A method is detailed enabling fits to calculated total electron densities using spheres of adjustable radii centeredon the nuclear positions. Best atomic radii are obtained for a series of molecules with use of Hartree-Fock models. Minimalsplit-valence and polarization basis set results are compared. The dependency of atom size (in molecules) on the electronegativityof attached groups and on steric and strain conditions is examined, and a set of average radii for use in molecular modelsis proposed. Comparisons between calculated radii and atomic charges obtained from Mulliken population analyses suggestthat the latter method generally underestimates the population of hydrogen and overestimates the population of lithium andsodium.

The 6-31 G* and 6-31 G·· basis sets previously introduced for first-row atoms have been extended through thesecond-row of the periodic table. Equilibrium geometries for one-heavy-atom hydrides calculated for the twobasissets and using Hartree-Fock wave functions are in good agreement both with each other and with theexperimental data. HF/6-31G· structures, obtained for two-heavy-atom hydrides and for a variety ofhypervalent second-row molecules, are also in excellent accord with experimental equilibrium geometries. Nolarge deviations between calculated and experimental single bond lengths have been noted, in contrast toprevious work on analogous first-row compounds, where limiting Hartree-Fock distances were in error by upto a tenth of an angstrom. Equilibrium geometries calculated at the HF /6-31 G level are consistently in betteragreement with the experimental data than are those previously obtained using the simple split-valance 3-21Gbasis set for both normal- and hypervalent compounds. Normal-mode vibrational frequencies derived from 6-31G· level calculations are consistently larger than the corresponding experimental values, typically by%-15%; they are of much more uniform quality than those obtained from the 3-21G basis set.Hydrogenation energies calculated for normal- and hypervalent compounds are in moderate accord withexperimental data, although in some instances large errors appear. Calculated energies relating to thestabilities of single and multiple bonds are in much better accord with the experimental energy differences.

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller-Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

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.