Vibrational softening of diatomic molecules

Abstract

An analysis of a model molecular oscillator is presented: a vibrating diatomic molecule carrying N 0 electrons. The energy derivatives over the number of electron (N) and the deformation (Q), ¶ n / ¶N n and ¶ n / ¶Q n have been analyzed up to second order (n 2), including the appropriate mixed derivatives. The eect of coupling between distortion of the electron density induced by DN and the vibrational deformation of the molecule has been studied. Anharmonicity of the oscillator has been shown to be a possible result of that coupling; new relations between the parameters characterizing the anharmonicity of the oscillator and the energy derivatives at density functional theory level have been obtained. Ab initio calculations for a set of diatomic molecules have been performed, yielding values for all the derivatives discussed and demonstrating the eect of coupling with vibrations.

DFT energy derivatives and their renormalization in molecular vibrations

“…The necessary data were taken from: Refs. [6] (, G, and ), [11] (k, , and ), and [10] ( ). The G and values employed here are the derivatives, without the 1/2 factor frequently used in older works, the source data have been multiplied accordingly.…”

“…Unfortunately, the workable results can be obtained only when the third-order terms are dropped [11], and they are:…”

“…The authors also presented analysis of ⌽ i and G i indices for normal vibrational modes [9] and elaborated on the role of these indices in determining the fluctuations in chemical potential (electronegativity) and hardness due to molecular oscillations [9,10]. The possibility of finding still higher derivatives has also been studied; ϭ Ϫ(Ѩ⌽/ѨQ) N and ϭ (ѨG/ѨQ) N for diatomic molecules have been found and proved to be useful in analyzing the source of anharmonicity of a molecular oscillator [11]. The authors have demonstrated connections between these derivatives and the vibrational force constants and thus exposed the need of a unified analysis of the energy function, which should contain the whole body of such derivatives [11,12].…”

“…The possibility of finding still higher derivatives has also been studied; ϭ Ϫ(Ѩ⌽/ѨQ) N and ϭ (ѨG/ѨQ) N for diatomic molecules have been found and proved to be useful in analyzing the source of anharmonicity of a molecular oscillator [11]. The authors have demonstrated connections between these derivatives and the vibrational force constants and thus exposed the need of a unified analysis of the energy function, which should contain the whole body of such derivatives [11,12]. Here also belongs the derivative first discussed by Fuentalba and Parr [13] as ␥ ϭ (Ѩ 3 E/ѨN 3 ) .…”

“…The complete analysis of couplings between the electronic and geometrical degrees of freedom was presented by Nalewajski [15] in the framework of his charge sensitivity analysis. The issue of renormalization of the energy function due to the coupling with oscillatory motion of nuclei was first raised by Luty [16] and further developed by Komorowski and Ordon [11]. The significance of this approach was indicated within the analysis of a local metallization as a possible source of explosive properties of RDX [17].…”