Anion-Anion Complexes Established between Aspartate Dimers

Stable dimers aspartate-aspartate have been studied in aqueous and gas phase through theoretical simulations. The polarizable continuum model (PCM) has been applied to simulate the effect of the hydration on monomers and complexes. The quantum theory of atoms in molecules (QTAIM) and the interacting quantum atoms (IQA) scheme has been used to inquire into if, in the aqueous phase, individual hydrogen bonds have attractive electrostatic components. In all cases a spontaneous formation of the complexes in the aqueous phase are observed, while in the gas phase a considerable energy barrier must be overcome (between 100.8 to 263.2 kJ mol⁻¹). The intermolecular distance at which this barrier is indicates when the hydrogen-bond interactions begin to take importance between the dimers and the corresponding molecular recognition among them. The IQA analysis shows that in aqueous phase, the hydrogen bonds N−H⋅⋅⋅O are mainly electrostatic in nature with a certain covalent character which increases linearly with the decrease of internuclear distances H⋅⋅⋅O. The H⋅⋅⋅H interactions observed are stabilizing and they are mainly quantum in nature.     

Steric repulsions, rotation barriers, and stereoelectronic effects: a real space perspective

Widely used chemical concepts like Pauli repulsion or hyperconjugation, and their role in determining rotation barriers or stereoelectronic effects, are analyzed from the real space perspective of the interacting quantum atoms approach (IQA). IQA emerges from the quantum theory of atoms in molecules (QTAIM), but is free from the equilibrium geometry constraint of the former. A framework with both electronically unrelaxed and relaxed wavefunctions is presented that leads to an approximate correspondence between the IQA concepts and those used in the EDA (energy decomposition analysis) or NBO (natural bond orbital) procedures. We show that no net force acts upon the electrons in an electronically relaxed system, so that any reasonable definition of Pauli repulsion must involve unrelaxed state functions. Using antisymmetrized fragments clarifies that Pauli repulsions are energetically connected to the IQA deformation energies, leaving footprints in the finally relaxed states. Similarly, EDA or NBO hyperconjugative stabilizations are found to be naturally related to the IQA electron delocalization patterns. Applications to the rotation barrier of ethane and other simple systems are presented, and the very often forgotten role of electrostatic contributions in determining preferred conformations is highlighted.     

Binding energies of first row diatomics in the light of the interacting quantum atoms approach

Binding energies of first row diatomics are revisited within the interacting quantum atoms (IQA) approach. This is a formalism in chemical bonding theory based upon the quantum theory of atoms in molecules. It is characterized by the preservation of the energetic identity of atoms within molecules. Quantum mechanically computed binding energies are recovered in IQA as a sum of small atomic deformation energies and large pairwise interaction terms. We show how this partition responds faithfully to chemical intuition, and how the different evolution of deformations and interactions accounts in a unified manner for the subtle variations of the binding energy of these molecules.     

Pauling resonant structures in real space through electron number probability distributions

A general hierarchy of the coarsed-grained electron probability distributions induced by exhaustive partitions of the physical space is presented. It is argued that when the space is partitioned into atomic regions the consideration of these distributions may provide a first step toward an orbital invariant treatment of resonant structures. We also show that, in this case, the total molecular energy and its components may be partitioned into structure contributions, providing a fruitful extension of the recently developed interacting quantum atoms approach (J. Chem. Theory Comput. 2005, 1, 1096). The above ideas are explored in the hydrogen molecule, where a complete statistical and energetic decomposition into covalent and ionic terms is presented.     

Performance of the density matrix functional theory in the quantum theory of atoms in molecules

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.     

The Activation Strain Model in the Light of Real Space Energy Partitions

The distortion/interaction or activation strain model (ASM) of chemical reactivity is examined in real space through the interacting quantum atoms (IQA) approach. Attention is paid to the role that the geometrically constrained ASM structures of the fragments play in the chemical interpretation of the driving forces that lead to a given reaction channel. These fictitious intermediate states are necessary in the ASM, but IQA may or may not use them at will. Similarities and differences are highlighted by studying the endo/exo preference rules of simple [4+2] Diels–Alder cycloadditions. Although overall the agreement is reasonable, we warn about a blind use of the plain ASM if no further energy decomposition analyses of its interaction energy are done.     

Charged versus Neutral Hydrogen‐Bonded Complexes: Is There a Difference in the Nature of the Hydrogen Bonds?

