A novel Gaussian-Sinc mixed basis set for electronic structure calculations

Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers: the Cartesian component-separated approach

Traditional methods in quantum chemistry rely on Hartree-Fock-based Slater-determinant (SD) representations, whose underlying zeroth-order picture assumes separability by particle. Here, we explore a radically different approach, based on separability by Cartesian component, rather than by particle [J. Jerke and B. Poirier, J. Chem. Phys., 2018, 148, 104101]. The approach appears to be very well suited for 3D grid-based methods in quantum chemistry, and thereby also for so-called "first-quantized" quantum computing. We first present an overview of the approach as implemented on classical computers, including numerical results that justify performance claims. In particular, we perform numerical calculations with four explicit electrons that are equivalent to full-CI matrix diagonalization with nearly 10¹⁵ SDs. We then present an implementation for quantum computers for which the number of quantum gates (and to a lesser extent, the number of qubits) can be dramatically reduced, in comparison with other quantum circuitry that has been envisioned for implementing first-quantized "quantum computational chemistry" (QCC).

Energy-Geometry Dependency of Molecular Structures: A Multistep Machine Learning Approach

There is growing interest in estimating quantum observables while circumventing expensive computational overhead for facile in silico materials screening. Machine learning (ML) methods are implemented to perform such calculations in shorter times. Here, we introduce a multistep method based on machine learning algorithms to estimate total energy on the basis of spatial coordinates and charges for various chemical structures, including organic molecules, inorganic molecules, and ions. This method quickly calculates total energy with 0.76 au in root-mean-square error (RMSE) and 1.5% in mean absolute percent error (MAPE) when tested on a database of optimized and unoptimized structures. Using similar molecular representations, experimental thermochemical properties were estimated, with MAPE as low as 6% and RMSE of 8 cal/mol·K for heat capacity in a 10-fold cross-validation.