Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

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.

From Intermolecular Interaction Energies and Observable Shifts to Component Contributions and Back Again: A Tale of Variational Energy Decomposition Analysis.

Quantum chemistry in the form of density functional theory (DFT) calculations is a powerful numerical experiment for predicting intermolecular interaction energies. However, no chemical insight is gained in this way beyond predictions of observables. Energy decomposition analysis (EDA) can quantitatively bridge this gap by providing values for the chemical drivers of the interactions, such as permanent electrostatics, Pauli repulsion, dispersion, and charge transfer. These energetic contributions are identified by performing DFT calculations with constraints that disable components of the interaction. This review describes the second-generation version of the absolutely localized molecular orbital EDA (ALMO-EDA-II). The effects of different physical contributions on changes in observables such as structure and vibrational frequencies upon complex formation are characterized via the adiabatic EDA. Example applications include red- versus blue-shifting hydrogen bonds; the bonding and frequency shifts of CO, N2, and BF bound to a [Ru(II)(NH3)5]2 + moiety; and the nature of the strongly bound complexes between pyridine and the benzene and naphthalene radical cations. Additionally, the use of ALMO-EDA-II to benchmark and guide the development of advanced force fields for molecular simulation is illustrated with the recent, very promising, MB-UCB potential.

A non-perturbative pairwise-additive analysis of charge transfer contributions to intermolecular interaction energies.

Energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs) decomposes the interaction energy between molecules into physically interpretable components like geometry distortion, frozen interactions, polarization, and charge transfer (CT, also sometimes called charge delocalization) interactions. In this work, a numerically exact scheme to decompose the CT interaction energy into pairwise additive terms is introduced for the ALMO-EDA using density functional theory. Unlike perturbative pairwise charge-decomposition analysis, the new approach does not break down for strongly interacting systems, or show significant exchange-correlation functional dependence in the decomposed energy components. Both the energy lowering and the charge flow associated with CT can be decomposed. Complementary occupied-virtual orbital pairs (COVPs) that capture the dominant donor and acceptor CT orbitals are obtained for the new decomposition. It is applied to systems with different types of interactions including DNA base-pairs, borane-ammonia adducts, and transition metal hexacarbonyls. While consistent with most existing understanding of the nature of CT in these systems, the results also reveal some new insights into the origin of trends in donor-acceptor interactions.

Probing radical-molecule interactions with a second generation energy decomposition analysis of DFT calculations using absolutely localized molecular orbitals.

Intermolecular interactions between radicals and closed-shell molecules are ubiquitous in chemical processes, ranging from the benchtop to the atmosphere and extraterrestrial space. While energy decomposition analysis (EDA) schemes for closed-shell molecules can be generalized for studying radical-molecule interactions, they face challenges arising from the unique characteristics of the electronic structure of open-shell species. In this work, we introduce additional steps that are necessary for the proper treatment of radical-molecule interactions to our previously developed unrestricted Absolutely Localized Molecular Orbital (uALMO)-EDA based on density functional theory calculations. A "polarize-then-depolarize" (PtD) scheme is used to remove arbitrariness in the definition of the frozen wavefunction, rendering the ALMO-EDA results independent of the orientation of the unpaired electron obtained from isolated fragment calculations. The contribution of radical rehybridization to polarization energies is evaluated. It is also valuable to monitor the wavefunction stability of each intermediate state, as well as their associated spin density profiles, to ensure the EDA results correspond to a desired electronic state. These radical extensions are incorporated into the "vertical" and "adiabatic" variants of uALMO-EDA for studies of energy changes and property shifts upon complexation. The EDA is validated on two model complexes, H2O˙F and FH˙OH. It is then applied to several chemically interesting radical-molecule complexes, including the sandwiched and T-shaped benzene dimer radical cation, complexes of pyridine with benzene and naphthalene radical cations, binary and ternary complexes of the hydroxyl radical with water (˙OH(H2O) and ˙OH(H2O)2), and the pre-reactive complexes and transition states in the ˙OH + HCHO and ˙OH + CH3CHO reactions. These examples suggest that this second generation uALMO-EDA is a useful tool for furthering one's understanding of both energetic and property changes associated with radical-molecule interactions.

