  We present an efficient quasi-Newton orbital solver optimized to reduce the
number of gradient (Fock matrix) evaluations. The solver optimizes orthogonal
orbitals by sequences of unitary rotations generated by the (preconditioned)
limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm
incorporating trust-region step restriction. Low-rank structure of the inverse
(approximate) Hessian is exploited not only in L-BFGS but also when solving the
trust-region problem. The efficiency of the proposed ``Quasi-Newton Unitary
Optimization with Trust-Region'' (QUOTR) method is compared to that of the
standard Roothaan-Hall approach accelerated by the Direct Inversion of
Iterative Subspace (DIIS), and other exact and approximate Newton solvers for
mean-field (Hartree-Fock and Kohn-Sham) problems.
