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Abstract

Sulfur oxide (SO) is a kind of well-known diatomic molecule which becomes one of the major pollutants in the atmosphere. Control of the heat capacity of SO molecule is of great significance for elucidating its macroscopic evolution process. In the research of macroscopic systems composed of many particles as well as several matters, it is an important approach to obtain macroscopic thermodynamic quantities of the system by constructing a partition function from the microscopic information of molecule. For diatomic molecules in a certain electronic state, the partition function can directly be obtained by calculating the rovibrational energy of the system to acquire the macroscopic molar heat capacities. In this work, the contribution of rotational behavior to molar heat capacity is further considered. The potential energy function for the ground electronic state of SO is constructed by the variational algebraic method (VAM) and RKR (Rydberg-Klein-Rees) method, in which the former one can determine the complete vibrational energy levels of an electronic state of a molecule. The rovibrational energy level of the system is obtained by analytical solution, and then the molar heat capacity of SO macroscopic gas in the temperature range of 300–6000 K is calculated by quantum statistical ensemble theory The above calculation depends only on the experimental vibrational energy, experimental rotational spectral constant and the dissociation energy of SO molecule. Fortunately, through comparison between theoretical calculation results and experimental data, we find that the molar heat capacity of gaseous SO molecule can be well predicted by employing the full set of rovibrational energy to describe the internal vibration and rotation of SO molecule. The idea of calculating the molar heat capacity by using the full set of rovibrational energy makes up for the shortcomings of previous work where molar heat capacity is calculated by using the approximate model characterizing the molecular rotational behavior, and also provides a new research paradigm for solving macro thermodynamic quantities based on micro statistical processes .

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Authors and contacts

Corresponding author:Fan Qun-Chao,fanqunchao@mail.xhu.edu.cn; Fan Zhi-Xiang,fanzhixiang235@126.com;

Funds:Project supported by the Fund for the Program of Science and Technology of Sichuan Province of China (Grant No. 2021ZYD0050), the National Natural Science Foundation of China (Grant Nos. 61722507, 11904295), and the Open Research Fund Program of the Collaborative Innovation Center of Extreme Optics, China (Grant No. KF2020003).

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Cited By

DownLoad: Full-Size Img PowerPoint

	$ {\omega _0} $	$ {\omega _{\text{e}}} $	$ {\omega _{\text{e}}}{x_{\text{e}}} $	$ {\omega _{\text{e}}}{y_{\text{e}}} $	$ {\omega _{\text{e}}}{z_{\text{e}}} $	$ {\omega _{\text{e}}}{t_{\text{e}}} $
实验^[34]		1148.19	6.12
CASS- CF^[35]		1161.80	6.50
CI-SD^[35]		1263.50	5.35
MP4 SDQ^[35]		1173.10	5.09
VAM	0.75	1147.71	5.99	–1.55×10^–2	7.59×10^–4	–1.30×10^–5

