The primitive L-pattern of angular momentum recoupling coefficients

Labarthes primitive L-patterns for the 3nj-symbols, where n=3,4,5,6,7, are reported. It is shown that, any L-patterns of the angular momentum recoupling coefficients can be expressed in terms of linear combinations of the primitive L-patterns and how the 3nj-symbols can be calculated from the expressions presented here.AMS subject classification: 81QShan-Tao Lai–Permanent Address for reprint requestYing-Nan ChiuAlso– Institute of Atomic and Molecular Sciences, Academia Sinica,Taipei, Taiwan, R.O.C.     

Effects of angular momentum recoupling on depolarization spectra in alkali-rare gas optical half collisions

The depolarization mechanisms of excited alkali atoms interacting with ground state rare gas atoms are investigated using the method of far wing spectroscopy of collision pairs under single collision conditions. From a semiclassical theory explicite expressions for the spectra of alkali multipole components σ _k ^(?) (ω _L ) are derived assuming quasistatic excitation at a localized internuclear separationR _L(ω _L ) related to the laserfrequency ω _L as well as realistic models for the half collision following excitation. The collision models are characterized by different Hund's coupling regions, where excitation takes place and which are traversed on the collision path. Due to selection rules for excitation of populations and coherences and for support of multipoles the σ _k ^(?) (ω _L ) are shown to depend strongly on the collision model. From the spectra thus a labelling of the initial molecular states and mapping of the change in coupling case is possible. Estimations of the contributions of the various angular momentum recoupling effects are given.     

C-Cl bond fission dynamics and angular momentum recoupling in the 235 nm photodissociation of allyl chloride

The photodissociation dynamics of allyl chloride at 235 nm producing atomic Cl((2)P(J);J=1/2,3/2) fragments is investigated using a two-dimensional photofragment velocity ion imaging technique. Detection of the Cl((2)P(1/2)) and Cl((2)P(3/2)) products by [2+1] resonance enhanced multiphoton ionization shows that primary C-Cl bond fission of allyl chloride generates 66.8% Cl((2)P(3/2)) and 33.2% Cl((2)P(1/2)). The Cl((2)P(3/2)) fragments evidenced a bimodal translational energy distribution with a relative weight of low kinetic energy Cl((2)P(3/2))/high kinetic energy Cl((2)P(3/2)) of 0.097/0.903. The minor dissociation channel for C-Cl bond fission, producing low kinetic energy chlorine atoms, formed only chlorine atoms in the Cl((2)P(3/2)) spin-orbit state. The dominant C-Cl bond fission channel, attributed to an electronic predissociation that results in high kinetic energy Cl atoms, produced both Cl((2)P(1/2)) and Cl((2)P(3/2)) atomic fragments. The relative branching for this dissociation channel is Cl((2)P(1/2))/[Cl((2)P(1/2))+Cl((2)P(3/2))]=35.5%. The average fraction of available energy imparted into product recoil for the high kinetic energy products was found to be 59%, in qualitative agreement with that predicted by a rigid radical impulsive model. Both the spin-orbit ground and excited chlorine atom angular distributions were close to isotropic. We compare the observed Cl((2)P(1/2))/[Cl((2)P(1/2))+Cl((2)P(3/2))] ratio produced in the electronic predissociation channel of allyl chloride with a prior study of the chlorine atom spin-orbit states produced from HCl photodissociation, concluding that angular momentum recoupling in the exit channel at long interatomic distance determines the chlorine atom spin-orbit branching.     

Magnetic circular dichroism measurements of the magnetisation properties of matrix-isolated species having spin angular momentum only

Magnetic circular dichroism has been used for the first time to study the magnetisation properties of some matrix-isolated species. The samples chosen for measurement have one, three, five and six unpaired electrons in their ground electronic states and, nominally, no orbital angular momentum. The experimental results follow the theoretical predictions very closely, but the nature of the magnetisation function is such that it is not easy to distinguish between different combinations of g-value and total spin angular momentum.     

