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Accurate theoretical study of potential energy curves, spectroscopic parameters, vibrational energy levels and spin-orbit coupling interaction on SiH+(X1Σ+) ion

Gao Feng ,  Zhang Hong ,  Zhang Chang-Zhe ,  Zhao Wen-Li ,  Meng Qing-Tian

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Accurate theoretical study of potential energy curves, spectroscopic parameters, vibrational energy levels and spin-orbit coupling interaction on SiH+(X1Σ+) ion

Gao Feng, Zhang Hong, Zhang Chang-Zhe, Zhao Wen-Li, Meng Qing-Tian
Acta Phys. Sin., 2021, 70(15): 153301.
doi: 10.7498/aps.70.20210450
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  • Abstract

    The analytical potential energy function (APEF) of SiH+(X1Σ+) is fitted by Aguado-Paniagua function with 112 ab initio energy points, which are calculated by Molpro 2012 Package with the multi-reference configuration interaction including the Davidson correction method using AVX Z and AVX dZ (X = Q, 5, 6) basis sets. Moreover, the calculated ab initio energy points are subsequently extrapolated to complete basis set (CBS) limit to avoid the basis set superposition error. All the fitting parameters of APEFs for AV6Z, CBS(Q, 5), AV6dZ, CBS(Qd, 5d), SA-AV6dZ and SOC-AV6dZ methods are gathered. The potential energy curves (PEC) and the corresponding ab initio points are also shown. As can be seen, the PECs show excellent agreement with the ab initio points and a smooth behavior both in short range and long range, which ensures the high quality of fitting process for the current APEFs. Based on these APEFs of different basis sets and methods including AVQZ, AV5Z, AV6Z, CBS(Q, 5), AVQdZ, AV5dZ, AV6dZ and CBS(Qd, 5d), the spectral constants De, Re, ωe, Be, αe and ωeχe are obtained. In addition, the effects of spin-orbit coupling interaction (SOC) on the system are also investigated. By comparing the spectral constants of SA-AV6dZ with the ones of SOC-AV6dZ, it is found that the effect of SOC on SiH+(X1Σ+) is small and can be ignored. We also compare the spectral constants in this work with the experimental values and other theoretical results. The results of this work accord well with the corresponding experimental and other theoretical results. It is worth noting that the deviation of dissociation energy between the theoretical calculations and experimental values is relatively large. Based on this conclusion, we suggest that the spectral constants including the dissociation energy for SiH+(X1Σ+) should be remeasured. Based on the APEF of SOC-AV6dZ which should be more accurate than others in theory, the top 23 vibrational states (j = 0) of SiH+(X1Σ+) are calculated first by solving the radial Schrödinger equation. All the vibrational energy levels, classical turning points, rotation constants and six centrifugal distortion constants are also provided. The results of this work can provide significant references for the experimental and other theoretical work.

    Authors and contacts

    • 1.

      School of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China

    • 2.

      School of Physics and Electronics, Shandong Normal University, Jinan 250358, China

      • Corresponding author: Zhao Wen-Li, zwl@sdau.edu.cn ; Meng Qing-Tian, qtmeng@sdnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11674198, 11804195)

    References

    [1]

    Grevesse N, Sauval A J 1970 Astron. Astrophys. 9 232
    [2]

    Douglas A E, Lutz B L 1970 Can. J. Phys. 48 247Google Scholar

    [3]

    Grevesse N, Sauval A J 1971a J. Quant. Spectrosc. Radiat. Transf. 11 65Google Scholar

    [4]

    Almeida A A, Sing P D 1978 Astrophys. Space Sci. 56 415Google Scholar

    [5]

    Gao W, Wang B B, Hu X J, Chai S, Han Y C, Greenwood J B 2017 Phys. Rev. A 96 013426Google Scholar

    [6]

    Wang B B, Han Y C, Gao W, Cong S L 2017 Phys. Chem. Chem. Phys. 19 22926Google Scholar

