1. Deperturbation Studies of d3Δi- a3r Transition of CS Molecule
69th International Symposium on Molecular Spectroscopy
June 16, 2014
Deperturbation Studies of d3Δi- a3r Transition of CS Molecule
M. D. Saksena
(Retd. from Bhabha Atomic Research Centre)
INDIA

2. DEPERTURBATION STUDIES OF d 3D- a 3 TRANSITION OF CS MOLECULE
ABSTRACT
DEPERTURBATION STUDIES OF d 3D- a 3 TRANSITION OF CS MOLECULE
K SUNANDA, Atomic and Molecular Physics , Bhabha Atomic Research center, Mumbai, Maharastra, India; M N DEO, High Pressure and Synchrotron Radiation Physics Division, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India; MADHAV DAS SAKSENA, A-10 Basera, Off Din-Quarry Road, Deonar, Mumbai, Maharashtra, India; KENTAROU KAWAGUCHI, Graduate School of Natural Science and Technology , Okayama University, Okayama, Japan.
The F. T. Spectrum of CS molecule was recorded with Bruker IFS 120 HR spectrometer at a spectral resolution of 0.03 cm-1using liquid nitrogen cooled InSb detector in the region cm-1. Intense spectrum of CS radical was excited by DC discharge of mixture of CS2 (120 mTorr) and He (2 Torr) in flowing condition. Two hours integration time was used for obtaining a good S/N ratio. The recorded spectrum is more intense compared to previous studies, therefore, it has been possible to excite lower values of v’ and v” for the d 3Δi – a 3r transition. The bands of three sub-systems occur with varying intensity. The following bands have been rotationally analyzed, viz. 1-0, 2-1, 3-2 (d 3Δ3- a 32); 2-0, 3-1, 4-2 (d 3Δ2 – a 31); and 1-1, 3-3 (d 3Δ1-a 30). The d 3Δi is state is highly perturbed. Using a Deperturbation program PGOPHER (C. M. Western, Univ. of Bristol, UK) the molecular constants of the two states have been derived.

3. Motivation for high resolution spectroscopy of CS
CS radical plays an important role in the formation of aerosols in troposphere & found in inter stellar medium, carbon rich stars and comets.
CS is similar to CO and SiO belonging to group IV-VI diatomics, therefore it presents itself as an excellent candidate to study off diagonal interactions, since the first two excited electronic configurations result in many rotational interactions in their spectra.
The rotational analysis of the high resolution spectra helps in evaluation of effective molecular constants and interactions viz. spin-orbit, spin-spin and rotation induced interactions. The true molecular constants can be determined only when all the perturbations have been completely taken into account.
Hence it is interesting to know the energy level structure of CS where each of the bands in the spectra has its own story to tell.

4. Brief history of CS
A1 -X1+ system of CS was first reported in in the near ultraviolet region by Crawford et.al.. Later perturbations in the A1 state were attributed to e 3- and a 3+ states by Lagerqvist et.al. [1958]. Barrow et.al. [1960] in their absorption study of the A-X system also introduced the d 3Δi state.
Rotational analysis of a 3 - X 1+ emission spectra was presented by Tewarson et.al. [1968] and Cossart, Horani and Rostas [1977].
Precision measurements of -doubling intervals Stark effects using optical double resonance technique were done by Field et.al. [1971].
The ab initio calculations of CS were given by Robbe et.al. [1976].
Detailed study of the lower excited states of CS along with the report of the d 3Δ- a 3+ system was done by Bergeman and Cossat [1981].
Fourier Transform spectrum of d 3Δ-a 3 is reported by Jong-in Choe et.al. [1991].
Ground state mw and ir study was presented by Ram et.al. [1995].
Chuanliang et.al. [2011,12,13] reported the perturbation analysis of the v=6, 7 and 8 levels of d 3Δ state and anomalous -doubling in 6 and 7 state by optical hetrodyne-concentration modulation abs. spectroscopy.

5. Recording of CS radical Spectra in the 1900 - 9500 cm-1
CS spectra were recorded on FT Bruker IFS 120 HR spectrometer at the Graduate School of Natural Science and Technology , Okayama University, Okayama, Japan.
Intense spectrum of CS radical was excited by DC discharge of mixture of CS2 (120 mTorr) and He (2 Torr) in flowing condition, with 2 hrs. Integration time.
Spectral resolution : 0.03 cm-1.
Recorded high resolution spectra of the d3 –a3 and a+–a3 system.
LN2 cooled InSb Detector.
Subject of this talk
CS Potentials from Cossart et.al.

