MP2-IQA: upscaling the analysis of topologically partitioned electron correlation

Exact decompositions of the total KS-DFT exchange-correlation energy into one- and two-center terms

In the so-called Interacting Quantum Atoms (IQA) approach, the molecular energy is numerically decomposed as a sum of atomic and diatomic contributions. While proper formulations have been put forward for both Hartree-Fock and post-Hartree-Fock wavefunctions, this is not the case for the Kohn-Sham density functional theory (KS-DFT). In this work, we critically analyze the performance of two fully additive approaches for the IQA decomposition of the KS-DFT energy, namely, the one from Francisco et al., which uses atomic scaling factors, and that from Salvador and Mayer based upon the bond order density (SM-IQA). Atomic and diatomic exchange-correlation (xc) energy components are obtained for a molecular test set comprising different bond types and multiplicities and along the reaction coordinate of a Diels-Alder reaction. Both methodologies behave similarly for all systems considered. In general, the SM-IQA diatomic xc components are less negative than the Hartree-Fock ones, which is in good agreement with the known effect of electron correlation upon (most) covalent bonds. In addition, a new general scheme to minimize the numerical error of the sum of two-electron energy contributions (i.e., Coulomb and exact exchange) in the framework of overlapping atoms is described in detail.

Non-covalent interactions from a Quantum Chemical Topology perspective

About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter’s role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.

Theoretical design and preparation research of molecularly imprinted polymers for steviol glycosides

In this paper, a novel molecularly imprinted polymer (MIP) for specific adsorption of steviol glycosides was designed, and the imprinting mechanism of self-assembly system between template and monomers was clearly explored. Firstly, steviol (STE) was chosen as dummy template, and the density functional theory (DFT) at B3LYP/6-31 + G (d, p) level was used to select monomers, imprinting molar ratios, solvents, and cross-linking agents. The selectivity to five steviol glycosides was also calculated. Importantly, reduced density gradient (RDG) theory combined with atom in molecules (AIM) and infrared spectrum (IR) was applied to investigate the bonding situation and the nature of noncovalent interaction in self-assembly system. The theoretical designed results showed that the template which interacts with acrylic acid (AA) has the minimum binding energy, and the complex with the molar ratio of 1 : 4 has the most stable structure. Toluene (TL) and ethylene glycol dimethacrylate (EGDMA) were chosen as the optimal solvent and cross-linking agent, respectively. Five hydrogen bonds formed in the self-assembly system are the key forces at the adsorption sites of MIPs through the RDG and AIM analyses. The MIPs were synthesized by theoretical predictions, and the results showed that the maximum adsorption capacity towards dulcoside A is 26.17 mg/g. This work provided a theoretical direction and experimental validation for deeper researches of the MIPs for steviol glycosides. In addition, the method of RDG theory coupled with AIM and IR also could be used to analyze other imprinting formation mechanisms systematically.

From the Linnett-Gillespie model to the polarization of the spin valence shells of metals in complexes

In this paper, we present a novel approach to track the origin of the metal complex structure from the topology of the α and β spin densities as an extension of the Linnett-Gillespie model. Usually, the theories that explain the metal-ligand interactions consider the disposition and the relative energies of the empty or occupied set of d orbitals, ignoring the spin contribution explicitly. Our quantum topological approach considers the spatial distribution of the α and β spin valence shells, and the energy interaction between them. We used the properties of the atomic graph, a topological object that summarises the charge concentrations and depletions on the valence shell of an atom in a molecule, and the interacting quantum atoms (IQA) energy partition scheme. Unlike the Linnett-Gillespie model, which is based on electron-electron repulsion, our approach states that the ligands provoke a redistribution of the electron density to maximize the nuclear-electron interactions in each spin valence shell to bypass the concentration of electron-electron interactions, resulting in a polarization pattern which determines the position of the ligands.

Photochemistry in Real Space: Batho- and Hypsochromism in the Water Dimer

The development of chemical intuition in photochemistry faces several difficulties that result from the inadequacy of the one-particle picture, the Born-Oppenheimer approximation, and other basic ideas used to build models. It is shown herein how real-space approaches can be efficiently used to gain valuable insights in photochemistry through a simple example of red and blue shift effects: the double hypso- and bathochromic shifts in the low-lying valence excited states of (H₂ O)₂ . It is demonstrated that 1) the use of these techniques allows the perturbative language used in the theory of intermolecular interactions, even in the strongly interacting short-range regime, to be maintained; 2) one and only one molecule is photoexcited in each of the addressed excited states and 3) the electrostatic interaction between the in-the-cluster molecular dipoles provides a fairly intuitive rationalisation of the observed batho- and hypsochromism. The methods exploited and illustrated herein are able to maintain the individuality and properties of the interacting entities in a molecular aggregate, and thereby they allow chemical intuition in general states, at any geometry and using a broad variety of electronic structure methods to be kept and built.

