# Fock operator for closed shell system

1. Jan 9, 2007

### greisen

Hey,

The Fock operator for a closed system is given by

f = H(core) + sum (2*f - k)

where f is the Coulomb operator and k is the exchange operator. The summation goes from 1 to N/2. My questions is why is the summation to N/2 and why does one have to multiply the Coulomb operator by 2?

Best regards

2. Jan 9, 2007

### greisen

N/2 is due to each orbital has to electrons hence 2*Coulombic.

3. Jan 9, 2007

### Gokul43201

Staff Emeritus
Correct. The spatial part of the single-particle wavefunctions for the two electrons in the same orbital are identical.