All-electron calculation of ground state vibration-rotation energy levels of 7Li2(0, ±1) molecular systems

Wang Qiao-Xia; Wang Yu-Min; Ma Ri; Yan Bing

doi:10.7498/aps.68.20190359

Abstract

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 R_e, the harmonic vibrational frequency ω_e, the anharmonic constant ω_ex_e, the equilibrium rotational constant B_e, and the dissociation energy D_e 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

Authors and contacts

Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin Province, Institution of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

Corresponding author: Ma Ri, rma@jlu.edu.cn ; Yan Bing, yanbing@jlu.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403300), the National Natural Science Foundation of China (Grant Nos. 91750104, 11574114, 11874177), and the Jilin Provincial National Science Foundation, China (Grant No. 20160101332JC).

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References

[1]	Gardet G, Rogemond F, Chermette H 1996 J. Chem. Phys. 105 9933 Google Scholar
[2]	Barakat B, Bacis R, Carrot F, Churassy S, Crozet P, Martin F, Verges J 1986 Chem. Phys. 102 215 Google Scholar
[3]	Maniero A M, Acioli P H 2005 Int. J. Quantum Chem. 103 711 Google Scholar
[4]	Schmidt-Mink I, Müller W, Meyer W 1985 Chem. Phys. 92 263 Google Scholar
[5]	Bernheim R A, Gold L P, Tipton T 1983 J. Chem. Phys. 78 3635 Google Scholar
[6]	Hessel M M, Vidal C R 1979 J. Chem. Phys. 70 4439 Google Scholar
[7]	Bernheim R A, Gold L P, Tipton T, Konowalow D D 1984 Chem. Phys. Lett. 105 201 Google Scholar
[8]	Blustin P H, Linnett J W 1974 J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 70 826 Google Scholar
[9]	Sarkas H W, Arnold S T, Hendricks J H, Slager V L, Bowen K H 1994 Z. Phys. D 29 209 Google Scholar
[10]	Hogreve H 2000 Eur. Phys. J. D 8 85 Google Scholar
[11]	Nasiri S, Zahedi M 2017 Comput. Theor. Chem. 1114 106 Google Scholar
[12]	Brito B G A, Hai G Q, Cândido L 2017 J. Chem. Phys. 146 174306 Google Scholar
[13]	Rabli D, McCarroll R 2017 Chem. Phys. 487 23 Google Scholar
[14]	魏长立, 梁桂颖, 刘晓婷, 颜培源, 闫冰 2016 物理学报 65 163101 Google Scholar Wei C L, Liang G Y, Liu X T, Yan P Y, Yan B 2016 Acta Phys. Sin. 65 163101 Google 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 13102 Google Scholar
[18]	Hampel C, Peterson K A, Werner H J 1992 Chem. Phys. Lett. 190 1 Google Scholar
[19]	Knowles P J, Hampel C, Werner H 1993 J. Chem. Phys. 99 5219 Google 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 094105 Google Scholar
[22]	Prascher B P, Woon D E, Peterson K A, Dunning T H, Wilson A K 2011 Theor. Chem. Acc. 128 69 Google Scholar
[23]	Wolf A, Reiher M, Hess B A 2002 J. Chem. Phys. 117 9215 Google Scholar
[24]	Le Roy R J 2017 J. Quant. Spectrosc. Radiat. Transf. 186 167 Google Scholar
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Cited By

图 1 Li₂^{(0, ±1)}的基态势能曲线(能量零点取为各自平衡核间距处能量)

Figure 1. Potential energy curves of ground states for Li₂^{(0, ±1)} (the energy zero-point is located at respective equilibrium internuclear distance).

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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⁺).

Method	R_e/Å	ω_e/cm^–1	ω_ex_e/cm^–1	B_e/cm^–1	D_e/eV
vCCSD(T)/TZ^a	2.6992	346.3556	2.6687	0.6596	1.038
CCSD(T)/TZ	2.6770	350.5609	2.7163	0.6706	1.046
CCSD(T)/QZ	2.6742	351.7784	2.7238	0.6720	1.052
CCSD(T)/5Z	2.6734	352.0222	2.7285	0.6724	1.053
实验^b	2.6734	351.42295	2.4417	0.66824	1.060
注: ^a未包含1s轨道电子关联; ^b激光诱导荧光傅里叶变换谱(LIF FTS)实验PKR拟合值^[2,6].

