Excitations of lithium ammonia complexes studied by inelastic x-ray scattering

We have carried out high-resolution inelastic x-ray scattering measurements of the excitations of lithium dissolved in ammonia. The incident x-ray energy was 21.6 keV and the resolution was about 2 meV. Several different excitations are observed in the energy range of 0-60 meV (0-500 cm(-1)). In addition to acoustic phonons at low energies, we see excitations that are associated with vibrations of Li(NH3)4+ complexes. We examined these excitations as a function of momentum transfer, lithium concentration, temperature, and state of the system (solid versus liquid). Data are compared with Hartree-Fock and density-functional theory calculations of the excitations of this complex, which agree well with the measured excitation energies.     

Bias in the temperature of helium nanodroplets measured by an embedded rotor

The rovibrational spectra of molecules dissolved in liquid 4He nanodroplets display rotational structure. Where resolved, this structure has been used to determine a temperature that has been assumed to equal that of the intrinsic excitations of the helium droplets containing the molecules. Consideration of the density of states as a function of energy and total angular momentum demonstrates that there is a small but significant bias of the rotor populations that make the temperature extracted from a fit to its rotational level populations slightly higher than the temperature of the ripplons of the droplet. This bias grows with both the total angular momentum of the droplet and with the moment of inertia of the solute molecule.     

Elastic scattering and rotational excitation of nitrogen molecules by sodium atoms

A quantal study of the rotational excitation of nitrogen molecules by sodium atoms is carried out. We present the two-dimensional potential energy surface of the NaN(2) complex, with the N(2) molecule treated as a rigid rotor. The interaction potential is computed using the spin unrestricted coupled-cluster method with single, double, and perturbative triple excitations (UCCSD(T)). The long-range part of the potential is constructed from the dynamic electric dipole polarizabilities of Na and N(2). The total, differential, and momentum transfer cross sections for rotationally elastic and inelastic transitions are calculated using the close-coupling approach for energies between 5 cm(-1) and 1500 cm(-1). The collisional and momentum transfer rate coefficients are calculated for temperatures between 100 K and 300 K, corresponding to the conditions under which Na-N(2) collisions occur in the mesosphere.     

Ultrafast collective dynamics in the charge-density-wave conductor K(0.3)MoO(3)

Low-energy coherent charge-density wave excitations are investigated in blue bronze (K(0.3)MoO(3)) and red bronze (K(0.33)MoO(3)) by femtosecond pump-probe spectroscopy. A linear gapless, acousticlike dispersion relation is observed for the transverse phasons with a pronounced anisotropy in K(0.33)MoO(3). The amplitude mode exhibits a weak (opticlike) dispersion relation with a frequency of 1.67 THz at 30 K. Our results show for the first time that the time-resolved optical technique provides momentum resolution of collective excitations in strongly correlated electron systems.     

Free energy in relation to order parameter in magnets and pyroelectrics

Theoretical models will be presented in which the internal energy of (a) a ferromagnet and (b) a pyroelectric material is expressed in terms of magnetization and electric polarization, respectively. For the ferromagnet, simple models of elementary excitations (e.g., spin wave theory in an insulator, to which Stoner excitations must be added in a metal) lead to formulas for the internal energy at low temperature as power laws in the change of magnetization from its saturation value. An unconventional use of two order parameters, the sublattice magnetization plus the metallic discontinuity in momentum distribution at the Fermi surface, allows the phase transition between metallic and insulating states of antiferromagnets to be treated at T = 0, the three-dimensional transition-metal dichalcogenides being an example here. The treatment of the internal energy of the ferromagnet is then extended to include the entropy also, using specifically the Ising model in nonzero external magnetic field. Its relevance to the Landau theory of phase transitions will be emphasized. Some comments will finally be made about the analogue for pyroelectrics. © 1996 John Wiley & Sons, Inc.     