    [7]

    Moore P L, Browne J C, Matsen F A 1965 J. Chem. Phys. 43 903Google Scholar

    [8]

    Cosby P C, Helm H, Moseley J T 1980 Astrophys. J. 235 52Google Scholar

    [9]

    Barinovs G, Hemert M C V 2006 Astrophys. J. 636 923Google Scholar

    [10]

    Ram R S, Engleman R, Bernath P F 1998 J. Mol. Spectrosc. 190 341Google Scholar

    [11]

    Singh P D, Vanlandingham F G 1978 Astron. Astrophys. 66 87Google Scholar

    [12]

    Carlson T A, Copley J, Duric N, Elander N, Erman P, Larsson M, Lyyra M 1980 Astron. Astrophys. 83 238
    [13]

    Hishikawa A, Karawajczyk A 1993 J. Mol. Spectrosc. 158 479Google Scholar

    [14]

    Davies P B, Martineau P M 1988 J. Chem. Phys. 88 485Google Scholar

    [15]

    Mosnier J P, Kennedy E T, Kampen P V, Cubaynes D, Guilbaud S, Sisourat N, Puglisi A, Carniato S, Bizau J M 2016 Phys. Rev. A 93 061401Google Scholar

    [16]

    Hirst D M 1986 Chem. Phys. Lett. 128 504Google Scholar

    [17]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum Che. 8 61Google Scholar

    [18]

    Matos J M O, Kello V, Roos B O, Sadlej A J 1988 J. Chem. Phys. 89 423Google Scholar

    [19]

    Sannigrahi A B, Buenker R J, Hirsch G, Gu J P 1995 Chem. Phys. Lett. 237 204Google Scholar

    [20]

    Werner H J, Knowles P J, Lindh R, Manby F R, Schutz M, et al. Molpro, A Package of ab initio Programs (Version 2015.1) http://www.molpro.net [2021-03-08]
    [21]

    Zhang Y G, Dou G, Cui J, Yu Y 2018 J. Mol. Struct. 1165 318Google Scholar

    [22]

    Neese F 2011 Wiley Interdisci. Rev. Comput. Mol. Sci. 2 73
    [23]

    Biglari Z, Shayesteh A, Ershadifar S 2018 J. Quant. Spectrosc. Radiat. Transf. 221 80Google Scholar

    [24]

    Werner H J, Knowles P J, Lindh R, Manby F R, Schutz M, et al. Molpro, A Package of ab initio Programs (Version 2012.1) http://www.molpro.net [2021-03-08]
    [25]

    Aguado A, Paniagua M 1992 J. Chem. Phys. 96 1265Google Scholar

    [26]

    Aguado A, Tablero C, Paniagua M 1998 Comput. Phys. Commun. 108 259Google Scholar

    [27]

    Varandas A J C 2007 J. Chem. Phys. 126 244105Google Scholar

    [28]

    Varandas A J C 2000 J. Chem. Phys. 113 8880Google Scholar

    [29]

    Jansen H B, Ross P 1969 Chem. Phys. Lett. 3 140Google Scholar

    [30]

    Liu B, McLean A D 1973 J. Chem. Phys. 59 4557Google Scholar

    [31]

    Karton A, Martin J M L 2006 Theor. Chem. ACC. 115 330Google Scholar

    [32]

    Yang C L, Huang Y J, Zhang X, Han K L 2003 J. Mol. Struc. Theochem. 625 289Google Scholar

    [33]

    Yang C L, Zhang X, Han K L 2004 J. Mol. Struc. Theochem. 676 209Google Scholar

    [34]

    Huber K P, Herzberg G 1979 Molecular Spectra and Molecular Structure (Vol. IV) (New York: Springer) p600
    [35]

    Roy R J L 2017 J. Quant. Spectrosc. Radiat. Transf. 186 167Google Scholar

  • 图 1  SiH+(X1Σ+)在CBS(Q, 5)和AV6Z基组下的势能曲线和从头算能量点

    Figure 1.  Potential energy curves and ab initio points at CBS(Q, 5) and AV6Z results.