DownLoad: CSV

T/K	${ C_\upsilon ^{ {\text{expt} } } }^{\rm\; a}$	${ \Delta C_{\upsilon {\text{, RKR} } }^{ {\text{cal} } } } ^{\rm\; b}$	${ \Delta C_{\upsilon {\text{, VAM} } }^{ {\text{cal} } } }^{\rm\; c}$	${ \Delta C_{\upsilon \_r{\text{, RKR} } }^{ {\text{cal} } } } ^{\rm\; d}$	${ \Delta C_{ {\text{This work} } }^{ {\text{cal} } } }^{\rm\; e}$
300	30.197	–0.025	–0.024	0.071	0.006
400	31.560	–0.041	–0.040	0.092	0.009
500	32.826	–0.057	–0.056	0.080	0.011
600	33.838	–0.073	–0.072	0.054	0.011
700	34.612	–0.088	–0.087	0.027	0.011
800	35.206	–0.108	–0.108	–0.001	0.005
900	35.672	–0.135	–0.136	–0.032	–0.008
1000	36.053	–0.177	–0.177	–0.071	–0.035
1100	36.379	–0.235	–0.235	–0.123	–0.079
1200	36.672	–0.313	–0.314	–0.192	–0.143
1300	36.946	–0.412	–0.413	–0.280	–0.228
1400	37.210	–0.532	–0.533	–0.386	–0.333
1500	37.469	–0.670	–0.670	–0.508	–0.455
1600	37.725	–0.822	–0.823	–0.645	–0.593
1700	37.980	–0.989	–0.989	–0.795	–0.743
1800	38.232	–1.163	–1.164	–0.952	–0.902
1900	38.482	–1.345	–1.346	–1.116	–1.068
2000	38.727	–1.530	–1.530	–1.282	–1.236
2100	38.967	–1.715	–1.716	–1.449	–1.404
2200	39.200	–1.899	–1.900	–1.614	–1.571
2300	39.425	–2.079	–2.079	–1.775	–1.733
2400	39.641	–2.254	–2.254	–1.929	–1.889
2500	39.847	–2.422	–2.421	–2.077	–2.038
2600	40.043	–2.582	–2.581	–2.217	–2.180
2700	40.229	–2.735	–2.733	–2.349	–2.313
2800	40.404	–2.879	–2.876	–2.472	–2.436
2900	40.568	–3.014	–3.009	–2.585	–2.549
3000	40.721	–3.140	–3.133	–2.689	–2.652
3100	40.864	–3.258	–3.248	–2.784	–2.746
3200	40.996	–3.367	–3.352	–2.869	–2.830
3300	41.119	–3.469	–3.449	–2.946	–2.904
3400	41.232	–3.562	–3.536	–3.015	–2.969
3500	41.336	–3.649	–3.615	–3.076	–3.025
3600	41.432	–3.729	–3.686	–3.130	–3.072
3700	41.520	–3.804	–3.749	–3.178	–3.111
3800	41.601	–3.874	–3.806	–3.220	–3.143
3900	41.676	–3.940	–3.857	–3.259	–3.168
4000	41.745	–4.002	–3.902	–3.293	–3.187
4100	41.810	–4.063	–3.943	–3.326	–3.202
4200	41.871	–4.122	–3.980	–3.356	–3.211
4300	41.929	–4.180	–4.014	–3.387	–3.217
4400	41.986	–4.241	–4.047	–3.419	–3.221
4500	42.042	–4.303	–4.079	–3.453	–3.224
4600	42.098	–4.367	–4.111	–3.490	–3.226
4700	42.156	–4.437	–4.144	–3.533	–3.229
4800	42.217	–4.512	–4.181	–3.581	–3.235
4900	42.282	–4.593	–4.221	–3.637	–3.244
5000	42.352	–4.682	–4.266	–3.702	–3.258
5100	42.429	–4.781	–4.318	–3.778	–3.279
5200	42.514	–4.891	–4.377	–3.865	–3.307
5300	42.608	–5.012	–4.445	–3.966	–3.344
5400	42.712	–5.146	–4.523	–4.080	–3.392
5500	42.829	–5.295	–4.614	–4.211	–3.453
5600	42.959	–5.459	–4.718	–4.359	–3.527
5700	43.104	–5.641	–4.837	–4.526	–3.617
5800	43.265	–5.841	–4.971	–4.714	–3.724
5900	43.444	–6.061	–5.123	–4.923	–3.849
6000	43.620	–6.280	–5.273	–5.133	–3.973
$ \Delta {C_{{\text{aver}}}} $^f		2.896	2.721	2.363	2.084
注: a. 实验热容; b. 基于实验振动能级运用近似模型所得热容值与实验值的误差; c. 基于VAM完全振动能级运用近似模型所得热容值与实验值的误差; d. 基于实验振转能级所得热容值与实验值的误差; e. 基于完全振转能级所得热容值与实验值的误差; f. $\Delta {C_{ {\text{aver} } } } = \dfrac{ {\text{1} } }{w} \displaystyle\sum {\left\| { {C_{\text{m} } } - {C_{ {\text{expt} } } } } \right\|}$,w为参与计算的热容值个数.

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