A Variational Linear-Scaling Framework to Build Practical, Efficient Next-Generation Orbital-Based Quantum Force Fields

Abstract

We introduce a new hybrid molecular orbital/density-functional modified divide-and-conquer (mDC) approach that allows the linear-scaling calculation of very large quantum systems. The method provides a powerful framework from which linear-scaling force fields for molecular simulations can be developed. The method is variational in the energy, and has simple, analytic gradients and essentially no break-even point with respect to the corresponding full electronic structure calculation. Furthermore, the new approach allows intermolecular forces to be properly balanced such that non-bonded interactions can be treated, in some cases, to much higher accuracy than the full calculation. The approach is illustrated using the second-order self-consistent charge density-functional tight-binding model (DFTB2). Using this model as a base Hamiltonian, the new mDC approach is applied to a series of water systems, where results show that geometries and interaction energies between water molecules are greatly improved relative to full DFTB2. In order to achieve substantial improvement in the accuracy of intermolecular binding energies and hydrogen bonded cluster geometries, it was necessary to extend the DFTB2 model to higher-order atom-centered multipoles for the second-order self-consistent intermolecular electrostatic term. Using generalized, linear-scaling electrostatic methods, timings demonstrate that the method is able to calculate a water system of 3000 atoms in less than half of a second, and systems of up to one million atoms in only a few minutes using a conventional desktop workstation.

Altered (transition) states: mechanisms of solution and enzyme catalyzed RNA 2′-O-transphosphorylation

“…This approach involves performing molecular dynamics simulations using a potential that treats the local environment of the reacting atoms with quantum mechanical (QM) methods to describe the electronic structure needed to predict chemical bond formation and cleavage, and the remainder of the solvated macromolecular environment with molecular mechanics (MM) using simpler potential energy functions [30]. QM treatments range from computationally economical semi-empirical approaches [31] to more accurate and computationally expensive density functional and ab inito methods [32]. Development of both fast and accurate multi-scale methods has great potential to facilitate analysis of free energy surfaces for rigorous comparison with experimental measurements and for identification of alternative mechanisms of RNA transphosphorylation [33,34].…”

Density functional tight binding: values of semi-empirical methods in an ab initio era

“…Finally, there is considerable effort in improving the description of non-covalent interactions in DFTB by going beyond the monopole approximation. 118,123 With a balanced description of conformational and non-covalent energetics, along with other algorithmic developments such as linear-scaling, the next generation of DFTB model is poised to be a powerful method uniquely suited for a broad range of chemical and biological applications, even in an ab initio era.…”

“…For realistic applications, full QM calculations at the ab initio level remains challenging, despite recent progress in linear scaling QM methods. There are several promising linear-scaling SE methods based on either AM1 117 or DFTB, 118 although much remains to be done to calibrate these models for a balanced treatment of non-covalent interactions and conformational (torsional) energetics.…”

Recent Advances toward a General Purpose Linear-Scaling Quantum Force Field

“…12,23 mDC and X-Pol are conceptually equivalent but differ in their details of how the fragments interact with one another. The X-Pol method interacts the fragments using a traditional QM/MM potential; however, this potential depends upon which fragment is considered to be the QM region.…”