Molecular Angular Momentum Research Articles

Effect of ground-state electron correlation on the (e,2e) reaction spectroscopy of H2( 1 Sigma g+).

A critical theoretical study of the electron momentum distributions obtained for ${\mathrm{H}}_{2}$${(\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{g}}^{+}$) by the (e,2e) reaction technique for transitions to the ground and the n=2 and 3 excited states is presented. Two very highly electron correlated ground-state wave functions for ${\mathrm{H}}_{2}$${(\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{g}}^{+}$), each of which yields more than 96% of the ``exact'' binding energy and the exact Born-Oppenheimer wave function of ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ in the ground and various excited states, were employed in the computations within the context of the plane-wave impulse approximation (PWIA). For the ground-state transition, the theoretical values computed from both correlated wave functions and a self-consistent-field wave function are all in relatively good agreement with experiments for recoil momenta in the range (0.11\ensuremath{\le}q\ensuremath{\le}1.0 a.u.). In order to discriminate among the various theoretical values reported here it is highly desirable to have experimental data for q smaller than 0.05 a.u. The experimental data for the transitions to the n=2 excited states (2s${\ensuremath{\sigma}}_{g}$, 2p${\ensuremath{\pi}}_{u}$, and 2p${\ensuremath{\sigma}}_{u}$) are surprisingly not in as good agreement with the theoretical values reported here. The failure to describe the transition to excited states with a molecular angular momentum quantum number other than zero may be due to (i) the inadequacy of the ground-state wave function, (ii) the failure of the Franck-Condon principle in the transition, (iii) the need to go beyond the PWIA, and/or (iv) the need for improved and extended experimental data.

Rotationally inelastic scattering of molecules from solid surfaces

Abstract A formal theory of rotationally inelastic scattering of 2 Π diatomic molecules from surfaces is developed. The Λ-doublet degeneracy of the molecule gives rise to an effective molecule-surface potential which has an additional dependence, not present in Σ-state molecule-surface systems, on the angle of rotation about the diatomic axis. Close-coupled scattering equations are derived for pure Hund's case (a) and pure Hund's case (b) representations of the molecular electronic-rotational states. The coordinate-representation sudden approximation is then applied, yielding simplifying expressions for various intensities of scattering from the surface. Propensity rules for rotational transitions between the Λ-doublets and between the spin-orbit manifolds for both the low and high final total molecular angular momentum regimes are derived. Trends in recent experimental observations on these transitions for the NO/Ag(111) system are explained within the present theoretical framework.

Rotationally inelastic scattering of 2Π molecules from solid surfaces

A formal theory of rotationally inelastic scattering of 2Π diatomic molecules from surfaces is developed. The Λ-doublet degeneracy of the molecule gives rise to an effective molecule-surface potential which has an additional dependence, not present in Σ-state molecule-surface systems, on the angle of rotation about the diatomic axis. Close-coupled scattering equations are derived for pure Hund's case (a) and pure Hund's case (b) representations of the molecular electronic-rotational states. The coordinate-representation sudden approximation is then applied, yielding simplifying expressions for various intensities of scattering from the surface. Propensity rules for rotational transitions between the Λ-doublets and between the spin-orbit manifolds for both the low and high final total molecular angular momentum regimes are derived. Trends in recent experimental observations on these transitions for the NO/Ag(111) system are explained within the present theoretical framework.

Laboratory Frame Cross Correlations in Chiral Liquids: Direct Observation of Rotation/Translation Coupling

Cross correlations of the type ⟨v(t)JT(0)⟩ are observable in the laboratory frame of reference for chiral molecules in the liquid state. Here v is the molecular centre of mass linear velocity and J the molecular angular momentum. Some of these cross correlations are illustrated by computer simulation for the enantiomers and racemic mixture of fluorochloroacetonitrile. The Langevin equation is adapted for rototranslation and analytical expressions derived, in the first approximation, for the dominant elements of ⟨v(t)JT(0)⟩.

