While the raising operator (a) over cap (+) does not have eigenvectors, coherent states are eigenvectors of the lowering operator (a) over cap. Therefore, operating with the operator exp[k (a) over cap (+2)] on coherent states poses a challenge, where k is an arbitrary constant. The result of this operation on coherent states has not yet been reported in a closed form. A closed-form expression for this problem is derived. The applicability and correctness of the result are tested by calculating the electronic dipole moment time correlation function and the corresponding Franck-Condon factors for systems with distorted Hamiltonian which arises in case of quadratic electron-phonon coupling which is significant in quantifying electronic dephasing. (C) 2012 Elsevier B. V. All rights reserved.