計算機模擬分子材料

計算機模擬與材料分子設(shè)計

ComputerSimulationandMolecularDesign

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

Lecture5

勢能面的構(gòu)筑及其最新動態(tài)

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

勢能面

到整廊是一種數(shù)學函數(shù)用來描述分子的能量

與其幾何結(jié)構(gòu)之間的關(guān)系。

?分子力學是把能量作為伸縮，彎曲，扭轉(zhuǎn)

等的函數(shù)。這個近似模型不能描述化學鍵斷

裂等情況，而且需要有合適的參數(shù)。

?量子力學給出一個能量函數(shù)適用于任何分

子，但是實際上使用的仍是近似的量子力學

模型以降低計算消耗。

；')DalianUniversity

yofTechnologyGraduateCourse,Lecture52010Autumn

最簡單的一維勢能面

StandardDiatomicBondStretch

B

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

一般勢能面的維數(shù)

?一般情況下勢能面究竟有幾維呢？定義一

個厚子的位置，原則上只需在三維空間里

取三個坐標(egx,y,andz)o

?但是，勢能面不能取決于原子的絕對位置,

而取決于其相對于周圍其他原子的位置

(i.e.Moleculargeometry)

?因此，典型的勢能面的維數(shù)應該等于分子

的自由度數(shù)(3N-6,N為原子數(shù)且大于2,分

子為非線性)

；')DalianUniversity

yofTechnologyGraduateCourse,Lecture52010Autumn

Exampleofpotentialenergysurface

globalmaximum

localmaximum

localminimum

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

StationarypointsonPES

>Stationarypointsinclude:

?Localminimum&Globalminimum

(equilibriumstructure,correspondingto

reactant,product,intermediate)

?Saddlepoint

(transitionstate,transitionstructure,

correspondingtotransitionstate)

?Localmaximum&Globalmaximum

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

SlicesofPotentialEnergySurface

由于多維勢能面很難圖示化，常取勢能面的一部分

Here,wetakeatwo-

dimensionalslice(the

mostwecaneasily

graph,sinceenergyisthe

thirdccx>rdinate)ofa

moleculewith3degrees

offreedom;itisthebond

anglethatisbeingheld

fixedthatdefinesthe

slice.

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

進一步理解勢能面

?勢能面不體現(xiàn)動能

?在T=0K(noKineticEnergy),分子將傾

向于處在最低勢能的狀態(tài)，比如勢能面上

的極小值(Minimum)。有效地找到這些極小

值的方法是很有意義的。

?在兩個極小值之間(valleybottoms)的最小

能路徑將通過一個鞍點(saddlepoint),在

化學上我們稱作該點的結(jié)構(gòu)為過渡態(tài)結(jié)構(gòu),

找到過渡態(tài)也是很有意義的。

；')DalianUniversity

yofTechnologyGraduateCourse,Lecture52010Autumn

勢能面片段

_Rateconstantforaminimum

“passingthroughatransition

stateapproximately

determinedas_

k=(kQT/hyer^1^(same

caveataboutAGandAE)

E

Equilibriumand

Equilibriumconstantbetweentwominimarateconstants:

approximatelydeterminedasK=e*"nowweYe

(somesmallcareneededtouseAGtalkingreal

insteadofsE)

chemistry

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

值得思考的幾個基本問題

很顯然，勢能面是一種有用的函數(shù)，那末對于一

個任意體系，我們?nèi)绾蝸順?gòu)筑它的勢能面呢？

很多情況下不需要整個勢能面，只需要勢能面上

一些重要結(jié)構(gòu)(MinimaandSaddlepoints)的能量,

那末，不通過構(gòu)筑整個勢能面，是否能夠找到這

些重要的結(jié)構(gòu)呢？

在不構(gòu)筑整個勢能面的情況下，我們怎樣確定所

有重要結(jié)構(gòu)的位置呢？這些重要結(jié)構(gòu)又是如何相

關(guān)的呢？

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

勢能面全貌自動搜索新方法

(GlobalReactionRouteMapping,GRRM)

----DevelopedbyOhno&Maeda

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

GlobalReactionRouteMapping(GRRM)

?Minimum(Equilibrium)andTS(TransitionState)are

extremalsonthePES

?GRRMcanbemadebyfine-tooth-combtestsof

mathematicalconditionatallpointsonPES

Asystemwith5atoms(9degreeoffreedom)

1009=1018

J

Ittakesmorethan30,000,000,000years!!

Therehadbeennoglobalreactionroutemapfor

systemscomposedofmorethan4atoms

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

GRRM萬法的原理

Whenchemicalbondsdissociateor

reorganizeviaaTSleadingtoEQ,the

AnharmonicDownwardDistortion

(ADD)shouldhappenonthepotential

energysurface.

ThemaximaldirectionofADDisa

signpostofthechemicalreaction.

