State-of-the-art {\em ab initio} techniques have been applied to compute the
potential energy curves for the SrYb molecule in the Born-Oppenheimer
approximation for the ground state and first fifteen excited singlet and
triplet states within the coupled-cluster framework. The leading long-range
coefficients describing the dispersion interactions at large interatomic
distances are also reported. The electric transition dipole moments have been
obtained as the first residue of the polarization propagator computed with the
linear response coupled-cluster method restricted to single and double
excitations. Spin-orbit coupling matrix elements have been evaluated using the
multireference configuration interaction method restricted to single and double
excitations with a large active space. The electronic structure data was
employed to investigate the possibility of forming deeply bound ultracold SrYb
molecules in an optical lattice in a photoassociation experiment using
continuous-wave lasers. Photoassociation near the intercombination line
transition of atomic strontium into the vibrational levels of the strongly
spin-orbit mixed b3Σ+, a3Π, A1Π, and C1Π states with
subsequent efficient stabilization into the v′′=1 vibrational
level of the electronic ground state is proposed. Ground state SrYb molecules
can be accumulated by making use of collisional decay from v′′=1
to v′′=0. Alternatively, photoassociation and stabilization to
v′′=0 can proceed via stimulated Raman adiabatic passage
provided that the trapping frequency of the optical lattice is large enough and
phase coherence between the pulses can be maintained over at least tens of
microseconds