On the Computational Characterization of Charge-Transfer Effects in Noncovalently Bound Molecular Complexes.

Charge-transfer (CT) is an important binding force in the formation of intermolecular complexes, and there have been a variety of theoretical models proposed to quantify this effect. These approaches, which typically rely on a definition of a "CT-free" state based on a partition of the system, sometimes yield significantly different results for a given intermolecular complex. Two widely used definitions of the "CT-free" state, the absolutely localized molecular orbitals (ALMO) method (where only on-fragment orbital mixings are permitted) and the constrained density functional theory (CDFT) approach (where fragment electron populations are fixed), are carefully examined in this work. Natural bond orbital (NBO) and the regularized symmetry-adapted perturbation theory (SAPT) are also briefly considered. Results for the ALMO and CDFT definitions of CT are compared on a broad range of model systems, including hydrogen-bonding systems, borane complexes, metal-carbonyl complexes, and complexes formed by water and metal cations. For most of these systems, CDFT yields a much smaller equilibrium CT energy compared to that given by the ALMO-based definition. This is mainly because the CDFT population constraint does not fully inhibit CT, which means that the CDFT "CT-free" state is in fact CT-contaminated. Examples of this contamination include (i) matching forward and backward donation (e.g., formic acid dimer) and (ii) unidirectional CT without changing fragment populations. The magnitude of the latter effect is quantified in systems such as the water dimer by employing a 3-space density constraint in addition to the orbital constraint. Furthermore, by means of the adiabatic EDA, it is shown that several observable effects of CT, such as the "pyramidalization" of the planar BH3 molecule upon the complexation with Lewis bases, already appear on the "CT-free" CDFT surface. These results reveal the essential distinctions between the ALMO and CDFT definitions of CT and suggest that the former is more consistent with accepted understanding of the role of CT in intermolecular binding.

Energy decomposition analysis in an adiabatic picture.

Energy decomposition analysis (EDA) of electronic structure calculations has facilitated quantitative understanding of diverse intermolecular interactions. Nevertheless, such analyses are usually performed at a single geometry and thus decompose a "single-point" interaction energy. As a result, the influence of the physically meaningful EDA components on the molecular structure and other properties are not directly obtained. To address this gap, the absolutely localized molecular orbital (ALMO)-EDA is reformulated in an adiabatic picture, where the frozen, polarization, and charge transfer energy contributions are defined as energy differences between the stationary points on different potential energy surfaces (PESs), which are accessed by geometry optimizations at the frozen, polarized and fully relaxed levels of density functional theory (DFT). Other molecular properties such as vibrational frequencies can thus be obtained at the stationary points on each PES. We apply the adiabatic ALMO-EDA to different configurations of the water dimer, the water-Cl- and water-Mg2+/Ca2+ complexes, metallocenes (Fe2+, Ni2+, Cu2+, Zn2+), and the ammonia-borane complex. This method appears to be very useful for unraveling how physical effects such as polarization and charge transfer modulate changes in molecular properties induced by intermolecular interactions. As an example of the insight obtained, we find that a linear hydrogen bond geometry for the water dimer is preferred even without the presence of polarization and charge transfer, while the red shift in the OH stretch frequency is primarily a charge transfer effect; by contrast, a near-linear geometry for the water-chloride hydrogen bond is achieved only when charge transfer is allowed.

Probing non-covalent interactions with a second generation energy decomposition analysis using absolutely localized molecular orbitals.

