William J. Meath

The University of Western Ontario, London, Ontario, Canada

Are you William J. Meath?

Claim your profile

Publications (123)213.17 Total impact

  • William J Meath, B N Jagatap
    [show abstract] [hide abstract]
    ABSTRACT: The effects of permanent dipoles, and the relative effects of the direct permanent dipole and the virtual state excitation mechanisms, are discussed for excitations involving the simultaneous absorption of two identical photons. Two molecular models for two-photon excitation, one dominated by the direct permanent dipole mechanism and the other having significant contributions from both excitation mechanisms, are used for this purpose. Resonance profiles, as a function of laser intensity, are evaluated for both models by employing the full Generalized Rotating Wave Approximation method and the recently developed Analytic Generalized Rotating Wave Approximation (AGRWA). The profiles are used to assess (1) the nature of the effects of permanent molecular dipoles, (2) the relative contributions of the two excitation mechanisms, and (3) the validity of the AGRWA for two-photon excitations. The AGRWA is a very useful interpretive∕predictive tool even for higher laser intensities where its validity becomes questionable. It can be used to suggest how to exploit the effects of molecular permanent dipoles to enhance two photon excitations using both excitation mechanisms.
    The Journal of Chemical Physics 10/2013; 139(14):144104. · 3.16 Impact Factor
  • William J Meath, B N Jagatap
    [show abstract] [hide abstract]
    ABSTRACT: One of the purposes of this paper is to develop an analytical many-level generalized rotating wave approximation (GRWA), including the effects of permanent dipoles, for the excitation of many-level molecules through the simultaneous absorption of two photons. Included are expressions for the two-photon laser–molecule coupling C, and its two components Cd and Cv corresponding to the direct permanent dipole and the virtual state excitation mechanisms, respectively, and related observables such as the time-dependent populations of the initial and final states of the excitation process and resonance profiles. This GRWA treatment also includes an energy shift parameter ε, which causes shifts in the position of the resonance energy as the laser intensity increases. The effects of permanent dipoles are very different in Cv and ε versus Cd. These effects have been discussed previously for Cd using analytic two-level RWA approaches. The analytical results for Cv and ε obtained here are new as is their use in discussing the influence of permanent dipoles in the parts of the two-photon excitation process involving virtual states. In the absence of permanent dipoles Cd is zero whereas Cv and ε are not; they equal the corresponding perturbation theory results. The GRWA and perturbative results are related by Bessel function damping functions which, for dipolar molecules, damp out the divergence of the perturbative results as the laser intensity increases. Illustrative examples are given for a two-photon excitation involving a model chromophore which has a significant virtual state contribution through both the laser–molecule coupling and the energy shift parameter.
    Journal of Physics B Atomic Molecular and Optical Physics 09/2011; 44(20):205401. · 2.03 Impact Factor
  • B. L. Jhanwar, William J. Meath, J. C. F. MacDonald
    [show abstract] [hide abstract]
    ABSTRACT: Dipole oscillator strength distributions (DOSDs) have been constructed for ground state ethylene, propene, and 1-butene. Each DOSD is constructed by using available experimental and theoretical photoabsorption cross sections and by constraining the resulting dipole oscillator strength data to satisfy the Thomas – Reiche–Kuhn sum rule and molar refractivity constraints. The latter were obtained from experimental refractive index measurements of relevant dilute gases. The recommended DOSDs, and the values of integrated "band" oscillator strengths, and the dipole oscillator strength sums Sk and Lk (for a variety of k values) obtained from them, are reported. The discussion includes an analysis of the reliability of the results using 1-butene as a detailed model.
    Canadian Journal of Physics 02/2011; 61(7):1027-1034. · 0.90 Impact Factor
  • Source
    B. L. Jhanwar, William J. Meath, J. C. F. MacDonald
    [show abstract] [hide abstract]
    ABSTRACT: Dipole oscillator strength distributions (DOSDs) have been constructed for ground state ethane, propane, n-butane, n-pentane, n-hexane, n-heptane, and n-octane. Each DOSD is constructed by using available experimental and theoretical photoabsorption cross sections and by constraining the resulting dipole oscillator strength data to satisfy the Thomas–Reiche–Kuhn sum rule and molar refractivity constraints. The latter were obtained using available experimental refractive index measurements of relevant dilute gases. The recommended DOSDs, and the values of integrated "band" oscillator strengths and the dipole oscillator strength sums Sk and Lk (for a variety of k values) obtained from them, are reported. The discussion includes an analysis of the accuracy of the results and a comparison with available literature values, which are scarce, for the dipole properties of the alkanes.
