A fresh look at dense hydrogen under pressure. III. Two competing effects and the resulting intra-molecular H-H separation in solid hydrogen under pressure

A preliminary discussion of the general problem of localization of wave functions, and the way it is approached in theoretical condensed matter physics (Wannier functions) and theoretical chemistry (localized or fragment orbitals) is followed by an application of the ideas of Paper II in this series to the structures of hydrogen as they evolve under increasing pressure. The idea that emerges is that of simultaneously operative physical (reduction of available space by an increasingly stiff wall of neighboring molecules) and chemical (depopulation of the σ(g) bonding molecular orbital of H(2), and population of the antibonding σ(u)? MO) factors. The two effects work in the same direction of reducing the intermolecular separation as the pressure increases, but compete, working in opposite directions, in their effect on the intramolecular (nearest neighbor, intra-pair) distance. We examine the population of σ(g) and σ(u)? MOs in our numerical laboratory, as well as the total electron transfer (small), and polarization (moderate, where allowed by symmetry) of the component H(2) molecules. From a molecular model of two interacting H(2) molecules we find a linear relationship between the electron transfer from σ(g) to σ(u)? of a hydrogen molecular fragment and the intramolecular H-H separation, and that, in turn, allows us to estimate the expected bond lengths in H(2) under pressure if the first effect (that of simple confinement) was absent. In essence, the intramolecular H-H separations under pressure are much shorter than they would be, were there no physical/confinement effect. We then use this knowledge to understand how the separate E and PV terms contribute to hydrogen phase changes with increasing pressure.     

A fresh look at dense hydrogen under pressure. I. an introduction to the problem, and an index probing equalization of H-H distances

In the first of a series of four papers on hydrogen under pressure, and its transitions from an initiating molecular state, we begin by defining carefully the problem, and setting the distance scale of interactions of protons and electrons in molecular aggregates of the first of the elements. Following a review of the experimental situation, in particular the phase diagram of hydrogen, in as much as it is known, and the behavior of its vibrons and rotons, we move onto the setting up of a numerical laboratory for probing the underlying physics and chemistry of interactions in hydrogen as the pressure increases. The laboratory consists of the preferred static structures emerging from calculations on the system in the range of 1 atm to 500 GPa, those of Pickard and Needs. The intermolecular (inter-pair) H···H separations naturally decrease with increasing pressure, first rapidly so, then more slowly. The intramolecular (intra-pair) H-H distances vary over a much smaller scale (0.05 A?) as the pressure increases, first decreasing, then increasing, and finally decreasing. We define an equalization function to gauge the approach to equality of the first neighbor and shortest next neighbor H (proton) separations in this numerical laboratory. And we find that metallization is likely to occur before bond equalization.     

Ab initio through‐space/bond interaction analysis of the long C–C bonds in Bi(anthracene‐9,10‐dimethylene) photoisomers

The bi(anthracene‐9,10‐dimethylene) photoisomer has remarkably long C–C single bonds. To examine the lengthening of the C–C bond, we propose a novel procedure for quantitatively analyzing orbital interactions in a molecule at the level of the ab initio molecular orbital method. In this procedure, we can cut off the specific through‐space/bond interactions in a molecule by artificially increasing the absolute magnitude of the exponents in a Gaussian function. Then, the spatial orbital interactions were perfectly cut off, and, each term that makes up the total energy, that is, the nuclear–electron attractions, the electron–electron repulsions, and the nuclear–nuclear repulsions cancel each other. Several model molecules of the photoisomer were analyzed by this procedure. It was found that the orbital interaction between the p orbital on the benzene ring and the σ* orbital on the C–C bond in question, σ→σ* electron transfer through π orbital, weakens the C–C bond efficiently when these orbitals were located in the “periplanar” conformation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

A novel method for superimposing molecules and receptor mapping

Superposition of molecules on a three-dimensional computer graphic display is an efficient means to compare three-dimensional molecular structures. Biologically active molecules, which are presumed to bind to the same receptor site, are thought to have common structural features. But, it is the physical and chemical properties arranged spatially through chemical structures that are important for specific binding to a receptor. Therefore, for the purpose of studies on biological activities, molecules should be superposed to those properties, not to the atomic positions as in the traditional methods. We have developed a program system for realizing this new concept. The concept stands on the general perceptions of organic chemists about hydrogen bondings and chemical isosterisms. The 'goodness of fit' values, which are estimated in realtime on the basis of spatial similarity of those properties between molecules, are displayed and updated throughout the superposing process. This program can construct a receptor cavity model and provide with the cavity size and shape, surface electrostatic potentials, hydrogen bonding sites and so on, by using all information supplied by the superposed molecules. This model can be modified by further superposing of another molecule. These constructed models would be of help for rational drug design, when the receptor structures are not yet known.     

