反應(yīng)物振動(dòng)量子數(shù)對(duì)O(1D)+HBr→OH+Br立體動(dòng)力學(xué)影響的研究

許慎德

(山東省莒縣第一中學(xué), 莒縣276500)

反應(yīng)物振動(dòng)量子數(shù)對(duì)O(1D)+HBr→OH+Br立體動(dòng)力學(xué)影響的研究

許慎德

(山東省莒縣第一中學(xué), 莒縣276500)

立體動(dòng)力學(xué); 準(zhǔn)經(jīng)典軌線; 產(chǎn)物轉(zhuǎn)動(dòng)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(xué)反應(yīng).隨著立體化學(xué)動(dòng)力學(xué)的發(fā)展, 此類反應(yīng)引起了高度的關(guān)注[1-3]. 而且它作為一個(gè)典型的原子與分子的基元反應(yīng), 可用來(lái)檢測(cè)新的理論與實(shí)驗(yàn)的標(biāo)準(zhǔn). 該反應(yīng)可以在單個(gè)勢(shì)能面得以完成[4], 并且存在兩種重要的競(jìng)爭(zhēng)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(shí)驗(yàn)以及理論方面對(duì)該反應(yīng)進(jìn)行了大量的研究. 包括HOBr的振動(dòng)轉(zhuǎn)動(dòng)光譜[5-6]以及分子偶極矩[7].Wineetal.采用時(shí)間分辨的共振熒光探測(cè)了反應(yīng)的產(chǎn)物通道[8]. 利用交叉分子束實(shí)驗(yàn)技術(shù), Balucanietal. 獲得了產(chǎn)物的分支比以及相應(yīng)的反應(yīng)截面[4].由于該反應(yīng)時(shí)間短, 產(chǎn)物BrO可以采用時(shí)間分辨的UV吸收光譜進(jìn)行測(cè)量[9].

理論方面, 也對(duì)該反應(yīng)進(jìn)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(jì)算得到了HOBr和異構(gòu)體HBrO的平衡結(jié)構(gòu)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(shì)能面[11].然而, 以往的工作主要研究對(duì)象為反應(yīng)的標(biāo)量屬性, 例如Tangetal. 采用含時(shí)波包理論計(jì)算了該反應(yīng)的反應(yīng)幾率和速率常數(shù), 結(jié)果表明反應(yīng)幾率與速率常數(shù)對(duì)溫度影響不敏感[12]. 為了更充分地揭示出標(biāo)題反應(yīng)的動(dòng)力學(xué)性質(zhì), 研究的重點(diǎn)不應(yīng)該局限于反應(yīng)的標(biāo)量屬性, 對(duì)反應(yīng)矢量性質(zhì)同樣應(yīng)該給予了足夠地重視.

準(zhǔn)經(jīng)典軌線(QCT)是一種研究反應(yīng)體系矢量性質(zhì)的有效方法, 多年來(lái)得到人們的廣泛應(yīng)用[13-14]. 已經(jīng)對(duì)許多重-輕-重反應(yīng)體系, 如 O+HCl[15], Sr+HF[16], 以及 Ca+HCl[17]進(jìn)行了研究. 迄今為止, 對(duì)于反應(yīng)物的振動(dòng)量子數(shù)對(duì)于具有深勢(shì)阱影響的研究還沒(méi)有報(bào)道. 采用量子的方法由于計(jì)算太大而非常困難, 準(zhǔn)經(jīng)典軌線方法可以解決上述的問(wèn)題. 本文中我們采用準(zhǔn)經(jīng)典軌線方法研究了反應(yīng)物v=0-7時(shí)該反應(yīng)的立體動(dòng)力學(xué)性質(zhì).

2 理論方法

本文計(jì)算是基于由Peterson等構(gòu)造的精確基態(tài)勢(shì)能面[18]. QCT詳細(xì)描述參見(jiàn)文獻(xiàn)[19-23]. 我們選用質(zhì)心坐標(biāo)系如圖1, Z軸平行于反應(yīng)物相對(duì)速度k, Y軸垂直于含有反應(yīng)物相對(duì)速度k和產(chǎn)物相對(duì)速度k′的xz平面.

圖 1 質(zhì)心坐標(biāo)系下描述 k, k′ 和 j′ 相關(guān)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(chǎn)物轉(zhuǎn)動(dòng)角動(dòng)量j’ 的空間分布可用如下公式展開(kāi)

(3)

參數(shù)

描述-k′、k′、j′三矢量的全三維角分布函數(shù)寫為：

(4)

3 結(jié)果與討論

我們給出了反應(yīng)振動(dòng)量子數(shù)分別為0-7時(shí)的反應(yīng)物相對(duì)速度矢量k和產(chǎn)物的轉(zhuǎn)動(dòng)角動(dòng)量矢量j’ 兩矢量相關(guān)的函P(θr)分布,P(θr)的分布直接反映了k,j′的兩矢量相關(guān). 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(shí)每一個(gè)反應(yīng)都關(guān)于θr=90°對(duì)稱. 隨著振動(dòng)量子數(shù)的增加, 峰值越來(lái)越大, 半高寬變窄表明反應(yīng)的產(chǎn)物OH的轉(zhuǎn)動(dòng)角動(dòng)量的取向性非常強(qiáng). 具體地說(shuō), 產(chǎn)物的轉(zhuǎn)動(dòng)角動(dòng)量矢量j′強(qiáng)烈地取向于垂直相對(duì)速度k的方向.

圖 2 反應(yīng)物在不同的振動(dòng)態(tài)時(shí)k-j′相關(guān)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(yīng)物在不同的振動(dòng)態(tài)時(shí)相應(yīng)于k-k′平面的p(θr)分布圖,從里向外振動(dòng)量子數(shù)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(yīng)O(1D)+HBr p(θr,φr)分布隨反應(yīng)物振動(dòng)量子數(shù)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(yīng)O(1D)+HBr在不同反應(yīng)物振動(dòng)量子數(shù)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(jié) 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(jì)算數(shù)學(xué)研究. E-mail: xushende9@163.com

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