(370a) Development of Bayesian Error Estimation Density Functionals with Range-Separated Exchange

The Kohn-Sham (KS) approach to density functional theory (DFT), owing to its simplicity and low cost, was instrumental in making computational chemistry a viable field of study. Development of density functionals within the KS ansatz involves approximations to the exchange-correlation (XC) potential between interacting electrons. The XC parameters are typically determined based on constraint satisfaction and compromise in accuracy between various chemical and material properties. Machine learning methods are very promising in this field since they provide a systematic approach to developing the optimal compromise between XC model complexity and accuracy.

Bayesian error estimation functionals (BEEF) employ ridge regression with least squares or robust loss functions to determine the XC model parameters. The Bayesian approach also allows for the estimation of uncertainties in calculated material properties arising from the functional approximation. The BEEF-vdW functional is a semilocal generalized gradient approximation (GGA) that includes vdw-DF2 type nonlocal correlation. The functional demonstrates superior accuracy relative to other GGAâ??s, especially with respect to surface adsorption chemistry. The meta-GGA implementations, mBEEF, and mBEEF-vdW further improve the description of bulk properties and surface chemistry.

Semilocal functional approximations, however, cannot accurately describe nonlocal phenomena such as bond breaking. Hybrid functionals overcome this limitation by adding a fraction of nonlocal Fock exchange to the XC energy. We are developing a hybrid implementation of BEEF that includes short-range exact exchange. The screening distance for short-range exchange is a nonlinear parameter in the XC energy. To retain the linear model framework for functional fitting and error estimation, therefore, we first scan the two-parameter space of screening distance and fraction of Fock exchange. Parameters that provide a reasonable compromise between material properties, especially the description of metallic density of states and charge separation in diatomic dissociations, are then employed in the construction of the hybrid functional. In addition, the space of available nonlocal correlation approximations is being explored in order to improve the description of noncovalent interactions. We will discuss both the cost as well as performance of the new BEEF hybrid functional with nonlocal correlation in the prediction of barrier heights and surface reaction energies.