IC/2001/36
United Nations Educational Scientific and Cultural Organization
and
International Atomic Energy Agency
THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS
ULTRAVIOLET BANDS OF POTASSIUM DIMER
K. Ahmed 1
Spectroscopy Research Laboratory, Department of Physics, University of Karachi,
Karachi-75270, Pakistan
and
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy,
LA. Khan and S.S. Hassan
Spectroscopy Research Laboratory, Department of Physics, University of Karachi,
Karachi- 75270, Pakistan.
Abstract
The ultraviolet band spectra of potassium dimer have been investigated. The studies were
performed in absorption in the second order of a 3.4 m Ebert spectrograph with a reciprocal
dispersion of 2.6 A/mm. A number of new bands in the electronic states G and H not previously
reported have been observed. The vibrational analysis is performed and molecular constants are
evaluated.
MIRAMARE - TRIESTE
May 2001
1
Regular Associate of the Abdus Salam ICTP. E-mail: [email protected]
1. Introduction
Potassium is the second most abundant matter present in the earth's crust and is desired to
be investigated heavily. In comparison with the other homonuclear alkali dimers,
potassium molecule is the least investigated by the spectroscopists. During the past
decade, important experimental efforts have been devoted to the laser spectroscopy of the
ground gerade and ungerade excited states (in moderate energy range) of K2 dimer.
Different laser spectroscopic techniques such as single photon absorption were used and
many excited states have been characterized experimentally [1-4]. Only, the Stwalley
research group has observed a number of gerade high lying excited states in UV region
by optical-optical double resonance technique [5]. Up till now, the experimentally
available information regarding electronic states of potassium molecule is not
satisfactory, because of the so many discrepancies present in the experimentally observed
and theoretically predicted result [6]. Due to lack of available UV tunable laser sources, it
is difficult for laser spectroscopists to investigate Rydberg ungerade states in UV region
of these molecules. Therefore, one has to depend on the conventional absorption
spectroscopic methods to investigate the electronic states near the ionization potential of
potassium dimer.
Potassium molecule has been studied since 1930's. First of all, Yoshinaga [7]
worked in UV region and performed the vibrational analysis of the bands observed in
absorption. Later, Sinha [8] worked in the same region and concluded that previous work
was not satisfactory but he did not perform vibrational analysis. In our previous reported
work [9,10] we observed new electronic transition named H—X system and later we also
found some new bands in the F—X and G—X (designated as systems IV and V by
Yoshinaga [7] respectively). In the present work, we have observed new data regarding
potassium dimer, while we were trying to record the spectra of KLi molecule. The
present paper describes the work extended in G—X and H—X transitions. These new
bands are observed due to less miscible property of lithium atoms. The analysis has been
performed to evaluate improved molecular constants.
2. Experimental
The vapor of potassium molecules was generated by heating spectroscopically pure,
lithium and potassium metal loaded with a ratio 1:6 inside a 1.5 meter long stainless steel
tube in an atmosphere of argon gas at 300 torr. This tube was directly heated by a high
current low voltage transformer providing 950 A at 10 V. Before introducing the sample
in the tube, it was thoroughly evacuated and was heated to about 200 °C. Later, the
loaded furnace was heated to a temperature of 750 °C. Both ends of the furnace tube were
water cooled to avoid vapor condensation at the quartz windows.
The ultraviolet absorption spectrum of potassium molecule was photographed in
second order of a 3.4 m Ebert spectrograph equipped with 1200 lines/mm plane grating.
The background source of radiation was a 450 W high-pressure xenon arc lamp. The
spectra were recorded on the Q-2 plates at 2.6 A/mm reciprocal dispersion with an
exposure time of about two hours. The photo-densitometer trace of the recorded
absorption spectrum covering the wavelength region 320 to 337 nm is shown in Fig.-l.
The wavelength calibration was achieved by superimposing the iron arc spectrum,
which possesses sharp lines covering this spectral region. The measurements of the band
heads were made on Zeiss Abbe comparator by comparison with iron arc lines to an
accuracy of ±0.2 A. The wavelengths were calculated using Chebychev polynomial fit of
comparator readings with the reference iron lines. The iron wavelengths have been
marked from MIT tables [11]. The vacuum wavenumbers of the wavelengths were
obtained by a computer program using Edlen's dispersion formula [12].
3. Results and Discussion
The spectrum was photographed in the region 320 to 360 nm. It revealed new vibrational
bands in G—X and H—X systems of K2 molecule. Actually, we were interested to record
the new electronic states of KLi molecule in the UV-region, will be submitted for
publication in future. Due to the less miscible property of lithium [13], we also observed
a number of bands of G—X and H—X systems of K2 molecule. A number of bands
belong to H—X system in the region 320 to 337 nm along with Lithium (2S-3P) and
potassium (4S-7P) atomic transitions can be seen in the spectrum Fig.-l. A large number
of bands of good quality are obtained in both transitions. This is also due to the improved
design of the absorption column and suitable experimental conditions in comparison of
our previous work [9, 10]. Thermally only three vibrational levels in the ground state
were able to populate. We have observed a total of 83 bands in the region 320 to 360 nm
belonging to G—X and H—X systems of K2 dimer (Fig.-l).
