The Kohn-Sham density of states and band gap of water: from small clusters to liquid water

Electronic properties of water clusters (H2O)(n), with n=2, 4, 8, 10, 15, 20, and 30 molecules were investigated by sequential Monte Carlo/density-functional theory (DFT) calculations. DFT calculations were carried out over uncorrelated configurations generated by Monte Carlo simulations of liquid water with a reparametrized exchange-correlation functional that reproduces the experimental information on the electronic properties (first ionization energy and highest occupied molecular orbital-lowest unoccupied molecular orbital gap) of the water dimer. The dependence of electronic properties on the cluster size (n) shows that the density of states (DOS) of small water clusters (n>10) exhibits the same basic features that are typical of larger aggregates, such as the mixing of the 3a1 and 1b1 valence bands. When long-ranged polarization effects are taken into account by the introduction of embedding charges, the DOS associated with 3a1 orbitals is significantly enhanced. In agreement with valence-band photoelectron spectra of liquid water, the 1b1, 3a1, and 1b2 electron binding energies in water aggregates are redshifted by approximately 1 eV relative to the isolated molecule. By extrapolating the results for larger clusters the threshold energy for photoelectron emission is 9.6+/-0.15 eV (free clusters) and 10.58+/-0.10 eV (embedded clusters). Our results for the electron affinity (V0=-0.17+/-0.05 eV) and adiabatic band gap (E(G,Ad)=6.83+/-0.05 eV) of liquid water are in excellent agreement with recent information from theoretical and experimental works.     

Alkyl chain conformation and the electronic structure of octyl heavy chalcogenolate monolayers adsorbed on Au(111)

Adsorption states of dioctyl dichalcogenides (dioctyl disulfide, dioctyl diselenide, and dioctyl ditelluride) arranged on Au(111) have been studied by X-ray photoelectron spectroscopy (XPS), infrared-visible sum-frequency generation (SFG), and ultraviolet photoelectron spectroscopy (UPS). XPS measurements suggest that dioctyl dichalcogenides dissociatively adsorbed on Au(111) surfaces to form the corresponding monolayers having chalcogen-gold covalent bonds. The elemental compositions of octanechalcogenolates on Au(111) indicate that the saturation coverages of the octyl heavy chalcogenolate (OcSe, OcTe) monolayers are lower than that of the octanethiolate (OcS) self-assembled monolayers (SAMs). The SFG observations of the CH(2) vibrational bands for the heavy chalcogenolate monolayers strongly suggest that a discernible amount of gauche conformation exists in the monolayers, while OcS SAMs adopt highly ordered all-trans conformation. The intensity ratio of the symmetric and asymmetric CH(3) stretching vibration modes measured by SFG shows that the average tilt angle of the methyl group of the OcSe monolayers is greater than that of the OcS SAMs. The larger tilt angle of the methyl group and the existence of a discernible amount of gauche conformation in the OcSe monolayers are due to the lower surface coverage of the OcSe monolayers compared with the OcS SAMs. The smaller polarization dependence in the angle-resolved UPS (ARUPS) spectra of the OcSe monolayers than that of the OcS SAMs is caused by the more disordered structures of the alkyl chain in the former. XPS, SFG, and ARUPS measurements indicate a similar tendency for the OcTe monolayers. The density of states (DOS) observed by UPS at around 1.3 eV for OcS adsorbed on Au(111) is considered to be the antibonding state of the Au-sulfur bond. Similar DOS is also observed by UPS at around 1.0 eV for the OcSe monolayers and at approximately 1.6 eV for the OcTe monolayers on Au(111).     