    DownLoad: Full-Size Img PowerPoint

    图 2  SiH+(X1Σ+)应用CBS(Qd, 5d)和AV6dZ基组的势能曲线和从头算能量点

    Figure 2.  Potential energy curves and ab initio points at CBS(Qd, 5d) and AV6dZ results.

    DownLoad: Full-Size Img PowerPoint

    图 3  SiH+离子的${{\rm{X}}^1}{\Sigma ^ + }$, ${{\rm{A}}^1}\Pi$, ${\rm{b}}{}^3{\Sigma ^ + }$和${{\rm{a}}^3}\Pi$态在SOC-AV6dZ基组下的从头算能量点

    Figure 3.  The ab initio points of ${{\rm{X}}^1}{\Sigma ^ + }$, ${{\rm{A}}^1}\Pi$, ${\rm{b}}{}^3{\Sigma ^ + }$ and ${{\rm{a}}^3}\Pi$ states for SiH+ cation at SOC-AV6dZ results.

    DownLoad: Full-Size Img PowerPoint

    图 4  SiH+(X1Σ+)在SA-AV6dZ和SOC-AV6dZ基组下的从头算能量点与拟合势能曲线

    Figure 4.  Potential energy curves and ab initio points at SA-AV6dZ and SOC-AV6dZ results.

    DownLoad: Full-Size Img PowerPoint

    图 5  SiH+(X1Σ+)离子在SOC-AV6 dZ方法下, j = 0时的前23个振动能级

    Figure 5.  Top 23 vibrational energy levels of SiH+(X1Σ+) when j = 0 at SOC-AV6 dZ result.

    DownLoad: Full-Size Img PowerPoint

    表 1  SiH+(X1Σ+) APEFs的拟合参数

    Table 1.  Parameters of APEFs for SiH+(X1Σ+).

    AV6ZCBS(Q, 5)AV6dZCBS(Qd, 5d)SA-AV6dZSOC-AV6dZ
    a00.50876826×1010.50552062×1010.50858283×1010.50691706×1010.50773275×1010.50772768×101
    a1–0.13804619×100–0.14563907×100–0.13801387×100–0.14215220×100–0.13720269×100–0.15322183×100
    a2–0.13563746×101–0.14531223×101–0.13570613×101–0.14215828×101–0.16375066×1010.30937784×100
    a3–0.51802913×102–0.49687570×102–0.51738027×102–0.50317640×102–0.42586263×102–0.92938545×102
    a40.62749955×1030.59645776×1030.62624067×1030.60422890×1030.45856480×1030.11152320×104
    a5–0.48068238×104–0.45486708×104–0.47942732×104–0.45972031×104–0.30344319×104–0.81653091×104
    a60.26148147×1050.24858810×1050.26073093×1050.24994077×1050.14706913×1050.40426343×105
    a7–0.98935973×105–0.94946694×105–0.98651660×105–0.94886015×105–0.51962969×105–0.13681997×106
    a80.24960293×1060.24200403×1060.24891691×1060.24047472×1060.12676883×1060.31028426×106
    a9–0.39722347×106–0.38879401×106–0.39620641×106–0.38442238×106–0.19927330×106–0.44979467×106
    a100.35937312×1060.35468541×1060.35853489×1060.34921672×1060.18029764×1060.37617755×106
    a11–0.14069370×106–0.13986829×106–0.14040272×106–0.13721966×106–0.71149416×106–0.13802294×106
    β10.68900.68000.68900.68400.68700.6870
    β20.74700.74700.74700.74700.74700.7470
    ∆Ermsd/
    (kcal·mol–1)    		1.60176420×10–21.61755859×10–21.60042370×10–21.627559848×10–29.45767662×10–31.11170443×10–2
    DownLoad: CSV

    表 2  SiH+(X1Σ+)的平衡键长Re, 解离能De, 振动频率ωe, 光谱常数ωeχe, αe和βe

    Table 2.  Spectroscopic constants compared with the experimental values and other theoretical results for SiH+(X1Σ+).

