Molecular Kinetic Energy Research Articles

Mixed quantum-classical studies of H2 dissociation on metals: Dependence upon molecular geometry and dimensionality

A mixed quantum-classical model is used to compute the probability for dissociation and rotational excitation for H2, HD, and D2 scattered from a Ni surface. The vibrational coordinate, the polar orientation angle, and the center of mass translation of the molecule normal to the surface are treated quantum mechanically using 3D spectral grid/fast Fourier transform techniques. The remaining degrees of freedom are treated classically. The dissociation probabilities are computed as a function of molecular kinetic energy and compared with those determined in a previous 2D study. An increase in rotational excitation coincides with an increase in dissociation as predicted by a recently developed analytical model. The dependence of the dissociation and rotational excitation probabilities on initial internal molecular state, molecular orientation, and surface impact site are also examined.

The use of kinetic energy distributions to determine the relative contributions of gas-phase and surface fragmentation in kiloelectronvolt ion sputtering of a quaternary ammonium salt

Kinetic energy distributions have been used to evaluate the extent to which gas-phase decompositions contribute to the production of fragment ions in organic secondary ion mass spectra of a quaternary ammonium salt. Molecular kinetic energy distributions demonstrate that many fragment ions have a prominent gas-phase component which may account for as much as 50% of the observed fragment ion signal obtained in a double focussing mass spectrometer.

Hyperthermal surface ionization: a novel ion source with analytical applications

We have found that a wide range of organic molecules with hyperthermal kinetic energy (1–20 eV) can undergo an efficient molecular ionization or dissociative ionization upon scattering from a surface. The molecular kinetic energy is obtained in a simple supersonic expansion of the organic heavy molecule seeded in hydrogen (or helium) carrier gas through a pinhole nozzle. Hyperthermal surface ionization (HSI) is a sensitive, selective and informative ionization method. It is characterized by several properties that make it attractive for analytical applications. The HSI mass spectra (negative and positive ions) exhibit unique fragmentation patterns. These HSI mass spectra are different from electron impact (EI) ionization mass spectra, and reveal structural and isomeric information. The ionization yield is determined by the molecular mass, electron affinity or ionization potential and thus extreme selectivity against common light gases is observed. The absence of the vacuum residual gases in the mass spectra combined with the high molecular ionization efficiency contributes to an improved signal-to-noise ratio and detection sensitivity. The supersonic jet chamber serves as an efficient high-load jet separator in the tail-free coupling of a gas chromatograph (GC) to a mass spectrometer (MS) and allows the use of beam modulation and lock-in amplification. The HSI ion source itself can serve as a selective and sensitive GC detector for many functional groups of molecules such as I, Br, Cl, F, PO 2, NO 2, CN, NH 2 polycyclic aromatic hydrocarbons and organometallics. Most notable among these are the organofluorine molecules whose mass spectra are demonstrated and discussed. A simple GC detector based on HSI is described. Intra-nozzle chemical reactions can be used for the selective and sensitive determination of olefins among paraffins.

A finite temperature theory of rotationally inelastic diffraction: H2, HD, and D2 on Cu(100)

The rotationally inelastic diffraction probabilities for H2, HD, and D2 from Cu(100) were computed as a function of surface temperature. The surface is treated in a quantum mechanical fashion using a recently developed formalism. The center of mass molecular translational motion is treated semiclassically, using Gaussian wave packets (GWPs), and the rotations are described quantum mechanically. Strong attenuation of the phonon elastic diffraction peaks with temperature is observed. This Debye–Waller-like attenuation increases with increasing molecular mass and kinetic energy, and decreases as the peaks become more off-specular. The phonon summed rotation–diffraction probabilities show a moderate temperature dependence for the most part. The 0→2 rotational excitation of D2 appears to be strongly phonon assisted above 300 K. At low temperatures our method reproduces the selection rules predicted by previous studies. As the temperature is increased these selection rules become less restrictive. The probability distribution for a scattering molecule exchanging an amount of energy ΔE with the surface was also computed. Rayleigh phonons were found to dominate the energy transfer, with bulk vibrations becoming more important for larger molecular masses, beam energies, and surface temperatures.

