許慎德

(山東省莒縣第一中學, 莒縣276500)

反應物振動量子數對O(1D)+HBr→OH+Br立體動力學影響的研究

許慎德

(山東省莒縣第一中學, 莒縣276500)

立體動力學; 準經典軌線; 產物轉動取向

1 引 言

本文所研究的O(1D)+HBr體系是星際中的一類重要的化學反應.隨著立體化學動力學的發(fā)展, 此類反應引起了高度的關注[1-3]. 而且它作為一個典型的原子與分子的基元反應, 可用來檢測新的理論與實驗的標準. 該反應可以在單個勢能面得以完成[4], 并且存在兩種重要的競爭途徑.

→Br+OHΔH0=-60.0±1.0kcal/mol

O(1D)+HBr→

→H+BrOΔH0=-13.9±1.4kcal/mol

在近三十年里, 從實驗以及理論方面對該反應進行了大量的研究. 包括HOBr的振動轉動光譜[5-6]以及分子偶極矩[7].Wineetal.采用時間分辨的共振熒光探測了反應的產物通道[8]. 利用交叉分子束實驗技術, Balucanietal. 獲得了產物的分支比以及相應的反應截面[4].由于該反應時間短, 產物BrO可以采用時間分辨的UV吸收光譜進行測量[9].

理論方面, 也對該反應進行了一系列的研究. 最早的理論研究可以追溯到McGrath和Rowland等人計算得到了HOBr和異構體HBrO的平衡結構以及諧振頻率[10]. Petersonetal. 等人用從頭算的方法獲得了比較精確的勢能面[11].然而, 以往的工作主要研究對象為反應的標量屬性, 例如Tangetal. 采用含時波包理論計算了該反應的反應幾率和速率常數, 結果表明反應幾率與速率常數對溫度影響不敏感[12]. 為了更充分地揭示出標題反應的動力學性質, 研究的重點不應該局限于反應的標量屬性, 對反應矢量性質同樣應該給予了足夠地重視.

準經典軌線(QCT)是一種研究反應體系矢量性質的有效方法, 多年來得到人們的廣泛應用[13-14]. 已經對許多重-輕-重反應體系, 如 O+HCl[15], Sr+HF[16], 以及 Ca+HCl[17]進行了研究. 迄今為止, 對于反應物的振動量子數對于具有深勢阱影響的研究還沒有報道. 采用量子的方法由于計算太大而非常困難, 準經典軌線方法可以解決上述的問題. 本文中我們采用準經典軌線方法研究了反應物v=0-7時該反應的立體動力學性質.

2 理論方法

本文計算是基于由Peterson等構造的精確基態(tài)勢能面[18]. QCT詳細描述參見文獻[19-23]. 我們選用質心坐標系如圖1, Z軸平行于反應物相對速度k, Y軸垂直于含有反應物相對速度k和產物相對速度k′的xz平面.

圖 1 質心坐標系下描述 k, k′ 和 j′ 相關圖Fig.1 The center-of-mass coordinate system used to describe the k, k′ and j′ correlations

(1)

(2)

其中

an=2

bn=2

產物轉動角動量j’ 的空間分布可用如下公式展開

(3)

參數

描述-k′、k′、j′三矢量的全三維角分布函數寫為：

(4)

3 結果與討論

我們給出了反應振動量子數分別為0-7時的反應物相對速度矢量k和產物的轉動角動量矢量j’ 兩矢量相關的函P(θr)分布,P(θr)的分布直接反映了k,j′的兩矢量相關. 從圖2可以很清晰地看出,P(θr)分布的峰值均位于θr=90°, 并且同時每一個反應都關于θr=90°對稱. 隨著振動量子數的增加, 峰值越來越大, 半高寬變窄表明反應的產物OH的轉動角動量的取向性非常強. 具體地說, 產物的轉動角動量矢量j′強烈地取向于垂直相對速度k的方向.

圖 2 反應物在不同的振動態(tài)時k-j′相關的p(θr)分布圖Fig.2 The distributions of p(θr) reflecting k-j′ correlations at different vibrational levels v=0-7 for the reagent vibrational excitation

圖 3 反應物在不同的振動態(tài)時相應于k-k′平面的p(θr)分布圖,從里向外振動量子數分別為0到7Fig.3 The dihedral angle distribution of p(φr) with respect to the k-k′ plane, plotted at reagent vibrational quantum numbers from inside to outside are v=0 to v=7, respectively

圖 4 反應O(1D)+HBr p(θr,φr)分布隨反應物振動量子數變化(a) v = 0; (b) v = 3 ; (c) v = 6Fig.4 Polar plots of the p(θr,φr) distributions with peaks and valleys at different vibrational levels. (a) v = 0; (b) v = 3 ; (c) v = 6

圖 5 反應O(1D)+HBr在不同反應物振動量子數的微分散射截面 (a) (k , q)=(0,0); (b) (k , q)= (2, 0)Fig.5 Two polarization-dependent generalized differential cross sectionsof the reagent vibrational quantum numbers with (a) (k , q)=(0,0); (b) (k , q)= (2, 0), respectively

4 結 論

VibrationLevelv=0v=1v=2v=3v=4v=5v=6v=7-0 36793-0 37516-0 37626-0 3749-0 39131-0 39459-0 39543-0 41659

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Influence of reagen vibration on the stereodynamics of theO(1D)+HBr→OH+Brreaction

XU Shen-De

(The first middle school of Juxian, Juxian 276500, China)

Stereodynamic; Quasi-classical trajectory; Product rotational alignment

103969/j.issn.1000-0364.2015.02.013

2013-12-20

許慎德(1970—), 男, 山東省莒縣人, 本科, 主要從事計算數學研究. E-mail: xushende9@163.com

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