Welcome to delegates of

Molecular Spectroscopy Symposium

(18-22 June 2007)

Columbus Ohio USA

By

Dr Subhash Behere

Dept. of Physics

Dr Babasaheb Ambedkar Marathwada University

Aurangabad

Maharashtra

India

The Fourier Transform Spectrum of B 2+ - X 2+ System of AlO

M. D. Saksena ; M. N. Deo ; Sunanda K [BARC Mumbai]

S. H. Behere and C. T. Londhe [ Dr. B. A. M. University, Aurangabad]

India

MF 07

18th June 2007

Historical Review – 1

• The blue green system, is known from last 100 years.

• AlO has astrophysical significance as the bands of AlO appear in normal Mira Giants and Mira Variables.

• In the stars having low temperature the absorption band of AlO (0,0) at 4842A0 is seen.

• In normal Mira Giants, due to higher temp. this band is seen in emission too.

• Mecke tried to give vibrational analysis, which was further improved by Roy. Recently Saksena et al have shown that the some of the band heads of this system are shifted due to interaction of A 2Πi state with X 2+ state.

Fig 1. Energy level diagram of AlO molecule

Historical Review – Continued

• A sudden drop in the intensities of (4,7), (6,7), (5,7) and (10,7) bands and those involving v" = 6 and 8 were seen by Rosen.

• He attributed the phenomenon to predissociation especially for v" = 6, 7 and 8 for N = 60, 44, and 18 respectively.

• He also concluded that the bands of v" = 9 progression were also predissociated.

• Lagerqvist later told that the observation by Rosen might be an illusion which was found to be true.

• In the bands with v" = 6 the rotational lines go off because of the perturbation and not because of predissociation.

• Shimauchi photographed the spectra of AlO in air, nitrogen, oxygen argon and used high grade Al- rods as electrodes. She could record bands with v'=16 and v" = 12 and noticed that v" = 9 level of X 2 state is raised by 10 cm-1 because of perturbation by some state.

• Goodlett and Innes, Mahieu, Coxon and Naxakis and Saksena et. al. tried to determine the sign of γ0

. But

Yamada et. al. gave most accurate value of γ0 from

microwave data

• Bernard and Gravina analysed six bands of A 2Πi - X 2+ transition. They have taken the spin doubling constant of v = 0,1 and 2 levels of X 2+ states as +0.00073, – 0.00022 and – 0.00134 cm-1 respectively.

In fact it is known that γ0 increases as v and has only

positive sign.

• Getting unique expression from band head measurements is not possible because

i)0 -H differ vastly from bands of +ve and –ve sequences.

ii) Due to rapid increase in v" for levels v" 4 to 7

the separation of R1 and R2, heads also increases very

rapidly.

• The spectrogram shown on the paper of Mahieu et. al. is not according to theoretical expectations, if the ratio of intensities of R2 / R1 and P2 / P1 is considered.

• As per Mulliken’s relation R1 and P1 branch members are somewhat intense as compared to R2 and P2 members at low values of N .

• Launila and Jonsson also photographed the same region of same band but because of large noise they could not see the expected intensity differences.

• It is also known that the v' of the B 2+ state is

negative and has almost a constant magnitude Therefore, to account for the large v' - v" the v'

and v" should have opposite signs.

• The positive sign of v" is in confirmation with both

Sen and Lagerqvist.

• Later, Coxon and Naxakis photographed the B-X band system using a microwave discharge (2450MHz, 100W) in a flowing mixture of AlCl3

and O2 at 0.1nm/mm and analysed 25 bands. They

tried to show that v' - v" depends on v" levels but

with some limitation (resolution wise and intensity wise, they could not go to high N values).

• The rotational perturbations in the v' = 0 - 4 levels of A2i

state caused by the interaction of the rotational levels of the ground state, X 2+ v" = 5-9 levels have been mapped out by Singh and Saksena. This was done by photographing the B-X system in the second order of 10.6 m Ebert grating spectrograph. Eighteen bands were analyzed. It was shown that, as the rotational levels in different vibrational levels of the A2i state approach closer to the respective rotational

levels of X2+ state, the spin doubling increases. It is dependent on both v and N also.

