Rotational Quantum State Distributions Research Articles

Full-dimensional quantum molecular dynamics calculations of the rovibrationally mediated X 1A′ → 2 1A′′ transition of nitrous oxide

A full dimensional time-dependent quantum wavepacket approach is used to study the photodissociation dynamics of nitrous oxide for the X 1A′ → 2 1A′′ bound–bound transition based on new highly accurate potential energy and transition dipole moment surfaces. The computed 2 1A′′ absorption spectra at room temperature are characterized by sharp vibrational structures that contribute slightly to the diffuse vibrational structures around the maximum peak at 180 nm of the first ultraviolet absorption band (from the contribution of 2 1A′, 1 1A′′, and 2 1A′′ states) of N2O. Transitions from different initial rovibrational states reveal that the sharp structures arise mainly from N2O bending vibrations, whereas, at higher temperatures, the N2O and NNO stretching vibrations are responsible for enhancing the intensity of the structures. At absorption wavelengths 166 nm and 179 nm, vibrational quantum state distributions of N2 product fragments decrease monotonically with increasing vibrational quantum number v = 0, 1, 2. At 166 nm, rotational quantum state distributions of N2 at fixed v = 0 and v = 1 display multimodal profiles with maximum peaks at j = 77 and j = 75, respectively, whereas, the distributions at the 179 nm absorption wavelength display bimodal profiles with maximum peaks at j = 73 and j = 71, respectively. Accordingly, the presence of rotationally hot N2 from previous experimental and theoretical works in the first band strongly implies a significant influence of the 2 1A′′ state in determining the final dissociation pathway of N2 + O. © 2016 Wiley Periodicals, Inc.

UV Photolysis of N2O Isotopomers: Isotopic Fractionations and Product Rotational Quantum State Distributions

The time-dependent quantum wave packet method is used to study the dynamics of the photodissociation processes for the isotopomers 14N14N16O, 14N15N16O, 15N14N16O, 15N15N16O, 14N14N17O, and 14N14N18O. In general, the computed isotopic fractionation factors derived from the absorption cross sections of five heavy isotopomers are in good agreement with the experimental results. Relative to the 14N14N16O isotopomer, the N2 rotational state distributions for the isotopically nitrogen substituted N2O are found to be entirely shifted to higher rotational states. Similar to its isotopic fractionation factors, the N2 rotational state distributions for the asymmetric isotopomers 14N15N16O and 15N14N16O are found to be observably different.

Quantum Mechanical Calculation of Energy Dependence of OCl/OH Product Branching Ratio and Product Quantum State Distributions for the O(1D) + HCl Reaction on All Three Contributing Electronic State Potential Energy Surfaces

OCl/OH product branching ratios are calculated as a function of total energy for the O( (1) D) + HCl reaction using quantum wavepacket methods. The calculations take account of reaction on all the three electronic state potential energy surfaces which correlate with both reactants and products. Our results show that reaction on the excited electronic state surfaces has a large effect on the branching ratio at higher energies and that these surfaces must therefore be fully taken into account. The calculations use the potential energy surfaces of Nanbu and co-workers. Product vibrational and rotational quantum state distributions are also calculated as a function of energy for both product channels. Inclusion of the excited electronic state potential energy surfaces improves the agreement of the predicted product vibrational quantum state distributions with experiment for the OH product channel. For OCl agreement between theory and experiment is retained for the vibrational quantum state distributions when the excited electronic state potential energy surfaces are included in the analysis. For the rotational state distributions good agreement between theory and experiment is maintained for energies at which experimental results are available. At higher energies, above 0.7 eV of total energy, the OCl rotational state distributions predicted using all three electronic state potential energy surfaces shift to markedly smaller rotational quantum numbers.

Quantum dynamical study of the O(D1)+HCl reaction employing three electronic state potential energy surfaces

Quantum dynamical calculations are reported for the title reaction, for both product arrangement channels and using potential energy surfaces corresponding to the three electronic states, 1 1A', 2 1A', and 1 1A", which correlate with both reactants and products. The calculations have been performed for J=0 using the time-dependent real wavepacket approach by Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)]. Reaction probabilities for both product arrangement channels on all three potential energy surfaces are presented for total energies between 0.1 and 1.1 eV. Product vibrational state distributions at two total energies, 0.522 and 0.722 eV, are also presented for both channels and all three electronic states. Product rotational quantum state distributions are presented for both product arrangement channels and all three electronic states for the first six product vibrational states.

