Atomic quantum similarity indices in position and momentum spaces

Quantum similarity for atoms is investigated using electron densities in position and momentum spaces. Contrary to the results in position space, the analysis in the momentum space shows how the momentum density carries fundamental information about periodicity and structure of the system and reveals the pattern of Mendeleev's table. A global analysis in the joint r-p space keeps this result.     

Electron pair density information measures in atomic systems

Shannon entropies of the pair density, conditional entropies, and mutual information are studied in position and in momentum space for ground state neutral atoms and selected excited states at the Hartree‐Fock level. We show that the mutual information, a measure of correlation, is larger in position space than in momentum space. This result also holds for a mutual information defined in terms of the exchange density; however, these quantities display much more structure than the corresponding ones based on the pair densities. The interpretation of this behavior is that exchange effects are smaller in momentum space than in position space in these systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Quantum information entropy of modified Hylleraas plus exponential Rosen Morse potential and squeezed states

In this article, some information theoretic concepts are analyzed for modified Hylleraas plus exponential Rosen Morse potential in position and momentum space. The angular and radial contributions of the information density are graphically demonstrated for different states. The entropy densities have asymmetric shape which depends on the values of quantum numbers. The information entropy is analytically obtained for ground state of the potential whereas the numerical calculations have been performed for the higher states and Bialynicki‐Birula and Mycielski inequality is tested for various states using different parameters of the potential. It is shown that the information entropy is reduced, both in position and momentum space, for careful selection of some parameters. Further, it is found that there exist eigenstates exhibiting squeezing in information entropy of modified Hylleraas plus exponential Rosen Morse and Eckart potential. Interestingly, in case of Eckart potential, the squeezed states are obtained in position as well as momentum space and are attempted to saturate for some values of the parameters.     

Long-Range interaction coefficients between H,He+, He,and Li+

Using the new expression for the dynamic multipole polarizabilities in terms of effective oscillator strengths and effective transition energies derived from the variational procedure based on the total energy expansion in terms of induced multipole moments, we have calculated the long-range dispersion force coefficients and the leading relativistic correction to the long-range potential between H, He⁺, He, and Li⁺. We have in addition calculated the oscillator strength sum rules for the above systems. Our results are comparable with those obtained using both a hydrodynamic model to quantum mechanics and double perturbation theory.     

Mutual information and electron correlation in momentum space

Mutual information and information entropies in momentum space are proposed as measures of the nonlocal aspects of information. Singlet and triplet state members of the helium isoelectronic series are employed to examine Coulomb and Fermi correlations, and their manifestations, in both the position and momentum space mutual information measures. The triplet state measures exemplify that the magnitude of the spatial correlations relative to the momentum correlations depends on and may be controlled by the strength of the electronic correlation. The examination of one- and two-electron Shannon entropies in the triplet state series yields a crossover point, which is characterized by a localized momentum density. The mutual information density in momentum space illustrates that this localization is accompanied by strong correlation at small values of p.     

Molecular macrocluster formation on silica surfaces in phenol-cyclohexane mixtures

The adsorption of phenol, an aromatic compound with a hydrogen-bonding group, onto a silica surface in cyclohexane was investigated by colloidal probe atomic force microscopy (AFM), attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), and adsorption isotherm measurements. ATR-FTIR measurements on the silica surface indicated the formation of surface macroclusters of phenol through hydrogen bonding. The ATR-FTIR spectra were also measured on the H-terminated silicon surface to observe the effect of the silanol groups on the phenol adsorption. The comparison of the ATR-FTIR spectra for both the silicon oxide and H-terminated silicon surfaces proved that the silanol groups are necessary for the formation of phenol clusters on the surface. The surface force measurement using colloidal probe AFM showed a long-range attraction between the two silica surfaces in phenol-cyclohexane mixtures. This long-range attraction resulted from the contact of the adsorbed phenol layers for the phenol concentrations below 0.6 mol %, at which no significant phenol clusters formed in the bulk solution. The attraction started to decrease at 0.6 mol % phenol due to the exchange of the phenol molecules between the clusters in the bulk phase and on the surface. The surface density of phenol in the adsorbed layer was calculated on the basis of the long-range attraction and found to be much smaller than the liquid phenol density. The plausible structure of the adsorbed phenol layer was drawn by referring to the crystal structure of the bulk phenol and orientation of the phenol molecules on the surface, estimated by the dichroic analysis of ATR-FTIR spectroscopy. The investigation of the phenol adsorption on the silica surface in a nonpolar solvent using this novel approach demonstrated the effect of the aromatic ring on the surface packing density.     