The effect of external electric fields on molecular liquids and induced translational motion

Abstract A computer simulation is reported of the enantiomer S CHBrClF subjected in the liquid state to intense external fields of force : i) uniaxial electric field EZ; ii) circularly polarised field at optical frequencies. The molecular dynamics are quantified in detail at field - on equilibrium in case i) using a range of auto correlation functions. The foremost result of the investigation is that the simple uniaxial field EZ makes the sample translate in a well defined direction. The direct effect of EZ on an isolated molecule of S-CHBrClF is purely rotational, but intramolecular rotation/translation coupling converts this rotation into coherent centre of mass translation. This gives rise to direct, laboratory frame , cross correlations of the type J T(o)> where v is the molecular centre of mass translational velocity and J T the transposed molecular angular momentum vector. (The existence of these invalidates the classical theory of the Kerr effect.) The molecular dynamics of the hypothetical chiral ion S-CHBrClF− are looked at with a view to corroborating the predictions by Baranova et al. concerning their response to electric field treatment. Despite the inherent instability of such an ensemble of like-charged ions the simulation can be used to produce a range of auto and cross-correlation functions with which to characterise the ionic dynamics. The effect of treating the ionic ensemble with a field EZ is reported briefly in terms of the non-vanishing ensemble averaged centre of mass velocity ;. The induced translation in an electric field may be demonstrated on most liquids using a simple experimental set up. Its importance in optically active systems is such that it may be used to separate a racemic mixture into its enantiomers, the translational motion induced in the one enantiomer is necessarily, by symmetry, opposite to that induced in the other enantiomer. The observation therefore has technological importance. Other applications are discussed.

Collisional energy transfer in the low-pressure-limit unimolecular dissociation of HO2

Classical trajectory calculations are used to investigate the energy transfer properties of HO2–He collisions under conditions where HO2 is initially excited to energies near dissociation. The emphasis in this investigation is on determining the dependence of vibrational energy transfer characteristics on heat bath temperature, total molecular energy, and total molecular angular momentum. Vibrational energy transfer is a function of all three variables. Energy transfer averages, correlation coefficients, and energy transfer cross sections are used to determine the energy transfer mechanism. Evidence is found for all types of energy transfer, but the specific mechanism for a particular ensemble is highly dependent on the initial variables. At fixed vibrational energy and heat bath temperature, the magnitude of the average vibrational energy transferred per collision ‖〈ΔE′〉‖ increases with increasing molecular angular momentum. At fixed initial molecular angular momentum and heat bath temperature, −〈ΔE′〉 increases as the total energy in the molecule increases, except for very low values of initial angular momentum. Increasing the heat bath temperature for fixed values of the other initial variables decreases the magnitude of 〈ΔE′〉. The relative importance of weak and strong collisions in governing the energy transfer characteristics is discussed. In particular, the probability density function for vibrational energy transfer is not well represented by a simple ‘‘exponential down’’ model. A double exponential function is required to represent the long tail of the distribution adequately. Total vibrational energy transer cross sections determined from vibrational energy transfer histograms are weak functions of total energy, total angular momentum, and heat bath temperature. They are systematically higher than the corresponding Lennard-Jones cross sections.

On a simple reaction mechanism for the collision-induced dissociation He + Li 2(B 1Π u) → He + Li(2 2S) + Li(2 2P)

A simple reaction mechanism is suggested for the dissociation of electronically excited Li 2(B 1Π u) in collision with rare-gas atoms. Experimental rate constants for dissociation of Li 2 in specific vibrational—rotational levels (ν1 J) show an unexpected behaviour as a function of the initial molecular energy and angular momentum. We propose that raction proceeds by a transition to the 1Π g state of Li 2. This may dissociate more readily since it is more weakly bound and has a larger equilibrium distance than the 1Π u state.

