VMI-fitting results for V(m+i), i=4-10

VMI-fitting results for V(m+i), i=4-10

Helgi Rafn Hróðmarsson – 31/7/14

• Two fitting formulas

• 1) I=A(1+b2P2(cosq))• 2) I=A(1+b2P2(cosq)+b4P4(cos ))q

V(m+4)

„Peak A“ – fit 1

• I=A(1+b2P2(cosq))


• I=A(1+b2P2(cosq)+b4P4(cos ))q

J‘ b2 (fit 1) Db2 b2 (fit 2) Db2 b4 (fit 2) Db4

0 1,6488 0,017 1,6591 0,0171 -0,02663 0,01321 1,0712 0,0628 1,1928 0,039 -0,29651 0,03392 1,1306 0,0703 1,1583 0,0758 -0,068 0,06673 0,869 0,0301 0,92743 0,0219 -0,13968 0,02044 0,54273 0,0458 0,6463 0,0336 -0,23991 0,03385 0,38393 0,0433 0,48213 0,0349 -0,22407 0,03666 0,41285 0,031 0,49846 0,0165 -0,19587 0,01737 0,27025 0,0271 0,33504 0,0219 -0,14625 0,02388 0,01811 0,0331 0,078555 0,0343 -0,13335 0,0393

• For Peak A, the second fitting formula gives generally better fits (as to be expected). For future references, we will thusly use the results of the second fit.

„Peak B“ – fit 1





0 0,78797 0,0321 0,79874 355 -0,02556 0,03451 0,18865 0,0413 0,32613 0,0093 -0,30805 0,01012 0,2283 0,0303 0,31634 0,0179 -0,19799 0,01953 0,24625 0,0375 0,36421 0,0141 -0,2657 0,01524 0,07417 0,0276 0,16334 0,0139 -0,19771 0,01565 -0,06256 0,034 0,044024 0,0224 -0,2334 0,02586 0,039067 0,0322 0,061667 0,0377 -0,04997 0,04347 -0,13348 0,0204 -0,1227 0,0245 -0,02345 0,02918 -0,07592 0,0437 -0,06621 0,0526 -0,02124 0,0619

• Again, the fits for the second formula give much better results, so they will be used.

„Peak D“ – fit 1





0 1,8545 0,182 1,8923 0,192 -0,10015 0,1391 1,7377 0,192 1,8192 0,2 -0,2131 0,1472 1,5114 0,138 1,5863 0,143 -0,1912 0,1123 1,4466 0,21 1,5281 0,224 -0,20664 0,1784 0,96951 0,251 1,3342 0,232 -0,88042 0,2035 1,2466 0,209 1,2946 0,227 -0,11906 0,1926 1,2021 0,22 1,2634 0,239 -0,15154 0,2047 0,9887 0,153 1,1738 0,136 -0,54136 0,1278 1,2743 0,284 1,243 0,304 0,077825 0,263

„Peak G“ – fit 1





0 1,487 0,101 1,5263 0,106 -0,09999 0,08451 1,5638 0,123 1,544 0,13 0,050664 0,1042 1,6289 0,0749 1,6417 0,0795 -0,03304 0,06153 1,0447 0,161 1,2737 0,145 -0,55694 0,1244 1,4149 0,274 1,3527 0,289 0,15713 0,2445 1,1635 0,227 1,165 0,246 -0,00371 0,2176 0,89705 0,116 1,0246 0,117 -0,30587 0,1077 0,68913 0,138 0,85478 0,143 -0,38911 0,1378 1,0506 0,264 0,88078 0,27 0,4134 0,265

V(m+5)






0 1,2189 0,0287 1,2488 0,0276 -0,07404 0,02371 0,64142 0,0768 0,84326 0,0296 -0,47193 0,02852 0,57808 0,0431 0,69487 0,0171 -0,27143 0,0173 0,47721 0,0314 0,53331 0,0292 -0,11291 0,03034 0,25824 0,0233 0,29722 0,0236 -0,08791 0,0258






0 0,10063 0,0125 0,1072 0,0147 -0,01459 0,01681 -0,20745 0,0136 -0,17662 0,0135 -0,06664 0,01622 -0,19441 0,0342 -0,10975 0,0324 -0,18324 0,03823 -0,10005 0,0138 -0,07613 0,0148 -0,05221 0,01754 -0,10907 0,0364 -0,0349 0,0374 -0,16176 0,0436






0 1,5287 0,0992 1,5704 0,104 -0,10649 0,08191 1,5877 0,111 1,5964 0,117 -0,02687 0,09692 1,429 0,151 1,4587 0,162 -0,07517 0,1313 1,37 0,117 1,3553 0,123 0,044624 0,1094 1,1182 0,195 1,0675 0,209 0,12423 0,19






0 1,5526 0,0602 1,6443 0,0392 -0,23508 0,03021 1,5034 0,0831 1,6248 0,0596 -0,30956 0,04622 1,2244 0,099 1,4259 0,0376 -0,49916 0,0313 1,3671 0,113 1,4871 0,106 -0,30153 0,08544 1,2738 0,121 1,2439 0,13 0,07446 0,112

V(m+4) & V(m+5)

V(m+6), V(m+7), V(m+8), V(m+9), V(m+10) – J‘=0





J‘=0 b2 (fit 1) Db2 b2 (fit 2) Db2 b4 (fit 2) Db4

V(m+6) -0,67914 0,00494 -0,69176 0,00508 0,026181 0,00628V(m+7) 1,3751 0,039 1,4342 0,0287 -0,14865 0,0234V(m+8) 1,5472 0,0377 1,6107 0,0195 -0,16266 0,0152V(m+9) 1,5503 0,0745 1,667 0,0461 -0,29896 0,0353

