Initial Rotational Quantum Number Research Articles

Extended calculations of nitrogen-induced line broadening coefficients in the [formula omitted] band of ethylene

Computations of room-temperature N2-broadening coefficients are performed for 3546 lines in the ν7 infrared absorption band of ethylene to provide data required for atmospheric studies but missing in spectroscopic databases. The calculations are done in the framework of a semi-classical exact-trajectory approach developed previously (Buldyreva and Nguyen, 2008). The active molecule is rigorously treated as an asymmetric top and the perturber is traditionally considered to be in its ground vibrational state. The data are provided for the P,RP-, P,RQ- and P,RR-subbranches (lines with ΔKa=±1 having observable intensities) for (initial) rotational quantum numbers J up to 22, limited by the available numerical energies for the excited vibrational level. Moreover, potentially detectable lines with ΔKa=±3 are also considered for J≤13, limited by high computational cost. Being validated by comparison with existing experimental results, these data can replace unavailable measurements and will be useful for atmospheric/industrial applications.

Bending Relaxation of H2 O by Collision with Para- and Ortho-H2.

We extend our recent theoretical work on the bending relaxation of H2 O in collisions with H2 by including the three water modes of vibration coupled with rotation, as well as the rotation of H2 . Our full quantum close-coupling method (excluding the H2 vibration) is combined with a high-accuracy nine-dimensional potential energy surface. The collisions of para-H2 O and ortho-H2 O with the two spin modifications of H2 are considered and compared for several initial states of H2 O. The convergence of the results as a function of the size of the rotational basis set of the two colliders is discussed. In particular, near-resonant energy transfer between H2 O and H2 is found to control the vibrational relaxation process, with a dominant contribution of transitions with = , and being respectively the H2 initial and final rotational quantum numbers. Finally, the calculated value of the H2 O bending relaxation rate coefficient at 295 K is found to be in excellent agreement with its experimental estimate.

Time-dependent quantum wave packet calculation for reaction S−(2P)+H2(1Σg+)→SH−(1Σ)+H(2S) on ab Initio potential energy surface

The time-dependent wave packet propagation method was applied to investigate the dynamic behaviours of the reaction S−(2P)+H2(1Σg+)→SH−(1Σ)+H(2S) based on the electronic ground state (2A′) potential energy surface of the SH2− ionic molecule. The collision energy dependent reaction probabilities and integral cross sections are obtained. The numerical results suggest that there are significant oscillation structures over all the studied range of the collision energies. The vibrational excitation and rotational excitation of the diatomic reagent H2 promote the reactivity significantly as suggested by the numerical total reaction probabilities with the initial rotational quantum number of j = 0, 2, 4, 6, 8, 10, and the vibrational quantum number v = 0, 1, 2, 3, 4. The numerical integral cross sections are quite consistent with the experimental data reported in previous work.

Competing Dynamical Mechanisms in Inelastic Collisions of H + HF.

The dynamics of inelastic collisions between HF and H has been investigated in detail by means of time-independent quantum mechanical calculations on the LWA-78 potential energy surface ( Li , G. ; et al. J. Chem. Phys. 2007 , 127 , 174302 ). Reaction probabilities, differential cross sections, and three-vector correlations have been calculated and analyzed. Our results show that there are two competing collision mechanisms that correlate with low and high impact parameters and show very different stereodynamical preferences. The mechanism promoted by high impact parameters is the only one present at low collision energies. We also observe the presence of an apparent threshold in the inelastic cross section for relatively high initial HF rotational quantum numbers, which is associated with the larger energy difference between adjacent rotational quantum states with increasing rotation.

A quasiclassical trajectory calculation to compute the reaction cross section and thermal rate constant for the cesium exchange reaction 133CsI + 135Cs → 133Cs + I135Cs

To compute the reaction cross section and the thermal rate constant of the cesium exchange reaction 133CsI + 135Cs → 133Cs + I135Cs in the temperature range 500–1500 K, we performed a quasiclassical trajectory calculation using a potential energy surface developed from an ab initio calculation at the MP2/def2-QZVPPD level. The state-specific cross sections and their dependences on the initial vibrational and rotational quantum numbers of 133CsI (v and j, respectively) were analyzed. The v-j thermally averaged cross section and its dependence on the collision energy was also analyzed. The thermally averaged rate constant is above 3.6 × 10−10 cm3 molecule−1 s−1 and slightly increases with temperature within the investigated temperature range. The positive temperature dependence might indicate that the title reaction is controlled by long-range dispersion forces. The subsequent dissociation step might also contribute to the positive temperature dependence.

