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
measurements is not possible because
band
head
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 A2Pi
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 A2Pi 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 2mm. 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 Dv = 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/P1doublets, 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) = N/2 + s1N(N+0.5)(N+1) - s2 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 bandheads are excluded the vibrational expression becomes
accurate.
• The anomalous spin-doubling in the X 2+ state,
caused due to the interaction of the A 2Pi 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 2Pr
state with B 2+ state.
Table 1: Measurements of the bands of B 2+ - X 2+ transition (in cm-1)
Dv = +4
Dv = +3
Sr.No.
v - v
R2 head
N†
R1 head
N†
D
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
5
(9,5)
23460.083*
12
23459.717*
11
0.366
6
(10,6)
23362.057*
12
23361.600*
12
0.457
7
(11,7)
23270.735*
12
23270.145*
12
0.590
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
12
(7,4)
22753.627*
13
22753.321*
12
0.306
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
* These are calculated positions, † rotational number N, where head is
formed.
Table continued…..
Dv = +2
Dv = -2
Dv = -1
Sr.No.
v - v
R2 head
N†
R1 head
N†
D
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
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
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
Table 2: Vacuum wavenumbers and rotational line assignments of
B2+- X2+ transitions of AlO.
R1
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
22.0
23.0
24.0
25.0
20643.727(-12)
20643.155(-11)
20642.507(-12)
0-0 band
P1
R2
20632.729( 56)
20631.298( 54)
20629.806( 65)
20628.239( 75)
20626.597( 82)
20624.759(-34)
20622.966(-31)
20621.098(-30)
20619.155(-31)
20617.151(-20)
20615.057(-27)
20612.902(-20)
20610.657(-31)
20608.352(-29)
20605.972(-29)
20603.531(-17)
20601.000(-22)
20598.408(-15) 20645.580( 35)
20595.742(-09) 20645.309( 27)
20590.182(-05) 20644.586( 53)
20587.290(-06) 20644.074( 27)
20584.322(-10) 20643.486(-01)
20581.278(-17) 20642.854( 01)
P2
20632.729( 35)
20631.298( 21)
20629.806( 19)
20628.239( 16)
20626.597( 11)
20624.880( 03)
20623.102( 08)
20621.234(-03)
20619.305(-03)
20617.301(-05)
20615.237( 06)
20613.083( 01)
20610.868( 07)
20608.563(-04)
20606.198(-01)
20603.757(-02)
20601.256( 11)
20598.665( 06)
20595.998(-01)
20590.469( 08)
20587.591( 08)
20584.638( 07)
20581.610( 03)
26.0
27.0
28.0
29.0
30.0
31.0
32.0
33.0
34.0
35.0
36.0
37.0
38.0
39.0
40.0
41.0
42.0
43.0
44.0
45.0
46.0
47.0
48.0
R1
20641.784(-13)
20640.985(-16)
20640.112(-19)
20639.177(-08)
20638.153(-12)
20637.053(-18)
20635.893(-08)
20634.643(-14)
20633.332(-05)
20631.931(-12)
20630.469(-05)
20628.917(-12)
20627.305(-04)
20625.618( 04)
20623.840(-03)
20622.002( 05)
20620.074(-02)
20618.070(-09)
20615.991(-15)
20613.851(-06)
20611.621(-12)
20609.331(-02)
20606.951(-05)
0-0 continued
P1
R2
20578.175(-10) 20642.130(-14)
20574.996(-05) 20641.362( 02)
20571.726(-19) 20640.503( 01)
20568.397(-19) 20639.584( 14)
20565.007(-06) 20638.575( 13)
20561.526(-12) 20637.490( 10)
20557.986(-03) 20636.330( 06)
20554.355(-13) 20635.095( 03)
20550.664(-09) 20633.784(-01)
20546.897(-09) 20632.398(-05)
20543.055(-10) 20630.951( 04)
20539.138(-13) 20629.415( 00)
20535.146(-18) 20627.803(-04)
