Polarization Dependent Generalized Differential Cross-sections Research Articles

Quasi-classical trajectory study of collision energy effect on the stereodynamics of H + BrO → O + HBr reaction**Project supported by the Science Fund from Jilin University, China (Grant No. 419080106440), the Chinese National Fusion Project for ITER (Grant No. 2010GB104003), and the National Natural Science Foundation of China (Grant No. 10974069).

Quasi-classical trajectory (QCT) studies on the stereodynamics of H + BrO → O + HBr reaction have been performed on the X1A' state of ab initio potential energy surface by Peterson [Peterson K A 2000 J. Chem. Phys. 113 4598] in a collision energy range from 0 kcal/mol to 6 kcal/mol. Two of the polarization-dependent generalized differential cross sections (PDDCSs), (2π/σ)(dσ00/dωt) (PDDCS00) and (2π/σ)(dσ20/dωt) (PDDCS20) are considered. The rotational polarizations of these products show sensitive behaviors to the calculated collision energy range. Furthermore, in order to gain more knowledge about vector correlations, the product angular distribution, P(θr), and the dihedral angle, P(ϕr), are calculated, and the results indicate that both the rotational alignment and orientation of the product are enhanced as collision energy increases.

Theoretical prediction of energy dependence for D + BrO → DBr + O reaction: The rate constant and product rotational polarization**Project supported by the Jilin University, China (Grant No. 419080106440), the Chinese National Fusion Project for the International Thermonuclear Experimental Reactor (ITER) (Grant No. 2010GB104003), and the National Natural Science Foundation of China (Grant No. 10974069).

A quasi-classical trajectory (QCT) calculation is used to investigate the vector and scalar properties of the D + BrO → DBr + O reaction based on an ab initio potential energy surface (X1A’ state) with collision energy ranging from 0.1 kcal/mol to 6 kcal/mol. The reaction probability, the cross section, and the rate constant are studied. The probability and the cross section show decreasing behaviors as the collision energy increases. The distribution of the rate constant indicates that the reaction favorably occurs in a relatively low-temperature region (T<100 K). Meanwhile, three product angular distributions P(θr), P(ϕr), and P(θr, ϕr) are presented, which reflect the positive effect on the rotational angular momentum j’ polarization of the DBr product molecule. In addition, two of the polarization-dependent generalized differential cross sections (PDDCSs), PDDCS00 and PDDCS20, are computed as well. Our results demonstrate that both vector and scalar properties have strong energy dependence.

Quasi-classical trajectory investigation on the stereodynamics of Li + DF (v = 1–6, j = 0) → LiF + D reaction

In this paper, the stereodynamics of Li + DF → LiF + D reaction is investigated by the quasi-classical trajectory (QCT) method on the 2A′ potential energy surface (PES) at a relatively low collision energy of 8.76 kcal/mol. The scalar properties of the title reaction such as reaction probability and cross section are studied with vibrational quantum number of v = 1–6. The product angular distributions P(θr) and P(φr) are presented in the same vibrational level range. Moreover, two polarization-dependent generalized differential cross sections (PDDCSs), i.e., the PDDCS00 and PDDCS22+ are calculated as well. These stereodynamical results demonstrate sensitive behaviors to the vibrational quantum numbers.

The reagent vibrational excitation effect on the stereodynamics of the reaction O(1D)+ HBr → OH + Br

Calculations on the dynamics of the reaction O(1D) + HBr → OH + Br are performed on the ab initio potential energy surfaces (PESs) of the ground state given by Peterson [Peterson K A J. Chem. Phys. 113 4598 (2000)] using the quasi-classical trajectory (QCT) method. The product distribution of the dihedral angle, P(φr), and that of the angle between k and j′, P (θr), are presented in three dimensions. Moreover, we also investigate the reagent vibrational excitation effects on the two polarization-dependent generalized differential cross sections (PDDCS), PDDCS00 and PDDCS20, in the center-of-mass frame. The results indicate that the vector properties are sensitive to the reagent vibrational quantum number.

Stereo-dynamics of the exchange reaction Ha+LiHb→LiHa+Hb and its isotopic variants

The quasi-classical trajectory (QCT) method is used to calculate the stereo-dynamics of the exchange reaction Ha+LiHb→LiHa+Hb and its isotopic variants based on an accurate potential energy surface reported by Prudente et al. [Prudente F V, Marques J M C and Maniero A M 2009 Chem. Phys. Lett. 474 18]. The reactive probability of the title reaction is computed. The vector correlations and four polarization-dependent generalized differential cross sections (PDDCSs) at different collision energies are presented. The influences of the collision energy and the reagent rotation on the product polarization are studied in the present work. The results indicate that the product rotational angular momentum j′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane. The product polarization distributions of the title reaction and its isotopic variants exhibit distinct differences which may arise from different mass combinations.

