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An ab initio study of the potential energy surfaces for Na+I2 system
2 April 2002
Chemical Physics Letters 355 (2002) 285–288 www.elsevier.com/locate/cplett
An ab initio study of the potential energy surfaces for Na þ I2 system Dacheng Feng, Congmin Kang, Chuansong Qi, Zhengting Cai
*
Institute of Theoretical Chemistry, Shandong University, Jinan 250100, Shandong, China Received 24 January 2001; in final form 25 January 2002
Abstract Three ab initio potential energy surfaces of 2 B2 , 2 A1 and 2 R states for the Na þ I2 collision system are calculated on the QCISD(T)/LANL2DZ level. Three reaction channels, neutral reaction, chemical ionization and collision ionization, have been obtained based on analyzing the minimum energy reaction paths. The valence potential energy surfaces 2 A1 and the ionic state 2 B2 are crossed approximately at Rc ¼ 0:508 nm. Na þ I2 ! Naþ þ I 2 is an electronic non-adiabatic process. Ó 2002 Published by Elsevier Science B.V.
Charge transfer and chemi-ionization processes between alkali metal atom M (M ¼ K, Na, Cs, etc.) and halogen molecule X2 (X ¼ I, Br, Cl, etc.) during collision are the well-known phenomena, from which valuable information of collisionally induced reaction dynamics can be obtained [1–3]. Among these reactions, the reaction of Na atom with I2 molecule is the typical one, attracting theoreticians and experimentalists to investigate its mechanism. Banares et al. [4] measured the differential reaction sections by laser-crossed beam experiment. In 1977, Aten et al. [5] developed a semi-empirical potential energy surface for the formation of ion-pair, Na þ I2 ! Naþ þ I 2 . They also performed a classical trajectory calculation for the surface hopping. On the same potential energy
*
Corresponding author. Fax: +86-531-856-4464. E-mail address: [email protected] (Z. Cai).
surface, Ma et al. [6] calculated the collinear reaction probabilities using a quantum reaction scattering method, LCAC-SW (linear combination arrangement channels-scattering wavefunction). To our knowledge, no ab intio potential surface for Na þ I2 system has been reported up to now. Since this reaction involves to a coupling of potential energy surfaces, in other words, the reaction undergoes with a electronically non-adiabatic crossing process, semi-empirical potential energy surface is thus not accurate to deal with. In the present Letter, ab initio potential energy surfaces for the Na þ I2 collision system based on the QCISD(T)/LANL2DZ level are reported. The coordinate system used in the calculations is presented in Fig. 1. Some calculation results are given in Table 1 and Figs. 2–5. The detailed illustration describes as the following: (1) A minimum energy of E ¼ 22:636729 a.u. is obtained by optimizing all the coordinates of the
0009-2614/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 2 4 9 - X
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D. Feng et al. / Chemical Physics Letters 355 (2002) 285–288
Fig. 1. Relative coordinates for system Na þ I2 .
Na þ I2 system in 2 B2 electronic state. The geometric structure of the species (presented by configuration A) has C2v symmetry (r1 ¼ 0:3542 nm, R ¼ 0:2468 nm). It is a long-lived complex, having a potential valley on the potential energy surface. From the population analysis, it is known that the species is a strong polar intermediate (the net charges on Na and each I are 0.90 and )0.45, respectively). The positive charge is almost centered at Na atom. Table 1 lists six possible product channels of the reaction between Na and I2 . The products are þ Na þ I2 , Naþ þ I 2 , NaI þ I, NaI þ I , Na + I + I þ and Na þ I þ I, respectively. Energetically, Na þ I2 ! NaI þ I is the most favorable channel, while Na þ I2 ! Naþ þ I þ I is the most unfavorable one. The calculated reaction energies for
the six product channels agree with the thermodynamic data [7]. (2) Fig. 2 shows the potential energy surface of the collinear collision system with C1v symmetry (a ¼ 180°, see Fig. 1). The potential energy surface of 2 R state has been obtained by scanning both r1 and r2 (step-length is 0.01 nm). The energy of the reactants Na þ I2 (r1 ¼ 0:293 nm and r2 ! 1) is 22:54788 a.u. There is no potential barrier in the pathway from the reactants to the collinear complex. A potential basin on the surface refers to a collinear complex NaI2 ðC1v Þ. The collinear complex is unstable and its energy is 22:61687 a.u., only 9.0 kJ/mol lower than that of NaI + I. The pathway from NaI2 to the products NaI + I is also very flat without potential barrier. (3) For the side-on attack (h ¼ 90° see Fig. 1), there are two potential energy surfaces for the collision system. Both are of C2v symmetry. The potential energy surfaces are calculated with the scanning for both the r1 and R with the same step-length 0.0255 nm. The equal-counter potential plots are shown in Fig. 3 for 2 A1 state and in Fig. 4 for 2 B2 state, respectively. The point r1 ¼ 0:3411 nm and R ¼ 0:9 nm at 2 B2 state is close to the ion-pair species Naþ þ I 2, and located at the entrance of the reaction path. The total energy of the system is 22:51180 a.u. The electric charges on the Na atom and on each I atom are 0.9995 and 0:4997, respectively. No potential barrier exists from the entrance to the complex A. From the natural population, at every point on the 2 B2 surface the net charge on atom Na
Table 1 Energies of several special points on the potential energy surfaces of Na þ I2 system Sample Na þ I2 Naþ þ I 2 NaI + I þ NaI þ I NaI2 (2 R; C1v ) NaI2 (2 B2 ; C2v ) Na + I + I Naþ þ I þ I
h (deg)
0 90
r1 (nm)
r2 (nm)
E (a.u.)
