum chemistry
Solid-state physics
Computational physics

Background:

Vibrational structure theory often relies on approximations.
Existing methods like VSCF and self-consistent phonon methods have limitations.
A unified theoretical framework is needed for accurate vibrational analysis.

Purpose of the Study:

Introduce novel mathematical constructs: Dyson coordinates and Dyson geometry.
Provide a unified perspective on vibrational theories.
Simplify calculations involving anharmonic corrections.

Main Methods:

Developed Dyson coordinates as a unitary transformation of normal coordinates.
Defined Dyson geometry as a specific point on the potential energy surface.
Utilized diagrammatic perturbation theory for corrections.

Main Results:

First-order Dyson coordinates diagonalize harmonic force constants and self-energy corrections.
First-order Dyson geometry aligns with VSCF vibrationally averaged geometry in the bulk limit.
Established a connection between Dyson coordinates/geometry and existing vibrational methods.

Conclusions:

Dyson coordinates and geometry offer a unified framework for vibrational analysis.
These constructs bridge vibrational self-consistent field theory and solid-state physics methods.
The introduced methods enhance the accuracy and understanding of molecular vibrations and lattice dynamics.