20531.108( 05) 20626.130( 05)
20526.965(-05) 20624.367( 00)
20522.746(-17) 20622.529(-05)
20518.467(-16) 20620.616(-09)
20514.128(-02) 20618.642( 02)
20509.699(-05) 20616.578(-02)
20505.194(-10) 20614.439(-05)
20500.629(-02) 20612.224(-08)
20495.989( 04) 20609.934(-11)
20491.273( 08) 20607.569(-12)
P2
20578.506(-03)
20575.342( 04)
20572.088(-07)
20568.773(-05)
20565.383(-05)
20561.918(-08)
20558.393( 03)
20554.777(-04)
20551.101( 02)
20547.334(-10)
20543.500(-16)
20539.620( 06)
20535.643( 03)
20531.590(-02)
20527.477( 05)
20523.273(-05)
20519.010( 00)
20514.671( 01)
20510.241(-15)
20505.767(-02)
20501.202(-07)
20496.576( 01)
20491.861(-07)
49.0
50.0
51.0
52.0
53.0
54.0
55.0
56.0
57.0
58.0
59.0
60.0
61.0
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
70.0
71.0
72.0
R1
20604.495(-09)
20601.964(-11)
20599.373( 02)
20596.691( 02)
20593.919(-13)
20591.101( 03)
20588.194( 06)
20585.195(-05)
20582.137( 00)
20579.003( 07)
20575.764(-14)
20572.480(-04)
20569.120( 08)
20565.670( 06)
20562.144( 06)
20558.450(-85)
20554.777(-77)
0-0 continued
P1
R2
20486.467(-05) 20605.143( 02)
20481.600(-06) 20602.612(-14)
20476.674( 08) 20600.020(-13)
20471.657( 05) 20597.369( 04)
20466.564(-02) 20594.612(-08)
20461.412( 07) 20591.794(-05)
20456.169(-02) 20588.887(-14)
20450.865( 01) 20585.919(-08)
20445.487( 04) 20582.860(-15)
20440.033( 04) 20579.742(-05)
20434.504( 04) 20576.532(-10)
20428.899( 00) 20573.263( 02)
20423.219(-04) 20569.903( 01)
20417.479( 05) 20566.453(-13)
20411.663( 12) 20562.943(-10)
20405.757( 03) 20559.357(-05)
20399.791( 07) 20555.681(-13)
20393.750( 11) 20551.944(-05)
20387.648( 27) 20548.133( 07)
20381.441( 12) 20544.215(-10)
20375.173( 10)
20368.830( 06)
20362.412( 02)
20355.919(-03)
P2
20487.085(-03)
20482.233(-01)
20477.307( 00)
20472.305(-01)
20467.227(-05)
20462.075(-09)
20456.847(-16)
20451.559(-09)
20446.195(-05)
20440.741(-17)
20435.242(-01)
20429.652(-01)
20423.987(-04)
20418.247(-07)
20412.432(-12)
20406.571( 11)
20400.590(-12)
20394.563(-07)
20388.446(-19)
20382.284(-01)
20376.017(-15)
20369.689(-16)
20363.316( 12)
20356.853( 24)
R1
73.0
74.0
75.0
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
84.0
85.0
86.0
87.0
88.0
89.0
90.0
91.0
92.0
93.0
94.0
95.0
0-0 continued
P1
R2
20349.365( 05)
20342.736( 11)
20336.016( 01)
20329.251( 20)
20322.381( 08)
20315.451( 09)
20308.445( 09)
20301.364( 09)
20294.192(-09)
20286.961(-12)
20279.684( 14)
20272.301( 07)
20264.875( 32)
20257.341( 23)
20249.687(-31)
20242.079( 34)
20234.300( 03)
20226.500( 25)
20218.590( 11)
20210.590(-19)
20202.540(-24)
20194.470( 25)
20186.258( 06)
P2
20350.269(-11)
20343.594(-63)
20336.950(-10)
20330.155(-34)
20323.330(-14)
20316.430( 06)
20309.439( 08)
20302.373( 10)
20295.202(-20)
20287.985(-21)
20280.750( 34)
20273.356( 04)
20265.913(-01)
20258.395(-07)
20250.817( 02)
20243.163( 09)
20235.389(-30)
20227.600(-10)
20219.705(-21)
20211.796( 27)
20203.720(-17)
20195.660( 30)
20187.419(-31)
R1
96.0
97.0
98.0
99.0
100.0
101.0
102.0
103.0
104.0
105.0
106.0
107.0
0-0 continued
P1
R2
20178.002( 17)
20169.656( 12)
20161.219(-09)
20152.721(-17)
20144.134(-41)
20135.546( 09)
20126.800(-25)
20118.000(-38)
20109.190( 12)
20100.300( 56)
20091.206(-30)
20082.160( 06)
P2
20179.208( 12)
20170.846(-21)
20162.499( 35)
20153.930(-57)
20145.391(-45)
20136.800(-10)
20128.125( 14)
20119.380( 42)
20110.500( 10)
20092.600( 27)
Table 3: Molecular constants (in cm-1) of B 2+ and X 2+ state of
AlO.
