Theoretical study on macroscopic thermodynamic properties of NO<sup>+</sup> ion system

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Abstract

NO ⁺is one of the most important ions in the atmospheric ionosphere and ionospheric phenomena such as auroras, and is one of the most stable diatomic cations existing in interstellar clouds. It is crucial to understand the thermodynamic properties of NO ⁺ion for exploring the composition of interstellar gas. To obtain macroscopic thermodynamic properties of diatomic molecules and ions, a practical theoretical method is to determine the partition function associated with a potential model. This approach can be used to calculate various thermodynamic properties of the system based on the microscopic information. In this work, the improved Hulbert-Hirschfelder (IHH) based potential energy model is used to simulate the potential energy curve of NO ⁺in the ground electronic state. Then, the rovibrational energy levels for the ground electronic state of the NO ⁺are obtained by numerically solving the radial Schrödinger equation through using the LEVEL program for the IHH potential function. Finally, the total partition function and the thermodynamic properties such as the molar heat capacity, entropy, enthalpy and reduced molar Gibbs free energy of NO ⁺in a temperature range of 100–6000 K are calculated in the frame of the quantum statistical ensemble theory. The comparison indicates that the potential energy curve calculated based on IHH potential energy function is in better agreement with the experimental data. The root mean square error of IHH potential and experimental Rydberg-Klein-Rees (RKR) potential is 96.9 cm ^–1, the root mean square error of Hulbert-Hirschfelder (HH) potential is 112.7 cm ^–1, and the root mean square error of MRCI/aug-cc-pV6Z potential is 133 cm ^–1. And the macroscopic thermodynamic properties of NO ⁺predicted by IHH are closer to the experimental values, which shows that the IHH potential model is also applicable to the ion system. A feasible method is presented to obtain the thermodynamic properties of gaseous diatomic ions based on microscopic information by constructing reliable analytical potential energy function associated with quantum statistical ensemble theory.

Keywords:

NO⁺ion/
improved Hulburt-Hirschfelder potential/
partition function/
thermodynamic properties

Authors and contacts

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

Funds:Project supported by the Central Government Funds of Guiding Local Scientific and Technological Development for Sichuan Province (Grant No. 2021ZYD0050), the Natural Science Foundation of Sichuan Province, China (Grant No. 2022NSFSC1857), the Open Research Fund of Computational Physics Key Laboratory of Sichuan Province, Yibin University (Grant No. ybxyjswl-zd-2020-006), and the National Undergraduate Innovation and Entrepreneurship Training Program of China (Grant No. S202210623057).

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Cited By

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r/Å	$ {E_{{\text{RKR}}}} $/cm^–1[36]	$ {E_{{\text{IHH}}}} $/cm^–1	$\left\| {\Delta {E_{ {\text{RKR–IHH} } } }} \right\|$/cm^–1	$ {E_{{\text{HH}}}} $/cm^–1	$ \left\| {\Delta {E_{{\text{RKR–HH}}}}} \right\| $/cm^–1	$ {E_{{\text{MRCI}}}} $/cm^–1[35]	$ \left\| {\Delta {E_{{\text{RKR–MRCI}}}}} \right\| $/cm^–1
0.926	16911.0	17037.50	127	16886.09	25	17113.82	203
0.934	14761.9	14825.64	64	14721.53	40	14833.44	72
0.943	12580.2	12561.20	19	12494.49	86	12417.22	163
0.953	10366.1	10382.87	17	10342.77	23	10343.47	23
0.963	8119.40	8115.441	4	8094.606	25	8111.838	8
0.977	5840.20	5839.586	1	5830.842	9	5833.200	7
0.995	3528.50	3522.741	6	3520.407	8	3526.113	2
1.022	1184.30	1161.440	23	1161.306	23	1142.913	41
1.109	1184.30	1187.712	3	1187.826	4	1160.835	23
1.147	3528.50	3505.745	23	3507.331	21	3502.362	26
1.175	5840.20	5886.843	47	5892.355	52	5887.909	48
1.199	8119.40	8269.826	150	8282.220	163	8289.580	170
1.211	10366.1	10285.10	81	10305.88	60	10179.40	187
1.241	12580.2	12581.93	2	12615.36	35	12503.09	77
1.261	14761.9	14905.62	144	14955.40	194	14955.96	194
1.280	16911.0	17187.37	276	17256.83	346	17219.91	309
RMSD			96.9		112.7		133

DownLoad: CSV

热力学量	HH	IHH
$ {C_{\text{m}}} $/(J·mol^–1·K^–1)	0.053912	0.021733
$ {S_{\text{m}}} $/(J·mol^–1·K^–1)	0.035233	0.022930
$\Delta H$/(kJ·mol^–1)	0.082503	0.034329
$ {G_{\text{r}}} $/(J·mol^–1·K^–1)	0.021079	0.017711

DownLoad: CSV

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Vol. 72, Issue 16 - 2023-08-20

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