Optical excitations of defects in realistic nanoscale silica clusters: comparing the performance of density functional theory using hybrid functionals with correlated wavefunction methods

Optical excitations of low energy silica (SiO(2))(4) clusters obtained by global optimization, as opposed to constructed by hand, are studied using a range of theoretical methods. By focusing on the lowest energy silica clusters we hope to capture at least some of the characteristic ways by which the dry surfaces of silica nanosystems preferentially terminate. Employing the six lowest energy (SiO(2))(4) cluster isomers, we show that they exhibit a surprisingly wide range of geometries, defects, and associated optical excitations. Some of the clusters show excitations localized on isolated defects, which are known from previous studies using hydrogen-terminated versions of the defect in question. Other clusters, however, exhibit novel charge-transfer excitations in which an electron transfers between two spatially separated defects. In these cases, because of the inherent proximity of the constituent defects due to the small cluster dimensions, the excitation spectrum is found to be very different from that of the same defects in isolation. Excitation spectra of all clusters were calculated using time-dependent density functional theory (TD-DFT) and delta-SCF DFT (DeltaDFT) methods employing two different hybrid density functionals (B3LYP and BB1K) differing essentially in the amount of incorporated Hartree-Fock-like exchange (HFLE). In all cases the results were compared with CASPT2 calculated values which are taken as a benchmark standard. In line with previous work, the spatially localized excitations are found to be well described by TD-DFT/B3LYP but which gives excitation energies that are significantly underestimated in the case of the charge-transfer excitations. The TD-DFT/BB1K combination in contrast is found to give generally good excitation energies for the lowest excited states of both localized and charge-transfer excitations. Finally, our calculations suggest that the increased quality of the predicted excitation spectra by adding larger amounts of HFLE is mainly due to an increased localization of the excited state associated with the elimination of spurious self-interaction inherent to (semi-)local DFT functionals.     

Excitation levels and magic numbers of small parahydrogen clusters (N<or=40)

The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of 1 molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies, the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes of N=13, 31, and 36, which is in agreement with the experiment.     

Phase control of molecular fragmentation with a pair of femtosecond-laser pulses

We demonstrate the control of molecular fragmentation of o-xylene (C(8)H(10)) on a femtosecond time scale in two-pulse measurements with a pair of femtosecond-laser pulses. Parent and fragment-ion yields were recorded as a function of interpulse delays, i.e., different relative phases of the excitation pulses. The experiments revealed different fragmentation mechanisms in the temporal region of direct overlapping pulses and for separated pulses. For overlapping pulses all ion yields followed the excitation intensity which oscillated as a function of interpulse delay due to the change of constructive and destructive interference of the light fields. For larger delays, in particular, the oscillations of the C(+) and CH(3) (+) fragment-ion yield showed a significant deviation from each other. The results are interpreted as a manifestation of optical phase-dependent electronic excitations mapped onto the nuclear fragmentation dynamics.     

Inelastic electron tunneling spectroscopy by STM of phonons at solid surfaces and interfaces

Inelastic electron tunneling spectroscopy (IETS) combined with scanning tunneling microscopy (STM) allows the acquisition of vibrational signals at surfaces. In STM-IETS, a tunneling electron may excite a vibration, and opens an inelastic channel in parallel with the elastic one, giving rise to a change in conductivity of the STM junction. Until recently, the application of STM-IETS was limited to the localized vibrations of single atoms and molecules adsorbed on surfaces. The theory of the STM-IETS spectrum in such cases has been established. For the collective lattice dynamics, i.e., phonons, however, features of STM-IETS spectrum have not been understood well, though in principle STM-IETS should also be capable of detecting phonons. In this review, we present STM-IETS investigations for surface and interface phonons and provide a theoretical analysis. We take surface phonons on Cu(1?1?0) and interfacial phonons relevant to graphene on SiC substrate as illustrative examples. In the former, we provide a theoretical formalism about the inelastic phonon excitations by tunneling electrons based on the nonequilibrium Green’s function (NEGF) technique applied to a model Hamiltonian constructed in momentum space for both electrons and phonons. In the latter case, we discuss the experimentally observed spatial dependence of the STM-IETS spectrum and link it to local excitations of interfacial phonons based on ab-initio STM-IETS simulation.     

