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.     

Extension of total angular momentum representation in energy space

A previously developed representation of total angular momentum in energy space for three atomic systems is extended to include reactions of the type CF₃CN → CF₃ + CN. The effects of internal CF₃ rotation on the angular momentum constraint are shown under different conditions. The representation is used for comparison with recent infrared multiphoton dissociation experiments on this system.     

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.     

Non-Born-Oppenheimer variational calculations of HT+ bound states with zero angular momentum

We report fully nonadiabatic calculations of all rotationless bound states of HT+ molecular ion (t+p+e-) carried out in the framework of the variational method. We show that, in all the states, except the two highest ones, the bond in the system can be described as covalent. In the highest two states the bond becomes essentially ionic and HT+ can be described as a T+H+ complex. The wave function of the system was expanded in terms of spherically symmetric, explicitly correlated Gaussian functions with preexponential multipliers consisting of powers of the internuclear distance. Apart from the total energies of the states, we have calculated the expectation values of the t-p, t-e, and p-e interparticle distances, their squares, and the nucleus-nucleus correlation functions.     

Unimolecular rovibrational bound and resonance states for large angular momentum: J=20 calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-->H+O2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.     

Quasiclassical determination of reaction probabilities as a function of the total angular momentum

This article presents a quasiclassical trajectory (QCT) method to determine the reaction probability as a function of the total angular momentum J for any given value of the initial rotational angular momentum j. The proposed method is based on a discrete sampling of the total and orbital angular momenta for each trajectory and on the development of equations that have a clear counterpart in the quantum-mechanical (QM) case. The reliability of the method is illustrated by comparing QCT and time-dependent wave-packet QM results for the H+D(2)(upsilon=0,j=4,10) reaction. The small discrepancies between both sets of calculations, when they exist, indicate some genuine quantum effects. In addition, a procedure to extract the reaction probabilities as a function of J when trajectories are calculated in the usual way using a continuous distribution of impact parameters is also described.     

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)].     

Local angular momentum as ring strain descriptor

A new method is demonstrated to quantify local ring strain, which is based on the expectation value of orbital angular momentum along the internuclear axis. In contrast to energy based methods which provide overall ring strain, this method is able to identify the local strain in every part of the ring. The formalism is benchmarked on several cycloalkanes in which the presence of ring strain is well understood. The ring strain plays a decisive role in carbon nanotubes (CNTs) properties; for instance, the hydrogen storage capability of CNTs is related to their diameter, which in turn has a close relation to the ring strain in their C? C bonds. On this basis, the ring strain in five CNTs with different diameters is analyzed and the results reflected meaningful correlation between the CNTs diameter and ring strain. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

CNDO/S calculations of magnetic circular dichroism of some mono-substituted benzenes using the complete angular momentum operator

Magnetic Circular Dichroism (MCD) B term calculations are performed using the CNDO/S method on mono-substituted benzene derivatives. The influence of geometry, origin dependency, extent of Configuration Interaction (CI) and the choice of the basis set is investigated numerically.For the lowest-lying singlet transitions in these molecules excellent agreement with experiment is obtained.     

Hydrogenic model for stark angular momentum transfer in rydberg atoms

A model for Δn = 0 angular momentum transfer due to electric fields is developed using rotation operators for the SO(4) invariance group of hydrogen. Time-averaged angular momentum transfer probabilities suggest increased radiative lifetimes (τ ∞ n⁴) for initial low-l atoms, due to field-induced transition to high-l states.     

One-dimensional quantum description of the bending vibrations of HCN/CNH for high values of the total angular momentum

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol. Spectrosc. 181 (1997) 403) for the bending deformations of HCN and CNH. In particular, we have examined the l-type resonances in highly excited rovibrational states within the framework of a one-dimensional model, i.e. along the reaction pathway for the isomerization reaction HCN/CNH. The potential energy surface used is that of Bowman et al. (J. Chem. Phys. 99 (1993) 308).     

Laser-induced forward-transfer with light possessing orbital angular momentum

Helical light fields may carry both orbital angular and spin angular momentum which is respectively associated with their helical wavefronts (optical vortices) and rotating transverse electric fields. Interestingly, these helical light fields interact with materials and the orbital angular momentum of these fields can physically twist a range of materials, including metals, semiconductors, polymers, and liquids. With the aid of spin angular momentum, these fields can also form a range of helical structures. This light-matter interaction based on transfer of angular momentum has the potential to revolutionize industrial processes and enable technologies, such as advanced non-contact and nozzle-free printing. In this review paper, we focus on this printing technique, a process which we herein refer to as optical vortex laser induced forward transfer, and we show how it can be used for the production of next generation printed photonics/electronics/spintronics devices. Herein we review the interactions between the angular momentum of light and materials, and we discuss the ways in which optical vortices can be used to produce a variety of exotic structures. We also discuss the current state-of-the art of laser-induced forward-transfer technologies and detail some of the most novel devices, which have been fabricated using this optical vortex laser induced forward transfer, including hexagonal close-packed photonic-rings and plasmonic nanocores.     