A theoretical study on some carboxylic acid dimers formed by positively or negatively charged molecules has been carried out by using DFT methods. The resulting dimers possess either a charge of +2 or ?2. In addition, the corresponding neutral complexes have also been considered. The electron density distribution described by the atoms in molecules and the natural bond orbital methods, as well as the electric field maps of the systems, have been analyzed and compared without finding significant differences between the neutral and ionic complexes. The interaction energy along the dissociation path of the charged dimers shows both a local minimum and a local maximum, defining a stability region between them. When this energetic profile is recalculated by removing the repulsion between the charged groups, it resembles to those of the neutral molecules. Hence, the characteristics of the charged dimers are similar to those of the neutral ones: the addition of a repulsion term for the charged groups permits to retrieve the energetic profiles dependence with the distance in the charged system. The interacting quantum atom (IQA) method has been used to calculate the interaction energy terms, including the classic Coulombic term between the whole molecules and the corresponding of the carboxylic acid groups. The IQA results show repulsive electrostatic interactions when the whole molecules are considered in the ionic complexes, but attractive ones between the carboxylic groups in both neutral and ionic complexes.     

Nature and Strength of Weak O⋅⋅⋅O Interactions in Nitryl Halide Dimers

The use of real space functions and molecular graphs has pushed some chemists to wonder: Are interactions between negatively charged oxygen atoms possible? In this contribution we analyze whether there is a real interaction between oxygen atoms in nitryl halide dimers (XNO₂)₂ (X=F, Cl, Br and I) and in tetranitromethane and derivatives. Based on ab-initio and density functional theories (DFT) methods, we show these complexes are weakly stabilized. Energy decomposition analyses based on local molecular orbitals (LMOEDA) and interacting quantum atoms (IQA) reveal both dispersion and exchange play a crucial role in the stabilization of these complexes. Electron charge density and IQA analyses indicate that the oxygen atoms are connected by privileged exchange channels. In addition, electrostatic interactions between O and N atoms are also vital for the stabilization of the complexes. Finally, a reasonable explanation is given for the dynamic behavior of nitryl groups in tetranitromethane and derivatives.     

Hydrogen‐Bond Cooperative Effects in Small Cyclic Water Clusters as Revealed by the Interacting Quantum Atoms Approach

The cooperative effects of hydrogen bonding in small water clusters (H₂O)_n (n=3–6) have been studied by using the partition of the electronic energy in accordance with the interacting quantum atoms (IQA) approach. The IQA energy splitting is complemented by a topological analysis of the electron density (ρ( r )) compliant with the quantum theory of atoms‐in‐molecules (QTAIM) and the calculation of electrostatic interactions by using one‐ and two‐electron integrals, thereby avoiding convergence issues inherent to a multipolar expansion. The results show that the cooperative effects of hydrogen bonding in small water clusters arise from a compromise between: 1) the deformation energy (i.e., the energy necessary to modify the electron density and the configuration of the nuclei of the isolated water molecules to those within the water clusters), and 2) the interaction energy (E_int) of these contorted molecules in (H₂O)_n. Whereas the magnitude of both deformation and interaction energies is enhanced as water molecules are added to the system, the augmentation of the latter becomes dominant when the size of the cluster is increased. In addition, the electrostatic, classic, and exchange components of E_int for a pair of water molecules in the cluster (H₂O)_n?1 become more attractive when a new H₂O unit is incorporated to generate the system (H₂O)_n with the last‐mentioned contribution being consistently the most important part of E_int throughout the hydrogen bonds under consideration. This is opposed to the traditional view, which regards hydrogen bonding in water as an electrostatically driven interaction. Overall, the trends of the delocalization indices, δ(Ω,Ω′), the QTAIM atomic charges, the topology of ρ( r ), and the IQA results altogether show how polarization, charge transfer, electrostatics, and covalency contribute to the cooperative effects of hydrogen bonding in small water clusters. It is our hope that the analysis presented in this paper could offer insight into the different intra‐ and intermolecular interactions present in hydrogen‐bonded systems.     

