Some questions about the equations between codes

[Liaokang123456]

Question 1: double orbitalOverlapTerm = exp(-(aaRabSq))(2a - aaRab - 1/Rab);
but the equation in paper is

Question 2: return J[i] + lambda * (k/2) * (alphaStar + betaStar + orbital - 2/(eta*sqrt(PI)));
but the equation in paper is

Question 3: return J[i] + lambda * (k/2)*sigmaStar;
but the eqation in paper is

There are some differences between codes and formulas, could you help me to understand its?
Thanks!