Orthogonalization hole

There is one other point we should make concerning this formulation. The orthogonali-zation in Eq. (D-1) punches a hole in the pseudo wave function at each core. We see in fact that for each state, a fraction <(c (p>, called the orthogonalization hole, is... 

For the exchange and correlation terms we thus obtain two contributions, namely from the homogeneous electron density no = Z I q outside the core region (since inside the core the orthogonalization hole repels the valence electrons), and a contribution from the density fluctuations. The first term thus gives a contribution ... 

Let us consider a conductive material with the conductivity a, in which have been machined relatively small discontinuities shaped like dead hole. The surface has been inspected with a transducer with orthogonal coils connected in an impedance bridge [11]. 

Under the title Shear Fracture, Cook (Ref 4, p 346) noted that under conditions in which the tensile forces cannot develop or are restricted, a type of fracturing that can be associated with trajectories of maximum shear stress may develop. Rinehart 8t Pearson (Ref 1) detonated a 1/8 inch layer of expl on the cylindrical surface of a 2)4 inch OD aluminum (24S-T) cylindrical block with a 3/4 inch cylindrical relief hole drilled thru the longitudinal axis. The shock wave moving in toward the relief hole developed at each point of the block two mutually orthogonal trajectories of maximum shear stress. The trajectories, where the shear stress was maximal, spread out in 8 to 12 curved continuous lines from points on the surface of the relief hole. The shear fraction patterns observed along trajectories of maximum shear resembled the "Luder s... 

The stress rising effect of orthogonal side-holes in high pressure vessels and pipings has been investigated by a number of authors [15] [16] [17] [18] [19] showing that shape factors of around three must be expected depending on the thickness ratio of the wall, the ratio between... 

Fig. 40 Thermal hole transfer processes in bismethyleneadamantane radical cation, 41, and bismethylenebishomocubane radical cation, 42 the former process is formally symmetry-forbidden, because the two active 77 MOs are orthogonal to each other, whereas the latter is symmetry-alio wed, because the two active 77 MOs lie in the same plane. The inset, 43, depicts the major symmetry-breaking vibration, a torsional mode, which facilitates HT in 41.

Hence, columnar (discotic) liquid crystals with an aromatic central core are of significant interest for application in OLEDs as an HTL, if the columnar phase can be aligned with the columns orthogonal to the substrate surface, i.e. the flow of holes from the anode to the ETL and/or emission layer is... 

Eq. (5) where the are localized molecular orbitals (LMOs) which are related to the familiar CMOs by a unitary transformation. Because of the orthogonality of molecular orbitals the autocorrelation function for the MO approximation is simply the sum of the time-dependent probability amplitudes for the hole to be in the various LMOs,... 

The pair density or second-order density matrix, obtained from a single determinantal function composed of orthogonal spin functions i is given in eqn (E1.4). Comparison of that expression for the pair density with that given in eqn (E7.10) yields for the Fermi hole for a reference electron of a spin at Tj... 

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