Second-order many-body perturbation study of solid hydrogen fluoride under pressure

A linear-scaling, embedded-fragment, second-order many-body perturbation (MP2) method with basis sets up to aug-cc-pVTZ is applied to the antiparallel structure of solid hydrogen fluoride and deuterium fluoride under 0-20 GPa of ambient pressure. The optimized structures, including the lattice parameters and molar volume, and phonon dispersion as well as phonon density of states (DOS), are determined as a function of pressure. The basis-set superposition errors are removed by the counterpoise correction. The structural parameters at 0 GPa calculated by MP2 agree accurately with the observed, making the predicted values at higher pressures a useful pilot for future experiments. The corresponding values obtained by the Hartree-Fock method have large, systematic errors. The MP2/aug-cc-pVDZ frequencies of the infrared- and Raman-active vibrations of the three-dimensional solids are in good agreement with the observed and also justify previous vibrational analyses based on one-dimensional chain models; the non-coincidence of the infrared and Raman mode pairs can be explained as factor-group (Davydov) splitting. The exceptions are one pair of modes in the librational region, for which band assignments based on a one-dimensional chain model need to be revised, as well as the five pseudo-translational modes that exist only in a three-dimensional treatment. The observed pressure dependence of Raman bands in the stretching region, which red-shift with pressure, is accounted for by theory only qualitatively, while that in the pseudo-translational region is reproduced with quantitative accuracy. The present calculation proves to be limited in explaining the complex pressure dependence of the librational modes. The hydrogen-amplitude-weighted phonon DOS at 0 GPa is much less structured than the DOS obtained from one-dimensional models and may be more realistic in view of the also broad, structureless observed inelastic neutron scattering spectra. All major observed peaks can be straightforwardly assigned to the calculated peaks in the DOS. With increasing pressure, MP2 predicts further broadening of bands and breach of the demarcation between the pseudo-translational and librational bands.     

Electronic delocalization in discotic liquid crystals: a joint experimental and theoretical study

Discotic liquid crystals emerge as very attractive materials for organic-based (opto)electronics as they allow efficient charge and energy transport along self-organized molecular columns. Here, angle-resolved photoelectron spectroscopy (ARUPS) is used to investigate the electronic structure and supramolecular organization of the discotic molecule, hexakis(hexylthio)diquinoxalino[2,3-a:2',3'-c]phenazine, deposited on graphite. The ARUPS data reveal significant changes in the electronic properties when going from disordered to columnar phases, the main feature being a decrease in ionization potential by 1.8 eV following the appearance of new electronic states at low binding energy. This evolution is rationalized by quantum-chemical calculations performed on model stacks containing from two to six molecules, which illustrate the formation of a quasi-band structure with Bloch-like orbitals delocalized over several molecules in the column. The ARUPS data also point to an energy dispersion of the upper pi-bands in the columns by some 1.1 eV, therefore highlighting the strongly delocalized nature of the pi-electrons along the discotic stacks.     

Direct observation of defect levels in InN by soft X-ray absorption spectroscopy

We have used synchrotron-based near-edge X-ray absorption fine structure (NEXAFS) spectroscopy to study the electronic structure of nitrogen-related defects in InN(0001). Several defect levels within the band gap or the conduction band of InN were clearly resolved in NEXAFS spectra around the nitrogen K-edge. We attribute the level observed at 0.3 eV below the conduction band minimum (CBM) to interstitial nitrogen, the level at 1.7 eV above the CBM to antisite nitrogen, and a sharp resonance at 3.2 eV above the CBM to molecular nitrogen, in full agreement with theoretical simulations.     

Topology, connectivity, and electronic structure of C and B cages and the corresponding nanotubes

After a brief discussion of the structural trends which appear with an increasing number of atoms in B cages, a one-to one correspondence between the connectivity of B cages and C cage structures will be proposed. The electronic level spectra of both systems from Hartree-Fock calculations is given and discussed. The relation of curvature introduced into an originally planar graphitic fragment to pentagonal "defects" such as are present in buckminsterfullerene is also briefly treated. A study of the structure and electronic properties of B nanotubes will then be introduced. We start by presenting a solution of the free-electron network approach for a "model boron" planar lattice with local coordination number 6. In particular the dispersion relation E(k) for the pi-electron bands, together with the corresponding electronic Density Of States (DOS), will be exhibited. This is then used within the zone-folding scheme to obtain information about the electronic DOS of different nanotubes obtained by folding this model boron sheet. To obtain the self-consistent potential in which the valence electrons move in a nanotube, "the March model" in its original form was invoked, and the results are reported for a carbon nanotube. Finally, heterostructures, such as BN cages and fluorinated buckminsterfullerene, will be briefly treated, the new feature here being electronegativity difference.     

