Collinear isotopes

Garret, B. C. and Truhlar, D. G. Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules and isotopically substituted hydrogen molecules, JPhys.Chem., 83 (1979), 1079-1112... 

Tunneling in VTST is handled just like tunneling in TST by multiplying the rate constant by k. The initial tunneling problem in the kinetics was the gas phase reaction H -(- H2 = H2 + H, as well as its isotopic variants with H replaced by D and/or T. For the collinear reaction, the quantum mechanical problem involves the two coordinates x and y introduced in the preceding section. The quantum kinetic energy operator (for a particle with mass fi) is just... 

There has been a long history in theoretical efforts to understand H + H/Cu(lll) and its isotopic analogs because it represents the best studied prototype of an ER/HA reaction. These have evolved from simple 2D collinear quantum dynamics on model PES [386] to 6D quasi-classical dynamics on PES fit to DFT calculations [380,387,388], and even attempts to include lattice motion on ER/HA reactions [389]. These studies show that there is little reflection of incident H because of the deep well and energy scrambling upon impact, i.e., a % 1. Although some of the... 

As discussed in the preceeding section, an extensive investigation of the rare-earth region is being performed by collinear laser spectroscopy. It includes a two-dimensional mapping of the (N, Z)-plane, covering not only scattered isotopic sequences but isotopes of a range of elements. 

Prior to about 1955 much of the nuclear information was obtained from application of atomic physics. The nuclear spin, nuclear magnetic and electric moments and changes in mean-squared charge radii are derived from measurement of the atomic hyperfine structure (hfs) and Isotope Shift (IS) and are obtained in a nuclear model independent way. With the development of the tunable dye laser and its use with the online isotope separator this field has been rejuvenated. The scheme of collinear laser/fast-beam spectroscopy [KAU76] promised to be useful for a wide variety of elements, thus UNISOR began in 1980 to develop this type of facility. The present paper describes some of the first results from the UNISOR laser facility. 

Barrier heights in bimolecular reactions depend on the approach angle. For example, in D + H2 — H + HD (and its isotopic variants), the lowest barrier is found when D attacks along the bond axis of H2, that is, collinearly. 

Fig. 3.1.3 Energy along the reaction coordinate for the reaction D + H — H —> D — H + H (and its isotopic variants), as a function of the approach angle. Note that the lowest barrier is found for the collinear approach. [Adapted from R.D. Levine and R.B. Bernstein, Molecular reaction dynamics and chemical reactivity (Oxford University Press, 1987).]...

S-Matrix Propagation along Delves Radial Coordinate. J. Manz and J. Romelt, Chem. Phys. Lett., 77, 172 (1981). Dissociative Collinear Reactions Evaluated by S-Matrix Propagation along Delves Radial Coordinate. J. Manz and J. Romelt, Chem. Phys. Lett. 81,179 (1981). On the Collinear 1+ HI and 1+ Mul Reactions. (Here Mu represents a muonium isotopic variant.)... 

The two maxima at 900 and 850 cm." show little or no isotope shift and occur in the frequency range expected for the asymmetric uranyl stretching mode. It does not seem likely that the 850 cm. band arises from the symmetric U—O stretch activated by site symmetry because the absorption is too strong. Other possibilities are that the uranyl group is not symmetrical, the O—U—O bonds are not collinear, or two different... 

Garrett B. C. and Truhlar D. G. (1979) Generalized Transition State Theoiy. Quantum Effects for Collinear Reactions of Hydrogen Molecules and Isotopically Substituted Hydrogen Molecules, J. P/zys. Chem. 79, 1079-1112. 

The potential energy surfaces (LEPS A from Refs. (8.10)). the effective potentials U (n=0 gerade and ungerade symmetry) and the bound states of the collinear IHI and lOI are shown in Fig. 4. As argued for the Cl+HCl system the reaction is very adiabatic, and thus the effective potentials and the adiabatic eigen-energies e (r) coincide within 10 eV. It should be noticed that isotopic suBstitution of the hydrogen atom by its heavier isotope deuterium tends to destabilize the vibrational bonded molecule. 

The development of collinear laser spectroscopy has enabled measurements of isotope shifts and hyperfme stmcture over long chains of isotopes. This makes it possible to derive nuclear properties of isotopes far from stability. The experimental development is reviewed and some future prospects discussed. 

The combination of collinear fast-beam laser spectroscopy and P-RADOP (radiation-detected optical pumping) has been used to measure nuclear spins and moments of neutron-rich isotopes of the light alkali elements jLi [72-74] and Na [75]. Here, the optically pumped fast atomic beam is implanted into a single crystal placed in a static magnetic field. The NMR signal is destroying the nuclear polarization detected by measuring the p-decay asymmetry. 

The isotopic sequence of die heaviest alkali element, francium, has been extensively studied at ISOLDE by the three atomic-beam techniques ABMR, atomic-beam laser spectroscopy and collinear fast-beam laser spectroscopy. 

Figure B3.4.1. The potential surface for the collinear D + H2 DH + H reaction (this potential is the same as for H + H2 H2 + H, but to make the products and reactants identification clearer the isotopically substituted reaction is used). The D + H2 reactant arrangement and the DH + H product arrangement are denoted. The coordinates are r, the H2 distance, and R, the distance between the D and the H2 centre of mass. Distances are measured in angstroms the potential contours shown are 4.7 eV,-4.55 eV,.. ., -3.8 eV. (The potential energy is zero when the particles are far from each other. Only the first few contours are shown.) For reference, the zero-point energy for H2 is -4.47 eV, i.e. 0.27 eV above the H2 potential minimum (-4.74 eV) the room-temperature thermal kinetic energy is approximately 0.03 eV. The graph uses the accurate Liu-Seigbahn-Truhlar-Horowitz (LSTH) potential surface [195).

B. C. Garrett, D. G. Truhlar, R. S. Grev, A. W. Magnuson, and J. N. L. Connor, Variational transition state theory, vibrationally adiabatic transmission coefficients, and the unified statistical model tested against accurate quantal rate constants for collinear F + H2, H + F2, and isotopic analogs, 7. Chem. Phys. 73 1721 (1980). 

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