hbr: f 1 d 2 (v´=1) v(v´=m+7) interaction: w 12 determination from line shifts:

HBr: F12(v´=1) <-> V(v´=m+7) interaction:W12 determination from line shifts:

agust,heima,...June11/Peaks of F1 and V(m+7) detlta2 for HCl state-141211jlak.xlsagust,www,....June11/PPT-141211aka.pptagust,heima,...June11/PXP-141211ak.pxp

agust,heima,...June11/HBr 79040_80120-151211.pxp

agust,heima,...June11/Peaks of F1 and V(m+7) detlta2 for HCl state-161211jlak.xlsagust,heima,...June11/PXP-161211ak.pxp

agust,heima,...June11/Overview spectra-131211hrh-291211ak.pxpagust,heima,...June11/PXP-291211ak.pxp

agust,heima,...Jan12/ Peaks of F1 and V(m+7) detlta2 for HCl state-161211jlak-020112ak.xlsagust,heima,...Jan12/ Overview spectra-131211hrh-020112ak.pxp

E(J´,J´-1)Q

49.0199165.1875

81.5216198.91389113.056

129.7394

J'012345678

E(J´,J´-1)Q

47.7536563.5010579.4166196.29238110.2204126.3927142.0013

J'0123456789

H79Br+ H81Br+

agust,heima,...June11/Peaks of F1 and V(m+7) detlta2 for HCl state-141211jlak.xls

120

100

80

60

876543

140

120

100

80

60

9876543

H79Br+ H81Br+

Clear deviations from linearity

E(J´,J´-1) derived from Qlines of F12

J´ J´agust,heima,...June11/PXP-141211ak.pxp

ERGO: W12 can be derived according to

http://www3.hi.is/~agust/rannsoknir/rempi/hcl/Jan11/PDF-020111ak.pdfAndhttp://www3.hi.is/~agust/rannsoknir/rempi/hcl/Jan11/PPT-190111ak.ppt

http://www3.hi.is/~agust/rannsoknir/rempi/hcl/Jan11/PDF-020111ak.pdf

http://www3.hi.is/%7Eagust/rannsoknir/rempi/hcl/Jan11/PPT-190111ak.ppt

120

100

80

60

876543

Coefficient values ± one standard deviation a = 0.60454 ± 0.0266 b = 16.142 ± 0.00488

H79Br+

agust,heima,...June11/PXP-141211ak.pxp

E(J´,J´-1)

J´

140

120

100

80

60

9876543

Coefficient values ± one standard deviation a = 0.6369 ± 0.0704 b = 15.713 ± 0.0108


E(J´,J´-1)

J´

35

30

25

20

15

10

4.03.53.02.52.01.51.0

agust,heima,...June11/PXP-141211ak.pxp; lay:2; Gr:4

V(v´=m+7)DE(J´,J´-1)79Br+

8.3177917.027227.419936.0875

J´

1234

VDE81Br+

7.9951616.182426.253634.901

E(J´,J´-1)

J´

70

60

50

40

30

20

10

8642

agust,heima,...June11/PXP-141211ak.pxp; lay:3; Gr:3

V(v´=m+7)DE(J´,J´-1)H+Use B´´and D´´ for i =79

V(v´=m+7)DE(J´,J´-1)H+Use B´´and D´´ for i =81

E(J´,J´-1)

J´

Lets have a look at the H+ REMPI spectrum:

20

10

0

-10

-20

x103

79.4579.4079.3579.3079.2579.20x10

3

F1 (v'=1)

QP R S2

4

68 2 3 4 5 62 3 542

Move J´=5 peak from + to +

agust,heima,...June11/HBr 79040_80120-151211.pxp; Lay:0 ; Gr:2

2h

i=79i=81

6

5

4

3

6

5

4

7

This is closer to what one might expect, i.e. a drop in E(6,5):


J´

F(v´=1)V(v´=m+7)

E(J´,J´-1)

J´

J´

Ca. 25 cm-1 drop!

