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

> **NIH NIH R43** · QUANTUMFUTURE SCIENTIFIC SOFTWARE LLC · 2020 · $150,000

## Abstract

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.

## Key facts

- **NIH application ID:** 9999749
- **Project number:** 1R43GM137612-01
- **Recipient organization:** QUANTUMFUTURE SCIENTIFIC SOFTWARE LLC
- **Principal Investigator:** Laszlo Fusti-Molnar
- **Activity code:** R43 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2020
- **Award amount:** $150,000
- **Award type:** 1
- **Project period:** 2020-06-01 → 2021-05-31

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/9999749

## Citation

> US National Institutes of Health, RePORTER application 9999749, Derivation and implementation of analytic atomic forces in a new extremely efficient linear scaling ab initio DFT program (1R43GM137612-01). Retrieved via AI Analytics 2026-05-23 from https://api.ai-analytics.org/grant/nih/9999749. Licensed CC0.

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