第25卷第6期原子與分子物理學(xué)報(bào)2008年12月JOURNAL OF ATOMIC AND MOLECULAR PHYSICSDec.2008文章編號:10000364(2008)06-143908DTO體系分子反應(yīng)動(dòng)力學(xué)阮文12,謝安東1,余曉光1,羅文浪12,朱正和2,傅依備2(1.井岡山大學(xué)數(shù)理學(xué)院,吉安343009;2,四川大學(xué)原子與分子物理研究所,成都610065摘要:基于DO分子(X1A1)的氫同位素效應(yīng),得到修正的 Born-Oppenheimer(BO)理論下多體展式分析勢能函數(shù),用準(zhǔn)經(jīng)典的 Monte-Carlo軌跡法研究了D+TO(0,0)和T+DO(0,0)的分子反應(yīng)動(dòng)力學(xué)過程結(jié)果表明:在碰撞能量較低時(shí)(<209.2km-1),D+TO(0,0)和T+DO(0,0)反應(yīng)主要生成O+DT,并且該反應(yīng)是無閡能的;有少量的交換反應(yīng)產(chǎn)物DO(TO)生成,并伴有極少量的絡(luò)合物產(chǎn)生,碰撞能大于209.2 kI.mol-后,逐漸出現(xiàn)分子被完全碰散成D,T,O原子的情形,反應(yīng)D+TO(0,0)→OD+T和T+DO(0,0)→OT+D是無熱反應(yīng)但是有閡能存在,由于D和T原子的同位素效應(yīng),置換產(chǎn)物軌線存在非致性關(guān)鍵詞:DTO;勢能函數(shù);分子反應(yīng)截面;軌線非對稱性中圖分類號:O643.1文獻(xiàn)標(biāo)識碼:ATheoretical study on molecular reaction dynamics of the DTo systemRUAN Wen,2, XIE An-Dong, YU Xiao-Guang, LUO Wen-Lang, 2, ZHU Zheng-He2, FU Yi-Bei2(1. College of Mathematics and Physics, Jinggangshan University, Ji'an 343009, China:2. Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China)Abstract: Based on the hydrogen isotopic effect and its nuclear motion, the analytical potential energy functionAPEF)of Dto(X' A1)is derived by many-body expansion method(MEM)under the correctional Born-Oppenheimer(B-O). Then the atomic and molecular reaction dynamics for D+ TO and T+DO have beenstudied on the potential energy function DTo(X'A1)by Monte-Carlo quasi-classical trajectory approach. Itis shown that the main reactions of D+ To--DT+O and T+Do--DT+O along with a few long-lived com-plex compounds have no threshold energy with low collision energy, which agrees with the potential surfaceWhen the collision energy is greater than 209.2 k/mol", the DTO molecules will decompose into D, T and Oatom completely, and these reactions have threshold energy. The other reactions of D+ToTO+D and T+DO-DO+ T are the reactions of non-decalescence, but they have threshold energy. However, the trajectoriesnd collision sections of reactions D+ To (0, 0)and T+ Do(0, 0) present variance distribution due to the iso-topic effect