v
Tv
B 2+ state
Bv
Be = 0.608976
Dv x 106
e = 0.00507
v
De = 0.116085 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
sv x 105
De = 0.098542 x 10-5
H x 1012
e = -0.000621 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
0.04
v"
0.03
v'
0.02
and
v" 0.01
0
0
-0.01
2
4
6
v and v
8
v'
-0.02
Fig. 5
10
12
v
11
10
9
8
7
6
5
4
3
2
1
0
 v '
 v"
-0.01105
-0.01072
-0.01116
-0.01121
-0.01094
0.03473
-0.01108
0.02429
-0.01091
0.0185
-0.01093
0.01253
-0.01098
0.00826
-0.01089
0.00532
-0.01097
0.00315
-0.01093 0.001723
Table 4: The v'-v" values (in cm-1) of a few bands of B 2+ - X 2+ system.
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
* 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
35
32
29
26
23
20
17
14
11
8
5
2
30000
Potential Energy (cm -1)
25000
20000
15000
10000
RKR
ex-Ryd.
5000
H-H
Zavitsas
0
1
1.2
1.4
1.6
1.8
2
r(A°)
2.2
2.4
2.6
2.8
(URKR – U)/De*100)
Figure 6 (a): RKR, H-H, Extended- Rydberg& Zavitsas Potential energy
curves for the ground state of AlO molecule
3
1
-1 1
1.2 1.4
1.6
1.8
2
2.2
2.4 2.6
2.8
ex-Ryd.
-3
-5
H-H
Zavitsas
r(A°)
Figure 6 (b): % Deviation of H-H, Extended- Rydberg & Zavitsas Potential
energy curves for the ground state AlO molecule
2
5
8
11
14
17
20
23
26
29
32
35
R
1.29761
1.30686
1.31669
1.32727
1.33882
1.35162
1.36601
1.38253
1.40198
1.42575
1.45666
1.50267
1.618
1.76852
1.85846
1.93502
2.00629
2.07523
2.14341
2.21181
2.28118
2.35213
2.42522
2.50101
2.58006
G(V)+Y00
26231.58
24647.11
22950.69
21140.86
19216.16
17175.14
15016.34
12738.29
10339.55
7818.65
5174.134
2404.545
0
2404.545
5174.134
7818.65
10339.55
12738.29
15016.34
17175.14
19216.16
21140.86
22950.69
24647.11
26231.58
R
1.29761
1.30686
1.31669
1.32727
1.33882
1.35162
1.36601
1.38253
1.40198
1.42575
1.45666
1.50267
1.618
1.76852
1.85846
1.93502
2.00629
2.07523
2.14341
2.21181
2.28118
2.35213
2.42522
2.50101
2.58006
Ex Ryd
29232.13
27015.81
24797.2
22559.66
20286.34
17962.57
15581.18
13128.65
10596.81
7976.796
5260.521
2439.561
0
2427.687
5216.564
7865.796
10375.7
12748.11
14986.93
17096.07
19081.25
20948.55
22704.87
24358.03
26000
% deviation
-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
-0.02282
0.068417
0.183936
0.313803
0.44732
0.571769
0.672398
0.53865
H-H
28539.88
26378.1
24224.68
22053.4
19848.97
17595.76
15279.07
12888.65
10414.47
7848.519
5181.241
2403.966
0
2402.966
5171.878
7821.105
10357.79
12788.33
15120.07
17359.14
19511.23
21581.81
23574.7
25493.38
27339.75
% deviation
-5.36915
-4.02632
-2.96333
-2.12257
-1.47191
-0.97837
-0.61112
-0.34973
-0.17426
-0.06947
-0.01653
0.001347
0
0.003675
0.005248
-0.00571
-0.04243
-0.11638
-0.24128
-0.42798
-0.68632
-1.02566
-1.45146
-1.96843
-2.57762
Zavitsas
29531.41
26684.48
24070.65
21606.08
19232.16
16906.04
14598.83
12279.14
9921.406
7498.865
4983.531
2342.227
0
2350.39
5041.715
7624.972
10113.03
12512.56
14828.29
17062.22
19216.12
21290.39
23284.87
25199.04
27031.29
