Product Vibrational State Research Articles

Mode selective chemistry in the reactions of OH with HBr and HCl

Quantum scattering calculations are reported for the reactions OH+HCl→H2O+Cl and OH+HBr→H2O+Br. The rotating bond approximation is used. This involves the explicit treatment of the bending vibration and local OH stretching vibration in H2O together with the vibration of HX (X=Cl,Br) and rotation of OH. Simple potential energy surfaces for the reactions are used which contain an accurate potential for H2O. The transition state of the potential for the OH+HCl reaction agrees quite well with ab initio data. The most likely product vibrational state of H2O is the ground state for the OH(j=0)+HCl reaction, and the combination band that has one quantum of energy in the H2O bending mode and one quantum in the local OH stretching mode of H2O for the OH(j=0)+HBr reaction. The reaction cross sections are found to depend on (2j+1)−1, where j is the initial rotational quantum number of OH. This results in a T−1/2 dependence in the rate constant for the OH+HBr reaction at low temperatures, in agreement with experiment.

A high resolution crossed molecular beam investigation of the absolute cross sections and product rotational states for the reaction F+D2 (v i=0; j i=0,1)→DF(v f;j f)+D

High resolution time of flight spectra of DF products have been measured for 12 different center-of-mass angles in the range θc.m.=114° to 180° for the reaction F+D2→DF+D at a center-of-mass collision energy of Ec.m.=82.5±2.6 meV. The resolution is sufficient to clearly resolve the different final product vibrational states and to extract rotational product distributions for each of the vibrational states. Absolute reactive cross sections for the final vibrational states vf=1, 2, 3, and 4 were determined from a careful calibration of the beam source intensities and detector sensitivity. For all final vibrational states, nearly the same large rotational surprisal values of Θ̄R=5.3 were found. From the rotational distributions, it has also been possible to estimate opacity functions for these final vf states via the method of Elsum and Gordon [J. Chem. Phys. 76, 3009 (1982)]. The angular distributions for different vf states are compared to recent infinite order sudden approximation (IOSA) and classical trajectory calculations and the general trends with angle are in good agreement. The absolute values of the differential cross sections differ by as much as a factor of 10. The overall reactive cross section is smaller by about a factor of 2 than the most recent classical trajectory calculations, but the difference is barely within the large experimental errors. These new experiments provide critical data for further improving the parameters of the potential hypersurface.

Dynamics and Product Vibrational State Distributions of the Reaction of the F-N=C→F-C≡N

用数值方案，在RHF／3－21G分子轨道从头算法的水平上，得到了氟化异氰FNC到氟化氰FCN重排反应的反应途径（内禀反应坐标IRC）．沿着IRC；讨论了反应过程中体系几何构型的变化，计算了沿IRC运动与垂直于IRC简正振动之间的耦合常数（BK，F），各振动模式对应的频率（ωK），使用统一的半经典徽扰和无限级突然（SCP－IOS）近似理论计算了在一定能量下产物的振动分配.结果表明，在过渡态后，耦合常数（BK,F）的大小强烈地影响产物的振动态分布,另外用传统过渡态、变分过渡态理论及相关的隧道效应校正计算了该反应的速率常数.

Theoretical studies of energy transfer and reaction in H+H2O and H+D2O collisions

We present the results of a quasiclassical trajectory study of vibration–rotation excitation and reaction in H+H2O(000) and H+D2O(000) collisions, including detailed comparisons with experiment. All calculations have used a semiempirical potential surface due to Schatz and Elgersma, and the H2O initial and final states were numerically determined by solving for the good action variables associated with vibrational motions. Our studies of collisional excitation emphasize comparisons with recent experiments by Lovejoy, Goldfarb, and Leone [J. Chem. Phys. 96, 7180 (1992)] in which fast hydrogen atoms produce vibrationally and rotationally excited water. As in the experiments, we find a propensity for the production of rotational states in which the rotational angular momentum vector is predominantly aligned perpendicular to the water molecule plane (c-axis excitation). This propensity is found for all excited vibrational states of H2O, but it is significantly stronger in the experiments [where only the (001) state was studied] than in the calculations. An analysis of trajectory motions indicates that the primary excitation mechanism for states which show the c-axis propensity involves a nearly planar collision in which the incoming H impulsively strikes one of the water hydrogens. Failed reactive collisions associated with either abstraction or exchange as well as reactive exchange collisions give the same propensity but they are not the dominant mechanism for producing aligned water. In studies of the reaction H+D2O→OD+HD, we analyze product vibrational and rotational state distributions in detail, making comparison with recent studies of Adelman, Filseth, and Zare [preceding paper, J. Chem. Phys. 98, 4636 (1993)] as well as earlier work. The product HD energy partitioning is found to be in excellent average agreement with experiment, with the HD receiving much more of the available energy than does OD. There are, however, differences in some of the HD rotational distributions, with the experiment showing a much stronger inverse correlation between HD rotational and vibrational excitation than is found in the calculations.

