The Landau-Zener formula for the probability that a nonadiabatic transition has taken place is derived without solving directly the usual second-order differential equation. This is achieved in just a few steps by using contour integration.

Time resolved, subpicosecond resolution measurements of photoinitiated NO2 unimolecular decomposition rates are reported for expansion cooled and room temperature samples. The molecules are excited by 375-402 nm tunable subpicosecond pulses having bandwidths 220 cm-' to levels which are known to be thorough admixtures of the 2B2 electronically excited state and the 2A1 ground electronic state. Subsequent decomposition is probed by a 226 nm subpicosecond pulse that excites laser-induced fluorescence (LIF) in the NO product. When increasing the amount of excitation over the dissociation threshold, an uneven, "step-like" increase of the decomposition rate vs energy is observed for expansion cooled samples. The steps are spaced by-100 cm-' and can be assigned ad hoc to bending at the transition state. Relying on experimental estimates for the near threshold density of states, we point out that simple transition state theory predictions give rates that are consistent with these measured values. The rates are sufficiently rapid to question the assumption of rapid intramolecular vibrational redistribution, which is implicit in transition state theories. In contrast to expansion cooled samples, room temperature samples exhibit a smooth variation of the reaction rate vs photon energy. By comparing rates for rotationally cold and room temperature NOZ, the ON-O bond is estimated to be-40% longer in the transition state than in the parent molecule.

The unimolecular reaction of a vibrationally excited molecule having low rotational excitation often leads to nascent products in which the vibrational degrees of freedom appear ‘‘hotter’’ than the rotation, translation (R,T) degrees of freedom. We show that this can derive from parent vibrations being ‘‘hot’’ while parent rotations remain ‘‘cold,’’ since the parentage of product vibration is parent vibration, while product R,T excitations are obtained from parent vibration as well as rotation. Calculations are performed for reactions having loose transition states and no reverse barriers, in which an ensemble of 3N–6 degrees of freedom are used to equilibrate parent vibrations, thereby providing a statistical distribution of product vibrational excitations. For each set of product vibrational states, all R,T excitations are then apportioned statistically using the phase space theory of unimolecular reactions (PST). The results indicate that for those energies above reaction threshold (E‡) which exceed the lowest product vibrational energies, product vibrations are more excited than with PST, while product R,T excitations are less than with PST. These differences increase with E‡, and rotational distributions obtained using the separate statistical ensembles (SSE) method peak at low N″ relative to PST. When product vibrations are energetically inaccessible, SSE and PST are identical. The calculations are compared to nascent distributions from the unimolecular dissociation of monoenergetic NCNO, and the agreement is excellent.

The H + NCO(X211) channel in the 193.3-nm photodissociation of HNCO has been examined by using high-n Rydberg hydrogen atom time-of-flight (HRTOF) spectroscopy, and the center-of-mass (cm) translational energy distribution has been obtained. The cm translational energy distribution peaks near the maximum available energy and shows considerable structure corresponding to NCO vibrational excitation. This is attributed to geometric changes in going from HNCO to the electronically excited potential surface then to products. Specifically, a strongly bent N-C-0 angle in excited HNCO accounts for the long NCO bending progression that is observed. A strongly anisotropic product angular distribution was observed, in agreement with an 'A" excited state and rapid dissociation via a repulsive surface. Do(H-NCO) is found to be 110.1 f 0.5 kcal mol-', in agreement with recent experimental and theoretical values.

Articles you may be interested inAlignment of CN from 248 nm photolysis of ICN: A new model of the à continuum dissociation dynamics J. Chem. Phys. 87, 303 (1987); 10.1063/1.453627 NCNO→CN+NO: Complete NO(E,V,R) and CN(V,R) nascent population distributions from wellcharacterized monoenergetic unimolecular reactions J. Chem. Phys. 83, 5573 (1985); 10.1063/1.449680 Erratum: Nascent PO(X 2Π) E,V,R,T excitations from collisionfree IR laser photolysis: Specificity toward the PO(X 2Π1 / 2) spinorbit state [J. Chem. Phys. 8 2, 1376 (1985)] J. Chem. Phys. 83, 2003 (1985); 10.1063/1.449871 Nascent PO(X 2Π) E,V,R,T excitations from collisionfree IR laser photolysis: Specificity toward the PO(X 2Π1/2) spinorbit stateThe 266 nm photolysis of leN: Recoil velocity anisotropies and nascent E,V,R,T excitations for the eN + 1( 2P 3/2) and eN + 1(2P 1 / 2 ) channels a )We report the detection of nascent CN(X 2 ~ + ,v" = 0) following the 266 nm photodissociation of 300 K ICN, using sub-Doppler resolution laser-induced fluorescence, and polarized photolysis and probe lasers. When monitoring a particular CN internal state, the translational energies of the I + CN and 1* + CN channels differ by the iodine spin-orbit splitting 7603 cm -I. This is used to determine the separate contributions from each channel. For I + CN, high N" are selectively produced, with little population below N" = 20 (E ro !) = 3300 ± 300 cm -I), whereas the 1* + CN channel is associated with a distribution peaked sharply at low N "( (Ero!) = 355 ± 35 cm -I). It is clear that the low and high N" derive from linear and bent exit channel geometries, respectively. The spatial anisotropy is high (.81 = 1.3 ± 0.2;/31. = 1.6 ± 0.2) and initial excitation is via a parallel transition(s), probably to a state which begins correlating with 1* + CN in the linear configuration. Nascent spin-rotation states (FI and F 2 ) are also resolved for each channel, and for the case of I + CN, and FI and F2 populations are quite different. There is very little vibrational excitation ( < 2%), and the rotational distributions and translational energies of v" = 1 and 2 correspond to those of the I + CN channel. Subsequent to initial excitation, both adiabatic and/or nonadiabatic processes can ensure access to potential surfaces not excited directly, and a model is discussed which rationalizes the present experimental results, as well as the known variation of nascent E, V, R, T excitations with the photolysis wavelength.