Attachment of molecular hydrogen to an isolated boron cation: an infrared and ab initio study

Structural properties of the B(+)-H2 electrostatic complex are investigated through its rotationally resolved infrared spectrum in the H-H stretch region (3905-3975 cm(-1)). The spectrum, which was obtained by monitoring B(+) photofragments while the IR wavelength was scanned, is consistent with the complex having a T-shaped structure and a vibrationally averaged intermolecular separation of 2.26 A, which decreases by 0.04 A when the H2 subunit is vibrationally excited. The H-H stretch transition of B(+)-H2 is red-shifted by 220.6 +/- 1.5 cm(-1) from that of the free H2 molecule, much more than for other dihydrogen complexes with comparable binding energies. Properties of B(+)-H2 and the related Li(+)-H2, Na(+)-H2, and Al(+)-H2 complexes are explored through ab initio calculations at the MP2/aug-cc-pVTZ level. The unusually large red-shift for B(+)-H2 is explained as due to electron donation from the H2 sigma(g) bonding orbital to the unoccupied 2p(z) orbital on the B(+) ion.     

A fresh look at dense hydrogen under pressure. IV. Two structural models on the road from paired to monatomic hydrogen, via a possible non-crystalline phase

In this paper, we examine the transition from a molecular to monatomic solid in hydrogen over a wide pressure range. This is achieved by setting up two models in which a single parameter δ allows the evolution from a molecular structure to a monatomic one of high coordination. Both models are based on a cubic Bravais lattice with eight atoms in the unit cell; one belongs to space group Pa3, the other to space group R3m. In Pa3 one moves from effective 1-coordination, a molecule, to a simple cubic 6-coordinated structure but through a very special point (the golden mean is involved) of 7-coordination. In R3m, the evolution is from 1 to 4 and then to 3 to 6-coordinate. If one studies the enthalpy as a function of pressure as these two structures evolve (δ increases), one sees the expected stabilization of minima with increased coordination (moving from 1 to 6 to 7 in the Pa3 structure, for instance). Interestingly, at some specific pressures, there are in both structures relatively large regions of phase space where the enthalpy remains roughly the same. Although the structures studied are always higher in enthalpy than the computationally best structures for solid hydrogen - those emerging from the Pickard and Needs or McMahon and Ceperley numerical laboratories - this result is suggestive of the possibility of a microscopically non-crystalline or "soft" phase of hydrogen at elevated pressures, one in which there is a substantial range of roughly equi-enthalpic geometries available to the system. A scaling argument for potential dynamic stabilization of such a phase is presented.     

Reaction of hydrogen with Ag(111): binding states, minimum energy paths, and kinetics

The interaction of atomic and molecular hydrogen with the Ag(111) surface is studied using periodic density functional total-energy calculations. This paper focuses on the site preference for adsorption, ordered structures, and energy barriers for H diffusion and H recombination. Chemisorbed H atoms are unstable with respect to the H(2) molecule in all adsorption sites below monolayer coverage. The three-hollow sites are energetically the most favorable for H chemisorption. The binding energy of H to the surface decreases slightly up to one monolayer, suggesting a small repulsive H-H interaction on nonadjacent sites. Subsurface and vacancy sites are energetically less favorable for H adsorption than on-top sites. Recombination of chemisorbed H atoms leads to the formation of gas-phase H(2) with no molecular chemisorbed state. Recombination is an exothermic process and occurs on the bridge site with a pronounced energy barrier. This energy barrier is significantly higher than that inferred from experimental temperature-programmed desorption (TPD) studies. However, there is significant permeability of H atoms through the recombination energy barrier at low temperatures, thus increasing the rate constant for H(2) desorption due to quantum tunneling effects, and improving the agreement between experiment and theory.     

