Renormalization of levels

It is well known that in bulk crystals there are inversions of relative stability between the HCP and the FCC structure as a fxmction of the d band filling which follow from the equality of the first four moments (po - ps) of the total density of states in both structures. A similar behaviour is also expected in the present problem since the total densities of states of two adislands with the same shape and number of atoms, but adsorbed in different geometries, have again the same po, pi, P2/ P3 when the renormalization of atomic levels and the relaxation are neglected. This behaviour is still found when the latter effects are taken into account as shown in Fig. 5 where our results are summarized. 

Then e is associated with a level shift (or mass renormalization) of the unperturbed level e ° while e" gives us the decay time. 

Keywords Density functional theory (DFT) Green s functions Keldysh non-equilibrium Green s functions (NEGF) linear combination of atomic orbitals (LCAO) tunnel junction metal-fullerene-metal junction density of states (DOS) transmission function Landauer formula renormalized molecular levels (RMLs) I-V curves. 

Here, again, the sum runs over the atoms of the molecule and i/, p are their orbital quantum numbers, respectively. Obviously, the obtained eigen-levels and orbitals are different from those of the free molecule because the interaction with the leads is taken into account in Eq. (8) through H. The correspondence to the free molecule levels and orbitals can be found by projecting TJ( )1 ( onto the orbitals of the free molecule. This way, the terms HOMO-derived or LUMO-derived levels can be used for the corresponding groups of renormalized molecular levels. 

Fig. 14 a, b. Renormalization of a double hole level in terms of (a) independent, interacting (dressed) holes and (b) effective interaction between dressed holes... 

The process of constructing ft and its matrix elements can be regarded as a renormalization of the formal primitive theory described in Sect. 4. At both primitive and renormalized levels of description we can reduce the n-electron Hamiltonians, H and respectively, to operators acting on only the Nj d-electrons, as in Eq. (1-5), by integrating out all the other electrons with the probability distribution Vlo Plo. and we therefore have the formal relations... 

To calculate the scaling functions we now follow the flow up to some fixed surface chosen far from the critical manifold, such that i/ C- The resulting macroscopic Hamiltonian allows for a perturbative treatment, all critical effects being absorbed into the renormalization of the couplings. On the purely formal level the precise choice of tliis manifold where the scaling... 

This statement implies that not only the Coulomb interaction is included in Er and Exc but also the (retarded) Breit interaction. It thus points at the fact that a consistent and complete discussion of many-electron systems and consequently of RDFT must start from quantum electrodynamics (QED). RDFT necessruily has to reflect the various features of QED, both on the formal level and in the derivation of explicit functionals. The most important differences to the noiu-elativistic situation arise from the presence of infinite zero point energies and ultraviolet divergencies. In addition, finite vacuum corrections (vacuum polarization, Casimir energy) show up in both fundamental quantities of RDFT, the four current and the total energy. These issues have to be dealt with by a suitable renormalization procedure which ultimately relies on the renormalization of the vacuum Greens functions of QED. The first attempt to take... 

If the renormalization of the wave function is also taken into account, the (1 - al) quantity is divided by ai, and the corresponding correction is called the renormalized Davidson correction. The effect of higher order excitations is thus estimated from the correlation energy obtained at the CISD level times a factor that measures how important the single-determinant reference is at the CISD level. The Davidson correction does not yield zero for two-electron systems, where CISD is equivalent to full Cl, and it is likely that it overestimates the higher order corrections for systems with few electrons. More complicated correction schemes have also been proposed, but are rarely used. 

In contrast to the Raman scattering results a temperature-dependent softening of the mode is observed between 300 and 5 K in phononic neutron scattering (Reichart and Niicker 1983). This has been attributed by Thalmeier (1984) to the temperature dependence of the vertex corrections, which have to be taken into account in higher-order perturbation theory. The vertex corrections yield a temperature-dependent renormalization of the phonon frequency proportional to the difference in occupation of the F and Fg CEF levels. 

For this expansion one has multiplicative renormalization at the two-loop level for the 9/9urinsertions decoupling the flow of the for different t Explicitly,this means that the renormalization of the 9/9ui-insertion is independent from that of d/dv( for > 1. It may be speculated that this scheme can be continued to higher loop orders [107]. The different series parameterized by the V( would then correspond to the fact that instead of a multicritical point we expect to find a series of critical points in this problem [113,22] generating a multifractal spectrum of exponents. ... 

Fig. 9.80 Comparison of calculated (a) and measured (b) line profiles of level-crossing signals under observation with different gate-delay times (in ns). The different curves have been renormalized to equal centered peak intensities [1306]...

In Sections 2 and 3, we set up a formalism for dealing with the dynamics of dense fluids at the molecular level. We begin in Section 2 by focusing attention on the phase space density correlation function from which the space-time correlation functions of interest in scattering experiments and computer simulations can be obtained. The phase space correlation function obeys a kinetic equation that is characterized by a memory function, or generalized collision kernel, that describes all the effects of particle interactions. The memory function plays the role of an effective one-body potential and one can regard its presence as a renormalization of the motions of the particles. 

The results of Refs. [26,27] related to heats of formation and equilibrium geometries obtained by the APSLG-MINDO/3 method are somewhat more accurate than those of the standard (SCF-)MINDO/3 method. The APSLG form of the trial wave function also ensures its correct asymptotic behavior under cleavage of chemical bonds which indirectly justifies some level of bonae fidelitatis of the wave function employed. The APSLG form of the wave function also allows to represent a renormalization of the bare R-subsystem Hamiltonian in terms of well-defined characteristics like atomic charges, bond polarizabilities and ionization potentials for the chemical bonds [74,91]. 

Neaton JB, Hybertsen MS, Louie SG (2006) Renormalization of molecular electronic levels at metal-molecule interfaces. Phys Rev Lett 97 216405... 

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