All-electron calculation of ground state vibration-rotation energy levels of 7Li2(0, &#177;1) molecular systems

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

doi:10.7498/aps.68.20190359

Journals >Acta Physica Sinica >Volume 68 >Issue 11 >Page 113102-1 > Article

Acta Physica Sinica
Vol. 68, Issue 11, 113102-1 (2019)

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

Qiao-Xia Wang, Yu-Min Wang, Ri Ma^*, and Bing Yan^*

DOI: 10.7498/aps.68.20190359 Cite this Article

Qiao-Xia Wang, Yu-Min Wang, Ri Ma, Bing Yan. All-electron calculation of ground state vibration-rotation energy levels of ⁷Li₂^{(0, ±1)} molecular systems [J]. Acta Physica Sinica, 2019, 68(11): 113102-1 Copy Citation Text

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

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

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Method	R_e/Å	ω_e/cm^–1	ω_ex_e/cm^–1	B_e/cm^–1	D_e/eV
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].
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

Table 1.

The spectroscopic constants of ⁷Li₂(X¹∑_g⁺).

⁷Li₂(X¹∑_g⁺)分子的光谱常数

Vibrational levels	本次结果	理论^a	实验^b
注: ^a FCIPP计算值^[3], ^b LIF FTS实验值^[2,6].
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%)	—

Table 2.

The vibrational levels G_v(J = 0) of ⁷Li₂(X¹∑_g⁺) (unit in cm^–1).

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

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

Table 3.

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

⁷Li₂(X¹∑_g⁺)分子的各振动能级的转动常数B_v与D_v

Species	Method	R_e/Å	ω_e/cm^–1	ω_ex_e/cm^–1	B_e/cm^–1	D_e/eV
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].
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)

Table 4.

The spectroscopic constants of ground-state ⁷Li₂^±1 systems.

⁷Li₂^±1分子体系基态的光谱常数

v	Li₂⁺				Li₂^–
v	理论^a	理论^b	理论^c	本次结果	理论^c	本次结果
注: ^a CCSD(T, FULL)/aug-cc-Pcvqz^[12]; ^b MP^[25]; ^c DMC^[12].
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

Table 5.

The vibration energy spacing G(v + 1)–G(v) of ground-state Li₂^± (unit in cm^–1)).

Li₂^± 基态振动能级间隔G(v + 1)–G(v) (单位: cm^–1)

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

Table 6.

The vibrational levels B_v and D_vof ⁷Li₂^±.

⁷Li₂^± 基态分子的各振动能级的转动常数B_v与D_v

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

Table 7.

The vibrational levels and rotational constants for isotope molecules of Li₂.

Li₂分子的同位素体系的振动能级与转动常数

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