Dynamics of the D+ + H2 and H+ + D2 reactions: a detailed comparison between theory and experiment

An extensive set of experimental measurements on the dynamics of the H(+) + D(2) and D(+) + H(2) ion-molecule reactions is compared with the results of quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical quasiclassical trajectory (SQCT) calculations. The dynamical observables considered include specific rate coefficients as a function of the translational energy, E(T), thermal rate coefficients in the 100-500 K temperature range. In addition, kinetic energy spectra (KES) of the D(+) ions reactively scattered in H(+) + D(2) collisions are also presented for translational energies between 0.4 eV and 2.0 eV. For the two reactions, the best global agreement between experiment and theory over the whole energy range corresponds to the QCT calculations using a gaussian binning (GB) procedure, which gives more weight to trajectories whose product vibrational action is closer to the actual integer QM values. The QM calculations also perform well, although somewhat worse over the more limited range of translational energies where they are available (E(T) < 0.6 eV and E(T) < 0.2 eV for the H(+) + D(2) and D(+) + H(2) reactions, respectively). The worst agreement is obtained with the SQCT method, which is only adequate for low translational energies. The comparison between theory and experiment also suggests that the most reliable rate coefficient measurements are those obtained with the merged beams technique. It is worth noting that none of the theoretical approaches can account satisfactorily for the experimental specific rate coefficients of H(+) + D(2) for E(T)≤ 0.2 eV although there is a considerable scatter in the existing measurements. On the whole, the best agreement with the experimental laboratory KES is obtained with the simulations carried out using the state resolved differential cross sections (DCSs) calculated with the QCT-GB method, which seems to account for most of the observed features. In contrast, the simulations with the SQCT data predict kinetic energy spectra (KES) considerably cooler than those experimentally determined.     

Investigation of photoelectrical properties and relaxation dynamics in photoexcited CdSe nanocrystals in thin film form

Electrical and photoelectrical properties of cubic CdSe nanocrystals in thin film form (including the relaxation dynamics of photocarriers) are investigated. Photoelectrical properties of the obtained films are controlled by chemical (varying the reagent concentration in the reaction system) and physical means (controlling the crystal dimensions). In the case of thin films with optimal photoelectrical properties, the calculated band gap energy and ionization energies of impurity levels (on the basis of experimentally obtained temperature dependence of dark electrical resistance) at 0 K are 1.85, 0.74 and 0.43 eV, correspondingly. The calculated optical band gap energy (on the basis of spectral dependence of photoconductivity) at room temperature of 1.75 eV is in excellent agreement with the value of 1.77 eV which is obtained on the basis of electronic absorption spectrum in the framework of parabolic approximation for dispersion relation. Upon thermal treatment of chemically deposited thin films of cubic CdSe quantum dots, as a result of processes of coalescence and crystal growth, the electronic contact between nanocrystals increases and the confinement effects irreversibly disappear. Relaxation of non-equilibrium charge carriers is practically carried out according to the linear mechanism. The calculated relaxation time of photoexcited charge carriers is 0.4 ms.     

