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15 Dec 1979

Volume 71, Issue 12, pp. 4771-5389

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Anisotropic hyperfine interaction in the electron spin resonance spectrum of the methyl radical trapped in CH3COONa⋅3D2O crystal at low temperatures

Shozo Kubota, Masamoto Iwaizumi, Yusaku Ikegami, and Kazuo Shimokoshi

J. Chem. Phys. 71, 4771 (1979); http://dx.doi.org/10.1063/1.438315 (6 pages) | Cited 6 times

Online Publication Date: 25 July 2008

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The electron spin resonance spectrum of the methyl radical produced by γ irradiation of CH3COONa⋅3D2O single crystal at 77 K has been measured at low temperatures. The spectrum observed at below 24 K consisted of eight lines with approximately equal intensities, instead of the four lines (1:3:3:1) at higher temperatures, due to the quantum tunneling of the rotational states. The transitions at low temperatures were angular dependent upon the applied field. From the analyses of the angular dependence of the spectrum with the aid of the theoretical calculation of the transition field for the tunneling methyl radical, the following anisotropic hyperfine tensor for the proton was determined (MHz): Axx=−31.4, Ayy=−93.7, Azz=−60.3, a (iso) =−61.8. These parameters provide the first experimental assessment of the well‐known theoretical results on the proton hyperfine anisotropy in the free methyl radical.
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82.50.-m Photochemistry
76.30.Rn Free radicals

Time‐dependent theory of Raman scattering

Soo‐Y. Lee and E. J. Heller

J. Chem. Phys. 71, 4777 (1979); http://dx.doi.org/10.1063/1.438316 (12 pages) | Cited 384 times

Online Publication Date: 25 July 2008

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A time‐dependent picture of vibrational Raman scattering in the weak field limit is presented. From this viewpoint we can separate the static effects, due to the coordinate dependence of the electronic transition dipole, from the dynamic effects that arise from wave packet propagation on the Born–Oppenheimer surfaces. Away from resonance, the energy uncertainty relation gives the propagation time necessary to obtain the cross section as being inversely proportional to the mismatch of the excitation frequency with the excited surface. The wave packet, given by the initial vibrational wave function times the transition dipole, hardly moves on the excited surface when the excitation frequency is far from resonance. As the excitation frequency is tuned closer to resonance, the propagated wave packet samples a larger portion of the surface. Using the short time approximation to the propagator, we obtain formulas for the cross section that are applicable for Raman scattering by polyatomics. The short time approximation is expected to be good away from resonance independent of the nature of the surface, and also on resonance with a repulsive surface. For an attractive surface, the approximation gives the average resonant cross section useful in the case when the vibrational structures cannot be observed.
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33.20.Fb Raman and Rayleigh spectra (including optical scattering)

A comparison of the vibrational structures of ethanol, acetic acid, and acetaldehyde adsorbed on alumina

H. E. Evans and W. H. Weinberg

J. Chem. Phys. 71, 4789 (1979); http://dx.doi.org/10.1063/1.438317 (10 pages) | Cited 19 times

Online Publication Date: 25 July 2008

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The adsorption on aluminum oxide of acetaldehyde (CH3CHO) and acetic acid (CH3COOH) has been studied by utilizing inelastic electron tunneling spectroscopy (IETS) to probe the vibrational structures of the surface species over the spectral range between 240 and 4000 cm−1. Results for temperatures between 295 and 475 K are compared with our previous IETS results for ethanol (CH3CH2OH) adsorption on alumina up to 575 K. Although all three hydrocarbons form acetate complexes with the surface under certain conditions, slight differences in bonding and structure are evident in the IET spectra. The formation of some bulk aluminum hydroxide is observed also in certain cases. Observed variations in surface concentrations, bulk hydration, and the nature of surface hydroxyl groups are related to previous experimental results. Mechanisms are substantiated for the initial adsorption and subsequent reaction of each hydrocarbon with the surface.
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68.43.-h Chemisorption/physisorption: adsorbates on surfaces
33.20.Tp Vibrational analysis

