# Showing papers in "Journal of Chemical Physics in 1978"

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TL;DR: The concept of electronegativity is defined in this paper as the negative of the chemical potential (the Lagrange multiplier for the normalization constraint) in the Hohenberg-Kohn density functional theory of the ground state: χ =−μ=−(∂E/∂N)v.

Abstract: Precision is given to the concept of electronegativity. It is the negative of the chemical potential (the Lagrange multiplier for the normalization constraint) in the Hohenberg–Kohn density functional theory of the ground state: χ=−μ=−(∂E/∂N)v. Electronegativity is constant throughout an atom or molecule, and constant from orbital to orbital within an atom or molecule. Definitions are given of the concepts of an atom in a molecule and of a valence state of an atom in a molecule, and it is shown how valence‐state electronegativity differences drive charge transfers on molecule formation. An equation of Gibbs–Duhem type is given for the change of electronegativity from one situation to another, and some discussion is given of certain relations among energy components discovered by Fraga.

2,279 citations

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TL;DR: In this article, a method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described, and the results are shown to be consistent with the corresponding Fokker-Planck results.

Abstract: A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker–Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution.

2,168 citations

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TL;DR: In this paper, the authors used time correlation function methods to discuss classical isomerization reactions of small nonrigid molecules in liquid solvents and derived molecular expressions for a macroscopic phenomenological rate constant.

Abstract: In this article, time correlation function methods are used to discuss classical isomerization reactions of small nonrigid molecules in liquid solvents. Molecular expressions are derived for a macroscopic phenomenological rate constant. The form of several of these equations depend upon what ensemble is used when performing averages over initial conditions. All of these formulas, however, reduce to one final physical expression whose value is manifestly independent of ensemble. The validity of the physical expression hinges on a separation of time scales and the plateau value problem. The approximations needed to obtain transition state theory are described and the errors involved are estimated. The coupling of the reaction coordinate to the liquid medium provides the dissipation necessary for the existence of a plateau value for the rate constant, but it also leads to failures of Wigner’s fundamental assumption for transition state theory. We predict that for many isomerization reactions, the transmissio...

1,186 citations

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TL;DR: In this article, the anomalous intensity arises from preresonant or resonant excitations of conduction electron resonances in adsorbate covered metal bumps on the surface, which form a two-dimensional colliodlike layer which displays a collective resonance at a frequency which depends on the bump density.

Abstract: Greatly enhanced Raman scattering from monolayers of pyridine adsorbed on silver has been reported by several authors. I propose that the anomalous intensity arises from preresonant or resonant excitations of conduction electron resonances in adsorbate covered metal bumps on the surface. The bumps form a two‐dimensional colliodlike layer which displays a collective resonance at a frequency which depends on the bump density. The model can account for the disparate excitation functions reported by two groups in terms of varying degrees of roughness. The apparent lack of enhancement with metals other than Group Ib is also explained.

664 citations

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TL;DR: In this paper, an accurate three-dimensional potential energy surface for H3 has been obtained by the configuration interaction (CI) method, with the energy of the saddle point taken to be zero, are believed to lie within 0.1 kcal/mole of the exact clamped nuclei limit.

Abstract: An accurate three‐dimensional potential energy surface for H3 has been obtained by the configuration interaction (CI) method. The calculated energies, for 156 nuclear configurations, with the energy of the saddle point taken to be zero, are believed to lie within 0.1 kcal/mole of the exact clamped‐nuclei limit. The CI calculations used an extended one‐particle basis set of 4 s‐type, 3 p‐type, and 1 d‐type contracted Gaussian functions, and a nearly complete n‐particle basis set. In order to solve the large secular problem, the direct CI method was adapted to the problem of complete CI for three valence electrons. The properties of the accurate H3 potential surface were used to evaluate ab initio and semiempirical methods for potential surface calculations, with emphasis on their applications to other exchange reactions.

602 citations

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TL;DR: In this paper, the symmetry-adapted cluster expansion of an exact wave function has been studied, which is suitable for open-shell systems as well as closed-shell ones.

