Efficient Implementation of Energy Decomposition Analysis for Second-Order Møller–Plesset Perturbation Theory and Application to Anion−π Interactions

Decoding energy decomposition analysis: Machine-learned Insights on the impact of the density functional on the bonding analysis

The concept of chemical bonding is a crucial aspect of chemistry that aids in understanding the complexity and reactivity of molecules and materials. However, the interpretation of chemical bonds can be hindered by the choice of the theoretical approach and the specific method utilized. This study aims to investigate the effect of choosing different density functionals on the interpretation of bonding achieved through energy decomposition analysis (EDA). To achieve this goal, a data set was created, representing four bonding groups and various combinations of functionals and dispersion correction schemes. The calculations showed significant variation among the different functionals for the EDA terms, with the dispersion correction terms exhibiting the highest variability. More information was extracted by using machine learning in combination with dimensionality reduction on the data set. Results indicate that, despite the differences in the EDA terms obtained from different functionals, the functional has the least significant impact, suggesting minimal influence on the bonding interpretation.

Path-dependency of energy decomposition analysis & the elusive nature of bonding

Here, we provide evidence of the path-dependency of the energy components of the energy decomposition analysis scheme, EDA, by studying a set of thirty-one closed-shell model systems with the D_2h symmetry point group. For each system, we computed EDA components from nine different pathways and numerically showed that the relative magnitudes of the components differ substantially from one path to the other. Not surprisingly, yet unfortunately, the most significant variations in the relative magnitudes of the EDA components appear in the case of species with bonds within the grey zone of covalency and ionicity. We further discussed that the role of anions and their effect on arbitrary Pauli repulsion energy components affects the nature of bonding defined by EDA. The outcome variation by the selected partitioning scheme of EDA might bring arbitrariness when a careful comparison is overlooked.

Here, we provide evidence of the path-dependency of the energy components of the energy decomposition analysis scheme, EDA, by studying a set of thirty-one closed-shell model systems with the D_2h symmetry point group.

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

A non-perturbative scheme for complete decomposition of energy and charge associated with charge transfer interaction into pairwise additive components.

Generalization of Block-Localized Wave Function for Constrained Optimization of Excited Determinants

The block-localized wave function method is useful to provide insights on chemical bonding and intermolecular interactions through energy decomposition analysis. The method relies on block localization of molecular orbitals (MOs) by constraining the orbitals to basis functions within given blocks. Here, a generalized block-localized orbital (GBLO) method is described to allow both physically localized and delocalized MOs to be constrained in orbital-block definitions. Consequently, GBLO optimization can be conveniently tailored by imposing specific constraints. The GBLO method is illustrated by three examples: (1) constrained polarization response orbitals through dipole and quadrupole perturbation in a water dimer complex, (2) the ground and first excited-state potential energy curves of ethene about its C-C bond rotation, and (3) excitation energies of double electron excited states. Multistate density functional theory is used to determine the energies of the adiabatic ground and excited states using a minimal active space (MAS) comprising specifically charge-constrained and excited determinant configurations that are variationally optimized by the GBLO method. We find that the GBLO expansion that includes delocalized MOs in configurational blocks significantly reduces computational errors in comparison with physical block localization, and the computed ground- and excited-state energies are in good accordance with experiments and results obtained from multireference configuration interaction calculations.

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.

The usefulness of energy decomposition schemes to rationalize host–guest interactions

The findings reported here reveal the robustness and practical application of EDA-NOCV in rationalizing molecular recognition situations in host–guest systems.

Energy components in energy decomposition analysis (EDA) are path functions; why does it matter?

Here, we discuss that unlike bond dissociation energy (BDE) that is a state function quantity, the energy components of the energy decomposition analysis (EDA), i.e. electrostatic interaction, Pauli repulsion, and orbital interaction, are path (process) function quantities. Being a path function means that EDA energy components are not uniquely defined, i.e. the relative magnitudes of the orbital interaction, Pauli repulsion, and electrostatic components may vary depending on the selected pathway for EDA. Therefore, at best, EDA can define whether closely related chemical bonds are more or less ionic/covalent compared with each other. However, a precise assessment of the nature of a certain type of chemical bond using EDA is a questionable task. Besides, we briefly discuss that the widely used EDA pathway, which is merely an arbitrary choice among infinite possible paths, comes to conclusions not consistent with our widely accepted knowledge of bond formation even for the simplest molecules.