of deuterium and tritium atom, which corresponds to the potential surfaceKey words: DTO, potential function, reactive section, trajectory asymmetrical distribution收稿日期:2008-0508基金項(xiàng)目:國家自然科學(xué)基金(10676022)資助項(xiàng)目;江西省教育廳科技研究ayH中國煤化工CNMHG省科技廳工業(yè)攻關(guān)項(xiàng)目[200621];井岡山大學(xué)校級自然科學(xué)研究項(xiàng)目作者簡介:阮文. E-mail: ruanwensongyan@126.cm通訊作者:朱正和.Emal:zhum@scu.edu.cn原子與分子物理學(xué)報(bào)第25卷1引言量和核振動(dòng)能計(jì)算,用核振動(dòng)能修正電子能量獲得DTO分子的勢能值.將勢能函數(shù)展開成鍵長和鍵眾所周知,氚對能源、環(huán)保、核材料和軍事具有角的泰勒級數(shù)19,用這組修正后的勢能值,通過最非常重要的意義,如何從重水中提取氚是當(dāng)今的一小二乘法擬合,得到泰勒級數(shù)二次項(xiàng)的系數(shù),則可大主要問題目前,從重水中提氚有多種方法,如氫獲得DIO分子的諧性力常數(shù)計(jì)算結(jié)果見表1水同位素交換-3,由D2交換分離出DT,是通過勢能函數(shù)采用多體項(xiàng)展式理論確定41.令反應(yīng)D2(氣)+DTO(蒸汽)→DT(氣)+D2O(蒸R1,R2和R3分別表示DTO分子的DO,TO和汽).長期以來,人們對水及其同位素分子進(jìn)行了大DT的鍵長,并設(shè)基態(tài)原子能量為零,則滿足離解量的研究, Cheng等(4采用同步加速輻射測定了氫極限的多體項(xiàng)展式分析勢能函數(shù)為同位素水分子在室溫下的吸收光譜;AtlG等5V=wg(D)+VB(R1,A2∑”)采用高精度(包括核、價(jià)鍵、相對論、量子電動(dòng)力學(xué)以及 Born-Oppenheimer修正對角化)的完全勢能V(R2,A2∑)+VB(R3)+面( CVRQD)方法獲得了H2O和D2O分子的平衡vBor(ri, R2, R3)幾何結(jié)構(gòu);wang等6研究了HO分子的勢能面及選擇基態(tài)原子的能量為零,v8(D2)為激發(fā)態(tài)原OH+D→OD+H的交換反應(yīng)速率常數(shù);Pab等]子O(D2)的能量,其值為1.967eV0,R1=R2采用 CVRQD方法獲得了H2O及氫同位素水分子=R,R3=Rm,兩體項(xiàng)選用Mure! Sorbie勢能的平衡幾何結(jié)構(gòu)、正則振動(dòng)頻率及H2O分子的勢函數(shù)1:114能面;我們曾采用密度泛函B3lyp6-311++gV=-De(1+a1P+a2p2+ a3p)exp(-a1p)方法,使用多體項(xiàng)展式理論,結(jié)合同位素效應(yīng)得到式中p=r-x2,r,分別為核間距和其平衡距離,了 Born-Oppenheimer(BO)近似理論下由同位素De為離解能,a1,a2,a3為勢能函數(shù)參數(shù)兩體項(xiàng)效應(yīng)修正的解析勢能函數(shù)8.事實(shí)上,O在微量參數(shù)見表2DT,以及D在微量OT存在下的反應(yīng)過程及機(jī)理三體項(xiàng)vBr(R1,R2,R3)一般可寫成十分復(fù)雜,有很多問題還未能給出明確回答因此,VEOr(Ri, R2, R3)=PT(1)進(jìn)一步開展有關(guān)理論研究,對深入認(rèn)識這種復(fù)雜反式(1)中的P為(R1,R2,R3)的多項(xiàng)式.T為量程應(yīng)體系機(jī)理有積極意義函數(shù),量程函數(shù)的一種可能選擇為量子力學(xué)從頭計(jì)算是研究分子結(jié)構(gòu)及其相作T=Ⅱ[1-tanh(yS2)],用勢分子微觀反應(yīng)動(dòng)力學(xué)及化學(xué)反應(yīng)過程機(jī)理的式(2)中%為參數(shù),S1為對稱內(nèi)坐標(biāo),當(dāng)S趨于無有效方法,理論研究結(jié)果與實(shí)驗(yàn)結(jié)果基本一致而窮大時(shí),T趨于零,從而保證當(dāng)任何一個(gè)原子移動(dòng)用密度泛函理論方法,研究分子體系的勢能函數(shù),無窮遠(yuǎn)時(shí),VB必為零的條件進(jìn)而研究反應(yīng)體系微觀分子反應(yīng)動(dòng)力學(xué)過程,已經(jīng)由于三體項(xiàng)需要表示為對稱內(nèi)坐標(biāo)的函數(shù),選為不少研究者成功應(yīng)用9-18.