Systems total energy

Show that if the total system charge Q is the charge q on one ion, the change in system total energy upon mutation of that charge from to q is... 

Figure 22. TBMD simulation for crystalline carbon for the period of 0.21 ps (300 MD time steps) with conjugate gradient tolerance t = 10 for system sizes of 64 and 216 carbon atoms (a) potential energy (i>) system total energy. (From Ref. 129.)...

System Total energy [Hartree] Relative Energy [kcal/mol]... 

The most important equation, derived in this work, is the extended Born-Handy formula, valid in the adiabatic limit as well as in the case of break down of the B-0 approximation. Since due to the many-body formulation the extended Born-Handy formula can be expressed in the CPHF compatible form, the extended CPHF equations, describing the non-adiabatic systems, will immediately follow from the presented theory. We shall call them COM CPHF equations. Whereas in the adiabatic limit the extended Bom-Handy formula represents only small corrections to the system total energy, in non-adiabatic systems it plays three important roles (1) removes the electron degeneracies, (2) is responsible for the symmetry breaking, and (3) forms the molecular and crystalline stmcture. 

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