令Equilibrium:EQ(Minimum)

?TransitionState:TS

HarmonicAnharmonic

')DalianUniversity

JofTechnologyGraduateCourse,Lecture52010Autumn

AnharmonicDownwardDistortion(ADD)

非簡諧向下形變

化學鍵的斷裂

導致離解反應

化學鍵的重排經(jīng)過

一過渡態(tài)(TS)生成

新物質(zhì)

(Equilibriumstructure)

DalianUniversity

yofTechnologyGraduateCourse,Lecture52010Autumn

AQuantumPrincipleofChemical

ReactionsforFindingaReactionRoute

?asignofadissociationchannelcanbedetectedasan

anharmonicdownwarddistortion(ADD).

?asignofachemicalreactionleadingtoanotherEQcan

bedetectedasanADD.

}DalianUniversity

JofTechnologyGraduateCourse,Lecture52010Autumn

GRRM方法的原理（續(xù)）

FordetectingADDaroundaEQ

IntroduceScaledNormalCoordinatetothe

iso-energyhypersurfaceofharmonicpotential(hyperelipsoide)

7/=41/2Qi

Theiso-energysurfacebecomessimplehypersphere

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

GRRM法工作的簡單原理

StartfromanEQ

Repeat

Findallreactionroutes

uphillUwalking

DissociationTransition

Channel(DC)Structure(TS)

downhillwalki1ng

DissociationEquilibrium

Channel(DC)Structure(EQ)

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

關(guān)于GRRM方法的參考文獻

Ohno,K.;Maeda,S.Chem.Phys.Lett.2004,384,277.

Maeda,S.;Ohno,K.J.Phys.Chem.A2005,109,5742.

Ohno,K.;Maeda,S.J.Phys.Chem.A2006,110,8933.

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

GRRM方法的應用

Case1:

Dialkyldithiophosphoratecuprous[Cu(I)]

Dissociationandisomerizationof

CuDDPanditsreactionwithCH3OO,.、H—Os

CuDDPisanengineoiladditive/PX/Cu

(antioxidationandantiware)H—OS

CuDDPamodelofCuDDP

Case2:

Titanocene-catalyzeddehydrocoupling3"^Me2N-BH2

2Me2NH-BH3

ofMe2NH-BH3-2唉H2B—NMe2

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

Case1

e

ReactionofCuDDPwithCH3OO

andCHoOOH

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

A

Oxidationofengine-oilandantioxidationofCuDDP

Oxidation:

Initiation

RH——，R-

Chain-reaction

R?+O2——ROO*(fast)(1)

ROO?+RH------'ROOH+R-(2)useantioxidantsto

undesirableduetocorrosiondecomposetheROO*

Antioxidation

Chain-termination(Peroxy-radicalscavenging)

Cu++ROO*------?Non-radicalproduct⑶

Cu++ROO?=RO-

oraligand-radicalforabstractingHfromROOH(4)

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

jE----------------------------------a

PreviousstudiesonCuDDP

Jf

Previousstudies

Onlyexperimentalstudiesonitssynthesisandapplication

Nocomputationalstudyfound

Knowledgeremainspoorlyunderstood:

EngineParts

EngineParts

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

CUDDP-OOCH3complex

c---------------------------------------(Energyinkcal/mol)------------------------------------------?

bond-rearrangementisomerizationperoxyl-radicaldecomposition

DalianUniversity

ofTechnologyG「aq椀息巡「游A(ecture52010Autumn

(OH)2PS2Cu-assistedCH3OOHdecomposition

(、TS[1-9]

lTS[3-4]\20.2TS[6-7]

a13.0\(10.0)13.2

F(1.0)(4.4)

a

TS[2-3]；

4.2；

TS[5-6]

(-6.9)ITS[1-2]\

0.2C影

It-0.91(-10.0)

H、(-11⑼

02

S1\\(-14.6)/z0.0[pCu—02

S2Z

/2(0.0)k

H

/Cu\，3-2.05

隊-2.7

S2‘CH(-12.0)、H-4.5

3(-13.0)

(-14.4)-6.2

(-15.5)

01

TS[7-8]

.01.CH3-19.9

H，,，，

S1z(-31.8)

\/CH3[P][S：cuf

[P]02

、S2—CuS2O2f

4：

-31.2；

-24.2

(-41.7)；

(-36.0)

9：S1CH3!8

S1——Cu—02-''H：-69.4

-68.8!隊/Cu、

H(-77.3)/：(-78.3)

HS202H2c21、

__：，、、H

H

儼%2/蘆晟[P]=(HO)2P、/S1、，

A

HomolysisHeterolysis

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

InsightsfromGRRMcalculation

[P][〉Cu[[P]=(HOOP：CH3

Computationssuggestthat(OH)2PS2Cu(I)-mediated

decompositionofCH3OOHleadstoformaldehydeandwater

moleculesvia0-0bondheterolysisandsubsequentintramolecular

hydrogentransfer,withretainmentofthecopper(I)complex.

DalianUniversity

ofTechnologyGraduateCourse,Lecture52010Autumn

Case2

Titanocene-catalyzed

dehydrocouplingofMe2NH-BH3

DalianUniversity

ofTechnologyGradu