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采用单参考与多参考耦合簇理论结合相关一致高斯基组计算研究了7Li2(0, ±1)分子体系的电子基态的势能曲线, 计算考虑了体系所有电子的关联效应与相对论效应, 拟合得到了体系的光谱常数, 并获得了电子基态的振动-转动能级信息. 计算得到的中性与阳离子体系的光谱常数与实验值符合得很好; 对于阴离子体系, 平衡核间距的计算仍需进一步改进, 其他光谱常数符合较好. 计算结果表明, 中性和阳离子体系基态波函数具有明显的单参考组态特点, 而阴离子分子基态应采用多参考组态波函数描述. 对于基态的振动-转动能级, 与现有实验值符合得很好; 尽管各种计算方法对阴离子基态的平衡核间距计算结果仍有差异, 但振动能级间隔的结果相互符合得很好. 本文的研究可为Li2分子体系基态, 尤其是光谱学信息很少的阴离子体系的电子结构与光谱的精确研究提供了有用的光谱信息.
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关键词:
- Li2分子/分子离子 /
- 多参考耦合簇理论 /
- 光谱常数 /
- 振-转能级
The investigation of spectroscopic information is important for understanding the mechanisms of molecular photochemical and photophysical reactions. As a prototype to study the electronic structures and spectra of diatomic molecular systems, the vibration-rotational spectra of alkali dimer and its ions have aroused considerable research interest in the last two decades. Single-reference and multi-reference coupled cluster theory in combination with correlation consistent Gaussian basis set are adopted to study the ground-state potential energy curves of 7Li2(0,± 1) molecular systems. The correlation effect and relativistic effect of all the electrons are taken into account in the calculation. And the spectroscopic constants, including the equilibrium internuclear distance Re, the harmonic vibrational frequency ωe, the anharmonic constant ωexe, the equilibrium rotational constant Be, and the dissociation energy De of the molecular system and vibration-rotational energy level information of the ground states are obtained by solving the radial Schrödinger equations. The calculated spectroscopic constants of the neutral and positive ion system accord well with the experimental values; however for the negative ion system, the calculation of equilibrium internuclear distance needs further improving, and other spectroscopic constants are consistent well with the experimental values. The present computational results indicate that the ground state wave functions of neutral and positive ion systems have obvious single reference configuration characteristics, while the ground state of negative ion molecule system should be described with multireference configuration wave functions. The vibration-rotational energy levels of ground state with different theoretical methods are in good agreement with the experimental values. The vibrational-rotational energy levels and spectroscopic constants of neutral and positive ion systems are well reproduced, and some experimental information about spectrum is still lacking. Although the difference among the equilibrium internuclear distances for the ground state of the negative ion, obtained from different theoretical methods are still existent, the results of the vibrational level interval accord well with each other. This study provides useful information about spectrum for accurately investigating the electronic structures and spectra of the ground state of Li2 molecular system and its two isotopic molecules, especially for the negative ion system with little information about spectrum.-
Keywords:
- Li2 molecule/molecular ion /
- multi-reference coupled cluster theory /
- spectroscopic constant /
- vibration-rotational energy level
