- Email: [email protected]
The polarization dependent differential cross sections of the reactions: H + LiH+(v = 0, j = 0) → H2 + Li+ and H+ + LiH(v = 0, j = 0) → H2+ + Li
Available online at www.sciencedirect.com
Chinese Chemical Letters 21 (2010) 376–378 www.elsevier.com/locate/cclet
The polarization dependent differential cross sections of the reactions: H + LiH+(v = 0, j = 0) ! H2 + Li+ and H+ + LiH(v = 0, j = 0) ! H2+ + Li Xiao Hu Li, Mei Shan Wang *, Chuan Lu Yang, Ling Zhi Ma, Ning Ma, Ji Cheng Wu School of Physics, Ludong University, Yantai 264025, China Received 17 August 2009
Abstract Quasi-classical trajectory (QCT) calculations have been carried out to study the generalized polarization dependent differential cross sections (PDDCSs) for the reactions H + LiH+(v = 0, j = 0) ! H2 + Li+ and H+ + LiH(v = 0, j = 0) ! H2+ + Li occurring on the two lowest-lying electronic states of the LiH2+ system, using the ab initio potential energy surfaces (PESs) of Martinazzo et al. [3]. Four PDDCSs, i.e., (2p/s)(ds00/dvt), (2p/s)(ds20/dvt), (2p/s)(ds22+/dvt), (2p/s)(ds21/dvt) have been discussed in detail. # 2009 Mei Shan Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved. Keywords: Quasi-classical trajectory; PDDCSs; Stereodynamics; Vector correlation
The LiH2+ system has recently received considerable attention due to its importance in the primordial universe [1]. In this letter, we discuss the four PDDCSs of the title reactions as an extended study of our previous calculations [2] by means of the adiabatically PESs computed and numerically fitted by Martinazzo et al. [3] for the two lowest-lying electronic states of LiH2+. The former one of the title reactions proceeds on the ground state PES while the latter one occurs on the first excited state PES.
1. Calculations We employed the standard quasi-classical trajectory (QCT) method (see the specific details in Refs. [4,5] and the references therein) to study the stereodynamics (see details in Refs. [6,7]) of the title reactions. The selected collision energies for the two reactions are 0.05 and 0.50 eV. Batches of 100,000 trajectories are run for each collision energy we ˚ between the H/ chose. The integration step size is 0.1 fs and the trajectories are started at an initial distance of 30.0 A + + H atom and the center of mass of the Li H/LiH molecule.
* Corresponding author. E-mail address: [email protected] (M.S. Wang). 1001-8417/$ – see front matter # 2009 Mei Shan Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved. doi:10.1016/j.cclet.2009.11.041
X.H. Li et al. / Chinese Chemical Letters 21 (2010) 376–378
377
2. Results and discussion The scattering direction of the product molecule and the k–k0 –j0 correlation are described by the PDDCSs. [8,9] The calculated PDDCSs of the H2 product for the H + LiH+ reaction occurring on the ground state PES at two collision energies are presented in Fig. 1. Note that despite the nonadiabatic effect is very important for most ion–molecule reactions [10,11], it can be ignored here because of the separating of a large energy gap between the two lowest-lying electronic states. [3] As can be seen in Fig. 1(a), the DCS shows a preference of forward scattering at the lower collision energy of 0.05 eV. At the higher energy of 0.50 eV, the DCS are dominated by the sideways and backward scattering. The PDDCS (2p/s)(ds20/dvt), whose value is the expectation value of the second Legendre moment < P2 (cos ur)>, is drawn in Fig. 1(b). The tendencies of the (2p/s)(ds20/dvt) are basically opposite to the DCSs, which indicates that j0 is preferentially polarized along the direction perpendicular to k. Clearly, when the energy increases from 0.05 to 0.50 eV, the degree of the rotational alignments of the products is decreased. The PDDCSs with q 6¼ 0 equal to zero at the extremities of forward (ur = 08) and backward (ur = 1808) scattering, are depicted in Fig. 1(c) and (d). The value of (2p/s)(ds22+/dvt) is negative for all scattering angles, as can be seen in Fig. 1(c), indicating the notable preference of product