[en] Within the framework of the projection theory of collective motion, a microscopic description of the rotational energy with band-mixing is formulated using a method based on an inverse power perturbation expansion in a quantity related to the expectation value of the operator Jsub(y)sup(2). The reliability of the present formulation is discussed in relation to the difference between the individual wave functions obtained from the variational equations which are established before and after projection. In addition to the various familiar quantities which appear in the phenomenological energy formula, such as the moment of inertia parameter, the decoupling factor and the band-mixing matrix element for ΔK=1, other unfamiliar quantities having the factors with peculiar phases, (-1)sup(J+1)J(J+1), (-1)sup(J+3/2)(J-1/2)(J+1/2)(J+3/2), (-1)sup(J+1/2)(J+1/2)J(J+1), (-1)sup(J)J(J+1)(J-1)(J+2) and [J(J+1)]² are obtained. The band-mixing term for ΔK=2 is also new. All these quantities are expressed in terms of two-body interactions and expectation values of the operator Jsub(y)sup(m), where m is an integer, within the framework of particle-hole formalism. The difference between the moment of inertia of an even-even and a neighboring even-odd nucleus, as well as the effect of band-mixing on the moment of inertia are studied. All results are put into the forms so as to facilitate comparisons with the corresponding phenomenological terms and also for further application