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This paper reports low-energy electron scattering with $ {{\mathrm{C}}}_{4}^{-} $ anions by using the ab initio R -matrix method in the single state close-coupling (CC) model and the fixed-nuclei approximation. We predict the elastic integral scattering cross sections (ICSs) of four conformers of $ {{\mathrm{C}}}_{4}^{-} $ ions in an energy range of 0 < E ≤12 eV and discuss the effects of configuration changes on resonance position and width. Additionally, the theoretical results and experimental data are compared and analyzed. The results indicate that the 8.8 eV resonance peak observed in experiment is mainly derived from the $ {{{\Sigma }}}_{{\mathrm{u}}}^{+} $ and $ {{{\Sigma }}}_{{\mathrm{u}}}^{-} $ resonances of the conformer A and the A2 resonance of the conformer C. The scattering cross-section reveals that the conformer A has five resonant states, and the conformer B has three resonances, while C and D each have four resonances. Finally, we use the Boltzmann distribution to calculate the populations of different conformers at different temperatures, and simulate the low-energy electron elastic integrated scattering cross-section at room temperature, which is in good agreement with available experimental results. We also find a shape resonance with a width of 0.20 eV at 3.3 eV in our total cross sections, which is not detected in the existing experimental results. This provides new opportunities for measurement.
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Keywords:
- electron scattering /
- conformers of $ {{\mathrm{C}}}_{4}^{-} $ ions /
- R-matrix method /
- resonance /
- cross section
[1] Douglas A E 1977 Nature 269 130
Google Scholar
[2] Gerhardt P, Loffler S, Homann K H 1987 Chem. Phys. Lett. 137 306
Google Scholar
[3] Bernath P F, Hinkle K H, Keady J J 1989 Symp. Int. Combust. 244 562
Google Scholar
[4] Tulej M, Kirkwood D A, Pachkov M, Maier J P 1998 Astrophys. J 506 69
Google Scholar
[5] Helden G V, Hsu M T, Kemper P R, Bowers M T 1991 J. Chem. Phys 95 3835
Google Scholar
[6] Helden G V, Kemper P R, Gotts N G, Bowers M T 1993 Science 259 1300
Google Scholar
[7] Helden G V, Hsu M T, Gotts N G, Bowers M T 1993 Chem. Phys. Lett 97 8182
Google Scholar
[8] Gotts N G, Helden G V, Bowers M T 1995 Int. J. Mass Spectrom. Ion Processes 149-150 217
Google Scholar
[9] Giuffreda M G, Deleuze M S, François J P 2002 J. Chem. Phys. 106 8569
Google Scholar
[10] Adamowicz L 1991 Chem. Phys. 156 387
Google Scholar
[11] Schmatz S, Botschwina P 1995 Int. J. Mass Spectrom. Ion Processes 149 621
Google Scholar
[12] Dreuw A, Cederbaum L S 2001 Phys. Rev. A 63 049904
Google Scholar
[13] Padellec A L, Rabilloud F, Pegg D, Neau A, Hellberg F, Thomas R D, Schmidt H T, Larsson M, Danared H, Kallberg A, Andersson K, Hanstorp D 2001 J. Chem. Phys. 115 10671
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[14] Fritioff K, Sandström J, Andersson P, Hanstorp D, Hellberg F, Thomas R, Larsson M, Österdahl F, Collins G F, Le Padellec A, Pegg D J, Gibson N D, Danared H, Källberg A 2004 J. Phys. B: At. Mol. Opt. Phys. 37 2241
Google Scholar
[15] Morgan L A, Gillan C J, Tennyson J, Chen X 1997 J. Phys. B: At. Mol. Opt. Phys. 30 4087
Google Scholar
[16] Morgan, L A, Tennyson J, Gillan C J 1998 Comput. Phys. Commun. 114 120
Google Scholar
[17] Mašín Z, Benda J, Gorfinkiel J D, Harvey A G, Tennyson J, 2020 Comput. Phys. Commun. 249 107092
Google Scholar
[18] Tennyson J 2010 Phys. Rep. 491 29
Google Scholar
[19] Carr J M, Galiatsatos P G, Gorfinkiel J D, Harvey A G, Lysaght M A, Madden D, Mašín Z, Plummer M, Tennyson J, Varambhia H N 2012 Eur. Phys J. D 66 58
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[20] Watts J D, Gauss J, Stanton J F, Bartlett R J 1992 J. Chem. Phys. 97 8372
Google Scholar
[21] Takeshi Y, Tew D P, Handy N C 2004 Chem. Phys. Lett. 393 51
Google Scholar
[22] Tirado-Rives J, Jorgensen W L 2008 J. Chem. Theory Comput. 4 297
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[23] Andersson M P, Uvdal P 2005 J. Phys. Chem. A 109 2937
Google Scholar
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图 1 $ {{\mathrm{C}}}_{4}^{-} $离子的四种异构体和相对能量(单位eV) (a) 异构体A (2Πg) 0.00; (b) 异构体B (2Σg) +1.09; (c) 异构体C (2B1) +1.36; (d) 异构体D (2B2g) +1.39; 使用的方法是CCSD(T), 基组为aug-cc-pVQZ
Figure 1. Four conformers of $ {{\mathrm{C}}}_{4}^{-} $ anion and there relative energy (In unit of eV): (a) Conformer A (2Πg) 0.00; (b) conformer B (2Σg) +1.09; (c) conformer C (2B1) +1.36; (d) conformer D (2B2g) +1.39. The theoretical method is CCSD(T) and the basis set is aug-cc-pVQZ.