alignment along the y-axis. The products display a stronger polarization at ur = 908 with the lower energy of 0.05 eV, while the same behavior emerges at ur close to 308, 908 and 1408 with the higher energy of 0.50 eV. In addition, the degree of the polarization is weakened when the collision energy increase. The distribution of (2p/ s)(ds21/dvt), which is related to < sin2ur cos2fr)>, is shown in Fig. 1(d). At the lower energy, the values of (2p/ s)(ds21/dvt) are very close to zero. But at the higher energy, the values of (2p/s)(ds21/dvt) are positive in the forward hemisphere and negative in the backward hemisphere, indicating that j0 is aligned along the direction of vector x + z in the forward hemisphere and along the direction of vector x–z in the backward hemisphere. The strongest polarization of the H2 are at ur = 668 and ur = 1418 in the forward and backward hemispheres, respectively. Fig. 2 shows the four PDDCSs for the reaction H+ + LiH (v = 0, j = 0) ! H2+ + Li proceeding on the first excited PES at the selected collision energies. The DCSs depicted in Fig. 2(a) exhibit a dominance of backward scattering at the lower energy of 0.05 eV, whereas forward-backward feature appears at the higher energy of 0.50 eV. The PDDCS (2p/s)(ds20/dvt) displayed in Fig. 2(b) shows an opposite trend to the DCS which indicates that j0 is preferentially polarized along the direction perpendicular to k, and when the energy increases from 0.05 to 0.50 eV, the degree of the rotational alignments of the products is decreased. The PDDCSs (2p/s)(ds22+/dvt) and (2p/s)(ds21/dvt), whose
Fig. 1. Four PDDCSs for the reaction H + LiH+ (v = 0, j = 0) ! H2 + Li+ at Ec = 0.05 eV (solid lines) and Ec = 0. 50 eV (dashed lines).
378
X.H. Li et al. / Chinese Chemical Letters 21 (2010) 376–378
Fig. 2. Four PDDCSs for the reaction H+ + LiH (v = 0, j = 0) ! H2+ + Li at Ec = 0.05 eV (solid lines) and Ec = 0. 50 eV (dashed lines).
values equal to zero at the extremities of forward (ur = 08) and backward (ur = 1808) scattering, are depicted in Fig. 2(c) and (d). The PDDCS (2p/s)(ds22+/dvt) has a minimum at ur close to 1208 with the lower energy of 0.05 eV, while the same behavior appears at ur close to 1508 with the higher energy of 0.50 eV. Note that the degree of the polarization is changeless when the collision energy increases. The PDDCS (2p/s)(ds21/dvt), whose values are close to zero at the higher energy of 0.50 eV, are drawn in Fig. 2(d). But at the lower energy of 0.05 eV, the (2p/s)(ds21/ dvt) appears a preference of negative values and has a tiny positive peak at ur close to 158 as well as a minimum at ur close to 1508. This indicates that j0 has a preference of aligned along the direction of vector x–z. Acknowledgments The authors are very grateful to Professor Gian Franco Tantardini and Rocco Martinazzo for providing the codes of the potential energy surfaces and Professor Keli Han for providing the QCT code of stereodynamics, as well as some precious advice. The authors are also very grateful to Doctor Ilaria Pino for the contributions of the PESs’ force and many helpful discussions. This work was supported by the National Natural Science Foundation of China (No. 10674114), and carried out in the Shuguang Super Computer Center (SSCC) of Ludong University. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
E. Bodo, F.A. Gianturco, R. Martinazzo, Phys. Rep. 384 (2003) 85. X.H. Li, M.S. Wang, I. Pino, et al. Phys. Chem. Chem. Phys. 11 (2009) 10438. R. Martinazzo, G. Tantardini, E. Bodo, et al. J. Chem. Phys. 119 (2003) 11241. W.L. Li, M.S. Wang, C.L. Yang, et al. Chem. Phys. Lett. 445 (2007) 125. M.D. Chen, K.L. Han, N.Q. Lou, J. Chem. Phys. 118 (2003) 4463. R.J. Li, K.L. Han, et al. Chem. Phys. Lett. 220 (1994) 281. K.L. Han, G.Z. He, N.Q. Lou, J. Chem. Phys. 105 (1996) 8699. M.L. Wang, K.L. Han, G.Z. He, J. Chem. Phys. 109 (1998) 5446. M.L. Wang, K.L. Han, G.Z. He, J. Phys. Chem. A 102 (1998) 10204. T.S. Chu, Y. Zhang, K.L. Han, Int. Rev. Phys. Chem. 25 (2006) 201. T.S. Chu, K.L. Han, Phys. Chem. Chem. Phys. 10 (2008) 2431.