Electronic properties of doped molecular thin films measured by Kelvin probe force microscopy

We report on high-resolution electronic measurements of doped organic thin-film transistors using Kelvin probe force microscopy. Measurements conducted on field effect transistors made of N,NI-diphenyl-N,NI-bis(1-naphthyl)-1,1I-biphenyl-4,4I-diamine p-doped with tetrafluoro-tetracyanoquinodimethane have allowed us to determine the rich structure of the doping-induced density of states. In addition, the doping process changes only slightly the Fermi energy position with respect to the highest occupied molecular orbital level center. The moderate change is explained by two counter-acting effects on the Fermi energy position: the doping-induced additional charge and the broadening of the density of states.     

Isotope quantum effects in the electron momentum density of water

The isotope quantum effects in the ground-state electron momentum density of water are studied at temperatures ranging from 5 to 90 degrees C by combining Compton scattering experiments utilizing synchrotron radiation and computational analysis within density functional theory. We observe clear differences in the momentum density between normal and heavy water at room temperature, which are interpreted as predominantly reflecting intramolecular structural differences. The changes in the momentum density upon increasing the temperature are found to be larger for heavy than for normal water, which is attributed primarily to temperature-induced intramolecular structural effects. Both model computations and an ab initio approach qualitatively reproduce the changes in the momentum density as a function of temperature.     

Microcanonical statistical study of ortho-para conversion in the reaction H3+ + H2-->(H5+)*-->H3+ + H2 at very low energies

The ortho-para conversion of H(3) (+) and H(2) in the reaction H(3) (+)+H(2)-->(H(5) (+))(*)-->H(3) (+)+H(2) in interstellar space is possible by scrambling the five protons via (H(5) (+))(*) complex formation. The product distribution of the ortho-para conversion reaction can be given by ratios of cumulative reaction probabilities (CRP) calculated by microcanonical statistical theory with conservation of energy, motional angular momentum, nuclear spin, and parity. A statistical method to calculate the state-to-state reaction probabilities for given initial nuclear spin species, rotational states, and collision energies is developed using a simple semiclassical approximation of tunneling and above-barrier reflection. A new calculation method of branching ratios for given total nuclear spins and scrambling mechanisms is also developed. The anisotropic long-range electrostatic interaction potential of H(2) in the Coulomb field of H(3) (+) is taken into account using the first-order perturbation theory in forming the complex. The CRPs and the product distribution of the ortho-para conversion reaction at very low energies with reactants in their ground vibronic and lowest rotational states for given initial nuclear spin species are presented as a function of collision energy assuming complete proton scrambling or incomplete proton scrambling. The authors show that the product distribution at very low energies (or very low temperatures) differs substantially from the high energy (or high temperature) limit branching ratios.     

Bubble-solid interactions in water and electrolyte solutions

Surface forces between an air bubble and a flat mica surface immersed in aqueous electrolyte solutions have been investigated using a modified surface force apparatus. An analysis of the deformation of the air bubble with respect to the mutual position of the bubble and the mica surface, the capillary pressure, and the disjoining pressure allows the air-liquid surface electrical potential to be determined. The experiments show that a long-range, double-layer repulsion acts between the mica (which is negatively charged) and an air bubble in water and in various electrolyte solutions at low concentration, thereby indicating that the air bubble surface is negatively charged. However, there is clear evidence that charge regulation occurs at the air-water interface to maintain a constant surface potential, and as a result of this, the charge at this interface changes from negative to positive as the bubble approaches the mica surface. Because of the attraction that arises as a result of the charge reversal, a finite force is required to separate the bubble from the mica, though the mica remains wetted by the aqueous phase. At the low concentrations investigated, the potential on the gas-liquid interface is independent of the electrolyte type within experimental uncertainty.     

