The quantum theory of atoms in positronic molecules: A case study on diatomic species

This article presents the first systematic study of a series of diatomic positronic species using the recently proposed regional approach: the quantum theory of atoms in positronic molecules (QTAIPM). This survey includes the LiH,e⁺, NaH,e⁺, LiF,e⁺, NaF,e⁺, BeO,e⁺, MgO,e⁺, CN^?,e⁺, and OH^?,e⁺ species as typical examples. The computational algorithm of the whole analysis is communicated and reviewed in detail. The topological analysis of the joint density distribution reveals topological structures similar to those observed for the purely electronic systems; that is, each system decomposes into two quantum atoms. By considering some of the regional properties of these quantum atoms, it is demonstrated that the positron affects them seriously through two different mechanisms: direct and indirect contributions, the latter refers to electronic and geometric relaxations. The computational results clearly reveal the fact that the regional properties of the quantum atoms of positronic molecules are not deducible from their purely electronic counterparts; thus, an independent analysis is required for each positronic molecule. The positronic population is considered as a typical regional property showing that the attachment of a positron to a purely electronic system enhances the polarization of the electronic distribution. The concept of regional positron affinities is also introduced and discussed as a nonroutine application of the QTAIPM. The results of this article set the stage for further study on the quantum atoms of polyatomic positronic species. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Positron binding energies for alkali hydrides

Ab initio multireference single- and double-excitation configuration interaction (MRD-CI) calculations are carried out to study the interactions of positrons with the members of the alkali hydride class of molecules. A new computer program has been constructed for this purpose that makes use of the Table-Direct-CI method for construction of the required Hamiltonian matrixes and electronic/positronic wave functions. The calculations indicate that the binding energy (positron affinity PA) of a single positron to these systems increases by an increment of 0.2-0.3 eV as the atomic number of the alkali atom is increased. It is found that the positron prefers a location in the more electronegative regions of such molecules, similarly as has been found in earlier calculations for the urea and acetone molecules. The positron orbital itself possesses a diffuse charge distribution with relatively small expectation values of the kinetic energy in all four systems considered. Each of the four positronic molecules is stable with respect to formation of either positronium (Ps) or HPs according to the present calculations. Relatively large changes in the equilibrium bond distance of the hydrides occur as a result of the positron interaction. The importance of bond dipole moments in producing the binding of positrons to molecules is discussed, as well as the role that the electronegativity of the constituent atoms plays in determining the magnitude of the PA for a given system.     

The quantum theory of atoms in positronic molecules: The subsystem variational procedure

This contribution deals with the subsystem variational procedure within the context of the quantum theory of atoms in positronic molecules (QTAIPM). Before introducing the subsystem energy functional termed as joint subsystem energy functional, a novel notation and the combination strategy are disclosed in detail by restating the positronic subsystem hypervirial theorem. They are employed in proposing the proper subsystem energy functional, the validity of which is checked by various criteria. The zero flux surfaces of the joint density distribution are used to define the topological atoms in the positronic molecules, and they are incorporated into the subsystem variational procedure as proper real space boundary conditions. The variational procedure finally yields the flux of the joint current property density that also appears in the positronic subsystem hypervirial theorem. At every stage, the corresponding equations for the purely electronic systems within the context of the quantum theory of atoms in molecules (QTAIM) are presented to clearly reveal the analogy between these two formalisms and to emphasize the importance of combining the property density distributions in the QTAIPM. The presented material demonstrates the internal consistency of the whole framework and discloses the fact that the QTAIM must be regarded as a variant of the QTAIPM. Furthermore, this formalism promises an extended QTAIM, which is hoped to resolve the issue of molecular structure beyond the clamp nuclei approximation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Binding Matter with Antimatter: The Covalent Positron Bond

We report sufficient theoretical evidence of the energy stability of the e⁺?H₂^2? molecule, formed by two H^? anions and one positron. Analysis of the electronic and positronic densities of the latter compound undoubtedly points out the formation of a positronic covalent bond between the otherwise repelling hydride anions. The lower limit for the bonding energy of the e⁺?H₂^2? molecule is 74 kJ mol^?1 (0.77 eV), accounting for the zero‐point vibrational correction. The formation of a non electronic covalent bond is fundamentally distinct from positron attachment to stable molecules, as the latter process is characterized by a positron affinity, analogous to the electron affinity.     

