Ab Initio Random Matrix Theory of Molecular Electronic Structure

TL;DR

This paper demonstrates that random matrix theory universality applies to molecular electronic spectra computed via ab initio methods, revealing universal spectral statistics and transitions under magnetic fields in complex molecules.

Contribution

It shows that RMT universality holds for ab initio molecular spectra and explores spectral behavior under magnetic fields, connecting quantum chemistry with statistical physics.

Findings

Spectra exhibit Wigner-Dyson statistics for low-symmetry molecules.

GOE statistics persist in extended helicene chains below ionization threshold.

Magnetic fields induce a transition from GOE to GUE statistics at high field strengths.

Abstract

We use ab initio electronic-structure methods to investigate random-matrix theory (RMT) universality in molecular electronic structure. Using single-reference electronic structure methods, including Hartree-Fock, configuration-interaction singles (CIS), density functional theory, and linear-response time-dependent density-functional theory, we compute single-particle orbital energies and many-electron excitations of several representative molecules (benzene, alanine, 1-phenylethylamine, methyloxirane, and helicene chains). For generic low-symmetry geometries, the unfolded spectra of these ab initio Hamiltonians exhibit Wigner-Dyson level statistics of the Gaussian orthogonal ensemble (GOE). For extended helicene chains we explicitly restrict to bound valence excitations below the ionization threshold and still observe GOE statistics, indicating that the RMT universality is present for physical states of direct relevance to real molecules. We further explore the electric and magnetic field dependence of the molecular electronic spectra. The variance of electric polarizability (level curvature K) is predicted to be non-analytic in the magnetic field which serves as an infrared cutoff, <K^2> proportional to log(1/|B|). We observe a transition to the Gaussian unitary ensemble (GUE) by increasing the magnetic fields, although it occurs only at magnetic fields far beyond experimentally accessible scales. Our results indicate that random matrix universality provides a general framework for organizing ab initio predictions of interacting electron spectra in complex systems.