Hyperthermal Surface Ionization

AbstractSurface ionization of molecules with hyperthermal kinetic energy (1–20 eV) was found to be very efficient, demonstrating several unique features. We have used the technique of aerodynamic acceleration in supersonic seeded beams in order to obtain molecular kinetic energies in the range 1–20 eV. Three types of hyperthermal surface ionization (HSI) processes were observed: (a) surface‐molecule electron transfer was demonstrated in the I2/diamond system where negative molecular iodine (I−2) ions were produced; (b) molecule‐surface electron transfer was found for the anthracene molecule where positive molecular anthracene ions were generated; (c) hyperthermal surface‐induced dissociative ionization (HSIDI) was observed in 1‐iodopropane, 1‐chloro‐3‐iodopropane, benzyl bromide, and many other molecules. In these processes, we have observed a large current of negative halogen ions and positive molecular residue ions (ion‐pair formation). The mechanism of HSI is described in terms of electron transfer processes. It occurs due to a curve crossing between the neutral scattering interaction potential surface and the ionic interaction potential surface and nonunity reneutralization second curve crossing of the scattered molecules or fragment ions.

Mean field approach to molecule–surface scattering at finite temperature: One phonon theory

A theory is presented for the phonon inelastic scattering of light atoms and molecules from surfaces. Both the gas species and the thermal fluctuations of the solid are treated in a fully quantum fashion. A self-consistent field method is used to reduce the evolution of the reduced density matrix to the propagation of a single wave function and a set of coefficients describing phonon excitation and annihilation. The method allows one to extend recent time dependent molecule–surface scattering theories to finite temperature, with only a small increase in computer time. Agreement is found with experimental data for the thermal attenuation of diffraction peaks for He scattered from Cu. Energy transfer is found to be sensitive to the steepness of the repulsive potential, the molecular kinetic energy, and the angle of incidence, and only weakly dependent on the well depth. The ‘‘Beeby correction’’ is examined and shown to be invalid, except at very low beam energies where there is a small correlation between well depth and inelastic scattering. For this model, energy transfer does not scale with the normal component of the beam energy.

Quantum and classical studies of the dissociation dynamics of H2 and its isotopes on Ni

A two-dimensional quantum mechanical model is used to study the dissociative adsorption of H2 and its heavier isotopes on Ni(100). Dissociation probabilities are computed as a function of molecular kinetic energy for H2 , D2 , T2 , and a hypothetical heavier isotope. It is demonstrated how the variation of the zero point energy with mass strongly influences the dynamics. A qualitative agreement with recent experimental results for H2 and D2 is obtained. Quasiclassical trajectory calculations are performed for the same systems. By comparison with the exact quantum calculations, the classical probabilities for H2 and D2 are shown to be too large at low kinetic energies. For molecules heavier than T2 , classical dynamics are shown to be adequate. The sources of error in the classical simulations are discussed.

Ceramic nozzle for molecular acceleration and its temperature measurement

An all ceramic nozzle is described, based on a watch jewel and having a very small heated volume (V<10−3 cc). Using this nozzle, molecular catalytic and thermal decomposition is minimized; thus, high molecular kinetic energies can be obtained for ‘‘unstable’’ organic molecules. The real nozzle temperature is measured by the variation of its backing pressure with its temperature, keeping constant gas flux conditions. The nozzle is capable of being heated to over 1500 °K with less than 20 W and is thermally isolated from the organic molecule oven that is differentially heated and separately temperature controlled.

Velocity dependent vibrational and rotational energy distributions of sputtered sulfur molecules

S 2 molecules are sputtered by keV ion bombardment from sulfur. With a laser induced fluorescence technique the vibrational and rotational energy distributions are measured. With an additional time-of-flight method a velocity selection is attained. This enables us to determine the internal energy of the S 2 as a function of the molecular velocity. The shape of the population distribution is found to resemble Boltzmann behaviour, yielding effective “temperatures” for vibration and rotation. The vibrational energy is almost independent of the velocity, T vip ∼− 1500 K. However, the average rotational excitation energy increases with both molecular velocity and vibrational quantum number. Approximated by Boltzmann behaviour, the “temperature” T rot varies from 300 to 1600 K. Sputtering with He + instead of Ar + ions gives identical results except for a higher ground vibrational level population. The results are compared with a double and single collision model of molecule sputtering. It is concluded that the single collision mechanism cannot explain the results. The following qualitative features of the energy partition are correctly predicted with the double collision model: the vibrational population for high molecular kinetic energies, the rotational populations of the ground vibrational state, increasing rotational excitation with vibrational quantum number and increasing rotational excitation with molecular velocity.

