Difference scheme explicit iteration

By combining Eqs. 16.2 and 16.6, the optimization procedure corresponds to iteratively solving a set of linear equations, for AKy, until a numerical convergence is obtained (i.e., A(5q) 0). At each step, the CG parameters are corrected by AKy. This optimization scheme explicitly accounts for cross-correlations among the different CG degrees of freedom, thus including the effects of the many-body interactions via a compact molecular basis set of structural observables, 5a. ... 

A different analysis applies to the LR approach (in either Tamm-Dancoff, Random Phase Approximation, or Time-dependent DFT version) where the excitation energies are directly determined as singularities of the frequency-dependent linear response functions of the solvated molecule in the ground state, and thus avoiding explicit calculation of the excited state wave function. In this case, the iterative scheme of the SS approaches is no longer necessary, and the whole spectrum of excitation energies can be obtained in a single run as for isolated systems. 

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