Pauli repulsions exist only in the eye of the beholder

This paper presents a rebuttal to the preceding paper in this issue entitled "Hydrogen-Hydrogen Bonding in Planar Biphenyl, Predicted by Atoms-In-Molecules Theory, Does Not Exist". The arguments presented therein are based on an arbitrary partitioning of the energy into contributions from physically unrealizable states of the system. The response given here is presented in terms of the Feynman, Ehrenfest, and virial theorems of quantum mechanics and the observable properties of a system. A reader is thus free to choose between subjectivity or physics.     

Testing theory beyond molecular structure: Electron density distributions of complex molecules

The electron density distribution (EDD) of a molecular system can be determined experimentally from elaborate X‐ray diffraction measurements or calculated with quantum mechanical methods: This provides a unique opportunity for mutual validation of the experimental and theoretical methods—a validation that goes far beyond comparison of molecular structures. Two examples of complex molecular systems of biologic relevance are presented. The first is the cocrystallized complex of betaine, imidazole, and picric acid, 1, which is a 75‐atom molecular complex serving as a model for the active site in the serine proteases class of enzymes, the so‐called catalytic triad. For 1 the experimental charge density was determined by combined modeling of single crystal synchrotron X‐ray and neutron diffraction data measured at 28(1) K, and it is compared with ab initio theoretical calculations at the B3LYP/6‐311G(d,p) level of theory. Overall, the agreement is good, but in one strong N? H? O hydrogen bond clear differences are observed. The second example concerns the EDD of the mixed valence trinuclear oxo‐centered iron carboxylate, [Fe₃O(OOCC(CH₃)₃)₆(NC₅H₅)₃], 2. This molecule contains 133 atoms (542 electrons) including three open‐shell iron atoms, and the experimental investigation is based on synchrotron X‐ray diffraction data. Calculations in the experimental geometry at the commonly used UB3LYP/LanL2DZ level of theory are not able to reproduce a number of experimentally observed electron density features. In particular, the sp³‐like distribution on the central oxygen atom and the electron deformations on the iron centers are at variance with experiment. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺ together with (ii) the anions F⁻, Cl⁻, Br⁻, NO₃⁻ and SO₄²⁻ with water clusters (H₂O)_n, n=1–8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.     

Bond paths as privileged exchange channels

Evidence that the bond paths of the quantum theory of atoms-in-molecules (QTAIM) signal preferred quantum-mechanical exchange channels is presented. We show how bond paths between an atom A and the atoms B in its environment appear to be determined by competition among the A-B exchange-correlation energies that always contribute to stabilize the A-B interactions. These pairwise additive stabilizations depend neither on the attractive or repulsive nature of the classical electrostatic interaction between the atoms' charge densities, nor on the change in the self energies of the atoms involved. These other terms may well cause an overall molecular-energy increase in spite of a possibly large A-B exchange-correlation stabilization. After our proposal, bond paths, both at and out of equilibrium geometries, are endowed with a specific energetic meaning that should contribute to reconcile the orthodox QTAIM interpretation with other widely accepted views, and to settle recent controversies questioning the meaning of hydrogen-hydrogen bonding and the nature of the so-called "steric interactions", the role of bond paths in endohedral complexes, and the generality of the results provided by the QTAIM. Implications for the nature of more general closed-shell interactions are also briefly discussed.     

Theoretical Study on the Hydrogen Bonding Interactions in Complexes of 5‐Hydroxytryptamine with Water

The energies, geometries and harmonic vibrational frequencies of 1:1 5‐hydroxytryptamine‐water (5‐HT‐H₂O) complexes are studied at the MP2/6‐311++G(d,p) level. Natural bond orbital (NBO), quantum theory of atoms in molecules (QTAIM) analyses and the localized molecular orbital energy decomposition analysis (LMO‐EDA) were performed to explore the nature of the hydrogen‐bonding interactions in these complexes. Various types of hydrogen bonds (H‐bonds) are formed in these 5‐HT‐H₂O complexes. The intermolecular C4H5^5‐HT···O^w H‐bond in HTW3 is strengthened due to the cooperativity, whereas no such cooperativity is found in the other 5‐HT‐H₂O complexes. H‐bond in which nitrogen atom of amino in 5‐HT acted as proton donors was stronger than other H‐bonds. Our researches show that the hydrogen bonding interaction plays a vital role on the relative stabilities of 5‐HT‐H₂O complexes.     