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表 2 ⁷Li₂(X¹∑_g⁺)分子的振动能级G_v(J = 0) (单位: cm^–1)

Table 2. The vibrational levels G_v(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].

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表 3 ⁷Li₂(X¹∑_g⁺)分子的各振动能级的转动常数B_v与D_v

Table 3. The rotational constants B_v and D_v of ⁷Li₂(X¹∑_g⁺).

v	B_v/cm^–1		D_v/10^-4 cm^–1
v	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

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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	R_e/Å	ω_e/cm^–1	ω_ex_e/cm^–1	B_e/cm^–1	D_e/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
	MP^b	3.122	263.08	1.2954	0.4945	1.2976
	CI^c	3.099	263.76	—	0.5006	1.2945
	DMC^d	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
	DMC^d	3.10	235.3	3.166	0.4652	0.7733
	MRDCI^e	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].

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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^–
v	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].

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表 6 ⁷Li₂^± 基态分子的各振动能级的转动常数B_v与D_v

Table 6. The vibrational levels B_v and D_v of ⁷Li₂^±.

v	B_v/cm^–1		D_v/10^-4 cm^–1
v	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

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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		B_v/cm^–1		D_v/10^-4 cm^–1
v	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

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[1]	Gardet G, Rogemond F, Chermette H 1996 J. Chem. Phys. 105 9933 Google Scholar
[2]	Barakat B, Bacis R, Carrot F, Churassy S, Crozet P, Martin F, Verges J 1986 Chem. Phys. 102 215 Google Scholar
[3]	Maniero A M, Acioli P H 2005 Int. J. Quantum Chem. 103 711 Google Scholar
[4]	Schmidt-Mink I, Müller W, Meyer W 1985 Chem. Phys. 92 263 Google Scholar
[5]	Bernheim R A, Gold L P, Tipton T 1983 J. Chem. Phys. 78 3635 Google Scholar
[6]	Hessel M M, Vidal C R 1979 J. Chem. Phys. 70 4439 Google Scholar
[7]	Bernheim R A, Gold L P, Tipton T, Konowalow D D 1984 Chem. Phys. Lett. 105 201 Google Scholar
[8]	Blustin P H, Linnett J W 1974 J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 70 826 Google Scholar
[9]	Sarkas H W, Arnold S T, Hendricks J H, Slager V L, Bowen K H 1994 Z. Phys. D 29 209 Google Scholar
[10]	Hogreve H 2000 Eur. Phys. J. D 8 85 Google Scholar
[11]	Nasiri S, Zahedi M 2017 Comput. Theor. Chem. 1114 106 Google Scholar
[12]	Brito B G A, Hai G Q, Cândido L 2017 J. Chem. Phys. 146 174306 Google Scholar
[13]	Rabli D, McCarroll R 2017 Chem. Phys. 487 23 Google Scholar
[14]	魏长立, 梁桂颖, 刘晓婷, 颜培源, 闫冰 2016 物理学报 65 163101 Google Scholar Wei C L, Liang G Y, Liu X T, Yan P Y, Yan B 2016 Acta Phys. Sin. 65 163101 Google 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 13102 Google Scholar
[18]	Hampel C, Peterson K A, Werner H J 1992 Chem. Phys. Lett. 190 1 Google Scholar
[19]	Knowles P J, Hampel C, Werner H 1993 J. Chem. Phys. 99 5219 Google 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 094105 Google Scholar
[22]	Prascher B P, Woon D E, Peterson K A, Dunning T H, Wilson A K 2011 Theor. Chem. Acc. 128 69 Google Scholar
[23]	Wolf A, Reiher M, Hess B A 2002 J. Chem. Phys. 117 9215 Google Scholar
[24]	Le Roy R J 2017 J. Quant. Spectrosc. Radiat. Transf. 186 167 Google Scholar
[25]	Magnier S, Rousseau S, Allouche A R, Hadinger G, Aubert-Frécon M 1999 Chem. Phys. 246 57 Google Scholar

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Vol. 68, Issue 11 - 2019-06-05

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All-electron calculation of ground state vibration-rotation energy levels of ⁷Li₂^{(0, ±1)} molecular systems

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Corresponding author: Ma Ri, rma@jlu.edu.cn ; Yan Bing, yanbing@jlu.edu.cn

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