V(v´=m+7)

20

10

0

-10

-20

x103

79.4579.4079.3579.3079.2579.20x10

3

F1 (v'=1)

QP R S2

4

68 2 3 4 5 62 3 542

Lets have a look at the H+ REMPI spectrum:

Move J´=5 peak from + to +

H+

J' Q0 79482.51 79473.72 79456.63 79432.84 79401.55 793586 79283.227 79219.28 79145.39 79065.6


i=79i=81 H+

J' Q0 79482.51 79473.72 79456.63 79432.84 79401.55 793586 79283.227 79219.28 79145.39 79065.6

i.e. line positions:



J´

E(J´,J´-1)V(v´=m+7)

F1D2 H79Br+ E DE DE0 E0 D(E-E0) EV(J´) EV0 W12J' Q Q Q Q Q Q Q

0 79482.5 1 79490.82 2 79310.7 79362.05 79362.05 0 79507.95 79507.95 3 79308.4 79411.06 49.01991 49.03054 79411.08 0.010631 79535.46 79535.45 4 79305.2 79476.25 65.1875 65.17254 79476.25 0.004325 79572.55 79572.55 5 79301.3 79557.77 81.52161 81.31454 79557.56 0.211395 79614.47 79614.26 6 79297.8 79656.69 98.91389 97.45654 79655.02 1.66874 79642.1 79643.77 4.6426167 79291.5 79769.74 113.056 113.5985 79768.62 1.126153 79697.44 79698.57 8.958 79285 79899.48 129.7394 129.7405 79898.36 1.125058 79759.78 79760.91

79833.14 H81Br+ DE J' Q Q

0 79482.5 1 79490.4 2 79310.4 79360.48 79360.48 0 79506.68 79506.68 3 79308.1 79408.23 47.75365 47.7759 79408.25 0.022255 79532.93 79532.91 4 79304.9 79471.73 63.50105 63.4889 79471.74 0.010107 79568.33 79568.32 5 79301 79551.15 79.41661 79.2019 79550.94 0.204604 79608.15 79607.94 6 79297.4 79647.44 96.29238 94.9149 79645.86 1.58208 79633.26 79634.84 4.4652917 79291.2 79757.66 110.2204 110.6279 79756.49 1.174562 79685.66 79686.84 9.128 79284.7 79884.05 126.3927 126.3409 79882.83 1.226332 79744.65 79745.889 79277.4 80026.06 142.0013 142.0539 80024.88 1.173711 79814.26 79815.43

H+ E DE

J' Q Q (original) Q(81) Q(79) 0 79482.5 79482.5 79482.5 79482.5 1 79473.7 79473.7 79490.4 79490.82 7.895161 8.317794 2 79456.6 79456.6 79506.68 79507.95 16.28236 17.12722 3 79432.8 79432.8 79532.93 79535.46 26.25365 27.51991 4 79401.5 79401.5 79568.33 79572.55 35.40105 37.0875 5 79358 79344.5 79608.15 79614.47 39.81661 41.92161 6 79283.22 79283.22 79633.26 79642.1 25.10738 27.62889 7 79219.2 79219.2 79685.66 79697.44 52.40538 55.34095 8 79145.3 79145.3 79744.65 79759.78 58.99267 62.33944 9 79065.6 79065.6 79814.26 79833.14 69.60128 73.35599


Assuming ca. linear behavior of E vs J´ ( for the V state, J´= 0 – 8):

i=79i=81


J´

EV(v´=m+7)

79.9

79.8

79.7

79.6

79.5

79.4

x103

2.52.01.51.00.50.0

agust,heima,...June11/HBr 79040_80120-151211.pxp; Lay:1; Gr:3

2

3

4

5

66

7

8

7

F(v´=1) V(v´=m+7)

E

Could it be that the relative position of levels is analogous to that shown inslide 15 (?), but not as shown in slide 10 ...in which case the shift could be like:

79.9

79.8

79.7

79.6

79.5

79.4

x103

2.52.01.51.00.50.0

2

3

4

5

66

7

8

7

E


F(v´=1) V(v´=m+7)

Better linearity:

i=79i=81


J´

E

V(v´=m+7)

79.9

79.8

79.7

79.6

79.5

79.4

x103

2.52.01.51.00.50.0

2

3

4

5

66

7

8

7

F(v´=1) V(v´=m+7)

