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     

One-Electron Pseudo-Potential Determination of Stable Isomers of the Li*Ar n Excited Clusters: Absorption Spectra

We present pseudo-potential calculations of geometrical structures of stable isomers of LiAr _n clusters with both an electronic ground state and excited states of the lithium atom. The Li atom is perturbed by argon atoms in LiAr _n clusters. Its electronic structure obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Li⁺Ar _n core, the Li⁺ and Ar atoms are replaced by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for the polarization and correlation of the inert core with the valence Lithium electron [J Chem Phys 116, 1839 1]. The geometry optimization of the ground and excited states of LiAr _n (n = 1–12) clusters is carried out via the Basin-Hopping method of Wales et al. [J Phys Chem 101, 5111 2; J Chem Phys 285, 1368 3]. The geometries of the ground and ionic states of LiAr _n clusters were used to determine the energy of the high excited states of the neutral LiAr _n clusters. The variation of the excited state energies of LiAr _n clusters as a function of the number of argon atoms shows an approximate Rydberg character, corresponding to the picture of an excited electron surrounding an ionic cluster core, is already reached for the 3s state. The result of optical transitions calculations shows that the absorption spectral features are sensitive to isomer structure. It is clearly the case for transitions close to the 2p levels of Li which are distorted by the cluster environment.     

Chemical bonding interactions in Zr2Al

The electronic structure of Zr₂Al with the Ni₂In-type structure has been calculated by the method of W. Kohn and N. Rostoker (Phys. Rev. 91, 1111 (1954)). The results include densities of states, both total and partial, and resolved according to the angular momentum quantum number, and calculated electron densities presented so as to display directional bonding characteristics of electrons in the valence and conduction regions of energy. It is concluded that: (1) the principal bonding involves aluminum s-type orbitals; (2) the aluminum p-type orbitals are principally nonbonding; and (3) the metallic interactions are principally between zirconium atoms.     

β‐Aminoacrolein: An ab initio,AIM and NBO study

The molecular structure and the intramolecular hydrogen bonding of β‐aminoacrolein and its simple derivatives were investigated at the MP2 and B3LYP levels of theory using the standard 6‐311++G(d, p) basis set. The “atoms in molecules” or AIM theory of Bader which is based on topological properties of the electron density (ρ), was used. Additionally, an analysis of the critical points was performed to study the nature hydrogen bonding in these systems. Natural bond orbital (NBO) analysis was also carried out for to better comprehend the nature of the intramolecular interactions in β‐aminoacrolein and its derivatives. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Kinetic Monte Carlo study of binary diffusion in silicalite

We report a Kinetic Monte Carlo (KMC) study of the diffusion of linear n-hexane (nC6) and 2,2-dimethylbutane (22DMB) mixture in zeolite silicalite. We first investigated the loading dependences of single component self- and corrected diffusivities of nC6 at 300 K. Anisotropic transition rates are implemented to account for the distribution of the molecules within the zeolite framework. Repulsive guest-guest interactions are modeled using the parameter introduced by Reed and Ehrlich (Surf. Sci. 102:588–601, 1981). The results are in good agreement with recent experimental Quasi Elastic Neutron Scattering data of Jobic et al. (J. Phys. Chem. B 110:2195–2201, 2006), although the influence of the adsorption isotherm inflection is not reproduced. The binary diffusion study of nC6/22DMB mixtures was performed by implementing the nC6 transition rates used for the single component study while 22DMB molecules propagate via intersection-intersection hops. This KMC model allows for different saturation capacities and accounts for interactions between molecules by introducing f _ij parameters. Results show the large impact of guest-guest interactions between nC6 and 22DMB on both self- and corrected diffusivities of the two components. Molecule-size effects are found to be predominant near 22DMB saturation capacity. Acceleration/deceleration effects already described in the literature are confirmed.     