An energy decomposition analysis (EDA) separates a calculated interaction energy into as many interpretable contributions as possible; for instance, permanent and induced electrostatics, Pauli repulsions, dispersion and charge transfer. The challenge is to construct satisfactory definitions of all terms in the chemically relevant regime where fragment densities overlap, rendering unique definitions impossible. Towards this goal, we present an improved EDA for Kohn-Sham density functional theory (DFT) with properties that have previously not been simultaneously attained. Building on the absolutely localized molecular orbital (ALMO)-EDA, this second generation ALMO-EDA is variational and employs valid antisymmetric electronic wavefunctions to produce all five contributions listed above. These contributions moreover all have non-trivial complete basis set limits. We apply the EDA to the water dimer, the T-shaped and parallel-displaced benzene dimer, the p-biphthalate dimer "anti-electrostatic" hydrogen bonding complex, the biologically relevant binding of adenine and thymine in stacked and hydrogen-bonded configurations, the triply hydrogen-bonded guanine-cytosine complex, the interaction of Cl(-) with s-triazine and with the 1,3-dimethyl imidazolium cation, which is relevant to the study of ionic liquids, and the water-formaldehyde-vinyl alcohol ter-molecular radical cationic complex formed in the dissociative photoionization of glycerol.

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation.

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.

Variational Energy Decomposition Analysis of Chemical Bonding. 1. Spin-Pure Analysis of Single Bonds.

We have designed an energy decomposition analysis (EDA) to gain a deeper understanding of single chemical bonds, that is, those in which the interacting fragments are doublet open-shell systems but the supersystem is closed-shell. The method is a spin-pure extension of the absolutely localized molecular orbital (ALMO) EDA to the one-pair perfect pairing energy (equivalently to an active space of two electrons in two orbitals). The total interaction energy is broken up into four terms: frozen interactions, spin-coupling, polarization, and charge-transfer. A variety of single bonds are analyzed and, in addition, we use this method to show how solvation changes the nature of bonds, producing different results in the gas-phase and with explicit solvent molecules.

A systematic study on Pt based, subnanometer-sized alloy cluster catalysts for alkane dehydrogenation: effects of intermetallic interaction.

Platinum-based bimetallic nanoparticles are analyzed by the application of density functional theory to a series of tetrahedral Pt3X cluster models, with element X taken from the P-block, preferably group 14, or from the D-block around group 10. Almost identical cluster geometries allow a systematic investigation of electronic effects induced by different elements X. Choosing the propane-to-propene conversion as the desired dehydrogenation reaction, we provide estimates for the activity and selectivity of the various catalysts based on transition state theory. No significant Brønsted-Evans-Polanyi-relation could be found for the given reaction. A new descriptor, derived from an energy decomposition analysis, captures the effect of element X on the rate-determining step of the first hydrogen abstraction. Higher activities than obtained for pure Pt4 clusters are predicted for Pt alloys containing Ir, Sn, Ge and Si, with Pt3Ir showing particularly high selectivity.

Defining the contributions of permanent electrostatics, Pauli repulsion, and dispersion in density functional theory calculations of intermolecular interaction energies.

In energy decomposition analysis of Kohn-Sham density functional theory calculations, the so-called frozen (or pre-polarization) interaction energy contains contributions from permanent electrostatics, dispersion, and Pauli repulsion. The standard classical approach to separate them suffers from several well-known limitations. We introduce an alternative scheme that employs valid antisymmetric electronic wavefunctions throughout and is based on the identification of individual fragment contributions to the initial supersystem wavefunction as determined by an energetic optimality criterion. The density deformations identified with individual fragments upon formation of the initial supersystem wavefunction are analyzed along with the distance dependence of the new and classical terms for test cases that include the neon dimer, ammonia borane, water-Na(+), water-Cl(-), and the naphthalene dimer.

Alternative definitions of the frozen energy in energy decomposition analysis of density functional theory calculations.

In energy decomposition analysis (EDA) of intermolecular interactions calculated via density functional theory, the initial supersystem wavefunction defines the so-called "frozen energy" including contributions such as permanent electrostatics, steric repulsions, and dispersion. This work explores the consequences of the choices that must be made to define the frozen energy. The critical choice is whether the energy should be minimized subject to the constraint of fixed density. Numerical results for Ne2, (H2O)2, BH3-NH3, and ethane dissociation show that there can be a large energy lowering associated with constant density orbital relaxation. By far the most important contribution is constant density inter-fragment relaxation, corresponding to charge transfer (CT). This is unwanted in an EDA that attempts to separate CT effects, but it may be useful in other contexts such as force field development. An algorithm is presented for minimizing single determinant energies at constant density both with and without CT by employing a penalty function that approximately enforces the density constraint.

