DQC: A Python program package for differentiable quantum chemistry

Abstract

Automatic differentiation represents a paradigm shift in scientific programming, where evaluating both functions and their derivatives is required for most applications. By removing the need to explicitly derive expressions for gradients, development times can be shortened and calculations can be simplified. For these reasons, automatic differentiation has fueled the rapid growth of a variety of sophisticated machine learning techniques over the past decade, but is now also increasingly showing its value to support ab initio simulations of quantum systems and enhance computational quantum chemistry. Here, we present an open-source differentiable quantum chemistry simulation code and explore applications facilitated by automatic differentiation: (1) calculating molecular perturbation properties, (2) reoptimizing a basis set for hydrocarbons, (3) checking the stability of self-consistent field wave functions, and (4) predicting molecular properties via alchemical perturbations.

Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry

“…In the case of combined forward and reverse mode for example, only about 6 n ( n : number of independent variables, single dependent variable) function evaluations are theoretically necessary to compute the full Hessian . Therefore, while early studies demonstrate proof-of-concept for AD in computing HF gradients, more recent efforts are focused on higher derivatives to arbitrary order for correlated wave function methods. , …”

“…Abbott and co-workers therefore demonstrate the immense potential of AD to efficiently and accurately calculate higher nuclear derivatives that are currently accessible only via error-prone numerical differentiation. AD can be extended easily to calculate other classes of derivatives for applications ranging from wave function stability analysis to alchemical perturbation . By leveraging rapid progress in programs such as JAX and implementing standard features of quantum chemistry that enhance speed and optimize memory use, AD of the future can be comparable to if not faster than analytical Hessians.…”

Automatic differentiation for the direct SCF approach to the Hartree-Fock method

“…It has been widely accepted in machine learning; the backward propagation algorithm is a special case of reverse-mode automatic differentiation. Thanks to the recent advancements in software techniques, AD has been adopted in various fields of chemistry, such as molecular dynamics [1] and density functional theory (DFT) [2], and several AD-based quantum chemistry software packages have been developed [3,4]. There are two types of AD: forward-mode and reverse-mode.…”

“…The tricky part of this approach is the orthonormality condition of molecular orbitals. An algorithm using QR decomposition to satisfy the orthonormality condition has been proposed [7], and it is implemented in a differentiable quantum chemistry library DQC [4]. The direct minimization approach is considered to be more robust [8], and it can be applied to large systems [9].…”

Differentiable quantum chemistry with PySCF for molecules and materials at the mean-field level and beyond

“…Both sets of difficulties are circumvented by applying AD, as shown in a few works very recently. For example, Tamayo-Mendoza et al 3 implemented a fully differentiable Hartree-Fock (HF) method with AD; Song et al 4 introduced an AD scheme to compute nuclear gradients for tensor hyper-contraction based methods; Abbott et al 5 applied AD to calculations of higher order nuclear derivatives with methods such as HF, second-order Møller-Plesset perturbation theory (MP2) and coupled cluster theory with single, double and perturbative triple excitations [CCSD(T)]; and Kasim et al 6 developed a differentiable quantum chemistry code called DQC for basis set optimizations, molecular property calculations etc. at the mean-field level.…”