The elusive excited states of bithiophene: a CASPT2 detective story

A systematic multi-reference perturbation theory investigation of the excitation energies and oscillator strengths for the lowest excited states of 2,2′-bithiophene unequivocally shows that its optical spectrum is produced by two ¹ B _u states separated from each other by approximately 1 eV. This picture is confirmed by additional calculations with alternative quantum chemical methods. Our findings are in strong contrast with the previous CASPT2 results of Rubio et al. [J Chem Phys 102:3580 (1995) and Chem Phys Chem 4:1308 (2003)], who predicted that the two lowest ¹ B _u states are quasi-degenerate. The methodological reasons responsible for the previous seemingly erroneous assignment of the optical spectrum of bithiophene are identified and explained in terms of unusually large coupling between the ¹ B _u states introduced by dynamical correlation effects. A general discussion of applicable computational techniques is offered aiming at avoiding similar problems for other molecular systems.     

Accurate atomic Gaussian basis functions for second-row atoms: Small split-valence 3-21SP and 4-22SP basis sets

Small split-valence Gaussian 3-21SP and 4-22SP basis sets, previously reported for the first-row atoms [Chem. Phys. Lett., 229 , 151 (1996)], have been extended for the second-row elements of the Periodic Table. The total energies of the ground states of the second-row atoms calculated with the new basis sets are significantly lower than those obtained with the well-known 3-21G (J. Am. Chem. Soc., 104 , 2797 (1982)] and 4-31G [J. Chem. Phys., 56 , 5255 (1972)] basis sets. This is because, as first noted in our previous work for first-row atoms, that the 3-21G and 4-31G basis sets only correspond to a local minimum of the Hartree–Fock energy functional, which is relatively far from its global minimum. The proposed basis sets have been tested by performing geometry optimizations and calculations of normal frequencies in the harmonic approximation of some diatomic and polyatomic molecules at the Hartree–Fock level. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1200–1210     

Ferromagnetic bonding: high spin copper clusters (n+1)Cu(n); n = 2-14) devoid of electron pairs but possessing strong bonding

Density functional theoretic studies are performed for the high-spin copper clusters (n)(+1)Cu(n) (n = 2-14), which are devoid of electron pairs shared between atoms, hence no-pair clusters (J. Phys. Chem. 1988, 92, 1352; Isr. J. Chem. 1993, 33, 455; J. Am. Chem. Soc. 1999, 121, 3165). Despite the lack of electron pairing, it is found that the bond dissociation energy per atom (BDE/n) is significant and converges (to within 1 kcal mol(-1)), around a cluster size (11)Cu(10), to a value of BDE/n = 19 kcal mol(-1). This is a very large bonding energy, much larger than has previously been obtained for no-pair clusters of lithium, BDE/n = 12 kcal mol(-1), or sodium clusters, BDE/n = 3 kcal mol(-1). This bonding, so-called ferromagnetic bonding (FM-bonding) is analyzed using a valence bond (VB) model (J. Phys. Chem. A 2002, 106, 4961; Phys. Chem. Chem. Phys. 2003, 5, 158). As such, FM-bonding in no-pair clusters is described as an ionic fluctuation, of the triplet pair, that spreads over all the close neighbors of a given atom in the clusters. Thus, if we refer to each triplet pair and its ionic fluctuations as a local FM-bond, we can regard the electronic structure of a given (n)(+1)M(n) cluster as a resonance hybrid of all the local FM-bonds between close neighbors. The model shows how a weak interaction in the diatomic triplet molecule can become a remarkably strong binding force that binds together mono-valent atoms without even a single electron pair. This is achieved because the growing number of VB structures exerts a cumulative effect of stabilization that is maximized when the cluster has a compact structure with an optimal coordination number for the atoms.     

