HCl, Deperturbation

E1, V14, V15 (slides 2-7 )E0, V10, V11 (slides 8-10 )

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PPT-300712ak.ppt https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/XLS-300712ak.xlshttps://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-010812ak.pxp

Instruction about how to perform deperturbation calculations:https://notendur.hi.is/jil3/Instruction/Deperturbedprocedure.htm &https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/DOC-020812jla.doc

Information sheet (for HCl, Ei; i = 0,1 & V(v´); v = 10,11,14,15):https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/DOC-020812jl.doc

86.4

86.3

86.2

86.1

86.0

85.9

85.8

85.7

x103

20015010050 W/cm-1

E1

V15

V14 Unrealistic region

123

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:0, Gr:0

v1,v2,v3

85836

9

8

7

6

5

4

3

220200180160140120100806040123

B1

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:1, Gr:1

Unrealistic region

W/cm-1

HCl, E1, V14, V15

-60

-50

-40

-30

-20

-10

0

10

20

x10-3

220200180160140120100806040123

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:2, Gr:2

D1

Deviation of D1 from 0 is a resonable measure of distortion, i.e. one might expect D1 (unperturbed) to be closeto zero analogous to that for X(HCl) (De= 5.3194E-4 = 0.53E-3=+0.00053<= NIST) andX(HCl+) (De= 5.477E-4 = 0.547E-3=+0.000547<= NIST )

Unrealistic region=-0.064426 ± 0.00651

=-0.050412 ± 0.0058

=-0.03616 ± 0.00592

=-0.021692 ± 0.00629

=-0.002102 ± 0.00724

W/cm-1

HCl, E1, V14, V15

v1 =85917 ± 1.87 =85912 ± 2.06 =85902 ± 2.57 =85884 ± 3.56 =85845 ± 7.54 =85842 ± 123 =85888 ± 704 =85954 ± 717 =86200 ± 2.89B1 =6.3818 ± 0.241 =6.8758 ± 0.238 =7.4842 ± 0.271 =8.3171 ± 0.334 =9.978 ± 0.52 =8.5108 ± 6.08 =7.6198 ± 32.8 =9.8162 ± 28.6 =2.2086 ± 0.428

D1=-0.064426 ± 0.00651

=-0.050412 ± 0.0058

=-0.03616 ± 0.00592

=-0.021692 ± 0.00629

=-0.002102 ± 0.00724

=-0.013809 ± 0.0586

=-0.003957 ± 0.258

=0.022498 ± 0.237

=0.014335 ± 0.00863

v2 =85674 ± 1.17 =85682 ± 1.31 =85697 ± 1.64 =85722 ± 2.34 =85770 ± 5.87 =85810 ± 115 =85822 ± 612 =85838 ± 520 =85814 ± 4.97B2 =6.162 ± 0.106 =6.0986 ± 0.117 =5.949 ± 0.146 =5.5754 ± 0.196 =4.3178 ± 0.384 =5.0287 ± 6.09 =5.7503 ± 31 =4.7002 ± 24.8 =5.9991 ± 0.536

D2=0.0058507 ± 0.00176

=0.0059503 ± 0.00196

=0.0055398 ± 0.00243

=0.0030923 ± 0.0032

=-0.0090158 ± 0.00543

=0.0070868 ± 0.0719

=0.0091504 ± 0.32

=-0.0074807 ± 0.288

=-0.052407 ± 0.0113

v3 =86403 ± 0.643 =86399 ± 0.695 =86393 ± 0.817 =86384 ± 0.973 =86376 ± 1.18 =86360 ± 10.6 =86336 ± 93 =86286 ± 190 =85977 ± 7

B3 =4.256 ± 0.0864 =4.2778 ± 0.0941 =4.2781 ± 0.113 =4.232 ± 0.139 =4.1278 ± 0.167 =4.0851 ± 0.798 =3.6812 ± 3.39 =2.7625 ± 4.53 =10.108 ± 0.816

D3=0.00077534 ± 0.00196

=0.0029304 ± 0.00215

=0.0054853 ± 0.00265

=0.0080898 ± 0.00335

=0.011192 ± 0.00416

=0.011843 ± 0.0199

=0.0032304 ± 0.0707

=0.025914 ± 0.262

=0.042671 ± 0.0156

W =25 ± 0 =50 ± 0 =75 ± 0 =100 ± 0=123 ± 0 =150 ± 0 =175 ± 0 =200 ± 0 =225 ± 0

B0 =10.44 ± 0=10.44 ± 0

=10.44 ± 0

=10.44 ± 0

=10.44 ± 0

=10.44 ± 0

=10.44 ± 0

=10.44 ± 0

=10.44 ± 0

D0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/XLS-300712ak.xls

HCl, E1, V14, V15

W12(max)=DE/2 = 246/2=

-5

-4

-3

-2

-1

0

1

x10-3

126.0125.5125.0124.5124.0123.5123.0122.5122.0121.5121.0120.5120.0

124.6

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:3, Gr:3

W/cm-1

D1

-6.71E-05-0.00078

+0.000596!0

HCl, E1, V14, V15

v1 =85853 ± 6.19 =85841 ± 8.22 =85840 ± 8.62 =85838 ± 9.04 =85836 ± 9.55 =85835 ± 10.1