Vibrational population relaxation of compressed nH2 fluid in the 15–110 K range

M. Chateau, C. Delalande, R. Frey, G. M. Gale, and F. Pradère

J. Chem. Phys. 71, 4799 (1979); http://dx.doi.org/10.1063/1.438318 (5 pages) | Cited 33 times

Online Publication Date: 25 July 2008

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Experimental observations of the population relaxation time of the first excited vibrational level of nH2 have been made in the fluid state over a very wide range of temperature and pressure (15–110 K, 0–500 atm). These extensive measurements yield new insight into the fundamental parameters governing energy relaxation in simple fluids.
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34.50.Ez Rotational and vibrational energy transfer
61.20.Ne Structure of simple liquids

A semiclassical model for vibrational energy relaxation in simple liquids and compressed fluids

C. Delalande and G. M. Gale

J. Chem. Phys. 71, 4804 (1979); http://dx.doi.org/10.1063/1.438319 (8 pages) | Cited 65 times

Online Publication Date: 25 July 2008

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Using a simple model intermolecular potential, a density dependence of the vibrational population relaxation time in liquids is obtained which is in qualitative and quantitative agreement with experiment, over the whole range of density and temperature studied. This model is applicable to systems where the energy transfer involved is large with respect to thermal energies and describes the variation of the relaxation time as being essentially related to the variation of the collision frequency on the strongly repulsive part of the intermolecular potential. The formalism employed demonstrates clearly the role of excluded volume at high density and of bound states at low density and temperature.
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34.50.Ez Rotational and vibrational energy transfer
61.20.Ne Structure of simple liquids

New study of CO adsorption at low temperature (90 K) on Pt (111) by EELS

A. M. Baró and H. Ibach

J. Chem. Phys. 71, 4812 (1979); http://dx.doi.org/10.1063/1.438320 (5 pages) | Cited 71 times

Online Publication Date: 25 July 2008

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We have performed a new study of the vibrational modes of CO adsorbed at low temperature (90 K) on Pt(111). As in previous work a sequential occupation of top and bridge sites is observed. At a certain bridge site coverage, however, a new vibrational mode with a frequency of 720 cm−1 appears. The mode is not observed at room temperature since sufficiently high coverages are not achieved there. The appearance of the 720 cm−1 mode is attributed to the C–Pt asymmetric stretching vibration becoming dipole active at higher coverages when, according to LEED results, an out‐of‐registry CO overlayer is formed.
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68.43.-h Chemisorption/physisorption: adsorbates on surfaces
33.20.Tp Vibrational analysis

High pressure studies of poly (N‐vinylcarbazole) excimer emission in polymer films

George Chryssomallis and H. G. Drickamer

J. Chem. Phys. 71, 4817 (1979); http://dx.doi.org/10.1063/1.438321 (7 pages) | Cited 2 times

Online Publication Date: 25 July 2008

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The excimer fluorescence properties of poly (N‐vinylcarbazole) (PVCA) dissolved in a variety of polymer films were investigated. The existence of two interchain excimers emitting from frozen preformed sites in the film was observed. Large hydrostatic pressures were used in order to change the local environment of the two sites. Changes with pressure of the ratio of respective intensities are interpreted according to a hopping singlet exciton diffusion model with the two sites acting as competing traps. There are two distinct mechanisms, one predominant at low and the other at high pressures. The assumption that a small rearrangement between the two excimers is possible at low pressures is valid since both glass transition temperatures and overall intensity changes support it. The change of volume in the transformation between the two excimers was calculated for the different films and is equal to or less than 3% of the monomer molar volume.
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36.20.Kd Electronic structure and spectra
33.50.Dq Fluorescence and phosphorescence spectra

Generalized sensitivity analysis in quantum collision theory

Larry Eno and Herschel Rabitz

J. Chem. Phys. 71, 4824 (1979); http://dx.doi.org/10.1063/1.438322 (8 pages) | Cited 13 times

Online Publication Date: 25 July 2008

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This paper considers the sensitivity of the scattering matrix with respect to variations of input parameters including those that persist asymptotically. The analysis shows that the first order sensitivity coefficients (i.e., the partial derivatives with respect to input parameters) of the scattering matrix may be expressed in terms of the available solution of the Schrödinger equation. This work encompasses earlier results which appear as special cases. As an application sensitivity with respect to the total energy is considered and the relevance of the result to the energy behavior of observables is discussed. In a second application, we show how sensitivity analysis may be used to estimate corrections to effective Hamiltonian results and also to examine their accuracy. The coupled states and infinite order sudden methods are chosen to illustrate the approach. Finally, the scope of sensitivity analysis in quantum collision theory is discussed.
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34.10.+x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.)
03.65.Nk Scattering theory