Correlated vH2 and jCO product states from formaldehyde photodissociation: Dynamics of molecular elimination

A detailed study of the photoinduced molecular elimination pathway of formaldehyde on the ground state surface was carried out using high-resolution dc slice ion imaging. Detailed correlated H(2) rovibrational and CO rotational product quantum state distributions were measured by imaging spectroscopically selected CO velocity distributions following photodissociation at energies from approximately 1800 to approximately 4100 cm(-1) above the barrier to molecular elimination. Excitation to the 2(1)4(1), 2(1)4(3), 2(2)4(1), 2(2)4(3), and 2(3)4(1) bands of H(2)CO are reported here. The dependence of the product rovibrational distributions on excitation energy are discussed in light of a dynamical model which has been formulated to describe the strong product state correlations observed.

Ab initio potential energy surfaces, total absorption cross sections, and product quantum state distributions for the low-lying electronic states of N2O

Adiabatic potential energy surfaces for the six lowest singlet electronic states of N(2)O (X (1)A('), 2 (1)A('), 3 (1)A('), 1 (1)A("), 2 (1)A(") and 3 (1)A(")) have been computed using an ab initio multireference configuration interaction (MRCI) method and a large orbital basis set (aug-cc-pVQZ). The potential energy surfaces display several symmetry related and some nonsymmetry related conical intersections. Total photodissociation cross sections and product rotational state distributions have been calculated for the first ultraviolet absorption band of the system using the adiabatic ab initio potential energy and transition dipole moment surfaces corresponding to the lowest three excited electronic states. In the Franck-Condon region the potential energy curves corresponding to these three states lie very close in energy and they all contribute to the absorption cross section in the first ultraviolet band. The total angular momentum is treated correctly in both the initial and final states. The total photodissociation spectra and product rotational distributions are determined for N(2)O initially in its ground vibrational state (0,0,0) and in the vibrationally excited (0,1,0) (bending) state. The resulting total absorption spectra are in good quantitative agreement with the experimental results over the region of the first ultraviolet absorption band, from 150 to 220 nm. All of the lowest three electronically excited states [(1)Sigma(-)(1 (1)A(")), (1)Delta(2 (1)A(')), and (1)Delta(2 (1)A("))] have zero transition dipole moments from the ground state [(1)Sigma(+)(1 (1)A('))] in its equilibrium linear configuration. The absorption becomes possible only through the bending motion of the molecule. The (1)Delta(2 (1)A('))<--X (1)Sigma(+)((1)A(')) absorption dominates the absorption cross section with absorption to the other two electronic states contributing to the shape and diffuse structure of the band. It is suggested that absorption to the bound (1)Delta(2 (1)A(")) state makes an important contribution to the experimentally observed diffuse structure in the first ultraviolet absorption band. The predicted product rotational quantum state distribution at 203 nm agrees well with experimental observations.

Energy disposal in collisions of nitric oxide with molecular adlayers on transition metal single crystal surfaces: Rotational energy disposal

The dynamics of the scattering of nitric oxide (NO) from well-characterized and ordered layers of carbon monoxide (CO) and ethylidyne (CCH3) adsorbed on a Pt(111) substrate have been investigated through resonance-enhanced multiphoton ionization (REMPI) measurements of the rotational quantum state distributions of the scattered NO molecules for a range of incident NO translational energies between 10 and 50 kJ mol−1 from scattering substrates at 108 and 300 K. The measurements reveal that, where in principle the interaction potential resembles that of the NO–Ag(111) system more so than that of the NO–Pt(111) system, the scattering differs remarkably from that expected from a weakly bound system in that it occurs both into a trapping-desorption channel and a direct inelastic channel. Experimental data are presented that indicate both an incident translational energy dependence and substrate surface temperature dependence of the scattering, which is interpreted in terms of a hard-cube model.

Scattering state spectroscopy of the reaction Mg*(3s3p 1P1)+CH4→MgH(v=0,1;N)+CH3

We report scattering state spectroscopic studies of the chemical quenching dynamics of Mg*(3p(1P)) by CH4. We have measured the final-state resolved action spectra for the MgH(v=1,N) reactive product channels, following excitation of the Mg*(3p)–CH4 transient bimolecular collision complex. As in earlier work on the ground vibrational state of the product, we have found a strong electronic orbital alignment effect: Reaction to the vibrationally excited product follows only on the attractive excited potential-energy surfaces in “Π-like” symmetry. For both MgH(v=0 and 1) product channels we have found that the rotational quantum state distribution is independent of laser excitation wavelength, indicating that the rotational energy partitioning is determined by exit channel dynamics. However, our results show that the product vibrational energy disposal is a function of excitation laser wavelength, suggesting that the vibrational energy partitioning is correlated with the collisional impact parameter. We have also carried out a careful search for the MgCH3 reactive product in this system, finding no evidence for any observable branching to this product. We discuss the implications of these results for the chemical dynamics of this metal-alkane reaction system.