B1 =9.6244 ± 0.462 =10.11 ± 0.549 =10.182 ± 0.566 =10.25 ± 0.584 =10.319 ± 0.606 =10.378 ± 0.628

D1 -0.0057505 -0.00078 -6.71E-05 0.000596 0.001277 0.001846

v2 =85760 ± 4.61 =85773 ± 6.52 =85775 ± 6.9 =85777 ± 7.31 =85779 ± 7.81 =85781 ± 8.31

B2 =4.6323 ± 0.321 =4.1936 ± 0.417 =4.1243 ± 0.437 =4.058 ± 0.456 =3.9883 ± 0.483 =3.9273 ± 0.508

D2 =-0.0057577 ± 0.00473 =-0.010315 ± 0.0058 =-0.011051 ± 0.00603 =-0.011743 ± 0.00623 =-0.012477 ± 0.00654 =-0.013092 ± 0.00683

v3 =86377 ± 1.13 =86375 ± 1.2 =86375 ± 1.22 =86375 ± 1.24 =86375 ± 1.26 =86375 ± 1.28

B3 =4.1458 ± 0.162 =4.1217 ± 0.169 =4.1188 ± 0.171 =4.1159 ± 0.172 =4.1127 ± 0.174 =4.1102 ± 0.176

D3 =0.010639 ± 0.00401 =0.011399 ± 0.00422 =0.011514 ± 0.00426 =0.011625 ± 0.00431 =0.011732 ± 0.00435 =0.011842 ± 0.00442

W 120 124 124.5 125 125.5 126

B0 =10.44 ± 0 =10.44 ± 0 =10.44 ± 0 =10.44 ± 0 =10.44 ± 0 =10.44 ± 0

D0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0 =0.000509 ± 0

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/XLS-300712ak.xls

HCl, E1, V14, V15

9.5

9.0

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

3.5

3.0

2.5

-60 -50 -40 -30 -20 -10 0 10 20x10-3

D1

B1

=> correlation between B1 and D1, i.e. highest B1 value for D1 closest to 0

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:8, Gr:8

( )

( )

( )

( )

( ): unrealistic points

84.1

84.0

83.9

83.8

83.7

83.6

x103

190180170160150

W/cm-1

E0

V11

V10

v1,v2,v3

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:7, Gr:7

HCl, E0, V10, V11

Unrealisticregion

83697

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

195190185180175170165160155150

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:4, Gr:4

B1

W/cm-1

HCl, E0, V10, V11

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

x10-3

195190185180175170165160155150

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:5, Gr:5

D1

W/cm-1

HCl, E0, V10, V11

9.0

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

-60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0x10-3 D1

B1

=> correlation between B1 and D1, i.e. highest B1 value for D1 closest to 0

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-300712ak.pxp Lay:6, Gr:6

HCl, E0, V10, V11

B1 D1 W v1 v2 v34.9336 -0.059136 150 83765 83513 841545.2599 -0.061566 160 83758 83525 84144

7.995 -0.013794 170 83739 83543 841417.5216 -0.024466 175 83736 83552 841377.6682 -0.01815 180 83727 83566 84134

8.268 -0.0088196 185 83713 83584 841328.4503 -0.0065942 186 83708 83588 84131

8.602 -0.0050225 187 83704 83593 841318.7473 -0.00438 189 83698 83601 841308.7626 -0.0042858 189.1 83697 83602 841308.7279 -0.0045835 189.2 83698 83602 841308.7793 -0.0042049 189.3 83697 83603 841308.7747 -0.0043186 189.4 83697 83603 841308.7699 -0.0043748 189.7 83696 83604 841298.6616 -0.0057388 190 83698 83604 84129

8.647 -0.0066091 191 83695 83607 841288.5023 -0.0088354 192 83695 83609 841277.8385 -0.017711 195 83698 83613 84123

HCl, E0, V10, V11

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/XLS-300712ak.xls

dep pert(J´=0) pert-dep.v1(E1;W=125) 85838 85919.4 81.36496 oursv1(E0;) 83697 83780.4 83.43347 oursv1) 2141 2138.931

vi(E0) 83706.9 83780.43 73.53347 Fieldv1) 2131.1

No significant change in v1)

Let´s perform dep. calculations for different W´s (i.e. WH WL) for E1,V14, V15:

