Extrapolation of Charge Density: Ver. 1.0
Taisuke Ozaki, RCIS, JAIST
Let us consider an extrapolation
of
the coordinate at the th molecular dynamic or geometry
optimization step [1,2] by a linear combination
of the previous coordinates
as
|
|
|
(1) |
where for three is an optimum choice in many cases.
To fit well the coordinate
to the real
coordinate , we consider the minimization of
a function :
|
|
|
(2) |
with respect to and .
The conditions
and
lead to
|
|
|
(3) |
By solving the linear equation, we may have an optimum choice of
a set of . Then, it is assumed that the difference charge
density
can be extrapolated well by the
same set of coefficients as
|
|
|
(4) |
where
is given by the superposition of atomic
charge densities at .
Using Eq. (4) it can be possible to estimate a good input charge density
at the th step in molecular dynamic simulations or
geometry optimizations.
-
- 1
-
T. A. Arias, M. C. Payne, and J. D. Joannopoulos,
Phys. Rev. B 45, 1538 (1992).
- 2
-
D. Alfe, Comp. Phys. Commun. 118, 32 (1999).
2007-08-16