% deviation
-7.67546
-4.73896
-2.60504
-1.0821
-0.03722
0.625948
0.971137
1.067992
0.972611
0.743824
0.443344
0.144954
0
0.125965
0.308008
0.450497
0.526894
0.525065
0.437399
0.262665
0.000106
-0.34782
-0.77732
-1.28381
-1.86014
1.45
1.4
BO
AlO
Rho
u+1
0.66479
0.684823
0.70885
0.738803
0.77866
0.839652
1
1.222268
1.360502
1.480781
1.594661
1.706372
1.818191
1.433771
1.367026
1.297124
1.224071
1.147869
1.068524
1
1.068524
1.147869
1.224071
1.297124
1.367026
1.433771
1.35
1.3
u+1
1.25
1.2
1.15
Rho
0.669522
0.683266
0.698883
0.717028
0.738685
0.765582
0.801259
0.855814
1
1.20344
1.332745
1.447093
1.55689
1.666012
1.776599
1.89006
2.007552
u+1
1.446971
1.399496
1.349282
1.296295
1.240499
1.181863
1.120351
1.05593
1
1.05593
1.120351
1.181863
1.240499
1.296295
1.349282
1.399496
1.446971
GaO
Rho
u+1
0.669973 1.457691
0.68469 1.411448
0.700772 1.361619
0.718953 1.308215
0.740298 1.251246
0.766609 1.190722
0.801503 1.126651
0.855287 1.059041
1
1
1.215627 1.059041
1.357516 1.126651
1.486762 1.190722
1.614478 1.251246
1.745219 1.308215
1.881911 1.361619
2.02704 1.411448
2.1831
1.457691
BO
1.1
AlO
1.05
GaO
•
1
0.5
0.75
1
1.25
1.5
1.75
2
2.25
ρ
Figure 7 The combined Reduced potential curves for the
ground state of BO, AlO and GaO molecules
•
•
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.
1.8
30000
1.7
25000
1.6
-1
Potential Energy (cm )
35000
1.5
U+1
20000
1.4
15000
1.3
10000
1.2
5000
1.1
0
1
1
1.5
2
2.5
r ( A °)
3
3.5
0
0.5
1
1.5
2
2.5
ρ
a
a'
Fig.8 The RKR (a) of AlO and RPC (a')
3
3.5
References:
[1] Mecke R., Phys. Zeits. 26 (1925) 217-225.
[2] W. C. Pomeroy, Phys. Rev. 29 (1927) 59-78.
[3] F.P. Dehalu, Bull. Acad. Roy. Belgium 23 (1937) 604-608.
[4] M. K. Sen, Ind. J. Phys. 11 (1937) 251-281.
[5] D. C. Roy, Ind. J Phys. 13 (1939) 231.
[6] F. P. Coheur, B. Rosen, Mem. Soc. Roy Sci. Liege 10 (1941)
405-413.
[7] B. Rosen, Phys. Rev., 68 (1945) 124-126.
[8] A. Lagerqvist, N.E.L. Nilson, R.F. Barrow, Proc. Phys. Soc.
(Lon) 69 (1956) 356-357
[9]
A. Lagerqvist, N.E.L. Nilson, R.F. Barrow, Arkiv Fysik 12
(1957) 543-546.
[10] M. Shimauchi, Sci. Light (Japan) 7 (1958) 101-111.
[11] V. W. Goodlett, K. K. Innes, Nature (London) 183 (1959) 243244.
[12] P. W. Merrill, A. J. Deutsch, P. C. Keenan, Ap. J. 136 (1962), 2134.
[13] B. Authier, J. E. Blamont, G. Carpentier, Ann. Geophys. 20
(1964) 342-345.
[14] O. Harang, Planet Space Sci. 12 (1964) 567-571.
[15] R. E. Johnson, J. Geophys. Res. 70 (1965) 1275-1277.
[16]
P. C. Keenan, A. J. Deutsch, R. F. Garrison, The Astro. J. 158
(1969) 261-268.
[17] J. K. McDonald, K. K. Innes, J. Mol. Spectrosc. 32 (1969) 501510.
[18] J. K. McDonald, V. W. Goodlett, T. W. Tolbert, J. Mol. Spectrosc.
32 (1969) 511-512.
[19] J Schamps, Chem. Phys. 2 (1973) 352-366
[20] J. M. Mahieu, D. Jacquinot, J. Schamps, J.A. Hall, J. Phys. B
At. Mol. Phys. 8 (1975) 308-312.
[21]
R.W. Nicholls, Annu. Rev. Astron. Astrophys., 15 (1977) 197234.