本文利用密度泛函用C2構(gòu)型的對稱變換換矩陣21,以R1:=1.528理論結(jié)合同位素效應(yīng)和多體展式理論方法8),得A,R2=R32=0.962A為參考點(diǎn),則內(nèi)坐標(biāo)向?qū)Φ交鶓B(tài)DTO分子的結(jié)構(gòu)與分子勢能函數(shù),基于準(zhǔn)稱內(nèi)坐標(biāo)的變換如下經(jīng)典分子反應(yīng)理論,研究反應(yīng)體系微觀分子反應(yīng)動(dòng)力學(xué)過程,進(jìn)一步研究DTO微觀反應(yīng)過程機(jī)理S2=01/21/22同位素效應(yīng)修正下的勢能函數(shù)s301/2-1/2人(p3P2=R1-R(i=1,2,3)本文通過計(jì)算同位素分子核的振動(dòng)能,修正則式(1)中P和T變換為S的多項(xiàng)式其形式為:BO近似下電子能量的方法來計(jì)算DTO的力常數(shù)8,運(yùn)用B3yp/6-311++g“方法,在DTO平衡+C1S1+C2S2+C3S2+C4S3+鍵長、鍵角值兩邊鄰域內(nèi)選取若干個(gè)點(diǎn),使這些點(diǎn)中國煤化工C7S+CsS1(s+處于近似諧性振動(dòng)范圍,然后逐一進(jìn)行單點(diǎn)電子能CNMHG第6期文等:DTO體系分子反應(yīng)動(dòng)力學(xué)T=[1-tanh(Y1 S:/2)][1-tanh(2S2/2)][1-tanhr3 S3/2)三體項(xiàng)參數(shù)見表3.表1基態(tài)DTO的結(jié)構(gòu)與力常數(shù)Table 1 Equilibrium Structure and Force constants of DToEquilibrium structure R/Aor/Dissociation energy D/evForce constants /auR1=0.962;R2=0.962f1=0.52567,f2=0.53084,f12=-0.0099351105,065fa=0.020371,fan=0.020539,f=0.14863表2Dr(x()和OD,OT(A2∑)的離解能及勢能函數(shù)的系數(shù)Table 2 Dissociation energy, Force constant and Coefficients of 2-body term of DT(X' >')and OD, OT(A221A-1ADT(X∑)3,9233.90673.3980.7414OD(A2∑+)5.56678.5474Or(A2(+)5.64367.11051,01242.5361表3DIO分子三體項(xiàng)分析勢能函數(shù)的參數(shù)Table 3 Coefficients of 3-body term of potential energy function for DhTOC0=-1.87335C1=1,66980C2=1.35304C3=-9.23512C4=-5.6874Cs=3.78958C6=4.14632C9=-0.42493y1=1.75外,由于D+OT和T+OD反應(yīng)生成DTO基態(tài)分1:-123eV2:-11.8eV;3:-10.5eV子存在很深的勢阱,所以可以生成穩(wěn)定的DTO分4:-9.0eV;5-7.5ev6:-6.0ev子,并且通過對勢能面逐點(diǎn)進(jìn)行單點(diǎn)能計(jì)算,發(fā)現(xiàn)7:4.5eV:8:-3.5eV9:-2.5e該反應(yīng)過程中不存在勢壘因此,說明這是一個(gè)無10:-2.0eV;ll:-1.0eV;12:0.5eV閾能的反應(yīng).從等值勢能圖中還可以發(fā)現(xiàn)D+OT和T+OD兩個(gè)反應(yīng)并不是嚴(yán)格對稱的(如等勢線8的位置分布可見),這可能是由于氘氚原子的質(zhì)量不同而引起的同位素效應(yīng)所有這些合理地體現(xiàn)了DTO的結(jié)構(gòu)特征3分子反應(yīng)動(dòng)力學(xué)計(jì)算方法OD/0.1 nm勢能函數(shù)確定以后,由準(zhǔn)經(jīng)典的 Monte- carlo圖1DIO分子的伸縮等值勢能面軌線法131,2求解三粒子保守體系的 HamiltonFig 1 Stretched vibrational contour of potential energy運(yùn)動(dòng)方程.