0.29318 0.34112 1 1 0.38025 0.35422 1 1
1 1 0.28454 0.33500 0.28500 0.30375 1 1
)22.54788 )22.45375 )22.61346 )22.42989 )22.61687 )22.63672 )22.51613 )22.41841
D. Feng et al. / Chemical Physics Letters 355 (2002) 285–288
Fig. 2. Scheme plot of the potential energy surface for Na þ I2 collinear collision system ða ¼ 180°Þ.
287
Fig. 4. Scheme plot of the potential energy surface for Na þ I2 collision system (h ¼ 90°, C2v symmetry, 2 B2 state).
Fig. 5. The nonadiabatic coupling of the potential energy sur). face of 2 B2 and 2 A1 states for Na þ I2 system (r1 ¼ 3:0 A
Fig. 3. Scheme plot of the potential energy surface for Na þ I2 collision system (h ¼ 90°, C2v symmetry, 2 A1 state).
is more than 0.90, therefore the 2 B2 state surface shown in Fig. 4 is an ionic surface. Another C2v state, 2 A1 , refers to the neutral products Na þ I2 . The entrance point of the reaction path, r1 ¼ 0:29316 nm and R ¼ 0:9 nm, is close to the reactant Na þ I2 . Its energy is 22:54791 a.u., natural charges are both 0.000 for atom Na and I, respectively. The potential energy surface of 2 A1 state (Fig. 3) can be obtained by the similar way of that of 2 B2 . No energy minimum on
2
A1 surface is found. The net electric charges either in atom Na or in atom I is almost zero. The minimum energy reaction pathways on the 2 A1 state and 2 B2 state can be found on Figs. 3 and 4, respectively. It is clear that the two potential energy surfaces, the neutral state or valence system 2 Na þ I2 ð A1 Þ and the ionic state or ionic system þ 2 Na þ I2 ð B2 Þ, are crossed. Fig. 5 shows a section of the two surfaces at r1 ¼ 0:3 nm. The crossed point between two profiles is approximately at Rc ¼ 0:508 nm, where the harpoon process of the electron leaping occurs [8]. Large ion-pair formation cross-section for Na þ I2 ! Naþ þ I 2 system
288
D. Feng et al. / Chemical Physics Letters 355 (2002) 285–288
has been calculated using this cross distance Rc to Landau–Zener model [8], which is in qualitative agreement with the laser-crossed beam experiment for Na þ I2 ! Naþ þ I 2 reaction [6]. Other reaction channels for the Na þ I2 system can be analyzed by means of the same procedure given above. Results will be presented in our future paper.
Acknowledgements This work was supported by the National Natural Scientific Foundation of China (No. 20173032).
References [1] A.P.M. Baede, Adv. Chem. Phys. 30 (1975) 463. [2] D.J. Auerbach, M.M. Hubers, A.P.M. Baeder, J. Los, Chem. Phys. 2 (1973) 107. [3] P.W. Harland, H.S. Carma Jr., L.F. Phillips, P.R. Brooks, J. Chem. Phys. 93 (1990) 1089. [4] L. Banares, M.G. Velarde, A.G. Urena, J. Chem. Phys. 95 (1991) 5474. [5] J.A. Aten, G.E.H. Lanting, J. Los, Chem. Phys. 19 (1977) 241. [6] W.Y. Ma, Z.T. Cai, D.H. Deng, Chem. Phys. Lett. 304 (1999) 117. [7] CRC Handbook of Chemistry and Physics, 73th edn., CRC Press Inc., Boca Raton, FL, 1992–1993. [8] H. Erying, S.H. Lin, S.M. Lin, Basic Chemical Kinetics, John Wiley & Sons, New York, 1980 (Chapter 6).
