Thank you very much for the comment. It will help me to improve some parts of the manuscript and to change some paragraphs to avoid misunderstandings.

The application examples should serve as a kind of confirmation of the procedure proposed in this manuscript. I.e. they should illustrate that in some cases the procedure given here leads to known results which have been obtained in other ways, perhaps very directly in some cases. (Nevertheless, some of these propagation formulae also seem to be new, for example some of the CP-related ones.) But I agree, that in a revised version more papers should be cited which present other ways of calculating. Especially the paper you mentioned, where a matrix of two 4x4 blocks represents the Liouvillian for the case of quadrupolar interaction + rf_x irradiation.

The connection between the Liouvillian and Hamiltonian eigenvalues was not mentioned in the original version of the manuscript, because eigenvalues do not immediately play a role here. (In fact, they do in some methods of matrix exponentialisation, but this was not considered in detail here.)

Do you mean "the propagator matrix is a real orthogonal matrix"? The matrix associated with the Liouville operator is skew symmetric and pure imaginary if a Hermitian operator basis is chosen. Therefore, it cannot be orthogonal (or even unitary) in general. This can be seen by inspecting Eqs. (35) and (54) of the main part, or the matrices A and B in the paper mentioned in the comment. At least for odd dimensions, the determinant of the Liouvillian matrix will be zero. An orthogonal matrix, on the other hand, has a determinant = 1. However, the matrix of the propagator is orthogonal in an Hermitian basis, otherwise "only" unitary, because it is the exponential of a skew-symmetric matrix.

The occurrence of a block structure of a matrix means that it can be written as direct product of the corresponding matrices related to subspaces. However, using the original procedure from the manuscript of finding an appropriate subspace (Section 3), no block structure will appear for the Liouvillian matrix. Instead, the procedure ends as soon as the dimension of a block is reached; the commutator of the last equation can be expanded without remainder in the operators already present. This result corresponds to a subspace whose basis includes the operator of the initial state. We could say that the procedure finds the block of the total matrix corresponding to a subspace containing the operator of the initial state.  

However, a block structure may occur if we use the modified procedure (last paragraph of subsection 3.4).

Please refer to the supplement file. Due to the mathematical equations contained, the text could not be inserted directly into this window.

Many thanks to reviewer 2 for the detailed list of many places in the manuscript that could be improved. I have summarized my response in the attached file because it also contains a number of mathematical expressions.