Hyperspherical analysis of kinetic paths for elementary chemical reactions and their angular momentum dependence

Exploiting the hyperspherical mapping of potential energy surfaces, the evolutions of minima (valley bottoms) and saddles (ridges) as a function of the kinetic radius are identified as kinetic paths for studying reaction mechanisms and dynamics. The effect of angular momentum is investigated quantum-mechanically in a hyperspherical harmonic basis and a lower bound to adiabatic evolution is established. By a classical stability analysis, the dependence of angular momentum effects on configuration is studied. Some features of kinetic paths (such as the occurrence of symmetry degeneracies and bifurcations related to elementary catastrophes) are briefly illustrated for kinetic paths on surfaces for H₃ and H₃⁺.     

Harmonic analysis and discrete polynomials. From semiclassical angular momentum theory to the hyperquantization algorithm

Orthogonal polynomials of a discrete variable have been widely investigated as fundamental tools of numerical analysis. This work aims to propose the extension of their use to quantum mechanical problems. By exploiting both their connection with coupling and recoupling coefficients of angular momentum theory and their asymptotic relationships (semiclassical limit) with spherical and hyperspherical harmonics, a discretization procedure, the hyperquantization algorithm, has been developed and applied to the study of anisotropic interactions and of reactive scattering. One of the most appealing features of this method turns out to be a drastic reduction of memory requirements and computing time for extensive dynamical calculations. Examples of the application of this technique to stereodirected dynamics via an exact representation for the S matrix as well as to the characterization of molecular beam polarization are also illustrated. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

On-top pair-density interpretation of spin density functional theory,with applications to magnetism

The on-top pair density P(r, r) gives the probability that one electron will be found on top of another at position r. We find that the local spin density (LSD) and generalized gradient (GGA) approximations for exchange and correlation predict this quantity with remarkable accuracy. We show how this fact and the usual sum-rule arguments explain the success of these approximations for real atoms, molecules, and solids, where the electron spin densities do not vary slowly over space. Self-consistent LSD or GGA calculations make realistic predictions for the total energy E, the total density n(r), and the on-top pair density P(r,r), even in those strongly “abnormal” systems (such as stretched H₂) where these approximations break symmetries and yield unrealistic spin magnetization densities m(r). We then suggest that ground-state ferromagnetic iron is a “normal” system, for which for LSD or GGA m(r) and the related local spin moment are trustworthy, but that iron above the Curie temperature and antiferromagnetic clusters at all temperatures are abnormal system for which the on-top pair density interpretation is more viable than the standard physical interpretation. As an example of a weakly abnormal system, we consider the four-electron ion with nuclear charge Z → ∞ © 1997 John Wiley & Sons, Inc.     

Symplectic integrators and the conservation of angular momentum

In this article we observe that generally symplectic integrators conserve angular momentum exactly, whereas nonsymplectic integrators do not. We show that this observation extends to multiple timesteps and to constrained dynamics. Both of these devices are important for efficient molecular dynamics simulations. © 1995 by John Wiley & Sons, Inc.     

Role of angular momentum conservation in unimolecular translational energy release: validity of the orbiting transition state theory

The translational kinetic energy release distribution (KERD) for the halogen loss reaction of the bromobenzene and iodobenzene cations has been reinvestigated on the microsecond time scale. Two necessary conditions of validity of the orbiting transition state theory (OTST) for the calculation of kinetic energy release distributions (KERDs) have been formulated. One of them examines the central ion-induced dipole potential approximation. As a second criterion, an adiabatic parameter is derived. The lower the released translational energy and the total angular momentum, the larger the reduced mass, the rotational constant of the molecular fragment, and the polarizability of the released atom, the more valid is the OTST. Only the low-energy dissociation of the iodobenzene ion (E approximately 0.45 eV, where E is the internal energy above the reaction threshold) is found to fulfill the criteria of validity of the OTST. The constraints that act on the dissociation dynamics have been studied by the maximum entropy method. Calculations of entropy deficiencies (which measure the deviation from a microcanonical distribution) show that the pair of fragments does not sample the whole of the phase space that is compatible with the mere specification of the internal energy. The major constraint that results from conservation of angular momentum is related to a reduction of the dimensionality of the dynamics of the translational motion to a two-dimensional space. A second and minor constraint that affects the KERD leads to a suppression of small translational releases, i.e., accounts for threshold behavior. At high internal energies, the effects of curvature of the reaction path and of angular momentum conservation are intricately intermeddled and it is not possible to specify the share of each effect.     

