韓曉琴
(商丘師范學(xué)院物理與電氣信息學(xué)院,河南商丘 476000)
SeOx(x=1,2)的從頭算勢(shì)能曲線(xiàn)和光譜常數(shù)
韓曉琴
(商丘師范學(xué)院物理與電氣信息學(xué)院,河南商丘 476000)
采用從頭算的多種方法和基組優(yōu)化計(jì)算SeOx(x=1,2)自由基的基態(tài)結(jié)構(gòu)、諧振頻率及離解能,優(yōu)選出QCISD(T)/6-311+G(2df)、B3LYP/6-311G(3d2f)方法分別對(duì)SeO、SeO2自由基進(jìn)行計(jì)算,計(jì)算結(jié)果與實(shí)驗(yàn)結(jié)果吻合很好.對(duì)SeO自由基擬合出Murrell-Sorbie勢(shì)能函數(shù)參數(shù),計(jì)算出SeO自由基的光譜常數(shù)和力常數(shù).計(jì)算出SeO2自由基力常數(shù),導(dǎo)出SeO2自由基的多體展式勢(shì)能函數(shù),發(fā)現(xiàn)SeO2自由基對(duì)稱(chēng)伸縮振動(dòng)勢(shì)能圖中在對(duì)稱(chēng)的O+SeO→SeO2反應(yīng)通道上有一鞍點(diǎn),其活化能約為48.24 kJ·mol-1,O原子需要越過(guò)0.5 eV的能壘才能生成SeO2的穩(wěn)定結(jié)構(gòu).
SeO;SeO2;光譜常數(shù);勢(shì)能函數(shù)
二氧化硒對(duì)光和熱穩(wěn)定并有吸濕性,易溶于水、甲醇、丙酮、濃硫酸等,常用于制備高純硒及其化合物,是有機(jī)化合物、氧化劑、催化劑、化學(xué)試劑以及各種無(wú)機(jī)硒化合物制造的原料,在復(fù)印機(jī)、整流器等中也有使用.自二十世紀(jì)五六十年代以來(lái),人們對(duì)SeO2的研究熱情不斷上漲[1-13].早在1969年,Hastie等在稀有氣體環(huán)境中測(cè)定了SO2、SeO2的紅外光譜和結(jié)構(gòu)[1].1975年,Verma等研究了在319~269 nm區(qū)域內(nèi)SeO的一種新發(fā)散光譜[2].1980年,Winter等觀察研究了在近紅外區(qū)SeO、SeS、Se2由激發(fā)態(tài)躍遷到基態(tài)的光譜數(shù)據(jù)[3]. 2008年,Xu等人計(jì)算了SeOn(n=1~5)及其負(fù)離子的結(jié)構(gòu)和電子親和能[4].對(duì)SeO、SeO2的結(jié)構(gòu)及勢(shì)能函數(shù)的研究也有報(bào)道[5,11],1970年,Takeo等研究了SeO2基態(tài)和激發(fā)態(tài)的微波光譜,并測(cè)出了其勢(shì)能函數(shù)常數(shù)[5],但這些常數(shù)是在振動(dòng)轉(zhuǎn)動(dòng)相互作用的基礎(chǔ)上得到的.并沒(méi)有對(duì)勢(shì)能面做出細(xì)致的討論.勢(shì)能函數(shù)是分子本身幾何及電子結(jié)構(gòu)的完全描述[14-17],隨著相關(guān)領(lǐng)域及實(shí)驗(yàn)技術(shù)的不斷完善,對(duì)小分子勢(shì)能函數(shù)的精度也提出了更高的要求.因此,獲得更為精確的勢(shì)能函數(shù)并對(duì)其做出細(xì)致分析仍是很必要的.
為此,采用從頭算的組態(tài)相互作用方法QCISD、QCISD(T)、CCSD、CCSD(T)和密度泛函的B3LYP方法配合多種基組對(duì)SeOx(x=1,2)自由基進(jìn)行優(yōu)化計(jì)算,通過(guò)與實(shí)驗(yàn)值對(duì)比,優(yōu)選出QCISD(T)/6-311+G(2df)方法對(duì)SeO自由基進(jìn)一步計(jì)算,得到其M-S勢(shì)能函數(shù).優(yōu)選出B3LYP/6-311G(3d2f)方法對(duì)SeO2自由基進(jìn)行計(jì)算,推導(dǎo)出SeO2自由基的多體展式勢(shì)能函數(shù).在此基礎(chǔ)上,討論了SeO2自由基的靜態(tài)勢(shì)能面特征.為該自由基的反應(yīng)化學(xué)動(dòng)力學(xué)研究提供重要的理論依據(jù).