    基组De(Eh)Re(a0)ωe/cm–1βe/cm–1αe/cm–1ωeχe/cm–1
    AVQZ0.1246402.8519252153.2457.6074400.21932742.373
    AV5Z0.1253882.8485892155.7927.6252720.21896042.220
    AV6Z0.1255842.8480012156.6867.6284100.21883342.189
    CBS(Q, 5)0.1258562.8470532157.1897.6335020.21862242.117
    AVQdZ0.1250672.8488772156.1877.6237290.21942742.343
    AV5dZ0.1254612.8480672156.7377.6280670.21901142.232
    AV6dZ0.1256222.8477282157.0467.6298810.21884942.190
    CBS(Qd, 5d)0.1258012.8477822156.6027.6295930.21853442.112
    SA-AV6dZ0.1272642.8485312163.4487.6255810.21672541.893
    SOC-AV6dZ0.1265332.8483822164.0337.6263780.21788542.158
    Expe[12,34]0.1232032.8423382157.177.66030.209634.24
    Theory[16]0.1186652.8345902155.47.67860.208238.8
    Theory[18]0.1239822.8440392172.0———
    Theory[21]0.1253172.8345902177.97.6984—36.7
    Theory[23]0.1249802.8421492154.37.66090.203235.0
    DownLoad: CSV

    表 3  SiH+(X1Σ+)离子在SOC-AV6dZ方法下, j = 0时的前23个振动能级G(v)、经典拐点和惯性转动常数Bv

    Table 3.  Vibrational levels G(v), classical turn point androtational constant Bv for SiH+(X1Σ+) when j = 0 at SOC-AV6dZ result.

    vG(v)/ cm–1Rmin(a0)Rmax(a0)Bv/ cm–1
    01074.4672.629813.111417.530487
    13171.2242.493473.338627.336827
    25200.5432.409843.515947.142529
    37162.2312.347563.674986.947281
    49055.7422.297613.825126.750433
    510880.1242.255953.970916.551101
    612634.0052.220313.915056.348250
    714315.6002.189344.260096.140735
    815922.7262.162134.407425.927312
    917452.8022.138034.558935.706603
    1018902.8352.116614.716505.477032
    1120269.3642.097524.882275.236702
    1221548.3632.080515.058884.983201
    1322735.0662.065405.249864.713296
    1423823.6942.052065.460164.422419
    1524807.0102.040415.697314.103776
    1625675.5992.030415.973793.746622
    1726416.6252.022086.312783.332604
    1827011.5792.015536.765452.826988
    1927432.5462.010967.483102.158867
    2027650.9562.008619.059751.323582
    2127734.4622.0077111.475530.838944
    2227769.2562.0073416.605760.360244
    DownLoad: CSV

    表 4  SiH+(X1Σ+)离子在SOC-AV6dZ方法下, j = 0时的前23个振动能级的6个离心畸变常数Dv, Hv, Lv, Mv, Nv和Ov

    Table 4.  Six centrifugal distortion constants Dv, Hv, Lv, Mv, Nv和Ov for the top 23 vibrational states of SiH+(X1Σ+) when j = 0 at SOC-AV6dZ result.

