Simple model for Crystal Field Theory

TL;DR

This paper introduces a simplified model for predicting 3d orbital splitting in metal ions within ligand environments, using a delta function to represent ligand interactions, and evaluates its effectiveness across various cases.

Contribution

It presents a novel, simplified approach to crystal field splitting prediction using a delta function model, highlighting its successes and limitations.

Findings

Model accurately predicts orbital splitting in several cases.

Model fails in some complex ligand environments.

Provides insights into the applicability of simplified models.

Abstract

We investigate a simple model for the prediction of the splitting of the $3d$ orbitals of a metal ion in the environment of ligands. The electrons are considered to be independent and their interaction with the ligands is represented by the Dirac delta function in three dimensions. We discuss several cases where the model is successful and a few ones where it is not.