Repulsive Region Research Articles

Time correlation function approach to liquid phase vibrational energy relaxation: H2 and D2 solutes in Ar solvent

The theoretical treatment in Paper I [D. W. Miller and S. A. Adelman, J. Chem. Phys. 117, 2672, (2002), preceding paper] of the vibrational energy relaxation (VER) of low-frequency, large mass dihalogen solutes is extended to the VER of the high-frequency, small mass molecular hydrogen solutes H2 and D2 in a Lennard-Jones argon-like solvent. As in Paper I, values of the relaxation times T1 predicted by the theory are tested against molecular dynamics (MD) results and are found to be of semiquantitative accuracy. To start, it is noted that standard Lennard-Jones site–site potentials derived from macroscopic data can be very inaccurate in the steep repulsive slope region crucial for T1. Thus, the H–Ar Lennard-Jones diameter σUV is not taken from literature values but rather is chosen as σUV=1.39 Å, the value needed to make the theory reproduce the experimental H2/Ar gas phase VER rate constant. Next, by MD simulation it is shown that the vibrational coordinate fluctuating force autocorrelation function 〈F̃(t)F̃〉0 of Paper I decays roughly an order of magnitude more rapidly for the molecular hydrogen solutions than for the dihalogen solutions. This result implies a relatively slow decay for the molecular hydrogen friction kernels β(ω)=(kBT)−1∫0∞〈F̃(t)F̃〉0 cos ω tdt, yielding for the H2/Ar and D2/Ar systems at T=150 K physical millisecond values for T1=β−1(ωl) despite the high liquid phase vibrational frequencies ωl of H2 and D2. The rapid decay of 〈F̃(t)F̃〉0 is due to both the steepness of the repulsive slope of the H–Ar potential and the small masses of H and D. Thus, the small value chosen for σUV is needed to avoid unphysically long T1’s. Next, an analytical treatment of the H2/D2 isotope effect on T1, based on the theory, is found to predict that the H2/Ar and D2/Ar T1’s are close in value due to the compensating effects of lower ωl but slower decay of 〈F̃(t)F̃〉0 for D2/Ar, a result in qualitative agreement with experiments. Applying the theory to numerically study the isothermal ρ dependencies of the VER rate constant k(T,ρ)=T1−1 at 150 K reveals that for both H2/Ar and D2/Ar, as for the solutions of Paper I, k(T,ρ) can be factorized as in the isolated binary collision (IBC) model. Moreover, the molecular theory and IBC rate isotherms differ only slightly for both solutions, a result interpreted in terms of the form of the H–Ar pair correlation function. The theoretical and experimental rate isotherms at 150 K are then compared. Agreement is very good for the H2/Ar solution, but for the D2/Ar solution the theoretical rates are about four times too large. Finally, the isochoric T dependencies of k(T,ρ) in the range 200–1000 K are found for both solutions to conform to an Arrhenius rate law.

Orbiting resonances and bound states in molecular scattering

A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states. Then a single pole trajectory, that connects a rotational band of bound states and orbiting resonances, is obtained. These complex angular momentum singularities are derived through a geometrical theory of the orbiting. The downward crossing of the phase-shifts through pi/2, due to the repulsive region of the molecular potential, is estimated by using a simple hard-core model. Some remarks about the difference between diffracted rays and orbiting are also given.

Effective interactions between parallel-spin electrons in two-dimensional jellium approaching the magnetic phase transition

We evaluate the effective interactions in a fluid of electrons moving in a plane, on the approach to the quantum phase transition from the paramagnetic to the fully spin-polarized phase that has been reported from Quantum Monte Carlo runs. We use the approach of Kukkonen and Overhauser to treat exchange and correlations under close constraints imposed by sum rules. We show that, as the paramagnetic fluid approaches the phase transition, the effective interactions at low momenta develop an attractive region between parallel-spin electrons and a corresponding repulsive region for antiparallel-spin electron pairs. A connection with the Hubbard model is made and used to estimate the magnetic energy gap and hence the temperature at which the phase transition may become observable with varying electron density in a semiconductor quantum well.

Photoinduced Electron Attachment to N2 Adsorbed on Platinum

Theoretical calculations on ground and excited electronic states of N2 adsorbed on Pt(100) are carried out to investigate the properties of photoinduced electron attachment states. The metal−adsorbate system is described by an embedded cluster method, and configuration interaction theory is used to resolve the electronic states. The N2 molecule is found to adsorb at an atop Pt atom site with an adsorption energy of 0.18 eV and with a vibrational frequency 70 cm-1 lower than in the gas phase. Only the perpendicular orientation is stable. An electron attachment state corresponding to excitation of an electron from the Fermi level of the metal to a π* orbital of N2 is found to occur at a vertical excitation energy of 4.2 eV (triplet state) and 4.3 eV (singlet state). The NN internuclear distance increases in the excited state and this leads to a range of excitation energies, from 3.6 eV to the minimum of the excited triplet state potential surface to 4.2 eV for the vertical excitation. The corresponding range for singlet states is 3.8 to 4.3 eV. The equilibrium distance of nitrogen from the surface is 2.09 Å for the ground state and 1.96 Å for the electron attachment state. Deexcitation from the excited state to the repulsive region of the ground-state potential can lead to desorption from the surface. Nitrogen does not desorb or dissociate in the excited electronic state.