Polarization contributions to intermolecular interactions revisited with fragment electric-field response functions.

The polarization energy in intermolecular interactions treated by self-consistent field electronic structure theory is often evaluated using a constraint that the atomic orbital (AO) to molecular orbital transformation is blocked by fragments. This approach is tied to AO basis sets, overestimates polarization energies in the overlapping regime, particularly in large AO basis sets, and lacks a useful complete basis set limit. These problems are addressed by the construction of polarization subspaces based on the responses of isolated fragments to weak electric fields. These subspaces are spanned by fragment electric-field response functions, which can capture effects up to the dipole (D), or quadrupole (DQ) level, or beyond. Schemes are presented for the creation of both non-orthogonal and orthogonal fragment subspaces, and the basis set convergence of the polarization energies computed using these spaces is assessed. Numerical calculations for the water dimer, water-Na(+), water-Mg(2+), water-F(-), and water-Cl(-) show that the non-orthogonal DQ model is very satisfactory, with small differences relative to the orthogonalized model. Additionally, we prove a fundamental difference between the polarization degrees of freedom in the fragment-blocked approaches and in constrained density schemes. Only the former are capable of properly prohibiting charge delocalization during polarization.

Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm.

Construction of the exact exchange matrix, K, is typically the rate-determining step in hybrid density functional theory, and therefore, new approaches with increased efficiency are highly desirable. We present a framework with potential for greatly improved efficiency by computing a compressed exchange matrix that yields the exact exchange energy, gradient, and direct inversion of the iterative subspace (DIIS) error vector. The compressed exchange matrix is constructed with one index in the compact molecular orbital basis and the other index in the full atomic orbital basis. To illustrate the advantages, we present a practical algorithm that uses this framework in conjunction with the resolution of the identity (RI) approximation. We demonstrate that convergence using this method, referred to hereafter as occupied orbital RI-K (occ-RI-K), in combination with the DIIS algorithm is well-behaved, that the accuracy of computed energetics is excellent (identical to conventional RI-K), and that significant speedups can be obtained over existing integral-direct and RI-K methods. For a 4400 basis function C68H22 hydrogen-terminated graphene fragment, our algorithm yields a 14× speedup over the conventional algorithm and a speedup of 3.3× over RI-K.

Spin-flip non-orthogonal configuration interaction: a variational and almost black-box method for describing strongly correlated molecules.

In this paper, we report the development, implementation, and assessment of a novel method for describing strongly correlated systems, spin-flip non-orthogonal configuration interaction (SF-NOCI). The wavefunction is defined to be a linear combination of independently relaxed Slater determinants obtained from all possible spin-flipping excitations within a localized orbital active-space, typically taken to be the singly occupied orbitals of a high-spin ROHF wavefunction. The constrained orbital optimization of each CI basis configuration is defined such that only non-active-space orbitals are allowed to relax (all active space orbitals are fixed). A number of simplifications and benefits arise due to the fact that only a restricted number of orbital rotations are permitted, (1) basis states cannot coalesce during SCF, (2) basis state optimization is better conditioned due to a larger effective HOMO-LUMO gap, (3) smooth potential energy surfaces are easily obtained, (4) the Hamiltonian coupling between two basis states with non-orthogonal orbitals is greatly simplified. To illustrate the advantages over a conventional orthogonal CI expansion, we investigate exchange coupling constants of bimetallic complexes, the avoided crossing of the lowest singlet states during LiF dissociation, and ligand non-innocence in an organometallic complex. These numerical examples indicate that good qualitative agreement can be obtained with SF-NOCI, but dynamical correlation must be included to obtain quantitative accuracy.

Dissociative photoionization of glycerol and its dimer occurs predominantly via a ternary hydrogen-bridged ion-molecule complex.

