Hamiltonian perturbational potential

As an alternative to the Ritz variational method, a variational perturbation method based on a perturbation expansion can be utilized. Here, the Hamiltonian is separated into an unperturbed Hamiltonian and a perturbing potential,... 

The latter has been employed so far in the calculation of three-body contributions adding to the reference Hamiltonian three perturbation potentials, one for each pair, and allows, as already mentioned, to decompose the total three-body term into physically meaningful contributions, such as repulsion, polarization and dispersion. 

The energy shift resulting from the perturbing potential can be evaluated by a coupling constant integration with respect to V. Scaling the external potential Hamiltonian by A,... 

For purely electric properties (Xo = 0) the perturbed potential V(A) is strictly even, and the resulting DKH expressions are significantly simplified. The familiar DKH expressions for the unperturbed Dirac Hamiltonian can be directly transferred to the full system just by replacing the electron-nucleus interaction V by the even perturbed potential... 

If applying a transformation derived from the decoupling of the unperturbed Dirac Hamiltonian was potentially unreliable for electric properties, for magnetic properties it simply will not work. The reason is that magnetic perturbations enter through the vector potential A and thus are odd operators. 

Two states /a and /b that are eigenfunctions of a Hamiltonian Hq in the absence of some external perturbation (e.g., electromagnetic field or static electric field or potential due to surrounding ligands) can be "coupled" by the perturbation V only if the symmetries of V and of the two wavefunctions obey a so-called selection rule. In particular, only if the coupling integral (see Appendix D which deals with time independent perturbation theory)... 

Perturbation terms in the Hamiltonian operator up to still lead to the uncoupling of the nuclear and electronic motions, but change the form of the electronic potential energy funetion in the equation for the nuclear motion. Rather than present the details of the Bom-Oppenheimer perturbation expansion, we follow instead the equivalent, but more elegant procedure of M. Bom and K. Huang (1954). 

DFT studies of the electronic structure perturbation of a molecule bound to an enzyme were pioneered by Bajorath et al.153-155. In these studies, the electrostatic potential arising from enzyme s electric charges (Vcxt) was included in the KS Hamiltonian ... 

UU is the Hamiltonian difference (the perturbation) the angle brackets represent a canonical ensemble average performed on an equilibrated system designated by the subscript. Usually the kinetic component of the Hamiltonian is not included in the free energy calculation, and A- //, n can be replaced by the potential energy difference AU = Ui - U0. 

If the problem is approached from the standpoint of considering the repulsion between the electrons as being a minor irregularity or perturbation in an otherwise solvable problem, the Hamiltonian can be modified to take into account this perturbation in a form that allows the problem to be solved. When this is done, the calculated value for the first ionization potential is 24.58 eV. 

---