[1] Gardet G, Rogemond F, Chermette H 1996 J. Chem. Phys. 105 9933Google Scholar
[2] Barakat B, Bacis R, Carrot F, Churassy S, Crozet P, Martin F, Verges J 1986 Chem. Phys. 102 215Google Scholar
[3] Maniero A M, Acioli P H 2005 Int. J. Quantum Chem. 103 711Google Scholar
[4] Schmidt-Mink I, Müller W, Meyer W 1985 Chem. Phys. 92 263Google Scholar
[5] Bernheim R A, Gold L P, Tipton T 1983 J. Chem. Phys. 78 3635Google Scholar
[6] Hessel M M, Vidal C R 1979 J. Chem. Phys. 70 4439Google Scholar
[7] Bernheim R A, Gold L P, Tipton T, Konowalow D D 1984 Chem. Phys. Lett. 105 201Google Scholar
[8] Blustin P H, Linnett J W 1974 J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 70 826Google Scholar
[9] Sarkas H W, Arnold S T, Hendricks J H, Slager V L, Bowen K H 1994 Z. Phys. D 29 209Google Scholar
[10] Hogreve H 2000 Eur. Phys. J. D 8 85Google Scholar
[11] Nasiri S, Zahedi M 2017 Comput. Theor. Chem. 1114 106Google Scholar
[12] Brito B G A, Hai G Q, Cândido L 2017 J. Chem. Phys. 146 174306Google Scholar
[13] Rabli D, McCarroll R 2017 Chem. Phys. 487 23Google Scholar
[14] 魏长立, 梁桂颖, 刘晓婷, 颜培源, 闫冰 2016 物理学报 65 163101Google Scholar
Wei C L, Liang G Y, Liu X T, Yan P Y, Yan B 2016 Acta Phys. Sin. 65 163101Google Scholar
[15] Yang X, Xu H, Yan B 2019 Chin. Phys. B 28 348
[16] Zhang L L, Gao S B, Meng Q T, Song Y Z 2015 Chin. Phys. B 24 201
[17] Wei C L, Zhang X M, Ding D J, Yan B 2016 Chin. Phys. B 25 13102Google Scholar
[18] Hampel C, Peterson K A, Werner H J 1992 Chem. Phys. Lett. 190 1Google Scholar
[19] Knowles P J, Hampel C, Werner H 1993 J. Chem. Phys. 99 5219Google Scholar
[20] Werner H J, Knowles P J, G Knizia, et al. http://www. molpro.net. [2019-3-10]
[21] Rolik Z, Szegedy L, Ladjánszki I, Ladóczki B, Kállay M 2013 J. Chem. Phys. 139 094105Google Scholar
[22] Prascher B P, Woon D E, Peterson K A, Dunning T H, Wilson A K 2011 Theor. Chem. Acc. 128 69Google Scholar
[23] Wolf A, Reiher M, Hess B A 2002 J. Chem. Phys. 117 9215Google Scholar
[24] Le Roy R J 2017 J. Quant. Spectrosc. Radiat. Transf. 186 167Google Scholar
[25] Magnier S, Rousseau S, Allouche A R, Hadinger G, Aubert-Frécon M 1999 Chem. Phys. 246 57Google Scholar
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表 1 7Li2 (X1∑g+)分子的光谱常数
Table 1. The spectroscopic constants of 7Li2 (X1∑g+).
表 2 7Li2 (X1∑g+)分子的振动能级Gv (J = 0) (单位: cm–1)
Table 2. The vibrational levels Gv (J = 0) of 7Li2 (X1∑g+) (unit in cm–1).
Vibrational levels 本次结果 理论a 实验b 0 0 0 0 1 346.17 346.05 346.46 2 687.11 686.65 687.86 3 1022.78 1021.71 1024.08 4 1353.13 1351.15 1355.01 5 1678.11 1674.88 1680.54 6 1997.67 1992.81 2000.56 7 2311.72 2304.85 2314.95 8 2620.21 2610.92 2623.58 9 2923.03 2910.90 2926.35 10 3220.09 3204.70 3223.11 11 3511.29 3492.23 3513.74 12 3796.49 3773.36 3798.10 13 4075.58 4048.00 4076.05 14 4348.39 4316.02 4347.45 15 4614.78 4577.31 4612.16 16 4874.55 4831.74 4870.02 17 5127.52 5079.52 5120.86 18 5373.46 5319.52 5364.53 19 5612.14 5552.59 5600.84 20 5843.27 5778.25 5829.63 21 6066.57 5996.35 6050.69 22 6281.67 6206.72 6263.83 23 6488.16 6409.20 6468.84 24 6685.58 6603.59 6665.49 RMS 8.68(0.16%) 33.93(0.65%) — 注: a FCIPP计算值[3], b LIF FTS实验值[2,6]. 表 3 7Li2 (X1∑g+)分子的各振动能级的转动常数Bv与Dv
Table 3. The rotational constants Bv and Dv of 7Li2 (X1∑g+).