    vDv (× 10–4)Hv (× 10–8)LvMvNvOv
    0–3.77121021.4824556–9.1045 × 10–134.1069 × 10–17–2.4011 × 10–216.9631 × 10–26
    1–3.73620901.4243863–8.8032 × 10–133.5297 × 10–17–4.1863 × 10–211.8363 × 10–25
    2–3.70398651.3618539–8.9866 × 10–132.9262 × 10–17–5.1444 × 10–211.9171 × 10–25
    3–3.67786871.2884893–9.4914 × 10–132.3397 × 10–17–5.8593 × 10–219.6796 × 10–26
    4–3.66080931.2011917–1.0216 × 10–121.6648 × 10–17–6.8904 × 10–21–1.1678 × 10–25
    5–3.65530381.0982022–1.1140 × 10–126.8522 × 10–18–8.7371 × 10–21–4.8697 × 10–25
    6–3.66351990.9774540–1.2320 × 10–12–9.1302 × 10–18–1.2003 × 10–20–1.1229 × 10–24
    7–3.68756610.8351772–1.3901 × 10–12–3.5900 × 10–17–1.7702 × 10–20–2.2781 × 10–24
    8–3.72986130.6645057–1.6143 × 10–12–8.0925 × 10–17–2.7799 × 10–20–4.5064 × 10–24
    9–3.79361800.4536483–1.9481 × 10–12–1.5748 × 10–16–4.6321 × 10–20–9.0505 × 10–24
    10–3.88350551.8293995–2.4663 × 10–12–2.9088 × 10–16–8.1928 × 10–20–1.8869 × 10–23
    11–4.0066389–0.1804552–3.3026 × 10–12–5.3251 × 10–16–1.5445 × 10–19–4.1577 × 10–23
    12–4.1741837–0.6927552–4.7113 × 10–12–9.9426 × 10–16–3.1311 × 10–19–9.8710 × 10–23
    13–4.4041727–1.4546951–7.2135 × 10–12–1.9417 × 10–15–6.9300 × 10–19–2.5871 × 10–22
    14–4.7268845–2.6591579–1.1978 × 10–11–4.0783 × 10–15–1.7160 × 10–18–7.7417 × 10–22
    15–5.1961278–4.7106022–2.1959 × 10–11–9.5527 × 10–15–4.9431 × 10–18–2.7809 × 10–21
    16–5.9157772–8.5688303–4.5904 × 10–11–2.6336 × 10–14–1.7665 × 10–17–1.2991 × 10–20
    17–7.1117968–16.938203–1.1615 × 10–10–9.3420 × 10–14–8.7454 × 10–17–9.0301 × 10–20
    18–9.3643712–39.467832–3.9578 × 10–10–4.9264 × 10–13–7.1396 × 10–16–1.1444 × 10–18
    19–14.323856–114.68916–1.7949 × 10–9–3.4005 × 10–12–7.1696 × 10–15–1.6154 × 10–17
    20–18.399913–47.3241911.5501 × 10–9–7.5768 × 10–13–3.7548 × 10–14–1.9274 × 10–17
    21–14.637253–291.40012–2.0665 × 10–8–1.4452 × 10–10–1.3084 × 10–12–1.3806 × 10–14
    22–57.213156–20756.133–1.6655 × 10–5–1.7512 × 10–6–2.1241 × 10–7–2.8187 × 10–8
    DownLoad: CSV
  • [1]

    Grevesse N, Sauval A J 1970 Astron. Astrophys. 9 232
    [2]

    Douglas A E, Lutz B L 1970 Can. J. Phys. 48 247Google Scholar

    [3]

    Grevesse N, Sauval A J 1971a J. Quant. Spectrosc. Radiat. Transf. 11 65Google Scholar

    [4]

    Almeida A A, Sing P D 1978 Astrophys. Space Sci. 56 415Google Scholar

    [5]

    Gao W, Wang B B, Hu X J, Chai S, Han Y C, Greenwood J B 2017 Phys. Rev. A 96 013426Google Scholar

    [6]

    Wang B B, Han Y C, Gao W, Cong S L 2017 Phys. Chem. Chem. Phys. 19 22926Google Scholar

    [7]

    Moore P L, Browne J C, Matsen F A 1965 J. Chem. Phys. 43 903Google Scholar

    [8]