E


80

60

40

20

0

-20

x10

3

79.3379.3279.3179.3079.2979.2879.27x10

3

F1 (v'=1)

Q

P

R

S

246823456

2354

2 Possible reassignment:

768 5

76

8

5

Indeed there is significant Br+ signal here

agust, heima, ...June11/HBr 79040_80120-081211.pxp

2h

In which case the the peak at 79219.2 is J´= 8 (not J´=7)!Thus for the following DE vs J´:


i=79i=81

J´

E

V(v´=m+7)

20

10

0

-10

-20

x10

3

79.579.479.379.279.1x10

3

F1 (v'=1)

QP R S2

4

68 2 3 4 5 62 3 542....the blue + hold instead of the red +:

567

89

10

567

89


2h

NB!: E vs J´will be distorted to some extend because of the interaction:

7 86J´

E(J´,J´-1) V(v´=m+7)


J´

E

Try:

V(v´=m+7)

20

10

0

-10

-20

x10

3

79.579.479.379.279.1x10

3

F1 (v'=1)

QP R S2

4

68 2 3 4 5 62 3 542....the blue + hold instead of the red +:


2h

140

120

100

80

60

9876543

H81Br+

Result of switching peaks J´=6 and 7:

agust,heima,...June11/PXP-161211ak.pxp; Lay:4, Gr:6

Coefficient values ± one standard deviation a =0.72958 ± 0.181 b =15.703 ± 0.0316

F(12)(v´=1)

J´

E(J´,J´-1)

120

100

80

60

876543

H79Br+

Result of switching peaks J´=6 and 7:

Coefficient values ± one standard deviation a =0.2396 ± 0.196 b =16.251 ± 0.0481

agust,heima,...June11/PXP-161211ak.pxp; Lay:5, Gr:5

F(12)(v´=1)

J´

E(J´,J´-1)

F1D2 H79Br+ E DE DE0 E0 D(E-E0) EV(J´) EV0 W12Q(orig) J' Q Q Q Q Q Q Q 0 79482.5 1 79490.82

79310.7 2 79310.7 79362.05 79362.05 0 79507.95 79507.95 79308.4 3 79308.4 79411.06 49.01991 48.9926 79411.04 0.027309 79535.46 79535.44 79305.2 4 79305.2 79476.25 65.1875 65.2436 79476.28 0.028795 79572.55 79572.52 79301.3 5 79301.3 79557.77 81.52161 81.4946 79557.78 0.001785 79620.47 79620.47 79297.8 6 79291.5 79650.39 92.61389 97.7456 79655.52 5.1335 79684.89 79679.75 12.2781579291.5 7 79297.8 79776.04 125.656 113.9966 79769.52 6.525853 79752.24 79758.77 10.61737

79285 8 79285 79899.48 123.4394 130.2476 79899.77 0.282302 79833.68 79833.97 79912.54 H81Br+ DE J' Q Q 0 79482.5 1 79490.4

79310.4 2 79310.4 79360.48 79360.48 0 79506.68 79506.68 79308.1 3 79308.1 79408.23 47.75365 47.1406 79407.62 0.613045 79532.93 79532.32 79304.9 4 79304.9 79471.73 63.50105 62.8436 79470.46 1.270493 79568.33 79567.06

79301 5 79301 79551.15 79.41661 78.5466 79549.01 2.140504 79614.15 79612.01 79297.4 6 79291.2 79641.24 90.09238 94.2496 79643.26 2.01672 79676.04 79674.02 8.13109479291.2 7 79297.4 79763.86 122.6204 109.9526 79753.21 10.65106 79740.46 79751.11 11.6528979284.7 8 79284.7 79884.05 120.1927 125.6556 79878.87 5.188132 79818.55 79823.74 79277.4 9 79277.4 80026.06 142.0013 141.3586 80020.22 5.830811 79893.66 79899.49

H+ E DE

J' Q Q (original) Q(81) Q(79) 0 79482.5 79482.5 79482.5 79482.5 1 79473.7 79473.7 79490.4 79490.82 7.895161 8.317794 2 79456.6 79456.6 79506.68 79507.95 16.28236 17.12722 3 79432.8 79432.8 79532.93 79535.46 26.25365 27.51991 4 79401.5 79401.5 79568.33 79572.55 35.40105 37.0875 5 79364 79344.5 79614.15 79620.47 45.81661 47.92161 6 79326 79283.22 79676.04 79684.89 61.89238 64.41389 7 79274 79219.2 79740.46 79752.24 64.42038 67.35595 8 79219.2 79145.3 79818.55 79833.68 78.09267 81.43944 9 79145 79065.6 79893.66 79912.54 75.10128 78.85599


Now, let´s check the effect of slight alterations in positions of V state peaks / levelson the evaluation of W12:

Later!