Interacting Quantum Atoms-A Review

The aim of this review is threefold. On the one hand, we intend it to serve as a gentle introduction to the Interacting Quantum Atoms (IQA) methodology for those unfamiliar with it. Second, we expect it to act as an up-to-date reference of recent developments related to IQA. Finally, we want it to highlight a non-exhaustive, yet representative set of showcase examples about how to use IQA to shed light in different chemical problems. To accomplish this, we start by providing a brief context to justify the development of IQA as a real space alternative to other existent energy partition schemes of the non-relativistic energy of molecules. We then introduce a self-contained algebraic derivation of the methodological IQA ecosystem as well as an overview of how these formulations vary with the level of theory employed to obtain the molecular wavefunction upon which the IQA procedure relies. Finally, we review the several applications of IQA as examined by different research groups worldwide to investigate a wide variety of chemical problems.

An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Study of the Halogen Bond with Explicit Analysis of Electron Correlation

Energy profiles of seven halogen-bonded complexes were analysed with the topological energy partitioning called Interacting Quantum Atoms (IQA) at MP4(SDQ)/6-31+G(2d,2p) level of theory. Explicit interatomic electron correlation energies are included in the analysis. Four complexes combine X₂ (X = Cl or F) with HCN or NH₃, while the remaining three combine ClF with HCN, NH₃ or N₂. Each complex was systematically deformed by translating the constituent molecules along its central axis linking X and N, and reoptimising its remaining geometry. The Relative Energy Gradient (REG) method (Theor. Chem. Acc. 2017, 136, 86) then computes which IQA energies most correlate with the total energy during the process of complex formation and further compression beyond the respective equilibrium geometries. It turns out that the covalent energy (i.e., exchange) of the halogen bond, X…N, itself drives the complex formation. When the complexes are compressed from their equilibrium to shorter X…N distance then the intra-atomic energy of N is in charge. When the REG analysis is restricted to electron correlation then the interatomic correlation energy between X and N again drives the complex formation, and the complex compression is best described by the destabilisation of the through-space correlation energy between N and the "outer" halogen.

Theoretical research of molecular imprinted polymers formed from formaldehyde and methacrylic acid

In recent years, with the development of molecular imprinting technology, the imprinting sites, nature of imprinting, selection of functional monomers, cross-linking agents, solvents, and the optimization of the imprinting ratio are all the hot spots of researchers. In this work, the theoretical prediction of the self-assembly system of formaldehyde (HCHO) molecularly imprinted polymer was carried out by the B3LYP/6-31 G(d,p) method. The geometric configuration and active sites of the stable complex of HCHO and methacrylic acid (MAA) were analyzed. The selection of the imprinting ratios, cross-linking agents, and solvents was discussed. The topological properties of electron density of HCHO-MAA complex were considered by using the topological analysis method of chemical bond electron density based on valence bond theory. This study cannot only reveal the relationship between the imprinting mechanism of molecularly imprinted polymers and the molecular structure and properties of molecularly imprinted polymers but also provide valuable reference for the design and preparation of molecularly imprinted polymers.

Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions

The quantum topological energy partitioning method Interacting Quantum Atoms (IQA) has been applied for over a decade resulting in an enlightening analysis of a variety of systems. In the last three years we have enriched this analysis by incorporating into IQA the two-particle density matrix obtained from Møller–Plesset (MP) perturbation theory. This work led to a new computational and interpretational tool to generate atomistic electron correlation and thus topologically based dispersion energies. Such an analysis determines the effects of electron correlation within atoms and between atoms, which covers both bonded and non-bonded “through -space” atom–atom interactions within a molecule or molecular complex. A series of papers published by us and other groups shows that the behavior of electron correlation is deeply ingrained in structural chemistry. Some concepts that were shown to be connected to bond correlation are bond order, multiplicity, aromaticity, and hydrogen bonding. Moreover, the concepts of covalency and ionicity were shown not to be mutually excluding but to both contribute to the stability of polar bonds. The correlation energy is considerably easier to predict by machine learning (kriging) than other IQA terms. Regarding the nature of the hydrogen bond, correlation energy presents itself in an almost contradicting way: there is much localized correlation energy in a hydrogen bond system, but its overall effect is null due to internal cancelation. Furthermore, the QTAIM delocalization index has a connection with correlation energy. We also explore the role of electron correlation in protobranching, which provides an explanation for the extra stabilization present in branched alkanes compared to their linear counterparts. We hope to show the importance of understanding the true nature of the correlation energy as the foundation of a modern representation of dispersion forces for ab initio, DFT, and force field calculations.

Atomic Partitioning of the MPn (n = 2, 3, 4) Dynamic Electron Correlation Energy by the Interacting Quantum Atoms Method: A Fast and Accurate Electrostatic Potential Integral Approach

Recently, the quantum topological energy partitioning method called interacting quantum atoms (IQA) has been extended to MPn (n = 2, 3, 4) wave functions. This enables the extraction of chemical insight related to dynamic electron correlation. The large computational expense of the IQA-MPn approach is compensated by the advantages that IQA offers compared to older nontopological energy decomposition schemes. This expense is problematic in the construction of a machine learning training set to create kriging models for topological atoms. However, the algorithm presented here markedly accelerates the calculation of atomically partitioned electron correlation energies. Then again, the algorithm cannot calculate pairwise interatomic energies because it applies analytical integrals over whole space (rather than over atomic volumes). However, these pairwise energies are not needed in the quantum topological force field FFLUX, which only uses the energy of an atom interacting with all remaining atoms of the system that it is part of. Thus, it is now feasible to generate accurate and sizeable training sets at MPn level of theory. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.