  Localization of molecular orbitals finds its importance in the representation
of chemical bonding (and anti-bonding) and in the local correlation treatments
beyond mean-field approximation. In this paper, we generalize the intrinsic
atomic and bonding orbitals [G. Knizia, J. Chem. Theory Comput. 2013, 9, 11,
4834-4843] to relativistic applications using complex and quaternion spinors,
as well as to molecular fragments instead of atomic fragments only. By
performing a singular value decomposition, we show how localized valence
virtual orbitals can be expressed in this intrinsic minimal basis. We
demonstrate our method on systems of increasing complexity, starting from
simple cases such as benzene, acrylic-acid and ferrocene molecules, and then
demonstrating the use of molecular fragments and inclusion of relativistic
effects for complexes containing heavy elements such as tellurium, iridium and
astatine. The aforementioned scheme is implemented into a standalone program
interfaced with several different quantum chemistry packages.