v Bv/cm–1 Dv/10-4 cm–1 Expt.[2,6] This work Expt.[2,6] This work 0 0.66907 0.66882 — 0.0987 1 0.66196 0.66171 — 0.0991 2 0.65479 0.65453 — 0.0996 3 0.64754 0.64728 — 0.1002 4 0.64019 0.63995 — 0.1007 5 0.63275 0.63252 — 0.1014 6 0.62521 0.62499 — 0.1021 7 0.61754 0.61733 — 0.1028 8 0.60974 0.60954 — 0.1037 9 0.60180 0.60160 — 0.1046 10 0.59368 0.59348 — 0.1056 11 0.58540 0.58518 — 0.1068 12 0.57692 0.57667 — 0.1080 13 0.56822 0.56793 — 0.1093 14 0.55918 0.55892 0.1097 0.1108 15 0.55000 0.54961 0.1119 0.1123 16 0.54055 0.53995 0.1143 0.1138 17 0.53061 0.52990 0.1146 0.1152 18 0.52044 0.51939 0.1180 0.1165 19 0.50992 0.50834 0.1215 0.1175 20 0.49885 0.49667 0.1246 0.1181 21 0.48726 0.48429 0.1265 0.1185 22 0.47845 0.47109 0.1182 0.1187 23 0.46246 0.45698 0.1340 0.1190 24 0.44913 0.44183 0.1401 0.1200 表 4 7Li2±1分子体系基态的光谱常数
Table 4. The spectroscopic constants of ground-state 7Li2±1 systems.
Species Method Re/Å ωe/cm–1 ωexe/cm–1 Be/cm–1 De/eV Li2+ 本次结果a 3.0986 262.7599 1.5640 0.5005 1.297 本次结果a2 3.1337 258.8211 1.5413 0.4893 1.279 本次结果a3 3.1038 262.3548 1.5669 0.4988 1.294 MPb 3.122 263.08 1.2954 0.4945 1.2976 CIc 3.099 263.76 — 0.5006 1.2945 DMCd 3.11 266.2 1.593 0.4753 1.2965 实验[5,7] 3.11 262 ± 2 1.7 ± 0.5 0.496 ± 0.002 1.2973 Li2- 本次结果a 3.0265 230.6457 1.5881 0.5247 0.850 本次结果a3 3.0396 231.1024 2.3115 0.5201 0.845 DMCd 3.10 235.3 3.166 0.4652 0.7733 MRDCIe 3.062 236.2 2.42 — 0.857 CCSD(T)f 3.00 240.7 3.166 0.5238 0.9085 实验[10] 3.094 ± 0.015 232 ± 35 — 0.502 ± 0.005 0.865 ± 0.022(D0) 注: a RCCSD(T)/5Z; a2vMRCCSD/TZ + 4s2p(未包含1s的电子关联); a3MRCCSD/TZ + 4s2p(包含1s的电子关联); bmodel potential (MP) method[25]; cconfiguration interaction (CI) with effective core potential[4]; ddiffusion quantum Monte-Carlo (DMC) method[12]; emultireference singly and doubly CI (MRDCI)[11]; f CCSD(T, full)/cc-pv5z[12]. 表 5 Li2± 基态振动能级间隔G (v + 1)–G (v) (单位: cm–1)
Table 5. The vibration energy spacing G (v + 1)–G (v) of ground-state Li2± (unit in cm–1)).
