Anharmonicity of a molecular oscillator

Abstract

ABSTRACT:The phenomenon of anharmonicity has been proved to be an effect of coupling between the change of nuclear positions in molecular vibrations (Q) and the electronic degrees of freedom as represented by the chemical potential () at constant number of electrons (N). The coupling parameters have well-founded meaning in the conceptual density functional theory (DFT), first approximations to their numerical values have recently become available. The effect of coupling between normal vibrational modes also appears to be the direct consequence of the electron-nuclear coupling. To show the pure anharmonic effect, calculations for a collection of diatomic molecules have been presented. The anharmonicity, described in the present work as d 3 E/dQ 3 0, has been proved to be the intrinsic property of every oscillating molecular system. A small anharmonic contribution exists even for the "strong harmonic" oscillator, when for the force constant k both a ϭ (Ѩk/ѨQ) N ϭ 0 and ϭ (Ѩk/ѨN) Q ϭ 0. The latter derivative of the force constant appears to be primary factor determining the anharmonic property of a molecule. An estimate of its values has been provided from the experimental data on the anharmonicity of diatomic molecules. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem 99: 153-160, 2004

DFT energy derivatives and their renormalization in molecular vibrations

“…As discussed before, G Ͻ 0 is expected [11]. Also, the recent calculations revealed Ͻ 0 for the set of molecules studied [20]. Hence, typically ⌬ ϭ ren Ϫ Ͻ 0 [Eq.…”

“…(63) is possible for the diatomic molecules since for one vibration l i ϭ l i and, consequently, F ϭ F , ϭ , G ϭ G ; however, k k, . As demonstrated elsewhere [12,20] for the diatomic molecule, with the neglect of ␥, very simple formulae apply:…”

“…This problem is addressed separately [20], as this current analysis is limited to the energy expansions rather than to the coupling effects. For the sake of completeness, the expansion of ⍀[, Q ␣ ] is presented only:…”

“…When possible, the derivatives have been related to already known energy derivatives in Table I, which then serve as a basis set for numerical studies. The analysis of analogs of the force constant k ij and the tensor of anharmonicity ã ijk (calculated at constant ), as well as the mixed derivative ij is presented separately [20].…”

Variation of the electronic dipole polarizability on the reaction path

“…The role of the specific external potential from the nuclei of a chemical entity has been analyzed by Ordon and Komorowski [12]. The authors analyzed the variety of energy derivatives over the nuclear displacement ( R i ) [13, 14]. Since the IRC analysis [15] operates with the variations of the atomic positions, the appropriate derivatives of the electronic energy over R i provide an equivalent description to the successfully used descriptors: F ξ , J ξ , Eqs.…”