Chinese Chemical Letters 21 (2010) 376–378 www.elsevier.com/locate/cclet
The polarization dependent differential cross sections of the reactions: H + LiH+(v = 0, j = 0) ! H2 + Li+ and H+ + LiH(v = 0, j = 0) ! H2+ + Li Xiao Hu Li, Mei Shan Wang *, Chuan Lu Yang, Ling Zhi Ma, Ning Ma, Ji Cheng Wu School of Physics, Ludong University, Yantai 264025, China Received 17 August 2009
Abstract Quasi-classical trajectory (QCT) calculations have been carried out to study the generalized polarization dependent differential cross sections (PDDCSs) for the reactions H + LiH+(v = 0, j = 0) ! H2 + Li+ and H+ + LiH(v = 0, j = 0) ! H2+ + Li occurring on the two lowest-lying electronic states of the LiH2+ system, using the ab initio potential energy surfaces (PESs) of Martinazzo et al. [3]. Four PDDCSs, i.e., (2p/s)(ds00/dvt), (2p/s)(ds20/dvt), (2p/s)(ds22+/dvt), (2p/s)(ds21/dvt) have been discussed in detail. # 2009 Mei Shan Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved. Keywords: Quasi-classical trajectory; PDDCSs; Stereodynamics; Vector correlation
The LiH2+ system has recently received considerable attention due to its importance in the primordial universe [1]. In this letter, we discuss the four PDDCSs of the title reactions as an extended study of our previous calculations [2] by means of the adiabatically PESs computed and numerically fitted by Martinazzo et al. [3] for the two lowest-lying electronic states of LiH2+. The former one of the title reactions proceeds on the ground state PES while the latter one occurs on the first excited state PES.
1. Calculations We employed the standard quasi-classical trajectory (QCT) method (see the specific details in Refs. [4,5] and the references therein) to study the stereodynamics (see details in Refs. [6,7]) of the title reactions. The selected collision energies for the two reactions are 0.05 and 0.50 eV. Batches of 100,000 trajectories are run for each collision energy we ˚ between the H/ chose. The integration step size is 0.1 fs and the trajectories are started at an initial distance of 30.0 A + + H atom and the center of mass of the Li H/LiH molecule.
* Corresponding author. E-mail address: [email protected] (M.S. Wang). 1001-8417/$ – see front matter # 2009 Mei Shan Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved. doi:10.1016/j.cclet.2009.11.041
X.H. Li et al. / Chinese Chemical Letters 21 (2010) 376–378
377
2. Results and discussion The scattering direction of the product molecule and the k–k0 –j0 correlation are described by the PDDCSs. [8,9] The calculated PDDCSs of the H2 product for the H + LiH+ reaction occurring on the ground state PES at two collision energies are presented in Fig. 1. Note that despite the nonadiabatic effect is very important for most ion–molecule reactions [10,11], it can be ignored here because of the separating of a large energy gap between the two lowest-lying electronic states. [3] As can be seen in Fig. 1(a), the DCS shows a preference of forward scattering at the lower collision energy of 0.05 eV. At the higher energy of 0.50 eV, the DCS are dominated by the sideways and backward scattering. The PDDCS (2p/s)(ds20/dvt), whose value is the expectation value of the second Legendre moment < P2 (cos ur)>, is drawn in Fig. 1(b). The tendencies of the (2p/s)(ds20/dvt) are basically opposite to the DCSs, which indicates that j0 is preferentially polarized along the direction perpendicular to k. Clearly, when the energy increases from 0.05 to 0.50 eV, the degree of the rotational alignments of the products is decreased. The PDDCSs with q 6¼ 0 equal to zero at the extremities of forward (ur = 08) and backward (ur = 1808) scattering, are depicted in Fig. 1(c) and (d). The value of (2p/s)(ds22+/dvt) is negative for all scattering angles, as can be seen in Fig. 1(c), indicating the notable preference of product alignment along the y-axis. The products display a stronger polarization at ur = 908 with the lower energy of 