The ridge of the specific opacity surface in heavy heavy–light chemical reactions

An approximate one-to-one correspondence between the value of the product vibrational state and the location of the interval of impact parameter open to reaction has been found for direct Mg+HF→MgF+H reactive collisions. This gives rise to a ridge in the specific opacity function surface.

The HeCl2 potential: A combined scattering-spectroscopic study

Total differential scattering angular distribution measurements for He scattering from Cl2 are reported. The scattering data are combined with previous excitation spectroscopy and vibrational predissociation product state distributions for He–Cl2 to determine the potential-energy surfaces for the ground X and excited B electronic states. The potentials are somewhat deeper, De=−38.2 cm−1 for the X state, than previously estimated. The X state potential minimum is for the ‘‘T’’ shaped configuration with a Rmin value of 3.55 Å. The potentials are quite successful at describing the scattering data, the rotationally resolved spectroscopy of the complex, and the product state distributions for vibrational predissociation. The B state potential underestimates the dependence of the rate of vibrational predissociation on the initial vibrational level.

Product rotational distributions and specific opacity functions for the reaction Ba +HI → BaI (v=0,4,8,12,16,18) +H

The reaction Ba+HI→BaI(v)+H was studied under beam-gas, single-collision conditions with an average center-of-mass collision energy of 13 kJ mol−1. BaI (v) rotational distributions were recorded for v=0, 4, 8, 12, 16, and 18 by means of selectively detected laser-induced fluorescence of the BaI C 2Π–X 2Σ+ band system. Each rotational distribution exhibits a maximum toward its high energy end and the range of rotational states becomes narrower as product vibration increases. Because the kinematic constraint causes almost all reagent orbital angular momentum to appear in product rotation, the principle of angular momentum conservation provides the means for determining specific opacity functions from the rotational distributions and the reagent relative velocity distribution. The specific opacity functions are narrow functions of the impact parameter. The peak values decrease smoothly from approximately 4.5 Å for v=0 to 1.5 Å for v=18, indicating a strong correlation between impact parameter and product vibrational state such that Ba+HI collisions with small impact parameter produce BaI with large vibrational excitation.

Measurement of relative state-to-state rate constants for the reaction D+H2(v, j)→HD(v′, j′)+H

We have measured state-to-state integral rate constants for the reaction D+H2(v,j) →HD(v′=0,1,2;j′)+H, in which the H2 reagent was either in the ground state, H2(v=0,j), or prepared in the first excited vibrational state, H2(v=1, j=1), by stimulated Raman pumping. Translationally hot D atoms were produced via UV photolysis of DI, generating two center-of-mass collision energies corresponding to the two I atom spin–orbit states. Resonance-enhanced multiphoton ionization and time-of-flight mass spectrometry were employed to detect the nascent HD product in a quantum-state-specific manner. Two experimental geometries were used: (1) a probe-laser-induced geometry, in which the same laser both initiated the reaction, by photolysis of DI, and detected the HD and (2) an independent-photolysis-source geometry, in which photolysis of DI was carried out by an independent laser. We find that vibrational excitation of the H2 reagent results in substantial HD rotational excitation for each product vibrational state, a shift in the vibrational product state distribution such that the rates for the reaction D+H2(v=1, j=1) into HD(v′=0) and HD(v′=1) are comparable, and somewhat surprisingly, almost no change in the total rate into HD(v′=0,1,2;j′). The experimental results are consistent with a model in which internal energy is conserved, i.e., internal energy of the reagents appears as internal energy of the products, while relative translational energy of the reagents appears primarily as translation of the products. Good to excellent agreement is found between the experiment and recent quantum-mechanical scattering calculations of Neuhauser, Judson, and Kouri. Minor discrepancies persist, however, between theory and experiment for some product rotational distributions.

