One needs to develop a special algorithm that runs only through the elements of the upper triangular matrix \mathbf{g} and have k as an index.
The expression to be derived in the following is of interest when computing the quantum force and the kinetic energy. It has the form
\frac{\mathbf{\nabla}_i\Psi_C}{\Psi_C} = \frac{1}{\Psi_C}\frac{\partial \Psi_C}{\partial x_i},for all dimensions and with i running over all particles.