The G—X system: In the region 340 nm to 360 nm a total 40 bands of G—X system of K2
molecule have been observed out of which 11 bands are new (Fig.-l). The band heads of
similar intensity are found to belong to mainly three distinct sets of red degraded bands
indicating that these bands mainly belong to three progressions (v1, 0), (v1, 1) and (v1, 2).
The general appearance of the band heads helps in making the tentative assignment of
vibrational numbers v', v" to the bands. Later, the exact assignment of vibrational
quantum numbers to the band heads is conveniently done by the already assigned values
of reported bands in literature [7-10]. Table-1 shows the assignment of the newly
observed band heads.
The term values of the upper vibrational state are constructed for all observed
bands using the data of the X ground vibrational state [14, 15] and is presented in Table 2. The vibrational quantum numbers as well as the vibrational constants are determined
by using the computer methods incorporating least square fit to find the values of Te, cue,
toexe, etc. for the G and H states. The relation [16] used is:
T = Te
The vibrational quantum number of the upper state is allowed to vary until the residual
variance becomes minimum. The values of AG(v+l/2) obtained in both progressions
agree within the accuracy of measurements (Tables-3 and 4). The vibrational constants
obtained are compared with those of previously reported [7,9,10] work and are listed in
Table-5.
The H—X transition: we have recorded 43 bands in the region 320 to 342 nm, the bands
of all these systems are red degraded and the bands of this system have been found to
belong to (v\ 0) and (v\ 1) progressions (Fig.-l). The progression belonging to (v1, 0)
bands lie at the same frequencies as those of previously reported work (Rafi et al. [9]). It
has provided an extension in the vibrational progression (v', 1) and thus newly observed
23 bands along with previously reported bands are presented in Table-6. There are few
band heads that could not be measured reliably. These band heads are therefore not
reported. The upper state terms are built by adding wave numbers of the band heads to X
ground vibrational level [14,15] Table-4. The vibrational assignment and evaluation of
constants were made in a manner as described in the case of G-X bands of potassium
dimer. The vibrational constants are compared with those of previous work and given in
(Table-5).
The D e of the X ground state of K2 molecule is estimated to be 4451 ±1.5 cm"1
[14], which is correlating it with the separated ground atomic states K(42S)+K(42S). The
correlation diagram is already presented and discussed in previous work of Rafi et. al [9].
The K2 excited molecular G and H states are comfortably correlated with the excited
atomic states K(52P)+K(42S) and K(42D)+K(42S) respectively [9]. These atomic states
have the average energies of 24710.82 cm"1 and 29003.50 cm"1 respectively. The
dissociation energies De of both G and H excited states of K2 dimer can be determined
from the correlation diagram using the following relation (Table-6).
De = De + rLs (atomic states) - Te
The dissociation energies are also calculated using the Birge-Sponer formula for
both states and are shown in Table-6 [16]:
4ft)
The dissociation energy De of the G state using correlation diagram is less than Birgesponer formula (BSF). The correlation-diagram suggests, the maximum vibration
quantum number of 20 that can be observed whereas we have seen vibrational band up to
v'=15. In Figure-2 AG versus band number v' has been plotted for both the G and H states
of potassium molecule. It is seen that G state has larger slope than for the H state. The
extrapolation is supported by the calculated value for G state which suggests the
dissociation at v'=20.
For the H state of K2 molecule the dissociation energy D e calculated using BSF is
quite large in comparison of correlation diagram value Table-6. The correlation diagram
in Rafi et. al [9] suggest the largest vibrational quantum number of 33 whereas we have
seen vibrational bands for v' up to 22. The extrapolation (in Figure-2) is also supported
by the calculated value using the available vibrational constants for H state which gives
dissociation around v=33.
Our analysis indicates both G and H states are not perturbed or predissociated by
other neighbouring states. The reduced mass of the K2 molecule is quite large, so the
rotational structure is very close and congested and could not be resolved under the
present experimental facilities. To get more information about rovibrational structure and
precise values of dissociation energies of G and H states of K2 dimer, high-resolution
spectroscopy is desired.