1.1 SeO的基態(tài)結(jié)構(gòu)、諧振頻率、勢(shì)能函數(shù)
采用從頭算的多種方法,配合不同基組對(duì)SeO自由基基態(tài)進(jìn)行優(yōu)化和頻率計(jì)算,優(yōu)化結(jié)果列于表1,同時(shí)得到SeO自由基的基態(tài)為,與文獻(xiàn)[2,13]的結(jié)果一致.
表中所列結(jié)果與實(shí)驗(yàn)值比較可知,選用QCISD(T)/6-311+G(2df)方法時(shí),得到的平衡鍵長(zhǎng)Re=0.164 87 nm與實(shí)驗(yàn)結(jié)果[2]Re=0.164 9 nm的誤差僅為0.018%,諧振頻率ωe=922.690 2 cm-1與實(shí)驗(yàn)結(jié)果[2]ωe=914.69 cm-1的誤差僅為0.867%,可見(jiàn)本文的計(jì)算結(jié)果與實(shí)驗(yàn)結(jié)果符合很好.QCISD (T)是包括單、雙取代并加入三重激發(fā)的二次組態(tài)相互作用方法,適用于較大原子Se的雙原子分子的非限制性開(kāi)殼層波函的計(jì)算.之后,采用同樣的方法,在Se原子和O原子間距不斷改變的情況下進(jìn)行單點(diǎn)能掃描計(jì)算,從而得到了一系列單點(diǎn)勢(shì)能值,用正規(guī)方程組將其擬合為M-S勢(shì)能函數(shù)[14]:
V=-De(1+a1ρ+a2ρ2+a3ρ3)exp(-a1ρ),(1)
圖1繪出了SeO(3∑-)的勢(shì)能曲線(xiàn).可以看出SeO自由基的平衡核間距為0.164 87 nm、離解能為5.571 9 eV,與計(jì)算結(jié)果完全吻合.擬合出的勢(shì)能曲線(xiàn)也正確反應(yīng)了SeO自由基勢(shì)能隨核間距的變化趨勢(shì).該雙原子勢(shì)能函數(shù)可用于SeO2自由基勢(shì)能函數(shù)的研究.
1.2 SeO2自由基的電子狀態(tài)與離解極限
SeO2自由基屬于C2V群,可由以下通道構(gòu)造出SeO2的基電子狀態(tài)X1A1.
根據(jù)微觀過(guò)程的可逆性原理可得基態(tài)SeO2自由基的可能離解極限為
上述三個(gè)過(guò)程都可將SeO2離解,但離解能最小的Se(3Pg)+O2()式是最優(yōu)能量過(guò)程.即SeO2自由基離解能De(SeO2)=3.358 6 eV.
1.3 SeO2自由基的基態(tài)結(jié)構(gòu)、諧振頻率、力常數(shù)
采用組態(tài)相互作用的QCISD、QCISD(T)、CCSD、CCSD(T)和密度泛函的B3LYP等方法,配有多種基組計(jì)算了SeO2自由基的鍵長(zhǎng)RSeO、鍵角∠OSeO、諧振頻率ω(對(duì)稱(chēng)伸縮振動(dòng)頻率ω1、彎曲振動(dòng)頻率ω2、反對(duì)稱(chēng)伸縮振動(dòng)頻率ω3),其結(jié)果見(jiàn)表3.并得到SeO2自由基基態(tài)為1A1,具有C2V構(gòu)型.
表3中,B3LYP/6-311G(3d2f)方法下計(jì)算得到的鍵長(zhǎng)RSeO=0.160 78 nm,鍵角∠OSeO=113.940 3°,諧振頻率ω1=371.783 2 cm-1,ω2=972.176 7 cm-1與實(shí)驗(yàn)值[1,6]符合最好.正是由于密度泛函的B3LYP方法計(jì)算庫(kù)倫作用時(shí)將電子密度對(duì)一組原子中心的函數(shù)進(jìn)行展開(kāi),而不計(jì)算所有的雙電子積分,所以能夠顯著提高計(jì)算效率,同時(shí)不犧牲預(yù)測(cè)的結(jié)構(gòu)、相對(duì)能量和分子性質(zhì)的精度.同時(shí)也計(jì)算出了相應(yīng)的力常數(shù)f11=0.496 14 a.u.、f12=0.014 12 a.u.、f13=0.004 31 a.u.、f33=0.309 24 a.u..這些數(shù)據(jù)可為進(jìn)一步研究SeO2自由基的性質(zhì)提供有力的參考.同時(shí)得到恒定體積的摩爾熱熔C=8.266 cal·mol-1,熵S=62.721 cal·mol-1.