Threshold photoelectron study of naphthalene, anthracene, pyrene, 1,2-dihydronaphthalene, and 9,10-dihydroanthracene

Threshold photoelectron spectra (TPESs) were obtained for naphthalene, anthracene, pyrene, 1,2-dihydronaphthalene, and 9,10-dihydroanthracene using imaging photoelectron photoion coincidence spectroscopy, from threshold to a photon energy of ～20 eV. Outer valence Green's function calculations at the OVGF∕cc-pVTZ level of theory were used to assign molecular orbitals to the observed TPES features. There is generally good agreement between the predicted and observed bands. Threshold regions for each molecule exhibit vibrational structure which is readily assigned based on previous PES studies. While the measured adiabatic ionization energies (IE(a)) for naphthalene, anthracene, and pyrene are in good agreement with previous works, new values are reported for the two dihydro species (1,2-dihydronaphthalene, 8.010 ± 0.010 eV and 9,10-dihydroanthracene, 8.335 ± 0.010 eV). A comparison is also made with the G3∕∕B3LYP composite method, which consistently overestimates the IE values by 0.06-0.09 eV. The double ionization energies for anthracene and pyrene have been measured to be 19.3 ± 0.2 and 19.8 ± 0.2 eV, respectively.     

Chemical deposition of semiconducting cadmium selenide quantum dots in thin film form and investigation of their optical and electrical properties

Cadmium selenide quantum dots with cubic crystal structure are chemically deposited in thin film form using selenosulfate as a precursor for selenide ions and ammonia buffer with double role: as a ligand and as a pH value controller. The optical band gap energies of as-deposited and thermally treated cadmium selenide thin films, calculated within the framework of parabolic approximation for the dispersion relation, on the basis of equations which arise from the Fermi's golden rule for electronic transitions from valence to conduction band, are 2.08 and 1.77 eV, correspondingly. The blue shift of band gap energy of 0.34 eV for as-deposited thin films with respect to the bulk value is due to the quantum size effects (i.e., nanocrystals behave as quantum dots) and this finding is in agreement with the theoretical predictions. During the thermal treatment the nanocrystals are sintered, the increase of crystal size being in correlation with the decrease of band gap energy. The annealed thin films are practically non-quantized. From the resistance-temperature measurements, on the basis of the dependence of ln(R/Ω) vs 1/T in the region of intrinsic conduction, the thermal band gap energy (at 0 K) of 1.85 eV was calculated.     

On the model dependence of kinetic shifts in unimolecular reactions: the dissociation of the cations of benzene and n-butylbenzene

Statistical adiabatic channel model/classical trajectory (SACM/CT) calculations have been performed for transitional mode dynamics in the simple bond fission reactions of C(6)H(6)(+) --> C(6)H(5)(+) + H and n-C(6)H(5)C(4)H(9)(+) --> C(7)H(7)(+) + n-C(3)H(7). Reduced-dimensionality model potentials have been designed that take advantage of ab initio results as far as available. Average anisotropy amplitudes of the potentials were fitted by comparison of calculated specific rate constants k(E,J) with measured values. The kinetic shifts of the calculated k(E) curves and the corresponding bond energies E(0)(J=0), derived as 3.90 +/- 0.05 eV for C(6)H(6)(+) and 1.78 +/- 0.05 eV for n-C(6)H(5)C(4)H(9)(+), were in good agreement with literature values from thermochemical studies. Kinetic shifts from fixed tight activated complex Rice-Ramsperger-Kassel-Marcus (RRKM) theory, which also reproduces the measured k(E), were larger than the present SACM/CT results as well as earlier results from variational transition state theory (for C(6)H(6)(+)). The approach using RRKM theory was found to underestimate E(0)(J=0) by about 0.2-0.3 eV. A simplified SACM/CT-based method is also proposed which circumvents the trajectory calculations and allows derivation of E(0)(J=0) on the basis of measured k(E) and which provides similar accuracy as the full SACM/CT treatment.     

