HCl, potentials, E vs. V state crossing and evaluation of FCF (ca. Relative W12)

agust,www,...hcl/June11/PPT-071111ak.pptagust,heima,....HCl/June11/PXP-071111ak.pxp

See also: http://www3.hi.is/~agust/rannsoknir/rempi/hcl/October08/HClPot-RyvsV-061108.ppt

agust,heima,....HCl/June11/PXP-081111ak.pxpagust,heima,...HCl/June11(XLS-081111ak.xls

110

105

100

95

90

85

80

x10

3

654321

From Gabriel et al.http://notendur.hi.is/agust/rannsoknir/papers/HCl/jcp134-204104-11.pdf

UVbb=76155.60325+25910.20228*(1-exp(-0.557896777*(rx1a-2.512)))^2

agust,heima,....HCl/June11/PXP-071111ak.pxp

UE vs reharmonic oscillator

r/A

E/cm-1

UE=82671.21667+7.14e4*(re-1.43387)^2 http://www3.hi.is/~agust/rannsoknir/rempi/hcl/October08/HClPot-RyvsV-061108.ppt

100

95

90

85

80

x10

3

3.02.52.01.51.0

Energy levels from Green

agust,heima,....HCl/June11/PXP-071111ak.pxp

v´=3

v´=14

v´=1

E

V

Crossing between the V and the E states according to functional representations ofboth states is close to v´(E) = 1 analogous to that found from Gabriels data. This also fits nicely with trends observed for B´vs v´and DE(v´,v´+1) vs v´ by us:

http://www.raunvis.hi.is/~agust/rempisvaedidir/jcp109585698.pdf

See next slide:

Largest perturbation

FCF calculations

1) Fit harmonic oscillator function for UE(r) :

110

105

100

95

90

85

80

x103

654321

Coefficient values ± one standard deviation K1 = 82713 ± 3.78e+03 K2 = 1.367e+06 ± 29.5 K3 = 0.22815 ± 3.55e+08 K4 = 1.4109 ± 1.81e+08

agust,heima,....HCl/June11/PXP-081111ak.pxp

UVbb=76155.60325+25910.20228*(1-exp(-0.557896777*(rx1a-2.512)))^2

UE=82671.21667+7.14e4*(re-1.43387)^2

Coefficient values ± one standard deviation for UE(r) K1 = 82713 ± 3.78e+03 = Te K2 = 1.367e+06 ± 29.5 = De = K3 = 0.22815 ± 3.55e+08 = beta K4 = 1.4109 ± 1.81e+08 = re

90x103

88

86

84

82

80

78

76

E [c

m-1

]

654321R [Å] agust,heima,....HCl/June11/PXP-081111ak.pxp; Gr1,Lay1

0

3

14

10

18

v´E V

90x103

88

86

84

82

80

78

76

E [c

m-1

]

54321R [Å]

3

14

10

1

18

v´

agust,heima,....HCl/June11/PXP-081111ak.pxp; Gr1,Lay1

E V

90x103

88

86

84

82

80

78

76

E [c

m-1

]

5432R [Å]

3

14

10

18

v´

agust,heima,....HCl/June11/PXP-081111ak.pxp; Gr1,Lay1

2

E V

v´(E) v´(V) FCF W12 (estimate (1)) W12 (estimate (2))

2 19 31 241 323

2 18 34 264 354

1 15 15.8 123 165

1 14 11.8 92 123

0 11 0.53 4.1 5.5

0 10 0.28 2.1 2.9

v´(E) v´(V) FCF W12 W12

estim(1) estim(2)

2 19 31 241.3291 323.1356

2 18 34 264.6835 354.4068

1 15 15.8 123 164.6949

1 14 11.8 91.86076 123

0 11 0.53 4.125949 5.524576

0 10 0.28 2.179747 2.918644

Clearly the overlap increases as v´(E) goes from 0 ->1->2

!

• Comments:

•FCF probably is not a good measure of W12 !