Fock operator for closed shell system

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SUMMARY

The Fock operator for a closed shell system is defined as f = H(core) + sum (2*f - k), where f represents the Coulomb operator and k denotes the exchange operator. The summation is conducted from 1 to N/2, reflecting that each orbital accommodates two electrons, necessitating the multiplication of the Coulomb operator by 2. This formulation is crucial for accurately describing the interactions of electrons within the same orbital, as their spatial wavefunctions are identical.

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greisen
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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?

Thanks in advance

Best regards
 
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N/2 is due to each orbital has to electrons hence 2*Coulombic.
 
greisen said:
N/2 is due to each orbital has to electrons hence 2*Coulombic.
Correct. The spatial part of the single-particle wavefunctions for the two electrons in the same orbital are identical.
 

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