Laser fluorescence study of the Pb+F2, Cl2 reactions: Internal state distribution of the PbCl product and radiative lifetimes of PbF(A,B) and PbCl(A)

The reactions of Pb atoms with molecular reagents F2 and Cl2 have been studied in a molecular beam apparatus by laser fluorescence detection of PbF and PbCl products. The experiments were performed in a beam-gas configuration under single-collision conditions. The PbCl product from Pb+Cl2 was observed in the vibrational levels v≤17 of the ground X1 electronic state. The PbCl product vibrational state distribution was derived; the average vibrational excitation was found to be 21% of the total available energy. For Pb+F2, PbF(X1) product was detected in only the v=0 and 1 vibrational levels, and the rovibrational state distribution could be characterized by a 300 K Boltzmann distribution. By modulating the Pb beam, it was concluded that this observed product was an artifact and did not arise from bimolecular gas-phase collisions. The radiative lifetimes of the PbF(A,B) and PbCl(A) states were also measured and were found to equal 4.9±0.3 μs, <10 ns, and 1.14±0.06 μs, respectively, averaged over the observed vibrational levels.

Vibrational predissociation in S1 indole van der Waals clusters

The excited state dynamics of the indole(Ar)1, indole(d1)(Ar)1, indole(Ar)2, and indole(CH4)1 van der Waals clusters have been investigated in a free jet expansion. Excited state vibrational frequencies were determined using multiphoton ionization and fluorescence excitation spectroscopy. Time resolved emission spectroscopic techniques were used to determine vibrational predissociation rates and product state distributions. All of the clusters were found to predissociate when excited with sufficient vibrational energy in the S1 state. The predissociation dynamics were found to be consistent with a serial model in which energy transfer from the indole skeletal modes to the van der Waals modes precedes the dissociation step. The density of van der Waals vibrational states was found to be the most important factor in determining the predissociation dynamics.

Spectroscopy and dynamics of He2Cl2: A quantum liquid cluster?

The two color pump–probe technique has been used to study the B←X excitation spectrum and vibrational predissociation product state distribution of He2Cl2. Although the excitation spectrum of the complex shows distinct rotational structure and the expected rotational temperature of the complex is below 1 K, we are unable to even approximately reproduce the band shape with a rigid rotor analysis. The main dissociation channel for the complex involves the transfer of two quanta of Cl2 stretching motion, almost certainly in a sequential process. The product Cl2 rotational distribution is remarkably similar to that of HeCl2 undergoing Δv=−2 dissociation. One reason for the similarity between the HeCl2 and He2Cl2 dissociation product state distributions is that vibrational excitation of the HeCl2 van der Waals modes has little effect on the product state distribution. He2Cl2 provides an example of an extremely floppy, liquidlike cluster whose spectroscopy and dynamics can be studied with detailed state resolution.

Converged three-dimensional quantum mechanical reaction probabilities for the F+H2 reaction on a potential energy surface with realistic entrance and exit channels and comparisons to results for three other surfaces

Accurate three-dimensional quantum mechanical reaction probabilities are presented for the reaction F+H2→HF+H on the new global potential energy surface 5SEC for total angular momentum J=0 over a range of translational energies from 0.15 to 4.6 kcal/mol. We find that the v′=3 HF vibrational product state has a threshold as low as for v′=2. We also find considerable structure in the reaction probability and cumulative reaction probability curves which may be indicative of resonance structures. We compare these results to those for another potential energy surface 5SEC-W, which differs from surface 5SEC in the magnitude of the van der Waals well in the entrance channel, and to those for two previous potential energy surfaces.

Influence of transition state resonances on integral cross sections and product rovibrational distributions for the Cl+HCl→ClH+Cl reaction

