Semi-Automated Creation of Density Functional Tight Binding Models through Leveraging Chebyshev Polynomial-Based Force Fields

Abstract

Density functional tight binding (DFTB) is an attractive method for accelerated quantum simulations of condensed matter due to its enhanced computational efficiency over standard density functional theory (DFT) approaches. However, DFTB models can be challenging to determine for individual systems of interest, especially for metallic and interfacial systems where different bonding arrangements can lead to significant changes in electronic states. In this regard, we have created a rapid-screening approach for determining systematically improvable DFTB interaction potentials that can yield transferable models for a variety of conditions. Our method leverages a recent reactive molecular dynamics force field where many-body interactions are represented by linear combinations of Chebyshev polynomials. This allows for the efficient creation of multi-center representations with relative ease, requiring only a small investment in initial DFT calculations. We have focused our workflow on TiH 2 as a model system and show that a relatively small training set based on unit-cell-sized calculations yields a model accurate for both bulk and surface properties. Our approach is easy to implement and can yield reliable DFTB models over a broad range of thermodynamic conditions, where physical and chemical properties can be difficult to interrogate directly and there is historically a significant reliance on theoretical approaches for interpretation and validation of experimental results.

Machine‐Learning a Solution for Reactive Atomistic Simulations of Energetic Materials

“…DFTB models generally exist within a "sweet-spot" between DFT and completely empirical MD models in terms of accuracy and ease of development. The quantum mechanical part of the calculation tends to be relatively accurate for many conditions and materials, allowing for a reasonable representation of the system's electronic ground state [28]. This is especially true under extreme conditions, where electron repulsions tend to dominate interactions and exchange-correlation interactions do not need to be determined as precisely [47].…”

“…ML-IAPs are generally capable of arbitrary complexity and high accuracy, although electronic degrees of freedom such as spin are typically neglected. In addition, ML-IAPs can be developed as corrections to approximate quantum methods such as DFTB [24][25][26][27][28] or to MM-IAPs such as ReaxFF [29]. Typically, correction approaches require fewer parameters and simpler functional forms than ML-IAPs that completely describe the IAP.…”

Benchmarks of the density functional tight-binding method for redox, protonation and electronic properties of quinones

“…Several recent methodological developments, like the development of the DFTB3 method 21 and its corresponding parameterization, 22 the use of long-range corrections, 23 improvement of the description of intermolecular 24 and dispersion interactions, 25–28 have significantly increased the accuracy of the method. For parameterization, several automated schemes and schemes which utilize machine learning have been developed, 29–37 increasing the applicability of the DFTB method to different systems and problems.…”

High Accuracy Semi-Empirical Quantum Models Based on a Reduced Training Set

“…12-14 DFTB models have been created for a broad range of materials, though the repulsive energy largely has been tuned to relatively low-level DFT data for condensed phases. [15][16][17][18][19] Recent efforts have been made to enhance the accuracy of DFTB through creation of more sophisticated and systematic approaches for determining the repulsive energy term. and the Curvature Constrained Splines methodology 14 have been used to create strictly pair-wise additive repulsive energies for several organic and inorganic systems.…”

“…The reliance on Chebyshev polynomials, which are orthogonal, allows the complexity of a ChIMES model to be systematically tuned to an arbitrary degree of accuracy and transferability, while also providing straightforward methods for regularization to minimize overfitting. 16 In this study, we determine an optimal DFTB/ChIMES model for C, H, N, O-containing systems using high level quantum chemical reference data. We use an iterative scheme to systematically expand our training set where at each iteration, a small fraction of the force configurations with largest deviation in our validation set are included in the next training set iteration.…”