評估各類密度泛函近似在 water dimer cation 的 Hemibonded 結構的表現

Assessment of density functional approximations for the hemibonded structure of water dimer radical cation

潘品睿(Piin-Ruey Pan)

指導教授 ： 蔡政達

共同指導教授 ： 郭哲來(Jer-Lai Kuo)

國立臺灣大學/理學院/物理研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.02339

摘要

因為一般密度泛函的自我作用誤差 (self-interaction errors) 在水的 hemibond 結構特別大，造成一般的密度泛函無法成功地將 (H 2 O)2+ 的 hemibond 結構，游離成 H2O 與 H2O + 。故分子束縛能的定義 (用 (H 2 O)2+ 的能量扣掉 H2O 與 H2O+ 的能量)，對 (H2O)2+ 來說，並不全面適用：即使一些密度泛函能給出正
確的 (H2O)2+ hemibond 結構的束縛能，但在計算此結構的游離曲線時，會給出較淺的位能；更甚者，許多密度泛函會預測該結構的游離曲線上，會出現一個屏障。出現這個屏障，是完全不合理的。這對想要用這些密度泛函來做分子動力學 (Molecular Dynamics) 的人來說，會造成非常嚴重的後果。因為用這些密度泛函算出來的 (H2O)2+ ，只要越過該屏障，很容易就會游離。為了比較不同的密度泛函在 (H2O)2+ 的表現，我們提供了三種不同的標準：(1) 分子束縛能。(2)
(H2O)2+ 的兩種構型與它們之間的過渡態，這三者之間的相對能量差。(3) 各種不同密度泛函，預測 (H2O)2+ 的游離曲線。我們發現，在這三個標準之中，平均表現最好的，莫屬 wB97X-2(LP) 了。此外，我們也解釋了：為何長距離修正的密度泛函 (long-range corrected hybrid functionals)，不若一般的全域密度泛函(global
hybrid functionals) 一樣，會錯誤地預測 (H2O)2+ 的游離曲線上，有一個假的屏障。

關鍵字

半鍵結 ； 帶正電雙水分子 ； 密度泛函

並列摘要

The reason why many exchange correlation functionals fail to give correct binding energies for the hemibonding structures of the ionized water clusters can be traced back to the dissociation behaviors of the hemibonded systems predicted by the exchange correlation functionals, since nearly most of the exchange-correlation functionals cannot predict that the hemibonded structure of the water dimer radical cation will dissociate into H2O and H2O+. Thus, the definition of the binding energies is unfair somehow: Although the previous suggested functionals such as BH&HLYP and MPW1K can give accurate equilibrium binding energies of the hemibonding structure, they fail to predict the correct dissociation limits. This will result in a potential curve which is too shallow. Thus, the hemibonded structure calculated by those functionals is much easier to dissociate than it actually should be. Therefore we propose three different criteria to reexamine the water dimer radi-cal cation: (i) The binding energies, (ii) the relative energies between the conformers of the ionized water dimer and (iii) the dissociation behaviors predicted by various exchange correlation functionals. We find that the functional which behaves well all over these three criteria is the wB97X-2 functional. Reasons that LC hybrid functionals generally work better than conventional density functionals for hemibonded systems is also explained in this work.

並列關鍵字

Hemibond ； water dimer cation ； ionized water dimer ； density functional theory

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