Peculiarities of inclusion complex formation in the 1,4-benzodiazepine-benzene system

5-Phenyl-1-methyl-7-bromo-3-hydroxy-1,2-dihydro-3H-1,4-benzodiazepin-2-one and its 5-(o-chloro)-phenyl analog form 2:1 (host:guest) inclusion compounds with benzene. The crystal structures of the compounds were studied by the single-crystal XRD method and were interpreted as host (H) (benzodiazepine) — guest (G) (benzene solvent molecule) complexes. The studied structures, revealing H-H and H-G interactions as both typical hydrogen bonds and π-π, C-H?π weak interactions, may serve as models for ligand-receptor binding.     

Electronic structures of large,extended, nonperiodic systems by using the elongation method: Model calculations for the cluster series of a polymer and the molecular stacking on a surface

The elongation method based on the molecular orbital (MO ) theory, which enables us to extend a polymer with any molecular fragments theoretically, has recently been developed by our group. As the next step, we introduced an approach based on the crystal orbital (CO ) theory into above treatment. In the present work, the elongation method was developed at the Hartree–Fock level with CNDO /2 parameters and applied to model systems composed of the cluster series of a polymer and the molecular stacking on a surface. In the cluster-series calculations, the hydrogen molecule [(H₂)_n], hydrogen fluoride [(HF)_n], polyethylene, and polyacetylene were created successively to approximate their one-dimensional periodic polymers by using the MO -based elongation method. In the molecular-stacking models, we described the hypothetical surface of crystal as periodically arranged hydrogen molecules by the CO s, and several hydrogen molecules were stacked up on the surface one after another with the elongation procedure. Furthermore, the lattice defect on surface in which a part of stacked layer is lacking was dealt with by our approach. We also treated carbon monoxide chemisorption on a periodic magnesium chain as a more realistic model. Results for these systems support the applicability of our method for nonperiodic interactions in one- and two-dimensional large systems. © 1995 John Wiley & Sons, Inc.     

Interaction of the important species HNO and HFSO2 in the atmosphere: Theoretical study of the N?H and S?H blue‐shifted hydrogen bonds

Ab initio molecular orbital and density functional theory (DFT) in conjunction with different basis sets calculations were performed to study the N? H…O and S? H…O blue‐shifted H‐bonds in the HNO…HFSO₂ complex. The geometric structures, vibrational frequencies, and interaction energies were calculated by both standard and CP‐corrected methods. Natural bond orbital (NBO) analysis was used to investigate the origin of blue‐shifted H‐bonds, showing that the decrease in the σ*(N? H) and σ*(S? H) is due to the electron density redistribution effect. The structure reorganization effect on the blue‐shifted hydrogen bonds was discussed in detail. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Bonding analysis using localized relativistic orbitals: water, the ultrarelativistic case and the heavy homologues H2X (X = Te, Po, eka-Po)

We report the implementation of Pipek-Mezey [J. Chem. Phys. 90, 4916 (1989)] localization of molecular orbitals in the framework of a four-component relativistic molecular electronic structure theory. We have used an exponential parametrization of orbital rotations which allows the use of unconstrained optimization techniques. We demonstrate the strong basis set dependence of the Pipek-Mezey localization criterion and how it can be eliminated. We have employed localization in conjunction with projection analysis to study the bonding in the water molecule and its heavy homologues. We demonstrate that in localized orbitals the repulsion between hydrogens in the water molecule is dominated by electrostatic rather than exchange interactions and that freezing the oxygen 2s orbital blocks polarization of this orbital rather than hybridization. We also point out that the bond angle of the water molecule cannot be rationalized from the potential energy alone due to the force term of the molecular virial theorem that comes into play at nonequilibrium geometries and which turns out to be crucial in order to correctly reproduce the minimum of the total energy surface. In order to rapidly assess the possible relativistic effects we have carried out the geometry optimizations of the water molecule at various reduced speed of light with and without spin-orbit interaction. At intermediate speeds, the bond angle is reduced to around 90 degrees , as is known experimentally for H(2)S and heavier homologues, although our model of ultrarelativistic water by construction does not allow any contribution from d orbitals to bonding. At low speeds of light the water molecule becomes linear which is in apparent agreement with the valence shell electron pair repulsion (VSEPR) model since the oxygen 2s12 and 2p12 orbitals both become chemically inert. However, we show that linearity is brought about by the relativistic stabilization of the (n + 1)s orbital, the same mechanism that leads to an electron affinity for eka-radon. Actual calculations on the series H2X (X = Te, Po, eka-Po) show the spin-orbit effects for the heavier species that can be rationalized by the interplay between SO-induced bond lengthening and charge transfer. Finally, we demonstrate that although both the VSEPR and the more recent ligand close packing model are presented as orbital-free models, they are sensitive to orbital input. For the series H2X (X = O, S, Se, Te) the ligand radius of the hydrogen can be obtained from the covalent radius of the central atom by the simple relation r(lig)(H) = 0.67r(cov)(X) + 27 (in picometers).     