    Canadian Journal of Physics 02/2011; 59(2):185-197. · 0.90 Impact Factor
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: Dipole oscillator strength distributions (DOSDs) have been constructed for ground state Li, N, O, H2, N2, O2, NH3, H2O, NO, and N2O by using experimental and theoretical photoabsoiption and high energy electron inelastic scattering cross sections. Each DOSD is required to satisfy the Thomas–Reiche–Kuhn sum rule and additional constraints derived from available accurate experimental refractivity and dispersion measurements. The DOSDs, the data and procedure used to construct the DOSDs, and the values of the dipole oscillator strength sums Sk and Lk (for a variety of k values) and related atomic and molecular properties obtained from the DOSDs are reported. The discussion includes comments regarding the importance of the constraints imposed on the DOSD with respect to the evaluation of various dipole sums and properties and the accuracy of the results.
    Canadian Journal of Physics 02/2011; 55(23):2080-2100. · 0.90 Impact Factor
  • B. L. Jhanwar, William J. Meath
    [show abstract] [hide abstract]
    ABSTRACT: Dipole oscillator strength distributions (DOSDs) have been constructed for ground state methanol, ethanol, and n-propanol and used to evaluate integrated ("band") oscillator strengths and the dipole oscillator strength sums Sk and Lk (for a variety of k values) for these molecules. Each DOSD is constructed by using available experimental and theoretical photoabsorption cross sections and by constraining the resulting dipole oscillator strength data to satisfy the Thomas–Reiche–Kuhn sum rule and molar refractivity constraints. The discussion includes an analysis of the reliability of the results.
    Canadian Journal of Chemistry 02/2011; 62(2):373-381. · 0.96 Impact Factor
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: Four potential energy surfaces are of current interest for the Ne-CO interaction. Two are high-level fully ab initio surfaces obtained a decade ago using symmetry-adapted perturbation theory and supermolecule coupled-cluster methods. The other two are very recent exchange-Coulomb (XC) model potential energy surfaces constructed by using ab initio Heitler-London interaction energies and literature long range dispersion and induction energies, followed by the determination of a small number of adjustable parameters to reproduce a selected subset of pure rotational transition frequencies for the (20)Ne-(12)C(16)O van der Waals cluster. Testing of the four potential energy surfaces against a wide range of available experimental microwave, millimeter-wave, and mid-infrared Ne-CO transition frequencies indicated that the XC potential energy surfaces gave results that were generally far superior to the earlier fully ab initio surfaces. In this paper, two XC model surfaces and the two fully ab initio surfaces are tested for their abilities to reproduce experiment for a wide range of nonspectroscopic Ne-CO gas mixture properties. The properties considered here are relative integral cross sections and the angle dependence of rotational state-to-state differential cross sections, rotational relaxation rate constants for CO(v=2) in Ne-CO mixtures at T=296 K, pressure broadening of two pure rotational lines and of the rovibrational lines in the CO fundamental and first overtone transitions at 300 K, and the temperature and, where appropriate, mole fraction dependencies of the interaction second virial coefficient, the binary diffusion coefficient, the interaction viscosity, the mixture shear viscosity and thermal conductivity coefficients, and the thermal diffusion factor. The XC model potential energy surfaces give results that lie within or very nearly within the experimental uncertainties for all properties considered, while the coupled-cluster ab initio surface gives results that agree similarly well for all but one of the properties considered. When the present comparisons are combined with the ability to give accurate spectroscopic transition frequencies for the Ne-CO van der Waals complex, only the XC potential energy surfaces give results that agree well with all extant experimental data for the Ne-CO interaction.
    The Journal of Chemical Physics 01/2010; 132(2):024308. · 3.16 Impact Factor
  • [show abstract] [hide abstract]