A comparison of the stereo-dynamical information between S(1D) + H2 and S(1D) + HD Reactions

Studies on the stereo-dynamical of the reaction S(1D)+H2 and its isotopic variants have been performed using quasi-classical trajectory (QCT) method on a globally smooth ab initio potential surface of the 1A′ state which is produced by Ho et al. [11] at the collision energy of 0–22.0kcal/mol. We present the reaction cross section as a function of collision energy, which show satisfactory agreement in the reaction cross section ofHoetal. [11].Four polarization dependent generalized differential cross-sections (PDDCSs) have been calculated in the center-of-mass frame. Comparisons of the distributions P(θr), P(φr) and P(θr,φr), which denotes respectively the distribution of angles between k and j′, the distribution of dihedral angle denoting k–k′–j′ correlation and the angular distribution of product rotational vectors in the form of polar plots, are given for the isotopic variants and collision energies.

Effect of the reagent vibration on stereodynamics of the reaction Ca + HCl → CaCl + H

Based on the new potential energy surface [G.Verbockhaven, C. Sanz, G.C. Groenenboom, O. Roncero, J. Chem. Phys. 122 (2005) 204307] constructed by means of the multireference configuration interaction, the influence of the reagent vibrational excitation on the Ca+HCl reaction has been investigated by the quasi-classical trajectory method. The vibrational level and rotational level of the reactant molecule are taken as v=0–2 and j=0 respectively. The polarization-dependent generalized differential cross sections (PDDCSs) and alignments of the product rotational angular momentum for all reactions are reported. The calculation results show that the vibrational quantum number has a considerable influence on the distribution of the k–j′ vector correlation, The CaCl product mainly tends to the backward scattering for v>0, the effects of initial vibrational excited state of reactant molecule on PDDCSs are also revealed.

Effect of Collision Energy on the Reactivity O++T2 → OT++T by the Quasiclassical Trajectory Method

The reactivity O++T2 → OT++T is studied by the quasiclassical trajectory method on the RODRIGO potential energy surface at the collision energies of 1.0, 1.3, 1.6 and 1.9 eV, respectively. The four polarization-dependent generalized differential cross sections (PDDCSs) (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt) and (2π/σ)(dσ21-/dωt) are calculated in the center-of-mass frame. Furthermore, the P(θr) distribution describing the k—j′ correlation, the distribution of dihedral angle P(φr) and the distribution of P(θr, φr), which describes the angular distribution of product rotational vectors in the form of polar plots in θr and φr are also investigated. The results demonstrate that the stereo-dynamical properties of the title reactivity are sensitive to collision energies.

Stereo-dynamics of the F + HCl → HF + Cl reaction

We present a quasi-classical trajectory (QCT) study on product polarization for the reaction F(2P) + HCl(v = 0, j = 0) ? HF + Cl(2P) on a recently computed 12A' ground-state surface reported by Deskevich et al. J Chem Phys, 2006, 124, 224303. Four polarization dependent generalized differential cross-sections (2p/s)(ds00/d?t), (2p/s)(ds20/d?t), (2p/s)(ds22+/d?t), and (2p/s)(ds21-/d?t) were calculated in the center-of-mass frame at four different collision energies. The obtained P(?r), P(?r), and P(?r, ?r), which denote respectively the distribution of angles between k and j', the distribution of dihedral angle denoting k-k'-j' correlation and the angular distribution of product rotational vectors in the form of polar plots, indicate that the degree of rotational alignment of the product HF molecule is strong and the degree of the rotational alignment decreases as collision energy increases. The product rotational angular momentum vector j' is not only aligned, but also oriented along the y-axis, and the molecular rotation of the product prefers an in-plane reaction mechanism rather than the out-of-plane mechanism.

Theoretical Study of Isotopic Effect of Oxygen Atom on the Stereodynamics for the O(3P) + D2 → OD + D Reaction

Quasi-classical trajectory theory is used to study the isotope effect of oxygen atoms on the vector correlations in the O(3P) + D2 reaction at a collision energy of 25kcal/mol using accurate potential energy surface of the 3A' triplet state. The distributions of p(θr) and the distribution of dihedral angel p(ϕr) as well as p(θr,ϕr) are calculated. Moreover, four polarization-dependent generalized differential cross sections (PDDCSs) of product are presented in the center-of-mass frame. The results indicate that the polarization of the product presents different characters for the isotope effect of oxygen atoms. Isotopic substitute can cause obviously different effects on the four PDDCSs.