Chemical Physics Letters 355 (2002) 285–288 www.elsevier.com/locate/cplett
An ab initio study of the potential energy surfaces for Na þ I2 system Dacheng Feng, Congmin Kang, Chuansong Qi, Zhengting Cai
*
Institute of Theoretical Chemistry, Shandong University, Jinan 250100, Shandong, China Received 24 January 2001; in final form 25 January 2002
Abstract Three ab initio potential energy surfaces of 2 B2 , 2 A1 and 2 R states for the Na þ I2 collision system are calculated on the QCISD(T)/LANL2DZ level. Three reaction channels, neutral reaction, chemical ionization and collision ionization, have been obtained based on analyzing the minimum energy reaction paths. The valence potential energy surfaces 2 A1 and the ionic state 2 B2 are crossed approximately at Rc ¼ 0:508 nm. Na þ I2 ! Naþ þ I 2 is an electronic non-adiabatic process. Ó 2002 Published by Elsevier Science B.V.
Charge transfer and chemi-ionization processes between alkali metal atom M (M ¼ K, Na, Cs, etc.) and halogen molecule X2 (X ¼ I, Br, Cl, etc.) during collision are the well-known phenomena, from which valuable information of collisionally induced reaction dynamics can be obtained [1–3]. Among these reactions, the reaction of Na atom with I2 molecule is the typical one, attracting theoreticians and experimentalists to investigate its mechanism. Banares et al. [4] measured the differential reaction sections by laser-crossed beam experiment. In 1977, Aten et al. [5] developed a semi-empirical potential energy surface for the formation of ion-pair, Na þ I2 ! Naþ þ I 2 . They also performed a classical trajectory calculation for the surface hopping. On the same potential energy
*
Corresponding author. Fax: +86-531-856-4464. E-mail address: [email protected] (Z. Cai).
surface, Ma et al. [6] calculated the collinear reaction probabilities using a quantum reaction scattering method, LCAC-SW (linear combination arrangement channels-scattering wavefunction). To our knowledge, no ab intio potential surface for Na þ I2 system has been reported up to now. Since this reaction involves to a coupling of potential energy surfaces, in other words, the reaction undergoes with a electronically non-adiabatic crossing process, semi-empirical potential energy surface is thus not accurate to deal with. In the present Letter, ab initio potential energy surfaces for the Na þ I2 collision system based on the QCISD(T)/LANL2DZ level are reported. The coordinate system used in the calculations is presented in Fig. 1. Some calculation results are given in Table 1 and Figs. 2–5. The detailed illustration describes as the following: (1) A minimum energy of E ¼ 22:636729 a.u. is obtained by optimizing all the coordinates of the
0009-2614/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 2 4 9 - X
286
D. Feng et al. / Chemical Physics Letters 355 (2002) 285–288
Fig. 1. Relative coordinates for system Na þ I2 .
Na þ I2 system in 2 B2 electronic state. The geometric structure of the species (presented by configuration A) has C2v symmetry (r1 ¼ 0:3542 nm, R ¼ 0:2468 nm). It is a long-lived complex, having a potential valley on the potential energy surface. From the population analysis, it is known that the species is a strong polar intermediate (the net charges on Na and each I are 0.90 and )0.45, respectively). The positive charge is almost centered at Na atom. Table 1 lists six possible product channels of the reaction between Na and I2 . The products are þ Na þ I2 , Naþ þ I 2 , NaI þ I, NaI þ I , Na + I + I þ and Na þ I þ I, respectively. Energetically, Na þ I2 ! NaI þ I is the most favorable channel, while Na þ I2 ! Naþ þ I þ I is the most unfavorable one. The calculated reaction energies for
the six product channels agree with the thermodynamic data [7]. (2) Fig. 2 shows the potential energy surface of the collinear collision system with C1v symmetry (a ¼ 180°, see Fig. 1). The potential energy surface of 2 R state has been obtained by scanning both r1 and r2 (step-length is 0.01 nm). The energy of the reactants Na þ I2 (r1 ¼ 0:293 nm and r2 ! 1) is 22:54788 a.u. There is no potential barrier in the pathway from the reactants to the collinear complex. A potential basin on the surface refers to a collinear complex NaI2 ðC1v Þ. The collinear complex is unstable and its energy is 22:61687 a.u., only 9.0 kJ/mol lower than that of NaI + I. The pathway from NaI2 to the products NaI + I is also very flat without potential barrier. (3) For the side-on attack (h ¼ 90° see Fig. 1), there are two potential energy surfaces for the collision system. Both are of C2v symmetry. The potential energy surfaces are calculated with the scanning for both the r1 and R with the same step-length 0.0255 nm. The equal-counter potential plots are shown in Fig. 3 for 2 A1 state and in Fig. 4 for 2 B2 state, respectively. The point r1 ¼ 0:3411 nm and R ¼ 0:9 nm at 2 B2 state is close to the ion-pair species Naþ þ I 2, and located at the entrance of the reaction path. The total energy of the system is 22:51180 a.u. The electric charges on the Na atom and on each I atom are 0.9995 and 0:4997, respectively. No potential barrier exists from the entrance to the complex A. From the natural population, at every point on the 2 B2 surface the net charge on atom Na
Table 1 Energies of several special points on the potential energy surfaces of Na þ I2 system Sample Na þ I2 Naþ þ I 2 NaI + I þ NaI þ I NaI2 (2 R; C1v ) NaI2 (2 B2 ; C2v ) Na + I + I Naþ þ I þ I
h (deg)
0 90
r1 (nm)
r2 (nm)
E (a.u.)