The dynamics of H2 dissociation on Ni(100): A quantum mechanical study of a restricted two-dimensional model

A quantum mechanical study of the dynamics of H2 dissociation on Ni is presented. The H2 molecule approaches the surface and is held parallel to the surface. The center of mass is atop a Ni atom and the dissociated atoms have minimum energy at bridge binding sites. This restricted molecular configuration allows us to propagate the molecular wave function in time numerically, using fast Fourier transform techniques. The probability for dissociative adsorption is computed as a function of initial molecular kinetic energy, for a variety of model gas–surface potentials. The way in which the height of the barrier to dissociation affects this energy dependence, as well as the nature of the transfer of energy from the center of mass into the relative motion of the H atoms is examined. By including effects due to H atom mobility it is demonstrated how barriers to surface diffusion can dominate dissociation rates by controlling the extent of recombination. Activation barriers to adsorption in the entrance channel are shown to attenuate the incoming molecular beam, and temporarily trap H2 near the surface. The dissociation of H2 is fairly nonclassical, particularly at thermal energies where much reflection occurs at barrier crossing even when the incident energy is above the barrier.

The gradient expansions of the kinetic energy and the mean momentum for light diatomic molecules

For eleven neutral diatomic systems and one positive ion we have numerically evaluated the three terms in the gradient expansion of the molecular kinetic energy T=T0+T2+T4. Hartree–Fock–Roothaan molecular densities were used throughout. For the molecules studied T2/T0 ∼0.1, T4/T2 ∼0.2. The contributions to these integrals from different regions of space were examined. We have also estimated the values of the two terms in the gradient expansion of the mean momentum P=P0+P2 and find P2/P0 ∼0.5. Lastly we make contact with earlier work of Mucci and March. D/N2 is found to correlate grossly with T2, where D is the dissociation energy and N the total number of electrons in the molecule.

Semiclassical investigation of vibrational state and molecular orientation effects in electron transfer reactions for the H+2/H2 collision

An accurate interaction potential is used in the semiclassical energy conserving trajectory formulation to investigate electron transfer reactions in the H+2/H2 collision for initial ion vibrational states 0≤ν′0 ≤5. The state-to-state cross sections are calculated at several initial molecular orientations and ion kinetic energies. The relative total charge transfer cross sections as a function of ν0 are in good agreement with experimental data. At the state-to-state level, the cross section for the resonant channel at low energies (16 and 32 eV) contributes more than 75% of the total charge transfer cross section at ν′0 =0, but decreases with ν0 to less than 50% at ν′0 =5. At high energies (400 and 800 eV) the cross section of many off-resonant channels are as large as that of the resonant channel. These detailed state-to-state results depend on the initial molecular orientations. We also show the charge transfer probabilities as a function of impact parameter. The oscillatory variation suggests the number of electron jumps between two colliding ion cores.

The correlation of molecular rotational and translational kinetic energy in liquid CH2Cl2 and CHCl3

A “molecular dynamics” computer simulation of liquid CH 2 Cl 2 and CHCl 3 has revealed a time dependence of the simple kinetic energy correlation function 〈v 2 (O)J 2 (t)〉/(〈v 2 (O)〉〈J 2 (O)〉) where v is the c. of m. linear velocity and J the molecular angular momentum. This is constant at unity for all t in conventional analytical theory, which is therefore in need of development. The variates v and J are not Gaussian during the approach to equilibrium.

Scientific Reduction and the Mind-Body Problem

IntroductionThe identity thesis (IT hereafter) asserts that for every psychological state P there is a neural state N such that P=N. In the hope of rendering IT clear and plausible many identity theorists have compared psycho-neural identity claims to such theoretical identities as temperature is identical with molecular mean kinetic energy. However such a comparison admits a weak and a strong interpretation. According to the weak interpretation, psycho-neural identities are said to be like theoretical identities in the sense that the former are contingent claims just as the latter are presumed to be. Identity theorists have appealed to the contingent status of IT in order to meet prima facie objections of the following sort. We can imagine ourselves undergoing a pain, although we are not undergoing the neural process which the identity theorist claims is identical with the pain. Indeed we can imagine ourselves being in pain and yet not having a brain at all. Hence IT is false. Identity theorists have replied by arguing that this objection merely shows that IT is not a necessary truth, or that psychological and neurological terms do not have the same meaning.