图 2 不同的活化空间下$ {{\mathrm{C}}}_{4}^{-} $离子异构体A弹性散射截面
Figure 2. Elastic scattering cross sections for the conformer A of $ {{\mathrm{C}}}_{4}^{-} $ anion in three different CAS.
图 3 $ {{\mathrm{C}}}_{4}^{-} $离子异构体A的低能弹性积分散射截面 (a) 不同基组的CC单态散射截面; (b) SEP, CC单态模型的散射截面. 方框为Fritioff等获得的实验数据
Figure 3. Low energy elastic integral cross section of the conformer A of $ {{\mathrm{C}}}_{4}^{-} $: (a) The cross sections of single state CC model with four different basis sets; (b) the cross sections of SEP and single state CC models. The experimental data obtained by Fritioff et al. is also shown.
图 4 $ {{\mathrm{C}}}_{4}^{-} $离子A异构体的弹性散射积分截面
Figure 4. Elastic integral cross sections of symmetry components of $ {{\mathrm{C}}}_{4}^{-} $ conformer A.
图 5 $ {{\mathrm{C}}}_{4}^{-} $离子B异构体的弹性散射积分截面
Figure 5. Elastic integral cross sections of symmetry components of $ {{\mathrm{C}}}_{4}^{-} $ conformer B.
图 6 $ {{\mathrm{C}}}_{4}^{-} $离子C异构体的弹性散射积分截面
Figure 6. Elastic integral cross sections of symmetry components of $ {{\mathrm{C}}}_{4}^{-} $conformer C.
图 7 $ {{\mathrm{C}}}_{4}^{-} $离子D异构体的弹性散射积分截面
Figure 7. Elastic integral cross sections of symmetry components of $ {{\mathrm{C}}}_{4}^{-} $ conformer D.
图 8 $ {{\mathrm{C}}}_{4}^{-} $四种异构体的电子弹性散射截面以及根据玻尔兹曼分布拟合的常温下的散射总截面
Figure 8. Total elastic scattering cross sections of four $ {{\mathrm{C}}}_{4}^{-} $conformers and cross sections of the mixed conformers fitted at room temperature according to the Boltzmann distribution.
表 1 $ {{\mathrm{C}}}_{4}^{-} $异构体A的键长
Table 1. Bond length of conformer A of $ {{\mathrm{C}}}_{4}^{-} $.
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表 2 $ {{\mathrm{C}}}_{4}^{-} $的异构体A的共振位置和宽度
Table 2. Resonance position and width of conformer A of $ {{\mathrm{C}}}_{4}^{-} $.
State Position/eV Width/eV $ {{{\Sigma }}}_{{\mathrm{g}}}^{+}/ $Ag 3.3 0.20 $ {{{\Sigma }}}_{{\mathrm{u}}}^{+}/ $B1u 8.8 0.75 $ {{{\Sigma }}}_{{\mathrm{u}}}^{-}/ $Au 9.1 1.99 $ {{{\Pi }}}_{{\mathrm{u}}}/ $B2u+B3u 10.1 0.15 $ {{{\Pi }}}_{{\mathrm{g}}}/ $B2g+B3g 10.4 0.15
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表 3 $ {{\mathrm{C}}}_{4}^{-} $的异构体B的共振位置和宽度
Table 3. Resonance position and width of conformer B of $ {{\mathrm{C}}}_{4}^{-} $.
State Position/eV Width/eV $ {{{\Sigma }}}_{{\mathrm{g}}}^{+}/ $Ag 2.1 0.23 $ {{{\Pi }}}_{{\mathrm{u}}}/ $B2u+B3u 9.6 2.2 $ {{{\Pi }}}_{{\mathrm{g}}}/ $B2g+B3g 10.1 0.14
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表 4 $ {\rm C}_{4}^{-}$ 的异构体C的共振位置和宽度
Table 4. Resonance position and width of conformer C of $ {{\mathrm{C}}}_{4}^{-} $.