Conformers of diheteroaryl ketones and thioketones: a quantum chemical study of their properties and fundamental intramolecular energetic effects

The conformational behavior of ten diheteroaryl ketones and thioketones is investigated using various quantum chemical methods. These ketones and thioketones are formed by the disubstitution of formaldehyde and thioformaldehyde with such a heteroaryl group as 2-furanyl, 2-thiophenyl, 2-selenophenyl, 2-pyrrolyl or 1-methyl-2-pyrrolyl. For these compounds, their conformational preference and the energetic ordering of their conformers are determined at the MP2 and B3LYP levels of theory. Energetic barriers resulting from the interconversion between conformations are also estimated. The natural bond orbital (NBO) and interacting quantum atoms (IQA) methods are used to study fundamental intramolecular energetic effects influencing the stability of individual conformers. The results of the two methods indicate the great significance of the effect associated with electron delocalization (in the form of either NBO donor–acceptor interactions or the IQA interatomic exchange–correlation interaction energy) in governing the conformational behavior of the investigated diheteroaryl ketones and thioketones.     

Efficient implementation of the interacting quantum atoms energy partition of the second-order Møller–Plesset energy

We describe an efficient implementation of the partition of the second-order Møller–Plesset (MP2) correlation energy within the interacting quantum atoms (IQA) energy decomposition. We simplify the IQA integration bottleneck by considering only the occupied to virtual elements of the second order reduced density matrix, a procedure that reduces substantially the size of the two-electron matrix, which has to be addressed. The algorithmic improvements described herein allow to perform the decomposition of the MP2 correlation energy for medium size molecular systems using moderate computational resources. We expect that the methods developed in this investigation will prove useful to understand electron correlation effects through a real space perspective.     

An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Analysis of the Anomeric Effect

The explanation of the anomeric effect in terms of underlying quantum properties is still controversial almost 70 years after its introduction. Here, we use a method called Relative Energy Gradient (REG), which is able to compute chemical insight with a view to explaining the anomeric effect. REG operates on atomic energy contributions generated by the quantum topological energy decomposition Interacting Quantum Atoms (IQA). Based on the case studies of dimethoxymethane and 2-fluorotetrahydropyran, we show that the anomeric effect is electrostatic in nature rather than governed by hyperconjugation.     

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.     

Interacting Quantum Atoms Analysis of the Reaction Force: A Tool to Analyze Driving and Retarding Forces in Chemical Reactions

The analysis of the reaction force and its topology has provided a wide range of fruitful concepts in the theory of chemical reactivity over the years, allowing to identify chemically relevant regions along a reaction profile. The reaction force (RF), a projection of the Hellmann-Feynman forces acting on the nuclei of a molecular system onto a suitable reaction coordinate, is partitioned using the interacting quantum atoms approach (IQA). The exact IQA molecular energy decomposition is now shown to open a unique window to identify and quantify the chemical entities that drive or retard a chemical reaction. The RF/IQA coupling offers an extraordinarily detailed view of the type and number of elementary processes that take reactants into products, as tested on two sets of simple reactions.     

Hydrogen–hydrogen interaction in planar biphenyl: A theoretical study based on the interacting quantum atoms and Hirshfeld atomic energy partitioning methods

The nature of H‐H interaction between ortho‐hydrogen atoms in planar biphenyl is investigated by two different atomic energy partitioning methods, namely fractional occupation iterative Hirshfeld (FOHI) and interacting quantum atoms (IQA), and compared with the traditional virial‐based approach of quantum theory of atoms in molecules (QTAIM). In agreement with Bader's hypothesis of H? H bonding, partitioning the atomic energy into intra‐atomic and interatomic terms reveals that there is a net attractive interaction between the ortho‐hydrogens in the planar biphenyl. This falsifies the classical view of steric repulsion between the hydrogens. In addition, in contrast to the traditional QTAIM energy analysis, both FOHI and IQA show that the total atomic energy of the ortho‐hydrogens remains almost constant when they participate in the H‐H interaction. Although, the interatomic part of atomic energy of the hydrogens plays a stabilizing role during the formation of the H? H bond, it is almost compensated by the destabilizing effects of the intra‐atomic parts and consequently, the total energy of the hydrogens remains constant. The trends in the changes of intra‐atomic and interatomic energy terms of ortho‐hydrogens during H? H bond formation are very similar to those observed for the H₂ molecule. © 2014 Wiley Periodicals, Inc.     