0.29318 0.34112 1 1 0.38025 0.35422 1 1
1 1 0.28454 0.33500 0.28500 0.30375 1 1
)22.54788 )22.45375 )22.61346 )22.42989 )22.61687 )22.63672 )22.51613 )22.41841
D. Feng et al. / Chemical Physics Letters 355 (2002) 285–288
Fig. 2. Scheme plot of the potential energy surface for Na þ I2 collinear collision system ða ¼ 180°Þ.
287
Fig. 4. Scheme plot of the potential energy surface for Na þ I2 collision system (h ¼ 90°, C2v symmetry, 2 B2 state).
Fig. 5. The nonadiabatic coupling of the potential energy sur). face of 2 B2 and 2 A1 states for Na þ I2 system (r1 ¼ 3:0 A
Fig. 3. Scheme plot of the potential energy surface for Na þ I2 collision system (h ¼ 90°, C2v symmetry, 2 A1 state).
is more than 0.90, therefore the 2 B2 state surface shown in Fig. 4 is an ionic surface. Another C2v state, 2 A1 , refers to the neutral products Na þ I2 . The entrance point of the reaction path, r1 ¼ 0:29316 nm and R ¼ 0:9 nm, is close to the reactant Na þ I2 . Its energy is 22:54791 a.u., natural charges are both 0.000 for atom Na and I, respectively. The potential energy surface of 2 A1 state (Fig. 3) can be obtained by the similar way of that of 2 B2 . No energy minimum on
2
A1 surface is found. The net electric charges either in atom Na or in atom I is almost zero. The minimum energy reaction pathways on the 2 A1 state and 2 B2 state can be found on Figs. 3 and 4, respectively. It is clear that the two potential energy surfaces, the neutral state or valence system 2 Na þ I2 ð A1 Þ and the ionic state or ionic system þ 2 Na þ I2 ð B2 Þ, are crossed. Fig. 5 shows a section of the two surfaces at r1 ¼ 0:3 nm. The crossed point between two profiles is approximately at Rc ¼ 0:508 nm, where the harpoon process of the electron leaping occurs [8]. Large ion-pair formation cross-section for Na þ I2 ! Naþ þ I 2 system
288
D. Feng et al. / Chemical Physics Letters 355 (2002) 285–288
has been calculated using this cross distance Rc to Landau–Zener model [8], which is in qualitative agreement with the laser-crossed beam experiment for Na þ I2 ! Naþ þ I 2 reaction [6]. Other reaction channels for the Na þ I2 system can be analyzed by means of the same procedure given above. Results will be presented in our future paper.
Acknowledgements This work was supported by the National Natural Scientific Foundation of China (No. 20173032).
References [1] A.P.M. Baede, Adv. Chem. Phys. 30 (1975) 463. [2] D.J. Auerbach, M.M. Hubers, A.P.M. Baeder, J. Los, Chem. Phys. 2 (1973) 107. [3] P.W. Harland, H.S. Carma Jr., L.F. Phillips, P.R. Brooks, J. Chem. Phys. 93 (1990) 1089. [4] L. Banares, M.G. Velarde, A.G. Urena, J. Chem. Phys. 95 (1991) 5474. [5] J.A. Aten, G.E.H. Lanting, J. Los, Chem. Phys. 19 (1977) 241. [6] W.Y. Ma, Z.T. Cai, D.H. Deng, Chem. Phys. Lett. 304 (1999) 117. [7] CRC Handbook of Chemistry and Physics, 73th edn., CRC Press Inc., Boca Raton, FL, 1992–1993. [8] H. Erying, S.H. Lin, S.M. Lin, Basic Chemical Kinetics, John Wiley & Sons, New York, 1980 (Chapter 6).