Chapter9多原子的半經(jīng)驗方法

Chapter9

多原子的半經(jīng)驗方法

1.π-electronapproximation2.Thefree-electronMOmethod3.TheHuckelMOmethod4.Conjugated

ChainMolecules

5.MonocyclicConjugatedPolyenes6.PolycyclicConjugatedPolyenes7.Charges,BondOrdersandFreeValences8.GeneralSemi-empiricalMOMethods1.π-electronapproximation(1)(2)由變分原理,極小化變分積V(i):第i個π電子在核與σ電子場中的勢能.2.Thefree-electronMOmethod

V=,outsidethisregion如果:忽略,且V=0,inacertainregion有:

(3)(4)(5)(6)

一維情況,有

(7)

由Pauli原理,有:(8)

對于Polyenes:設單鍵長,l1,雙鍵長,l2,考慮MOs離域,兩端分別增加.則電子運動的區(qū)域:代入(8)式有:3.TheHuckelMOmethod(11)

(12)

(13)

由線性變分法有:r=1,2,3,….nc

(14)

久期方程:(15)

積分

forCr&Csbonded(16)

forCr&Csnotbondedtogether(17)

(18)

歸一化條件(normalizationcondition)(19)

(20)

4.Conjugated

ChainMolecules(21)

本征方程:

(22)

(23)

由行列式理論有:k=1,2,3,…,N

(24)

k=1,2,3,…,N

u=1,2,3,…,N

(25)

例子:丁二烯

(26)

ci=1.618,0.618,-0.618,-1.618波函數(shù):

分子軌道節(jié)面與能級(NodalPlanesandEnergyLevels)

:

ThegroundstateofButadineinC2h

symmetry

HOMOLUMO

一般情況:HOMO:

LUMO:

5.MonocyclicConjugatedPolyenes.

HMOresults:

k=0,1,…,nc-1MOlevels:

4n+2rule(占滿成鍵軌道)

C4H4atripletgroundstate分子軌道C6H6

k=0

k=1

k=5

k=2

k=4

k=3

簡并軌道的線性組合實MOSimilarly

MOSymmetryspeciesThesymmetryspeciesofMOs

Thegroundstate:6.PolycyclicConjugatedPolyenesNaphthealene久期方程:r=1,2,…,10久期行列式:利用,對波函數(shù)進行分類:原子軌道等價組:

C1=C2=C3=C4

C5=C6=C7=C8C9=C10根據(jù)Huckel近似:

令:x=-1,,,x=1,

7.p-ElectronCharges,BondOrders,FreeValence丁二烯:ElectronchargesWherethesumisovertheMOsFor1,3-butadiene,Theorem.Forthegroundstatesofaneutralalternanthydrocarbon,alltheHuckelelectronchargesqrare1.BondOrdersForbutadiene,P12P23

Thetotalbondordersare[bondcontributionincluded]CorrelationofBondlengthswithBondOrders

Rc-cvsPrsFree–ValenceIndex8.GeneralSemi-empiricalMOMethodsTheExtendedHuckelMethod.

價電子Hamilton看作單電子Hamiltonian的求和

分子軌道看作價原子軌道的線性組合

價單電子方程

應用變分法有:

由Koopmans’定理引入VSIP參數(shù)化VSIP=Valence-stateionizationP