Analytical solutions of the Hartree-Fock method for Be, B and C

The analytical Hartree-Fock method for determining the ground state of Li can be extended to Be, B and C. The energy equations to minimise using Excel Solver for Be, B and C are

$E_{Be}=E_{Li}+H_4+J_{14}+J_{24}+J_{34}-K_{24}$

$E_{B}=E_{Be}+H_5+J_{15}+J_{25}+J_{35}+J_{45}-K_{15}-K_{35}$

$E_{C}=E_{B}+H_6+J_{16}+J_{26}+J_{36}+J_{46}+J_{56}-K_{16}-K_{36}-K_{56}$

respectively; where $E_{Li}=H_1+H_2+H_3+J_{12}+J_{13}+J_{23}-K_{13}$ .

The results for Be are

The final theoretical value of $E_{Be}=-14.5560520$ has a deviation of about 0.76% versus the experiment data of the ground state of Be.

The results for B are

The final theoretical value of $E_{B}=-24.4987443$ has a deviation of about 0.65% versus the experiment data of the ground state of B.

The results for C are

The final theoretical value of $E_{C}=-37.6037854$ has a deviation of about 0.66% versus the experiment data of the ground state of C.