Abstract: The symmetry‐adapted‐cluster (SAC) expansion of an exact wavefunction is given. It is constructed from the generators of the symmetry‐adapted excited configurations having the symmetry under consideration, and includes their higher‐order effect and self‐consistency effect. It is different from the conventional cluster expansions in several important points, and is suitable for applications to open‐shell systems as well as closed‐shell systems. The variational equation for the SAC wavefunction has a form similar to the generalized Brillouin theorem in accordance with the inclusion of the higher‐order effect and the self‐consistency effect. We have expressed some existing open‐shell orbital theories equivalently in the conventional cluster expansion formulas, and on this basis, we have given the pseudo‐orbital theory which is an extension of open‐shell orbital theory in the SAC expansion formula.

584 citations

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TL;DR: In this paper, an unconventional time dependent formula for total photodissociation cross sections is presented, which is directly applicable to polyatomic photofragmentation, and as a spinoff is derived the polyatomic generalization of the (diatomic) reflection method.

Abstract: An unconventional time dependent formula for total photodissociation cross sections shows the importance of short time dynamics in direct photofragmentation. This is exploited to provide a systematic expansion in powers of h/ for the cross section. The lowest order term is a classical cross section which is shown to be an improvement upon the venerable reflection approximation. Terms to higher order in h/ lead to even greater improvements in accuracy as shown by simple numerical examples. Our formulas are directly applicable to polyatomic photofragmentation, and as a spinoff we derive the polyatomic generalization of the (diatomic) reflection method.

559 citations

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TL;DR: In this paper, a detailed investigation of the steady-state and nonsteady-state reaction CO+1/2O2→CO2 on Pd (111) has been carried out with the molecular beam technique.

Abstract: A detailed investigation of the steady‐state and nonsteady‐state reaction CO+1/2O2→CO2 on Pd (111) has been carried out with the molecular beam technique. It could be shown conclusively that the reaction proceeds between two adsorbed species (Langmuir–Hinshelwood mechanism) throughout the temperature and pressure range investigated. For low CO coverages, the activation energy of the reaction was determined to be 25 kcal/mole, whereas at moderate CO coverages, a rearrangement of the oxygen adlayer takes place resulting in a reduction of the activation energy to 14 kcal/mole. It is not possible to formulate a simple kinetic expression for the reaction rate which is valid over the entire range of temperatures and pressures due to changes in the adsorption rate for O2, coadsorption of CO and O2, to diffusion in the adlayer, and to changes in the geometrical arrangement within the adlayer with varying coverage.

522 citations

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TL;DR: In this article, Liu and Siegbahn made an accurate least square fit to the potential energy surface start for H+H2 with a root-mean-square error of 0.17 kcal/mol.

Abstract: Liu and Siegbahn’s recent calculations on the potential energy surface start for H+H2 provide us with the most accurately known potential energy surface for any chemical reaction. We have made an accurate least‐squares fit to this surface which satisfies several criteria for use in scattering calculations, including essentially exact agreement with all saddle point properties and being reasonably compact. With eight nonlinear parameters and 15 linear parameters we fit all 267 ab initio points with a root‐mean‐square error of 0.17 kcal/mol and a maximum absolute deviation of 0.55 kcal/mol. The spherical average of the interaction potential is in good agreement with the recent experimental estimate of Gengenbach, Hahn, and Toennies.

521 citations

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TL;DR: In this article, normal coordinate calculations are carried out for all the inplane modes of octaethylporphyrinato-Ni (II) and its meso-deuterated and 15N substituted derivatives.

Abstract: Normal coordinate calculations are carried out for all the in‐plane modes of octaethylporphyrinato‐Ni (II) and its meso‐deuterated and 15N substituted derivatives. With 37 constants of a modified Urey–Bradley force field and a structural model with D4h symmetry, 59 resonance Raman lines (A1g+B1g +A2g+B2g) and 38 infrared bands (Eu) of these three molecules are assigned. The vibrational modes of the Raman active species are represented in terms of the Cartesian atomic displacement vectors. Based on the present results, some important resonance Raman lines of hemoproteins are interpreted. The so‐called ’’oxidation state maker’’ (Band IV) is due to an in‐phase breathing‐like mode of four pyrrole rings although being somewhat deformed by the large contribution of the Cα–N symmetric stretching term. The spin state sensitive Raman lines, namely, Band I and III, are associated mainly with methine bridge (Cα–Cm) stretching modes. Two prominent anomalously‐polarized Raman lines of hemoproteins around 1580 and 1300...

