Electron propagator theory approximations

Flores-Moreno, R., Melin, J., Dolgounitcheva, O., Zakrzewski, V.G., Ortiz, J.V. Three approximations to the nonlocal and energy-dependent correlation potential in electron propagator theory. Int. J. Quantum Chem. 2010,110, 706-15. 

Net atomic charges of about -0.2 at each H were calculated with an ab initio MO-SCF method [2], with the semiempirical CNDO/2 method [11], and with another semiempirical method using localized bond orbitals for Cl [12]. A lower value came from an EH calculation [3]. A radial electron density distribution was calculated within the united-atom approximation [10]. Two different dipole moments were obtained with an MO-SCF calculation (yielding also quadrupole and octupole moments) [2] and with the electron propagator theory (EPT) [13]. 

The lowest, virtual, canonical HF orbitals of the neutrals consist chiefly of valence s and p basis functions. Singly occupied spin orbitals that occur only in UHF calculations on the anion are composed of the same AOs. Both types of these one-electron wave funetions may be considered approximations to the Dyson orbitals [85,86] corresponding to the EAs of the beryllium clusters. In the framework of the electron propagator theory [85], the Dyson orbitals are overlaps between an N-electron reference state and final states with N electrons. They form an overcomplete set and are not necessarily normalized to unity. 

R. Flores-Moreno, J. Melin, O. Dolgounitcheva, V. G. Zakrezewski, and J. V. Ortiz, Int. ]. Quantum Chem., 110, 706-715 (2010). Three Approximations to the Nonlocal and Energy-Dependent Correlation Potential in Electron Propagator Theory. 

If the Kohn-Sham orbitals [52] of density functional theory (DFT) [53] are used instead of Hartree-Fock orbitals in the reference state [54], the RI can become essential for the realization of electron propagator calculations. Modern implementations of Kohn-Sham DFT [55] use the variational approximation of the Coulomb potential [45,46] (which is mathematically equivalent to the RI as presented above), and four-index integrals are not used at all. A very interesting example of this combination is the use of the GW approximation [56] for molecular systems [54],... 

This demonstrates the equivalence of this development to that of the undilated electron propagator. The structural equivalence at any order of perturbation theory between the dilated propagator G(r/) and the unrotated case, demonstrated by the corresponding choice of projection manifolds and density operators, guarantees the ease with which the dilated propagator coalesces into the undilated one for 0 = 0 at any level of approximation. For example, choosing p = pQ, h = h1 h3, and h = h1 h3 with... 

One possible way to treat such a case is to use an approximated approach of the nonadiabatic electron wavepacket theory, the phase-space averaging and natural branching (PSANB) method [493], or the branching-path representation, in which the wavepackets propagate along non-Born-Oppenheimer branching paths. 

Our primary goal was the simulation of entire atomic systems, thus made of electrons and nuclei. As mentioned earlier (see Sect. 2.3), in a large class of systems (e.g. not too high temperature) one can decouple the motion of nuclei and electrons within the Born-Oppenheimer approximation. The previous section was then devoted to the Density Functional Theory solution of the electronic structure problem at fixed ionic positions. By computing the Hellmann-Feynman forces (11) we can now propagate the dynamics of an ensemble of (classical) nuclei as described in Sect. 2.3, using e.g. the velocity verlet algorithm [117]. 

One somewhat displeasing detail in the approximate polarization propagator methods discussed in the previous section is the fact that concern needs to be made as to which formulation of wave mechanics that is used. This point has been elegantly resolved by Christiansen et al. in their quasi-energy formulation of response theory [23], in which a general and unified theory is presented for the evaluation of response functions for variational as well as nonvariational electronic structure methods. 

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