Transformation of complex spherical harmonics under rotations

The algorithm rotating the complex spherical harmonics is presented. The convenient and ready to use formulae for l=0, 1, 2, 3 are listed. Any rotation in R-3 space is determined by the rotation axis and the rotation angle. The complex spherical harmonics defined in the fixed coordinate system is expanded as a linear combination of the spherical harmonics defined in the rotated coordinate system having 2l+1 terms, which are given explicitly. The derived formulae could be applied in quantum molecular calculations. The algorithm is based on the Cartesian representation of the spherical harmonics. The possible application of the algorithm to the evaluation of molecular integrals between slater type orbitals (STO) is described.