Charge-order fluctuations

Then, the DFT total energy functional is expanded up to second order with respect to the charge density fluctuations Sp around the reference po [22] (p Q = po(r ),... 

Only the former quantity is experimentally accessible, but the longitudinal component of the latter depends on the TCF of solvent charge density fluctuations, Fqq(k,ty9 a quantity that one would naturally associate with the solvent response to electrostatic perturbations. Indeed, the A -dependence of qq (k, t) resembles closely the leading multipolar order (w) in the solute charge distribution perturbation dependence of even for nondipolar liquids, so further... 

The second-order terms contain the contributions arising from the charge density fluctuations Sp = p - p0, which describe the deviation of the ground state density p from the reference density [28], This term is represented by a sum of atomic contributions... 

In this work, a recently developed semi-empirical method, SCC-DFTB method, is employed to account for the electronic structure of QM part. The details of this method and its implementation to CHARMM have been summarized elsewhere [6, 22-24]. Here we just give a short description. This method is derived by a second order expansion of the DFT total energy functional with respect to the charge density fluctuation around a given reference density. The total energy can be expressed as following [22] ... 

The last four terms depend only on the reference density, po, and represent the repulsive energy contribution, Flcp, discussed above. Thus, we just have to deal with the second-order terms. The second-order term in the charge density fluctuations dp(r), that is, the second term in Equation 5.51, is approximated by writing Ap as a superposition of atomic contributions, Ap0 = Apv. This approach decays quickly with the increasing distance from the corresponding center. To simplify the second term further, Elstner applied a monopole approximation ... 

The diagonal terms yvv model the dependence of the total energy on charge density fluctuations of the second order. The monopole approximation restricts the change of the electron density considered, and no spatial deformations are included. Only the change of energy with respect to... 

The charge density fluctuations are approximated by monopolar charge fluctuations at the atom a, / qa = q - The second order term in 6p in the energy expression is then approximated as... 

To define Kab and more general multicenter indices at a post Hartree-Fock level, one must invoke more sophisticated techniques [64-67]. We follow our work [36] in which the full Cl and some approximated models were considered in detail. The conventional definition of the generalized bond index is based on identification of Kab with a charge density fluctuation measured via the second-order joint statistical moment [64] (generally, the joint cumulant) ... 

Mandd with a quite different method. They applied the decoupling (Eq. 10) in the equation of motion for the double-time-retarded commutator of the charge density fluctuation operators, and imposed conservation of frequency moments to all orders in the Hartree-Fock approximation for the... 

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