Acknowledgments
We acknowledge the Pakistan Science foundation for the financial assistance to carry out
this work under research grant S-KU-Phys(72). We are indebted to Professor M. A. Baig,
Department of Physics, Quaid-I-Azam University, Pakistan for the use of photodensitometer. We are grateful Professor Dr. M. Rafi for his enthusiasm, initiating this
experiment and useful discussion during this analysis. K. Ahmed also thanks the Abdus
Salam ICTP, Trieste, Italy for giving the opportunity to visit the centre under the regular
associate-ship program and for using the library facilities during writing the manuscript
of this article.
References
[I] Kowalczyk P, Katern A and Engelke F 1990 Z. Phys. D, 17, 47
[2] Jastrzebskib W and Kowalczyk P 1993 Chem. Phys. Lett. 206 69
[3] Jastrzebski W and Kowalczyk P 1994 Chem. Phys. Lett. 227 283
[4] L. Li L, Lyrra A M, Luh T H and Stwalley W C 1990 J. Chem. Phys. 93(12) 845:
Jong G, Li L, Whang T J, and Stawlley W C 1992 J. Mol. Spectrosc. 1992 155 115
[5] Kim J T, Tsai C C and Stwalley W C 1995 J. Mol. Spectrosc. 171, 200
[6] Magnier S and Millie Ph., 1996 Phys. Rev. 54(1), 204
[7] Yoshinaga M, Proc. Phys. Math. Soc. Jpn. 1937 19,847
[8] Sinha S P 1947 Proc. Phys. Soc. Lond. 59 610
[9] Rafi M, Ahmed K, Khan I A and Husain M R 1991 Z. Phys. D. 18, 379
[10] Rafi M, Naqvi S M, Jahangir S, Mahmood S and Khan I A 1993 Z. Phys. D. 27 61
[II] Harrison G H, M.I.T. Tables 1959 (New York, N.Y.)
[12] Edlen B 1953 J. Opt. Soc. Am. 53 339
[13] Breford E J, Engelke F 1979 J. Chem. Phys. 71(5) 1994
[14] Amiot C 1991 J. Mol. Spectrosc, 146, 370
[15] Ross A J, Crozet P, D'Incan J and Effantin C 1986 J. Phys. B. 19L 145
[16] G. Herzberg, Molecular spectra and molecular structure 1950 (Van Nostrand New
York, N. Y.).
Table-1. Term values (in cm"1) of G—X system of K2 molecules.
Excited
state
(v)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Ground State (v")
0
28127.4
189.4
251.2
312.9
371.1
430.7
489.2
544.5
599.7
658.4
710.4
763.7
815.0
867.0
916.9
28126.6
189.9
249.8
312.4
370.0
429.1
488.9
543.8
600.2
656.5
711.5
764.3
815.6
865.5
916.7
965.7
28126.5
187.5
249.2
Average
28126.1
371.9
488.8
543.7
656.5
710.8
28126.6
188.9
249.9
312.6
371.0
429.9
488.9
544.0
599.9
657.1
710.9
764.0
815.3
866.2
916.8
965.7
Table-2. Term values (in cm"1) of H—X system of K2 molecules.
Excited state
(V)
o
w
i
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Ground state (v")
0
1
7Q96Q 1
10
l y
20
21
22
9Q96Q 1
±*yL\jy. 1
349.2
428.6
508.3
589.5
669.5
750.4
830.5
910.3
989.0
30068.6
146.7
227.1
306.2
383.0
461.2
540.1
617.3
693.5
847.1
924.2
Average
29351.2
430.9
510.1
591.0
672.3
752.4
832.8
912.9
991.3
30069.7
148.9
227.9
307.0
383.9
462.3
540.5
617.8
694.5
350.2
429.7
509.2
590.2
670.9
751.4
831.6
911.6
990.1
30069.1
147.8
227.5
306.6
383.4
461.7
540.3
617.5
694.0
770 S
/ / w.o
770
8
/ / yj.o
846.7
922.8
998.5
846.9
923.5
998.5
Table-3. Band head positions of G—X system of K2 molecules.
(v',v")
Wavelength
A
V) ( )
(0,0)
3560.0
3552.1
(1,0)
3544.4
(2,0)
3536.7
(3,0)
3529.3
(4,0)
3522.0
(5,0)
3514.7
(6,0)
3507.9
(7,0)
3501.2
(8,0)
3593.1
(9,0)
3487.5
*(10,0)
3481.2
*(H,0)
3474.9
*(12,0)
3468.7
*(13,0)
3462.7
*(14,0)
3571.8
(0,1)
3563.7
(1,1)
3556.1
(2,1)
3548.2
(3,1)
3540.9
(4,1)
3533.6
(5,1)
3526.1
(6,1)
3519.3
(7,1)
3512.3
(8,1)
3505.4
(9,1)
3498.8
(10,1)
3492.2
*(H,1)
3485.1
*(12,1)
3479.9
•(13,1)
3473.7
*(14,1)
3467.8
*(15,1)
3583.4
(0,2)
3575.6
(1,2)
3567.5
(2,2)
3552.1
(4,2)
3537.5
(6,2)
3530.6
(7,2)
3516.6
(9,2)
(10,2)
3509.9
3595.1
(0,3)
* Observed new bands
Wavenumber (obs.)