Quantum theory of molecular collisions in a magnetic field: efficient calculations based on the total angular momentum representation

An efficient method is presented for rigorous quantum calculations of atom-molecule and molecule-molecule collisions in a magnetic field. The method is based on the expansion of the wave function of the collision complex in basis functions with well-defined total angular momentum in the body-fixed coordinate frame. We outline the general theory of the method for collisions of diatomic molecules in the (2)Σ and (3)Σ electronic states with structureless atoms and with unlike (2)Σ and (3)Σ molecules. The cross sections for elastic scattering and Zeeman relaxation in low-temperature collisions of CaH((2)Σ(+)) and NH((3)Σ(-)) molecules with (3)He atoms converge quickly with respect to the number of total angular momentum states included in the basis set, leading to a dramatic (>10-fold) enhancement in computational efficiency compared to the previously used methods [A. Volpi and J. L. Bohn, Phys. Rev. A 65, 052712 (2002); R. V. Krems and A. Dalgarno, J. Chem. Phys. 120, 2296 (2004)]. Our approach is thus well suited for theoretical studies of strongly anisotropic molecular collisions in the presence of external electromagnetic fields.     

Rotational angular momentum polarization: the influence of stray magnetic fields

We show that weak residual magnetic fields can significantly affect the preparation and measurement of molecular rotational angular momentum alignment in a typical gas-phase stereodynamics apparatus. Specifically, polarization spectroscopy, a third-order nonlinear spectroscopic technique, is used to prepare and probe the collisional and noncollisional losses of rotational angular momentum alignment of OH X (2)Pi. Residual magnetic fields of the order of the geomagnetic field are shown to have a significant effect on the prepared polarization on a submicrosecond timescale. This can be expected to be a significant effect for many gas-phase free radicals, such as those of interest in combustion, atmospheric chemistry, and the burgeoning field of cold molecules. We demonstrate a simple experimental remedy for this problem.     

Parent-molecule rotational depolarization of photofragment angular momentum distributions: diatomic and polyatomic molecules

We extend the A(q)(k) polarization-parameter model, which describes product angular momentum polarization from one photon photodissociation of polyatomic molecules in the molecular frame [J. Chem. Phys., 2010, 132, 224310], to the case of rotating parent molecules. The depolarization of the A(q)(k) is described by a set of rotational depolarization factors that depend on the angle of rotation of the molecular axis γ. We evaluate these rotational depolarization factors for the case of dissociating diatomic molecules and demonstrate that they are in complete agreement with the results of Kuznetsov and Vasyutinskii [J. Chem. Phys., 2005, 123, 034307] obtained from a fully quantum mechanical approach of the same problem, showing the effective equivalence of the two approaches. We further evaluate the set of rotational depolarization factors for the case of dissociating polyatomic molecules that have three (near) equal moments of inertia, thus extending these calculations to polyatomic systems. This ideal case yields insights for the dissociation of polyatomic molecules of various symmetries when we compare the long lifetime limit with the results obtained for the diatomic case. In particular, in the long lifetime limit the depolarization factors of the A(0)(k) (odd k), Re(A(1)(k)) (even k) and Im(A(1)(k)) (odd k) for diatomic molecules vanish; in contrast, for polyatomic molecules the depolarization factors for the A(0)(k) (odd k) reduce to a value of 1/3, whereas for the Re(A(1)(k)) (even k) and Im(A(1)(k)) (odd k) they reduce to 1/5.     

