  Automatic differentiation has become an important tool for optimization
problems in computational science, and it has been applied to the Hartree-Fock
method. Although the reverse-mode automatic differentiation is more efficient
than the forward-mode, eigenvalue calculation in the self-consistent field
method has impeded the use of the reverse-mode automatic differentiation. Here,
we propose a method to directly minimize Hartree-Fock energy under the
orthonormality constraint of the molecular orbitals using reverse-mode
automatic differentiation by avoiding eigenvalue calculation. According to our
validation, the proposed method was more stable than the conventional
self-consistent field method and achieved comparable accuracy.
