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7 Oct 2006

Volume 125, Issue 13, Articles (13xxxx)

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back to top Methods, Theoretical and Experimental

Manipulation of slow molecular beams by static external fields

Timothy J. McCarthy, Michael T. Timko, and Dudley R. Herschbach

J. Chem. Phys. 125, 133501 (2006); http://dx.doi.org/10.1063/1.2202829 (11 pages) | Cited 7 times

Online Publication Date: 3 October 2006

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Deflection by magnetic or electric field gradients has long been used to analyze or to alter the translational trajectories of neutral gas-phase atoms or molecules. Recent work has developed sources of slow, cold molecular beams that offer means to enhance markedly the attainable deflections, which are inversely proportional to the translational kinetic energy. The sensitivity and resolution can thus be much increased, typically by factors of 102–104. We illustrate ways to exploit this enhanced deflection capability, particularly when balancing electric and magnetic deflections. Chemical scope can be greatly extended by utilizing feeble but ubiquitous interactions, especially the induced electric dipole due to the molecular polarizability and magnetic moments resulting from molecular rotation or nuclear spins. We also examine the effect of non-Maxwellian velocity distributions produced by supersonic expansions or by quantum statistics (pertinent for ultracold beams). Generic plots are provided, employing dimensionless variables, to facilitate the design and interpretation of experiments with deflections amplified by low kinetic energy.
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37.20.+j Atomic and molecular beam sources and techniques
33.15.Kr Electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility
34.90.+q Other topics in atomic and molecular collision processes and interactions (restricted to new topics in section 34)

A new time evolving Gaussian series representation of the imaginary time propagator

Jiushu Shao and Eli Pollak

J. Chem. Phys. 125, 133502 (2006); http://dx.doi.org/10.1063/1.2207142 (6 pages) | Cited 20 times

Online Publication Date: 3 October 2006

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Frantsuzov and Mandelshtam [J. Chem. Phys. 121, 9247 (2004)] have recently demonstrated that a time evolving Gaussian approximation (TEGA) to the imaginary time propagator exp(−βH) is useful for numerical computations of anharmonically coupled systems with many degrees of freedom. In this paper we derive a new exact series representation for the imaginary time propagator whose leading order term is the TEGA. One can thus use the TEGA not only as an approximation but also to obtain the exact imaginary time propagator. We also show how the TEGA may be generalized to provide a family of TEGA’s. Finally, we find that the equations of motion governing the evolution of the center and width of the Gaussian may be thought of as introducing a quantum friction term to the classical evolution equations.
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03.65.-w Quantum mechanics

Construction and calibration of an instrument for three-dimensional ion imaging

Konrad Koszinowski, Noah T. Goldberg, Andrew E. Pomerantz, and Richard N. Zare

J. Chem. Phys. 125, 133503 (2006); http://dx.doi.org/10.1063/1.2217742 (10 pages) | Cited 10 times

Online Publication Date: 4 October 2006

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We describe a new instrument based on a delay-line detector for imaging the complete three-dimensional velocity distribution of photoionized products from photoinitiated reactions. Doppler-free [2+1] resonantly enhanced multiphoton ionization (REMPI) of H and D atoms formed upon photolysis of HBr and DBr in the range 203 nm ⩽ λphotolysis ⩽ 243 nm yields radial speeds measured to be accurate within 1% of those calculated. The relative speed resolution is about 5% and limited by photoionization recoil broadening. A relative speed resolution of 3.4% is obtained for [3+1] REMPI, which minimizes the ionization recoil. We also determine the branching ratio between ground-state and spin-orbit-excited product channels and their associated anisotropies. We find that DBr photolysis dynamics differs slightly from its HBr counterpart.
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82.50.-m Photochemistry
82.80.-d Chemical analysis and related physical methods of analysis
82.30.Cf Atom and radical reactions; chain reactions; molecule-molecule reactions
06.20.fb Standards and calibration
82.20.Tr Kinetic isotope effects including muonium

Local angular momentum–local impact parameter analysis: Derivation and properties of the fundamental identity, with applications to the F+H2, H+D2, and Cl+HCl chemical reactions

P. D. D. Monks, Chengkui Xiahou, and J. N. L. Connor

J. Chem. Phys. 125, 133504 (2006); http://dx.doi.org/10.1063/1.2210480 (13 pages) | Cited 7 times

Online Publication Date: 4 October 2006

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The technique of local angular momentum–local impact parameter (LAM-LIP) analysis has recently been shown to provide valuable dynamical information on the angular scattering of chemical reactions under semiclassical conditions. The LAM-LIP technique exploits a nearside-farside (NF) decomposition of the scattering amplitude, which is assumed to be a Legendre partial wave series. In this paper, we derive the “fundamental NF LAM identity,” which relates the full LAM to the NF LAMs (there is a similar identity for the LIP case). Two derivations are presented. The first uses complex variable techniques, while the second exploits an analogy between the motion of the scattering amplitude in the Argand plane with changing angle and the classical mechanical motion of a particle in a plane with changing time. Alternative forms of the fundamental LAM-LIP identity are described, one of which gives rise to a CLAM-CLIP plot, where CLAM denotes (Cross section)×LAM and CLIP denotes (Cross section)×LIP. Applications of the NF LAM theory, together with CLAM plots, are reported for state-to-state transitions of the benchmark reactions F+H2→FH+H, H+D2→HD+D, and Cl+HCl→ClH+Cl, using as input both numerical and parametrized scattering matrix elements. We use the fundamental LAM identity to explain the important empirical observation that a NF cross section analysis and a NF LAM analysis provide consistent (and complementary) information on the dynamics of chemical reactions.
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82.30.Cf Atom and radical reactions; chain reactions; molecule-molecule reactions
82.20.Db Transition state theory and statistical theories of rate constants
82.20.Hf Product distribution
82.20.Ln Semiclassical theory of reactions and/or energy transfer

Numerical generation of hyperspherical harmonics for tetra-atomic systems

Bruno Lepetit, Desheng Wang, and Aron Kuppermann

J. Chem. Phys. 125, 133505 (2006); http://dx.doi.org/10.1063/1.2218515 (13 pages) | Cited 10 times

Online Publication Date: 5 October 2006

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A numerical generation method of hyperspherical harmonics for tetra-atomic systems, in terms of row-orthonormal hyperspherical coordinates—a hyper-radius and eight angles—is presented. The nine-dimensional coordinate space is split into three three-dimensional spaces, the physical rotation, kinematic rotation, and kinematic invariant spaces. The eight-angle principal-axes-of-inertia hyperspherical harmonics are expanded in Wigner rotation matrices for the physical and kinematic rotation angles. The remaining two-angle harmonics defined in kinematic invariant space are expanded in a basis of trigonometric functions, and the diagonalization of the kinetic energy operator in this basis provides highly accurate harmonics. This trigonometric basis is chosen to provide a mathematically exact and finite expansion for the harmonics. Individually, each basis function does not satisfy appropriate boundary conditions at the poles of the kinetic energy operator; however, the numerically generated linear combination of these functions which constitutes the harmonic does. The size of this basis is minimized using the symmetries of the system, in particular, internal symmetries, involving different sets of coordinates in nine-dimensional space corresponding to the same physical configuration.
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31.10.+z Theory of electronic structure, electronic transitions, and chemical binding
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