1.4 SeO2自由基的多體項(xiàng)展式勢(shì)能函數(shù)
對(duì)于SeO2自由基,設(shè)基態(tài)原子能量為零,滿(mǎn)足(3)式離解極限的多體項(xiàng)展式為
其中R1、R2、R3分別為Se與O、Se與O、O與O原子的核間距(R1=RSeO,R2=RSeO、R3=ROO),式中為兩體項(xiàng)SeO(X3∑-),SeO(X3∑-),OO(X3∑-)的勢(shì)能函數(shù),(R1,R2,R3)為三體項(xiàng)SeO2(X1A1)的勢(shì)能函數(shù),采用文獻(xiàn)[14]形式為
其中,對(duì)稱(chēng)內(nèi)坐標(biāo)Si的多項(xiàng)式量程函數(shù)
式中λ1、λ3是非線(xiàn)性系數(shù).
基態(tài)SeO2自由基的平衡結(jié)構(gòu)為C2V,為了方便研究勢(shì)能函數(shù),根據(jù)勢(shì)能面的結(jié)構(gòu)特征,采用優(yōu)化內(nèi)坐標(biāo).取SeO2的兩個(gè)平衡鍵長(zhǎng)為參考結(jié)構(gòu),==0.160 78 nm,=0.269 6 nm,故內(nèi)坐標(biāo)ρi經(jīng)下列變換成優(yōu)化內(nèi)坐標(biāo)Si
式中ρi=Ri-(i=1,2,3),S2對(duì)R1、R2的交換是反對(duì)稱(chēng)的,但R1和R2交換后分子是相同的,為了滿(mǎn)足這一物理意義,S2只能含偶次項(xiàng).由以上可知,只有確定(6)式中的七個(gè)線(xiàn)性系數(shù)(C1,C2,C3,C4,C5,C6,C7)和(7)式中的兩個(gè)非線(xiàn)性系數(shù)(λ1、λ3)就能得到三體項(xiàng)SeO2的勢(shì)能函數(shù).依據(jù)表3列出的平衡結(jié)構(gòu)參數(shù)以及文中得到的SeO2的離解能、力常數(shù)等,可以確定勢(shì)能函數(shù)式(5)的參數(shù)值分別是C1=7.747 8、C2=7.567 6、C3=-4.826 7、C4=2.903、C5=8.424 7、C6=-12.451 5、C7=9.686 3、λ1=1.2、λ3=0.8.為了直觀地分析勢(shì)能函數(shù)的物理意義,展示SeO2自由基的結(jié)構(gòu)及形成機(jī)理,下面給出基態(tài)SeO2自由基的伸縮振動(dòng)圖和旋轉(zhuǎn)圖[23-28].
圖2是固定∠OSeO=113.940 3°時(shí)的對(duì)稱(chēng)伸縮振動(dòng)勢(shì)能圖,該圖顯示了SeO2自由基的C2V結(jié)構(gòu)特征.并且在RSeO=0.160 78 nm處有一勢(shì)阱,阱深約為3.358 6 eV,這與從頭算得到的結(jié)果RSeO=0.160 78 nm,De=3.358 6 eV一致,表明在該處形成穩(wěn)定的SeO2自由基.在兩個(gè)等價(jià)的通道O+SeO→SeO2上有兩個(gè)對(duì)稱(chēng)鞍點(diǎn),分別在(0.258 6 nm,0.168 2 nm)和(0.168 2 nm,0.258 6 nm)處,其活化能約為48.24 kJ·mol-1.且在RSeO=ROSe=0.255 nm處出現(xiàn)一勢(shì)壘,勢(shì)壘高度大約為2.0 eV.說(shuō)明該反應(yīng)是只能通過(guò)兩個(gè)等價(jià)的通道越過(guò)勢(shì)壘才能進(jìn)行的有閾能反應(yīng).圖中清晰顯示O與SeO反應(yīng)時(shí)需要越過(guò)的勢(shì)壘低于在RSeO=ROSe=0.255 nm處出現(xiàn)的勢(shì)壘.
圖3為固定O-Se鍵在X軸上,O-Se鍵的中垂線(xiàn)為Y軸,讓另一個(gè)O原子繞Se-O鍵旋轉(zhuǎn)的等值勢(shì)能圖.圖中清晰看到當(dāng)O原子轉(zhuǎn)到(0.145 6 nm,0.146 9 nm)處時(shí),出現(xiàn)一深度為3.358 6 eV的勢(shì)阱,這與從頭算結(jié)果一致,并且在大約(0.206 7 nm,0.233 7 nm)處有一勢(shì)壘,壘高大約為2.0 eV,與圖2的結(jié)果完全吻合.