An accurate quantum scattering calculation for the Cl+HCl→ClH+Cl reaction has been performed. In particular, we study the influence of the lowest transition state resonance on the energy dependence of the state-to-state integral cross sections and product rovibrational distributions. The calculations use a recently developed centrifugal sudden hyperspherical (CSH) coordinate reactive scattering code. The Bondi–Connor–Manz–Römelt semiempirical potential energy surface is employed. All 161 partial waves needed for the convergence of the cross sections are included in the calculations. We find that the resonance perturbs certain reagent and product rotational levels of the vibrational ground state (v=0, j=14–16), as well as all open rotational levels (j=0–8) of the first vibrationally excited state (v=1). Transitions from the ground reagent to the ground product vibrational state, such as v=0, j=15→v′=0, j ′=15, show almost no resonance structure in the integral cross sections; rather direct scattering dominates the partial wave sum. On the other hand, transitions between perturbed v=0 rotational states and any v′=1 rotational state, or between any v=1 state and perturbed v′=0 states, or between any v=1 and any v′=1 state, show a novel resonance feature in the integral cross sections. This novel feature is a sudden smooth ‘‘step’’ in the integral cross section, centered at the resonance energy for the partial wave with zero total angular momentum quantum number (J=0). The step has a width equal to the J=0 resonance width. Sometimes this step is superimposed on a slowly varying background which arises from direct scattering. A quantitative description of these resonant steps in the integral cross sections is developed using a J-shift approximation. Because the resonance influences all rotational states for v=v′=1 in a similar way, there is no significant effect on the product rotational distributions due to the resonance. However, the resonance does produce detectable stepping behavior in the product vibrational distribution.

Bond-breaking without barriers. II. Vibrationally excited products

Ketene is photolyzed in a supersonic jet, and the vibrationally excited singlet methylene CH2 (ã 1A1), produced is detected by laser-induced fluorescence. The appearance thresholds and yield curves of individual methylene rovibrational states are obtained by scanning the photolysis laser wavelength. As observed previously by probing the (0,0,0) state at lower photolysis energies, there are no barriers to dissociation and nuclear spin is conserved. Sharp steps are observed just above the energetic threshold in each of these photofragment excitation (PHOFEX) curves. This suggests that the rotational state distributions are given by phase space theory (PST). The quantum yield of the (0,1,0)101 rovibrational state is measured and the quantum yield for (0,1,0) inferred. These values are larger than predicted by PST, and are close to values predicted by variational Rice–Ramsberger–Kassel–Marcus (RRKM) theory and by the separate statistical ensembles (SSE) method. This indicates that near the (0,1,0) energy threshold the (0,0,0) yield is constrained, as by a tight transition state. The appearance of steps spaced by the energies of a free CO rotor in the PHOFEX curves close to the thresholds of each vibrational state probed indicates that the near threshold flux of vibrationally excited products is controlled by a loose ‘‘transition state’’ on a vibrationally adiabatic surface. These observations are consistent with the variational RRKM theory for dissociations without barriers in which each product vibrational state evolves on its own vibrationally adiabatic potential surface and has its own transition state. As the energy increases above the threshold for a vibrational state, its transition state moves in along the reaction coordinate and tightens. Thus total rates increase less rapidly with energy than in PST and vibrational distributions are skewed towards higher levels than in PST.

State resolved photodissociation of vibrationally excited water: Rotations, stretching vibrations, and relative cross sections

The state resolved photodissociation of highly vibrationally excited water molecules using laser induced fluorescence detection of the OH product demonstrates the control that the initially selected state exerts over product state populations. These vibrationally mediated photodissociation experiments, in which one photon prepares a highly vibrationally excited molecule and a second photon dissociates it, determine the role of overall rotations and of O–H stretching vibrations as well as measure the relative cross section for the photodissociation of water. The rotational state of the vibrationally excited water molecule governs the rotational state of the OH product of the dissociation, in agreement with ab initio calculations and previous measurements on single rotational states excited in the fundamental asymmetric stretching vibration band. The initially selected vibrational state of the water molecule determines the vibrational energy disposal in the products, which agrees with a simple qualitative model based on the pattern of the initially selected vibrational wave function. Dissociating vibrational states with similar energies but very different nuclear motions produces dramatically different product vibrational state populations. The vibrational energy initially present in the surviving bond primarily appears as vibrational excitation of the product. Dissociation of the ‖04〉− state produces no vibrationally excited OH, but dissociation of the ‖13〉− state produces mostly vibrationally excited products. These qualitative notions agree well with recently detailed ab initio calculations. The relative photodissociatiuib cross section of the highly vibrationally excited molecule shows structure over the wavelength range of 218.5 to 266 nm that reflects the nodal pattern of the intermediate vibrational state in the dissociation and confirms the predictions of theoretical calculations.