• Launila and Jonsson recorded F T spectrum of A-X band system at 2m. The hyperfine structure, was evident which is attributed to X 2+ state. The derived values of 1",2"

and 3" are very much different compared to earlier

values. It was not clear how the hyperfine splitting affects the spin doubling constant of X 2+ state.

Present Work:

Source of excitation is 2450MHz, 150W microwave discharge through a flowing mixture of AlCl3 and oxygen

vapours. The BOMEM DA8 F.T. spectrometer was used at apodized resolution of 0.05 cm-1 to record the B – X band system. Fig. 2 shows the excitation set up and Fig 3 shows the spectrum. Nineteen bands of v = 1, 0, -1, and -2 sequences have been analysed.

The (3,2), (4,3), (2,3), (3,4), (4,5), (5,6) and (6,7) bands were analyzed for the first time.

The rotational line frequencies of these R2/R1 and P2/P1-

doublets, along with twenty earlier bands, totaling 7200, have been fitted in a simultaneous least squares fit.

Fig 2: schematic diagram of the discharge tube

Fig 3: Overview of the Fourier transform spectrum of B2+ –X2+ band system of AlO.

Fig 4: Rotational fine structure of the 0-0 band of B2+ –X2+ transition of AlO.

• The analysis was also extended to high N values. In this fit 0 was fixed as 0.001743192 cm-1 as given by Yamada.

The molecular constants are presented in Table 3.

• The higher N value rotational lines of (0,0) & (0,1) bands could be included only when H0 and H1 were taken in to

consideration.

• Also the overall deviation of the fit was minimized only when a cubic and fifth power term in N was included in the expression of spin doubling of X 2+ state

F = N/2 + 1N(N+0.5)(N+1) - 2 N2(N+0.5) (N+1)2

• The v' - v" values derived in the present study are

compared in table 4 with those of earlier workers.

• The vibrational constants are reported in table 5.

Conclusions:

• Prior to our studies it was not possible to give accurate vibrational expression for B – X system of AlO mainly because of splitting of some of the R2 and R1

heads due to large spin-doubling in the higher vibrational levels of the X 2+ ground state and a few heads being shifted due to perturbations. Only when these band-heads are excluded the vibrational expression becomes accurate.

• The anomalous spin-doubling in the X 2+ state, caused due to the interaction of the A 2i state could

be explained by including a cubic and fifth power term in the spin-doubling expression.

•The high resolution F.T. spectrum has helped in determining more precise molecular constants of B 2+ (v = 0 to 11) and X 2+ ( v = 0 to 7) states.

•The spin-doubling constant v', of the B 2+ state does

not change with v but changes slightly after v 8. This may be due to the fact that perhaps at higher v values the spin-doubling increases due to interaction of C 2r

state with B 2+ state.

Table 1: Measurements of the bands of B 2+ - X 2+ transition (in cm-1) Sr.No. v - v R2 head N† R1 head N†

1 (5,1) 23919.005* 10 23918.846* 10 0.159

2 (6,2) 23794.177* 11 23793.977* 11 0.200

3 (7,3) 23676.038* 11 23675.806* 11 0.232

4 (8,4) 23564.653* 11 23564.369* 11 0.284

6 (10,6) 23362.057* 12 23361.600* 12 0.457

7 (11,7) 23270.735* 12 23270.145* 12 0.590

5 (9,5) 23460.083* 12 23459.717* 11 0.366

8 (3,0) 23210.161* 11 23210.004* 11 0.157

9 (4,1) 23085.894* 12 23085.717* 12 0.177

10 (5,2) 22968.421* 12 22968.207* 12 0.214

11 (6,3) 22857.673* 12 22857.420* 12 0.253

13 (8,5) 22656.430* 12 22656.045* 12 0.385

14 (9,6) 22565.902* 13 22565.402 * 13 0.500

15 (10,7) 22482.120* 14 22481.439* 14 0.681

12 (7,4) 22753.627* 13 22753.321* 12 0.306

v = +4

v = +3

Table continued…..