Dynamics of condensation of wetting layer in time-dependent Ginzburg-Landau model

The dynamics of liquid condensation on a substrate or within a capillary is studied when the wetting film grows via interface-limited growth. We use a phenomenological time-dependent Ginzburg-Landau (TDGL)-type model with long-range substrate potential. Using an order parameter, which does not directly represent the density, we can derive an analytic formula for the interfacial growth velocity that is directly related to the substrate potential. Using this analytic expression the growth of wetting film is shown to conform to a power-law-type growth, which is due to the presence of a long-range dispersion force.     

AFM surface force measurements conducted with silica in CnTACl solutions: Effect of chain length on hydrophobic force

Surface forces were measured using an AFM with silica surfaces immersed in C_nTACl (n = 12–18) solutions in the absence of added salt. The results showed long-range attractive forces that cannot be explained by the DLVO theory. The long-range attractions increased with increasing surfactant concentration, reaching a maximum at the point of charge neutralization (p.c.n.) and then decreased. The long-range forces decayed exponentially, with the decay lengths increasing from 3 to 32 nm as the chain length of the surfactants increased from C-12 to C-18. The measured forces can be fitted to the charged-patch model of Miklavic et al. [S.J. Miklavic, D.Y.C. Chan, L.R. White, T.W. Healy, J. Phys. Chem. 98 (1994) 9022–9032] by assuming patch sizes that are much larger than the values reported in the literature.

It was found that the decay length decreases linearly with the effective concentration of the CH₂/CH₃ groups of the C_nTACl homologues raised to the power of −1/2, which is in line with the Eriksson et al.'s hydrophobic force model derived using a mean-field approach. It appears, therefore, that the long-range attractions observed in the present work are hydrophobic forces originating from changes in water structure across the thin surfactant solution film between the silica surfaces. It is conceivable that hydrocarbon chains in solution disrupt the surface-induced water structure and cause a decrease in hydrophobic force. This observation may also provide an explanation for the very long-range forces observed with silylated, LB-deposited, and thiol-coated surfaces.     

Diatomic interactions in momentum space. The effect of polarization and floating functions

The method of momentum density for interatomic interactions is used to investigate the pictures and roles of the polarization and floating functions in momentum (p-) space. Referring to the previous results from the minimal LCAO (Finkelstein-Horowitz) momentum density, we quantitatively discuss the effect of these functions for the bonding process in the ground state of H ₂ ⁺ system. The essence of the polarization and floating effects is found to be a modulation of the oscillation in the two-center part of the momentum density. The polarization function introduces a term with a phase and the floating function enlarges the period of the oscillation. An increased migration of the density from the one-center to the two-center part is also important. As a result, both the functions contribute to emphasize the contraction and expansion of momentum density observed previously. However, the floating function disturbs the density distribution in high momentum region, reflecting the destruction of cusps in position (r-) space. We point out an error in the pioneer work of Duncanson.     

Fourier analysis of the Compton profile: Atoms and molecules

Recent work has shown that the one-dimensional projection of the electron momentum density, the Compton profile, can be usefully interpreted as a position space quantity. This has led to an examination of B(r), the Fourier transform of the momentum density. A number of theoretical results relating to this new observable are given. The wave-mechanical representation with (natural) orbitals is employed, and this forms the basis for the subsequent analysis of B(r). The relationship of B(r) to overlap integrals and more generally to other electron density functions is considered. Atomic wavefunctions for krypton are used to illustrate the potential of this new approach to the analysis of momentum density data. General expressions are derived for atoms and molecules, and the radial and angular dependence of B(r) for various orbitals is displayed. The possibility of extracting accurate bond lengths from B(r) is assessed, and an example is given using some recent theoretical data for the fluorine molecule.     

