-
18
-
-
84927325280
-
-
In this discussion, spin states are not resolved. Accordingly, the occupation factor fs is assumed to contain a factor 2 representing double occupation of each orbital.
-
-
-
-
19
-
-
84927325279
-
-
For further details of the matrix Green's-function method, see Ref. 2.
-
-
-
-
20
-
-
84927325278
-
-
If needed, Gij (Z) can be computed for i and j outside the set of orbitals which overlaps the adatom-induced potential. As indicated by Eq. (15), this can be done via simple matrix multiplications, making use when necessary of the symmetry of Gij (Z) under interchange of i and j.
-
-
-
-
21
-
-
84927325277
-
-
Evidently the effects of Friedel oscillations and possible long-ranged potentials due to image effects need to be considered. Here I assume that one can choose the adatom-affected region to be large enough that these effects are negligible. They are discussed further below.
-
-
-
-
23
-
-
84927325276
-
-
The output Hij is obtained as follows: Equation (15) is solved for Gij (Z), Eq. (13) then yields the output ρ (r), and Eq. (8) the corresponding output one-electron Hamiltonian, Hij [ ρ (r)].
-
-
-
-
24
-
-
0642265166
-
-
(b) The simple derivation which follows is due to A. R. Williams (private communication).
-
(1967)
Phys. Rev.
, vol.154
, pp. 515
-
-
Callaway, J.1
-
28
-
-
84927325275
-
-
In this and what follows, I am not allowing for the possibility of a substitutional defect with a nuclear valence different from that of the substrate atoms. Thus the fic of the reference atoms for the substrate are presumed to be the same in the adsorption problem as in the clean surface case.
-
-
-
-
32
-
-
84927325274
-
-
The zeroth-order energy of the adsorption system is independent of adatom position; thus the gradient of the adsorption binding energy is the same as that of the total energy.
-
-
-
-
36
-
-
84927325273
-
-
Note that however impressive, this degree of accuracy is only adequate for obtaining binding energies to the 0.001 Ry level if care is exercised relative to the evaluation of Coulomb term cancellations as described in the discussion following Eq. (66). Otherwise the fact that there may easily be 25 atoms ``inside the box'' means that the apparently small error associated with a single atom will be multiplied by 25. At that point the ``small error'' is no longer small enough.
-
-
-
-
39
-
-
84927325272
-
-
This result follows from the series expansion of the hyperbolic tangent function. See I. S. Gradshteyn and I. M. Rhyzhik, Table of Integrals, Series and Products (Academic, New York, 1965), p. 36, Eq. 1.41.2.
-
-
-
-
40
-
-
84927325271
-
-
Using a finite temperature in the clean surface problem has the advantage that states can be partially occupied instead of having to have occupation numbers of 0 or 1. Partial occupation of states corresponding to different surface Brillouin-zone vectors circumvents oscillations in the course of iteration to self-consistency that can arise when two states near EF at two different k vecpara's change their relative binding energies depending on which is occupied. Partial occupation of both states damps out the oscillation.
-
-
-
-
41
-
-
84927325270
-
-
The agreement is much worse if the caveats following Eq. (57) are ignored. If, for example, Eq. (66) is used in place of Eq. (65) in obtaining a formula for Wb,es the zero of the force curve is displaced from the minimum of the energy curve by about 0.1aB. This is because the requirements of mesh convergence are considerably more stringent if different approximation schemes are used to calculate the adsorption-induced change in the sum of the one-electron energies and the corresponding ``overcounting'' correction.
-
-
-
-
42
-
-
84927325269
-
-
C. E. Moore, Atomic Energy Levels, Natl. Bur. of Stand. (U.S.) Circ. No. 467 (U.S. GPO, Washington, D.C., 1949), Vol. I.
-
-
-
|