設(shè)三原子體系為ABC,其質(zhì)量分別為function for DTOmA,mg,mc,在直角坐標(biāo)系下,它們的坐標(biāo)分別為DTO分子的等值勢能面如圖1,在圖1中固定A(q1,q2,q3),B(q4,q5,q6)和C(q7,q8,q).故三粒子體系的 Hamilton運(yùn)動(dòng)方程有18個(gè),即∠DOT=105.065°,OD和OT鍵對稱伸縮振動(dòng)從圖中發(fā)現(xiàn),在RDo=Ror=0.96201A附近,出現(xiàn)一個(gè)很深的勢阱(-12.3eV),也即在平衡點(diǎn)H中國煤化工…,9)(R1=R2=0.96201A),準(zhǔn)確地再現(xiàn)了基態(tài)DTO在質(zhì)CNMH、離為質(zhì)心運(yùn)動(dòng)的分子的離解能12306eV,構(gòu)型是C2v的結(jié)構(gòu)另 Hamilton函數(shù)How和相對運(yùn)動(dòng)的 Hamilton函數(shù),前者包含六個(gè)描述質(zhì)心運(yùn)動(dòng)的變量,后者包1442原子與分子物理學(xué)報(bào)第25卷含了其余十二個(gè)變量.這樣描述粒子相對運(yùn)動(dòng)的的軌線數(shù),bm為最大碰撞參數(shù),E1為初始相對平Hamilton方程簡化為十二個(gè)獨(dú)立變量的微分方動(dòng)能,V,J分別為振動(dòng)和轉(zhuǎn)動(dòng)量子數(shù)在計(jì)算中N程引入廣義相對坐標(biāo),經(jīng)坐標(biāo)變換,獲得十二個(gè)相取有限值,其大小由結(jié)果所允許誤差的范圍來確對運(yùn)動(dòng)方程,即:定,本文實(shí)際計(jì)算20000條軌線,bmx值的確定方BnQ=1(=12,…,6),(6)法參照文獻(xiàn)23ahne /aP:= Q31D(2S2)+OT(A2∑+)碰撞分子反應(yīng)動(dòng)力學(xué)(Q1,Q2,Q3)表示粒子C相對粒子B為坐標(biāo)原點(diǎn)結(jié)果與分析的直角坐標(biāo),(Q4,Q5,Q6)表示粒子A相對于分對于D(2S)+O(A2∑+)體系的碰撞反應(yīng)產(chǎn)子BC的質(zhì)心為坐標(biāo)原點(diǎn)的直角坐標(biāo),(Q7,Q8,物有5種通道Q9)表示整個(gè)三粒子體系質(zhì)心的直角坐標(biāo)對應(yīng)于D(2S2)+TO(A2∑+)→Q的共軛動(dòng)量為P,上式中 Hamilton函數(shù)HmO(D2)+DT(X∑)1通道為D(2S)+10(A2∑+)2通道Hd: P2+1 2P2+U(Q1T(2s)+OD)(A2∑+)3通道(10DTO(XA14通道其中OD2)+D(2s2)+T(2S2)5通道11+11=1當(dāng)D原子的初始平動(dòng)能為E1=0.4184~627.60ABC B c A, BCkJ/mol時(shí),D(2S2)+OT(A2∑+)反應(yīng)產(chǎn)物分布及式(7)中,U(Q1,Q2,…,Q6)為分析勢能函數(shù)經(jīng)反應(yīng)截面,見表4從表4可見,隨D原子初始相過坐標(biāo)變換,可以建立內(nèi)由坐標(biāo)(RAB,RBC,RcA)對平動(dòng)能的增加,交換反應(yīng)1通道的數(shù)量逐漸降表示的勢能函數(shù)的 Hamilton運(yùn)動(dòng)方程十二個(gè),粒低,而交換反應(yīng)3通道的數(shù)量隨D原子初始相對子相對運(yùn)動(dòng)的 Hamilton函數(shù)(7)式變?yōu)槠絼?dòng)能的增加逐漸增加,至E2=209.20 kJ/mol后Hrd=22P2+2u12I隨D原子初始相對平動(dòng)能的增加又逐漸降低;非P2+反應(yīng)2通道的數(shù)量隨D原子初始相對平動(dòng)能的增V(RAB, RBC, RcA),(8)加而逐漸增加;反應(yīng)4通道(生成絡(luò)合物的通道)的通過對這十二個(gè)方程進(jìn)行 