* These are calculated positions, † rotational number N, where head is formed.

Sr.No. v - v R2 head N† R1 head N†

16 (2,0) 22362.536* 13 22362.365* 12 0.171

17 (3,1) 22245.623 13 22245.421 13 0.202

18 (4,2) 22135.484 13 22135.253 13 0.231

19 (5,3) 22032.095 14 22031.819 13 0.276

20 (6,4) 21935.480 14 21935.127 14 0.353

27 (0,1) 19682.250 19 19682.021 16 0.206

28 (1,2) 19594.361 20 19594.018 19 0.229

29 (2,3) 19513.194 21 19512.785 19 0.343

30 (3,4) 19438.842 22 19438.318 20 0.409

31 (4,5) 19371.420 23 19370.738 21 0.524

32 (5,6) 19310.854 25 19309.900 22 0.682

33 (6,7) 19257.550 33 19256.224 24 0.954

21 (0,2) 18733.664 24 18733.287 23 0.377

22 (1,3) 18660.020 25 18659.530 24 0.490

23 (2,4) 18593.223 26 18592.635 26 0.588

24 (3,5) 18533.528 28 18532.655 27 0.873

25 (4,6) 18480.752 31 18479.588 30 1.164

26 (5,7) 18435.915 37 18434.105 34 1.810

v = -1

v = -2

v = +2

0-0 band R1 P1 R2 P2 2.0 20632.729( 56) 20632.729( 35) 3.0 20631.298( 54) 20631.298( 21) 4.0 20629.806( 65) 20629.806( 19) 5.0 20628.239( 75) 20628.239( 16) 6.0 20626.597( 82) 20626.597( 11) 7.0 20624.759(-34) 20624.880( 03) 8.0 20622.966(-31) 20623.102( 08) 9.0 20621.098(-30) 20621.234(-03) 10.0 20619.155(-31) 20619.305(-03) 11.0 20617.151(-20) 20617.301(-05) 12.0 20615.057(-27) 20615.237( 06) 13.0 20612.902(-20) 20613.083( 01) 14.0 20610.657(-31) 20610.868( 07) 15.0 20608.352(-29) 20608.563(-04) 16.0 20605.972(-29) 20606.198(-01) 17.0 20603.531(-17) 20603.757(-02) 18.0 20601.000(-22) 20601.256( 11) 19.0 20598.408(-15) 20645.580( 35) 20598.665( 06) 20.0 20595.742(-09) 20645.309( 27) 20595.998(-01) 22.0 20590.182(-05) 20644.586( 53) 20590.469( 08) 23.0 20643.727(-12) 20587.290(-06) 20644.074( 27) 20587.591( 08) 24.0 20643.155(-11) 20584.322(-10) 20643.486(-01) 20584.638( 07) 25.0 20642.507(-12) 20581.278(-17) 20642.854( 01) 20581.610( 03)

Table 2: Vacuum wavenumbers and rotational line assignments of

B2+- X2+ transitions of AlO.