The generalized moment method for transport phenomena in dense fluids

Byung Chan Eu

J. Chem. Phys. 71, 4832 (1979); http://dx.doi.org/10.1063/1.438323 (12 pages) | Cited 10 times

Online Publication Date: 25 July 2008

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Based on the kinetic equation reported previously, the generalized moment method is presented for dense fluids in this paper. The equations of change are presented for stress tensor and heat flux in nonuniform dense fluids and by solving them up to second order by a perturbation method, constitutive relations and various linear and nonlinear transport coefficients are obtained. Comparison of the transport coefficients with the counterparts in the generalized Chapman–Enskog (GCE) method shows that two results agree with each other if the first Chapman–Enskog approximants are used for the GCE results and some potential energy contributions are neglected in the molecular expressions for fluxes. Discussions are given regarding the constitutive relation for the Stokes fluids and the non‐Newtonian behavior of real fluids.
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51.10.+y Kinetic and transport theory of gases

A theory for magnetic resonance measurements of diffusion in anisotropic fluids

Bret Berner

J. Chem. Phys. 71, 4844 (1979); http://dx.doi.org/10.1063/1.438297 (5 pages) | Cited 1 time

Online Publication Date: 25 July 2008

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Electron spin resonance (ESR) spin exchange and the enhancement of nuclear spin relaxation frequencies due to the presence of paramagnetics can be used to study diffusion in liquid crystals and membranes. Previous analyses of the diffusion data obtained in this manner assumed isotropic diffusion. In this paper derivations are given for the dependence of the relaxation frequencies measured in these two experiments on the diffusion constants parallel and perpendicular to the director, D∥ and D⊥, respectively.
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61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects on order
76.30.-v Electron paramagnetic resonance and relaxation
66.10.C- Diffusion and thermal diffusion

Ultrasonic measurement of the vibrational relaxation in liquid SO2

D. B. Fenner, D. E. Bowen, and M. P. Eastman

J. Chem. Phys. 71, 4849 (1979); http://dx.doi.org/10.1063/1.438298 (5 pages) | Cited 2 times

Online Publication Date: 25 July 2008

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Measurements of the absorption and velocity of ultrasound in liquid sulfur dioxide have been made over a wide range of temperatures, greatly extending the temperature range of the measurements of Bass and Lamb on the same system. The data are complete now from 203 to 323 K in the frequency range from 6 to 90 MHz. All the data have been fit satisfactorily to a single‐relaxation description, and give a temperature‐independent relaxation frequency of 22.5±1 MHz. The relaxation amplitude has a strong temperature dependence of the Arrhenius type, with an energy of activation of ∼3 kcal/mole, the temperature behavior of which can be satisfactorily calculated on the basis of reported vibrational frequencies of the SO2 molecule. The velocity of sound, as measured, is a linear function of the temperature. Measurements are also reported for dilute mixtures of cyclohexane in SO2 where no shift in the measured relaxation frequency is observed, contrary to the usual situation for vibrational relaxations.
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43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions
34.50.Ez Rotational and vibrational energy transfer

HTFFR kinetics studies of the Al/SO2 reaction from 700 to 1600 K. Implications for D(Al–O)

Arthur Fontijn and William Felder

J. Chem. Phys. 71, 4854 (1979); http://dx.doi.org/10.1063/1.438299 (6 pages) | Cited 4 times

Online Publication Date: 25 July 2008

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Measurements of the kinetics of the bimolecular Al/SO2 reaction over the temperature range 700 to 1600 K have yielded a k (T) = (1.6±0.8) ×10−10 exp[(=2000±300)/T]cm3 molecule−1  s−1. This k (T is significantly larger than that for the Al/CO2 reaction in the same temperature range. This temperature dependence indicates with 95% probability that the Al–O dissociation energy ?126 kcal mol−1, somewhat higher than most often thought. AlO laser fluorescence has been used to identify AlO+SO as a major, and probably the only, product channel. A k of 2×10−12 cm3 molecule−1 s−1 is measured for the AlO/SO2 reaction near 940 K.
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82.20.Pm Rate constants, reaction cross sections, and activation energies