Full variational molecular orbital method: Application to the positron-molecule complexes

Optimal Gaussian-type orbital (GTO) basis sets of positron and electron in positron-molecule complexes are proposed by using the full variational treatment of molecular orbital (FVMO) method. The analytical expression for the energy gradient with respect to parameters of positronic and electronic GTO such as the orbital exponents, the orbital centers, and the linear combination of atomic orbital (LCAO) coefficients, is derived. Wave functions obtained by the FVMO method include the effect of electronic or positronic orbital relaxation explicitly and satisfy the virial and Hellmann–Feynman theorems completely. We have demonstrated the optimization of each orbital exponent in various positron-atomic and anion systems, and estimated the positron affinity (PA) as the difference between their energies. Our PA obtained with small basis set is in good agreement with the numerical Hartree–Fock result. We have calculated the OH⁻ and [OH⁻; e⁺] species as the positron-molecular system by the FVMO method. This result shows that the positronic basis set not only becomes more diffuse but also moves toward the oxygen atom. Moreover, we have applied this method to determine both the nuclear and electronic wave functions of LiH and LiD molecules simultaneously, and obtained the isotopic effect directly. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 491–501, 1998     

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

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     

Structural properties and the effect of 2,6‐diaminoanthraquinone on G‐tetrad,non‐G‐tetrads,and mixed tetrads—A density functional theory study

Telomerase inhibitor causes the attrition of telomere length and consequently leading to senescence which require a lag period for cancer cells to stop proliferating. Telomeric sequences form quadruplex structures stabilized by tetrads. The structural and electronic properties related with interaction of 2,6‐diaminoanthraquinone and tetrads are the key step to elucidate the anticancer activity. The present study has been focused on the stability of the isolated tetrads and the effect of interaction of 2,6‐diaminoanthraquinone with G‐tetrad, non‐G‐tetrads, and mixed tetrads using density functional theory method in both gas and aqueous phases. The solvent interaction with the molecular systems has increased the stability of the isolated tetrads and complexes. The sharing of electron density between the interacting molecules is shown through electron density difference maps. The atoms in molecules theory and natural bond orbital analysis have been performed to study the nature of hydrogen bonds in the inhibitor interacting complexes. The linear correlation is shown between electron density [ρ(r)], and its Laplacian [(²ρ(r)] at the bond critical points. The strong binding nature of 2,6‐diaminoanthraquinone with studied tetrads reveals that this inhibitor is suitable to stabilize the above tetrads and inhibit the telomerase activity. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Information distance analysis of molecular electron densities

The information‐theoretic basis of the Hirshfeld partitioning of the molecular electronic density into the densities of the “stockholder” atoms‐in‐molecules (AIM) is summarized. It is argued that these AIM densities minimize both the directed divergence (Kullback–Leibler) and divergence (Kullback) measures of the entropy deficiency between the AIM and their free atom analogs of the promolecule. The local equalization of the information distance densities of the Hirshfeld components, at the local value of the corresponding global entropy deficiency density, is outlined and several approximate relations are established between the alternative local measures of the missing information and the familiar function of a difference between the molecular and promolecule densities. Various global (of the system as a whole) and atomic measures of the entropy deficiency or the displacements relative to the isoelectronic promolecule, defined for densities or probabilities (shape functions) in both the local resolution and the Hirshfeld AIM discretization, are introduced and tested. This analysis is performed also for the valence electron (frozen‐core) approximation. Illustrative results for representative linear molecules, including diatomics, triatomics, and tetraatomics, are reported. They are interpreted as complementary characteristics of changes in the net AIM charge distribution and of the displacements in the information content of the electron distributions of bonded atoms. These numerical results confirm the overall similarity of the stockholder AIM to their free atom analogs and reflect the information displacements due to the AIM polarization and charge transfer in molecules. They also demonstrate the semiquantitative nature of the approximate relations established between the entropy deficiency densities and the related functions involving the density difference function. This development extends the range of interpretations based on the density difference diagrams into probing the associated information displacements in a molecule accompanying the formation of the chemical bonds. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

N, P, and As ylides and aza- and arsa-Wittig reactions from topological analyses of electron density

The nature of bonding between N, P, and As constituent atoms in ylide systems with the R(3)XYR' formula (X = N, P, As; Y = N, P, As; R = F, H; R' = H, CH(3)) has been characterized by ab initio (MP2/6-311++G**) and density functional theory (B3LYP/6-311++G**) calculations. Its electronic structure has been analyzed through electron density with the quantum theory of atoms in molecules and the electron localization function (ELF). The characteristics of the central bond are inspected with the calculated rotational barriers. The results show that N has a behavior different from that of the remaining pnicogen atoms (P, As), where the bond is much stronger. Fluorine substituents strengthen the X-Y bond, reduce the bond distance, and increase the electron density in the central bond so that the substituent pulls charge from the bond in the pnicogen X atom. For the N-pnicogen ylides, the results showed different bonding characters between F and X atoms; depending on the position of the F atom, the difference of the bond character is sensed by the basin synaptic order, as it is deduced from the analysis of the ELF basins. The energy profiles of the rotational barriers have been calculated at the MP2/6-311++G** level, indicating that the electronegativity of the substituents is a relevant factor that has consequences in the characteristics of the X-Y bond.     