0-0 continued

R1 P1 R2 P2 26.0 20641.784(-13) 20578.175(-10) 20642.130(-14) 20578.506(-03) 27.0 20640.985(-16) 20574.996(-05) 20641.362( 02) 20575.342( 04) 28.0 20640.112(-19) 20571.726(-19) 20640.503( 01) 20572.088(-07) 29.0 20639.177(-08) 20568.397(-19) 20639.584( 14) 20568.773(-05) 30.0 20638.153(-12) 20565.007(-06) 20638.575( 13) 20565.383(-05) 31.0 20637.053(-18) 20561.526(-12) 20637.490( 10) 20561.918(-08) 32.0 20635.893(-08) 20557.986(-03) 20636.330( 06) 20558.393( 03) 33.0 20634.643(-14) 20554.355(-13) 20635.095( 03) 20554.777(-04) 34.0 20633.332(-05) 20550.664(-09) 20633.784(-01) 20551.101( 02) 35.0 20631.931(-12) 20546.897(-09) 20632.398(-05) 20547.334(-10) 36.0 20630.469(-05) 20543.055(-10) 20630.951( 04) 20543.500(-16) 37.0 20628.917(-12) 20539.138(-13) 20629.415( 00) 20539.620( 06) 38.0 20627.305(-04) 20535.146(-18) 20627.803(-04) 20535.643( 03) 39.0 20625.618( 04) 20531.108( 05) 20626.130( 05) 20531.590(-02) 40.0 20623.840(-03) 20526.965(-05) 20624.367( 00) 20527.477( 05) 41.0 20622.002( 05) 20522.746(-17) 20622.529(-05) 20523.273(-05) 42.0 20620.074(-02) 20518.467(-16) 20620.616(-09) 20519.010( 00) 43.0 20618.070(-09) 20514.128(-02) 20618.642( 02) 20514.671( 01) 44.0 20615.991(-15) 20509.699(-05) 20616.578(-02) 20510.241(-15) 45.0 20613.851(-06) 20505.194(-10) 20614.439(-05) 20505.767(-02) 46.0 20611.621(-12) 20500.629(-02) 20612.224(-08) 20501.202(-07) 47.0 20609.331(-02) 20495.989( 04) 20609.934(-11) 20496.576( 01) 48.0 20606.951(-05) 20491.273( 08) 20607.569(-12) 20491.861(-07)

0-0 continued R1 P1 R2 P2 49.0 20604.495(-09) 20486.467(-05) 20605.143( 02) 20487.085(-03) 50.0 20601.964(-11) 20481.600(-06) 20602.612(-14) 20482.233(-01) 51.0 20599.373( 02) 20476.674( 08) 20600.020(-13) 20477.307( 00) 52.0 20596.691( 02) 20471.657( 05) 20597.369( 04) 20472.305(-01) 53.0 20593.919(-13) 20466.564(-02) 20594.612(-08) 20467.227(-05) 54.0 20591.101( 03) 20461.412( 07) 20591.794(-05) 20462.075(-09) 55.0 20588.194( 06) 20456.169(-02) 20588.887(-14) 20456.847(-16) 56.0 20585.195(-05) 20450.865( 01) 20585.919(-08) 20451.559(-09) 57.0 20582.137( 00) 20445.487( 04) 20582.860(-15) 20446.195(-05) 58.0 20579.003( 07) 20440.033( 04) 20579.742(-05) 20440.741(-17) 59.0 20575.764(-14) 20434.504( 04) 20576.532(-10) 20435.242(-01) 60.0 20572.480(-04) 20428.899( 00) 20573.263( 02) 20429.652(-01) 61.0 20569.120( 08) 20423.219(-04) 20569.903( 01) 20423.987(-04) 62.0 20565.670( 06) 20417.479( 05) 20566.453(-13) 20418.247(-07) 63.0 20562.144( 06) 20411.663( 12) 20562.943(-10) 20412.432(-12) 64.0 20558.450(-85) 20405.757( 03) 20559.357(-05) 20406.571( 11) 65.0 20554.777(-77) 20399.791( 07) 20555.681(-13) 20400.590(-12) 66.0 20393.750( 11) 20551.944(-05) 20394.563(-07) 67.0 20387.648( 27) 20548.133( 07) 20388.446(-19) 68.0 20381.441( 12) 20544.215(-10) 20382.284(-01) 69.0 20375.173( 10) 20376.017(-15) 70.0 20368.830( 06) 20369.689(-16) 71.0 20362.412( 02) 20363.316( 12) 72.0 20355.919(-03) 20356.853( 24)

