# VeloxChem: Large-Scale DFT Calculations of Geometric Derivatives up to Second Order for Simulation of IR Spectra

## TL;DR

VeloxChem enables efficient large-scale DFT calculations for simulating IR spectra, including second-order geometric derivatives and GPU acceleration.

## Contribution

Implementation of analytic second-order geometric derivatives for IR spectra simulations in DFT using GPU acceleration and efficient parallelization.

## Key findings

- Gradient calculations scale efficiently and are computationally cheaper than SCF optimizations.
- Hessian calculations scale as N^3.5 and benefit from GPU acceleration for solving perturbed Kohn–Sham equations.
- Successful simulation of IR spectrum for ubiquitin with 1,152 atoms shows excellent agreement with experimental amide I band.

## Abstract

A software implementation of analytic geometric derivatives
of
electron-repulsion integrals up to second order is presented for the
modeling of vibrational spectroscopies at the level of first-principles
Kohn–Sham density functional theory (DFT). In line with the
general goals of the VeloxChem program, it targets efficient execution
in high-performance computing environments with a hybrid MPI/OpenMP
parallelization model and is based on the technique of automatic C++
code generation for high versatility. Gradient calculations scale
identically with conventional Fock matrix constructions, and also
with the prefactor taken into account, the computational cost of the
gradient is significantly lower than that of the self-consistent field
(SCF) optimization of the reference state. The Hessian calculation
shows a scaling of N
3.5 with N being the number of contracted Gaussian basis functions. The computational
bottleneck in the Hessian calculation is the solving of the coupled-perturbed
Kohn–Sham equations that with VeloxChem can be offloaded to
GPU-accelerated nodes. The large-scale virtues of the presented software
module are demonstrated by the DFT/B3LYP calculation of the IR spectrum
of the entire ubiquitin protein with 1,152 atoms in the quantum mechanical
(QM) region and TIP3P water in the molecular mechanics (MM) region.
The simulated amide I band shows to be in excellent agreement with
experiment.