6. Energy level scheme of CS

7. (Steps followed for Rotational Analysis)
BRIEF INTRODUCTION
(Steps followed for Rotational Analysis)
Using known Vibrational Constants bands-positions are located and from the known molecular constants of the lower state combination differences are determined and the rotational analysis of the various bands was carried out.
The rotational constants were obtained using the PGOPHER Program for Simulating Vibl., Rotl. And Electronic Spectra ( Colin M. Western, Bristol, UK)
In the spectra of d 3 -a 3 system only the =0 sub-bands appear implying that the two states involved could be best described in Hund’s case(a)
A few perturbed lines were then also included invoking the perturbation parameters.
The -doubling in the ≠0 states arises from the perturbations with the ± states and is strongest for  states.
In general the -doubling in the 30 is the largest, while for other components 31,2 and in 31,2,3 states is very small that could be resolved and is J dependent.

8. BRIEF INTRODUCTION
The molecular Hamiltonian consists of the following terms
H = Hev + Hrot + Hso +Hss + Hsr
For unperturbed electronic states the effective Hamiltonian consists of Hev[Te] Vibronic part and Hrot [B( R)] Rotational part of the Hamiltonian one for each parity.
For near degeneracy between vibronic levels of two electronic states, the Hamiltonian needs to incorporate the off-diagonal matrix elements : HSO is the spin-orbit, HSS [] the spin-spin, HSR[] the spin-rotation interactions treated by second-order perturbation theory.
The rotational [B] and spin-orbit [A] constants being function of the internuclear distance have non-zero matrix elements off diagonal in vibrational quantum numbers are also treated as second order parameters giving rise to centrifugal distortion constants [D] and [Ad] respectively. Ad along with spin–rotation [] and spin–spin [] parameter is required to fit the observed spin splitting for states with  0 and S0.
The interaction of  ~  levels require the second order -doubling parameters p, q and o (a parity dependent spin-spin term) in the Hamiltonian to fit the lambda doublets observed in the  state.

9. PERTURBATIONS BRIEF INTRODUCTION
The most important aspect of this molecule is the presence of interaction between the close lying vibronic levels of different electronic states
Of these the first excited electronic configuration 4* (a3, A1 states) interact with the vibronic levels of the second excited configuration 32*(a3+, d3Δ, e3-, A1+, 1-,1Δ states).
The perturbations between the states of the two groups are due to the electronic spin-orbit matrix elements (AL±) and the electronic rotation matrix elements (BL±) also known as the l-uncoupling operator.
It has been reported that both these terms are relatively large in CS.
Thus the Perturbation parameters can be determined from the analysis of the interaction of the vibronic levels between any two electronic states , given as
  ½  3,v│AL ± │3Δ/3, v =0
   3,v│B(R)L±│3Δ/3, v
A   3,v│A L±S±│1 Δ /1±,v =±1

10. New bands of d3i-a3 system of CS

11. The bands of d 3i-a 3 system included in the fit
3Δ1-30
3Δ2-31
3Δ3-32
0-3*
3-3*
0-2*
1-2*
1-1*
1-0*
2-1*
2-0*
3-2*
3-1*
3-0
4-2*
4-0
5-0
6-0
7-1
7-0
8-1
8-0
9-2
9-1
9-0
10-2
10-1
10-0
11-2
11-1
11-0
12-2
12-1
12-0
13-2
13-1
14-2
14-1
*Our new data & Ref: Choe et.al.[1991]: bands