圖4為固定O-O鍵在X軸上,其中一O原子為原點(diǎn)建立Y軸并讓Se原子繞O-O鍵旋轉(zhuǎn)的等值勢(shì)能圖.圖中清晰看到SeO2自由基的C2V結(jié)構(gòu).并且圖中顯示當(dāng)Se原子轉(zhuǎn)到(0.134 8 nm,0.087 6 nm)處時(shí)形成穩(wěn)定的SeO2自由基.這與圖2,3的結(jié)果完全一致.
在化學(xué)動(dòng)力學(xué)研究中,精確的勢(shì)能面是動(dòng)力學(xué)計(jì)算的基礎(chǔ),圖2~圖4以不同的旋轉(zhuǎn)方式分析得到了SeO2自由基的精確勢(shì)能面,該勢(shì)能面符合三原子分子的幾何構(gòu)型,也表明SeO2自由基的勢(shì)能函數(shù)能準(zhǔn)確呈現(xiàn)出其結(jié)構(gòu)特征和能量變化的特性.可用于進(jìn)一步研究SeO2自由基的動(dòng)力學(xué).
采用從頭算的QCISD(T)/6-311+G(2df)方法優(yōu)化出SeO自由基的幾何構(gòu)型和諧振頻率,計(jì)算結(jié)果達(dá)到了更高精度,擬合出SeO自由基的M-S勢(shì)能函數(shù)參數(shù)并研究了SeO自由基勢(shì)能隨核間距的變化.采用B3LYP/6-311G(3d2f)方法對(duì)SeO2(X1A1)自由基進(jìn)行計(jì)算,發(fā)現(xiàn)其平衡結(jié)構(gòu)、諧振頻率與實(shí)驗(yàn)值符合很好,根據(jù)推導(dǎo)出的離解極限確定了SeO2自由基的基態(tài)及離解能,進(jìn)一步計(jì)算了該自由基的力常數(shù).運(yùn)用多體項(xiàng)展式理論導(dǎo)出SeO2自由基的解析勢(shì)能函數(shù),繪出它的伸縮和旋轉(zhuǎn)勢(shì)能曲線(xiàn).從圖中清晰看出該函數(shù)正確反應(yīng)了體系的結(jié)構(gòu)和能量變化特征,并給出一些動(dòng)力學(xué)信息.發(fā)現(xiàn)SeO2自由基的等值勢(shì)能圖中在等價(jià)的O+SeO→SeO2反應(yīng)通道上有一鞍點(diǎn),O原子需要越過(guò)2.0 eV的能壘才能生成SeO2的穩(wěn)定結(jié)構(gòu).
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ab Initio Potential Energy Curves and Spectral Constants of SeOx(x=1,2)
HAN Xiaoqin
(Department of Physics,Shangqiu Normal College,Shangqiu 476000,China)
Possible ground state structures,harmonic frequency and dissociation energy of SeOx(x=1,2)free radical are optimized by different methods and base sets included in Gaussian 09.Among them,QCISD(T)/6-311+G(2df)and B3LYP/6-311G(3d2f)are the most suitable for SeO,SeO2.Calculation results are in good agreement with experiment.For SeO free radical,Murrell-Sorbie potential energy functional constant are calculated,according to which spectral parameters and force constants are shown.It provides basis for further investigation on SeOx(x=1,2).For SeO2free radical,force constants are calculated at the same time.And potential energy functions of SeO2are derived with many-body expansion theory.In a symmetric stretching vibration potential energy diagram of SeO2,saddle points in reaction kinetics O+SeO→SeO2in the symmetry dilation potential energy are found.Activation energy is 48.24 kJ·mol-1.A stable SeO2free radical could be formed as O atom with energy surpassing 0.5 eV.
SeO;SeO2;spectral constant;potential energy function
date:2013-07-01;Revised date:2013-10-29
O561.1
A
1001-246X(2014)03-0357-06
2013-07-01;
2013-10-29
國(guó)家自然科學(xué)基金(11074160)及河南省科技攻關(guān)計(jì)劃(102102210037)資助項(xiàng)目
韓曉琴(1975-),女,碩士,講師,主要從事原子分子結(jié)構(gòu)與動(dòng)力學(xué)研究,E-mail:hanxiaoqin88@163.com