Linker IT Software
Google
Web www.oraxcel.com
menubar-top-links menubar-top-rechts
Home Help Search Login
Welcome, Guest. Please Login.
SQL*XL: Database to Excel bridge litLIB: Excel power functions pack ExcelLock: Locking and securing your valuable Excel spreadsheets encOffice: Protect your Excel file easy and safe encOffice: Protect your Excel file easy and safe
Pages: 1
Coulomb integrals (Read 2110 times)
Gerrit-Jan Linker
YaBB Administrator
*****




Posts: 75
Coulomb integrals
27.08.09 at 13:03:10
 
Coulomb integrals
 
Two electron coulomb integrals in different notations:
 
Jij = <ΦiΦjiΦj> =  Φi(r1j(r2)|  r12-1i(r1j(r2)>  
The indices for r are 12 and 12!
Note that the scalar r12 is |r1 - r2|
 
Jij = (ΦiΦijΦj) = ∫|Φi(r1)|² r12-1  |Φj(r2)|² dr1dr2
The indices for r are 11 and 22!
 
We recognise |Φj(r)|² as the electron density. ρj(r) = |Φj(r)|²
In words: The electron density of electron j in position r is given by the square of the orbital of electron j in that position.
 
Therefore we can also write:
 
Jij = ∫|Φi(r1)|² r12-1  |Φj(r2)|² dr1dr2
     = ∫ ρi(r1) r12-1 ρj(r2) dr1dr2
 
We have written the Coulomb integral  as an integral over electron densities ρ
Back to top
 
« Last Edit: 10.09.09 at 08:31:57 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
Email WWW Gerrit-Jan Linker   IP Logged
Pages: 1