    ABSTRACT: Exchange-Coulomb model potential energy surfaces have been developed for the Ne-CO interaction. The initial model is a three-dimensional potential energy surface based upon computed Heitler-London interaction energies and literature results for the long-range induction and dispersion energies, all as functions of interspecies distance, the orientation of CO relative to the interspecies axis, and the bond length of the CO molecule. Both a rigid-rotor model potential energy surface, obtained by setting the CO bond length equal to its experimental spectroscopic equilibrium value, and a vibrationally averaged model potential energy surface, obtained by averaging the stretching dependence over the ground vibrational motion of the CO molecule, have been constructed from the full data set. Adjustable parameters in each model potential energy surface have been determined through fitting a selected subset of pure rotational transition frequencies calculated for the (20)Ne-(12)C(12)O isotopolog to precisely known experimental values. Both potential energy surfaces provide calculated results for a wide range of available experimental microwave, millimeter-wave, and midinfrared Ne-CO transition frequencies that are generally far superior to those obtained using the best current literature potential energy surfaces. The vibrationally averaged CO ground state potential energy surface, employed together with a potential energy surface obtained from it by replacing the ground vibrational state average of the CO stretching dependence of the potential energy surface by an average over the first excited CO vibrational state, has been found to be particularly useful for computing and/or interpreting mid-IR transition frequencies in the Ne-CO dimer.
    The Journal of Chemical Physics 07/2009; 130(24):244310. · 3.16 Impact Factor
  • William J. Meath
    [show abstract] [hide abstract]
    ABSTRACT: The dependence of the population of the target state, and the excitation cross section and rate, on pulse duration Q, laser intensity I, and a molecular matrix element A is discussed for two-photon molecular excitation. Perturbative and rotating wave approximation (RWA) expressions for the observables are obtained; the latter are used to discuss the validity of the former. For example, the perturbative cross section and rate increasingly underestimate the RWA results as I increases for given A and Q. Two- and ten-level model dipolar molecules are employed for illustrative purposes. The results are relevant for understanding two-photon excitation processes and their enhancement and include discussions of the roles the permanent dipole- and virtual-state mechanisms in such processes and of the validity of using intensity-independent cross sections to gauge the strength of such excitations.
    Journal of the Optical Society of America B 04/2008; 25(5):865-876. · 2.21 Impact Factor
  • Joseph O. Hirschfelder, William J. Meath
    03/2007: pages 3 - 106; , ISBN: 9780470143582
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: The reliability of five N2-Ar potential-energy surfaces in representing the N2-Ar interaction has been investigated by comparing their abilities to reproduce a variety of experimental results, including interaction second viral coefficients, bulk transport properties, relaxation phenomena, differential scattering cross sections, and the microwave and infrared spectra of the van der Waals complexes. Four of the surfaces are the result of high-level ab initio quantal calculations; one of them utilized fine tuning by fitting to microwave data. To date, these four potential-energy surfaces have only been tested against experimental microwave data. The fifth potential-energy surface, based upon the exchange-Coulomb potential-energy model for the interaction of closed-shell species, is developed herein: it is a combination of a damped dispersion energy series and ab initio calculations of the Heitler-London interaction energy, and has adjustable parameters determined by requiring essentially simultaneous agreement with selected quality interaction second viral coefficient and microwave data. Comparisons are also made with the predictions of three other very good literature potential-energy surfaces, including the precursor of the new exchange-Coulomb potential-energy surface developed here. Based upon an analysis of a large body of information, the new exchange-Coulomb and microwave-tuned ab initio potential-energy surfaces provide the best representations of the N2-Ar interaction; nevertheless, the other potential-energy surfaces examined still have considerable merit with respect to the prediction of specific properties of the N2-Ar van der Waals complex. Of the two recommended surfaces, the new exchange-Coulomb surface is preferred on balance due to its superior predictions of the effective cross sections related to various relaxation phenomena, and to its reliable, and relatively simple, representation of the long-range part of the potential-energy surface. Moreover, the flexibility still inherent in the exchange-Coulomb potential form can be further exploited, if required, in future studies of the N2-Ar interaction.