How polarization damping affects ion solvation dynamics

In a recent paper (Sala et al. in J Chem Phys 133:234101, 2010), static properties of chloride in water have been addressed using a polarizable force field and by adding screening functions to damp short-range electrostatic interactions. In this contribution, we further explore the impact of damping polarizable interactions on system dynamics. To this end, results from Car–Parrinello molecular dynamics simulations have been used as benchmark for assessing the impact of damping schemes on the ion solvation dynamics of chloride in water. The results are of general validity, and the methodology could be easily implemented in all methods used to include polarization.     

Nonlinear pair population analysis: The study of basis‐set dependence

The nonlinear pair population analysis recently introduced as a new means of visualization of bonding in molecules with complex bonding patterns was tested for the assumed sensitivity of calculated populations to the quality of the basis set. The testing was performed on a series of several simple molecules ranging from systems well represented by the classical Lewis model of localized two‐center two‐electron (2c–2e) bonds to electron‐deficient boranes containing three‐center bonding. It has been shown that even if this basis‐set sensitivity is slightly greater than for the closely related linear population analysis the dependence is not important enough to question the usefulness of this new approach for the analysis and visualization of bonding molecular systems. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 127–137, 1999     

A Topological Study of the Ferromagnetic “No-Pair Bonding” in Maximum-Spin Lithium clusters: n+1Li n (n=2–6)

The nature of the bonding between lithium atoms, in low-spin and maximum-spin clusters, was investigated using the topological electron localization function (ELF) approach. The maximum-spin clusters are especially intriguing since their bonding is sustained without having even a single electron pair! Hence this type of bonding had been called “no-pair ferromagnetic-bonding” [Danovich, Wu, Shaik J Am Chem Soc 121:3165 (1999); Glokhovtsev, Schleyer Isr J Chem 33: 455 (1993); de Visser, Danovich, Wu, Shaik J Phys Chem A 106:4961 (2002)]. The following conclusions were reached in the study: (a) In the ground state of Li _n , covalent bonding between Li atoms is accounted by the presence of the disynaptic valence basins, which exhibit a significant degree of inter-basin delocalization. (b) Except for the ³Li₂ case, the valence basins of all maximum-spin clusters are populated by unpaired electrons. The valence basins are located off Li–Li axis (or Li–Li–Li plane), so that their spatial distribution minimizes the mutual Pauli repulsion and screens the electrostatic repulsion between the Li cores. The inter-basin delocalization is rather high, thereby indicating that the unpaired electrons are virtually delocalized over all the valence basins. (c) The ELF analysis shows that Li atoms in the low-spin clusters are bonded by “two-center two-electron” and “three-center two-electron” bonds. (d) In the maximum-spin species, bonding is sustained by “two-center one-electron” and “three-center one-electron” bonds. The latter picture is complementary to the valence bond picture [Danovich, Wu, Shaik J Am Chem Soc 121 3165 (1999); de Visser, Danovich, Wu, Shaik J Phys Chem A 106: 4961 (2002)], in which the bicentric ferromagnetic-bonding is delocalized over all the short Li–Li contacts, by the mixing of the ionic structures and other nonredundant structures into the repulsive high-spin covalent structure in which all the electrons populate the 2s atomic orbitals, i.e., the configuration. In such a manner bonding can be sustained from “purely ferromagnetic interactions” without electron pairing.Dedicated to Jean-Paul Malrieu, a friend and a poet-scientist     

Variational solution of the single-particle Dirac equation in the field of two nuclei using relativistically adapted Slater basis functions

A variational method for solving the time-independent single-particle Dirac equation in the Coulomb field of two nuclei is described. A minimax variational principle and basis functions that have the proper analytic behavior, i.e. behave like r ^γ,γ non-integer, in the neighborhood of a nucleus, are used. A momentum space integration scheme for computing the necessary two-center integrals is described. Results are given for a standard test problem on two nuclei with Z=90 with an internuclear separation of 2.0/Z. The results confirm those of a previous calculation [F.A. Parpia and A.K. Mohanty, Chem Phys Lett 238: 209 (1995)]. Received: 13 May 1998 / Accepted: 22 June 1998 / Published online: 28 August 1998     

Unified treatment of complex and real rotation-angular functions for two-center overlap integrals over arbitrary atomic orbitals

The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can be useful in the study of different quantum mechanical problems in both the theory and practice of calculations dealing with atoms, molecules, nuclei and solids when the integer and noninteger n complex and real atomic orbitals basis sets are emploed. This work presented the development of our previous paper (I.I. Guseinov in Phys Rev A 32:1864, 1985).     

