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本文中,首先证明了C_nX_4(n=28,40;X=H,F,Cl)分子最稳定的结构具有T_d对称性。利用密度泛函理论研究了C_nX_4的振动光谱。从频率分析中我们得到当修饰性的原子位于T_d对称性的C_(28)X_4和C_(40)X_4的势能面上的4个顶点时,分子的能量具有最低值。我们还将C_nH_4(n=28,40;X=H,F,Cl)和CX_4的振动光谱进行对比,得出笼的骨架振动。频率分析中具有最大波数的频率对应分子的笼骨架振动,所以对于C_(28)X_4(X=H,F,Cl)或C_(40)X_4(X=H,F,Cl)来说,修饰原子的改变对这个频率值基本上没有影响,但是碳笼骨架上碳原子数的改变对这个频率的影响非常大。
In this paper, we first prove that the most stable structure of C_nX_4 (n = 28,40; X = H, F, Cl) has T_d symmetry. The vibrational spectra of C_nX_4 were studied by using density functional theory. From the frequency analysis, we obtain the lowest energy of the molecule when the modifying atom is located on the four vertices of the potential energy surfaces of C_ (28) X_4 and C_ (40) X_4 with T_d symmetry. We also compare the vibrational spectra of C_nH_4 (n = 28, 40; X = H, F, Cl) with CX_4 to derive cage vibration. The frequency with the largest wavenumber in the frequency analysis corresponds to the caged cage vibration of the molecule, so that for C_ (28) X_4 (X = H, F, Cl) or C_ (40) X_4 Atomic changes have essentially no effect on this frequency, but the effect of changes in the number of carbon atoms on the carbon cage skeleton on this frequency is very large.