Hi!!

a) : At lesson I don't understand very well how is the general correct form for a Wave Function ψ of a molecule using the lcao method(ie using the MO)...

b) Also, the professor said that for a multi-electron system the general wave function ψ=ψ(1,2,3...n) can be factored in ψ=Φ(1)Φ(2)Φ(3)...*Φ(n)...where Φ(i) is the i-esimal wave function that describes the i-esimal electron in this system.

c) another consideration that we have done at lesson is that: for a multi-electron wave function ψ(1,2...n) i have to consider also the SPIN part and the complete spin-orbital wave function must observe the antisymmetric principle

So considering all these key points how can I imagine the general form of a wave function ψ for a multi-electron system??

For example the molecule of B_2 has 10 electrons whose collocation in MO's are:

1sσ)

^{2} 1sσ*)

^{2}2sσ

^{2}2sσ*

^{2}2pxπ

^{1}2pyπ

^{1}So the system B_2 con be described by the using of 6 MO,each of these can be found through the LCAO method:

1sσ= 1s_A+1s_B] (where A,B are the two different atoms of Boron)

1sσ= 1s_A-1s_B

2sσ= c_32s_A+2s_B

ECC...

The correct form of these MO actually requires the Variational method in order to find the correct value of each (coefficients c_i)OA that is involved in the LCAO ( for every MO):

Ψ= c_(1A) 1s_A + c_(1B) 1s_B + c_(2A) 2s_A + c_(2B) 2s_B + c_(3A) 2px_A + c_(3B) 2px_B + ...

I have 10 OA involved in the LCAO so i'll get 10 MO,each one with some particular value of the coefficients c_i:

Φ_1 =

Φ_2

.

.

.

Φ_10

Now that i know the numeric expression of these 10 MO Φ_i how can write the general wave function of the system B_2

As a prodcut of these MO??Ψ=Φ_1*Φ_2*Φ_3*...*Φ_10

I don't think this is correct ...because i'm not considering yet:

a) the spin parts ( because if the MO Φ_i contains two electrons I think I have to introduce the spin part α /β for the wave function Φ_i --- > Φ_i(1,2 electron)=Φ_i(1,2)*ω_i(α,β) =Φ_i(1)*Φ_i(2) *α(1)*β(2)+ Φ_i(1)*Φ_i(2) *α(2)*β(1) )

b)but the last expression is not correct yet, because must be osbserved, for the total wave function ψ, the antisymmetric principle( so I think I have to write the SLATER DETERMINANTAL WAVE FUNCtION)...

Someone can tell me if my assumptions are correct...and how is the correct general form for the wave function ψ(1,2....10) of B_2 atom?? (or how concepts i have to consider in order to write it in the correct form)

Thanks VERY much!!

(sorry for my bad english)