v(vac) (cm"1)
28081.5
143.4
205.2
266.9
326.0
384.8
443.3
498.6
553.7
723.1
665.5
717.7
769.0
821.1
871.0
27989.2
28052.5
112.4
175.0
232.6
291.7
351.5
406.4
462.8
519.0
572.1
626.8
678.2
728.1
779.3
828.3
27898.2
959.0
28022.9
143.6
260.2
315.5
428.7
482.5
27807.5
10
Wavenumbers
(calc.) v(vac) (cm"1)
28080.5
143.2
204.1
265.8
325.6
384.4
442.3
499.3
555.3
723.3
664.3
717.4
769.5
820.7
870.9
27989.0
28051.8
113.5
174.3
234.1
293.0
350.9
407.8
463.8
518.8
572.9
625.1
678.1
729.3
779.5
828.7
27898.2
960.9
28022.6
143.2
259.9
316.9
427.9
482.0
27807.8
Table-4. Band head positions of H—X system of K2 molecules.
(v\v")
Wavelength
*<*) (A)
(0,0)
(1,0)
(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)
*(20,0)
•(21,0)
3420.9
3411.6
3402.4
3392.2
3383.7
3374.7
3365.5
3356.4
3347.5
3338.7
3329.9
3321.2
3312.3
3303.7
3295.3
3286.9
3278.4
3270.0
3261.1
3245.6
3237.5
3422.0
•0,1)
3412.7
*(2,1)
3403.5
*(3,1)
3394.2
*(4,1)
3384.8
*(5,1)
3375.7
*(6,1)
3366.5
•(7,1)
3357.5
•(8,1)
3348.7
*(9,1)
3339.9
•(10,1)
3331.1
*(1.1,1)
3322.3
*(12,1)
3313.6
*(13,1)
3305.2
*(14,1)
3296.6
•(15,1)
3288.2
*(16,1)
3279.8
*(17,1)
3271.6
*(18,1)
3263.5
*(19,1)
3255.4
•(20,1)
3247.3
*(21,1)
*(22,1)
3239.4
* Observed new bands
Wavenumber (obs.)
V(vaC) (cm')
29223.2
303.3
382.7
462.2
544.6
623.6
704.5
784.5
864.4
943.2
30022.6
100.8
181.2
260.3
337.1
415.3
494.2
571.4
647.6
802.0
878.3
29213.8
293.5
373.6
453.6
534.8
614.1
695.4
775.5
853.9
932.3
30011.5
090.5
169.7
246.5
324.9
403.1
480.4
557.0
633.5
694.9
785.4
861.1
11
Wavenumbers
(calc.) v(vac) (cm"1)
29223.3
303.6
383.9
464.3
544.9
624.8
704.5
784.8
864.6
944.2
30023.5
102.6
181.5
260.0
338.3
416.3
493.9
571.2
648.3
801.3
877.4
29212.1
292.5
372.8
453.1
533.3
613.9
693.4
773.2
852.7
932.0
30011.2
090.0
168.8
246.9
324.8
402.5
479.8
556.8
633.5
694.2
785.9
861.6
Table-5. Molecular constants (in cm"1) of K2 molecules.
State
Te
a
H
29228.5+0.6
b
H
29228.0+0.4
Ga
28094.710.5
c
G
28094.310.3
a
Present work
cog
(Q e x e
80.70± 0.04
0.037+0.005
81.092+0.034
0.094± 0.001
63.67+0.04
0.49 ± 0.06
63.78+0.08
0.49± 0.04
>c
° Rafietal. [9,10]
coeye
0.00263± 0.00005
Table-6. Dissociation energies (in cm"1) of excited G and H states of K dimer.
Molecular
state
H
G
Atomic
Dissociation energy (cm"1)
state Correlation diagram Birge-sponer formula
4D
2620.1
44003.3
5P
1067
2068.3
12
z\
Absorption Intensity
to
i
o
CD
1
I
U)
CD
00
o
CD
in
o'
CD
O
P-+-
U)
O
00
B
o
o"
Li atomic line (2S-3P)
to
o
K atomic line (4S-7P)
80-
°
a
o
eo
o eo.oo.c
\
G-state
.
/
60-
H -state
St3s
QDtr
••-
,.-••""•"•"
,-•••'
\
40-
\
\
\
\
\
\\
\
]
20-
0-
1
0
i
10
•
i
<
20
i
30
Band Number (v1)
Fig.-2. Vibrational quanta (AG) as a function of v in the G and H states of K2
40