Runge-Kutta-Gill法和數(shù)量很少且隨D原子初始相對平動(dòng)能的增加而迅Adms- Moulton法聯(lián)合數(shù)值求解可以確定出ABC速減小,對此特別計(jì)算了一下:當(dāng)D原子初始相對三粒子體系中碰撞運(yùn)動(dòng)的軌線,從而計(jì)算出化學(xué)反平動(dòng)能到了E1=20.920kJ/mo時(shí)就沒有絡(luò)合物應(yīng)的反應(yīng)截面,反應(yīng)閾能、反應(yīng)活化能以及反應(yīng)產(chǎn)生成了;5通道(碰散的通道)在E4>209.20kJ物的分布和各量子態(tài)粒子數(shù)分布等信息,實(shí)現(xiàn)從原mol后隨D原子初始相對平動(dòng)能增加逐漸增加,其子分子水平上研究分子反應(yīng)動(dòng)力學(xué)反應(yīng)截面用下主要原因是由于TO的離解能為2.5361eV,只要式計(jì)算D原子的初始平動(dòng)能約為244.68596kJ/mol就有碰散的可能性,因此到E1>209.20kJ/mol時(shí)5通a、(E,V,J)=2xP(E,V,,b)如b=道就有反應(yīng)從整個(gè)計(jì)算結(jié)果看,在低能部分ME,如mN(E,V,0.484-41.8401/m0,D原子把O置換出來相對其他反應(yīng)較為容易;而在高能部分209.20D)627.60kJ/mol,以反應(yīng)碰撞和5通道(碰散的通式中N與N分別為計(jì)算的總軌線與指定生成物道)為主中國煤化工CNMHG第6期阮文等:DO體系分子反應(yīng)動(dòng)力學(xué)1443表4D+TO(0,0)產(chǎn)物分布及bm和a與E的關(guān)系Table 4 Distributions of products, bmx, nd a, for different channels versus relative translational energy e for D+ TOEra,(1)I channel 2 channel 3 channel 4 channel 5 channelAkJ.mo/nm20.41841505.57300.73480.00790.0034143334.78900.51650.00680.00120.00880.000820.92038540.014541.8401263362510000.02700.0416111900.08360.05980.000040612.98800.01830.02940.0000136344532.87900.00990.01390.0000439.32139342.86200.00950,0104502.081457145342.75500.00720.00340.0000151662.43500.0610.001000(3)0.70(4)0030.0b0000.0020.001-00010501001503003504004505005500.0圖3D+TO→T+ OD and DTO反應(yīng)的a-E2曲線圖2D+TO→DI+O反應(yīng)的a,bmx-E4曲線Fig 3 The reactive cross-section vs Et for D+ To-T+Fig.2 The reactive cross-section and the maximum colli-OD and DTosion parameter vs E for D+ TO--DT+O初始相對平動(dòng)能E:與反應(yīng)截面a和最大碰交換反應(yīng)3通道大體是無熱反應(yīng),但是有閾能,因撞參數(shù)bm的關(guān)系曲線如圖2,3.在所計(jì)算的能量為截面a隨平動(dòng)能E先增加后減小,只不過閾能范圍內(nèi)D(2S)+O(A2∑+)的反應(yīng)碰撞主要表值很小而已當(dāng)平動(dòng)能增加到334.72 kJmol時(shí)現(xiàn)為交換反應(yīng)1通道和非反應(yīng)碰撞2通道交換反由于5通道軌線數(shù)增加,導(dǎo)致3通道軌線數(shù)又開始應(yīng)(1通道)是強(qiáng)烈無閾能放熱反應(yīng),在0.4184-降低20.920kJ/mdl低能量范圍伴隨有絡(luò)合物生成,由3.2r(s2)+DO(A2∑+)碰撞的分子反應(yīng)動(dòng)力學(xué)于生成絡(luò)合物的反應(yīng)不滿足動(dòng)力學(xué)軌道受陷條件結(jié)果與分析所以低能時(shí)雖然有極少量絡(luò)合物,但是其反應(yīng)截面+∩TA2+)體系的碰撞反應(yīng)產(chǎn)遠(yuǎn)小于1通道這說明D()+Or(A2)(O物也中國煤化工(Dg)+DT(X(∑g)交換反應(yīng)很容易發(fā)生.