Transmission of 0–15 eV monoenergetic electrons through thin‐film molecular solids

Leon Sanche

J. Chem. Phys. 71, 4860 (1979); http://dx.doi.org/10.1063/1.438300 (23 pages) | Cited 121 times

Online Publication Date: 25 July 2008

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The transmission coefficient for monoenergetic electrons (0.04 eV FWHM) passing through thin films (∼100 Å) of molecular solids is measured as a function of electron energy in the range 0–15 eV. The visibility of sharp maxima in the transmission spectra is enhanced by measuring the negative value of the second energy derivative of the transmitted current with respect to electron energy. In benzene, fluorobenzene, pyridine, benzaldehyde, furan, cyclohexene and 1,3‐ and 1,4‐cyclohexadiene, the spectra exhibit from six to eight maxima, whereas in pyrrole and thiophene four structures are resolved. With the exception of the first two features in fluorobenzene and the first feature for the other solids investigated, all other maxima correlate within at least ±0.5 eV with the gas‐phase electronic transitions. This correlation is achieved by increasing the energy scale of the transmission spectra relative to the gas‐phase electronic energy levels. These findings corroborate previous experiments on solid organic films by Hamill and co‐workers who attributed peaks in the first energy derivative of the transmitted current to energy‐loss events. It is shown that the transmission features can arise either from an increase in the overall transmission coefficient due to the production of inelastically scattered electrons or from the formation of an electron–exciton complex through the temporary capture of an injected excess electron by field of a Frenkel exciton. The first low‐energy feature in each spectrum may possibly arise from an enhancement of vibrational excitation related to the energy dependence of the structure factor.
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34.80.-i Electron and positron scattering
68.90.+g Other topics in structure, and nonelectronic properties of surfaces and interfaces; thin films and low-dimensional structures (restricted to new topics in section 68)

Mechanism of thermal electron attachment in O2–C2H4, O2–CO2, and O2–neopentane mixtures

Yu‐ichi Kokaku, Yoshihiko Hatano, Hiroshi Shimamori, and Richard W. Fessenden

J. Chem. Phys. 71, 4883 (1979); http://dx.doi.org/10.1063/1.438301 (5 pages) | Cited 22 times

Online Publication Date: 25 July 2008

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Thermal electron attachment of O2 in O2–C2H4, O2–CO2, and O2–neopentane mixtures has been investigated at room temperature, using a microwave conductivity technique combined with pulse radiolysis. The measurements have been extended to a higher pressure region (∼850 Torr) than previous observations in order to compare them with the results of an electron swarm method at very high pressures. From low pressure data, the values of (2.0±0.3) ×10−30, (3.2±0.3) ×10−30, and (7±1) ×10−30 cm6/molecule2 sec are determined for the overall three body attachment rate constants of O2 with the stabilizing partners C2H4, CO2, and neopentane, respectively. In each case, the effective rate constant continued to increase with increased density and exceeded those predicted by the Bloch–Bradbury mechanism by sizeable amounts. The excess attachment is suggested to involve pre‐existing van der Waals complexes such as (O2⋅C2H4). Some quantitative conclusions which follow from this mechanism are given.
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82.50.Kx Processes caused by X-rays or γ-rays
82.33.Tb Atmospheric chemistry

Test of mean‐field behavior by light scattering in three phases of a fluid mixture near its tricritical point