Photodissociation of acrylonitrile at 193 nm: the CN-producing channel

We report the rotational and vibrational quantum state distribution of the CN(X 2 Σ +) products formed in the 193 nm photolysis of acrylonitrile (vinyl cyanide). The CN product is formed in v = 0 and v = 1 with relative populations of 0.86 and 0.14, respectively. The rotational distributions in both v-levels are well fit to a temperature of approximatelt 1450 K. The results are consistent with a prompt dissociation on the excited electronic potential surface.

Prediction of fragment rotational quantum state distributions in molecular photodissociation processes: HOCl + hv → OH ( j) + Cl

The objective of this Letter is to emphasise the importance of using the correct angular momentum selection rules and angular momentum coupling algebra when computing fragment rotational quantum state distributions in molecular photodissociation processes. Because the effort required for the computation of the quantum molecular dynamics of a dissociating polyatomic molecule increases significantly with increasing total angular momentum quantum number J, it has become common place to treat both the initial and final state in a polyatomic photodissociation process as possessing zero total angular momentum (i.e. J= J′=0). Using the example of the photodissociation of HOCl we show that such a treatment may lead to an incorrect rotational quantum state distribution of the photofragments. The computations and theory are based on a time-dependent quantum dynamical treatment of the problem. The normal approximation ( J= J′=0) is shown to lead to an incorrect estimation of the total photodissociation cross section.

Algebraic variational and propagation formalisms for quantal dynamics calculations of electronic-to-vibrational, rotational energy transfer and application to the quenching of the 3p state of sodium by hydrogen molecules

Two approaches, the outgoing wave variational principle (OWVP) and R-matrix propagation (RMProp), are presented for quantum dynamics calculations of inelastic scattering in systems involving two coupled potential energy surfaces (PES). The two formalisms are applied to Na(3p 2P) collisions with H2 at a total energy of 2.426 eV with zero and unit total angular momentum. This provides a challenging test case because the accessible region of the excited-state potential energy surface intersects the ground-state surface conically and involves H–H internuclear distances that are far larger than their equilibrium values in the ground state. We present the details of the formalisms for treating coupled surfaces, and we present converged results for the quenching probability and final vibrational–rotational quantum state distributions of the quenching agent. Convergence of the transition probabilities is established by convergence checks within each formalism, by obtaining the same results with laboratory-frame and body-frame basis functions in the OWVP formalism, and by obtaining the same results with the OWVP as with RMProp.

Surprising positive correlation between rotational and vibrational excitation in the H+ CDCl 3→HD + CCl 3 reaction

The rotational quantum state distributions of the HD product of the H + CDCl 3→HD + CCl 3 reaction at 1.6 eV collision energy have been measured using coherent anti-Stokes Raman scattering. We observe HD products in v′=0, 1 and 2 with the fraction of available energy in HD rotation increasing as the energy in HD vibration increases. Despite the presumed pseudo-atomic nature of the CCl 3 radical in the reaction, the behavior of this reaction is closer to that of the H + alkane hydrogen atom abstraction reactions than that of the H + HX→H 2 + X (XCl, Br, I) reactions.

State-to-state dynamics of atom+polyatom abstraction reactions. II. The H+C2H6/C3H8→H2(v′,J′) +C2H5/C3H7 reactions

The rotational and vibrational quantum state distributions for the H2 products of the H+HR→H2+R reactions (HR=C2H6 and C3H8 ) at 1.6 eV collision energy have been measured using coherent anti-Stokes Raman scattering. Total reaction cross sections have also been determined. For the total cross sections we find 1.5±0.5 Å2 for the ethane reaction and 2.9±0.8 Å2 for the propane reaction. Although several vibrational states are energetically accessible, we observe H2 products only in v′=0 and v′=1, with the majority in the ground vibrational state. The H2 products are on average rotationally cold as well, and 20% or less of the total energy is partitioned to H2 internal energy. However, the quantum state distributions show a positive correlation of H2 product rotational and vibrational energy. That is, the average rotational energy of the H2 in v′=1 is substantially greater than the average rotational energy of the H2 in v′=0. Comparison with state-to-state dynamics results previously obtained for the kinematically and energetically similar H+CD4→HD+CD3 and H+HCl→H2+Cl reactions seems to indicate that this anomalous energy disposal is an intrinsic characteristic of H + alkane hydrogen atom abstraction reactions at high collision energy. We speculate that this anomalous behavior is the result of inelastic encounters between the nascent H2 and alkyl radical products in the reaction exit channel.