Description of an air temperature sensor based on O2 absorption spectroscopy.

In this paper, we describe in detail an assembled open-path optical cavity to act as a temperature sensor of air. A metal absorption cell in a temperature-regulated tube furnace is placed at the center of an optical cavity. The optical cavity consists of two mirrors, two nitrogen buffer sleeves, and the open cell. The air is injected through a fitting in one extreme of the metal tube and travels half the tube length through a channel in the wall of the tube. The channel directs the air towards the center of the cell. The air flowing is heated at the temperature of the metal tube in contact with the furnace. The heated air injected at the center of the tube, flows towards the open extremes of the tube. The nitrogen buffer sleeves protect the mirrors from the heated air. The temperature of the air flowing through the tube is determined by measuring the absorption of the A band of oxygen as a function of the wavenumber in the 769-755 nm wavelength range. The absorption technique is phase-shift cavity ring down spectroscopy. To obtain the temperature, the energy of the lower rotational state for eleven selected rotational transitions is linearly fitted to a logarithmic function that contains the relative intensity of the rotational transition, the initial and final rotational quantum numbers and the energy of the transition. Accuracy of the measurement is determined by comparing the calculated temperature from the spectra with the analog reading of the temperature-regulated tube furnace. This technique is proposed for exhaust air temperature measurements of combustion chambers and cooling air after passing through the blades of a turbine.

Energy transfer dynamics for H+HF(<italic>v, j</italic>)→H+HF(<italic>v</italic><italic><x content-type="symbol">¢</x></italic><italic>, j</italic><italic><x content-type="symbol">¢</x></italic>)

A series of vibrational relaxation rate constants for H+HF( v =1, j )→H+HF( v ′ =0, j ′ ) were calculated by time-independent close coupling approach, based on the CSZ potential energy surface. Within the temperature range from 295 to 500 K, all the rotational-resolved rate constants increase monotonically with temperature, and the rotational quantum number of the dominating final state is larger than the initial rotational quantum number. At room temperature, the vibrational-resolved rate constant is in reasonably agreement with some experimental data. The rate constants for the pure rotational energy transfer process H+HF( v =1, j )→H+HF( v ′ =1, j ′ ) at 500 K were also calculated. They are several magnitudes larger than the ro-vibational relaxation rates. It was found that the rate constants of Δ j = − 1 are approximately twice as large as those of Δ j = 1 , except for the (1,1) initial state.

Cavity Ring-Down Absorption of O2 in Air as a Temperature Sensor for an Open and a Cryogenic Optical Cavity.

The A-band of oxygen has been measured at low resolution at temperatures between 90 K and 373 K using the phase shift cavity ring down (PS-CRD) technique. For temperatures between 90 K and 295 K, the PS-CRD technique presented here involves an optical cavity attached to a cryostat. The static cell and mirrors of the optical cavity are all inside a vacuum chamber at the same temperature of the cryostat. The temperature of the cell can be changed between 77 K and 295 K. For temperatures above 295 K, a hollow glass cylindrical tube without windows has been inserted inside an optical cavity to measure the temperature of air flowing through the tube. The cavity consists of two highly reflective mirrors which are mounted parallel to each other and separated by a distance of 93 cm. In this experiment, air is passed through a heated tube. The temperature of the air flowing through the tube is determined by measuring the intensity of the oxygen absorption as a function of the wavenumber. The A-band of oxygen is measured between 298 K and 373 K, with several air flow rates. To obtain the temperature, the energy of the lower rotational state for seven selected rotational transitions is linearly fitted to a logarithmic function that contains the relative intensity of the rotational transition, the initial and final rotational quantum numbers, and the energy of the transition. Accuracy of the temperature measurement is determined by comparing the calculated temperature from the spectra with the temperature obtained from a calibrated thermocouple inserted at the center of the tube. This flowing air temperature sensor will be used to measure the temperatures of cooling air at the input (cold air) and output (hot air) after cooling the blades of a laboratory gas turbine. The results could contribute to improvements in turbine blade cooling design.