Calculate HBr F(1D2)<-<-X spectrum for H81Br:

40

30

20

10

0

x10-3

-120 -100 -80 -60 -40 -20 0

T B´(P), D´(P)

P

1hv

Is thisO-peak?

J´=2

3

4

5

6

7

8


40

30

20

10

0

x10-3

-120 -100 -80 -60 -40 -20 0

From previous Calculation/ slide

O-lines

O, Q lines

T B´(O,Q), D´(O,Q)

J´=2

3

4


NB! Upper levels corresponding to P and R lines in F1D2 will not interact with The V state (https://notendur.hi.is/agust/rannsoknir/papers/jcp131-044324-09.pdf See fig. 5):

Analogous energy level structure isfor the F 12 state

i.e. energy levelsexcided in P and Rlines do have oppositeparities to those inthe V state with same J´ values

What about the S lines?:

https://notendur.hi.is/agust/rannsoknir/papers/jcp131-044324-09.pdf

0.20

0.15

0.10

0.05

0.00

100806040200-20

Ephasising P & R simulation:

T B´(P,R), D´(P,R)

agust,heima,...June11/PXP-291211ak.pxp: Lay:1, Gr:1

Difficult to obtain simultaneous Q and S simulation(?)

Lets check Longs spectrum

It looks identical to HRH´s spectrum

020112:

Evaluate E(J´) from S serie and use these to recalcuate positions of QLines:

H81Br+ E E E E

J' O P Q R S P Q R S DE(Q-S) S(orig) nju(Q) Dnju(Q)

0

1

79310.4 2 79257.7 79310.4 79343.8 79359.4 79357.83 79360.48 79360.5 79359.4 1.077524 79359.4 79309.32 1.077524

79308.1 3 79236.1 79308.1 79357.4 79387.2 79402.93 79408.23 79407.48 79403.9 4.336008 79387.2 79303.76 4.336008

79304.9 4 79216.2 79304.9 79369.4 79417.7 79466.35 79471.73 79469.53 79467.78 3.954693 79417.7 79300.95 3.954693

79301 5 79301 79380.5 79446.7 79551.15 79547.33 79546.83 4.317659 79446.7 79296.68 4.317659

79297.4 6 79297.4 79477.6 79647.44 79644.43 3.008987 79477.6 79294.39 3.008987

79291.2 7 79291.2 79506.4 79757.66 79756.55 1.112758 79477.6 79290.09 1.112758

79284.7 8 79284.7 79884.05

79277.4 9 79277.4 80026.06

from HRH

See +in next figure

See +in next figure

agust,heima,...Jan12/ Peaks of F1 and V(m+7) detlta2 for HCl state-161211jlak-020112ak.xls; sheet4

200

150

100

x103

79.32x10379.3179.3079.2979.2879.27

E [cm-1

]

F12 (1,0), Q

210

H81

Br+

Br+ atomic line

79692.94 cm-1

79Br

+

H+

H+

79Br

+

81Br

+

H81

Br+

H79

Br+

3456789

agust,heima,...Jan12/ Overview spectra-131211hrh-020112ak.pxp; Lay:0, Gr:1

According to spectra

Peak positionsBased on E(J´) values derived from S lineserie

(i.e. “regular assignment”)

Strange (??)

