  For the single-molecule magnet Mn12, Cornia et al. recently proposed that
solvent molecules may cause the quantum tunneling that requires a lower
symmetry than S4. However, magnetic quantum tunneling and electron paramagnetic
resonance experiments suggested that the proposed theory may not correspond to
the measurements. In this regard, we consider positional disorder induced by
the solvent molecules and orientational disorder by the methyl groups of a Mn12
molecule. We calculate, within density-functional theory, the second-order
transverse magnetic anisotropy parameter E and an easy-axis tilting angle
induced by the positional disorder and the E value by the orientational
disorder. We also calculate the local magnetic anisotropy and the local easy
axis for each inequivalent Mn site in different environments to investigate
their effects on the global E value. We find that the hydrogen bonding between
a Mn12 molecule and the solvent molecule is crucial to obtain a substantial E
value and that the E value increases upon geometry relaxations. Our
calculations on relaxed geometries show that the largest calculated E value is
0.016 K and that the largest tilting angle is 0.5 degrees. Our largest E value
is comparable to experimental results but larger than Cornia et al.'s.