M. W. Kim, W. I. Goldburg, P. Esfandiari, and J. M. H. Levelt Sengers

J. Chem. Phys. 71, 4888 (1979); http://dx.doi.org/10.1063/1.438302 (11 pages) | Cited 15 times

Online Publication Date: 25 July 2008

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Measurements are reported of the angular dependence of intensity and spectral width of light scattered quasielastically from three coexistent liquid phase α, β, γ near a tricritical point. From the data, the susceptibilities χ and correlation lengths ξ in each of the phases were calculated. Two predictions from mean‐field theory were tested, namely ’’Griffiths’ first sum rule’’: χα1/2+χγ1/2 =χβ1/2 or ξα+ξγ=ξβ, and ’’Griffiths’ second sum rule’’: χα−1/2+χγ−1/2−χβ−1/2∝ (T−Ttr), or ξα−1+ξγ−1−ξβ−1 ∝ (T−Ttr). The second sum rule is found to hold within the accuracy of our data. The first sum rule is violated for the correlation lengths. It is found to hold for the susceptibilities, but only after the scattered intensities are properly corrected for differences, between phases, in the derivative of the dielectric constant with respect to order parameter. This derivative was obtained from model calculations of Kaufman and Griffiths. The viscosities of the coexisting phases were measured; combined with the spectral width and correlation length data, they confirmed, with no adjustable parameters, Kawasaki’s equation for the Rayleigh linewidth of a critical fluid.
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64.60.Kw Multicritical points
64.75.-g Phase equilibria
78.35.+c Brillouin and Rayleigh scattering; other light scattering

High magnetic field Mössbauer studies of deoxymyoglobin, deoxyhemoglobin, and synthetic analogues: Theoretical interpretations

T. A. Kent, K. Spartalian, and G. Lang

J. Chem. Phys. 71, 4899 (1979); http://dx.doi.org/10.1063/1.438303 (10 pages) | Cited 14 times

Online Publication Date: 25 July 2008

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Mössbauer spectra of deoxymyoglobin, deoxyhemoglobin, and the synthetic analogues, iron (ii) 2‐methylimidazole meso‐tetraphenylporphyrin, and iron (ii) 1,2‐dimethylimidazole meso‐tetraphenylophorphyrin, observed in high magnetic fields and over a wide range of temperature, have been examined theoretically in an effort to correlate them with known susceptibility data, and a search for a satisfactory model within the 5D term has been carried out. It is shown in a general way that any solution within 5D would demand the use of magnetic hyperfine coupling constants about half as large as the smallest previously observed. Even allowing this anomaly we have failed to find a solution within 5D. An interesting result is that the myoglobin appears to have a singlet ground state while the 2‐methyl substituted model has a nearly degenerate ground doublet, approximately describable as Sz=±2. Yet the hyperfine fields of these materials are very similar at elevated temperatures. It appears that the introduction of low lying states of different spin multiplicity will be needed to accommodate this behavior and to provide the observed magnitude of magnetic hyperfine coupling.
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87.15.M- Spectra of biomolecules
76.80.+y Mössbauer effect; other γ-ray spectroscopy

Intramolecular rate processes in highly vibrationally excited benzene

Robert G. Bray and Michael J. Berry

J. Chem. Phys. 71, 4909 (1979); http://dx.doi.org/10.1063/1.438304 (14 pages) | Cited 190 times

Online Publication Date: 25 July 2008

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Intracavity cw dye laser techniques incorporating photoacoustic detection have been used to measure visible absorption spectra of gas phase benzene (C6H6 and deuterated analogues C6H5D, p‐C6H2D4, and C6HD5). The prominent spectral features are attributable to CH stretch overtones that correspond to highly localized (’’bond‐selective’’) excitations of individual CH oscillators. These features have broad (∼100 cm−1 FWHM) Lorentzian line shapes that narrow as a function of increasing vibrational energy for most isotopic species. A simple model is presented to interpret the broad line shapes and their energy dependence as a manifestation of intramolecular V→V′ (vibration‐to‐vibration) energy redistribution and/or dephasing processes that occur rapidly (on 5×10−14 sec time scales), but nonstatistically, in isolated benzene and other polyatomic molecules.
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33.20.Kf Visible spectra
82.20.Rp State to state energy transfer

A study of the ground states and ionization energies of H2, C2, N2, F2, and CO molecules by the variational cellular method