Photoelectron spectroscopy of phosphorus hydride anions

Negative-ion photoelectron spectroscopy is applied to the PH-, PH2-, P2H-, P2H2-, and P2H3-molecular anions. Franck-Condon simulations of the photoelectron spectra are used to analyze the spectra and to identify various P2H(n)- species. The simulations employ density-functional theory calculations of molecular geometries and vibrational frequencies and normal modes, and coupled-cluster theory calculations of electron affinities. The following electron affinities are obtained: EA0(PH) = 1.027 +/- 0.006 eV, EA0(PH2) = 1.263 +/- 0.006 eV, and EA0(P2H) = 1.514 +/- 0.010 eV. A band is identified as a mixture of trans-HPPH- and cis-HPPH-. Although the trans and cis bands cannot be definitively assigned from experimental information, using theory as a guide we obtain EA0(trans-HPPH)= 1.00 +/- 0.01 eV and EA0(cis-HPPH) = 1.03 +/- 0.01 eV. A weak feature tentatively assigned to P2H3- has a vertical detachment energy of 1.74 eV. The derived gas-phase acidity of phosphine is delta(acid)G298(PH3) < or = 1509.7 +/- 2.1 kJ mo1(-1).     

Low-frequency electronic and optical properties of rhombohedral graphite

Low-energy electronic and optical properties of ABC-stacked graphite are respectively studied by the tight-binding model and gradient approximation. The band structures include linear and parabolic bands with and without degeneracy. They show strongly anisotropic dispersions. ABC-stacked graphite is a semimetal due to the slight overlap near the Fermi level between the conduction and valence bands. The interlayer interactions change the energy dispersion, state degeneracy, and the positions of band-crossings and band-edge states. When the state energy is higher than the degenerate energy of the conduction band (E(2d)(c)) or lower than that of the valence bands (E(2d)(v)), a greater number of states might exist. The special band structures would be reflected in the density of states (DOS), the joint density of states (JDOS), and the absorption spectra (A(ω)). For example, the DOS exhibits a cave-like structure at ω = E(2d)(c) and E(2d)(v). Both a special jump in the JDOS and a turning point in the A(ω) occur at ω = E(2d)(c) - E(2d)(v). The DOS and A(ω) could be respectively verified by scanning tunneling spectroscopy and optical absorption spectroscopy.     

Electron emission from amorphous solid water after proton impact: Benchmarking PTra and Geant4 track structure Monte Carlo simulations

Track structure Monte Carlo simulations of ionising radiation in water are often used to estimate radiation damage to DNA. For this purpose, an accurate simulation of the transport of densely ionising low-energy secondary electrons is particularly important, but is impaired by a high uncertainty of the required physical interaction cross section data of liquid water.A possible tool for the verification of the secondary electron transport in a track structure simulation has been suggested by Toburen et al. (2010), who have measured the angle-dependent energy spectra of electrons, emitted from a thin layer of amorphous solid water (ASW) upon a passage of 6 MeV protons.In this work, simulations were performed for the setup of their experiment, using the PTB Track structure code (PTra) and Geant4-DNA. To enable electron transport below the ionisation threshold, additional excitation and dissociative attachment anion states were included in PTra and activated in Geant4. Additionally, a surface potential was considered in both simulations, such that the escape probability for an electron is dependent on its energy and impact angle at the ASW/vacuum interface.For vanishing surface potential, the simulated spectra are in good agreement with the measured spectra for energies above 50 eV. Below, the simulations overestimate the yield of electrons by a factor up to 4 (PTra) or 7 (Geant4-DNA), which is still a better agreement than obtained in previous simulations of this experimental situation. The agreement of the simulations with experimental data was significantly improved by using a step-like increase of the potential energy at the ASW surface.     

