The Excitation Propagator

The energy representations in Eq. (4.13) or Eq. (4.17) show that the appropriate energy differences corresponding to excitations of the A -electron system are obtained from the excitation propagator, ie., the one with the field operator basis 

For fractional occupation numbers, the division between occupied and unoccupied spin orbitals gets blurred and one could have a situation where (n ) = (nj). Operators q, and their adjoints for which this situation occurs are simply excluded from the basis. This avoids a singular metric. 

Show that when B-f C and B-C are positive, the second variation of H) for the single determinantal Hartree-Fock ground state is positive. 

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Figure 9 is a diagram of the local currents flowing along the nerve fiber during passage of an excitation impulse. To review the excitation propagation mechanism described in Section 1 it is convenient to consider Figure 9. The downstream-oriented axial current inside the fiber crosses the membrane as capacitive current, i.e., charges the membrane. When a certain threshold is exceeded, an inward ionic current appears apart from capacitive current. Further on, the outward current begins to dominate and returns the potential...

For real orbitals and geminal coefficients gi, the excitation propagator P E) is written in the geometric approximations as before, but now with the augmented set of field operators. Considering the block... 

The excitation propagator (particle-hole propagator) at the RPA level of approximation can be expressed as... 

The T amplitudes contain infinite order contributions to each excitation level from the HF state. Thus, replacing the RSPT K amplitudes with the CC T amplitudes may be considered a renormalization procedure since certain classes of perturbation terms or diagrams are summed to infinite order. This idea was employed in work on both the electron propagator and the excitation propagator... 

The excitation propagator is of importance for the understanding of electronic excitation spectra, polarizabilities, indirect nuclear spin-spin coupling tensors, and many other quantities. It has been treated in higher order approximations and is capable of yielding predictive results. An approach analogous to the one followed for the electron propagator is quite feasible. 

An explicit treatment of the excitation propagator through second order in electron interaction is presented in the following. First the projection manifold is limited to f = (q ql qq), and the superoperator... 

Through second order, the excitation propagator can then be expressed as P- E) = ) (12-16)... 

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