    Cosby P C, Helm H, Moseley J T 1980 Astrophys. J. 235 52Google Scholar

    [9]

    Barinovs G, Hemert M C V 2006 Astrophys. J. 636 923Google Scholar

    [10]

    Ram R S, Engleman R, Bernath P F 1998 J. Mol. Spectrosc. 190 341Google Scholar

    [11]

    Singh P D, Vanlandingham F G 1978 Astron. Astrophys. 66 87Google Scholar

    [12]

    Carlson T A, Copley J, Duric N, Elander N, Erman P, Larsson M, Lyyra M 1980 Astron. Astrophys. 83 238
    [13]

    Hishikawa A, Karawajczyk A 1993 J. Mol. Spectrosc. 158 479Google Scholar

    [14]

    Davies P B, Martineau P M 1988 J. Chem. Phys. 88 485Google Scholar

    [15]

    Mosnier J P, Kennedy E T, Kampen P V, Cubaynes D, Guilbaud S, Sisourat N, Puglisi A, Carniato S, Bizau J M 2016 Phys. Rev. A 93 061401Google Scholar

    [16]

    Hirst D M 1986 Chem. Phys. Lett. 128 504Google Scholar

    [17]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum Che. 8 61Google Scholar

    [18]

    Matos J M O, Kello V, Roos B O, Sadlej A J 1988 J. Chem. Phys. 89 423Google Scholar

    [19]

    Sannigrahi A B, Buenker R J, Hirsch G, Gu J P 1995 Chem. Phys. Lett. 237 204Google Scholar

    [20]

    Werner H J, Knowles P J, Lindh R, Manby F R, Schutz M, et al. Molpro, A Package of ab initio Programs (Version 2015.1) http://www.molpro.net [2021-03-08]
    [21]

    Zhang Y G, Dou G, Cui J, Yu Y 2018 J. Mol. Struct. 1165 318Google Scholar

    [22]

    Neese F 2011 Wiley Interdisci. Rev. Comput. Mol. Sci. 2 73
    [23]

    Biglari Z, Shayesteh A, Ershadifar S 2018 J. Quant. Spectrosc. Radiat. Transf. 221 80Google Scholar

    [24]

    Werner H J, Knowles P J, Lindh R, Manby F R, Schutz M, et al. Molpro, A Package of ab initio Programs (Version 2012.1) http://www.molpro.net [2021-03-08]
    [25]

    Aguado A, Paniagua M 1992 J. Chem. Phys. 96 1265Google Scholar

    [26]

    Aguado A, Tablero C, Paniagua M 1998 Comput. Phys. Commun. 108 259Google Scholar

    [27]

    Varandas A J C 2007 J. Chem. Phys. 126 244105Google Scholar

    [28]

    Varandas A J C 2000 J. Chem. Phys. 113 8880Google Scholar

    [29]

    Jansen H B, Ross P 1969 Chem. Phys. Lett. 3 140Google Scholar

    [30]

    Liu B, McLean A D 1973 J. Chem. Phys. 59 4557Google Scholar

    [31]

    Karton A, Martin J M L 2006 Theor. Chem. ACC. 115 330Google Scholar

    [32]

    Yang C L, Huang Y J, Zhang X, Han K L 2003 J. Mol. Struc. Theochem. 625 289Google Scholar

    [33]

    Yang C L, Zhang X, Han K L 2004 J. Mol. Struc. Theochem. 676 209Google Scholar

    [34]

    Huber K P, Herzberg G 1979 Molecular Spectra and Molecular Structure (Vol. IV) (New York: Springer) p600
    [35]

    Roy R J L 2017 J. Quant. Spectrosc. Radiat. Transf. 186 167Google Scholar

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Publishing process
  • Received Date:  08 March 2021
  • Accepted Date:  24 March 2021
  • Available Online:  07 June 2021
  • Published Online:  05 August 2021

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