v Li2+ Li2– 理论a 理论b 理论c 本次结果 理论c 本次结果 0 259.51 260 259.74 259.74 227.53 228.64 1 256.30 257 256.54 256.54 222.71 223.96 2 253.11 254 253.35 253.35 217.93 219.69 3 249.95 251 250.19 250.19 213.21 216.12 4 246.81 248 247.04 247.04 208.54 213.32 5 243.68 244 243.92 243.92 203.95 211.08 6 240.57 241 240.81 240.81 199.42 208.91 7 237.49 236 237.72 237.72 194.97 206.46 8 234.41 235 234.65 234.65 190.61 203.52 9 231.35 232 231.59 231.59 186.34 200.06 10 228.31 228 228.55 228.55 182.16 196.15 11 225.28 226 225.51 225.51 178.08 191.88 12 222.26 222 222.50 222.50 174.12 187.33 13 219.24 220 219.48 219.48 170.26 182.59 14 216.24 216 216.48 216.48 166.53 177.72 15 213.24 214 213.48 213.48 162.92 172.77 16 210.25 210 210.50 210.50 159.45 167.78 17 207.26 207 207.50 207.50 156.11 162.77 18 204.28 205 204.53 204.53 152.91 157.79 19 201.30 201 201.55 201.55 149.87 152.82 注: a CCSD(T, FULL)/aug-cc-Pcvqz[12]; b MP[25]; c DMC[12]. 表 6 7Li2± 基态分子的各振动能级的转动常数Bv与Dv
Table 6. The vibrational levels Bv and Dv of 7Li2±.
v Bv/cm–1 Dv/10-4 cm–1 Li2+ Li2– Li2+ Li2- 0 0.49776 0.52021 0.07223 0.10558 1 0.49235 0.51129 0.07168 0.10438 2 0.48698 0.50214 0.07114 0.10106 3 0.48164 0.49226 0.07062 0.09317 4 0.47635 0.48106 0.07011 0.07966 5 0.47109 0.46824 0.06961 0.06296 6 0.46586 0.45407 0.06912 0.04741 7 0.46067 0.43920 0.06865 0.03586 8 0.45551 0.42426 0.06819 0.02862 9 0.45037 0.40969 0.06775 0.02462 10 0.44527 0.39571 0.06732 0.02265 11 0.44019 0.38238 0.06690 0.02180 12 0.43513 0.36971 0.06649 0.02155 13 0.43009 0.35766 0.06611 0.02159 14 0.42507 0.34617 0.06573 0.02177 15 0.42007 0.33520 0.06537 0.02201 16 0.41508 0.32469 0.06503 0.02226 17 0.41010 0.31461 0.06470 0.02252 18 0.40514 0.30492 0.06439 0.02276 19 0.40018 0.29558 0.06410 0.02300 20 0.39522 0.28656 0.06382 0.02324 21 0.39026 0.27784 0.06356 0.02347 22 0.38531 0.26939 0.06332 0.02370 23 0.38035 0.26120 0.06310 0.02392 24 0.37538 0.25324 0.06290 0.02416 表 7 Li2分子的同位素体系的振动能级与转动常数
Table 7. The vibrational levels and rotational constants for isotope molecules of Li2.