[22] M. Singh, M.D. Saksena, Can. J. Phys. 61 (1983) 1347- 1358.
[23] A. Bernard, R. Gravina, Z. Naturforsch 39a (1984) 1049-1055.
[24] A.P. Walvekar, M.A. Rama, Ind. J Pure and Applied Phys., 22
(1984) 53-55.
[25] M. Singh, M.D. Saksena, Can. J. Phys. 63 (1985) 1162- 1172.
[26] M. Singh, G.V. Zope and S.L.N.G. Krishnamachari, J. Phys. B
At. Mol. Phys. 18 (1985) 1743-1745.
[27] J. A. Coxon, S. Naxakis, J. Mol. Spectrosc. 111 (1985) 102-113.
[28] M. D. Saksena, G. S. Ghodgaonkar, M. Singh, J. Phys. B At.
Mol. Phys. 22 (1989) 1993-1996.
[29] C. Yamada, E. A. Cohen, M. Fujitake, E. Hirota, J. Chem.
Phys., 92(4) (1990) 2146-2149
[30] O. Launila, J. Jonsson, J. Mol. Spectrosc. 168 (1994) 1-38.
[31] R. S. Mulliken, Rev. Mod. Phys. 3 (1931) 89-155.
[32] G. Hertzberg, ‘Molecular Spectra and Molecular Structure,
Vol. 1, Spectra of Diatomic Molecules,’, Van Nostrand,
NY,1950.
[33] Rydberg R, Z Phys, 73,376 (1932)
[34] Rydberg R, Z Phys, 80,514 (1933)
[35] Klein O, Z Phys, 76,226 (1932)
[36] Rees A L G, Proc Phys Soc., 59,998 (1947)
[37] Vanderslice J T, Meson E A, Maisch W G and Lippincott E R,
J. Chem. Phys., 33,614 (1960)
[38] Vanderslice J T, Meson E A, Maisch W G and Lippincott E R,
J. Mol. Spectrosc., 3,17 (1959) and 5, 83 (1960)
[39] R. R. Reddy et al Astrophysics & Space Sci. 262: 223 (1999)
[40]
A. Sharma J. Quant. Spectrosc. Radiat. Transfer , 7,23, 283
(1967)
[41] Chakraborty B. and Pan Y. K., Applied spectroscopy Review, 7,
283 (1973)
[42] Sharp C. M., Astron. Astrophys. Suppl. Ser., 55, 33 (1984)
[43] Nicholls R. W., J. Quant. Spectrosc. Radiat. Transfer, 28, 481
(1982)
[44]
W. R. Jarmain and J. C. McCallum, J. Quant. Spectrosc.
Radiat. Transfer, 11, 421 (1971)[
[45] Jarmain W R and Nicholls R W, J. Quant. Spectrosc. Radiat.
Transfer; 23, 229-235 (1980)
[46]
Hulbert H M and Hirschfelder J O, J. Chem. Phys., 9, 61,
(1941) ibid 35, 1901 (1961)
[47]
Morse P M, Phys., Rev., 34, 57 (1929)
[48]
Murrell J N and Sorbie K S, Faraday, Tranjections, 70,
1152 (1974)
[49] Huxely P and Murrell J N, J. Chem. Soc. Faraday, 7A, part
2, 323 (1983)
[50] Zavitsas A A, American chem. soc., 113, 13, 4755 (1991)
[51] Jenc F and Brandt B A, J. Mol. Spectrosc., 165, 590 (1994)
[52] Le Roy R J, Uni. of waterloo, Chem., Phys. Research report
CP-425 (1992)
[53] Castano J de Juan and Martinez E, J. Chem., Edu., 60, 291
(1983)
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.
Glimpses of Aurangabad
and around
International Conference on Advances in Computer Vision
and Information Technology
November 28 – 30, 2007
Organized by
Department of Computer Science & Information Technology
Dr. Babasaheb Ambedkar Marathwada University,
Aurangabad (MS) 431004 India.
Details on website: www.bamu.net
www.acvit.org
International conference on Microwaves and Optoelectronics
December 17 – 20, 2007
Organized by
Department of Computer Science & I. T.
And
Department of Physics
Dr. Babasaheb Ambedkar Marathwada University, Aurangabad
(MS) 431004 India.
Details on web site: www.icmo2007.org
Wel-Come
Dr. Babasaheb Ambedkar Marathwada University,
Aurangabad.