Congested molecules. Where is the steric repulsion? An analysis of the electron density by the method of interacting quantum atoms

The computed electron density of several congested saturated hydrocarbons and halogenated derivatives has been analyzed by the method of interacting quantum atoms (IQA). For all the molecules studied, the calculations show the existence of a bond path between the congested atoms and which, according to the Quantum Theory of Atoms in Molecules, indicates that there is a stabilizing interaction between these atoms. The bond path is found to exist up to interatomic distances well‐beyond the sum of the van der Waals radii. The IQA results indicate that steric hindrance is not a repulsive force between the congested atoms but that is the result of an increase in the intra‐atomic or self‐energy of the congested atoms. This increase in self‐energy is caused by the deformation of the atomic basin of the congested atoms. © 2013 Wiley Periodicals, Inc.     

Forced Bonding and QTAIM Deficiencies: A Case Study of the Nature of Interactions in He@Adamantane and the Origin of the High Metastability

Calculations within the framework of the interacting quantum atoms (IQA) approach have shown that the interactions of the helium atom with both tertiary, tC, and secondary, sC, carbon atoms in the metastable He@adamantane (He@adam) endohedral complex are bonding in nature, whereas the earlier study performed within the framework of Bader’s quantum theory of atoms in molecules (QTAIM) revealed that only He???tC interactions are bonding. The He???tC and He???sC bonding interactions are shown to be forced by the high pressure that the helium and carbon atoms exert upon each other in He@adam. The occurrence of a bonding interaction between the helium and sC atoms, which are not linked by a bond path, clearly shows that the lack of a bond path between two atoms does not necessarily indicate the lack of a bonding interaction, as is asserted by QTAIM. IQA calculations showed that not only the destabilization of the adamantane cage, but also a huge internal destabilization of the helium atom, contribute to the metastability of He@adam, these contributions being roughly equal. This result disproves previous opinions based on QTAIM analysis that only the destabilization of the adamantane cage accounts for the endothermicity of He@adam. Also, it was found that there is no homeomorphism of the ρ( r ) and ‐v( r ) fields of He@adam. Comparison of the IQA and QTAIM results on the interactions in He@adam exposes other deficiencies of the QTAIM approach. The reasons for the deficiencies in the QTAIM approach are analyzed.     

Arrangement and nature of intermolecular hydrogen bonding in complex biomolecular systems: modeling the vitamin C---L-alanine interaction

Vitamin C is known as an essential dietary supplement and implicated in diverse biological processes. We present here a theoretical study on the nature of hydrogen bonding of vitamin C in biological systems. For this reason, the complexes of vitamin C (VC) with neutral and zwitterionic L-alanine (as the simplest chiral amino acid) were studied at the MP2/6-311++G(d,p) level of theory. In the gas phase, neutral L-alanine leads to more stable complexes than the zwitterionic forms while the reverse is true in the aqueous phase. The complexes are formed via two hydrogen bond interactions, which result in a ring-like hydrogen-bonded networks. The nature of H-bonds was characterized in terms of natural bond orbital and quantum theory of atoms in molecule analyses (QTAIM). The H-bonds in the studied complexes were electrostatic in nature; however, in the case of shorter and directional H-bonds and ionic interactions, contributions of covalent character were also non-negligible. Natural energy decomposition analysis of hydrogen-bonded complexes reveals that the charge transfer and electrical components are the largest contributors for the interaction energies of complexes. Natural resonance theory analysis suggests higher resonance weight for charge-assisted interactions of vitamin C---alanine (zwitterionic) complexes, where the total interaction energy is considerably higher than that of neutral alanine.     

Atom-atom partitioning of total (super)molecular energy: the hidden terms of classical force fields

Classical force fields describe the interaction between atoms that are bonded or nonbonded via simple potential energy expressions. Their parameters are often determined by fitting to ab initio energies and electrostatic potentials. A direct quantum chemical guide to constructing a force field would be the atom-atom partitioning of the energy of molecules and van der Waals complexes relevant to the force field. The authors used the theory of quantum chemical topology to partition the energy of five systems [H2, CO, H2O, (H2O)2, and (HF)2] in terms of kinetic, Coulomb, and exchange intra-atomic and interatomic contributions. The authors monitored the variation of these contributions with changing bond length or angle. Current force fields focus only on interatomic interaction energies and assume that these purely potential energy terms are the only ones that govern structure and dynamics in atomistic simulations. Here the authors highlight the importance of self-energy terms (kinetic and intra-atomic Coulomb and exchange).