Comments on some chemical properties of diphenyl disulfide and its derivatives: II.Correlating the studies of reductive cleavage of disulfide bonds with the studies of anti-human immunodeficiency virus activity with lowest unoccupied molecular orbital properties

The higher anti-human immunodeficiency virus activity of a symmetrical 2,2′-disubstitued derivative of diphenyl disulfide (DPDS) has been explained by the lower energy of the lowest unoccupied molecular orbital (LUMO), resulted from a better hydrogen bond stabilization of the σ*_SS bond orbital (BO). This conclusion entails the participation of σ*_SS BO in constructing the LUMO. The higher content of σ*_SS BO, compared to π*_CC BOs of phenyl groups, in LUMO of DPDS has been found through analysis of the LUMO of DPDS expanded in the BO space. The high content of σ*_SS BO (%σ*_SS) in the LUMO of DPDS has laid the foundation for the formation of σ-type radical anion intermediate in the stepwise reductive cleavage of disulfide bond in the symmetrical 4,4′-disubstitued DPDS derivatives. For the nine 4,4′-disubstituted DPDS-derivatives under reductive cleavage studies, the increasing %σ*_SS in the LUMOs is parallel to the increasing value of inner reorganization energy.     

Ab initio molecular dynamics study of H2 formation inside POSS compounds

The mechanism and dynamics of the formation of a hydrogen molecule by incorporating two hydrogen atoms in a stepwise manner into the cavity of some POSS (polyhedral oligomeric silsesquioxanes) compounds has been investigated by ab initio molecular orbital and ab initio molecular dynamics (AIMD) methods. The host molecules in the present reactions are two types of POSS, T(8) ([HSiO(1.5)](8)) and T(12)(D(2d)) ([HSiO(1.5)](12)). AIMD simulations were performed at the CASSCF level of theory, in which two electrons and two orbitals of the colliding hydrogen atoms are included in the active space. The trajectories were started by inserting the second hydrogen atom into the hydrogen atom-encapsulated-POSS (H + H@T(n) → H(2)@T(n); n = 8 and 12). In many cases, the gradual formation of a hydrogen molecule has been observed after frequent collisions of two hydrogen atoms within the cages. The effect of the introduction of an argon atom in T(12) is discussed as well.     

Nature of a hydride-halogen bond. A SAPT-, QTAIM-, and NBO-based study

The nature of a hydride-halogen bond is investigated by means of high-level quantum mechanical calculations expended with symmetry-adapted perturbation theory (SAPT), quantum theory of atoms in molecules (QTAIM), and natural bond orbital (NBO) methods. As model hydride-halogen bonded systems complexes between either LiH or HBeH and either XCF(3) or XCCH (X = F, Cl, Br, I) are used. It is shown that the formation of a hydride-halogen bond leads to the elongation of the R(δ+)-H(δ-) hydride bond, which is accompanied by the blue shift of the ν(R-H) stretching vibration frequency and the increase of the IR intensity of this mode. All these effects, although untypical in the case of, e.g., hydrogen bonds, can be considered as rather typical for hydride-halogen bonded systems. The decomposition of the interaction energy based on the SAPT method clearly indicates the dominant role of the induction term, thus the inductive nature of a hydride-halogen bond in opposition to previous findings. NBO-based analysis indicates the charge transfer from the hydride molecule to the more remote parts of the halogen donor and that the elongation of the R-H bond is caused by the charge outflow from the σ(RH) bonding orbital.     