Adsorption dynamics of CO2 on Zn-ZnO(0001): a molecular beam study

Presented are initial S(0) and coverage Theta dependent, S(Theta), adsorption probability measurements, respectively, of CO(2) adsorption on the polar Zn-terminated surface of ZnO, parametric in the impact energy E(i), the surface temperature T(s), the impact angle alpha(i), varied along the [001] azimuth, the CO(2) flux, and the density of defects, chi(Ar(+)), as varied by rare gas ion sputtering. S(0) decreases linearly from 0.72 to 0.25 within E(i)=0.12-1.33 eV and is independent of T(s). Above E(i)=0.56 eV, S(0) decreases by approximately 0.2 with increasing alpha(i). The shape of S(Theta) curves is consistent with precursor-mediated adsorption (Kisliuk shape, i.e., S approximately const) for low E(i); above E(i)=0.56 eV, however, a turnover to adsorbate-assisted adsorption (S increases with Theta) has been observed. The initial slope of S(Theta) curves decreases thereby with increasing alpha(i), chi(Ar(+)), and T(s), i.e., the adsorbate-assisted adsorption is most distinct for normal impact on the pristine surface at low T(s) and is independent of the CO(2) flux. The S(Theta) curves have been parametrized by analytic precursor models and Monte Carlo simulations have been conducted as well. The temperature dependence of the saturation coverage shows two structures which could be assigned to adsorption on pristine and intrinsic defect sites, respectively, in agreement with a prior thermal desorption spectroscopy study. The heat of adsorption E(d) for the pristine sites amounts to 34.0-5.4Theta, whereas for adsorption on the intrinsic defect sites E(d) of approximately 43.6 kJ/mol could be estimated. Thus, a kinetic structure-activity relationship was present.     

Collective excitations in an ionic liquid

Collective dynamics in a representative model of ionic liquids, namely, 1-butyl-3-methylimidazolium chloride, have been revealed by molecular dynamics simulation. Dispersion of energy excitation, omega versus k, of longitudinal acoustic (LA) and transverse acoustic (TA) modes was obtained in the wave vector range 0.17 < k < 1.40 Angstroms(-1), which encompasses the main peak of the static structure factor S(k). Linear dispersion of acoustic modes is observed up to k approximately 0.7 Angstroms(-1). Due to mixing between LA and TA modes, LA spectra display transverselike component, and vice versa. Due to anisotropy in short-time ionic dynamics, acoustic modes achieve distinct limiting omega values at high k when the cation displacement is projected either along the plane or perpendicular to the plane of the imidazolium ring. In charge current spectra, branch with negative dispersion of omega versus k is a signature of optic modes in the simulated ionic liquid. Conductivity kappa estimated by using ionic diffusion coefficients in the Nernst-Einstein equation is higher than the actual kappa calculated by integrating the charge current correlation function. From TA spectra, a wave vector dependent viscosity eta(k) has been evaluated, whose low-k limit gives eta in reasonable agreement with experimental data.     

Evidence of conformational exchange averaging in the thermal rotational spectrum of ethyl cyanoformate

The Stark modulated low resolution microwave spectrum of ethyl cyanoformate between 21.5 and 24.0 GHz at 210, 300, and 358 K, which shows the J + 1 <-- J = 8 <-- 7 bands of three species, is compared to simulations based on electronic structure calculations at the MP2/6-311++G theory level. Calculations at this theory level reproduce the relative energies of the syn-anti and syn-gauche conformers, obtained in a previous study, and indicate that the barrier to conformer exchange is approximately 360 cm(-1) higher in energy than the syn-anti minimum. Simulated spectra of the eigenstates of the calculated O-ethyl torsional potential function reproduce the relative intensities and shapes of the lower and higher frequency bands which correspond to transitions of the syn-anti and syn-gauche conformers, respectively, but fail to reproduce the intense center band in the experimental spectra. A model incorporating exchange averaging reproduces the intensity of the center band and its temperature dependence. These simulations indicate that a large fraction of the thermal population at all three temperatures undergoes conformational exchange with an average energy specific rate constant, , of approximately 25 GHz. This model can explain anomalies present in rotational spectra of many other compounds composed of mixtures of conformers.     