Influence of Vibrational Excitation on Stereodynamics for O(3P)+D2→OD+D Reaction

Theoretical investigations on the stereodynamics of the O(3P)+D2 reaction have been calculated by means of the quasi-classical trajectory to study the product rotational polarization at collision energy of 104.5 kJ/mol on the potential energy surface of the ground 3A″ triplet state. The vector properties including angular momentum alignment distributions and four polarization dependent generalized differential cross-sections of product have been presented. Furthermore, the influence of reagent vibrational excitation on the product vector properties has also been studied. The results indicate that the vector properties are sensitively affected by reagent vibrational excitation.

STEREODYNAMICS STUDY OF THE REACTION Cl(2p3/2) + C2D6 (v = 0, j = 0) → DCl + C2D5

The product angular momentum polarization of the Cl + C2D6 → DCl + C2D5 reaction is calculated via the quasiclassical trajectory (QCT) method at the collision energy of 0.25 eV. A new London–Eyring–Polanyi–Sato (LEPS) potential energy surface (PES) is used in this reaction. There is a "late" barrier and a "deep" well on this new LEPS PES. The four polarization-dependent "generalized" differential cross sections (PDDCSs) are presented in the center-of-mass frame. In the meantime, the distributions of P(ϕr), P(θr), and P(θr, ϕr) are calculated. The calculations are in good agreement with the experimental data. In addition, the rotational alignment factors [Formula: see text], [Formula: see text], and [Formula: see text] in the stationary-target frame (STF) are also calculated.

Theoretical study of stereodynamics for the O( 3P) + H 2 ( v = 0–2, j = 0) → OH + H reaction

Studies on the Stereodynamics of the O( 3 P) + H 2 reaction have been performed via the Quasi-classical trajectory method (QCT) at collision energy of 34.6 kcal/mol on BMS1 potential energy surface [8] for the lowest 3A″ state. The results of cross-sections are good agreed with the quantum calculation. The distribution of angle between k and j ′ P( θ r ) and the dihedral angle distribution P( ϕ r ) characterizing the k – k ′– j ′ correlation are calculated and discussed. We also present two polarization dependent generalized differential cross-sections (PDDCSs) (2 π/ σ)( dσ 00/ dω t ) and (2 π/ σ)( dσ 20/ dω t ) in the center of mass frame. Furthermore, the influence of reagent vibrational excitation on the product vector properties has also been studied in the present work. The results indicate that the vector properties are sensitively affected by vibrational excitation.

Quasi-classical Trajectory Study of the Intramolecular Isotope Effect in the Reaction O(3P)+H2/HD

Theoretical studies of the dynamics of the reactions O(3P)+H2/HD(v = 0, j = 0)OH+H have been performed with quasi-classical trajectory method (QCT) on an ab initio potential surface for the lowest triplet electronic state of H2O(3A). The QCT-calculated integral cross sections are in good agreement with the earlier time-dependent quantum mechanics results. The state-resolved rotational distributions reveal that the product OH rotational distributions for O+HD have a preference for populating highly internally excited states compared with the O+H2 reaction. Distributions of differential cross sections show that directions of scattering are strongly dependent on the choice of quantum state. The polarization dependent generalized differential cross-sections and the distributions were calculated and a pronounced isotopic effect is revealed. The calculated results indicate that the product polarization is very sensitive to the mass factor.

Theoretical study of the stereo-dynamics of the reaction H + FO → OH + F

Based on the adiabatic potential energy surface of the 1 3A″ triplet state, the influences of collision energy and reagent of rotational excitation on product polarization for the reaction H + FO(0, j) → OH + F are studied by using quasi-classical trajectory (QCT) method. Four polarization dependent generalized differential cross-sections (2 π/ σ)(d σ 00/d ω t ), (2 π/ σ)(d σ 20/d ω t ), (2 π/ σ)(d σ 22+/d ω t ) and (2 π/ σ)(d σ 21−/d ω t ) have been calculated in the center-of-mass frame. The obtained P( θ r ), P( φ r ) and P( θ r , φ r ), which denotes respectively the distribution of angles between k and j ′, the distribution of dihedral angle denoting k – k ′– j ′ correlation and the angular distribution of product rotational vectors in the form of polar plots, indicate that both the orientation and the alignment of the rotational angular moment are all impacted by collision energies.

Stereodynamics Study of the Reaction of O(3P) with CH4 (v = 0 ,j = 0)

A new London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES) is used in the O + CH4 → OH + CH3 reaction via the quasiclassical trajectory method (QCT). Comparing with the experiments and the former ab initio calculations, the new LEPS PES describes the actual potential energy surface of the O + CH4 reaction successfully. The four polarization dependent “generalized” differential cross sections (PDDCS) are presented in the center of mass frame. In the meantime, the distribution of dihedral angle [P(φr), the distribution of angle between k and j′ (P(θr)] and the angular distribution of product rotational vectors in the form of polar plots in θr and φr (P(θr, φr) are calculated. The isotope effect for the reactions O + CD4 is also calculated. These results are in good agreement with the experiments.

