Fast computation of DFT nuclear gradient with multiresolution This article is dedicated to Dr. Russell J. Boyd for his distinguished career in chemical research

We present an efficient algorithm for evaluating the exchange-correlation contribution to the nuclear gradients of density-functional theory calculation within the local spin-density approximation. The algorithm is an extension of the multiresolution exchange-correlation (mrXC) method, which treats smooth and compact parts of the electron density separately. The nuclear gradient of the smooth density is calculated on the even-spaced grid while the compact part of the density is handled on the normal atom-centered grid (ACG). The overall formulism is still formally based on the ACG, and thus does not change the results of the existing ACG-based algorithms for all-electron density-functional theory (DFT) calculations. The variation of the positions and weights of ACG owing to the nuclear perturbation is also handled rigorously. Benchmark calculations with different basis sets and sizes of ACG show that mrXC reduces the computational cost by several times without loss of accuracy. It also lessens the impact on the CPU time when the size of the ACG is increased.