An Effective Hamiltonian for Symmetric Diarylmethanes from a Series of Analogous Quantum Chemical Models

TL;DR

This paper develops a unified effective Hamiltonian model to describe the electronic structure of symmetric diarylmethanes, revealing systematic changes in charge distribution across the series using advanced quantum chemical methods.

Contribution

It introduces a single functional form for the Hamiltonian that captures the low-energy electronic states of various symmetric diarylmethanes based on an isolobal analogy.

Findings

The effective Hamiltonian fits all dyes with a single functional form.

The bridge-charged state's structure varies regularly across the series.

Charge on the bridge switches from electron pair to hole along the series.

Abstract

We propose a single effective Hamiltonian to describe the low-energy electronic structure of a series of symmetric cationic diarylmethanes, which are all bridge-substituted derivatives of Michler's Hydrol Blue. Three-state diabatic Hamiltonians for the dyes are calculated using four-electron three-orbital state-averaged complete active space self-consistent field and multi-state multi-reference perturbation theory models. The approach takes advantage of an isolobal analogy that can be established between the orbitals spanning the active spaces of the different substituted dyes. The solutions of the chemical problem are expressed in a diabatic Hilbert space that is analogous to classical resonance models. The effective Hamiltonians for all dyes can be fit to a single functional form that depends on the mixing angle between a bridge-charged diabatic state and a superposition representing the canonical resonance. We find that the structure of the bridge-charged state changes in a regular fashion across the series. The change is consistent with an inversion of the sign of the charge carrier on the bridge, which changes from an electron pair to a hole as the series is traversed.