Cold atomic and molecular collisions: approaching the universal loss regime

We investigate the behaviour of single-channel theoretical models of cold and ultracold collisions that take account of inelastic and reactive processes using a single parameter to represent short-range loss. We present plots of the resulting energy-dependence of elastic and inelastic or reactive cross-sections over the full parameter space of loss parameters and short-range phase shifts. We then test the single-channel model by comparing it with the results of coupled-channel calculations of rotationally inelastic collisions between LiH molecules and Li atoms. We find that the range of cross-sections predicted by the single-channel model becomes increasingly accurate as the initial LiH rotational quantum number increases, with a corresponding increase in the number of open loss channels. The results suggest that coupled-channel calculations at very low energy (in the s-wave regime) could in some cases be used to estimate a loss parameter and then to predict the range of possible loss rates at higher energy, without the need for explicit coupled-channel calculations for higher partial waves.

Two dimensional symmetric correlation functions of the ${\rm \hat S}$Ŝ operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the Ŝ operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Quasi-classical trajectory study of the reaction N(4S) + H2 and its reverse reaction: Role of initial vibrational and rotational excitations in chemical stereodynamics

To investigate the effects of reagent vibrational and rotational states on the stereodynamical properties of the N(4S) + H2(v, j) → NH + H reaction and its reverse reaction of H(2S) + NH(v, j) → N(4S) + H2, we reported a detailed quasiclassical trajectory study using the 4A″ double many-body expansion potential energy surface and at the collision energy of 35 kcal/mol. The density distribution of P(θ r) as a function of the angle between \(\boldsymbol{k}\) and \(\boldsymbol{j^\prime} \), and that of P(ϕ r) as a function of the dihedral angle between the plane containing \(\boldsymbol{k}\)–\({\boldsymbol{k^\prime}} \) and the plane containing \(\boldsymbol{k^\prime}\)–\(\boldsymbol{j^\prime} \), the normal differential cross-sections as well as the averaged product rotational alignment parameter \(\left\langle {P_2 \left({\boldsymbol{j^\prime} \cdot \boldsymbol{k}} \right)} \right\rangle \) are calculated and reported. Comparison between the two reactions has showed that the degrees of alignment and orientation of products related to reagent rovibrational state have marked differences for the two reactive systems. The calculated average rotational alignment parameter \(\left\langle {P_2 \left({\boldsymbol{j^\prime} \cdot \boldsymbol{k}} \right)} \right\rangle \) as a function of the initial vibrational and rotational quantum numbers for the N(4S) + H2 and NH + H(2S) reactions, illustrating the dependence of the product alignment on initial vibrational and rotational excitations.

A quasi-classical trajectory study of the reagent initial rotation quantum state effect on the reaction He + T2+→ HeT+ + T using an improved ab initio potential energy surface

In this work, we employed the quasi-classical trajectory (QCT) method to study the vector correlations and the influence of the reagent initial rotational quantum number j for the reaction He + T2+(v = 0, j = 0–3) → HeT+ + T on a new potential energy surface (PES). The PES was improved by Aquilanti co-workers (Chem. Phys. Lett. 2009. 469: 26–30). The polarization-dependent differential cross sections (PDDCSs) and the distributions of P(θr), P([Formula: see text]r), and P(θr, [Formula: see text]r) are presented in this work. The plots of the PDDCSs provide us with abundant information about the distribution of the product angular momentum polarization. The P(θr) is used to describe the correlation between k (the relative velocity of the reagent) and j′ (the product rotational angular momentum). The distribution of dihedral angle P([Formula: see text]r) shows the k–k′–j′ (k′ refers to the relative velocity of the product) correlation. The PDDCS calculations illustrate that the product of this reaction is mainly backward scatter and it has the strongest polarization in the backward and sideways scattering directions. At the same time, the results of the P([Formula: see text]r) demonstrate that the product HeT+tends to be oriented along the positive direction of the y axis and it tends to rotate right-handedly in planes parallel to the scattering plane. Moreover, the distribution of the P(θr) manifests that the product angular momentum is aligned along different directions relative to k. The direction of the product alignment may be perpendicular, opposite, or parallel to k. Moreover, our calculations are independent of the initial rotational quantum number.

