Electrostatic Domination of the Effect of Electron Correlation in Intermolecular Interactions

Regularized Second-Order Møller-Plesset Theory: A More Accurate Alternative to Conventional MP2 for Noncovalent Interactions and Transition Metal Thermochemistry for the Same Computational Cost

Second-order Møller-Plesset theory (MP2) notoriously breaks down for π-driven dispersion interactions and dative bonds in transition metal complexes. Herein, we investigate three physically justified forms of single-parameter, energy-gap dependent regularization which can yield high and transferable accuracy for a variety of noncovalent interactions (including S22, S66, and L7 test sets) and (mostly closed shell) transition metal thermochemistry. Regularization serves to damp overestimated pairwise additive contributions, renormalizing first-order amplitudes such that the effects of higher-order correlations are incorporated. The optimal parameter values for the noncovalent and transition metal sets are 1.1, 0.7, and 0.4 for κ, σ, and σ² regularizers, respectively. However, such regularization slightly degrades the accuracy of conventional MP2 for some small-molecule test sets, most of which have relatively large average frontier energy gaps. Our results suggest that appropriately regularized MP2 models may improve double hybrid density functionals, at no additional cost over conventional MP2.

Correlation Effects in Trimeric Acylphloroglucinols

Trimeric acylphloroglucinols (T-ACPLs) are a subclass of the large class of acylphloroglucinols—derivatives of 1,3,5-trihydroxybenzene containing an R–C=O group. T-ACPL molecules contain three acylphloroglucinol moieties linked by methylene bridges. Many of them are present in natural sources and exhibit biological activities, often better than the corresponding activities of monomeric acylphloroglucinols. All the stable conformers of T-ACPLs contain seven intramolecular hydrogen bonds, which constitute the dominant stabilising factors. A total of 38 different T-ACPLs, including both naturally occurring and model molecules, have been calculated at the HF and DFT/B3LYP levels. The DFT/B3LYP calculations were carried out both without and with Grimme’s dispersion correction, to highlight the dispersion (and, therefore, also electron correlation) effects for these molecules. The roles of dispersion are evaluated considering the effects of Grimme’s correction on the estimation of the conformers’ energies, the description of the characteristics of the individual hydrogen bonds, the conformers’ geometries and other molecular properties. Overall, the results offer a comprehensive overview of the conformational preferences of T-ACPL molecules, their intramolecular hydrogen bond patterns, and the correlation effects on their properties.

Exploring the Limits of Second- and Third-Order Møller-Plesset Perturbation Theories for Noncovalent Interactions: Revisiting MP2.5 and Assessing the Importance of Regularization and Reference Orbitals

This work systematically assesses the influence of reference orbitals, regularization, and scaling on the performance of second- and third-order Møller-Plesset perturbation theory wave function methods for noncovalent interactions (NCIs). Testing on 19 data sets (A24, DS14, HB15, HSG, S22, X40, HW30, NC15, S66, AlkBind12, CO2Nitrogen16, HB49, Ionic43, TA13, XB18, Bauza30, CT20, XB51, and Orel26rad) covers a wide range of different NCIs including hydrogen bonding, dispersion, and halogen bonding. Inclusion of potential energy surfaces from different hydrogen bonds and dispersion-bound complexes gauges accuracy for nonequilibrium geometries. Fifteen methods are tested. In notation where nonstandard choices of orbitals are denoted as methods:orbitals, these are MP2, κ-MP2, SCS-MP2, OOMP2, κ-OOMP2, MP3, MP2.5, MP3:OOMP2, MP2.5:OOMP2, MP3:κ-OOMP2, MP2.5:κ-OOMP2, κ-MP3:κ-OOMP2, κ-MP2.5:κ-OOMP2, MP3:ωB97X-V, and MP2.5:ωB97X-V. Furthermore, we compare these methods to the ωB97M-V and B3LYP-D3 density functionals, as well as CCSD. We find that the κ-regularization (κ = 1.45 au was used throughout) improves the energetics in almost all data sets for both MP2 (in 17 out of 19 data sets) and OOMP2 (16 out of 19). The improvement is significant (e.g., the root-mean-square deviation (RMSD) for the S66 data set is 0.29 kcal/mol for κ-OOMP2 versus 0.67 kcal/mol for MP2) and for interactions between stable closed-shell molecules, not strongly dependent on the reference orbitals. Scaled MP3 (with a factor of 0.5) using κ-OOMP2 reference orbitals (MP2.5:κ-OOMP2) provides significantly more accurate results for NCIs across all data sets with noniterative O(N⁶) scaling (S66 data set RMSD: 0.10 kcal/mol). Across the entire data set of 356 points, the improvement over standard MP2.5 is approximately a factor of 2: RMSD for MP3:κ-OOMP2 is 0.25 vs 0.50 kcal/mol for MP2.5. The use of high-quality density functional reference orbitals (ωB97X-V) also significantly improves the results of MP2.5 for NCI over a Hartree-Fock orbital reference. All our assessments and conclusions are based on the use of the medium-sized aug-cc-pVTZ basis to yield results that are directly compared against complete basis set limit reference values.