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.     

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.     

Direct evaluation of the lifetime matrix by the hyperquantization algorithm: narrow resonances in the F + H2 reaction dynamics and their splitting for nonzero angular momentum

We propose a new method for the direct and efficient evaluation of the Felix Smith's lifetime Q matrix for reactive scattering problems. Simultaneous propagation of the solution to a set of close-coupled equations together with its energy derivative allows one to avoid common problems pertinent to the finite-difference approach. The procedure is implemented on a reactive scattering code which employs the hyperquantization algorithm and the Johnson-Manolopoulos [J. Comput. Phys. 13, 455 (1973); J. Chem. Phys 85, 6425 (1986)] propagation to obtain the complete S matrix and scattering observables. As an application of the developed formalism, we focus on the total angular momentum dependence of narrow under-barrier resonances supported by van der Waals wells of the title reaction. Using our method, we fully characterize these metastable states obtaining their positions and lifetimes from Lorentzian fits to the largest eigenvalue of the lifetime matrix. Remarkable splittings of the resonances observed at J>0 are rationalized in terms of a hyperspherical model. In order to provide an insight on the decay mechanism, the Q-matrix eigenvectors are analyzed and the dominant channels populated during the decomposition of metastable states are determined. Possible relevance of the present results to reactive scattering experiments is discussed.     

Symmetrization of eigenfunctions of angular momentum in point groups

The eigenfunctions |jm〉 of angular momentum can combine linearly to make basis functions of irreducible representations of point groups. We surmount the projection operator and find a new method to calculate the combination coefficients. It is proven that these coefficients are components of eigenvectors of some hermitian matrices, and that for all pure rotation point groups, the coefficients can be made real numbers by properly choosing the azimuth angles of symmetry elements of point groups in the coordinate system. We apply the coupling theory of angular momentum to obtain the general formulas of the basis functions of point groups. By use of our formulas, we have calculated the basis functions with half‐integers j from 1/2 to 13/2 of double‐valued irreducible representations for the icosahedral group. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 286–302, 2001     

Construction of orbital angular momentum eigenfunctions for many-particle systems by harmonic projection

Formulas are derived which allow the direct construction of total orbital angular momentum eigenfunctions for many-particle systems without the use of Clebsch–Gordan coefficients. One of the equations is closely analogous to Dirac' identity for the total spin operator. This equation describes the action of L² on a function of the particle coordinates in terms of a class operator of the symmetric group and a "contraction operator." A general projection operator for constructing symmetric eigenfunctions of L² is presented.     

Representing and selecting vibrational angular momentum states for quasiclassical trajectory chemical dynamics simulations

Linear molecules with degenerate bending modes have states, which may be represented by the quantum numbers N and L. The former gives the total energy for these modes and the latter identifies their vibrational angular momentum jz. In this work, the classical mechanical analog of the N,L-quantum states is reviewed, and an algorithm is presented for selecting initial conditions for these states in quasiclassical trajectory chemical dynamics simulations. The algorithm is illustrated by choosing initial conditions for the N = 3 and L = 3 and 1 states of CO2. Applications of this algorithm are considered for initial conditions without and with zero-point energy (zpe) included in the vibrational angular momentum states and the C-O stretching modes. The O-atom motions in the x,y-plane are determined for these states from classical trajectories in Cartesian coordinates and are compared with the motion predicted by the normal-mode model. They are only in agreement for the N = L = 3 state without vibrational angular momentum zpe. For the remaining states, the Cartesian O-atom motions are considerably different from the elliptical motion predicted by the normal-mode model. This arises from bend-stretch coupling, including centrifugal distortion, in the Cartesian trajectories, which results in tubular instead of elliptical motion. Including zpe in the C-O stretch modes introduces considerable complexity into the O-atom motions for the vibrational angular momentum states. The short-time O-atom motions for these trajectories are highly irregular and do not appear to have any identifiable characteristics. However, the O-atom motions for trajectories integrated for substantially longer period of times acquire unique properties. With C-O stretch zpe included, the long-time O-atom motion becomes tubular for trajectories integrated to approximately 14 ps for the L = 3 states and to approximately 44 ps for the L = 1 states.     

A generalised friction model for the evaluation of angular momentum auto correlation functions

A theory of brownian motion where the friction coefficient is a finite correlation function of molecular torque is used to derive an expression for the angular velocity autocorrelation function, ψ(r). This is related to the orientational a.c.f., φ(t), using an analysis of bandshapes due to Kubo and extended by Shimizu. Both functions φ(t) and ψ(t) contain inherent weaknesses since ψ(t) has a MacLaurin expansion even up to t⁴ only, and π(t) does not reduce to the Kummer function for an ensemble of free rotors in the so-called limit of vanishing friction. Reasons for this behaviour are discussed.