The infinite-order-sudden-approximation calculations of reactive cross sections and product angular distributions for the F+H2 reaction and its isotopic variants on a modified London–Eyring–Polanyi–Sato potential energy surface

The reactive cross sections and product angular distributions for the F+H2,F+D2 and F+HD reactions have been calculated using the infinite-order-sudden approximation on a modified London–Eyring–Polanyi–Sato potential energy surface which has a nonlinear saddle point. This surface was constructed previously so as to reproduce the experimentally obtained product angular distributions by the quasiclassical trajectory calculations. The calculated branching ratios of different vibrational states of products, HF(v′) and DF(v′) from above three reactions, were all in qualitative agreement with those experimentally obtained; however, the product angular distributions calculated were not better than those calculated by the quasiclassical trajectory method. These results are compared with those calculated on different potential surfaces which predict collinear transition states.

The hydrogen exchange reaction: Discrepancies between experimental state-resolved differential cross sections and 3-D quantun dynamics

Measured time-of-flight (TOF) distributions, corresponding to speed- and angle-resolved differential cross sections for the reaction D + H2 > HD + H, are compared with recently published 3-D quantum calculations. The comparison is made in the man- ner least susceptible to distortion: the energy-, angle- and state-resolved theoretical results in center-of-mass (c.m.) coordinates are projected onto the laboratory angle-time axis, and averaged over all experimental resolution parameters to predict the mea- sured TOF distributions. Features directly visible in the experimental data are: (1) relative populations of the v 1 = 0 and v 1 = 1 product vibrational states, (2) the extent of HD product rotational excitation, and (3) the ratio of differential cross sections near 180 ° c.m. to those near 70° c.m. Significant discrepancies with theory are found with respect to features (2) and (3).

Application of hyperspherical coordinates to four-atom reactive scattering: H2+CN→H+HCN

We develop the use of Delves’ hyperspherical coordinates to study the reactive scattering of four-atom systems within the collinear approximation. We present quantum mechanical calculations of reaction probabilities for the collinear exothermic reaction H2+CN →H+HCN. We use a potential energy surface which reproduces the essential characteristics of the reaction. The effect of freezing the CN bondlength to its equilibrium value during the reaction is also investigated and is found to be a good approximation. It is found that HCN product vibrational states with the C–H stretch excited are produced preferentially in the reaction.

Vibrational heating of CuF desorbing from defined copper surfaces in reactions with molecular or atomic fluorine

This study reports on a laser-induced fluorescence product state analysis of nascent CuF formed in the reaction of fluorine with solid copper. To our knowledge, this is the first state-specific investigation of an etching reaction. In the experiment a molecular or atomic fluorine beam impinges on a Cu(111), (110) single-crystal surface or on a polycrystalline sample. When He seeded beams are used, the reagent translation is increased to ∼ 40 kJ mol . The temperature of the surface is regulated up to 1050 K. The LIF analysis of the reaction products is based on excitation of the C 1 Π −X 1Σ + transitions of CuF by means of a CW dye laser. The onset of CuF release into the gas phase occurs at about 750 K.The temperature dependence of the relative rate of CuF formation implies an apparent activation energy of ∼ 110 kJ mol . which is regarded as a lower limit for the desorption of CuF from the substrate. This value does not significantly vary when the orientation of the surface is changed from (110) to (111) or when a polycrystalline sample etched. It also holds for both atoms and molecules as reactants. The vibrational product state analysis in the X 1Σ + ground state of CuF yields distributions of the Boltzmann type. However, the vibrational temperatures are about 200–300 K higher than the corresponding surface temperatures in the regime of 770–1000 K. This observation again holds for both atoms and molecules and was also verified for the three different copper surfaces. No effect of increased reagent beam velocity was observed. The experimentally determined product state distributions are compared with coupled channel calculations based on a simplified model. Good agreement was obtained.

Converged three-dimensional quantum mechanical reaction probabilities and delay times for the F+H 2 reaction on a potential energy surface with a realistic exit valley

Fully converged quantum mechanical F+H 2→HF+H reaction probabilities are reported for initial rotational quantum numbers j=0, 2, and 4, total angular momentum J=0, and a range of translational energies from 0.7 to 3.4 kcal/mol for potential energy surface No. 5A of Steckler et al. State-to-state delay times are also calculated and are used to test for the occurrence of resonances. We find that the ν′=3 HF product vibrational state has no delay in its threshold compared to ν′=2. Furthermore, no resonance structure is observed in the time delays for orbital angular momentum l=0. Both findings are consistent with experiment. The ν′=3 probability is higher than that for ν′=2 for initial l=0, but the ratio decreases for higher l.