    The Journal of Chemical Physics 02/2006; 124(3):034308. · 3.16 Impact Factor
  • William J. Meath, B. N. Jagatap, A. E. Kondo
    [show abstract] [hide abstract]
    ABSTRACT: The dynamics and the cross sections associated with the excitation of a ground-state dipolar molecule to an excited state, by the simultaneous absorption of two photons, are discussed using the rotating wave approximation and time-dependent perturbation theory. The excitations of ten- and two-energy level representations of model dipolar molecules are used for illustrative purposes. The temporal development of the final state of the excitation process and the two-photon excitation cross sections are discussed as functions of laser intensity, laser-molecule interaction time and the two types of excitation mechanism (which are available for dipolar molecules, relative to the one mechanism for a non-polar molecule). The results are used to discuss the validity of perturbation theory treatments of the problem and various strategies for the enhancement of the intrinsically weak two-photon excitation process.
    Journal of Physics B Atomic Molecular and Optical Physics 01/2006; 39. · 2.03 Impact Factor
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: An improved three-dimensional potential energy surface for the H(2)-Kr system is determined from a direct fit of new infrared spectroscopic data for H(2)-Kr and D(2)-Kr to a potential energy function form based on the exchange-Coulomb model for the intermolecular interaction energy. These fits require repetitive, highly accurate simulations of the observed spectra, and both the strength of the potential energy anisotropy and the accuracy of the new data make the "secular equation perturbation theory" method used in previous analyses of H(2)-(rare gas) spectra inadequate for the present work. To address this problem, an extended version of the "iterative secular equation" method was developed which implements direct Hellmann-Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.
    The Journal of Chemical Physics 03/2005; 122(8):84321. · 3.16 Impact Factor
  • Ashok Kumar, B. L. Jhanwar, William J. Meath
    [show abstract] [hide abstract]
    ABSTRACT: Recommended isotropic dipole oscillator strength distributions (DOSDs) have been constructed for the methanol and ethanol molecules through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength (DOS) data; the DOS data employed are recent experimental results not available at the time of the original constrained DOSD analysis of these molecules. The constraints are furnished by molar refractivity data and the Thomas-Reiche-Kuhn sum rule. The DOSDs are used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecules. Pseudo-DOSDs for these molecules, and for propan-1-ol based on an earlier constrained DOSD analysis for this molecule, are also presented. They are used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C<sub>6</sub>, for the interactions of the alcohols with each other and with 36 other species, and the triple-dipole dispersion energy coefficients C<sub>9</sub> for interactions involving any triple of molecules involving methanol, ethanol and propan-1-ol.
    01/2005;
  • M. K. Ali, W. J. Meath
    [show abstract] [hide abstract]
    ABSTRACT: Closed form one centre partial wave perturbation results are obtained through second order in the energy for H-like molecules with arbitrary nuclear charges. The expansion centre for the method is taken at an arbitrary point along the internuclear axis and the zeroth-order wave function is a screened “1s” function centred at the expansion point. Various fixed one centre calculations of other workers for the lsσ states of H and HeH++ and for the 2pσ state of HeH++ are generated as limiting cases of this more general treatment. The floating one centre perturbation results for the 1sσ states of H2+ and HeH++ are used as models for discussing the usefulness of allowing the expansion centre in the one centre method to be a function of nuclear configuration.
    International Journal of Quantum Chemistry 10/2004; 6(5):949 - 966. · 1.31 Impact Factor
  • William J. Meath, Ashok Kumar
    [show abstract] [hide abstract]
    ABSTRACT: Molecular dipole oscillator strength distributions (DOSDS), which are reliable in the sense of yielding accurate results for the various dipole properties of molecules, can be constructed if sufficient input information is available. The DOSDS are constructed from extensive experimental and theoretical information, including oscillator strength and photoabsorption cross section data, and are constrained to reproduce accurate refractivity measurements of the relevant dilute gases and to satisfy oscillator strength sum rules. The techniques for obtaining the DOSDS, and related properties, are well established for the evaluation of reliable isotropic dipolar dispersion energies. In this paper they are extended to the evaluation of anisotropic dipole properties, with particular emphasis on anisotropic dispersion energies. The approach used will be illustrated with applications involving H2, N2, and the rare gases. Also included will be brief discussions on (i) the use of reliable results for the dipole–dipole and triple–dipole dispersion energies in constructing complete two- and many-body potential energies and (ii) the advantages of constrained DOSD methods, relative to other approaches, for determining all the dipole properties of molecules.