HO2 ro-vibrational bound-state calculations for large angular momentum: J = 30, 40, and 50

The Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization scheme incorporating doubling of the autocorrelation functions have been employed to compute the HO2 ro-vibrational states for high total angular momenta, J = 30, 40, and 50. For such computationally challenging calculations, we have adopted a parallel computing strategy to perform the matrix-vector multiplications. Low-lying bound states and high-lying bound states close to the dissociation threshold are reported. For low-lying bound states, a spectroscopic assignment has been attempted and the widely used approximate J-shifting method has been tested for this deep-well system. For high-lying bound states, the attempted spectroscopic assignments as well as the J-shifting approximation fail because of very strong Coriolis mixing, indicating that the Coriolis couplings are important for this system.     

Relation between momentum and angular momentum correlation times. analysis of the uncorrelated successive binary-collision approximation

A relation between the correlation times τ_P and τ_J for a system of hard spheres of arbitrary roughness has been found in the uncorr     

Theory and applications of supercycled symmetry-based recoupling sequences in solid-state nuclear magnetic resonance

We present the theoretical principles of supercycled symmetry-based recoupling sequences in solid-state magic-angle-spinning NMR. We discuss the construction procedure of the SR26 pulse sequence, which is a particularly robust sequence for double-quantum homonuclear dipole-dipole recoupling. The supercycle removes destructive higher-order average Hamiltonian terms and renders the sequence robust over long time intervals. We demonstrate applications of the SR26 sequence to double-quantum spectroscopy, homonuclear spin counting, and determination of the relative orientations of chemical shift anisotropy tensors.     

Silylenes: a unified picture of their stability, acid-base and spin properties, nucleophilicity, and electrophilicity via computational and conceptual density functional theory

Conceptual DFT gives sharp definitions for many long-known, but rather vaguely defined chemical concepts. In this study DFT-based reactivity indices are applied to silylenes in order to elucidate the relationships among their properties: stability, acid-base, and spin properties, nucleophilicity and electrophilicity. On the basis of a detailed, comparative analysis of previously published data, it is shown that the properties of simple silylenes can be tuned by varying one single factor, the pi-electron donating ability of the substituents of the silicon atom leading to well-characterized and systematic changes in the stability/reactivity pattern of the molecule. In order to test the model a series of new compounds are studied: including CH3SiR (where R = CH3, NH2, OH and SH), Si(Si(CH3)3)2, Si(CF3)2 and benzo-, pyrido-, pyridazo-, and pyrimido-anellated-1,3,2lambda2-diazasiloles.     

Formaldehyde photodissociation: dependence on total angular momentum and rotational alignment of the CO product

Quasiclassical trajectory calculations are reported to investigate the effects of rotational excitation of formaldehyde on the branching ratios of the fragmentation products, H2+CO and H+HCO. The results of tens of thousands of trajectories show that increased rotational excitation causes suppression of the radical channel and enhancement of the molecular channel. Decomposing the molecular channel into "direct" and "roaming" channels shows that increased rotation switches from suppressing to enhancing the roaming products across our chosen energy range. However, decomposition into these pathways is difficult because the difference between them does not appear to have a distinct boundary. A vector correlation investigation of the CO rotation shows different characteristics in the roaming versus direct channels and this difference is a potentially useful signature of the roaming mechanism, as first speculated by Kable and Houston in their experimental study of photodissociation of acetaldehyde [P. L. Houston and S. H. Kable, Proc. Nat. Acad. Sci. 103, 16079 (2006)].     

Grazing incidence specular reflectivity: theory,experiment, and applications

An overview is given of the theory and experimental implementation of grazing incidence specular reflectivity. Special attention is paid to the latest developments in data analysis methods. The overview is completed by a number of experimental studies showing the possibilities of grazing incidence reflectivity in thin film characterization.