铂配位的腺嘌呤质子化的理论研究

用量子化学从头算研究一系列平面四方金属配体作用于腺嘌呤N₇位点对其质子化的影响。计算结果表明气相中，配合物质子化能力主要受长程静电效应影响，不同金属离子的影响差别甚微。综合考虑极性溶剂影响后长程静电效应影响显著降低。NBO电荷布居分析表明质子化位点电子云密度的变化直接影响该位点质子化能力。     

Theoretical investigations of the momentum densities for molecular hydrogen

A method previously used to solve the Hartree-Fock or the MC SCF molecular equation in momentum space obtained by applying a Dirac transform to the corresponding equations in position space is used to determine numerical wavefunctions directly in p-space. Theoretical radial momentum wavefunctions, total momentum density and density difference (molecule—isolated atoms) maps are compared when going from separated atoms to molecule (taking into account or not configuration interaction effects) and are examined in detail in terms of electronic momentum distributions in chemical bonding. Some comparisons with binary (e,2e) experimental data are performed. An attempt is made to explain the increase of accuracy compared with previous results.     

Accelerated long-range corrected exchange functional using a two-gaussian operator combined with one-parameter progressive correlation functional [LC-BOP(2Gau)]

Recently, we proposed a simple yet efficient method for the computation of a long-range corrected (LC) hybrid scheme [LC-DFT(2Gau)], which uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. This method dramatically reduced the computational time while maintaining the improved features of the LC density functional theory (DFT). Here, we combined an LC hybrid scheme using a two-Gaussian attenuating operator with one-parameter progressive correlation functional and Becke88 exchange functional with varying range-separation parameter values [LC-BOP(2Gau) with various μ values of 0.16, 0.2, 0.25, 0.3, 0.35, 0.4, and 0.42] and demonstrated that LC-BOP(2Gau) reproduces well the thermochemical and frontier orbital energies of LC-BOP. Additionally, we revised the scaling factors of the Gaussian multipole screening scheme for LC-DFT(2Gau) to correspond to the angular momentum of orbitals, which decreased the energy deviations from the energy with the no-screening scheme. © 2018 Wiley Periodicals, Inc.     

Long-range interactions between an atom in its ground S state and an open-shell linear molecule

Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a nonzero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nondiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown that for the interactions of molecules in excited states that are connected to the ground state by multipolar transition moments additional terms in the long-range induction energy appear. All these theoretical developments are illustrated with the numerical results for systems of interest for the sympathetic cooling experiments: interactions of the ground state Rb((2)S) atom with CO((3)Π), OH((2)Π), NH((1)Δ), and CH((2)Π) and of the ground state Li((2)S) atom with CH((2)Π).     

AFM forces measured between gold surfaces coated with self-assembled monolayers of 1-hexadecanethiol

An atomic force microscope (AFM) was used to measure the forces between gold surfaces with and without hydrophobizing them by the self-assembly of 1-hexadecanethiol. The forces measured between bare gold surfaces were fitted to the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory with a Hamaker constant of 1.2 x 10 (-20) J, which was close to the value determined using the methylene iodide contact angle method but was lower than that calculated using the Lifshitz theory. When the surfaces were hydrophobized in a 0.01 mM thiol-in-ethanol solution for 10 min, the measured forces exhibited a long-range force with a decay length of 35 nm. Despite its high water contact angle (105 degrees ), the force curve was smooth and exhibited no steps. When the surfaces were hydrophobized in a 1 mM thiol solution for longer than 6 h, however, the force curves exhibited steps, indicating that the long-range attractions were caused by bridging bubbles. When the measurements were conducted after washing the substrates with organic solvents, the steps disappeared and long-range attractive forces appeared. In the presence of ethanol, the water contact angle decreased to below 90 degrees , the attraction became weaker, and the force curves became smooth. On the basis of the results obtained in the present work, possible mechanisms for the long-range attractions are discussed.