508 citations

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TL;DR: In this paper, a self-consistent field description of coupled anharmonic oscillators was formulated for a model problem of two coupled an-harmonic OO and energy eigenvalues compared with previous exact quantum and semiclassical ones.

Abstract: We formulate a self‐consistent field description of coupled anharmonic oscillators. The SCF equations are solved numerically for a model problem of two coupled anharmonic oscillators and energy eigenvalues compared with previously published exact quantum and semiclassical ones.

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TL;DR: In this article, computer simulation by the molecular dynamics technique has been used to investigate a modification of the previously introduced "central force model" for liquid water, with periodic boundary conditions and Ewald summation.

Abstract: Computer simulation by the molecular dynamics technique has been used to investigate a modification of the previously introduced ’’central force model’’ for liquid water. The simulation involved 216 molecules, with periodic boundary conditions and Ewald summation, at 29.5°C and 1 g/cm3. In all respects considered (pressure, energy, pair correlation functions, self‐diffusion rate) the revised set of interactions represents water more accurately than the earlier set.

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TL;DR: In this paper, a semi-empirical pair potential for molecular hydrogen and deuterium was derived by fitting to solid state data, and the potential was bounded to conform asymptotically to short and long-range theoretical results.

Abstract: A semiempirical pair potential for molecular hydrogen and deuterium has been derived by fitting to solid state data. The potential is bounded to conform asymptotically to short‐ and long‐range theoretical results. In the solid, many‐body effects are accounted for by including a spherical form of the nonnegligible Axilrod–Muto–Teller three‐body forces. The potential can be used to successfully describe isotropic properties in the solid and gas phases.

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TL;DR: In this paper, a new Monte Carlo simulation procedure is developed which is expected to produce more rapid convergence than the standard Metropolis method, and the trial particle moves are chosen in accord with a Brownian dynamics algorithm rather than at random.

Abstract: A new Monte Carlo simulation procedure is developed which is expected to produce more rapid convergence than the standard Metropolis method. The trial particle moves are chosen in accord with a Brownian dynamics algorithm rather than at random. For two model systems, a string of point masses joined by harmonic springs and a cluster of charged soft spheres, the new procedure is compared to the standard one and shown to manifest a more rapid convergence rate for some important energetic and structural properties.

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TL;DR: In this article, the Torrey theory was extended to include effects of one type of spin that is rapidly relaxing, diffusion by jumps of finite size, and frequency-dependent diffusion coefficients in the theory of spin relaxation by intermolecular dipolar interactions.

Abstract: Hwang and Freed have previously given solutions for the relative diffusion of molecules that include the proper boundary condition (i.e., an excluded volume due to a distance of minimum approach) which has usually been neglected in spin relaxation theories. In this work their results are extended to include effects of (1) one type of spin that is rapidly relaxing, (2) diffusion by jumps of finite size, and (3) frequency‐dependent diffusion coefficients in the theory of spin relaxation by intermolecular dipolar interactions. These results are mathematically simpler and sounder than those commonly employed. In particular, it is shown that for case (2) measurements of J (O), the zero‐frequency spectral density cannot solely be used to determine the jump size, in constrast to the Torrey theory, which did not consider the boundary‐value problem.

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TL;DR: Isotopic effects on the molecular diffusion coefficients of H2, 16O, HD16O, and H2 18O have been determined by two independent methods as mentioned in this paper, where the evaporation of liquid water under controlled laminar flow conditions was investigated and the transport of water vapor through a diffusion tube was measured.

Abstract: Isotopic effects on the molecular diffusion coefficients of H2 16O, HD16O, and H2 18O have been determined by two independent methods. In the first one, the evaporation of liquid water under controlled laminar flow conditions was investigated. In the second one, the transport of water vapor through a diffusion tube was measured. The molecular diffusion coefficient of natural water vapor in nitrogen was redetermined. At 21 °C and P=760 Hg mm, D=0.244±0.004 cm2/sec. For the isotopic molecules we have DHD16O/DH216O=0.9757±0.0009 and DH218O/DH216O=0.9727±0.0007. Agreement between the data obtained in the pure gas phase experiment and the two‐phase experiment shows that the condensation coefficients of the isotopically substituted molecules are identical. Interpretation of the isotopic effects on molecule diffusivities indicates that the relative mass differences between H2 16O, HD16O, and H2 18O alone cannot account for the experimental results. This is more important for the D–H substitution in which the asy...