State Position/eV Width/eV A1 4.7 0.42 A2 8.6 1.36 B2 10.6 3.23 A1 11.0 0.56
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表 5 $ {{\mathrm{C}}}_{4}^{-} $的异构体D的共振位置和宽度
Table 5. Resonance position and width of the conformer D of $ {{\mathrm{C}}}_{4}^{-} $.
State Position/eV Width/eV B1g 5.76 0.47 Ag 6.0 0.14 Ag 9.2 5.20 B1u 11.0 1.80
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表 6 $ {{\mathrm{C}}}_{4}^{-} $四种异构体随温度变化的百分比
Table 6. Proportions of the four conformers vary with temperature.
异构体 温度T /K 100 200 298.15 400 800 1500 3000 10000 A 99.43 89.00 74.15 62.50 42.79 33.93 29.27 26.24 B 0.38 5.51 11.47 15.55 21.34 23.41 24.31 24.82 C 0.11 2.92 7.49 11.32 18.21 21.51 23.31 24.50 D 0.08 2.58 6.89 10.63 17.65 21.15 23.11 24.44
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[1] Douglas A E 1977 Nature 269 130
Google Scholar
[2] Gerhardt P, Loffler S, Homann K H 1987 Chem. Phys. Lett. 137 306
Google Scholar
[3] Bernath P F, Hinkle K H, Keady J J 1989 Symp. Int. Combust. 244 562
Google Scholar
[4] Tulej M, Kirkwood D A, Pachkov M, Maier J P 1998 Astrophys. J 506 69
Google Scholar
[5] Helden G V, Hsu M T, Kemper P R, Bowers M T 1991 J. Chem. Phys 95 3835
Google Scholar
[6] Helden G V, Kemper P R, Gotts N G, Bowers M T 1993 Science 259 1300
Google Scholar
[7] Helden G V, Hsu M T, Gotts N G, Bowers M T 1993 Chem. Phys. Lett 97 8182
Google Scholar
[8] Gotts N G, Helden G V, Bowers M T 1995 Int. J. Mass Spectrom. Ion Processes 149-150 217
Google Scholar
[9] Giuffreda M G, Deleuze M S, François J P 2002 J. Chem. Phys. 106 8569
Google Scholar
[10] Adamowicz L 1991 Chem. Phys. 156 387
Google Scholar
[11] Schmatz S, Botschwina P 1995 Int. J. Mass Spectrom. Ion Processes 149 621
Google Scholar
[12] Dreuw A, Cederbaum L S 2001 Phys. Rev. A 63 049904
Google Scholar
[13] Padellec A L, Rabilloud F, Pegg D, Neau A, Hellberg F, Thomas R D, Schmidt H T, Larsson M, Danared H, Kallberg A, Andersson K, Hanstorp D 2001 J. Chem. Phys. 115 10671
Google Scholar
[14] Fritioff K, Sandström J, Andersson P, Hanstorp D, Hellberg F, Thomas R, Larsson M, Österdahl F, Collins G F, Le Padellec A, Pegg D J, Gibson N D, Danared H, Källberg A 2004 J. Phys. B: At. Mol. Opt. Phys. 37 2241
Google Scholar
[15] Morgan L A, Gillan C J, Tennyson J, Chen X 1997 J. Phys. B: At. Mol. Opt. Phys. 30 4087
Google Scholar
[16] Morgan, L A, Tennyson J, Gillan C J 1998 Comput. Phys. Commun. 114 120
Google Scholar
[17] Mašín Z, Benda J, Gorfinkiel J D, Harvey A G, Tennyson J, 2020 Comput. Phys. Commun. 249 107092
Google Scholar
[18] Tennyson J 2010 Phys. Rep. 491 29
Google Scholar
[19] Carr J M, Galiatsatos P G, Gorfinkiel J D, Harvey A G, Lysaght M A, Madden D, Mašín Z, Plummer M, Tennyson J, Varambhia H N 2012 Eur. Phys J. D 66 58
Google Scholar
[20] Watts J D, Gauss J, Stanton J F, Bartlett R J 1992 J. Chem. Phys. 97 8372
Google Scholar
[21] Takeshi Y, Tew D P, Handy N C 2004 Chem. Phys. Lett. 393 51
Google Scholar
[22] Tirado-Rives J, Jorgensen W L 2008 J. Chem. Theory Comput. 4 297
Google Scholar
[23] Andersson M P, Uvdal P 2005 J. Phys. Chem. A 109 2937
Google Scholar
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