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.

Components of the interaction energy of the odd-electron halogen bond: an ab initio study

In the realm of non-covalent interactions (NCI), the odd-electron halogen bond offers a fertile ground to explore the nature of such weak interactions. Here, an ab initio study of odd-electron halogen bonding (XB) is reported. The interactions of five radicals with several freons and interhalogens are studied using the Møller-Plesset (MP2) method. The regioselectivity, interaction energy and the components of the interaction energy of odd-electron XB were tuned by judicial selection of donor-acceptor pairs as revealed by scrutinizing the conceptual DFT parameters, NCI plot and LED-DLPNO-CCSD(T) analysis. The contribution from dispersion interaction is rather high for all XB bonded complexes and it increases when the interacting atom of the XB donor is highly polarizable. Additionally, the polarisation and intermolecular charge-transfer also contribute significantly when both the donor and acceptor atoms are soft species, resulting in a soft-soft interaction. We believe that our finding will not only shed new light on non-covalent interaction of odd-electron XB but will also be able to capture the pnictogen, chalcogen and tetrel bonding interactions. The ability of conceptual DFT parameters to predict the interaction energy and its components shown in this study will be helpful for tuning of substrates for desired products, modelling bio/macromolecules and crystal engineering.

Effect of Electron Correlation on Intermolecular Interactions: A Pair Natural Orbitals Coupled Cluster Based Local Energy Decomposition Study

The development of post-Hartree-Fock (post-HF) energy decomposition schemes that are able to decompose the HF and correlation components of the interaction energy into chemically meaningful contributions is a very active field of research. One of the challenges is to provide a clear-cut quantification to the elusive London dispersion component of the intermolecular interaction. London dispersion is well-known to be a pure correlation effect, and as such it is not properly described by mean field theories. In this context, we have recently developed the local energy decomposition (LED) analysis, which provides a chemically meaningful decomposition of the interaction energy between two or more fragments computed at the domain-based local pair natural orbitals coupled cluster (DLPNO-CCSD(T)) level of theory. In this work, this scheme is used in conjunction with other interpretation tools to study a series of molecular adducts held together by intermolecular interactions of different natures. The HF and correlation components of the interaction energy are thus decomposed into a series of chemically meaningful contributions. Emphasis is placed on discussing the physical effects associated with the inclusion of electron correlation. It is found that four distinct physical effects can contribute to the magnitude of the correlation part of intermolecular binding energies (Δ E_int^C): (i) London dispersion, (ii) the correlation correction to the reference induction energy, (iii) the correlation correction to the electron sharing process, and (iv) the correlation correction to the permanent electrostatics. As expected, the largest contribution to the correlation binding energy of neutral, apolar molecules is London dispersion, as in the argon dimer case. In contrast, the correction for the HF induction energy dominates Δ E_int^C in systems in which an apolar molecule interacts with charged or strongly polar species, as in Ar-Li⁺. This effect has its origin in the systematic underestimation of polarizabilities at the HF level of theory. For similar reasons, electron sharing largely contributes to the correlation binding energy of covalently bound molecules, as in the beryllium dimer case. Finally, the correction for HF permanent electrostatics significantly contributes to Δ E_int^C in molecules with strong dipoles, such as water and hydrogen fluoride dimers. This effect originates from the characteristic overestimation of dipole moments at the HF level of theory, leading in some cases to positive Δ E_int^C values. Our results are apparently in contrast to the widely accepted view that Δ E_int^C is typically dominated by London dispersion, at least, in the strongly interacting region. Clearly, post-HF energy decomposition schemes are very powerful tools to analyze, categorize, and understand the various contributions to the intermolecular interaction energy. Hopefully, this will eventually lead to insights that are helpful in designing systems with tailored properties. All analysis tools presented in this work will be available free of charge in the next release of the ORCA program package.