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TL;DR: In this paper, the authors used the flowing afterglow technique at 300 °K for the quenching of a large number of small molecules by using a set of thermal cross sections to test correlations between the magnitudes of the cross sections and properties of the reagents.

Abstract: Rate constants have been measured by the flowing afterglow technique at 300 °K for the quenching of Ar(3P2), Ar(3P0), Kr(3P2), and Xe(3P2) by a large number of small molecules. For the same reagent, the magnitudes of the cross‐sections usually increase in the series Ar(3P2), Ar(3P0), Kr(3P2), and Xe(3P2). The Ar(3P2) and Ar(3P0) data are compared to results in the literature for these states and to data for Ar(3P1) and Ar(1P1). The set of thermal quenching cross sections are used to test the correlations between the magnitudes of the cross sections and properties of the reagents as predicted by the orbiting, absorbing‐sphere, golden rule, and curve‐crossing mechanisms for quenching. The best correlation is between the cross sections and the C6 coefficient. The analysis supports the proposition that the orbiting‐controlled, curve‐crossing model is the general mechanism governing the magnitude of the thermal cross sections for quenching of the metastable states. This model explains the very large quenching cross sections of F2 and OF2 (relative to other molecules composed of first row elements) because covalent–ionic curve crossing occurs outside the conventional orbiting radius. The validity of the simple van der Waals dispersion forces as being the dominant entrance channel interaction between the excited state rare gas atoms and the reagents is discussed.

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TL;DR: In this paper, a new model was constructed which treated H+ and O2− particles as the basic dynamical and structural elements, and the model yields water molecules which have the correct geometry and dipole moment, and which engage in hydrogen bonding to one another.

Abstract: In order to achieve a simple description of aggregates of deformable water molecules, a new model has been constructed which treats H+ and O2− particles as the basic dynamical and structural elements. The H+ units are bare protons, while the O2− units possess a form of nonlocal polarizability consistent with their electronic structure. The model yields water molecules which have the correct geometry and dipole moment, and which engage in hydrogen bonding to one another. Minimum‐energy structures have been determined for the water dimer and trimer and for small hydrate clusters of H+ and OH−; comparison with relevant experiments and quantum–mechanical calculations is satisfactory.

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TL;DR: In this article, a simple direct derivation of the rotational infinite order sudden (IOS) approximation in molecular scattering theory is given, and connections between simple scattering amplitude formulas, choice of average partial wave parameter, and magnetic transitions are reviewed.

Abstract: A simple, direct derivation of the rotational infinite order sudden (IOS) approximation in molecular scattering theory is given. Connections between simple scattering amplitude formulas, choice of average partial wave parameter, and magnetic transitions are reviewed. Simple procedures for calculating cross sections for specific transitions are discussed and many older model formulas are given clear derivations. Total (summed over rotation) differential, integral, and transport cross sections, useful in the analysis of many experiments involving nonspherical molecules, are shown to be exceedingly simple: They are just averages over the potential angle of cross sections calculated using simple structureless spherical particle formulas and programs. In the case of vibrationally inelastic scattering, the IOSA, without further approximation, provides a well‐defined way to get fully three dimensional cross sections from calculations no more difficult than collinear calculations. Integral, differential, viscosit...

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TL;DR: In this article, the renormalized numerov method has been generalized to bound states of the coupled-channel Schroedinger equation and a method for detecting wave function nodes is presented.

Abstract: The renormalized Numerov method, which was recently developed and applied to the one‐dimensional bound state problem [B. R. Johnson, J. Chem. Phys. 67, 4086 (1977)], has been generalized to compute bound states of the coupled‐channel Schroedinger equation. Included in this presentation is a generalization of the concept of a wavefunction node and a method for detecting these nodes. By utilizing node count information it is possible to converge to any specific eigenvalue without the need of an initial close guess and also to calculate degenerate eigenvalues and determine their degree of degeneracy. A useful interpolation formula for calculating the eigenfunctions at nongrid points is also given. Results of example calculations are presented and discussed. One of the example problems is the single center expansion calculation of the 1sσg and 2sσg states of H+2.

