I have started with the space-time metric in a weak gravitational field (with the assumption of low velocity):
ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2)
Where \phi<<1 is the gravitational potential. Using the standard form for the Christoffel symbols have found:
\Gamma^0_{00}=\phi_{,0}...
I have started with the space-time metric in a weak gravitational field (with the assumption of low velocity):
ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2)
Where \phi<<1 is the gravitational potential. Using the standard form for the Christoffel symbols have found...
Well because we've been working in Rydberg units I thought the External potential was:
-\frac{2Z}{r}
In that case I think we may be summing the wrong energy; at the moment we're inputting an initial density of double the Hydrogen 1s density. We then use this to get a hartree potential and an...
Cool, So I've got it so that it converges on an energy (having used a simple mixing scheme). Unfortunately its the wrong energy! I've solved Possions equation in order to get the Hartree energy of the Helium atom and used the exchange-correlation functional of:
V_{xv}[n(r)] =...
Ok, I guess I underestimated this one! Thus far I have an exchange-correlation term of:
E_{xc}= -\frac{3}{4}\sqrt[3]{\frac{3n(r)}{\pi}}+\frac{0.44}{r_s+7.8}
Where n(r) is the density of electrons and [ tex ] r_s [/tex] is the Wigner radius. Is this an acceptable expression? I have then...
As to what I'm trying to achieve:
"I'm trying to calculate the ground state energy of Helium"
As to how I plan on doing it:
"density functional theory"
And admittedly I wasn't particularly clear on the problems but in particular finding a reasonably accurate exchange-correlation term. I'd read...
Im trying to calculate the ground state energy of Helium using a density functional theory approach combined with the local density approximation. So far I have set up universal functionals and I mainly need help with the actual algorithm the evaluation of the Hartree energy functional.