The Identity Thesis and Neuropsychology

The psycho-neural identity thesis (IT) is roughly the assertion that psychological states are identical with certain physical states of the nervous system. There are, of course, many more precise formulations of IT. In particular, there are two versions of IT depending on whether we take 'states' to refer to types or tokens. Token materialism is a weaker claim than type materialism, assuming that a token of type x may be identical with a token of type y even though x and y are different types. Thus, type materialism entails token materialism, but not conversely. In this paper, IT shall be construed as asserting that psychological states are type-identical with certain neural states. One well-known argument for IT is based on an appeal to the theoretical nature of the claim. Psycho-neural identities are thought of as reduction-functions or bridge-laws necessary for the micro-reduction of psychological theories to neurological ones. Thus, the justification for IT is of the same kind as the justification for such scientific identities as temperature is molecular mean kinetic energy. While there is much to be said about this way of understanding IT, we may simply notice that it presupposes that psycho-neural identities are type-to-type identities.' In a recent paper ([1]), N. J. Block and J. A. Fodor argue that type materialism is very likely false. While they advance three distinct arguments in behalf of this claim, we shall consider only one of these in detail. This argument is based on an appeal to the Lashleyan doctrine of neurological equipotentiality, which holds that any of a wide variety of psychological states can be served by any of a wide variety of neural structures. Thus, a given psychological state may in fact be associated

Kinetic theory, temperature, and equilibrium

Statements of the relationship of the postulates of the kinetic theory of gases to the concept of temperature and discussions of the molecular basis for the general validity of a proportionality between the mean molecular kinetic energy and the absolute temperature in systems at equilibrium may give a misleading impression about the status of temperature.

Molecular Motion and the Moment Analysis of Molecular Spectra. II. The Rotational Raman Effect

The rotational Raman effect is analyzed in terms of moments of its intensity distribution. Each moment may be expressed as an equilibrium property of the molecular distribution in a scattering substance. The first and second moments of rotational Raman spectra are shown to obey the simple proportionality M(1)/M(2)=ℏ/2kT in the high-temperature, or classical limit. This relation is necessary in order that a classical system remain in equilibrium with its black-body radiation. It is the analog for two-photon scattering processes of the Einstein relation for the single photon processes of absorption and emission. The third and higher moments are found to depend on statistical averages of angular derivatives of the intermolecular potential energy, the angular correlation between molecules, and the molecular rotational kinetic energy. The analysis may be applied to the experimental determination of the nonspherical part of intermolecular forces from the rotational Raman effect in compressed gases.

Molecular Motion and the Moment Analysis of Molecular Spectra in Condensed Phases. I. Dipole-Allowed Spectra

Molecular absorption and emission spectra (of a vibrational transition or of a single vibrational component of an electronic transition) are analyzed in terms of moments of their intensity distributions. The results are valid for an arbirtary intermolecular potential energy. The first-moment formula allows one to identify, in an experimental spectrum, the shifted band origin. The second moment is found to have additive contributions from dynamical terms and from fluctuations in the environmental frequency shift. The dynamical terms depend on the average molecular rotational kinetic energy, the principal moments of inertia of the molecule, and the direction of the transition moment relative to the principal axes of inertia. In the classical limit, the average rotational kinetic energy is determined by the temperature, and the dynamical terms of the second moment are then independent of the intermolecular potential energy. If general, the measurement of a second moment gives an upper limit to the average rotational kinetic energy. If the shift fluctuation effect is small, the second moment measures the rotational kinetic energy. The third and higher moments depend on averages of angular derivatives of the intermolecular potential energy, as well as on the rotational kinetic energy and shift-fluctuation-type terms found in the second moment. For example, one of the contributions to the fourth moment of a linear molecule is the mean squared torque on the molecule.

The Change of Molecular Kinetic Energy into Molecular Potential Energy

The Change of Molecular Kinetic Energy into Molecular Potential Energy

The Foundations of Dynamics

DYNAMICAL investigations are often made to depend upon the following three propositions, viz., the principle of linear momentum, the principle of angular momentum, and the principle of energy. In treatises which are concerned with ordinary mechanical systems, such as rigid bodies, elastic solids and frictionless fluids, the word energy is generally employed in the restricted sense of mechanical energy, and is confined to two particular species, viz. kinetic energy arising from such motions of the system as can be controlled by ordinary mechanical agencies, and potential energy arising from the configuration of the system or from its position in space. All other forms of energy, such as molecular kinetic energy arising from the production of heat by friction, and chemical potential energy contained in fuel, explosive compounds, &c., are excluded from consideration. In systems of this kind the sum of the kinetic and potential energies is an invariable quantity, and this proposition may be termed the principle of the conservation of mechanical energy.