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TL;DR: In this article, a formalism is presented that describes the time behavior of the spin density matrix of a nuclear spin system with arbitrary spin in terms of fictitious spin −(1/2) operators.

Abstract: A formalism is presented that describes the time behavior of the spin density matrix of a nuclear spin system with arbitrary spin in terms of fictitious spin −(1/2) operators. This formalism is an extension of that used earlier for nuclei with spin I=1. For a spin system with n eigenstates we define for every pair of eigenstates ‖i〉 and ‖j〉 three operators Ii−jp, with p=x, y, and z, according to the three 2×2 Pauli matrices σx, σy, and σz. These operators together constitute a complete set of n2−1 independent Hermitian operators, and we can write the n×n density matrix and the spin Hamiltonian of the system in terms of the Ii−jp operators. The commutation relations among the operators make it possible in many cases to solve the equation of motion of the density matrix analytically. Three examples of the use of the Ii−jp operators are presented. Firstly a system of noninteracting spins with I=1 is considered. The Ii−jp operators for this case are compared with the Iq,k operator defined earlier. The cw sign...

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TL;DR: In this article, the electron spin correlation tensor is derived from the theory of rotational diffusion, and the effect of electron hopping between molecules on the spin correlations is analyzed in the context of a radical pair.

Abstract: The coherent electron spin motion in radicals induced by the hyperfine coupling to nuclear spins is described semiclassically. The nuclear spins are treated as constant classical vectors around which the electron spin precesses. The ensemble average over all nuclear spin configurations is taken yielding the electron spin correlation tensor

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TL;DR: In this article, the electrical conductivity of the halogen doped transpolyacetylene system, (CH)x, was studied in terms of a model of the doping process based on charge transfer.

Abstract: A study of the electrical conductivity of the halogen doped transpolyacetylene system, (CH)x, is reported. When films of trans‐ (CH)x are exposed to chlorine, bromine, or iodine vapor, uptake of halogen occurs; and the conductivity increases markedly, over eleven orders of magnitude in the case of iodine. The behavior of the halogenated polyacetylene is like that of a series of semiconductors with activation energies which vary with halogen content. The results are discussed in terms of a model of the doping process based on charge transfer.

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TL;DR: In this paper, the authors developed a theory required to extract detailed motional information from NMR relaxation times of nuclei in an amino acid side chain containing multiple internal rotation axes attached to a large macromolecule of cylindrical symmetry.

Abstract: The theory required to extract detailed motional information from NMR relaxation times of nuclei in an amino acid side chain containing multiple internal rotation axes attached to a large macromolecule of at least cylindrical symmetry is developed. Emphasis is placed on the analysis of 13C‐NMR of protonated carbons where dipolar relaxation is predominant. Extension to other relaxation processes is straightforward. The spectral density from which the relaxation times can be calculated is obtained for various models for the motion of the side chain. The existing theory which assumes that internal rotations are both independent and free is generalized to incorporate excluded volume effects in a heuristic way by restricting the amplitude of the internal rotations. It is found that small amplitude motions are ineffective in causing relaxation. Thus jump models involving a relatively small number of configurations are appropriate to describe the motion of the side chain. The advantage of jump models is twofold:...

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TL;DR: In this paper, the interpretation of the dependence on coverage of the stretching frequency of CO adsorbed of metal sufaces is re-examined, taking into account substrate image effects and dielectric screening of the adorbed layer.

Abstract: The interpretation, in terms of dipole interactions, of the dependence on coverage of the stretching frequency of CO adsorbed of metal sufaces is re‐examined. We take into account substrate image effects and dielectric screening of the adsorbed layer. We also provide a theory of the statistical fluctuations in random, partially filled layers. The dipole interactions provide a frequency shift of about 10 cm−1, which is only about one third of that usually observed.

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TL;DR: In this paper, the time-dependent Smoluchowski equation with a Coulomb potential is solved analytically for a general boundary condition, and expressions for the distribution function, reaction rate, and survival probability are given.

