This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design.

Psi4 is a free and open-source ab initio electronic structure program providing Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of Psi4's core functionality via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSchema data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCArchive Infrastructure project, make the latest version of Psi4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs. File list (2) download file view on ChemRxiv psi4.pdf (4.37 MiB) download file view on ChemRxiv supplementary_material.pdf (297.86 KiB)

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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.

The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ∼20 electrons in ∼20 orbitals due to exponential growth in the computational cost. We show that employing the Adaptive Sampling Configuration Interaction (ASCI) method as an approximate Full

The Pipek-Mezey scheme for generating chemically intuitive, localized molecular orbitals is generalized to incorporate various ways of estimating the atomic charges, instead of the ill-defined Mulliken charges used in the original formulation, or Löwdin charges, which have also been used. Calculations based on Bader, Becke, Voronoi, Hirshfeld, and Stockholder partial charges, as well as intrinsic atomic orbital charges, are applied to orbital localization for a variety of molecules. While the charges obtained with these various estimates differ greatly, the resulting localized orbitals are found to be quite similar and properly separate σ and π orbitals, as well as core and valence orbitals. The calculated results are only weakly dependent on the basis set, unlike those based on Mulliken or Löwdin charges. The effect of varying the penalty exponent on the charge in the objective function was studied briefly and was found to lead to some changes in the localized orbitals when degeneracies are present. The various localization methods have been implemented in ERKALE, an open source program for electronic structure calculations.

Although many programs have been published for fully numerical Hartree-Fock (HF) or density functional (DF) calculations on atoms, we are not aware of any programs that support hybrid DFs, which are popular within the quantum chemistry community due to their better accuracy for many applications, or that can be used toWe present two applications of the novel code. The first application is the calculation of atoms in finite electric fields. Finite electric field calculations allow, for instance, the extraction of atomic static dipole polarizabilities, which are a well-known challenge for theoretical methods [20] and the best values for which have been recently reviewed by Schwerdtfeger and Nagle. [21] Atomic static dipole polarizabilities are related to global softness and the Fukui function. [22] As the molecule with the lowest static dipole polarizability tends to be the chemically most stable, [23][24][25] the accuracy of static dipole polarizabilities can be considered a proxy for thermochemical accuracy. Various density functionals have been shown to outperform HF for molecular static dipole polarizabilities, with hybrid functionals yielding the best results, [26][27][28][29][30] as the error in polarizabilities typically arises from the exchange part. [30] Fully numerical all-electron HF results for atoms [31][32][33][34] and density functional results for molecules [35] have been reported in the literature, whereas post-HF and relativistic DFT results have been calculated using Gaussian basis sets. [36][37][38][39][40] In our application, we study the Li + and Sr 2+ ions with HF and show that we are able to reproduce the fully numerical HF limit values from Ref. [41]. In addition, we report dipole moments and polarizabilities with the LDA, [42][43][44] PBE, [45,46] PBEh, [47,48] TPSS, [49,50] and TPSSh [51] functionals.Our second application is the benchmark of Gaussian basis set energies for a variety of neutral, cationic, and anionic species with HF and the BHHLYP [10] functional. Atomic anions are especially challenging to model with DFT. [52][53][54][55][56] For instance, it has been shown that calculations on the well-bound F − anion may require extremely diffuse basis functions with exponents as small as (!) α = 6.9 × 10 −9 to achieve converged results. [54] The use of such small exponents requires extensive modifications to the used Gaussian-basis quantum chemistry program to ensure sufficient numerical accuracy. [54,56] In contrast, the finite element method (FEM) has none of these issues: because the basis set has local support and is never ill-conditioned, calculations are extremely stable numerically. We will show below that the absolute energies reproduced by the large Gaussian basis set used in Refs. [56,57] are too large by several microhartrees for most systems. The second part of the present series [58] presents analogous applications to diatomic molecules, where the deficiencies of Gaussian basis sets are considerably more noticeable. [6,58] The layout of the article is the following. Next,...

A variational, self-consistent implementation of the Perdew-Zunger self-interaction correction (PZ-SIC), based on a unified Hamiltonian and complex optimal orbitals, is presented for finite systems and atom-centered basis sets. A simplifying approximation allowing the use of real canonical orbitals is proposed. The algorithm is based on two-step self-consistent field iterations, where the updates of the canonical orbitals and the optimal orbitals are done separately. Calculations of the energy of atoms ranging from H to Ar are presented, using various generalized gradient functionals (PBE, APBE, PBEsol) and a meta-generalized gradient functional (TPSS). While the energy of atoms is poorly described by PBEsol, which is a functional optimized to reproduce properties of solids, the PZ-SIC brings the calculations into good agreement with the best ab initio estimates. The importance of using complex optimal orbitals becomes particularly clear in calculations using the TPSS functional, where the original functional gives good results while the application of PZ-SIC with real orbitals gives highly inaccurate results. With complex optimal orbitals, PZ-SIC slightly improves the accuracy of the TPSS functional. The charge localization problem that plagues Kohn-Sham DFT functionals, including hybrid functionals, is illustrated by calculations on the CH3 + F(-) complex, where even PBEsol with PZ-SIC is found to give estimates of both energy and charge with accuracy comparable to that of coupled cluster calculations.