0-0 continued R1 P1 R2 P2 73.0 20349.365( 05) 20350.269(-11) 74.0 20342.736( 11) 20343.594(-63) 75.0 20336.016( 01) 20336.950(-10) 76.0 20329.251( 20) 20330.155(-34) 77.0 20322.381( 08) 20323.330(-14) 78.0 20315.451( 09) 20316.430( 06) 79.0 20308.445( 09) 20309.439( 08) 80.0 20301.364( 09) 20302.373( 10) 81.0 20294.192(-09) 20295.202(-20) 82.0 20286.961(-12) 20287.985(-21) 83.0 20279.684( 14) 20280.750( 34) 84.0 20272.301( 07) 20273.356( 04) 85.0 20264.875( 32) 20265.913(-01) 86.0 20257.341( 23) 20258.395(-07) 87.0 20249.687(-31) 20250.817( 02) 88.0 20242.079( 34) 20243.163( 09) 89.0 20234.300( 03) 20235.389(-30) 90.0 20226.500( 25) 20227.600(-10) 91.0 20218.590( 11) 20219.705(-21) 92.0 20210.590(-19) 20211.796( 27) 93.0 20202.540(-24) 20203.720(-17) 94.0 20194.470( 25) 20195.660( 30) 95.0 20186.258( 06) 20187.419(-31)

0-0 continued R1 P1 R2 P2 96.0 20178.002( 17) 20179.208( 12) 97.0 20169.656( 12) 20170.846(-21) 98.0 20161.219(-09) 20162.499( 35) 99.0 20152.721(-17) 20153.930(-57) 100.0 20144.134(-41) 20145.391(-45) 101.0 20135.546( 09) 20136.800(-10) 102.0 20126.800(-25) 20128.125( 14) 103.0 20118.000(-38) 20119.380( 42) 104.0 20109.190( 12) 20110.500( 10) 105.0 20100.300( 56) - 106.0 20091.206(-30) 20092.600( 27) 107.0 20082.160( 06)

Table 3: Molecular constants (in cm-1) of B 2+ and X 2+ state of AlO.

v Tv Bv Dv x 106 v v x 105 H x 1012

B 2+ state Be = 0.608976 e = 0.00507 De = 0.116085 x 10-5 e = -0.000621 x 10-5

11 29725.899 (22) 0.553502 (54) 1.038 (30) -0.01105 (31)

10 28936.304 (08) 0.557909 (13) 1.096 (04) -0.01072 (17)

9 28139.282 (06) 0.562226 (08) 1.104 (02) -0.01116 (12)

8 27334.844 (05) 0.566540 (06) 1.105 (01) -0.01121 (10)

7 26523.048 (05) 0.570884 (05) 1.114 (01) -0.01094 (10)

6 25703.946 (05) 0.575229 (07) 1.121 (02) -0.01108 (09)

5 24877.478 (04) 0.579596 (05) 1.124 (01) -0.01091 (08)

4 24043 681 (04) 0.584006 (04) 1.135 (01) -0.01093 (07)

3 23202.579 (03) 0.588413 (04) 1.139 (01) -0.01098 (06)

2 22354.163 (03) 0.592853 (03) 1.144 (01) -0.01089 (06)

1 21498.399 (03) 0.597345 (03) 1.153 (01) -0.01097 (05)

0 20635.308 (03) 0.601853 (03) 1.158 (01) -0.01093 (04)

X 2+ state Be = 0.641653 e = 0.00593 De = 0.098542 x 10-5 e = 0.005815 x 10-5

7 6463.107 (07) 0.596839 (15) 1.658 (08) 0.03473 (35) 0.190 (17)

6 5581.933 (05) 0.603110 (07) 1.273 (02) 0.02429 (20) 0.206 (04)

5 4686.685 (04) 0.609176 (04) 1.184 (01) 0.01850 (13) 0.069 (02)

4 3777.517 (04) 0.615111 (04) 1.149 (01) 0.01253 (07) 0.003 (02)

3 2854.208 (03) 0.621018 (03) 1.139 (01) 0.00826 (06) 0.190 (17)