12. Matrix elements of the Hamiltonian: 3Π and 3Δ States
|32
31
30
32
+ Origin*1
+ B*(J+J^2-2)
+ A*1
+ D*(2*J+J^2-2*J^3-J^4)
+ AD*(((J+J^2-2)*sqrt(6))/sqrt(6))
+ B*(-sqrt(2*J+2*J^2-4))
+ gamma*(sqrt(2*(J*(J+1)-2))/2)
+ D*((2*J+2*J^2)*sqrt(2*J+2*J^2-4))
+ AD*((-sqrt(6*(2*J+2*J^2-4)))/(2*sqrt(6)))
± D*(-2*sqrt(-2*J+J^2+J^4-2*J^2+2*J^3))
± q*(sqrt(J*(J*(J+1)-2)*(J+1))/2)
+ B*(J+J^2+2)
+ gamma*-2
+ D*(-8*J-9*J^2-2*J^3-J^4)
± q*((J*(J+1))/2)
+ B*(-sqrt(2*J+2*J^2))
+ gamma*(sqrt(2*J*(J+1))/2)
+ D*((2*J+2*J^2+4)*sqrt(2*J+2*J^2))
+ AD*(sqrt(6*(2*J+2*J^2))/(2*sqrt(6)))
+ p*((-sqrt(2*J*(J+1)))/2)
+ q*(-sqrt(2*J*(J+1)))
+ A*-1
+ D*(-6*J-7*J^2-2*J^3-J^4-4)
+ AD*(((-J-J^2-2)*sqrt(6))/sqrt(6))
± o*1
+ p*1
+ q*1 H
3Δ3
3Δ2
3Δ1
+ Origin*1
+ B*(J+J^2-4)
+ A*2
+ LambdaSS*(2/3)
+ gamma*1
+ D*(6*J+5*J^2-2*J^3-J^4-4)
+ AD*((2*(J+J^2-4)*sqrt(6))/sqrt(6))
+ B*(-sqrt(2*J+2*J^2-12))
+ gamma*(sqrt(2*(J*(J+1)-6))/2)
+ D*((2*J+2*J^2-2)*sqrt(2*J+2*J^2-12))
+ AD*((-sqrt(6*(2*J+2*J^2-12)))/sqrt(6))
+ D*(-2*sqrt(-8*J+J^2+J^4-8*J^2+2*J^3+12))
+ B*(J+J^2+2)
+ LambdaSS*(-4/3)
+ gamma*-2
+ D*(-8*J-9*J^2-2*J^3-J^4+12)
+ B*(-sqrt(2*J+2*J^2-4))
+ gamma*(sqrt(2*(J*(J+1)-2))/2)
+ D*((2*J+2*J^2+6)*sqrt(2*J+2*J^2-4))
+ AD*(sqrt(6*(2*J+2*J^2-4))/sqrt(6))
+ B*(J+J^2+4)
+ A*-2
+ gamma*-3
+ D*(-10*J-11*J^2-2*J^3-J^4-12)
+ AD*((2*(-J-J^2-4)*sqrt(6))/sqrt(6))

13. Rotational structure the 2-1 band of d 31 –a 30 sub-system
Observed
Simulated
Observed
Stimulated

14. Combined fit of d 3i(v=1-12) - a 3r(v=0) system of CS
Combined fit of d 3i(v=1-12) - a 3r(v=0) system of CS (Incorporating only few perturbation interactions)
Observed perturbations evaluated are at
d3Δ3(v=1) ~ a32(v=8) at J=7
d3Δ2(v=2) ~ a30(v=9) at J=16
d3Δ3(v=5) ~ a32(v=11) at J=13
d3Δ0(v=6) ~ a32(v=12) at J=15
d3Δ3(v=6) ~ A12(v=1) at J=16
Most of the vibrational levels of a 3 interact with those of d 3Δ at J >25 implying two states are highly mixed.
For higher v’s of the d 3Δ state, the interaction results in perturbation such that some of the components of the sub system could not be observed.
It was observed in the fit that constants for only those perturbing terms could be evaluated with good standard deviations and reproducibility for which the data were available.

15. States of CS d 3 v=12 a 3 A 1 4 v=11 v=10 15 3 v=9 14 v=8 2 13 v=7
v=4 10 1  1 2 3
v=3 9
v=2
v=1 8
v=0
Reduced term values

16. Residual fit before incorporating perturbation
Residual fit after incorporating few perturbation parameters
Simulated data and fit of the d (v=1-12)–a (v=0) bands
Residual fit before incorporating perturbation

