DFT analysis of fluctuations in electronegativity and hardness of a molecular oscillator

The Journal of Chemical Physics

Tachibana

2007

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Nuclear stiffness, expressed as a hardness derivative, appears to be a good measure of the slope of global hardness. The authors analyze molecular states for which hardness has a maximum value. Maximum hardness principle (MHP) has been discussed. At the ground state hardness function does not obtain a maximum value versus spatial coordinates within a constant number of electrons (N), but is so within constant chemical potential (mu) constraint. The authors apply this feature to evaluate an energy third derivative (gamma). MHP has been analyzed via symmetry considerations of nuclear stiffness and nuclear reactivity. Nuclear stiffness has been also applied to study the hardness profile for a chemical reaction. In this case, the authors seek molecular states for which hardness is at a minimum. They have examined systems for which they have recently obtained regional chemical potentials [P. Ordon and A. Tachibana, J. Mol. Model. 11, 312 (2005); J. Chem. Sci. 117, 583 (2005)]. The transition state is found not to be the softest along the chemical reaction path. Nuclear stiffness reflects well the softest conformation of a molecule, which has been found independently along the intrinsic reaction coordinate profile. Electronic energy-density [A. Tachibana, J. Mol. Mod. 11, 301 (2005)] has been used to visualize the reactivity difference between the softest state and the transition state.

Section: ͑3͒mentioning

confidence: 75%

Section: ͑3͒mentioning

confidence: 75%

Use of nuclear stiffness in search for a maximum hardness principle and for the softest states along the chemical reaction path: A new formula for the energy third derivative γ

The Journal of Chemical Physics

Tachibana

2007

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“…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.…”

Section: Resultsmentioning

confidence: 99%

“…The derivative of global hardness () was introduced by Ordon and Komorowski as the nuclear stiffness: G i ϭ (Ѩ/ѨQ i ) N [6]. 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].…”

mentioning

confidence: 98%

DFT energy derivatives and their renormalization in molecular vibrations

Int J of Quantum Chemistry

Komorowski

2004

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ABSTRACT:Properties of the energy function E(N, Q) and the thermodynamic potential ⍀(, Q) expressed in terms of the number of electrons (N) and the nuclear positions (Q) rather than conventionally, by the electrostatic potential, (r), have been analyzed. The whole body of derivatives up to the third order is presented for each function. Renormalization of the basic derivatives explored in conceptual density functional theory has been demonstrated (chemical potential , global hardness , number of electrons N, global softness S) as a result of coupling between the oscillatory motion of nuclei and the change in N or , for E and ⍀, respectively. Exact result of renormalization crucially depends on the level of approximation. Extending the analysis beyond the second order was possible by adopting the Liu and Parr-type approximation to the energy function. It has been determined that first derivatives (, N) change their values when found beyond the vibrational energy minimum only. Second derivatives (, S) both get renormalized even at the energy minimum, and they no longer conform to the reciprocity condition (S 1). Possible implications for the reactivity of oscillating species have been indicated.

“…2 ѨQ i ) for its properties, including thermal fluctuations of electronegativity and global hardness [10,11]. We have previously reported an analysis of the possible role of still higher-energy derivatives [12]; the first preliminary account has been provided, demonstrating that the anharmonicity of a molecule might be determined by means of the DFT energy derivatives.…”

Section: E/ѩnmentioning

confidence: 98%

Anharmonicity of a molecular oscillator

Komorowski

Int J of Quantum Chemistry

2004

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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