Probing the electronic structure of [MoOS(4)](-) centers using anionic photoelectron spectroscopy

Using photodetachment photoelectron spectroscopy (PES) in the gas phase, we investigated the electronic structure and chemical bonding of six anionic [Mo(V)O](3+) complexes, [MoOX(4)](-) (where X = Cl (1), SPh (2), and SPh-p-Cl (3)), [MoO(edt)(2)](-) (4), [MoO(bdt)(2)](-) (5), and [MoO(bdtCl(2))(2)](-) (6) (where edt = ethane-1,2-dithiolate, bdt = benzene-1,2-dithiolate, and bdtCl(2) = 3,6-dichlorobenzene-1,2-dithiolate). The gas-phase PES data revealed a wealth of new electronic structure information about the [Mo(V)O](3+) complexes. The energy separations between the highest occupied molecular orbital (HOMO) and HOMO-1 were observed to be dependent on the O-Mo-S-C(alpha) dihedral angles and ligand types, being relatively large for the monodentate ligands, 1.32 eV for Cl and 0.78 eV for SPh and SPhCl, compared to those of the bidentate dithiolate complexes, 0.47 eV for edt and 0.44 eV for bdt and bdtCl(2). The threshold PES feature in all six species is shown to have the same origin and is due to detaching the single unpaired electron in the HOMO, mainly of Mo 4d character. This result is consistent with previous theoretical calculations and is verified by comparison with the PES spectra of two d(0) complexes, [VO(bdt)(2)](-) and [VO(bdtCl(2))(2)](-). The observed PES features are interpreted on the basis of theoretical calculations and previous spectroscopic studies in the condensed phase.     

Relative partial cross sections for single, double, and triple photoionization of C60 and C70

Partial cross sections for the photoion formation from C(60) and C(70) were determined from the yields of singly, doubly, and triply charged ions which were measured by mass spectrometry combined with tunable synchrotron radiation at hnu = 25-120 eV. The dependence of the detection efficiencies on the mass-to-charge ratio was evaluated by using the formula proposed by Twerenbold et al. Corrections of the detection efficiency were found to be critical for obtaining accurate partial cross sections for photoionization of fullerenes. Revisions were made of the partial cross-section curves for single and double photoionization of C(60) and C(70). The curve for triple photoionization of C(70) was newly proposed. The ratios between the cross sections for double and single photoionization increase with hnu and reach saturated values of 0.78 at 85 eV for C(60) and approximately 1.3 at 100 eV for C(70). In contrast, the ratios at 120 eV between the cross sections for triple and single photoionization of C(60) and C(70) amount to 0.14 and approximately 0.38, respectively. The formation mechanism of multiply charged fullerene ions was discussed in terms of valence-electron excitation to antibonding unoccupied orbitals and/or spherical standing waves inside the cavity of a fullerene. This excitation could be followed by Spectator Auger processes and transmission of the excess electronic energy among numerous vibrational degrees of freedom.     

Vibrational density of states and Lindemann melting law

We examine the Lindemann melting law at different pressures using the vibrational density of states (DOS), equilibrium melting curve, and Lindemann parameter delta(L) (fractional root-mean-squared displacement, rmsd, at equilibrium melting) calculated independently from molecular dynamics simulations of the Lennard-Jones system. The DOS is obtained using spectra analysis of atomic velocities and accounts for anharmonicity. The increase of delta(L) with pressure is non-negligible: delta(L) is about 0.116 and 0.145 at ambient and extreme pressures, respectively. If the component of rmsd normal to a reflecting plane as in the Debye-Waller-factor-type measurements using x rays is adopted for delta(L), these values are about 0.067 (+/-0.002) and 0.084 (+/-0.003), and are comparable with experimental and calculated values for face-centered-cubic elements. We find that the Lindemann relation holds accurately at ambient and high pressures. The non-negligible pressure dependence of delta(L) suggests that caution should be exerted in applying the Lindemann law to obtaining the high pressure melting curve anchored at ambient pressure.