The molecular dynamics of camphor: An essay on the role of correlation between rotation and translation

Abstract The available literature on the molecular dynamics of camphor is reviewed with the purpose of explaining some observable racemic modifications in terms of the cross-correlation matrix v (t) J T(O)>m. Here v is the molecular centre of mass velocity and J the molecular angular momentum in a moving frame of reference defined by the principal moments of inertia. For example, the observable pseudo-eutectic in the solid-state λ transition temperatures for various mixtures of R in S camphor may be used to provide direct information on the nature of v (t) J T(O)>m through the intermediacy of Grigolini's reduced model theory or using developments in computer simulation.

Computer simulation inverse Raman and far infra-red study of rototranslational correlation in optically active molecules: Part 2; 1,1 fluoroiodoethane, 3 methyl cyclopentanone and 3 methylcyclohexanone

Abstract Computer simulation is used to investigate the statistical correlation between the molecular centre of mass velocity ( v ) and molecular angular momentum ( J ) of the optically active molecule 1,1 fluoroiodoethane in the liquid state. Of the nine elements of the moving frame correlation matrix v (t) J T(o)>m, the diagonal elements vanish by symmetry for all t. The other elements exist, in principle, for t > o, but the (1,3) and (3,1) elements are small in magnitude, and therefore buried in the computer noise, for both the R and S enantiomers and their racemic mixture. The molecular dynamical nature of the two enantiomers is therefore almost identical in the laboratory and any moving frame of reference. This implies that the laboratory frame autocorrelations of each enantiomer are similar to those in the racemic mixture, in marked contrast to 1,1 fluorochloroethane [12] where differences in the structure of the (1,3) and (3,1) elements for each enantiomer lead to large and observable differences between laboratory frame autocorrelations in either enantiomer and their racemic mixture. These differences are direct measures of rotation/translation correlation on a fundamental single molecule level. The simulation is supported by measurements in the far infra-red on the (+) enantiomers and racemic mixtures of 3 methyl cyclohexanone and 3 methyl cyclopentanone in the liquid state at 293K.

ChemInform Abstract: HIGH RESOLUTION FLUORESCENCE EXCITATION AND QUANTUM BEAT SPECTROSCOPY OF THE FIRST ELECTRONICALLY ALLOWED TRANSITION OF PERDEUTEROMETHYLGLYOXAL

Laser induced fluorescence excitation spectra of supersonic nozzle beam cooled methylglyoxal‐d4 reveal that a deformation occurs during the radiative electronic transition that destroys the planarity of the carbonyls. Consistent with the expectation that deuteration results in an increased number of low frequency vibrations, the number of observed vibronic lines increased and the energy of the breakoff of sharp vibronic structure above the O–O band decreased compared to the protonated molecule. As for the protonated molecule, the observed vibronic structure can be almost completely assigned on the basis of two fundamentals and a repeating pattern of lines that involves the methyl internal rotation and the cis–trans internal rotation of the carbonyls. Systematic anharmonicities involving the pattern and only one of the two fundamentals suggests which molecular motions correspond to the observed fundamentals. Quantum beat and Zeeman effect experiments unambiguously show the triplet states that are responsible for the radiationless dynamics that are known to occur in these molecules. All quantum beat data were analyzable using our previously published perturbation theory method and yield triplet densities which are intermediate compared to methylglyoxal‐h4 and biacetyl‐h6 and in good agreement with an estimate obtained by direct state coupling. The density of effectively coupled triplet states increases with the energy of the initially prepared singlet state and the intramolecular coupling is 2–15 MHz independent of the amount of vibrational‐rotational excitation present. Radiationless transitions in these highly excited molecules are evidently not subject to any overriding selection rules other than spatial symmetry and conservation of total energy, total angular momentum, and nuclear spin. Zeeman experiments indicate extensive coupling of all molecular angular momenta which initially decouple at only ∼10 G. In this low field regime complicated splittings are observed which correspond roughly to g values of about 67% that of a free electron. At larger fields of about 50–60 G, the microsecond fluorescence is nearly completely quenched, and although we cannot completely explain this effect at present, we suspect both intra‐ and intermolecular processes are possible.Laser induced fluorescence excitation spectra of supersonic nozzle beam cooled methylglyoxal‐d4 reveal that a deformation occurs during the radiative electronic transition that destroys the planarity of the carbonyls. Consistent with the expectation that deuteration results in an increased number of low frequency vibrations, the number of observed vibronic lines increased and the energy of the breakoff of sharp vibronic structure above the O–O band decreased compared to the protonated molecule. As for the protonated molecule, the observed vibronic structure can be almost completely assigned on the basis of two fundamentals and a repeating pattern of lines that involves the methyl internal rotation and the cis–trans internal rotation of the carbonyls. Systematic anharmonicities involving the pattern and only one of the two fundamentals suggests which molecular motions correspond to the observed fundamentals. Quantum beat and Zeeman effect experiments unambiguously show the triplet states that are responsib...