Orbital interactions in large molecular systems: Adsorption of H2 on Ni surfaces

The concept of orbital interactions is applied to the adsorption of H₂ on to the Ni (110) and (111) surfaces. We calculate first two orbitals of a Ni cluster one of which forms an orbital pair with the σ MO and the other with the σ*MO of a H₂ molecule. Contributions of these paired orbitals of fragments to the density of states of the surface-adsorbate extended system are then examined. It is shown that the orbital of the surface that participates in electron delocalization to σ* of the H₂ molecule is located significantly below the Fermi level both in the (110) and in the (111) adsorption models. The σ MO of H₂ and its counterpart of the surface represent mainly overlap repulsion which is shown to be stronger on the (111) surface than on the (110) surface. It is feasible to understand chemical interactions of large systems by using the paired interacting orbitals.     

Hydrogen-hydrogen bonding: a stabilizing interaction in molecules and crystals

Bond paths linking two bonded hydrogen atoms that bear identical or similar charges are found between the ortho-hydrogen atoms in planar biphenyl, between the hydrogen atoms bonded to the C1-C4 carbon atoms in phenanthrene and other angular polybenzenoids, and between the methyl hydrogen atoms in the cyclobutadiene, tetrahedrane and indacene molecules corseted with tertiary-tetra-butyl groups. It is shown that each such H-H interaction, rather than denoting the presence of "nonbonded steric repulsions", makes a stabilizing contribution of up to 10 kcal mol(-1) to the energy of the molecule in which it occurs. The quantum theory of atoms in molecules-the physics of an open system-demonstrates that while the approach of two bonded hydrogen atoms to a separation less than the sum of their van der Waals radii does result in an increase in the repulsive contributions to their energies, these changes are dominated by an increase in the magnitude of the attractive interaction of the protons with the electron density distribution, and the net result is a stabilizing change in the energy. The surface virial that determines the contribution to the total energy decrease resulting from the formation of the H-H interatomic surface is shown to account for the resulting stability. It is pointed out that H-H interactions must be ubiquitous, their stabilization energies contributing to the sublimation energies of hydrocarbon molecular crystals, as well as solid hydrogen. H-H bonding is shown to be distinct from "dihydrogen bonding", a form of hydrogen bonding with a hydridic hydrogen in the role of the base atom.     

Ni(100)表面吸附SO2的密度泛函研究

以原子簇Ni14为模拟表面,采用DFT/B3LYP方法研究了二氧化硫(SO2)分子在Ni(100)表面的吸附构型、能量、电荷及态密度。结果表明,SO2分子通过S原子平铺吸附在Ni(100)的桥位最有利,计算结果与实验相符。电荷密度及态密度分析表明,Ni原子的d轨道与SO2分子的空p轨道之间存在明显的s-p作用和电荷转移,这一作用可能导致SO2分子发生解离。     

Interpretation of scoring functions using 3D molecular fields. Mapping the diacyl-hydrazine-binding pocket of an insect ecdysone receptor

A method is presented for the interpretation of receptor docking score values (rough measures of binding affinities) of ligands in terms of 3D molecular field interaction contributions. The FlexX and FlexX-Pharm methods were used to dock the structures of designed sets of ligands into the ligand-binding pocket of a selected receptor. In the next step the relationship was investigated between the FlexX and CScore scores and 3D molecular fields obtained for the docked conformations of the ligands, using the CoMFA (Comparative Molecular Field Analysis) and CoMSIA (Comparative Molecular Similarity Indices Analysis) methods. The approach yielded highly significant CoMFA and CoMSIA models demonstrating that a high portion of the variance in the docking score values of the ligands can be explained by steric, electrostatic, hydrophobic, and hydrogen bond donor and acceptor molecular field interaction contributions. The approach was exemplified by using the crystal structure of the ligand-binding domain of the ecdysone receptor (EcR) of the moth Heliotis virescens as well as virtual molecule libraries of analogues of known diacyl-hydrazine (DAH) type ecdysteroid agonists. By docking appropriately designed virtual compound libraries into the DAH binding pocket of EcR followed by CoMFA and CoMSIA of the docked conformations, hitherto unexplored regions of the receptor cavity could be mapped. By mapping the significant molecular field interaction contributions onto the model of the receptor-ligand complex, important receptor-ligand interactions could be highlighted that may help the design of novel highly scored receptor ligands. An advantage of the method is that no experimental biological activity data are required to exhaustively map the receptor-binding site.