2 1916.854 (03) 0.626874 (03) 1.113 (01) 0.00532 (05)

1 965.455 (03) 0.632692 (05) 1.112 (02) 0.00315 (06) -0.909 (222)

0 0 000 0.63849184 * 1.101 (01) 0.001723* -1.058 (046)

* Kept fixed in our calculations. Values in parentheses are the standard deviations of the constant given in units of the last digit quoted

Graph

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 2 4 6 8 10 12v and v

v'

and

v"

v'

v"

v v' v" 11 -0.01105

10 -0.01072

9 -0.01116

8 -0.01121

7 -0.01094 0.03473

6 -0.01108 0.02429

5 -0.01091 0.0185

4 -0.01093 0.01253

3 -0.01098 0.00826

2 -0.01089 0.00532

1 -0.01097 0.00315

0 -0.01093 0.001723Fig. 5

v' v" This work* Sen Lagerqvist et.al. Mahieu et. al. Coxon & Naxakis

0 0 0.01269 0.0127 0.0127 0.01251 -

1 0 0.01269 0.0139 - 0.01189 -0.01289

0 1 0.01412 0.0130 0.0138 0.01364 -0.01399

1 1 0.01412 0.0142 0.0146 0.01300 -

2 1 0.01412 0.0148 - 0.01338 -0.01428

1 2 0.01629 0.0158 0.0157 0.01292 -0.01587

0 2 0.01629 - 0.0162 0.01354 -0.01573

1 3 0.01923 - 0.0184 0.01540 -0.01864

Table 4: The v'-v" values (in cm-1) of a few bands of B 2+ - X 2+ system.

* For the B2+ state v' = 0.01097 is the average value for v= 0-7 (see table 3)

Table 5: Vibrational constants of the X 2+ and B 2+ states of AlO ( in

cm-1)

State X 2+ B 2+

Te 0.000 20685.041 (23)

e 979.524 (20) 870.369 (18)

exe 7.036 (8) 3.651 (4)

eye -0.00106 (73) 0.00096 (23)

6:

V R G(V)+Y00 Ex Ryd H-H Zavitsas35 1.2976132 1.3068629 1.3166926 1.3272723 1.3388220 1.3516217 1.3660114 1.3825311 1.401988 1.425755 1.456662 1.50267

1.6182 1.768525 1.858468 1.9350211 2.0062914 2.0752317 2.1434120 2.2118123 2.2811826 2.3521329 2.4252232 2.5010135 2.58006

26231.5824647.1122950.6921140.8619216.1617175.1415016.3412738.2910339.557818.65

5174.1342404.545

02404.5455174.1347818.65

10339.5512738.2915016.3417175.1419216.1621140.8622950.6924647.1126231.58

0

5000

10000

15000

20000

25000

30000

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8r(A°)

Po

ten

tial E

nerg

y (

cm-1

)

RKR

ex-Ryd.

H-H

Zavitsas

-5

-3

-1

1

3

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

r(A°)

(UR

KR

– U

)/De*

100)

ex-Ryd.

H-H

Zavitsas

Figure 6 (a): RKR, H-H, Extended- Rydberg& Zavitsas Potential energy curves for the ground state of AlO molecule

Figure 6 (b): % Deviation of H-H, Extended- Rydberg & Zavitsas Potential energy curves for the ground state AlO molecule

29232.1327015.8124797.2

22559.6620286.3417962.5715581.1813128.6510596.817976.7965260.5212439.561

02427.6875216.5647865.79610375.7

12748.1114986.9317096.0719081.2520948.5522704.8724358.03

26000

28539.8826378.1

24224.6822053.4

19848.9717595.7615279.0712888.6510414.477848.5195181.2412403.966

02402.9665171.8787821.10510357.7912788.3315120.0717359.1419511.2321581.8123574.7

25493.3827339.75

29531.4126684.4824070.6521606.0819232.1616906.0414598.8312279.149921.4067498.8654983.5312342.227