The photoionization and dissociative photoionization of glycerol are studied experimentally and theoretically. Time-of-flight mass spectrometry combined with vacuum ultraviolet synchrotron radiation ranging from 8 to 15 eV is used to investigate the nature of the major fragments and their corresponding appearance energies. Deuterium (1,1,2,3,3-D5) and (13)C (2-(13)C) labeling is employed to narrow down the possible dissociation mechanisms leading to the major fragment ions (C3H(x)O2(+), C2H(x)O2(+), C2H(x)O(+), CH(x)O(+)). We find that the primary fragmentation of the glycerol radical cation (m/z 92) occurs only via two routes. The first channel proceeds via a six-membered hydrogen-transfer transition state, leading to a common stable ternary intermediate, comprised of neutral water, neutral formaldehyde, and a vinyl alcohol radical cation, which exhibits a binding energy of ≈42 kcal/mol and a very short (1.4 Å) hydrogen bond. Fragmentation of this intermediate gives rise to experimentally observed m/z 74, 62, 44, and 45. Fragments m/z 74 and 62 both consist of hydrogen-bridged ion-molecule complexes with binding energy >25 kcal/mol, whereas the m/z 44 species lacks such stabilization. This explains why water- or formaldehyde-loss products are observed first. The second primary fragmentation route arises from cleaving the elongated C-C bond. Also for this channel, intermediates comprised of hydrogen-bridged ion-molecule complexes exhibiting binding energies >24 kcal/mol are observed. Energy decomposition analysis reveals that electrostatic and charge-transfer interactions are equally important in hydrogen-bridged ion-molecule complexes. Furthermore, the dissociative photoionization of the glycerol dimer is investigated and compared to the main pathways for the monomeric species. To a first approximation, the glycerol dimer radical cation can be described as a monomeric glycerol radical cation in the presence of a spectator glycerol, thus giving rise to a dissociation pattern similar to that of the monomer.

Unrestricted absolutely localized molecular orbitals for energy decomposition analysis: theory and applications to intermolecular interactions involving radicals.

Radical-closed shell and radical-radical intermolecular interactions are less well-understood than those between closed shell species. With the objective of gaining additional insight, this work reports a generalization of the absolutely localized molecular orbital (ALMO) energy decomposition analysis (EDA) to open shell fragments, described by self-consistent field methods, such as standard density functional theory. The ALMO-EDA variationally partitions an intermolecular interaction energy into three separate contributions; frozen orbital interactions, polarization, and charge transfer. The first examples involve comparison of the interactions of alkanes and alkyl radicals (methyl radical, methane, tertiary butyl radical, and isobutane) with sodium, potassium, hydronium, and ammonium cations. A second series of examples involve benzene cation interacting with a series of nucleophiles in both on-top and side-on geometries. The ALMO-EDA yields a variety of interesting insights into the relative roles of its component contributions as the interacting partners and their geometries are changed.

Examination of the hydrogen-bonding networks in small water clusters (n = 2-5, 13, 17) using absolutely localized molecular orbital energy decomposition analysis.

Using the ωB97X-D and B3LYP density functionals, the absolutely localized molecular orbital energy decomposition method (ALMO-EDA) is applied to the water dimer through pentamer, 13-mer and 17-mer clusters. Two-body, three-body, and total interaction energies are decomposed into their component energy terms: frozen density interaction energy, polarization energy, and charge transfer energy. Charge transfer, polarization, and frozen orbital interaction energies are all found to be significant contributors to the two-body and total interaction energies; the three-body interaction energies are dominated by polarization. Each component energy term for the two-body interactions is highly dependent on the associated hydrogen bond distance. The favorability of the three-body terms associated with the 13- and 17-mer structures depends on the hydrogen-donor or hydrogen-acceptor roles played by each of the three component waters. Only small errors arise from neglect of three-body interactions without two adjacent water molecules, or beyond three-body interactions. Interesting linear correlations are identified between the contributions of charge-transfer and polarization terms to the two and three-body interactions, which permits elimination of explicit calculation of charge transfer to a good approximation.