Collision induced dissociation of protonated urea with N 2: Effects of rotational energy on reactivity and energy transfer via chemical dynamics simulations

In the present work we have investigated the gas phase reactivity of protonated urea after collision with the diatomic inert gas N 2, by studying the energy transfer and fragmentation induced by collisions. We first developed an analytical pair potential to describe the interaction between the projectile and the ion, and then performed QM/MM direct chemical dynamics simulations of the collision between the projectile and protonated urea in its two most stable isomers. In particular, the effect of the diatomic projectile, and the role of its initial rotational state, were compared with the fragmentation and energy transfer obtained previously ( J. Phys. Chem. A 2009, 113, 13853) for the monoatomic projectile Ar. The diatomic projectile was found to be less efficient in energy transfer compared to the monoatomic projectile. In addition, rotational activation of UreaH + is dependent on the initial rotational quantum number of N 2. Finally, we investigated the UreaH + gas phase reactivity as a function of its rovibrational activation by means of chemical dynamics simulations where the initial structure for the simulations is the transition state (TS) that the system can reach after collisional activation of the most stable isomer. The simulation time-length is not able to directly access this TS from the most stable isomer since its lifetime is notably longer, of about two order of magnitude in time.

Influence of Reagent Rotation on (H-, D2) and (D-, H2) Collisions: A Quantum Mechanical Study

Time-independent quantum mechanical (TIQM) approach (helicity basis truncated at k = 2) has been used for computing differential and integral cross sections for the exchange reaction H- + D2 (v = 0, j = 0-4) --> HD + D- and D- + H2 (v = 0, j = 0-3) --> HD + H- in three dimensions on an accurate ab initio potential energy surface. It is shown that the j-weighted differential reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder at four different relative translational energies (Etrans = 0.55, 0.93, 1.16 and 1.48 eV) for (H-, D2) and at one relative translational energy (Etrans = 0.6 eV) by Haufler et al. for both (H-, D2) and (D-, H2) collisions. The j-weighted integral reaction cross section values are in good agreement with the crossed beam measurements by Zimmer and Linder in the Etrans range 0.5-1.5 eV and close to the guided ion beam results by Haufler et al. for (H-, D2) in the range 0.8-1.2 eV. Time-dependent quantum mechanical (TDQM) results obtained using centrifugal sudden approximation are reported in the form of integral reaction cross section values as a function of Etrans in the range 0.3-3.0 eV for both reactions in three dimensions on the same potential energy surface. The TDQM reaction cross section values decline more sharply than the TIQM results with increase in the initial rotational quantum number (j) for the D2 molecules in their ground vibrational state (v = 0) for (H-, D2) collisions. The computed j-weighted reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder for (H-, D2) collisions and guided ion beam results by Haufler et al. for both (H-, D2) and (D-, H2) collisions for energies below the threshold for electron detachment channel.

Rotational effects in the dissociative adsorption of H2 on the Pt(211) stepped surface

Rotational effects in the dissociative adsorption of H2 on the Pt211 stepped surface have been studied using classical trajectory calculations on a six-dimensional, density-functional theory potential-energy surface. Reaction of rotating molecules via an indirect trapping mechanism exhibits an unexpected nonmonotonic dependence on the initial rotational quantum number J. Indirect reaction is first quenched with increasing J but is enhanced again for high J initial states. The quenching is attributed to rotational-to-translational energy transfer, which facilitates escape from the chemisorption wells responsible for molecular trapping. For high J, rotational and translational motions decouple, and the energy transfer is no longer possible, which leads again to trapping. Degeneracy-resolved calculations show that for high initial J, molecules rotating in a "cartwheel" fashion (mJ=0) are more likely to become trapped and react indirectly than "helicoptering" molecules (mJ=J). Experimental confirmation of this finding would lend strong support to the existence of the chemisorption wells that trap molecules prior to reaction.

Reaction cross sections for the H+D2(ν=1)→HD+D and D+H2(ν=1)→DH+H systems. A multiconfiguration time-dependent Hartree (MCTDH) wave packet propagation study

Cumulative initial-state-selected reaction cross sections of the H+D2 and D+H2 systems are computed for collision energies up to 1.6 eV and initial vibrational and rotational quantum numbers ν0=1 and j0=0–4. The Boothroyd–Keogh–Martin–Peterson (BKMP2) potential energy surface is taken as interaction potential. For comparison the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential energy surface is also considered, however, for j0=0 only. The cross sections are computed by propagating wave packets employing the multiconfiguration time-dependent Hartree scheme. The reactive flux, which determines the integral cross section, is evaluated through the interaction of the wave packet with a complex absorbing potential. A new approach of J-interpolation for the reaction probabilities has been developed. This approach allows to skip about every second of the individual propagations. The presence of weak oscillations appearing in the total integral cross sections has been observed. As in our previous calculations [J. Phys. Chem. 105, 2604 (2001)] on ν0=0, we attribute them to transition state resonances associated with excitations of the bending motion. Some of the present results are compared with previous results obtained by using the coupled states approximation.