    International Journal of Quantum Chemistry 10/2004; 38(S24):501 - 520. · 1.31 Impact Factor
  • T. R. Singh, J. F. Bukta, W. J. Meath
    [show abstract] [hide abstract]
    ABSTRACT: A one center method, based on the work of Karplus and Kolker, is discussed and used to calculate the induction energy, through O(R−8), for the H(ls) – H+ interaction employing two types of Gaussian basis sets constructed from functions of the form {rje−αr2}. The effective hydrogen atom excitation energies and transition multipole moment matrix elements generated in these calculations are used to calculate the dispersion energy for the H(ls) – H(ls) interaction, through O(R−10), and the R−9 triple dipole energy corresponding to the interaction of three H(ls) atoms. The results indicate that Gaussian functions can form good basis sets for obtaining long range forces for a variety of multipole interaction energies.
    International Journal of Quantum Chemistry 10/2004; 6(2):201 - 209. · 1.31 Impact Factor
  • M. K. Ali, W. J. Meath
    [show abstract] [hide abstract]
    ABSTRACT: Exact separated atom nuclei and centre of nuclear charge centred partial wave solutions for the Schrödinger equation are obtained for the 1sσ, 2sσ, 3sσ, 2pσ, 3dσ, and 3pσ states of HeH++ as a function of the internuclear separation R and the number of partial waves used to represent the wave functions for the molecules. If the expansion centre is chosen appropriately one-centre techniques are in general very efficient for these Coulomb dominated interactions relative to molecules like H+2(1sσg) which have a large electron exchange contribution to their interaction energy. In general the centre of nuclear charge is not the most suitable expansion centre for heteronuclear molecules for most values of R.
    International Journal of Quantum Chemistry 10/2004; 12(5):897 - 914. · 1.31 Impact Factor
  • M. K. Ali, William J. Meath
    [show abstract] [hide abstract]
    ABSTRACT: A semi-analytical solution for the nucleus and the internuclear midpoint centred partial wave equations representing the Schrödinger equation for the H-like molecule is discussed. Explicit proton and internuclear midpoint centred results for the interaction energy and the wave function for the 1sσg state of H are obtained as a function of the internuclear distance R and the number of coupled differential equation NN ≦ 14 used to represent the Schrödinger equation for the molecule. These, together with some energy optimized floating one centre results for the interaction energy, are used to (1) discuss the convergence of the partial wave calculation as a function of R,N, and the position of the expansion centre, (2) discuss the concept of Coulomb versus electron exchange interaction energies, and (3) discuss briefly the convergence problems of analogous one centre perturbation theory treatments for the ground state H molecule. The electron exchange H (1sσg) molecule provides a severe test for the uefulness of partial wave methods.
    International Journal of Quantum Chemistry 08/2004; 12(1):35 - 59. · 1.31 Impact Factor
  • Source
    B. N. Jagatap, William J. Meath
    [show abstract] [hide abstract]
    ABSTRACT: The role of both permanent molecular dipoles and virtual molecular states, for two- and three-photon molecular excitation, is discussed in the context of the two- and three-photon excitation cross sections, with a ten-energy-level giant-dipole molecule as a model. Two types of excitation mechanisms are involved, that which requires permanent dipole moments and that which requires virtual molecular excited states. The results are relevant to the understanding of two- and three-photon excitation processes and for the design of fluorophores with large multiphoton absorption cross sections.
    Journal of the Optical Society of America B 10/2002; 19(11):2673-2681. · 2.21 Impact Factor

Publication Stats

251 Citations
12 Downloads
213.17 Total Impact Points

Institutions

  • 1155–2013
    • The University of Western Ontario
      • Department of Chemistry
      London, Ontario, Canada
  • 2009–2010
    • Punjabi University, Patiala
      • Department of Physics
      Patiāla, State of Punjab, India
  • 2007
    • University of Wisconsin–Madison
      Madison, Wisconsin, United States
  • 2005
    • University of Waterloo
      • Department of Chemistry
      Waterloo, Ontario, Canada