THEORETICAL STUDY OF PRODUCT POLARIZATION FOR THE REACTION Ba + CH3I → BaI + CH3

Using quasi-classical trajectory (QCT) method, the vector correlation between products and reagents for the exothermic reaction Ba + CH3I → BaI + CH3 has been studied on the extended Lond–Eyring–Polanyi–Sato (LEPS) potential energy surface (PES) at three collision energies of 1.6, 3.3, and 5.6 kcal/mol. The P(θr) distribution of the products describing the k-j' correlation and the dihedral angle distribution P(ϕr) describing k-k'-j' correlation are calculated in center-of-mass (CM) frame. Four polarization dependent generalized differential cross-sections (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), and (2π/σ)(dσ21-/dωt) have also been presented in the CM frame as well. The results indicate that the product rotational angular momentum j' is not only aligned, but also oriented along the direction perpendicular to the scattering plane. In addition, the alignment and the orientation of the BaI product rotational angular momentum depend very sensitively on the collision energy.

Theoretical study of the stereodynamics of the reactions of D − + H 2 → H − + HD and H − + D 2 → D − + HD

The product rotational polarization of the ion-molecule reactions of D − + H 2 → H − + HD and H − + D 2 → D − + HD has been calculated by means of the quasi-classical trajectory method on a potential energy surface (PES) constructed by Panda and Sathyamurthy [J. Chem. Phys. 121, 9343 (2004)]. Comparing the dynamics of D − + H 2 → H − + HD with H − + D 2 → D − + HD, four polarization dependent generalized differential cross-sections (2π/ σ)(d σ 00/d ω t), (2π/ σ)(d σ 20/d ω t), (2π/ σ)(d σ 22+/d ω t), (2π/ σ)(d σ 21−/d ω t) have been presented in the center of mass frame, respectively. The distribution of dihedral angle p( ϕ r), the distribution of angle between k and j′, p( θ r), and the angular distribution of product rotational vectors in the form of polar plots in θ r and ϕ r are calculated as well. A pronounced isotopic effect is also revealed. It may be ascribed to the significant difference of the effective potential barrier height or the difference of the mass factor in the two reactions.

Theoretical study of the stereodynamics of the reaction Cl+C3H8→C3H7+HCl

The product rotational polarization of the reaction Cl + C 3 H 8 → C 3 H 7 + HCl is calculated via the quasiclassical trajectory method based on extended London–Eyring–Polanyi–Sato potential energy surface (PES) at collision energies of 6.0, 7.4, and 8.0 kcal/mol. Compared the dynamics of Cl substituting the primary and secondary hydrogen of C 3 H 8 , four polarization dependent generalized differential cross-sections (2π/ σ )(d σ 00 /d ω t ), (2π/ σ )(d σ 20 /d ω t ), (2π/ σ )(d σ 22+ /d ω t ) and (2π/ σ )(d σ 21− /d ω t ) have been presented in the center of mass frame, respectively. The distribution of dihedral angle p ( ϕ r ), the distribution of angle between k and j ′, p ( θ r ), and the angular distribution of product rotational vectors in the form of polar plots in θ r and ϕ r are calculated as well. The different character of the abstraction of primary vs. secondary hydrogen atoms from C 3 H 8 may be ascribed to that the different PESs and substituent site. The calculated results are in agreement with the experimental data.

Product rotational polarization: Stereodynamics of the reaction Cl(2P3/2)+CD4(v=0,j=0)→DCl(v′=0,j′=1)+CD3

The angular momentum polarization of the products of the reaction Cl(2P3/2)+CD4(v=0,j=0)→DCl(v′=0,j′=1)+CD3 is calculated via the quasiclassical trajectory method (QCT) based on extended London–Eyring–Polanyi–Sato (LEPS) potential energy surface (PES) at a collision energy of 0.28 eV (6.46 kcal/mol). In the stationary target frame (STF), the rotational alignment factor A0(2)stf has been calculated. In the meantime, we also present four polarization dependent “generalized” differential cross sections (PDDCS) (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), and (2π/σ)(dσ21−/dωt) in the center of mass frame. Furthermore, the distribution of dihedral angle P(φr), the distribution of angle between k′ and J′, P(θtr), and the angular distribution of product rotational vectors in the form of polar plots in θr and φr are calculated as well. The calculated results are in good agreement with the experimental data.