Contact resonance imaging — a simple approach to improve the resolution of AFM for biological and polymeric materials

It is frequently observed that high resolution is difficult to achieve when using atomic force microscopy (AFM) to image “soft-and-sticky” surfaces, such as polymers and biomaterials. A new and simple method, contact resonance imaging (CRI), is introduced to address these issues. In CRI, the sample is modulated at a resonance frequency of the tip-sample contact, while the average position of the tip still remains in contact with the surface, i.e. in the repulsive region of the force–distance curve. The improvement in image resolution is demonstrated using various biological and polymeric specimens under ambient laboratory conditions and in liquid media. The possible mechanism of the resolution improvement is discussed in comparison to other techniques, such as tapping-mode imaging.

Direct Study of C12E5 Aggregation on Mica by Atomic Force Microscopy Imaging and Force Measurements

Atomic force microscopy (AFM) was used to study the aggregation structure and kinetics of nonionic surfactant penta(oxyethylene) dodecyl ether (C12E5) on mica as a function of temperature. Surface forces and topographical images of surfactant aggregates at the liquid/solid interface were captured in the vicinity of 21 °C. The surfactant molecular aggregates were imaged by choosing an imaging force in the steric repulsion region so that the AFM tip was just outside the surface of the aggregates. At below 21 °C, C12E5 adsorbed as fragments of tens of nanometers in size. The fragments consist of 1−2 nm thick strongly adsorbed species and weakly adsorbed species extending as far as 15 nm from the substrate surface. The fragments gradually increased in number and attached to each other to form clusters connected in one dimension (strings) and two dimensions (networks). With increasing surface coverage, the surface force changed from a purely attractive one to one showing a repulsive force barrier. At above 21 ...

One-dimensional Bose-Hubbard model with nearest-neighbor interaction

We study the one-dimensional Bose-Hubbard model using the Density-Matrix Renormalization Group (DMRG).For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott-insulators and charge density wave phases are determined. We find a direct phase transition between the charge density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. It is known from Luttinger liquid theory that a single impurity causes the system to be insulating if the effective interactions are repulsive, and that an even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac-conductivity in the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.

An ab Initio Calculation of the Potential for the Interaction of a Hydrogen Atom with an Ethane Molecule

In this paper ab initio methods including PMP2/aug-cc-pVTZ, CCSD(T)/6-311++G(d,p), and G2 methods are used to calculate the interaction potential for a hydrogen atom approaching ethane along the carboncarbon axis of ethane. The potential shows a shallow minimum at about 4.0 A and a strong repulsive core. The position of the minimum moves to smaller distances as the size of the basis set increases. Concurrently, the strength of the core repulsion decreases and the well depth increases. PMP2 calculations show a slightly shallower well than do CCSD(T) calculations, but the repulsive potentials are virtually identical. The potential is well represented by a Morse potential. An exponential-6 potential, a simple exponential, an anti-Morse potential or a Kihara potential fit the data less well. A Lennard-Jones potential and a Mie potential show substantial deviations. A new exponentially damped exponential-6 potential fits the repulsive region slightly better than the Morse exponential-6, anti-Morse, and Lennard-Jones potentials. Potential parameters are included in the paper.

Intermolecular forces from density functional theory. III. A multiproperty analysis for the Ar(1S)-CO(1Σ) interaction

The full anisotropic interaction between one Ar atom and the CO(1Σ) molecule treated as a rigid rotor (RR) at its equilibrium geometry is evaluated using density functional theory (DFT) to describe the short-range repulsive region (and its orientational anisotropy) as well as the well region and its angular dependence. The long-range dispersion forces are added from the results of perturbation theory and a scaling procedure is suggested for their correct matching with the DFT data. The computational results are found to agree very well with more sophisticated calculations and to improve on earlier empirical estimates. An extensive comparison with available transport property measurements is also carried out and using, among others, new experimental data for thermal diffusion [Shashkov et al., Inzh. Fiz. Zh. 71, 182 (1998)] analyzed in this work for the first time. The present modifications of DFT treatment of the interaction using the correct dispersion terms therefore appears to provide a realistic description of the Ar–CO potential and of several dynamical properties of this molecular mixture in the gas phase.

