Derivation and implementation of analytic atomic forces in a new extremely efficient linear scaling ab initio DFT program

A revolutionary efficient linear scaling Coulomb and Exchange-Correlation methods has been developed and implemented during the last 18 months at QuantumFuture Scientific Software company. The new Coulomb algorithm is based on the Fourier Transform Coulomb (FTC) method with two major significant improvements in two special two electron integral categories that the original FTC scheme was not able to evaluate in accurate manner. The result is almost complete elimination of the computational expenses of the traditional two electron integrals. In order to speed up the Exchange- Correlation part of the calculations new version of the Multi-Resolution Exchange- Correlation (MRXC) method has been developed and generalized to gradient corrected (GGA) functionals as well. Detailed results generated with Slater and PBE functionals using 6-311G(2df,p) basis set are shown, as preliminary research highlighting both the efficiency and the accuracy of the method. The computer program based on these new algorithms is 15-50 times faster for a medium sized drug-like compound and about 30-65 times faster for the dimer of the same molecule than other standard state of the art today’s DFT programs without loosing any accuracy of the calculations. The proposed goal of this phase I work is to make this technology applicable for computational drug design purposes with such computational efficiency that is not available today by deriving and implementing the analytical atomic forces for geometry optimizations. The equations for analytical force calculations of the original FTC technique have been published and implemented already in two commercial DFT programs (PQS and QCHEM). The analytical equation for the new developments of the FTC energy terms has to be derived and implemented. Similarly, the analytical equations for the new version of the MRXC need to be derived and efficiently implemented for both LDA and GGA density functional families. The impact of such large efficiency improvements in Gaussian basis set based all electron DFT calculations will be very substantial over the large range of computational drug design areas from conformation search, torsion scans, organic crystal predictions to accurate protein-ligand interactions. Very large amounts of computational time, computational costs, energy and carbon footprint could be saved this way. The success of this project can be evaluated by testing the analytical forces of the new FTC and MRXC energy terms by their approximate numerical derivatives.Narrative An extremely cost-efficient new technology has been worked out at QuantumFuture to perform accurate ab initio electronic structure calculations for drug sized molecules significantly faster than today’s widely used programs. The proposed research and development project of deriving and implementing analytical atomic forces is a necessary step to be able to optimize geometries of molecules, molecular clusters, later protein structures and organic crystal structures. This new capability will drastically reduce the computational times, costs and carbon footprints of existing modelling workflows as well as opens the opportunity to perform much more and much larger calculations using currently available computational resources in order to find better medicines, in order for better understanding important molecular interactions and reactions for reducing illnesses, disabilities and improving health.