PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science.

We demonstrate that electrochemically etched, hydrogen capped Si n H x clusters with n larger than 20 are obtained within a family of discrete sizes. These sizes are 1.0 (Si 29 ), 1.67 (Si 123 ), 2.15, 2.9, and 3.7 nm in diameter. We characterize the particles via direct electron imaging, excitation and emission optical spectroscopy, and colloidal crystallization. The band gaps and emission bands are measured. The smallest four are ultrabright blue, green, yellow and red luminescent particles. The availability of discrete sizes and distinct emission in the red, green and blue ͑RGB͒ range is useful for biomedical tagging, RGB displays, and flash memories.

We describe QWalk, a new computational package capable of performing Quantum Monte Carlo electronic structure calculations for molecules and solids with many electrons. We describe the structure of the program and its implementation of Quantum Monte Carlo methods. It is opensource, licensed under the GPL, and available at the web site http://www.qwalk.org.

We investigate the accuracy of trial wave functions for quantum Monte Carlo based on Pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-Pfaffian pairing wave functions. We show that a small number of Pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that Pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.

We investigate pfaffian trial wave functions with singlet and triplet pair orbitals by quantum Monte Carlo methods. We present mathematical identities and the key algebraic properties necessary for efficient evaluation of pfaffians. Following upon our previous study, 1 we explore the possibilities of expanding the wave function in linear combinations of pfaffians. We observe that molecular systems require much larger expansions than atomic systems and linear combinations of a few pfaffians lead to rather small gains in correlation energy. We also test the wave function based on fully-antisymmetrized product of independent pair orbitals. Despite its seemingly large variational potential, we do not observe additional gains in correlation energy. We find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions and exhibit the minimal number of two nodal domains in agreement with recent results on fermion nodes topology. We analyze the nodal structure differences of Hartree-Fock, pfaffian and essentially exact large-scale configuration interaction wave functions. Finally, we combine the recently proposed form of backflow correlations 2,3 with both determinantal and pfaffian based wave functions.