0.05 eV, while the same behavior emerges at ur close to 308, 908 and 1408 with the higher energy of 0.50 eV. In addition, the degree of the polarization is weakened when the collision energy increase. The distribution of (2p/ s)(ds21/dvt), which is related to < sin2ur cos2fr)>, is shown in Fig. 1(d). At the lower energy, the values of (2p/ s)(ds21/dvt) are very close to zero. But at the higher energy, the values of (2p/s)(ds21/dvt) are positive in the forward hemisphere and negative in the backward hemisphere, indicating that j0 is aligned along the direction of vector x + z in the forward hemisphere and along the direction of vector x–z in the backward hemisphere. The strongest polarization of the H2 are at ur = 668 and ur = 1418 in the forward and backward hemispheres, respectively. Fig. 2 shows the four PDDCSs for the reaction H+ + LiH (v = 0, j = 0) ! H2+ + Li proceeding on the first excited PES at the selected collision energies. The DCSs depicted in Fig. 2(a) exhibit a dominance of backward scattering at the lower energy of 0.05 eV, whereas forward-backward feature appears at the higher energy of 0.50 eV. The PDDCS (2p/s)(ds20/dvt) displayed in Fig. 2(b) shows an opposite trend to the DCS which indicates that j0 is preferentially polarized along the direction perpendicular to k, and when the energy increases from 0.05 to 0.50 eV, the degree of the rotational alignments of the products is decreased. The PDDCSs (2p/s)(ds22+/dvt) and (2p/s)(ds21/dvt), whose
Fig. 1. Four PDDCSs for the reaction H + LiH+ (v = 0, j = 0) ! H2 + Li+ at Ec = 0.05 eV (solid lines) and Ec = 0. 50 eV (dashed lines).
378
X.H. Li et al. / Chinese Chemical Letters 21 (2010) 376–378
Fig. 2. Four PDDCSs for the reaction H+ + LiH (v = 0, j = 0) ! H2+ + Li at Ec = 0.05 eV (solid lines) and Ec = 0. 50 eV (dashed lines).
values equal to zero at the extremities of forward (ur = 08) and backward (ur = 1808) scattering, are depicted in Fig. 2(c) and (d). The PDDCS (2p/s)(ds22+/dvt) has a minimum at ur close to 1208 with the lower energy of 0.05 eV, while the same behavior appears at ur close to 1508 with the higher energy of 0.50 eV. Note that the degree of the polarization is changeless when the collision energy increases. The PDDCS (2p/s)(ds21/dvt), whose values are close to zero at the higher energy of 0.50 eV, are drawn in Fig. 2(d). But at the lower energy of 0.05 eV, the (2p/s)(ds21/ dvt) appears a preference of negative values and has a tiny positive peak at ur close to 158 as well as a minimum at ur close to 1508. This indicates that j0 has a preference of aligned along the direction of vector x–z. Acknowledgments The authors are very grateful to Professor Gian Franco Tantardini and Rocco Martinazzo for providing the codes of the potential energy surfaces and Professor Keli Han for providing the QCT code of stereodynamics, as well as some precious advice. The authors are also very grateful to Doctor Ilaria Pino for the contributions of the PESs’ force and many helpful discussions. This work was supported by the National Natural Science Foundation of China (No. 10674114), and carried out in the Shuguang Super Computer Center (SSCC) of Ludong University. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
E. Bodo, F.A. Gianturco, R. Martinazzo, Phys. Rep. 384 (2003) 85. X.H. Li, M.S. Wang, I. Pino, et al. Phys. Chem. Chem. Phys. 11 (2009) 10438. R. Martinazzo, G. Tantardini, E. Bodo, et al. J. Chem. Phys. 119 (2003) 11241. W.L. Li, M.S. Wang, C.L. Yang, et al. Chem. Phys. Lett. 445 (2007) 125. M.D. Chen, K.L. Han, N.Q. Lou, J. Chem. Phys. 118 (2003) 4463. R.J. Li, K.L. Han, et al. Chem. Phys. Lett. 220 (1994) 281. K.L. Han, G.Z. He, N.Q. Lou, J. Chem. Phys. 105 (1996) 8699. M.L. Wang, K.L. Han, G.Z. He, J. Chem. Phys. 109 (1998) 5446. M.L. Wang, K.L. Han, G.Z. He, J. Phys. Chem. A 102 (1998) 10204. T.S. Chu, Y. Zhang, K.L. Han, Int. Rev. Phys. Chem. 25 (2006) 201. T.S. Chu, K.L. Han, Phys. Chem. Chem. Phys. 10 (2008) 2431.