v G(v)/cm–1 Bv/cm–1 Dv/10-4 cm–1 6Li7Li 6Li2 6Li7Li 6Li2 6Li7Li 6Li2 0 0 0 0.72431 0.77978 0.1158 0.13429 1 360 373 0.71629 0.77082 0.11635 0.13495 2 714 741 0.70819 0.76176 0.11695 0.13568 3 1063 1102 0.70001 0.75260 0.11761 0.13647 4 1406 1457 0.69173 0.74333 0.11832 0.13735 5 1743 1805 0.68333 0.73392 0.11911 0.13832 6 2074 2148 0.67480 0.72436 0.11999 0.13939 7 2400 2484 0.66613 0.71462 0.12095 0.14058 8 2719 2813 0.65729 0.70469 0.12201 0.14189 9 3032 3135 0.64827 0.69453 0.12318 0.14335 10 3338 3451 0.63904 0.68412 0.12448 0.14496 11 3639 3760 0.62958 0.67343 0.12591 0.14673 12 3932 4062 0.61986 0.66242 0.12747 0.14863 13 4219 4356 0.60984 0.65104 0.12913 0.15062 14 4500 4643 0.59949 0.63924 0.13088 0.15262 15 4773 4922 0.58875 0.62695 0.13262 0.1545 16 5038 5193 0.57756 0.61407 0.13426 0.1561 17 5297 5456 0.56584 0.60052 0.13567 0.15725 18 5547 5710 0.55352 0.58617 0.13671 0.15786 19 5789 5956 0.54048 0.57089 0.13733 0.15794 20 6023 6192 0.52662 0.55456 0.13755 0.15775 21 6249 6418 0.51182 0.53703 0.13757 0.15778 22 6465 6633 0.49596 0.51815 0.1378 0.15879 23 6671 6838 0.47890 0.49776 0.13886 0.16187 24 6866 7031 0.46051 0.47564 0.14162 0.16834 -
[1] Gardet G, Rogemond F, Chermette H 1996 J. Chem. Phys. 105 9933Google Scholar
[2] Barakat B, Bacis R, Carrot F, Churassy S, Crozet P, Martin F, Verges J 1986 Chem. Phys. 102 215Google Scholar
[3] Maniero A M, Acioli P H 2005 Int. J. Quantum Chem. 103 711Google Scholar
[4] Schmidt-Mink I, Müller W, Meyer W 1985 Chem. Phys. 92 263Google Scholar
[5] Bernheim R A, Gold L P, Tipton T 1983 J. Chem. Phys. 78 3635Google Scholar
[6] Hessel M M, Vidal C R 1979 J. Chem. Phys. 70 4439Google Scholar
[7] Bernheim R A, Gold L P, Tipton T, Konowalow D D 1984 Chem. Phys. Lett. 105 201Google Scholar
[8] Blustin P H, Linnett J W 1974 J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 70 826Google Scholar
[9] Sarkas H W, Arnold S T, Hendricks J H, Slager V L, Bowen K H 1994 Z. Phys. D 29 209Google Scholar
[10] Hogreve H 2000 Eur. Phys. J. D 8 85Google Scholar
[11] Nasiri S, Zahedi M 2017 Comput. Theor. Chem. 1114 106Google Scholar
[12] Brito B G A, Hai G Q, Cândido L 2017 J. Chem. Phys. 146 174306Google Scholar
[13] Rabli D, McCarroll R 2017 Chem. Phys. 487 23Google Scholar
[14] 魏长立, 梁桂颖, 刘晓婷, 颜培源, 闫冰 2016 物理学报 65 163101Google Scholar
Wei C L, Liang G Y, Liu X T, Yan P Y, Yan B 2016 Acta Phys. Sin. 65 163101Google Scholar
[15] Yang X, Xu H, Yan B 2019 Chin. Phys. B 28 348
[16] Zhang L L, Gao S B, Meng Q T, Song Y Z 2015 Chin. Phys. B 24 201
[17] Wei C L, Zhang X M, Ding D J, Yan B 2016 Chin. Phys. B 25 13102Google Scholar
[18] Hampel C, Peterson K A, Werner H J 1992 Chem. Phys. Lett. 190 1Google Scholar
[19] Knowles P J, Hampel C, Werner H 1993 J. Chem. Phys. 99 5219Google Scholar
[20] Werner H J, Knowles P J, G Knizia, et al. http://www. molpro.net. [2019-3-10]
[21] Rolik Z, Szegedy L, Ladjánszki I, Ladóczki B, Kállay M 2013 J. Chem. Phys. 139 094105Google Scholar
[22] Prascher B P, Woon D E, Peterson K A, Dunning T H, Wilson A K 2011 Theor. Chem. Acc. 128 69Google Scholar
[23] Wolf A, Reiher M, Hess B A 2002 J. Chem. Phys. 117 9215Google Scholar
[24] Le Roy R J 2017 J. Quant. Spectrosc. Radiat. Transf. 186 167Google Scholar
[25] Magnier S, Rousseau S, Allouche A R, Hadinger G, Aubert-Frécon M 1999 Chem. Phys. 246 57Google Scholar
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