A Linear-Scaling Method for Noncovalent Interactions: An Efficient Combination of Absolutely Localized Molecular Orbitals and a Local Random Phase Approximation Approach

A novel method for the accurate and efficient calculation of interaction energies in weakly bound complexes composed of a large number of molecules is presented. The new ALMO+RPAd method circumvents the prohibitive scaling of coupled cluster singles and doubles while still providing similar accuracy across a diverse range of weakly bound chemical systems. Linear-scaling procedures for the Fock build are given utilizing absolutely localized molecular orbitals (ALMOs), resulting in the a priori exclusion of basis set superposition errors. A bespoke data structure and algorithm using density fitting are described, leading to linear scaling for the storage and computation of the two-electron integrals. Electron correlation is included through a new, linear-scaling pairwise local random phase approximation approach, including exchange interactions, and decomposed into purely dispersive excitations (RPAxd). Collectively, these allow meaningful decomposition of the interaction energy into physically distinct contributions: electrostatic, polarization, charge transfer, and dispersion. Comparison with symmetry-adapted perturbation theory shows good qualitative agreement. Tests on various dimers and the S66 benchmark set demonstrate results within 0.5 kcal mol^-1 of coupled cluster singles and doubles results. On a large cluster of water molecules, we achieve calculations involving over 3500 orbital and 12,000 auxiliary basis functions in under 10 min on a single CPU core.

Nature of halogen bonding involving π-systems, nitroxide radicals and carbenes: a highlight of the importance of charge transfer

The recently developed adiabatic absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) has proven to be useful in determining the effects of different energy components on the geometries of complexes bound by intermolecular interactions. The authors have applied it to systems such as the water dimer, water-ion complexes, metallocenes and lone-pair type halogen-bonded (XB) dimers. In this study, we have extended the second-generation ALMO-EDA method to 40 different XB complexes by benchmarking against its classical counterpart and symmetry-adapted perturbation theory (SAPT). In addition, we have examined the nature of halogen bonding involving less studied XB acceptors, namely π-systems, radicals and carbenes, using the adiabatic ALMO-EDA analyses, particularly to shed light on how each energy component affects the geometries of the XB complexes. Our results show that the second-generation ALMO-EDA predicts a higher electrostatic energy contribution in all XB complexes compared to SAPT and classical ALMO-EDA schemes. On the other hand, when comparing across different XB acceptors, all three partition schemes produced the same qualitative finding. The adiabatic ALMO-EDA analyses indicate that while the inclusion of a charge transfer contribution is important in achieving accurate XB bond lengths and interaction energies, as well as recovering the binding site specificity of XB involving benzene and naphthalene acceptors, it is sufficient to obtain the linearity of the XB complexes in the frozen approximation.

Co-operativity in non-covalent interactions in ternary complexes: a comprehensive electronic structure theory based investigation

The structure and stability of various ternary complexes in which an extended aromatic system such as coronene interacts with ions/atoms/molecules on opposite faces of the π-electron cloud were investigated using ab initio calculations. By characterizing the nature of the intermolecular interactions using an energy decomposition analysis, it was shown that there is an interplay between various types of interactions and that there are co-operativity effects, particularly when different types of interactions coexist in the same system. Graphical abstract Weak OH-π, π-π and van der Waals-π ternary systems are stabilized through dispersion interactions. Cation-π ternary systems are stabilized by through-space electrostatic interactions.

Characterizing the interplay of Pauli repulsion, electrostatics, dispersion and charge transfer in halogen bonding with energy decomposition analysis

Variational energy decomposition analysis establishes charge-transfer as the origin of halogen bond strength differences that go against electrostatics.

Quantifying the Role of Orbital Contraction in Chemical Bonding

This work reports an approach to variationally quantify orbital contraction in chemical bonds by an extension of an energy decomposition analysis (EDA). The orbital contraction energy is defined as the energy lowering due to optimization of the isolated fragments (that combine to form the bond) with a specially constructed virtual set of contraction/expansion functions. This set contains one function per occupied orbital, obtained as the linear response to scaling the nuclear charges. EDA results for a variety of single bonds show substantial changes in the importance of orbital contraction; it plays a critical role for bonds to H but only a very minor role in the bonds between heavier elements. Additionally, energetic stabilization due to rehybridization is separated from inductive polarization by the fact that no mixing with virtual orbitals is involved and is shown to be significant in fragments such as NH₂, OH, and F.