How about to use E(J´) derived from the Q lines and use these to Predict S line positions (i.e. the opposite of the previous calculation!):

nju(S)

79360.4879391.5479421.6579451.0279480.6179507.5179534.0179559.59

J'0123456789


160

140

120

100

80

x10

3

79.55x103

79.5079.4579.4079.3579.30E [cm

-1]

9

F1 (1,0), S

72

H81

Br+

Br+ atomic line

79692.94 cm-1

79Br

+

H+

H+79

Br+81

Br+

H81

Br+

H79

Br+

Looks only slightly shifted except for the J´=2 peak; NB!: isn´t the energy for + and – levels the same for J´=2 for =2 states?...let´s check Herzberg....in which case the formulation for rotational levels only holds for J´>2!

4 5


See alsoSlide 36

The suggestion at bottom of slide 38 might explain why it is difficult toobtain simltaneous simulation for the Q and S series as mentioned in slide 34above.

Also try the “switched case”

nju(S)

79360.4879391.5479421.6579451.0279474.4179513.7179534.0179559.59

J'0123456789


160

140

120

100

80

x10

3

79.55x103

79.5079.4579.4079.3579.30E [cm

-1]

9

F1 (1,0), S

72

H81

Br+

Br+ atomic line

79692.94 cm-1

79Br

+

H+

H+79

Br+81

Br+

H81

Br+

H79

Br+


Regular Q lines

For J´= 6 and 7 Q- lines switched

Effect of “switching”What peak is this?:Most probably V(m+7) peak.

Most likely the Q peaks are regular, i.e. that J´=6 and 7 arenot switched.

NB!: according to “regulars” it looks as if peaks J´=6 and 7 are enhanced in intensity both in the Q and the S series.

030112: concerning comment at bottom of slide 38:

Indeed the energy is degenerate for no rotation as indicated on figure in slide 32:This is discussed in Herzberg (1950) page 239 and p 129:

Herzberg, p: 239:

Herzberg, p: 129:

Now, let´s check the effect of slight alterations in positions of V state peaks / levelson the evaluation of W12:

Lets try to obtain more smooth but realistic E vs J´curve for V(m+7):


20

10

0

-10

-20

x10

3

79.579.479.379.279.1x10

3

F1 (v'=1)

QP R S2

4

68 2 3 4 5 62 3 542

20

10

0

-10

-20

x10

3

79.579.479.379.279.1x10

3

F1 (v'=1)

QP R S2

4

68 2 3 4 5 62 3 542

agust,heima,...June11/Peaks of F1 and V(m+7) detlta2 for HCl state-161211jlak-020112ak.xls

++

Notice that anly small shift of peaks changes the DE vs J´curve for V(m+7) significantly

J´ EV(J´) EV0 W12Q

79482.5 79490.82 79507.95 79507.95 79535.46 79535.45 79572.55 79572.55 79614.47 79614.26

6 79642.1 79643.77 4.6426167 79697.44 79698.57 8.95

79759.78 79760.9179833.14

79482.5 79490.4

79506.68 79506.68 79532.93 79532.91 79568.33 79568.32 79608.15 79607.94

6 79633.26 79634.84 4.4652917 79685.66 79686.84 9.12

79744.65 79745.8879814.26 79815.43

J´ 79482.5 79490.82 79507.95 79507.95 79535.46 79535.45 79571.05 79571.05 79605.47 79605.26

6 79643.89 79645.56 4.3098937 79697.44 79698.57 8.952801

79759.78 79760.91 79833.14

79482.5 79490.4

79506.68 79506.68 79532.93 79532.91 79566.83 79566.82 79599.15 79598.94

6 79635.04 79636.62 4.1370067 79685.66 79686.84 9.120794

79744.65 79745.88 79814.26 79815.43

agust,heima,...Jan12/Peaks of F1 and V(m+7) detlta2 for HCl state-161211jlak-020112ak.xls

agust,heima,...Jan12/Peaks of F1 and V(m+7) detlta2 for HCl state-161211jlak-050112ak.xls

Calc 1

Calc 2

No major change in W12 evaluations

Assuming W12 = W12´(J+(J´+1))1/2

Morereliable

W12(J=6) = 4.4 +/- 0.3 W12´= 0.68 +/- 0.06

hbr: f 1 d 2 (v´=1) v(v´=m+7) interaction: w 12 determination from line shifts:

Documents

h agust

j 1234vde81br

hcl state

june11peaks of f1

j1jh79br coefficient

h jq079482

jan12 peaks of f1

h rempi spectrum