Abstract: The time‐dependent Smoluchowski equation with a Coulomb potential is solved analytically for a general boundary condition, and expressions for the distribution function, reaction rate, and survival probability are given. The expressions are evaluated numerically and the long‐time behavior is derived. The theoretical results apply to experiments involving ion recombination without an electric field (or where there is a time delay in the application of the field), to scavenging experiments, and to fluorescence quenching.

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TL;DR: In this article, the simulation of conformational relaxation processes in polymer chains is presented, where the authors obtain relationships between the stochastic difference equations that form the basis for computer simulation, and equivalent Langevin differential equations and Smoluchowski diffusion equations.

Abstract: Methods are presented for the simulation of conformational relaxation processes in polymer chains. The chains interact with the solvent through frictional and Langevin forces, have constrained bond lengths and angles, and smooth rotational energy functions. Relationships are obtained between the stochastic difference equations that form the basis for computer simulation, and equivalent Langevin differential equations and Smoluchowski diffusion equations. The presence of constraints and the associated action of potential forces and Langevin forces on the same time scale leads to somewhat intricate algorithms and correction terms. However, the time increment during a simulation step can be increased by a factor of 1000 or more over what is required if vibrational potentials are used to preserve the primary chain structure. Computation time is proportional to chain length in the absence of hydrodynamic interaction and excluded volume forces.

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TL;DR: In this article, a theory of unimolecular reactions induced by coherent, monochromatic infrared radiation (URIMIR) in the absence of collisions is presented, where it is shown that the set of first order linear differential equations for the amplitudes of molecular states (Schrodinger equation) can be reduced, under specified conditions, to a much smaller set of First Order Linear Differential Equations for the coarse grained populations of levels for polyatomic molecules (master equation), and four limiting situations are identified in which such linear rate equations provide a reasonable approximation.

Abstract: A theory of unimolecular reactions induced by coherent, monochromatic infrared radiation (URIMIR) in the absence of collisions is presented. It is shown that the set of first order linear differential equations for the amplitudes of molecular states (Schrodinger equation) can be reduced, under specified conditions, to a much smaller set of first order linear differential equations for the coarse grained populations of levels for polyatomic molecules (master equation). Four limiting situations are identified in which such linear rate equations provide a reasonable approximation. Rate coefficients are obtained as a function of spectroscopic parameters (energy levels and transition moments). Solutions for the master equations are given as a function of time and at steady‐state. Simple limiting cases (Strong Field Limit, Weak Field Limit, Reaction Threshold Bottleneck, etc.) are identified and very simple rate expressions are obtained for these cases. A complete statistical mechanical theory of URIMIR is form...

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TL;DR: In this paper, a time dependent formulation of total photodissociation cross sections is exploited to give a qualitative explanation of line shapes and absorption envelopes for symmetric triatomic (XY2) vacuum uv spectra.

Abstract: A recent time dependent formulation of total photodissociation cross sections is exploited to give a qualitative explanation of line shapes and absorption envelopes for symmetric triatomic (XY2) vacuum uv spectra. Attention is given to the dependence of the cross section on potential surface parameters and on the nature of the initial vibrational wavefunctions. The symmetric triatomic case treated here is illustrative of techniques which can be applied to more complicated, unsymmetric polyatomic situations.

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TL;DR: In this article, photoionization near the threshold allows identification of Naxx?16, Kxx?12, and NaxKyx+y?6, which is the longest contiguous series of any property as a function of cluster size.

Abstract: In supersonic nozzle beams of sodium, potassium, and Na/K molecular aggregates Mx have been investigated by several techniques based on mass spectrometry. By electron impact ionization with energy of 20 eV clusters with x≳4 are not observable. Photoionization near the threshold allows identification of Naxx?16, Kxx?12, and NaxKyx+y?6. Single photon ionization thresholds for Naxx?14 are given, this being the hitherto longest contiguous series of any property as a function of cluster size. For Kxx?8 and for 8 Na/K mixed clusters PI thresholds are similarly determined. Very accurate two photon photoionization thresholds for Na2 and K2 have been obtained. Theoretical models of metal clusters from recent publications are not able to adequately interpret the electronic properties of these particles as reflected by the ionization potentials.