Relativistic Quantum Chemistry by Reiher Markus Wolf Alexander

Author:Reiher, Markus, Wolf, Alexander [Reiher, Markus, Wolf, Alexander]
Language: eng
Format: epub
Published: 0101-01-01T00:00:00+00:00

κi + γi [

d −

r( s)] γi Q

s

w 2 r( s)

i [ r( s)]

1

[ r( s)] γi

− cw 2 [ Vi[ r( s)] − ǫi] [ r( s)] γiPi[ r( s)] = − cw 2 XPi[ r( s)] (9.228) where we introduced the operator identity in the original variable r and wrote

r( s) in order to denote that a grid point will be determined in s so that the

corresponding value for r is then fixed. For γi = 0 these equations pass into

the original Eqs. (9.223) and (9.224) for nonsingular potentials, i.e., in finite

nucleus cases, which yield solution functions that are automatically analytic

at the origin. The equations above are of the following general form in the

new variable s,

d yU +

d

F

s

UU ( s) yU ( s) + FUL( s) yL( s)

= G( s)

(9.229)

d y

−

L +

d

F

s

LU ( s) yU ( s) + FLL( s) yL( s)

=

H( s)

(9.230)

whose discretization on the equidistant mesh of grid points have to be consid-

ered.

9.7.3.3 Poisson Equations

To derive the transformed differential equation for the two-electron potential

functions Yklν([ r( s)]) from Eq. (9.88) we take advantage of the operator iden-

tity

d2

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.