A unique trapping by crystal forces of a hydronium cation displaying a transition state structure

An hydronium cation has been discovered which is unique among all crystallographic such ions of the Cambridge Database. Of composition H₇O₃⁺ it has a structure that is totally different from those classically known with structures H₂O-H₂O-H₃O⁺ and H₂O-(H₃O⁺)-H₂O. Unlike the crystallographically classical ones, the cation discussed here has a bifurcated hydrogen bond. From a central H₃O⁺ moiety a single hydrogen bond donor extends to two adjacent water molecules. Quantum chemical calculations in absence of the crystal environment demonstrate that the bifurcated hydrogen bond structure is that of a transition state for the H₇O₃⁺ complex. Thus remarkably, it appears that crystal forces have captured the ion in what would otherwise be a short-lived and unstable transition state formation.     

The localized electrons detector as an ab initio representation of molecular structures

The local single particle momentum is proposed as a localized‐electrons detector (LED) that provides a direct three‐dimensional representation of bonding interactions in molecules. It is given exclusively in terms of the electron density and its gradient. We show that the graphical representation of bonding interactions given by LED is consistent with the local curvatures of the electron density as given by the eigenvalues of the Hessian matrix, according to a local symmetry classification of the critical points here introduced. LED consistently complements the topological analysis of the electron density given by the quantum theory of atoms in molecules, by providing a graphical representation of the symmetry of the bonding interactions in molecular systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2418–2425, 2010     

Hydrogen–hydrogen bonding in biphenyl revisited

The evidence for the stabilizing nature of the H–H bonding in planar biphenyl is succinctly reviewed. The stabilizing nature of the H–H bonding is revealed through a comparison of the atomic energy of every atom in planar biphenyl with the same atom in the twisted equilibrium structure. It is shown that the barrier to rotation via the planar transition state is the net resultant of a stabilisation of the four ortho-hydrogen atoms (by 8 kcal/mol each), a stabilisation of the two para-carbon atoms (by 3 kcal/mol each) and by the dominant destabilisation of the two carbon atoms joining the two rings—the two junction carbon atoms—(by 22 kcal/mol each). The energetic stabilisation of the four ortho-hydrogen atoms is further shown to be in large proportion due to the formation of the hydrogen–hydrogen interatomic surface. Furthermore, neither the “bond order” between the two junction carbon atoms nor the total electron delocalisation between the two rings exhibit a significant change in going from the planar to the twisted equilibrium geometry. These findings are in contrast with the classical view of a balance between “steric non-bonded repulsion” and better electron delocalisation as a function of the twist dihedral angle. Similar conclusions have been recently reached by Pacios and Gómez through a study of the electrostatic potential at the position of the hydrogen nuclei. We dedicate this article to Professor TM Krygowski on the occasion of his 70th birthday wishing him a long and productive life.     

AIM and ELF Analyses of Halogen Bonding in NCS:BrCl Complexes

The nature of halogen bonding in five complexes formed between the thiocyanate (NCS) radical and a BrCl molecule was analyzed by quantum theory of atoms in molecules (QTAIM) and electron‐localization function (ELF) in this paper. The calculated results show that the geometry of the halogen atom bonded at the N‐atom is stable than those bonded at S‐ or C‐atom. The molecular electrostatic potentials determine the geometries and stabilities of the complexes. The valence basin of the S‐ or N‐atom in the electron‐donating NCS radical is compressed and its population decreases during the process of formation of the halogen‐bonded complexes.     

A Full Topological Analysis of Unstable and Metastable Bond Critical Points

Researchers are developing conceptually based models linking the structure and dynamics of molecular charge density to certain properties. Here we report on our efforts to identify features within the charge density that are indicative of instability and metastability. Towards this, we use our extensions to the quantum theory of atoms in molecules that capitalize on a molecule’s ridges to define a natural simplex over the charge density. The resulting simplicial complex can be represented at various levels by its 0‐, 1‐, and 2‐skeleton (dependent sets of points, lines, and surfaces). We show that the geometry of these n‐skeletons retains critical information regarding the structure and stability of molecular systems while greatly simplifying charge density analysis. As an example, we use our methods to uncover the fingerprints of instability and metastability in two much‐discussed systems, that is, the di‐benzene complex and the He and adamantane inclusion complex.     