Local energy decomposition analysis of hydrogen-bonded dimers within a domain-based pair natural orbital coupled cluster study

The local energy decomposition (LED) analysis allows for a decomposition of the accurate domain-based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] energy into physically meaningful contributions including geometric and electronic preparation, electrostatic interaction, interfragment exchange, dynamic charge polarization, and London dispersion terms. Herein, this technique is employed in the study of hydrogen-bonding interactions in a series of conformers of water and hydrogen fluoride dimers. Initially, DLPNO-CCSD(T) dissociation energies for the most stable conformers are computed and compared with available experimental data. Afterwards, the decay of the LED terms with the intermolecular distance (r) is discussed and results are compared with the ones obtained from the popular symmetry adapted perturbation theory (SAPT). It is found that, as expected, electrostatic contributions slowly decay for increasing r and dominate the interaction energies in the long range. London dispersion contributions decay as expected, as r-6. They significantly affect the depths of the potential wells. The interfragment exchange provides a further stabilizing contribution that decays exponentially with the intermolecular distance. This information is used to rationalize the trend of stability of various conformers of the water and hydrogen fluoride dimers.

Formation of Agostic Structures Driven by London Dispersion

Agostic interactions between a C-H bond and a transition metal are commonly crucial in catalytic polymerization processes. Herein, a quantitative study of the nature of β-agostic interactions in a series of systems of importance in C-H bond activation reactions is reported. The analysis, characterized by the use of a coupled-cluster-based energy decomposition scheme, demonstrates that short-range London dispersion between the agostic C-H bond and the metal center plays a fundamental role in affecting the structural stability of these systems, contrary to a widely held view. These results are used to rationalize a series of previously published experimental findings.

Machine Learning of Dynamic Electron Correlation Energies from Topological Atoms

We present an innovative method for predicting the dynamic electron correlation energy of an atom or a bond in a molecule utilizing topological atoms. Our approach uses the machine learning method Kriging (Gaussian Process Regression with a non-zero mean function) to predict these dynamic electron correlation energy contributions. The true energy values are calculated by partitioning the MP2 two-particle density-matrix via the Interacting Quantum Atoms (IQA) procedure. To our knowledge, this is the first time such energies have been predicted by a machine learning technique. We present here three important proof-of-concept cases: the water monomer, the water dimer, and the van der Waals complex H₂···He. These cases represent the final step toward the design of a full IQA potential for molecular simulation. This final piece will enable us to consider situations in which dispersion is the dominant intermolecular interaction. The results from these examples suggest a new method by which dispersion potentials for molecular simulation can be generated.

The Transferability of Topologically Partitioned Electron Correlation Energies in Water Clusters

The electronic effects that govern the cohesion of water clusters are complex, demanding the inclusion of N-body, Coulomb, exchange and correlation effects. Here we present a much needed quantitative study of the effect of correlation (and hence dispersion) energy on the stabilization of water clusters. For this purpose we used a topological energy partitioning method called Interacting Quantum Atoms (IQA) to partition water clusters into topological atoms, based on a MP2/6-31G(d,p) wave function, and modified versions of GAUSSIAN09 and the Quantum Chemical Topology (QCT) program MORFI. Most of the cohesion in the water clusters provided by electron correlation comes from intramolecular energy stabilization. Hydrogen bond-related interactions tend to largely cancel each other. Electron correlation energies are transferable in almost all instances within 1 kcal mol^-1 . This observed transferability is very important to the further development of the QCT force field FFLUX, especially to the future modelling of liquid water.

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.