Exercise 2.1 Given a set of K orthonormal spatial functions, {v}(r)}, and another set of K orthonormal functions, {v{(r)}, such that the first set is not orthogonal to the second set, i.e., S dr vi*(r)vf(r) = Sij where S is an overlap matrix, show that the set {xi} of 2K spin orbitals, formed by multiplying vir) by the a spin function and f(r) by the B spin function, i.e. Xzi-1(x) = vi(r)a(6) ,k X2/(x) = v(r)(0) }i=1,2,.. 1 is an orthonormal set