而CNMHG1444第25卷T(2S2)+DO(A2∑+)對平動(dòng)能的變化,該體系的反應(yīng)特點(diǎn)與D(2s)+O(D2)+D(X∑g)1通道OT(A2∑+)體系的反應(yīng)特點(diǎn)類似,但各對應(yīng)初始(2s2)+DO(A2∑+)2通道相對平動(dòng)能下的最大碰撞參數(shù)bmx比較D(2S2)+D(2s)+OT(A2∑+)3通道(11)OmA2∑+)有所增大,1和3通道的反應(yīng)截面aDTO(XAJ)4通道也較D(2s2)+Or(A2∑+)有所增大,相反4通道O(D2)+D(2S2)+T(2S)5通道的反應(yīng)截面σ,有所下降,反應(yīng)4通道(生成絡(luò)合物當(dāng)T原子的初始平動(dòng)能為E=0,4184~627.60的通道)的數(shù)量也較D(2S)+Or(A2∑+)更少,但kJ/mol時(shí),T(s2)+DO(A2+)反應(yīng)產(chǎn)物分布及是出現(xiàn)絡(luò)合物的初始相對平動(dòng)能增加到了E=反應(yīng)截面a見表5.從表5可見,隨T原子初始相表5T+DO(0,0)產(chǎn)物分布及bm和a與E的關(guān)系Table 5 Distributions of products, bmax and o, for different channels versus relative translational energy Et for T+DOI channel 2 channel 3 channel 4 channel 5 channel0.41845.63300.75020.01270.00124.1840146644.84900.54170.01280.0006144054.60100.47910.01390.000320.920137634.26200.39280.02230.0000314540.31640,000033.83300.26710.0490.000083,6801064266203.71500.23070.0593209.2065753.31000.1132334.7223983.10200.03630.07451577376850962.99600.02220.0531439.3215430.02160.0479502,080.01830.0341627,6001111582.82500.01630.01430.自Eb0.002-0.001500圖4T+DO→·DT+O的a,bm-E2曲線圖5T+DO→D+TO和DTO的a1-E2曲線Fig. 4 The reactive cross-section and the maximum colli中國煤化工EfrT+DO→D+sion parameter vs Et for T+ Do-DT+OTTHCNMHG阮文等:DO體系分子反應(yīng)動(dòng)力學(xué)1445初始相對平動(dòng)能E1對反應(yīng)截面a,和最大碰(2S)+TO(A2∑+)和T(2s2)+DO(A22+)兩個(gè)撞參數(shù)b。的關(guān)系曲線如圖4,5在所計(jì)算的能量反應(yīng)體系的反應(yīng)特點(diǎn)相似;但是在相同碰撞能量范圍內(nèi),交換反應(yīng)(1通道)是強(qiáng)烈無閾能放熱反時(shí),最大碰撞參數(shù)以及各對應(yīng)反應(yīng)通道的碰撞截面應(yīng)在0.4184~41.840kJ/mol低能量范圍伴隨有等存在一定的差異.可以設(shè)想若體系為普通水分子極少量絡(luò)合物生成,由于生成絡(luò)合物的反應(yīng)也不滿(HO)的反應(yīng)碰撞,這種差異應(yīng)該是不存在的,本足動(dòng)力學(xué)軌道受陷條件,所以低能時(shí)雖然有極少量文出現(xiàn)的這種差異以及前面勢能面上的輕微不對絡(luò)合物的反應(yīng)發(fā)生,但是其反應(yīng)截面遠(yuǎn)小于1通稱現(xiàn)象可能是由于氘氚原子的質(zhì)量不同而引起的道這說明T(2Sx)+DO(A2+)→O(Dg)+DT同位素效應(yīng)(x∑g)交換反應(yīng)容易得多交換反應(yīng)3通道也是參考文獻(xiàn)有閾能的無熱反應(yīng)總體反應(yīng)特點(diǎn)與D(2s2)+TO(A2+)的反應(yīng)碰撞特點(diǎn)相似可以設(shè)想如果是普10uM,LoYM,Hmn,aa., Experimental study on通水H2O,兩個(gè)體系反應(yīng)的產(chǎn)物軌線分布、各對應(yīng)Hydrogen isotopic Deuterium and Tritium from gas通道的反應(yīng)截面σ、最大碰撞參數(shù)bm等與能量phase to liquid phase by Hydrogen-water exchange [J]的對應(yīng)關(guān)系應(yīng)該是完全相同的,但是通過比較兩個(gè)At.Ener.Sci. 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