Accurate Band Gap Predictions of Semiconductors in the Framework of the Similarity Transformed Equation of Motion Coupled Cluster Theory

Abstract

In this work, we present a detailed comparison between wave-function-based and particle/hole techniques for the prediction of band gap energies of semiconductors. We focus on the comparison of the back-transformed Pair Natural Orbital Similarity Transformed Equation of Motion Coupled-Cluster (bt-PNO-STEOM-CCSD) method with Time Dependent Density Functional Theory (TD-DFT) and Delta Self Consistent Field/DFT (Δ-SCF/DFT) that are employed to calculate the band gap energies in a test set of organic and inorganic semiconductors. Throughout, we have used cluster models for the calculations that were calibrated by comparing the results of the cluster calculations to periodic DFT calculations with the same functional. These calibrations were run with cluster models of increasing size until the results agreed closely with the periodic calculation. It is demonstrated that bt-PNO-STEOM-CC yields accurate results that are in better than 0.2 eV agreement with the experiment. This holds for both organic and inorganic semiconductors. The efficiency of the employed computational protocols is thoroughly discussed. Overall, we believe that this study is an important contribution that can aid future developments and applications of excited state coupled cluster methods in the field of solid-state chemistry and heterogeneous catalysis.

Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

“…Regarding excited state properties of solids, embedding approaches are most suited to systems with a substantial band gap. For such systems, STEOM–CCSD has been shown to provide reliable predictions for band gap energies . For metallic systems, periodic approaches are the method of choice and here the pioneering work using the EOM–CCSD framework is the Gaussian‐based periodic implementation of Chan and coworkers .…”

“…While these are already good results, once the dressing step is also implemented in the PNO basis, the performance of DLPNO–STEOM is expected to approach that of DLPNO–EA and the method will become genuinely O ( N 4 ) scaling. However, already the bt–PNO variant of STEOM can be usefully employed in the computation of band gap energies in the embedding approach illustrated in Figure b, using as many as 1,700 basis functions …”

A local similarity transformed equation of motion approach for calculating excited states

“…Another recent application involves the calculation of optical band gap values for semiconductor materials. [ 40 ] This requires embedding a quantum mechanically treated core region in a point charge field and a boundary region of Gaussian charge distributions. Once a uniform charge distribution is ensured, and the results are converged with respect to the size of the quantum region, DLPNO‐STEOM offers a reliable way of predicting optical band gaps.…”

Predicting band gaps of semiconductors with quantum chemistry

“…2) is introduced interjacent. The core potentials satisfy on a simplified level the quantum mechanical interactions of the QC surface with the embedding [21,22].…”