Kinetic energies of hydrogen atoms photodissociated from alkyl radicals

A series of alkyl halides was photodissociated at 205.1 nm, forming halogen atoms and alkyl radicals. The latter were in turn dissociated at the same wavelength into alkenes and hydrogen atoms. The average kinetic energies of the hydrogen atoms are large (1.5–2.0 eV) and decrease only slowly with increasing chain length. The inference is that the dissociation mechanism involves crossing from the Rydberg state surface to a repulsive region of the ground state surface at a point near the center of a C–C bond. As had been previously found by Koplitz and coworkers, isotope scrambling was seen in CH 3CD 2 radicals.

Multiple Binding Modes in 3D-QSAR: Microbial Degradation of Polychlorinated Biphenyls

The published microbial degradation rates of nineteen polychlorinated biphenyls (PCB) were correlated with their structure and properties. A Free-Wilson-like calculation of the de novo binding energy contributions of the chlorine substituents was applied, considering simultaneous realization of up to four binding modes for each congener. Influence of the PCB concentration in the vicinity of the degrading enzyme on the degradation rate was taken into account assuming pseudo-equilibrium PCB distribution in the microbial biomass. The resulting map of the binding site has two attractive regions and two repulsive regions positioned in the way that the PCB congeners bind to them in a non-planar conformation. The results are consistent with two commonly accepted perceptions of PCB degradation: (1) for majority of the studied congeners, the attack starts in non-chlorinated 2,3-position or equivalent position; (2) the less chlorinated phenyl ring is usually degraded first.

Load-Dependency of Friction Coefficient Between Silicon-Oxides and Diamond Under Ultra-Low Contact Load

The load-dependency of the friction coefficient under a contact load in the order of sub-micronewtons was revealed. The frictional force was measured experimentally with a diamond tip of 0.1 μm radius on silicon-oxide surfaces in a laboratory atmosphere. The frictional force was obtained even under a certain amount of negative external force. The contact load was regarded as the sum of the external force and the attractive force between two surfaces, the latter being estimated from an elastic contact theory which took into account the van-der-Waals force. The friction coefficient, as the ratio of the frictional force to the contact load (not to the external force), was plotted against the contact load. Below 0.4 μN in the contact load, the friction coefficient increased in inverse proportion to the decrease in contact load. Above 0.4 μN in the contact load, the friction coefficient was stable at about 0.1. We discussed this load-dependency, and derived a hypothesis that the real area of contact should include some part of the attractive region around the repulsive region at the contact point when the contribution of the attractive force is not negligible to the contact load.

Van der Waals Radii of Pt(II) and Pd(II) in Molecular Mechanics Models and an Analysis of Their Relevance to the Description of Axial M.H(-C), M.H(-N), M.S, and M.M (M = Pd(II) or Pt(II)) Interactions.

Parameters have been developed for the molecular mechanics modeling of nonbonded interactions involving Pt(II) and Pd(II). The value obtained for the van der Waals radius-about 1.7 Å-accords well with the value proposed by Bondi (J. Chem. Phys. 1964, 68, 441-451). This model has been used to investigate close M.H(-C), M.H(-N), M.H(-O), M.S, and M.M (M = Pd(II) or Pt(II)) contacts that have previously been described as weak or agostic bonds. It is argued that the M.H(-C) interactions are best described as van der Waals interactions that are in the repulsive region but the results are in accord with the description of M.H(-N) and M.H(-O) contacts as weak hydrogen bonds. M.S and M.M separations in systems without pi-acceptor ligands were accurately reproduced by using the same van der Waals parameters.

Formation of dusty plasma molecules

Abstract The electrostatic interaction potential energy for two Debye shielded macroscopic grains or impurities is obtained for all values of intergrain separation both in the plasma as well as in the plasma sheath. The predicted cohesive energy assumes a form familiar from molecular physics but with no ad hoc assumptions regarding the form of the repulsive and attractive regions and no phenomenological adjustable parameters. The result is significant as a molecular model and constitutes an important element for understanding the interaction forces responsible for the formation of the novel Coulomb or plasma crystal systems.

The steering of molecules in simple dissociation reactions

The effectiveness of steering in simple dissociation reactions has been studied by performing classical and quantum simulations on a wide range of model potentials. By parametrically varying the PES landscape, it is shown how trends in the translational energy dependence of the dissociation probability may be related to particular topographical features. The relationship between the strength of attractive and repulsive regions determines the force which a molecule feels, but in addition we show that the range of the force helps determine the degree of repositioning and reorientation. The presence of wells along the reaction coordinate is considered, and it is shown how the snarled trajectories which frequently result relate to precursor-like behaviour even in the absence of dissipative processes.

