# Predicting S1 TDDFT Energies from ZINDO Calculations Using Message-Passing ΔML with Electronically Informed Descriptors

## TL;DR

This paper introduces a machine learning method that improves the accuracy of energy predictions for organic molecules, making low-cost calculations as reliable as more expensive ones.

## Contribution

A novel ΔML framework using message-passing neural networks and electronic descriptors to correct ZINDO calculations toward TDDFT accuracy.

## Key findings

- The ΔML model improved ZINDO S1 energy correlation from 0.77 to 0.96 on a 9500 molecule test set.
- The model achieved a 0.99 correlation on 24,000 molecules when mapping ZINDO to ωB97X-D/6-31G* energies.
- The method also enhanced S1 oscillator strength predictions from 0.524 to 0.839 correlation.

## Abstract

We present a machine
learning approach (ΔML) capable of enhancing
the accuracy of semiempirical excited-state energy calculations to
a level close to that of Time-Dependent Density Functional Theory
(TDDFT). Using a data set of 7600 organic π-conjugated molecules
calculated at the ZINDO and M06-2X/3-21G* TDDFT computational levels,
we trained a set of models to learn the systematic errors of the low-level
method and correct it toward higher-level accuracy values. The best
performing model improved the correlation of ZINDO S1 energy
predictions from 0.77 to 0.96 on a 9500 molecule test set of TDDFT
target energies. Our ΔML-ZINDO model presents a negligible additional
cost (∼2 ms per molecule) to a standard ZINDO calculation (∼2
s per molecule), enabling the computational screening of large data
sets of molecules. Critical to the performance of the model is the
AttentiveFP Message-Passing Neural Network with added electronic information
derived from ZINDO calculations such as particle-hole densities. We
also investigate the utility of the Morgan fingerprint and a novel
descriptor designed to capture the electronic structure of molecules:
a molecular orbital-weighted radial distribution function. The ΔML
framework is retrainable to other low- and high-level calculation
pairs, achieving an improvement in correlation from 0.88 to 0.99 on
a test set of 24,000 molecules from the QCDGE data set, when mapping
ZINDO to ωB97X-D/6-31G* energies. We also adapt ΔML-ZINDO
for S1 oscillator strength prediction, improving ZINDO
predictions from a correlation of 0.524 to 0.839 on our M06-2X/3-21G*
target test set, thus enabling the identification of emissive molecules.