Analytical density-dependent representation of Hartree—Fock atomic potentials

A procedure to represent atomic electron charge densities [L. Fernandez Pacios, J. Phys. Chem., 95 , 10653 (1991); J. Phys. Chem., 96 , 7294 (1992)] is here generalized to obtain simple analytical functions for potential energy contributions. Based upon suitable functions to describe atomic electron densities in a physically meaningful form, the procedure is developed to define density-dependent analytical expressions for the electrostatic (classical) and exchange (quantum) potentials by means of proper approximate functionals. Calculations of correlation energies by using various density-functional approaches are also performed. The whole scheme is used to represent Hartree–Fock limit atomic wave functions by Clementi–Roetti. This way, a set of analytically simple, nonbasis set-dependent functions are defined with the aim to be further implemented in energy decomposition schemes for molecular interactions studies using atomic instead of electronic building blocks. © 1993 John Wiley & Sons, Inc.     

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.     

On the strength of hydrogen bonding within water clusters on the coordination limit

Hydrogen bonds (HB) are arguably the most important noncovalent interactions in chemistry. We study herein how differences in connectivity alter the strength of HBs within water clusters of different sizes. We used for this purpose the interacting quantum atoms energy partition, which allows for the quantification of HB formation energies within a molecular cluster. We could expand our previously reported hierarchy of HB strength in these systems (Phys. Chem. Chem. Phys., 2016, 18 , 19557) to include tetracoordinated monomers. Surprisingly, the HBs between tetracoordinated water molecules are not the strongest HBs despite the widespread occurrence of these motifs (e.g., in ice I_h). The strongest HBs within H₂O clusters involve tricoordinated monomers. Nonetheless, HB tetracoordination is preferred in large water clusters because (a) it reduces HB anticooperativity associated with double HB donors and acceptors and (b) it results in a larger number of favorable interactions in the system. Finally, we also discuss (a) the importance of exchange-correlation to discriminate among the different examined types of HBs within H₂O clusters, (b) the use of the above-mentioned scale to quickly assess the relative stability of different isomers of a given water cluster, and (c) how the findings of this research can be exploited to indagate about the formation of polymorphs in crystallography. Overall, we expect that this investigation will provide valuable insights into the subtle interplay of tri- and tetracoordination in HB donors and acceptors as well as the ensuing interaction energies within H₂O clusters.     

Theoretical investigation on charge‐assisted halogen bonding interactions in the complexes of bromocarbons with some anions

A series of dimeric complexes formed between bromocarbon molecules and two anions (Br^? and CN^?) have been investigated by using MP2 method. The quantum theory of atoms in molecules (QTAIM) and the second‐order perturbation natural bond orbital (NBO) approaches were applied to analyze the electron density distributions of these complexes and to explore the nature of charge‐assisted halogen bonding interactions. As anticipated, these interactions are significantly stronger relative to the corresponding neutral ones. The results derived from ab initio calculations described herein reveal a major contribution from the electrostatic interaction on the stability of the systems considered. Beside the electrostatic interaction, the charge‐transfer force and the second‐order orbital interaction also play an important role in the formation of the complexes, as a NBO analysis suggested. The presence of halogen bonds in the complexes has been identified in terms of the QTAIM methodology, and several linear relationships have been established to provide more insight into charge‐assisted halogen bonding interactions. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

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