A quantum mechanical calculation of photofragment absorption or emission polarization

The polarization of light emitted by excited state diatomic photofragments produced using linear polarized radiation to dissociate a triatomic molecule is calculated using a quantum mechanical treatment of molecular rotational angular momentum and assuming direct dissociation. The photofragment emission polarization is found to depend upon the relative orbital angular momentum of the separating fragments as well as the individual angular momenta of the parent and fragment molecules.

Role of angular momentum for atomic scattering in intense laser fields

We have used nonperturbative quantum-mechanical close-coupled scattering calculations to investigate inelastic atomic collisions induced by strong laser fields. If a partialwave expansion in molecular total angular momentum states is used for the scattering wave function, the selection rule $\ensuremath{\Delta}J=\ifmmode\pm\else\textpm\fi{}1$ for the radiative interaction matrix elements results in an infinite set of close-coupled equations. Model calculations for the total laser-induced inelastic cross section for both beam and homogeneous-gas experiments are carried out for two $^{1}\ensuremath{\Sigma}$ states coupled by linearly polarized light. A truncated expansion is used with a sufficient number of rotational states to ensure convergence of the cross section. The results show that the exact cross section saturates much more slowly with increasing laser intensity than the cross section calculated for a two-state $J$-conserving model. Angular momentum changes larger than \ifmmode\pm\else\textpm\fi{}1 are possible when the laser intensity is sufficiently high. Thus, a sufficient number of rotational states must be included in the expansion basis to take into account scattering paths that can lead to large changes in angular momentum.

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

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

The role of molecular angular momentum in generalized hydrodynamics

Various sets of generalized hydrodynamic equations for liquids composed of non-spherical molecules are considered. The most general one studied involves five coupled linear transport equations for the five collective dynamical density variables is the curl of the momentum, the molecular orientations, the intrinsic (molecular) angular momentum, the symmetric and the antisymmetric components, respectively of an unspecified second rank tensor. is the only conserved quantity and the choice of the others is somewhat arbitrary. If is nearly equal to the antisymmetric stress tensor (), then the five variable theory reduces to the three variable theory; if differs appreciably from , then the five variable theory reduces to the four variable theory which was used successfully in a recent analysis of VH depolarized light scattering from viscoelastic fluids.

A theoretical study of depolarized rayleigh spectral linewidths in gases

The semiclassical theoretical approach to molecular spectral line broadening developed by Marcus and co-workers is extended to treat depolarized Rayleigh (DPR) linewidths for gases of linear molecules in the binary collision regime. The resulting expression, derived from an exact quantum mechanical starting point, is essentially a classical-like ensemble average of the molecular angular momentum reorientation. For computational convenience, the DPR line broadening cross section, σ DPR, is expressed as a multiple integral over precollisional values of dynamical variables which comprise a complete, three-dimensional, dynamical description of two linear rigid rotors. The DPR cross section is then evaluated by a Monte Carlo technique involving the computation of exact classical trajectories. By using a short-range anisotropic model intermolecular potential recently proposed by MacRury, Steele and Berne, good agreement with measured values of σ DPR was found for the pure gases N 2 and CO 2, at room temperature.