Nascent rotational quantum state distribution of NaH (NaD) from the reaction of Na*(4 2P) with H2, D2, and HD

The nascent rotational quantum state distributions of NaH and NaD products resulting from the reactions of Na*(4 2Pj) with H2, D2, and HD have been determined using the laser pump–probe technique. We have observed a bimodal rotational distribution with a minor component peaking at low J and a major component peaking at high J. We have observed no evidence for a kinematic isotope effect on the product distribution. Our results are consistent with a model wherein the reaction occurs predominantly on the attractive 2B2 potential energy surface in near C2v geometry with the rotational distribution being determined late in the exit channel.

Dynamics of H2 elimination from cyclohexadiene

A comprehensive study of the dynamics of H2 elimination from 1,4 and 1,3 cyclohexadiene is reported. Rotational and vibrational quantum state distributions as well as translation energy distributions for the H2 product are measured. State specific detection of H2 is accomplished with a transform limited vacuum ultraviolet–extreme ultraviolet laser system via (1+1) resonance enhanced multiphoton ionization (REMPI). Rate constants for the H2 elimination and 1,4 to 1,3 isomerization reactions are derived. A (v,J) correlation for H2 with v∥J primarily is observed from anisotropy in the Doppler profiles. A clear picture of the transition state configuration of 1,4 cyclohexadiene is provided from the information obtained.

Dynamics of the reactions of Zn(4s4p 3P1) with H2, HD, and D2: Rotational and vibrational quantum-state distributions of ZnH (ZnD) products

The complete initial vibrational and rotational quantum state distributions of ZnH(ZnD) products in the reactions of Zn(4s4p 3P1) with H2, HD, and D2 have been determined using a laser ‘‘pump-and-probe’’ technique. The most striking result is that the quantum-state distributions of ZnH (or ZnD) products are essentially unchanged when the mass of the leaving atom is doubled, from H to D. It is suggested that this indicates that simple impulsive bond breaking cannot play a large role in the reaction of Zn(3P1) with H2, and that potential surface anisotropy in the decomposition of bent H–Zn–H insertion intermediates could be responsible for the rotational energy distributions of the products. Similar isotopic results for reactions of Cd(5s5p 3P1), Hg(6s6p 3P1), and O(1D2) with H2, HD, and D2 are noted, and the general implications of the lack of an isotope effect are discussed in detail. The branching ratio of ZnD vs ZnH formation in the reaction of Zn(3P1) with HD was determined to be 1.1±0.2 and it was pointed out that several ‘‘insertion’’ reactions have now been shown to have branching ratios for reaction with HD which are very near 1.0, inconsistent with earlier qualitative arguments that such processes should lead to high branching ratios.

Dynamics of the reactions of Mg(3s3p 1p 1) with H 2, HD, and D 2: Rotational quantum state distributions of MgH (MgD) products

The initial bimodal distributions of product MgH(ν = 0) rotational states in the reaction of Mg( 1P 1) with H 2 or HD are found to be identical. Similar results were found for MgD (ν = 0) produced from D 2 or HD. From these as well as other recent results, it is proposed that both the predominant “high- N” as well as the minor “low- N” components of the distributions result from insertion of Mg( 1P 1) into the H-H bond, and that there are two different primary modes of decomposition of the isotopic H-Mg-H intermediates.

