heitler - london model with fixed exponent orbitals and two-electron interaction from bohr model
DESCRIPTION
Heitler - London model with fixed exponent orbitals and two-electron interaction from Bohr model. Radius of orbit of valence electron. Energy functional. Kinetic energy. (This expression is given for R =0. For arbitrary R it is more lengthy). Be H molecule. Mg H molecule. - PowerPoint PPT PresentationTRANSCRIPT
Heitler - London model with fixed exponent orbitals and two-electron interaction from Bohr model
Radius of orbit of valence electron
Li Na K
Bohr model 3.85 8.93 14.61
Book of Slater 2.83 2.93 4.16
2 4 6 8 1 0r
0 .2
0 .2
0 .4
0 .6
P r R ad ia l w av e fu n c tio n s fo r H , L i, N a , an d K
0 2 4 6 8 10 12 14 16 18 20
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
K2 "exact"
Na2 "exact"
Bohr
K2, Na2E
-2E
K ,
a.u
.
R, a.u.
2 4 6 8 1 0r
0 .1
0 .1
0 .2
0 .3
0 .4
0 .5
P r R a d ia l w a v e fu n c tio n fo r L i
R
1r
2r
1
2
Energy functional
22
21
221
221
221
2121
111111
),,(),,(
rrRrRrRrrR
RrrTRrrE
Kinetic energy
2121 ,22
21,21 ),,( rrrrRrrT
)/exp()/exp()/exp()/exp(),( 1221221121, 21rrrrrrrrrr abbarr
(This expression is given for R=0. For arbitrary R it is more lengthy)
Be H molecule
2 4 6 8 1 0R
0 .0 8
0 .0 6
0 .0 4
0 .0 2
0 .0 0
E
B e H
Mg H molecule
2 4 6 8 1 0R
0 .0 5
0 .0 4
0 .0 3
0 .0 2
0 .0 1
0 .0 0
0 .0 1E
H M g
Other diatomic molecules
SCF wave function for Li H molecule
Li H molecule
2 4 6 8 1 0R
0 .0 8
0 .0 6
0 .0 4
0 .0 2
0 .0 0
0 .0 2
0 .0 4
E
L i H
2 4 6 8 1 0R
0 .1 0
0 .0 8
0 .0 6
0 .0 4
0 .0 2
0 .0 0
0 .0 2
0 .0 4
E
L i H
1 2 3 4 5 6R
0 .1 5
0 .1 0
0 .0 5
0 .0 0
0 .0 5E
H 2
2 4 6 8 1 0 1 2R
0 .0 4
0 .0 3
0 .0 2
0 .0 1
0 .0 0
0 .0 1
0 .0 2E
L i2
2 4 6 8 1 0R
0 .0 8
0 .0 6
0 .0 4
0 .0 2
0 .0 0
0 .0 2E
N a H
2 4 6 8 1 0 1 2 1 4R
0 .0 3
0 .0 2
0 .0 1
0 .0 0
0 .0 1E
N a L i
2 4 6 8 1 0 1 2 1 4R
0 .0 2 5
0 .0 2 0
0 .0 1 5
0 .0 1 0
0 .0 0 5
0 .0 0 0
0 .0 0 5
0 .0 1 0E
N a N a
2 4 6 8 1 0 1 2 1 4R
0 .0 1 5
0 .0 1 0
0 .0 0 5
0 .0 0 0
0 .0 0 5
0 .0 1 0E
K K