Simultaneous optimization of Gaussian type function exponents for electron and positron with full-CI wavefunction – application to ground and excited states of positronic compounds with multi-component molecular orbital approach

In order to obtain the best wavefunction of positronic compound with molecular orbital (MO) treatment, the full-configuration interaction (full-CI) fully variational MO (FVMO) method is proposed for multi-component systems, in which all the variational parameters in electronic and positronic wavefunctions are optimized under the full-CI scheme. We have applied the full-CI multi-component FVMO method to the ground and positronic-excited states of [H⁻;e⁺] system. Our treatment gives good improvement in the basis functions for positronic compounds owing to the extension of flexibility in the variational space, though the convergence of electron–positron correlation term is slower than that of conventional electron correlation.     

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.     

Atoms-in-molecules from the Stockholder Partition of the Molecular Two-electron Distribution

The effective one-electron distributions of bonded atoms obtained from the “stockholder” partition of the molecular two-electron density are reported. These two-electron stockholder (S) atoms are compared with their one-electron analogs represented by the corresponding Hirshfeld (H) one-electron stockholder pieces of the molecular electron density. The influence of the exchange (Fermi) and Coulomb correlation between electrons on the resultant shapes of bonded atoms is investigated The vertical (for the fixed molecular electron density) and horizontal (involving the electron density displacement) correlation influences on the two-electron stockholder atoms are examined. The two sets of bonded stockholder atoms in the near-dissociation bond-elongated diatomics are compared for different approximations of the electron correlation effects. The cluster components in atomic resolution of the S-partitioning scheme are investigated for illustrative homonuclear and heteronuclear diatomics: H₂, LiH, HF, LiF, and N₂. This framework facilitates an understanding of the origins of the observed differences between the S and H variants of Atoms-in-Molecules. With the exception of hydrogen atoms, especially in light molecules, the two sets of bonded atoms were found to be practically identical. For H₂ and LiH the S atoms were shown to exhibit a distinctly higher degree of the bonding character, compared to their H analogs. The main electron correlation effects have been found to be well represented already at the exchange-only level, e.g., in the unrestricted Hartree–Fock (UHF) theory. An inclusion of the extra vertical Coulomb correlation exerts a marginal moderating influence on the ionic/covalent composition of the chemical bond already predicted by the UHF approximation, in the direction of a slightly more covalent (less ionic) bond character. The horizontal shifts of the molecular density due to Coulomb correlation, relative to the UHF reference, often act in the opposite direction.     

Do one-step mechanisms always involve simultaneous evolution of electron density? QTAIM/IQA analysis of the Curtius rearrangement

The Curtius rearrangement reaction is studied by using quantum theory of atoms in molecules (QTAIM) analysis of the electron density and the interacting quantum atoms (IQA) formalism. Although the rearrangements take place in one stage, two phases are distinguished when the rearranged atom is H: the first one corresponds to the separation of N₂, and the second one to the N-H/C-H bond rearrangement. The transition state (TS) for the reaction does not represent an intermediate between reagent and product for the migration but for the isolation of the N₂ molecule. When the migration is undergone by a fluorine atom, no electronic phases can be distinguished and the process is really concerted. As the migration happens closer to the TS, the TS is more similar to the product. The IQA analysis reveals different electron density evolutions for H and F migrations, and the scarce relevance (in terms of energy) of the point where BCPs appear or disappear.     

A vector‐based representation of the chemical bond for the normal modes of benzene

We introduce a vector‐based interpretation of the chemical bond within the quantum theory of atoms in molecules (QTAIM), the bond‐path framework set B = {p, q, r}, to follow variations in the 3D morphology of all bonds for the four infrared active normal modes of benzene. The bond‐path framework set B comprises three unique paths p, q, and r where r is the familiar QTAIM bond concept of bond‐path (r) while the two new paths p and q are formulated from the least and most preferred directions of electron density accumulation, respectively. We find 3D distortions including bond stretching/compression, torsion, and curving. We introduce two fractional measures to quantify these variations away from linearity of the bond.