Orbitally selective chemical reaction in Hg–H2 van der Waals complexes

A new technique is described for probing the reaction dynamics of ‘‘half-collisions’’ in systems where ‘‘full-collision’’ chemical dynamics can also be studied. By selective laser excitation of an atom–molecule van der Waals complex, an electronically excited atom can be created at a known distance from, and with a known orbital symmetry with respect to, the reactive molecule. From spectra of the complex and from detection of nascent products in a state-resolved fashion, not only can a great deal be learned about the dynamics of the half-collision, but comparison can also be made with analogous full-collision dynamical information. Reported here are initial results involving the Hg⋅H2 van der Waals complex. When the Hg (6s 1S0)⋅H2 ground-state complex is excited to the Hg(6p 3P1)⋅H2 complex with frequencies near that of the Hg(6 1S0–6 3P1) free atom transition, the molecular product HgH(X 2Σ+) is readily detected. No fluorescence of the Hg(6p 3P1)⋅H2 complex is observed, nor is Hg(6p 3P0) detected as a major product. The two electronic configurations of the excited Hg(6p 3P1)⋅H2 complex, 3Σ and 3Π (which correspond approximately to axial and perpendicular orientation, respectively, of the p orbital with respect to the freely rotating H2 molecule) exhibit different behavior. The reaction to form HgH (X 2Σ+) via the 3Π complex is ‘‘direct,’’ i.e., occurs within 0.1 ps, since the HgH(X 2Σ+) action spectrum for 3Π excitation is continuous. In contrast, there is rovibrational structure in the HgH (X2 Σ+) action spectrum for 3Σ excitation, showing that HgH(X 2Σ+) formation in this case is ‘‘indirect,’’ i.e., occurs on a time scale between 2 ps and 1 ns. Furthermore, the HgH (X 2Σ+, v=0) rotational quantum-state distribution from 3Σ complex excitation is bimodal, with a major component quite similar to that resulting from excitation of the 3Π complex, but with a minor component present at low N. Possible explanations of these results, which definitely show orbitally selective chemical reactivity, are discussed. Because the initial total angular momentum of the Hg⋅H2 complex is approximately zero in the cold supersonic jet, the distribution of exit–channel impact parameters could be determined from HgH (X 2Σ+, v=0) rotational state distributions. For 3Π excitation the fairly narrow distribution is peaked at 1.2 Å, and geometrical considerations indicate that energy release into rotation most likely results from the angular dependence of the exit–channel potential surface of an H–Hg–H species and not from H–H bond-breaking impulsion. The angular dependence could result from transitions from the bent excited triplet to the linear ground-state singlet surface of H–Hg–H. The HgH (X 2Σ+, v=0) initial rotational state distribution from the thermal reaction Hg(6p 3P1) +H2 → HgH(X 2Σ+)+H, measured independently at 300 K, was found to be similar to that for half-collision excitation of Hg⋅H2(3Π), but somewhat broadened. This was interpreted to mean that the thermal reaction proceeds via insertive Π attack of the H–H bond, and that exit-channel forces, rather than initial orbital angular momentum, play the dominant role in determining rotational energy disposal in this reaction. From preliminary measurements of HgH (X 2Σ+, v=1,2) rotational state distributions, it is also proposed that the known Hg(1S)+H+H product channel in the 300 K thermal reaction results merely from the known predissociation of highly rotationally excited HgH (X 2Σ+, v=1,2) produced initially.

Nascent internal energy distributions of MgH produced in the reaction of Mg(3s3p 1P1) with a variety of polyatomic molecules

Nascent rotational quantum state distributions of MgH(v=0,1) produced in the reactions of excited Mg(3s3p 1P1) with a variety of polyatomic molecules have been determined using the laser pump-and-probe technique. The distributions are generally bimodal, with one component peaked at low rotational energy and another component at high values of the rotational quantum number N. Except for (CH3)2O, and (C2H5)2O, which produced very little rotationally excited MgH, all compounds with C–H, N–H, and or O–H bonds showed microscopic branching ratios for the ‘‘high-N’’ component of 0.5±0.1. For the reactants SiH4, GeH4, and PH3, the high-N branching ratio was ≥0.9. The results are interpreted in terms of competition between side-on, insertive, and end-on, abstractive attack of the reagent bonds. Little vibrational energy was found in MgH product for any molecule, consistent with extremely ‘‘late’’ energy release for these heavy–light–heavy kinematic conditions. The results are compared to those from similar studies of the reactions of O(3P), O(1D), and F(2P).

Reaction of Mg(3s3p1P1) with a variety of alkyl C–H bonds: Identical initial MgH(X 2Σ+, v=0) rotational quantum state distributions

The initial distributions of rotational quantum states of MgH(X 2Σ+, v=0) produced in the reaction of electronically excited Mg(3s3p1P1) with a variety of hydrocarbons containing alkyl C–H bonds have been found to be identical within experimental error. The distribution is peaked at fairly low values of rotational angular momentum (N≂10). This is in stark contrast to the reaction of Mg(1P1) with H2, where very high rotational excitation is observed and has been ascribed to side-on attack of the H–H bond. It is proposed that Mg(1P1) attacks alkyl C–H bonds directly in a relatively narrow cone of angles around the C–H bond axis and that the strength or location of a particular C–H bond has little effect on the dynamical process. Possible reasons for the differences in H2 and hydrocarbon as reactants are discussed, and the hydrocarbon results are compared to those reported by Luntz and co-workers on the reactions of O(3P) and O(1D2) with alkyl C–H bonds.