Non-gaussian distributions in computer triatomics

A molecular dynamics simulation of 108 triatomic molecules of C 2v symmetry reveals markedly non-gaussian statistical distributions of vectors such as the centre-of-mass linear velocity, molecular angular momentum, positional and orientational coordinates. The results are reproduced qualitatively in the case of linear velocity by a straightforward extension of the Fokker-Planck equation.

Nuclear-spin-lattice relaxation times forH2in solid nonmagnetic hosts

We calculate the nuclear-spin relaxation times ${T}_{1}$ and ${T}_{2}$ for isolated ortho ($J=1$) ${\mathrm{H}}_{2}$ molecules in solid nonmagnetic hosts located at sites with various crystal fields. The mechanism considered for the relaxation of a nuclear spin to lattice equilibrium proceeds via the molecular angular momentum and is valid in the limit where molecular spin-lattice decay rates are much greater than molecular-nuclear-spin coupling frequencies. We find that many relaxation properties, including the value of ${T}_{1}$ at the ${T}_{1}$ minimum and the product of ${T}_{1}{T}_{2}$ at temperatures well below the temperature of the ${T}_{1}$ minimum, depend crucially on the crystal field at the ${\mathrm{H}}_{2}$ molecular site. Thus measurements of ${T}_{1}$ and ${T}_{2}$ can yield definite information about the environment of ${\mathrm{H}}_{2}$ molecules in a host lattice.

An angular momentum approximation for molecular collisions in the presence of intense laser radiation

An approximation to a previously presented rigorous description of molecular (atom-atom) collisions occurring in the presence of intense radiation is investigated. This rigorous description explicitly considers the angular momentum transferred between the molecule and the radiation field in the absorption or emission of a photon, but involves a complicated system of close-coupled equations which must be solved independently for each projection M of the initial, total molecular angular momentum. (This is a direct consequence of the lack of rotational invariance in the molecule-field problem). These equations are solved for a model system which mimics the collision of a halogen with a rare gas atom. Empirical observations made in the course of performing these calculations lead to the development of an approximation which avoids the repeated calculations for each initial M. This orientational average approximation greatly reduces the effort required to describe the system, and for the model calculation, yields accurate results for field intensities as high as 10 GW/sq cm.

The vibrational Raman spectrum of compressed solid hydrogen

The frequencies of the pure vibrational lines, Q(0) and Q(1), in the Raman spectrum of solid H2 have been measured when the solid was subjected to a number of pressures between 400 and 1000 kg cm−2, corresponding to solid densities up to ~ 1250 amagat. Most samples studied had orthohydrogen concentrations ≥ 0.60. For these the frequency of Q(0) increased as the density increased but that of Q(1) showed little change. This can be explained if it is assumed that (i) the isotropic repulsive overlap interaction between a pair of molecules increases more rapidly than the attractive dispersion-type interaction, (ii) the effect of vibrational coupling between molecules in the same J-state increases asp2, and (iii) the lowering of the excitation energy of the ν = 1,J = 1 stale by electric quadrupolar interactions increases as ρ5/3. There is evidence that at higher densities ordering of the molecular angular momenta may occur at temperatures up to 4 K. The intensity of Q(1) relative to Q(0) is further enhanced at higher densities.

Effect of spin polarization on the thermal conductivity of polyatomic gases

Expressions are developed for the thermal conductivity and Eucken factor of a polyatomic gas which include the effects of spin polarization (molecular angular momentum) in terms of experimentally accessible quantities. Comparisons are made of calculations based on these equations with results for the loaded sphere and spherocylinder models, and for nitrogen. Although the effect of spin polarization is small, it is greater than the uncertainty in present experimental thermal conductivity measurements. The numerical importance of spin polarization appears to be greater than the effect of equating the diffusion coefficient for internal energy to the self-diffusion coefficient.