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Computational quantum chemistry can be more than just numerical experiments when methods are specifically adapted to investigate chemical concepts. One important example is the development of energy decomposition analysis (EDA) to reveal the physical driving forces behind intermolecular interactions. In EDA, typically the interaction energy from a good-quality density functional theory (DFT) calculation is decomposed into multiple additive components that unveil permanent and induced electrostatics, Pauli repulsion, dispersion, and charge-transfer contributions to non-covalent interactions. Herein, we formulate, implement and investigate decomposing the forces associated with intermolecular interactions into the same components. The resulting force decomposition analysis (FDA) is potentially useful as a complement to the EDA to understand chemistry, while also providing far more information than an EDA for data analysis purposes such as training physics-based force fields. We apply the FDA based on absolutely localized molecular orbitals (ALMOs) to analyze interactions of water with sodium and chloride ions as well as in the water dimer. We also analyze the forces responsible for geometric changes in carbon dioxide upon adsorption onto (and activation by) gold and silver anions. We also investigate how the force components of an EDA-based force field for water clusters, namely MB-UCB, compare to those from force decomposition analysis.

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree-Fock (post-HF) methods all the way to linear scaling in insulating molecules. Revealing the numerical sparsity of the 4-index electron repulsion (ERI) tensor is central to achieving linear scaling in local correlation methods. For second order Møller-Plesset theory (MP2), one of the simplest post-HF methods, only the $(ia|jb)$ ERIs are needed, coupling occupied orbitals $i,j$, and virtuals $a,b$. In this paper, we compare the numerical sparsity (called the "ragged list representation") and the low-rank sparsity of the $(ia|jb)$ ERI tensor. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual (VV-HV) set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor relative to 4 other good choices: projected atomic orbitals (PAOs), Boys localized virtuals, Pipek-Mezey localized virtuals, and Cholesky localized virtuals. To further compress the $(ia|jb)$ ERI tensor, the low-rank (pair-natural orbital) representation uses different sets of virtual orbitals for different occupied orbital pairs. Our results indicate that while the low-rank representation achieves significant rank reduction, it also requires more memory than the ragged list representation. An approximation (called the "fixed sparsity pattern") for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern using this representation is therefore promising.

While bonding molecular orbitals exhibit constructive interference relative to atomic orbitals, antibonding orbitals show destructive interference. When full localization of occupied orbitals into bonds is possible, bonding and antibonding orbitals exist in 1:1 correspondence with each other. Antibonding orbitals play an important role in chemistry because they are frontier orbitals that determine orbital interactions, as well as much of the response of the bonding orbital to perturbations. In this work, we present an efficient method to construct antibonding orbitals by finding the orbital that yields the maximum opposite spin pair correlation amplitude in second order perturbation theory (AB2) and compare it with other techniques with increasing basis set size. We conclude the AB2 antibonding orbitals are a more robust alternative to the Sano orbitals as initial guesses for valence bond calculations due to having a useful basis set limit. The AB2 orbitals are also useful for efficiently constructing an active space, and they work as good initial guesses for valence excited states. In addition, when combined with the localized occupied orbitals, and relocalized, the result is a set of molecule-adapted minimal basis functions that is built without any reference to atomic orbitals of the free atom. As examples, they are applied to the population analysis of halogenated methane derivatives, H–Be–Cl, and SF6, where they show some advantages relative to good alternative methods.

Oxidation states represent the ionic distribution of charge in a molecule and are significant in tracking redox reactions and understanding chemical bonding. While effective algorithms already exist based on formal Lewis structures as well as using localized orbitals, they exhibit differences in challenging cases where effects such as redox noninnocence are at play. Given a density functional theory (DFT) calculation with chosen total charge and spin multiplicity, this work reports a new approach to obtaining fragment-localized orbitals that is termed oxidation state localized orbitals (OSLO), together with an algorithm for assigning the oxidation state using the OSLOs and an associated fragment orbital localization index (FOLI). Evaluating the FOLI requires fragment populations, and for this purpose a new version of the intrinsic atomic orbital (IAO) scheme is introduced in which the IAOs are evaluated using a reference minimal basis formed from on-the-fly superposition of atomic density (IAO-AutoSAD) calculations in the target basis set and at the target level of theory. The OSLO algorithm is applied to a range of challenging cases including high valent metal oxide complexes, redox noninnocent NO and dithiolate transition metal complexes, a range of carbene-containing TM complexes, and other examples including the potentially inverted ligand field in [Cu(CF3)4]-. Across this range of cases, OSLO produces generally satisfactory results. Furthermore, in borderline cases, the OSLOs and associated FOLI values provide direct evidence of the emergence of covalent interactions between fragments that nicely complements existing approaches.

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the ( ia| jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

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. 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.

Given the piecewise approach to modeling intermolecular interactions for force fields, they can be difficult to parameterize since they are fit to data like total energies that only indirectly connect to their separable functional forms. Furthermore, by neglecting certain types of molecular interactions such as charge penetration and charge transfer, most classical force fields must rely on, but do not always demonstrate, how cancellation of errors occurs among the remaining molecular interactions accounted for such as exchange repulsion, electrostatics, and polarization. In this work we present the first generation of the (many-body) MB-UCB force field that explicitly accounts for the decomposed molecular interactions commensurate with a variational energy decomposition analysis, including charge transfer, with force field design choices that reduce the computational expense of the MB-UCB potential while remaining accurate. We optimize parameters using only single water molecule and water cluster data up through pentamers, with no fitting to condensed phase data, and we demonstrate that high accuracy is maintained when the force field is subsequently validated against conformational energies of larger water cluster data sets, radial distribution functions of the liquid phase, and the temperature dependence of thermodynamic and transport water properties. We conclude that MB-UCB is comparable in performance to MB-Pol, but is less expensive and more transferable by eliminating the need to represent short-ranged interactions through large parameter fits to high order polynomials.

We report three design principles for obtaining extra-large pore openings and cages in the metal-organic analogues of inorganic zeolites, zeolitic imidazolate frameworks (ZIFs). Accordingly, we prepared a series of 15 ZIFs, members of which have the largest pore opening (22.5 Å) and the largest cage size (45.8 Å) known for all porous tetrahedral structures. The key parameter allowing us to access these exceptional ZIFs is what we define as the steric index (δ), which is related to the size and shape of the imidazolate linkers employed in the synthesis. The three principles are based on using multiple linkers with specific range and ratios of δ to control the size of rings and cages from small to large, and therefore are universally applicable to all existing ZIFs. The ZIF with the largest cage size (ZIF-412) shows the best selectivity of porous materials tested toward removal of octane and p-xylene from humid air., Support for synthesis and characterization by BASF SE (Ludwigshafen, Germany), with support for hydrocarbon sorption studies by U.S. Department of Defense, Defense Threat Reduction Agency (DTRA). Researchers at Wuhan University (H. D., Q. L., and H. C.) were supported by the 1000 Talent Plan of China, National Natural Science Foundation of China (21471118, 91545205, and 91622103), and National Key Basic Research Program of China (No. 2014CB239203). Support from Advanced Light Source by the Director, Office of Science, Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231; support from single crystal XRD beamline BL15U, BL17U1, and BL17B in Shanghai Synchrotron Radiation (SSRF) and CheXray in UC Berkeley (NIH Shared Instrumentation Grant S10-RR027172) are acknowledged. Support from the Recruitment Program for Young Professionals & NSFC 21522105 is acknowledged.