85.890

85.885

85.880

85.875

85.870

85.865

85.860

85.855

85.850

85.845

x103

180176172168164160156152148144140136132128124

W3 / WH

v1HCl, E1, V14, V15 for W2 = 123

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-010812ak.pxp; Lay:2, Gr:2

11.4

11.2

11.0

10.8

10.6

10.4

10.2

10.0

180176172168164160156152148144140136132128124

W3 / WH

B1

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-010812ak.pxp; Lay:0, Gr:0

HCl, E1, V14, V15 for W2 = 123

24

22

20

18

16

14

12

10

8

6

4

2

0

-2

x10-3

180176172168164160156152148144140136132128124

W3 / WH

D1HCl, E1, V14, V15 for W2 = 123

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-010812ak.pxp; Lay:1, Gr:1

(D1) = 0 – 0.001 cm-1

11.4

11.2

11.0

10.8

10.6

10.4

10.2

10.0

242220181614121086420-2x10

-3

D1

B1HCl, E1, V14, V15 for W2 = 123, W3 CHANGES as above

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-010812ak.pxp; Lay:3, Gr:3

(D1) = 0 – 0.001 cm-1

Only small increase in W3 from 123 to about 129 (for W2 = 123) -improves D1 (= +0.0006 cm-1)-increases B1 from 9.97 to 10,096 cm-1 -causes small increase in v1 ( 85845 -> 85848 cm-1)

v1 B1 D1 W2 W385845 9.9748 -0.00215 123 12385846 10.015 -0.00121 123 12585847 10.053 -0.00032 123 12785848 10.075 0.000154 123 12885848 10.096 0.000609 123 12985849 10.116 0.00107 123 13085856 10.327 0.005588 123 14085868 10.695 0.01259 123 15585877 10.986 0.017543 123 16585892 11.53 0.025886 123 180

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/XLS-300712ak.xls

HCl, E1, V14, V15 for W2 = 123, W3 CHANGES

I tried

a)–to fix D1, and to vary W2 & W3 => W2 = 123 W3 = 110 +/- big error (typically)!b)- to use W2 = 125 and to vary W3 => W3 ca. 125 best!

Now let´s check E0,....:

Comparison with Fields work:https://notendur.hi.is/agust/rannsoknir/papers/HCl/jcp109-8374-98.pdf:

Try this

83.74

83.73

83.72

83.71

83.70

83.69

83.68

x103

228224220216212208204200196192188

W3 / WH

v1

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-020812ak.pxp ; Lay:6, Gr:6

9.0

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

3.5

3.0

228224220216212208204200196192188

W3 / WH

B1

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-020812ak.pxp ; Lay:4, Gr:4

HCl, E0, V10, V11 for W2 = 187

-80

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

x10-3

228224220216212208204200196192188

W3 / WH

D1

(D1) = 0 – 0.001 cm-1

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-020812ak.pxp ; Lay:5, Gr:5

HCl, E0, V10, V11 for W2 = 187

9.0

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

3.5

3.0

-80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0x10-3

D1

B1

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/PXP-020812ak.pxp ; Lay:7, Gr:7

HCl, E0, V10, V11 for W2 = 187, W3 CHANGES as above

v1 B1 D1 W2 W383704 8.611 -0.00488 187 18783707 8.6086 -0.0045 187 18883713 8.8675 -0.0008 187 19283715 8.9542 -6.81E-05 187 19383715 9.0138 0.00038 187 193.583716 9.0665 0.000731 187 19483718 9.2962 0.00233 187 19683730 9.1723 0.001679 187 20083748 8.6123 -0.00223 187 20583672 2.7465 -0.08097 187 231

dep pert(J´=0) pert-dep.v1(E1;W2=123;W3=129) 85848 85919.36 71.36496v1(E0;W2=187,W3=193.5) 83715 83780.43 65.43347 oursv1) 2133 2138.931

v1(E0) 83706.9 83780.43 73.53347 Fieldv1) 2141.1

https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/XLS-300712ak.xls

No significant change in v1)

Now it looks like:

1) E1: B1= 10.10, D1 = +0.0006 , W2 = 123, W3 = 1292) E0: B1= 9.01, D1= +0.0004, W2 = 187, W3= 193.5

2) Could it be that W2 <187 and W3 > 193.5 For E0, V10,V11?Search for D1 <0.001 and B1 > 9.01 for E0, V10,V11

=>By trying W2 =180 and varying W3 > 180 =>B1(max)= 8.37 only for D1(min) = -0.0051 (for W3 = 197) and V1= 83755 (which is even higher and makes (v1) still smallerErgo: this is not convincing

Could W2 > 187 and W3 still higher?

Tried: W2=190 and varying W3 >190 =>B1(max)= 9.1 for D1(min) = 0 (for W3 = 193) and V1 = 83700 => no big change in (v1)&Tried: W2 = 195 and varying W3 > 195 =>B1(max)=9.2 for D1(min) = -0.0009 (NB D1 <0, always)V1 = 83709 => no big change in (v1)

No improvements!

Best Results!

See: https://notendur.hi.is/agust/rannsoknir/rempi/hcl/July12/XLS-300712ak.xls

In agreement with Field et al.!