The general setting for the zero‐flux condition: The lagrangian and zero‐flux conditions that give the heisenberg equation of motion

Generalizing our recent work on relativistic generalizations of the quantum theory of atoms in molecules, we present the general setting under which the principle of stationary action for a region leads to open quantum subsystems. The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero‐flux surface. Alternatively, with this method, one can design a Lagrangian that leads to a surface of interest (though this Lagrangian may not be, and indeed probably will not be, “reasonable”). For any reasonable Lagrangian for the electronic wave function and any two‐component method (related by integration by parts to the Hamiltonian) considered, the Bader definition of an atom is recaptured. © 2018 Wiley Periodicals, Inc.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.     

Structures,vibrational frequencies,topologies, and energies of hydrogen bonds in cysteine‐formaldehyde complexes

The hydrogen bonding interactions between cysteine (Cys) and formaldehyde (FA) were studied with density functional theory regarding their geometries, energies, vibrational frequencies, and topological features of the electron density. The quantum theory of atoms in molecules and natural bond orbital analyses were employed to elucidate the interaction characteristics in the Cys‐FA complexes. The intramolecular hydrogen bonds (H‐bonds) formed between the hydroxyl and the N atom of cysteine moiety in some Cys‐FA complexes were strengthened because of the cooperativity. Most of intermolecular H‐bonds involve the O atom of cysteine/FA moiety as proton acceptors, while the strongest H‐bond involves the O atom of FA moiety as proton acceptor, which indicates that FA would rather accept proton than providing one. The H‐bonds formed between the CH group of FA and the S atom of cysteine in some complexes are so weak that no hydrogen bonding interactions exist among them. In most of complexes, the orbital interaction of H‐bond is predominant during the formation of complex. The electron density (ρ_b) and its Laplace (?²ρ_b) at the bond critical point significantly correlate with the H‐bond parameter δR, while a linearly relationship between the second‐perturbation energy E(2) and ρ_b has been found as well. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Chemical bonding in view of electron charge density and kinetic energy density descriptors

Stalke's dilemma, stating that different chemical interpretations are obtained when one and the same density is interpreted either by means of natural bond orbital (NBO) and subsequent natural resonance theory (NRT) application or by the quantum theory of atoms in molecules (QTAIM), is reinvestigated. It is shown that within the framework of QTAIM, the question as to whether for a given molecule two atoms are bonded or not is only meaningful in the context of a well‐defined reference geometry. The localized‐orbital‐locator (LOL) is applied to map out patterns in covalent bonding interaction, and produces results that are consistent for a variety of reference geometries. Furthermore, LOL interpretations are in accord with NBO/NRT, and assist in an interpretation in terms of covalent bonding. © 2008 Wiley Periodicals, Inc.J Comput Chem, 2009.     

A practical and efficient method to calculate AIM localization and delocalization indices at post-HF levels of theory

A practical and efficient method is proposed for calculating localization and delocalization indices at post-Hartree-Fock levels, and the method is tested at the CISD/6-311G++(2d, 2p) level for a large set of molecules. Our method, which utilizes wave functions written in the natural molecular orbital format and obtained with GAUSSIAN 94 or GAUSSIAN 98, convincingly extends the concepts established at the HF level.     

Hybrid density functional theory for pi-stacking interactions: application to benzenes, pyridines, and DNA bases

The suitability of a hybrid density functional to qualitatively reproduce geometric and energetic details of parallel pi-stacked aromatic complexes is presented. The hybrid functional includes an ad hoc mixture of half the exact (HF) exchange with half of the uniform electron gas exchange, plus Lee, Yang, and Parr's expression for correlation energy. This functional, in combination with polarized, diffuse basis sets, gives a binding energy for the parallel-displaced benzene dimer in good agreement with the best available high-level calculations reported in the literature, and qualitatively reproduces the local MP2 potential energy surface of the parallel-displaced benzene dimer. This method was further critically compared to high-level calculations recently reported in the literature for a range of pi-stacked complexes, including monosubstituted benzene-benzene dimers, along with DNA and RNA bases, and generally agrees with MP2 and/or CCSD(T) results to within +/-2 kJ mol(-1). We also show that the resulting BH&H binding energy is closely related to the electron density in the intermolecular region. The net result is that the BH&H functional, presumably due to fortuitous cancellation of errors, provides a pragmatic, computationally efficient quantum mechanical tool for the study of large pi-stacked systems such as DNA.