Born–Oppenheimer Interatomic Forces from Simple, Local Kinetic Energy Density Functionals

Abstract

Rapid calculation of Born-Oppenheimer (B-O) forces is essential for driving the so-called quan- tum region of a multi-scale molecular dynamics simulation. The success of density functional theory (DFT) with modern exchange-correlation approximations makes DFT an appealing choice for this role. But con- ventional Kohn-Sham DFT, even with various linear-scaling implementations, really is not fast enough to meet the challenge of complicated chemo-mechanical phenomena (e.g. stress-induced cracking in the presence of a solvent). Moreover, those schemes involve approximations that are difficult to check practi- cally or to validate formally. A popular alternative, Car-Parrinello dynamics, does not guarantee motion on the B-O surface. Another approach, orbital-free DFT, is appealing but has proven difficult to imple- ment because of the challenge of constructing reliable orbital-free (OF) approximations to the kinetic energy (KE) functional. To be maximally useful for multi-scale simulations, an OF-KE functional must be local (i.e. one-point). This requirement eliminates the two-point functionals designed to have proper linear-response behavior in the weakly inhomogeneous limit. In the face of these difficulties, we demon- strate that there is a way forward. By requiring only that the approximate functional deliver high-quality forces, by exploiting the "conjointness" hypothesis of Lee, Lee, and Parr, by enforcing a basic positivity constraint, and by parameterizing to a carefully selected, small set of molecules we are able to generate a KE functional that does a good job of describing various Hq SimOn clusters as well as CO (providing encouraging evidence of transferability). In addition to that positive result, we discuss several major neg- ative results. First is definitive proof that the conjointness hypothesis is not correct, but nevertheless is useful. The second is the failure of a considerable variety of published KE functionals of the generalized gradient approximation type. Those functionals yield no minimum on the energy surface and give com- pletely incorrect forces. In all cases, the problem can be traced to incorrect behavior of the functionals near the nuclei. Third, the seemingly obvious strategy of direct numerical fitting of OF-KE functional parameters to reproduce the energy surface of selected molecules is unsuccessful. The functionals that result are completely untransferable.