The photoinitiated unimolecular decomposition of formaldehyde via the H+HCO radical channel has been examined at energies where the S0 and T1 pathways both participate. The barrierless S0 pathway has a loose transition state (which tightens somewhat with increasing energy), while the T1 pathway involves a barrier and therefore a tight transition state. The product state distributions which derive from the S0 and T1 pathways differ qualitatively, thereby providing a means of discerning the respective S0 and T1 contributions. Energies in excess of the H+HCO threshold have been examined throughout the range 1103⩽E†⩽2654 cm−1 by using two complementary experimental techniques; ion imaging and high-n Rydberg time-of-flight spectroscopy. It was found that S0 dominates at the low end of the energy range. Here, T1 participation is sporadic, presumably due to poor coupling between zeroth-order S1 levels and T1 reactive resonances. These T1 resonances have small decay widths because they lie below the T1 barrier. Alternatively, at the high end of the energy range, the T1 pathway dominates, though a modest S0 contribution is always present. The transition from S0 dominance to T1 dominance occurs over a broad energy range. The most reliable value for the T1 barrier (1920±210 cm−1) is given by the recent ab initio calculations of Yamaguchi et al. It lies near the center of the region where the transition from S0 dominance to T1 dominance takes place. Thus, the present results are consistent with the best theoretical calculations as well as the earlier study of Chuang et al., which bracketed the T1 barrier energy between 1020 and 2100 cm−1 above the H+HCO threshold. The main contribution of the present work is an experimental demonstration of the transition from S0 to T1 dominance, highlighting the sporadic nature of this competition.

The high-n Rydberg time-of-flight (HRTOF) technique has been used to obtain translational energy distributions of hydrogen atoms deriving from weakly-bound (HI)2 clusters photoexcited at 266 nm. A number of distinct features were observed and were used to establish much of the photophysics and photochemistry. Though the geometric structure of (HIh has not been determined experimentally, equilibrium geometries have been estimated by using several semiempirical theoretical methods, all of which predict an approximately 90" L-shaped structure with one hydrogen localized between the two iodine atoms (the interior hydrogen) and the other pointing outward (the exterior hydrogen). Zero-point amplitudes are expected to be large. The photolytic removal of the exterior hydrogen yields I-HI and I*-HI radical-molecule clusters whose properties can be described, at least qualitatively, by using the formalism put forth by Hutson and co-workers, who carried out detailed calculations for the analogous C1-k HCl system. Photodissociation of the HI moiety whose hydrogen is interior can also yield radical-molecule clusters, as well as initiate intracluster reactive and/or inelastic scattering processes. Photoproducts that contain the HI chromophore such as HI(vj), I-HI, and I*-HI can also be efficiently photoexcited, yielding hydrogen atoms having signatures that reflect their parentages. Peaks in the translational energy distribution corresponding to photodissociation of HI in v = 1 and 2 are identified and confirmed by H -D substitution. Furthermore, v = 0 rotational levels having 7 5 j 5 13 are just barely resolved. The most likely source of intemally excited HI is believed to be inelastic scattering in which the internal hydrogen strikes the adjacent HI. This is deduced from the theoretical work of Aker and Valentini, who employed the method of quasiclassical trajectories with a potential surface developed by Last and Baer and modified by Clary. These calculations suggest that the likely L-shaped geometry of (HI);? is compatible with inelastic scattering via a failed reaction mechanism, whereas the hydrogen exchange reaction has low probability since it favors near-linear H-IH approaches. Low-energy shoulders offset slightly from the monomer peaks are most likely due to inelastic and elastic scattering of the internal hydrogen as it leaves. The photolysis of I*-HI clusters can be identified by an inelastic process in which I* is deactivated, thereby yielding hydrogen atoms having translational energies in excess of the highest monomer peak by slightly less than the iodine spin-orbit splitting. Such a peak in the TOF spectrum is observed. It is inevitable that some 12 is formed with large interatom separation via the photolytic removal of hydrogen, which can occur by either H2 formation (hydrogen abstraction) or sequential photolysis.

Laser induced fluorescence spectra of expansion-cooled NOz/Ne samples (1 and 2 K) are reported for transitions that originate from the lowest rovibronic levels and terminate on levels near Do. At I K, nearly all transitions originate from N"=O. With the present resolution of 0.02 cm -1, the I K spectra are resolved rather well. The high density of transitions is due to couplings between rovibronic levels with different Nand K quantum numbers and with electronic characters that borrow oscillator strength from bright B 2 vibronic species of the mixed 2 A 1;2 B 2 electronic system. Just above reaction threshold, such rovibronic species comprise the manifold of levels sampled by optically prepared wave packets. However, at higher energies we argue that the density of B z vibronic species is a more relevant parameter to describe the nature of unimolecular reactions. Nuances of the optical excitation process are discussed.