  We investigate how different chemical environment influences magnetic
properties of terbium(III) (Tb)-based single-molecule magnets (SMMs), using
first-principles relativistic multireference methods. Recent experiments showed
that Tb-based SMMs can have exceptionally large magnetic anisotropy and that
they can be used for experimental realization of quantum information
applications, with a judicious choice of chemical environment. Here, we perform
complete active space self-consistent field (CASSCF) calculations including
relativistic spin-orbit interaction (SOI) for representative Tb-based SMMs such
as TbPc$_2$ and TbPcNc in three charge states. We calculate low-energy
electronic structure from which we compute the Tb crystal-field parameters and
construct an effective pseudospin Hamiltonian. Our calculations show that
ligand type and fine points of molecular geometry do not affect the zero-field
splitting, while the latter varies weakly with oxidation number. On the other
hand, higher-energy levels have a strong dependence on all these
characteristics. For neutral TbPc$_2$ and TbPcNc molecules, the Tb magnetic
moment and the ligand spin are parallel to each other and the coupling strength
between them does not depend much on ligand type and details of atomic
structure. However, ligand distortion and molecular symmetry play a crucial
role in transverse crystal-field parameters which lead to tunnel splitting. The
tunnel splitting induces quantum tunneling of magnetization by itself or by
combining with other processes. Our results provide insight into mechanisms of
magnetization relaxation in the representative Tb-based SMMs.