Ab Initio Calculations of Intermolecular Interaction Potentials of Corannulene Dimer

The intermolecular interaction potential of the corannulene dimer in a parallel (D5h) orientation was calculated by ab initio methods using basis sets up to 6-311G(2d) quality, with MP2 level electron correlation energy correction. The calculated potentials have their minima at a separation between the two five-membered rings of 3.2 A. An interaction energy of −13.39 kcal mol-1 was calculated at the MP2/6-311G(2d) level. The calculated electron correlation energy is −24.25 kcal mol-1, indicating that the dispersion interaction is the dominant term in the interaction of the corannulene dimer. The calculated potential in the repulsive region is less steep than those obtained from the Lennard-Jones type atom−atom potential parameters commonly used for the MD simulations of C60. It is suggested that the intermolecular interaction potential derived from the corranulene dimer will outperform atom−atom potentials for molecular dynamics studies of the bulk properties of fullerenes.

Correlation between the intensities of vibrational overtone transitions and the repulsive branch of the molecular potential

Energy levels εn and n←0 vibrational overtone transition intensities for a distorted Morse potential (DMP) and a linear dipole moment function are calculated, and then are treated as “observed” quantities. The values of (εn−ε0)/n vs n fall on a straight line very closely. A linear least-squares fit provides an effective anharmonicity parameter (xe)eff which is then used to construct an “effective” Morse potential (EMP). The EMP closely follows the DMP near equilibrium but declines in the far repulsive and attractive regions. The intensities calculated for the EMP systematically overestimate or underestimate the DMP intensities, depending on whether the repulsive branch of the EMP above the dissociation limit runs over or under that of the DMP, respectively, and the discrepancies rapidly increase with the overtone number. This effect of the repulsive branch is further investigated quantitatively by comparing the steepness of the repulsive potential β calculated directly from the potential curve with its value found from the rate of the intensities falloff with the overtone energy. It is shown that these two β values coincide with each other in a wide range of parameters, as predicted by the quasiclassical theory. A semiempirical potential for hydroxyl radical is tested for the occurrence of the effect of the repulsive branch. The EMP and RKR potentials are simulated, and the latter is fitted with a kth-order polynomial, k=6–12. In all cases the energy levels and lower overtone intensities are reproduced with a high precision, but the higher overtone intensities are accurate only when the repulsive branch of the fitting function is close enough to that of the original semiempirical potential. An interpolation/extrapolation procedure commonly used to represent the RKR potential is also discussed.

Finite sized dusty plasma molecules

The electrostatic interaction potential energy for two Debye shielded finite radius grains as a function of separation distance has a form familiar from molecular models with both attractive and repulsive regions predicted. In the background plasma sheath, in addition to this spherically symmetric contribution, the plasma inhomogeneity leads, in first order, to grain coagulation above a critical grain size.

Computed and measured thermal diffusion factor for CO-He mixtures: a test of recent interaction potentials

Several anisotropic interaction potentials which describe the He–CO gaseous mixture were tested via the detailed analysis of recently measured thermal diffusion factors, as functions of both temperature and concentration. The calculations were carried out using the quantum treatment of collision dynamics via the infinite order sudden (IOS) coupling scheme between angular momenta, and further using two additional schemes of approximation to second order: the Chapman–Cowling and the Kihara expansions. The results made it possible to test the relative behaviour of the repulsive regions of the various interactions examined in this work, among which those given by the density functional approach for describing van der Waals forces turn out to give fairly realistic values for the anisotropy of the repulsive wall, but have difficulties in generating the well region correctly. These new calculations confirm also the reliability of an earlier multiproperty potential when treating transport properties at temperatures above 100 K, and therefore when examining features which do not depend much on the details of the attractive well.

The intersection seam between the 1 1 A ′ and 2 1 A ′ states of ozone

The intersection seam between the two lowest 1A′ states of ozone has been determined. The potential energy surfaces and the seam are calculated and discussed in perimetric coordinates which exhibit the full three-dimensional symmetry. The seam is shown to form a closed curve which crosses the C 2 v -restricted coordinate planes at six points. Three of these correspond to the previously determined intersection, the starting point of the present search. The other three correspond to highly repulsive regions on the potential energy surface where two atoms approach each other to within two-thirds of the O2 bond length. At the former three points both states have 1 A 1 symmetry, but at the latter three points one state has 1 A 1 symmetry whereas the other has 1 B 2 symmetry. Consequently, there exist three additional branches of the intersection seam between these two states. Each of these branches lies entirely in one C 2 v -restricted coordinate plane and connects to the previously discussed C s -seam at one point. The existence of a further intersection seam is established. A novel method for determining intersection points is described.