Rovibrational eigenenergy structure of the [H,C,N] molecular system

The vibrational-rotational eigenenergy structure of the [H,N,C] molecular system is one of the key features needed for a quantum mechanical understanding of the HCN?HNC model reaction. The rotationless vibrational structure corresponding to the multidimensional double well potential energy surface is well established. The rotational structure of the bending vibrational states up to the isomerisation barrier is still unknown. In this work the structure of the rotational states for low and high vibrational angular momentum is described from the ground state up to the isomerisation barrier using hot gas molecular high resolution spectroscopy and rotationally assigned ab initio rovibronic states. For low vibrational angular momentum the rotational structure of the bending excitations splits in three regions. For J < 40 the structure corresponds to that of a typical linear molecule, for 40 < J < 60 has an approximate double degenerate structure and for J > 60 the splitting of the e and f components begins to decrease and the rotational constant increases. For states with high angular momentum, the rotational structure evolves into a limiting structure for v(2) > 7--the molecule is locked to the molecular axis. For states with v(2) > 11 the rotational structure already begins to accommodate to the lower rotational constants of the isomerisation states. The vibrational energy begins to accommodate to the levels above the barrier only at high vibrational excitations of v(2) > 22 just above the barrier whereas this work shows that the rotational structure is much more sensitive to the double well structure of the potential energy surface. The rotational structure already experiences the influence of the barrier at much lower energies than the vibrational one.     

Isothermal and non-isothermal water transport in porous membranes. II. The steady state

Thermoosmotic behaviour was studied in simple systems constituted of grossly porous hydrophobic membranes permeated by distilled water. Attention was focused on steady-state conditions, characterized by absence of net transmembrane volume flow, obtained equilibrating thermoosmotic pressure with an external counterpressure. Comparison of hydraulic and thermoosmotic fluxes with steady-state pressure gives insight in the peculiar thermofluidodynamics of volume flow in non-isothermal membrane channels. This investigation was extended to volume transport caused by combination of the two thermodynamic forces constituted of the temperature and pressure gradients, synergic or antagonistic across the membrane. The experimental findings can be fruitfully compared with theoretical predictions of the system's behaviour derived from different approaches. Results obtained with six different membrane types, under a wide range of experimental conditions, lend support to the “thermal radiation pressure theory” which attributes the various effects of matter transport produced by a temperature gradient to the transfer of momentum from drifting thermal excitations to atoms and molecules in the material crossed by heat flow.     

Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order M?ller-Plesset perturbation theory, fourth-order M?ller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values.     

Influence of electronic correlation in monoelectronic density in p-space

The radial molecular monoelectronic density and their orbital contributions have been calculated in the momentum space. For these purposes, densities for the ground state of several atoms and molecules, using a cc-pVTZ basis set at HF level, as well as some post-HF and DFT methods are computed. The difference between the radial monoelectronic density computed with each method and that using the HF wave function is used as a tool to study the influence of the electronic correlation in the momentum space. Densities obtained with post HF calculations show a similar behavior around p = 1.0 and 2.0, that are different from the DFT results. Radial momentum densities (p-densities) are more influenced by the electronic correlation than the exchange part of the DFT methods. CISD p-density is more affected than DFT p-density when the intermolecular distance increases. An analysis of the powers of moments calculated with different methods has been carried out. Contribution to the Serafin Fraga Memorial Issue.     

Electron momentum distributions from valence-bond wave functions

Momentum densities obtained from the Heitler-London (HL) wave functions for diatomic molecules and those from the corresponding valence-bond (VB) wave functions including ionic terms are compared. In each case they shown maxima in the direction perpendicular to the bond. However, the dependence of momentum densities on mutual orientations of the two electronic momenta is quite complex in the latter case. The improvement in the Compton profile on including the ionic terms is illustrated with the example of H₂. The momentum denmsities obtained from the VB wave function constructed from orthogonalized atomic orbitals (OAO) have also been examined. The HL wave function with OAOS leads to the same momentum distribution as the repulsive state HL wave function constructed from overlapping AOS.     

Theoretical investigation of rotationally inelastic collisions of the methyl radical with helium

Rotationally inelastic collisions of the CH(3) molecule in its ground X(2)A(2)' electronic state have been investigated. We have determined a potential energy surface (PES) for the interaction of rigid CH(3), frozen at its equilibrium geometry, with a helium atom, using a coupled-cluster method that includes all single and double excitations, as well as perturbative contributions of connected triple excitations [RCCSD(T)]. The anisotropy of the PES is dominated by repulsion of the helium by the hydrogen atoms. The dissociation energy D(e) was computed to equal 27.0 cm(-1). At the global minimum, the helium atom lies in the CH(3) plane between two C-H bonds at an atom-molecule separation R = 6.52 bohr. Cross sections for collision-induced rotational transitions have been determined through quantum scattering calculations for both nuclear spin modifications. Rotationally inelastic collisions can cause a change in the rotational angular momentum n and its body-frame projection k. Because of the anisotropy of the PES due to the hydrogen atoms, there is a strong propensity for Δk = ±3 transitions. Thermal rate constants for state-specific total collisional removal have also been determined.