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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Morse potential ： ウィキペディア英語版 Morse potential The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule. It is a better approximation for the vibrational structure of the molecule than the QHO (quantum harmonic oscillator) because it explicitly includes the effects of bond breaking, such as the existence of unbound states. It also accounts for the anharmonicity of real bonds and the non-zero transition probability for overtone and combination bands. The Morse potential can also be used to model other interactions such as the interaction between an atom and a surface. Due to its simplicity (only three fitting parameters), it is not used in modern spectroscopy. However, its mathematical form inspired the MLR (Morse/Long-range) potential, which is the most popular potential energy function used for fitting spectroscopic data. ==Potential energy function== The Morse potential energy function is of the form :$V(r)\; =\; D\_e\; (\; 1-e^\; )^2$ Here $r$ is the distance between the atoms, $r\_e$ is the equilibrium bond distance, $D\_e$ is the well depth (defined relative to the dissociated atoms), and $a$ controls the 'width' of the potential (the smaller $a$ is, the larger the well). The dissociation energy of the bond can be calculated by subtracting the zero point energy $E(0)$ from the depth of the well. The force constant of the bond can be found by Taylor expansion of $V(r)$ around $r=r\_e$ to the second derivative of the potential energy function, from which it can be shown that the parameter, $a$, is :$a=\backslash sqrt,$ where $k\_e$ is the force constant at the minimum of the well. Since the zero of potential energy is arbitrary, the equation for the Morse potential can be rewritten any number of ways by adding or subtracting a constant value. When it is used to model the atom-surface interaction, the energy zero can be redefined so that the Morse potential becomes :$V(r)\; =\; D\_e\; ((\; 1-e^\; )^2\; -1)$ which is usually written as :$V(r)\; =\; D\_e\; (\; e^-2e^\; )$ where $r$ is now the coordinate perpendicular to the surface. This form approaches zero at infinite $r$ and equals $-D\_e$ at its minimum, i.e. $r=r\_e$. It clearly shows that the Morse potential is the combination of a short-range repulsion term (the former) and a long-range attractive term (the latter), analogous to the Lennard-Jones potential. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Morse potential」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.