Luiz M. Brescansin, J. R. Leite, and L. G. Ferreira

J. Chem. Phys. 71, 4923 (1979); http://dx.doi.org/10.1063/1.438305 (8 pages) | Cited 18 times

Online Publication Date: 25 July 2008

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Self‐consistent calculations for the ground state potential curves and ionization energies are reported for the molecules H2, C2, N2, F2, and CO, using the recent proposed variational cellular method. For all these molecules the results are quite good. The calculated binding energies, equilibrium interatomic distances, and energy ionization spectra are in excellent agreement with the available experimental findings.
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34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions
82.20.Kh Potential energy surfaces for chemical reactions
31.15.A- Ab initio calculations
33.15.Ry Ionization potentials, electron affinities, molecular core binding energy

Studies of H+, H+2, and H+3 dissociative ionization fragments from methane, ethane, methanol, ethanol, and some deuterated methanols using electron‐impact excitation and a time‐of‐flight method incorporating mass analysis

M. D. Burrows, S. R. Ryan, W. E. Lamb, and L. C. McIntyre

J. Chem. Phys. 71, 4931 (1979); http://dx.doi.org/10.1063/1.438306 (10 pages) | Cited 15 times

Online Publication Date: 25 July 2008

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Kinetic energy distributions and relative intensities of energetic (≳1eV) H+,H+2, and H+3 dissociative–ionization fragments from methane, ethane, ethanol, and methanol have been measured using pulsed electron‐impact excitation and a time‐of‐fight method incorporating a new mass analysis technique. The various deuterated analogs of H+, H+2, and H+3 fragments were also observed from CH3OD, CD3OH, and CD3OD. Results for these deuterated fragments show that energetic H+2 and H+3 fragments originate primarily from the −CH3 group, rather than from H atom extraction from both the−CH3 and −OH groups. Comparisons among the kinetic energy distributions of these light fragments from CH3OH, CD3OD, and CD3OH reveal no major isotope effects for fragment energies exceeding 2 eV.
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34.80.Gs Molecular excitation and ionization

Resonance fluorescence as a probe to elucidate mechanisms of intramolecular relaxation processes

Kuo‐mei Chen and Edward S. Yeung

J. Chem. Phys. 71, 4941 (1979); http://dx.doi.org/10.1063/1.438307 (10 pages) | Cited 4 times

Online Publication Date: 25 July 2008

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Density matrix formalism is used to study resonance fluorescence processes of isolated gaseous molecules. The Wangsness–Bloch–Fano theory is applied to the irreversible intramolecular relaxation process. In the present treatment, it is assumed that the rotational angular momentum J is a constant of motion in the zeroth order approximation. Thus intramolecular interactions can be classified as tensor operators with respect to J. The fluorescence decay patterns depend on excitation bandwidths and monitoring conditions. Under narrow band excitation, the population (monopole), orientation (dipole), and alignment (quadrupole) of the excited state density matrix ρe can be prepared. For a sharply prepared angular momentum state under pulsed excitation, the population does not undergo radiationless decay and the resonance fluorescence intensity is a sum of three exponentials in general. For cw experiments, where lifetime limited linewidth or polarized fluorescence intensities are measured, the population can decay via an intramolecular relaxation channel providing the orientation component is initially prepared. Explicit J dependences of lifetimes are given for pulsed experiments. Under broad band excitation, quantum beats due to the coherence of ρe are derived from the Liouville equation. Most important of all, the population can decay under pulsed, broad‐band excitation conditions. The scalar part of the nonadiabatic coupling becomes an additional contributor to the intramolecular relaxation process in this last case.
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33.50.Dq Fluorescence and phosphorescence spectra
31.70.Hq Time-dependent phenomena: excitation and relaxation processes, and reaction rates

Direct determination of the intermolecular interaction contribution to the refractive index of carbon dioxide and sulfur hexafluoride

J. M. St‐Arnaud and T. K. Bose

J. Chem. Phys. 71, 4951 (1979); http://dx.doi.org/10.1063/1.438308 (5 pages) | Cited 34 times

Online Publication Date: 25 July 2008

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The experimental values of the first and the second refractivity virial coefficients have been determined for carbon dioxide and sulfur hexafluoride. In the case of carbon dioxide the experimental second refractivity virial coefficient is less than the classically calculated theoretical value and for sulfur hexafluoride the experimental value is larger than the theoretical value. Combined with the earlier values of the second dielectric virial coefficient, the present experimental results agree well with the integrated collision induced absorption in the infrared and the far infrared.
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78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity)
42.25.Gy Edge and boundary effects; reflection and refraction
34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions

Action‐angle variables in quantum mechanics

Stuart D. Augustin and Herschel Rabitz

J. Chem. Phys. 71, 4956 (1979); http://dx.doi.org/10.1063/1.438309 (13 pages) | Cited 26 times

Online Publication Date: 25 July 2008

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Conventional quantum mechanical treatments of many systems have worked with coordinates and momenta that are not canonically conjugate. In this work it is shown how the quantum expressions may be reformulated in terms of the canonical set of action‐angle variables, and specific examples of the harmonic oscillator, linear rotor, and triaxial rotor are presented. When expressed in these terms, the quantum mechanics take on a form which can be directly related to analogous results from classical mechanics. In addition, it becomes possible to express the Hamiltonian in the minimum number of coordinates. It is also shown that the common assumption of an exponential form for the overlap of canonical coordinate and momentum eigenstates is false for an asymmetric rotor. This has important implications for the quantization rules applicable to nonseparable systems.
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03.65.Ca Formalism

A treatment of open shells

L. Bouscasse and H. H. Jaffé

J. Chem. Phys. 71, 4969 (1979); http://dx.doi.org/10.1063/1.438310 (5 pages) | Cited 1 time

Online Publication Date: 25 July 2008

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The minimization conditions for open shells in RHF theory are obtained without use of LaGrange multipliers. The formulation given for these conditions permits an easy way of defining coupling operations and is particularly adapted to a given problem.
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31.15.A- Ab initio calculations

Interaction potentials and their effect on crystal nucleation and symmetry

C. S. Hsu and Aneesur Rahman

J. Chem. Phys. 71, 4974 (1979); http://dx.doi.org/10.1063/1.438311 (13 pages) | Cited 80 times

Online Publication Date: 25 July 2008

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Molecular dynamics technique has been used to study the effect of the interaction potential on crystal nucleation and the symmetry of the nucleated phase. Four systems, namely rubidium, Lennard‐Jones, rubidium‐truncated, and Lennard‐Jones‐truncated, have been studied each at reduced density 0.95. Two types of calculations were performed. Firstly, starting from a liquid state, each system was quenched rapidly to a reduced temperature of ∼0.1. The nucleation process for these systems was monitored by studying the time dependence of temperature and the pair correlation function, and the resulting crystalline structure analyzed using among other properties the Voronoi polyhedra. Only in the case of rubidium was a b.c.c. structure nucleated. In the other three cases we obtained a f.c.c. ordering. Secondly, we have studied the effect of changing the interaction potential in a system which has already achieved an ordered state under the action of some other potential. After establishing a b.c.c. structure in a rubidium system, the change in the symmetry of the system was studied when the pair potential was modified to one of the other three forms. The results from both types of calculations are consistent: the rubidium potential leads to a b.c.c. structure while the other three potentials give an f.c.c. structure. Metastable disordered structures were not obtained in any of the calculations. However, the time elapse between the moment when the system is quick‐quenched and the moment when nucleation occurs appears to depend upon the potential of interaction.
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82.60.Nh Thermodynamics of nucleation
34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions

The singlet and triplet state rotational potential surfaces for dihydroxycarbene

David Feller, Weston Thatcher Borden, and Ernest R. Davidson

J. Chem. Phys. 71, 4987 (1979); http://dx.doi.org/10.1063/1.438312 (6 pages) | Cited 27 times

Online Publication Date: 25 July 2008

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Potential surfaces have been computed for rotation of the OH groups in C(OH)2 for both the lowest singlet and triplet state. The minima on the singlet surface occur at planar geometries, which represent maxima on the triplet surface. This result is interpreted in terms of different modes of pi electron donation from oxygen being favored in the two states. Evidence is presented that shows pi electron donation is chiefly responsible for making dihydroxycarbene a ground state singlet.
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82.20.Kh Potential energy surfaces for chemical reactions
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