02350.39

5041.7157624.97210113.0312512.5614828.2917062.2219216.1221290.3923284.8725199.0427031.29

R % deviation % deviation % deviation1.297611.306861.316691.327271.338821.351621.366011.382531.401981.425751.456661.50267

1.6181.768521.858461.935022.006292.075232.143412.211812.281182.352132.425222.501012.58006

-6.97932-5.50963-4.29501-3.30015-2.48924-1.83156-1.31382-0.90797-0.59838-0.36785-0.20094-0.08145

0-0.05383-0.09869-0.10966-0.08409-0.022820.0684170.1839360.3138030.447320.5717690.6723980.53865

-5.36915-4.02632-2.96333-2.12257-1.47191-0.97837-0.61112-0.34973-0.17426-0.06947-0.016530.001347

00.0036750.005248-0.00571-0.04243-0.11638-0.24128-0.42798-0.68632-1.02566-1.45146-1.96843-2.57762

-7.67546-4.73896-2.60504-1.0821-0.037220.6259480.9711371.0679920.9726110.7438240.4433440.144954

00.1259650.3080080.4504970.5268940.5250650.4373990.2626650.000106-0.34782-0.77732-1.28381-1.86014

BO AlO GaORho u+1 Rho u+1 Rho u+1

• These RPC curves show similarity with the corresponding RKR curves, which is one of the crieteria obeyed by RPC.

• All of them show minima at (1,1) i.e. ρ = 1 and u + 1 = 1. The combined RPC of all these molecules is shown in Fig.6.12.

• The outer most curves are due to GaO as Gallium is heaviest atom compared to Boron and Aluminium; the innermost RPC is of BO.

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

0.5 0.75 1 1.25 1.5 1.75 2 2.25

ρ

u+1

BO

AlO

GaO

Figure 7 The combined Reduced potential curves for the ground state of BO, AlO and GaO molecules

0.66479 1.4337710.684823 1.3670260.70885 1.297124

0.738803 1.2240710.77866 1.147869

0.839652 1.0685241 1

1.222268 1.0685241.360502 1.1478691.480781 1.2240711.594661 1.2971241.706372 1.3670261.818191 1.433771

0.669973 1.4576910.68469 1.411448

0.700772 1.3616190.718953 1.3082150.740298 1.2512460.766609 1.1907220.801503 1.1266510.855287 1.059041

1 11.215627 1.0590411.357516 1.1266511.486762 1.1907221.614478 1.2512461.745219 1.3082151.881911 1.3616192.02704 1.4114482.1831 1.457691

0.669522 1.4469710.683266 1.3994960.698883 1.3492820.717028 1.2962950.738685 1.2404990.765582 1.1818630.801259 1.1203510.855814 1.05593

1 11.20344 1.05593

1.332745 1.1203511.447093 1.1818631.55689 1.240499

1.666012 1.2962951.776599 1.3492821.89006 1.399496

2.007552 1.446971

0

5000

10000

15000

20000

25000

30000

35000

1 1.5 2 2.5 3 3.5r(A°)

Po

ten

tia

l En

erg

y (

cm

-1)

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0 0.5 1 1.5 2 2.5 3 3.5ρ

U+

1

Fig.8 The RKR (a) of AlO and RPC (a')

a a'

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ACKNOWLEDGEMENTS

• We thank Dr. S. M. Sharma, Head, High Pressure Physics Division for access to F.T. spectrometer and Dr. S. C. Sabharwal, Head, Spectroscopy Division for continuous encouragement during the course of this work. The authors are also thankful to Dr. A. V. Venugopalan for many helpful discussions.

• One of us S. H. Behere, is thankful to Dr. N. G. Kotapalle, the Vice chancellor of Dr. B. A. M. University, Aurangabad for financial assistance to attend this conference.

• We are also thankful to Dr. Terry Miller for the hospitality extended to us.

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International Conference on Advances in Computer Vision and Information Technology

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