V(m+10) 1,6934 0,042 1,6857 0,0443 0,02006 0,0339






V(m+6) 0,69321 0,0316 0,65747 0,0322 0,083996 0,0326V(m+7) 1,2832 0,098 1,2096 0,0981 0,18342 0,0863V(m+8) 0,97405 0,0919 0,91639 0,0968 0,13927 0,0918V(m+9) 0,57049 0,0549 0,62749 0,0586 -0,13039 0,0593

V(m+10) 1,3592 0,0458 1,3263 0,0441 0,099806 0,0394






V(m+6) 2,0183 0,177 1,99 0,182 0,091099 0,137V(m+7) 2 0,347 2 0,337 0,44249 0,235V(m+8) 1,661 0,244 1,7725 0,255 -0,289 0,19V(m+9) 1,8085 0,201 1,6281 0,164 0,56971 0,141

V(m+10) 1,9017 0,186 1,8866 0,196 0,040398 0,142






V(m+6) 1,8527 0,127 1,9483 0,122 -0,25303 0,0869V(m+7) 1,5703 0,276 1,9131 0,229 -0,8802 0,172V(m+8) 1,8235 0,217 1,627 0,191 0,51842 0,155V(m+9) 1,9747 0,12 2,0244 0,12 -0,15953 0,0886

V(m+10) 1,5868 0,139 1,7724 0,0807 -0,57386 0,0645

Summary figures:

V(m+4); J´= 0-8; fit 2 V(m+5); J´= 0-4; fit 2

V(m+i); i = 6-10 (J´= 0); fit 2

b2 vs i and J´

See explanation below



Comment:

1) The drop in b2 from i= 4 to i = 5 (and from i = 8 to i = 9), for the„H*+Br“ channel (peak B), i.e. an increasing perpendicular transition contribution, is for those V(m+i) states which experience largest interactions with the E(0) (and E(1)) state(s),See: http://www.raunvis.hi.is/~agust/rempisvaedidir/jcp109585698.pdf :

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

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

-hence those states which experience largest E state character, but according to

E 1S([2P;s1p3]5pp1)…..B….

1,3S ([2P ;s1p3s*1]5pp1)1,3P ([B2S+;s2(px1py

1)s*1]5pp1)

2P3/2,1/2 (s2p3 )

V 1S(s1p4s*1)

[2P ;s1p3s*1]

e- e-

p pp║s s*

║p s*

┴

HBr**

HBr+*/HBr+

HBr#

HBr+*

H* +Br

H* +Br*

H +Br+

H+ +Br

b)

-e-

-e-

[B2S+;s2(px1py

1)s*1]

Fig. from HBr-VMI manuscript

-an increased E character will result in an enhanced perpendicular transition contributionThe perpendicular transition contribution is even larger for J´s larger than zero (J´>0)

:::

2) The drop (enhanced perpendicular contribution) in the „H* + Br*“ for i = 6 is a bit of a surprise and could possibly be because of a signal overlap or interaction with the f3D1(1) state(?). …SEE below

More about V(m+6) and f3D1(v): https://notendur.hi.is/~agust/rannsoknir/papers/jcp93-4624-90.pdf:

https://notendur.hi.is/~agust/rannsoknir/papers/jcp93-4624-90.pdf


80

60

40

20

0

x103

79.0078.9578.9078.8578.80x10

3

H81

Br

81Br

H79

Br

79Br

H

H81Br+

H79Br+

81Br+

79Br+

H+V(m+6);Q

J´= 5 4 3 2 1 0 ?

https://notendur.hi.is/~agust/rannsoknir/Crete/PXP-140802.pxp :

https://notendur.hi.is/~agust/rannsoknir/papers/jcp93-4624-90.pdf:

These look likeQ lines of a Rydberg state

https://notendur.hi.is/~agust/rannsoknir/Crete/PXP-140802.pxp




Þ It does not look as if there is any overlap between V(m+6), J´= 0 and f3D1(1) peaks-anyway the KER for V(m+6) fits nicely into the trend of the KER´s for V(m+i); i = 4-10 (see Fig. below)

Þ BUT: possibly there is a strong near –resonanace interaction between V(m + 6), J´= 0 and f3D1(v´=1), J´= 0 resulting in an enhanced perpendicular character of the V(m + 6) photodissociation! NB according to C&G (see slide 87 above) the energy difference is only DE J´= 9.4 cm-1!....

3.02.52.01.51.00.50.0

V1S+(v � = m + i); J � = 1H* + Br*(1/2)

H* + Br(3/2) HBr+*(1/2,v+)

HBr+ (3/2,v+)

c)

i =

87

65

4

910

H+ kinetic energy release / eV

0

: Fig. from HBr-VMI manuscript

https://notendur.hi.is/~agust/rannsoknir/papers/jcp93-4624-90.pdf:



-10

-5

0

5x1

03

78.9678.9578.9478.93

x103

H81

Br81

BrH79

Br

79Br

H

Possibly this is the J´= 0 peak and that peak # is J´= 1 but not J´=0


# = peak measured in Crete

…NB: J´= 0 level of V(m+6) should not be affected by f3D1(v´=1) since W = 1, hence J´= 0 does not exist!

BUT:

H+

79Br+

V(m+6);Q

x103/cm-1



Documents

VMI-fitting results for V(m+i), i=4-10