Vibrational de-excitation of v=1 H2 during collisions with a Cu(100) surface

The dynamics of vibrational de-excitation of v=1 H2 on a Cu(100) surface is studied using a six-dimensional quantum wave packet method. The de-excitation probability increases with increasing collision energy and initial molecular rotational quantum number, j. A strong dependence on molecular orientation is found with molecules rotating with helicoptering motion (mj=j) exhibiting larger de-excitation probabilities, in general, than those with cartwheeling motion (mj=0). The final j-state distribution and quadrupole alignment are computed as functions of collision energy. The competition between vibrational de-excitation and other dynamic processes during the collision is analyzed. The total de-excitation probability is in good agreement with vibrational inelasticities from experiment but the calculations overestimate the population of scattered H2 in (v=0, j) for large j.

Quasi-classical trajectory study of the DCl/HCl product branching ratios for the Cl+HD reaction on BW2 potential energy surface

The dynamics of the Cl + HD reaction has been studied by means of quasi-classical trajectory calculations on BW2 potential energy surface. The integral cross-sections versus collision energy and the DCl/HCl product branching ratios calculated quasi-classically on BW2 potential energy surface predict a clear preference to the production of DCl over HCl. The computed results also show that the integral cross-sections and the DCl/HCl product branching ratios strongly depend on the initial rotational quantum numbers j and the vibrational quantum numbers v. The calculated results are in reasonable agreement with experimental data, and some other theoretical results as well.

Quantum-classical correspondence in the O(3P)+HCl and Cl(2P)+OH reactions for total angular momentum J=0

A method for carrying out quasiclassical trajectory (QCT) calculations of A+BC(v,j) reactive collisions for the special case of the total angular momentum J=0 is described. Since quantum reactive scattering calculations involving heavier atoms are not straightforward for the J>0 case, this method is useful to establish the extent to which classical mechanics is applicable to a particular reaction. The method is tested by comparing the results of trajectory calculations for the J=0 case with analogous quantum-mechanical (QM) calculations for the O(3P)+HCl reaction and the reverse reaction Cl(2P)+OH. The S4 potential surface, which is based on MRCI+Q/cc-pVTZ energies scaled by the scaled external correlation method [B. Ramachandran et al., J. Chem. Phys. 111, 3862 (1999)], is used for these calculations. The QCT and QM cumulative reaction probabilities are found to be in good agreement, especially for the Cl+OH reaction. The agreement between the two types of state-resolved reaction probabilities is less striking but improves considerably as the initial diatomic rotational quantum number j increases. A comparison is also made between the exact and J-shifted QCT thermal rate coefficients. These are found to be in excellent agreement, which is in keeping with similar agreement observed in the case of the quantum-mechanical exact and J-shifted thermal rate coefficients.

Nearside-farside analysis of differential cross sections: The reaction I + HI → IH + I

We have carried out quantum calculations of differential cross sections for the state selected reaction, I + HI(i, ji) → IH(f, jf) + I, where i, ji and f, jf are initial and final vibrational and rotational quantum numbers respectively. The extended London–Eyring–Polanyi–Sato potential energy surface A of Manz and Römelt (J. Manz and J. Römelt, Chem. Phys. Lett., 1981, 81, 179) was employed. The scattering matrix elements were computed by a quantum method which applies a Born–Oppenheimer type separation to the motion of the light and heavy atoms; a centrifugal-sudden approximation was also made. The scattering calculations were performed for three values of the total energy. Eighteen differential cross sections are reported, which display forward, sideward and backward scattering. Structure in the angular distributions is analysed using a semiclassical optical model. In addition, a nearside-farside (NF) decomposition is applied to the Legendre partial wave series representation of the scattering amplitude. The semiclassical optical model supplies a physical interpretation of the backward scattering in terms of simple classical concepts, but fails to interpret the sideward and forward scattering. In contrast, NF theory nearly always provides a physically clear explanation of the forward, sideward and backward scattering.