17. Molecular constants for the d 3Δ and a 3 states
Present work
Literature {BC}
d3 (v=1-12)
Te (v=1)
(878)
Te (v=5)
(485)
(7)
Te (v=9)
(419)
(6) B
(190)
(12)
(122)
(7)
(141)
(23) A
(451)
(461)
SS
7.0995(787)
6.8818(725) D
1.99(21)e-6
1.6e-6
1.770(121)e-6
1.635(23)e-6
2.05(18)e-6
1.63(17)e-6 AD
3.69(29)e-4
(14)
-6.6(31)e-5
(8)
Te (v=2)
(840)
Te (v=6)
(478)
(5)
Te (v=10)
(892)
(42
(147)
0.6223(4)
(124)
(12)
(266)
(475)
6.7188(739)
2.123(143)e-6
1.993(130)e-6
1.52(11)e-6
3.7(42)e-7
1.70e-6
-3.109(413)e-4
(5)
(7)
Te (v=3)
(413)
(6)
Te (v=7)
(283)
(3)
Te (v=11)
(890)
(7)
(122)
(22)
(169)
(16)
(249)
(45)
(459)
(1410)
4.7103(730)
6.4481(710)
2.368(122)e-6
1.55(20)e-6
2.156(118)e-6
1.58(18)e-6
2.84(29)e-6
1.93(63)e-6
-6.63(28)e-4
-3.427(588)e-4
(3)
Te (v=4)
(407)
(6)
Te (v=8)
(417)
(5)
Te (v=12)
(915)
(6)
(112)
(20)
(126)
(24)
(489)
(27)
(459)
(460)
3.6900(730)
6.5281(723)
3.739(102)e-6
1.62(5)e-6
2.079(131)e-6
1.8(11)e-6
1.2(4)e-6
(282)e-3
-2.45(29)e-4
0.0004(4)
a3 (v=0)
Perturbation parameters Te
(2)
3Di <a3Pi_8|LS|v=1> Value
42.25(57)
18.34/-0.06
(111)
(5)
3Di <a3pi_9|LS|v=2> Value
26.902(817)
35.214(21)/ (9)
(1092)
3Di <a3Pi_11|LS|v=5> Value
31.19(15)
9.29(12)/ (54)
1.2196(652)
3Di <a3Pi_12|LS|v=6> Value
6.72(14)
-1.15(16)/ (11) o
(33)
3Di <a3Pi_13|LS|v=7> Value
21.586(3383)
-11.13/0.02 
(2992)
(3)
3Di <a3Pi_15|LS|v=10> Value
17.290(308)
-3.70(15)/0.13(2) p
1.89(78)e-3
0.0042(2)
3Di <A1Pi_1|LS|v=6> Value
27.70(109)
20.98(5) q
-5.8(11)e-4
3Di <A1Pi_2|LS|v=7> Value
-1.39
1.923(106)e-6
0.154(4)e-5
3Di <A1Pi_3|LS|v=9> Value
10.93(33)
(6031)e-3
(1)
Error : No of Observations : Parameters derived : 73

18. Residuals from fit before and after incorporating perturbation terms
Deperturbation fit of the 6-0 band of d 3-a 3 transition

19. Summary
The intense bands of CS molecule in the cm-1 recorded using the FT spectrometer at a resolution of cm-1 helped in assigning new bands involving low v’s for the first time in the two systems, viz. a 3+- a 3 and the d 3Δ-a 3 transitions.
Compiling the data on the CS a 3+, a 3 and d 3Δ states from previous studies and our new data helped in obtaining effective molecular constants for these states, most of them previously known only through perturbation with the A 1 state.
The set of constants were obtained by least square fit of the Hamiltionian matrix to the observed rotational spectral data using the PGOPHER fitting software.
The deperturbation of the rotational spectrum gave the perturbing parameters viz. the spin-orbit, spin-rotation, second order -doubling constants and perturbing parameters for a few levels of d 3Δ ~( 3 and 1) could also be determined.

20. REFERENCES
F. H. Crawford, and W. A. SHURCLIFFP, Phys. Rev. 45, 860 (1934).
A. Lagerqvist, H Westerlund, CV Wright and RF Barrow, Arkiv Fysik 14,387 (1958)
R. F. BARROW, R. N. DIXON, A. LAGERQVISTA, NDC . WRIGHT, Ark. Fys. 18, 543 (1960).
J. M. Robbe and J. Schamps, J. Chem. Phys. 65, 5420 (1976).
R. W. Field and T. H. Bergeman, J. Chem. Phys. 54, 2936 (1971).
A. Tewarson, H.B. Palmer, J. Mol. Spectrosc –251 (1968).
D. Cossart, M. Horani, J. Rostas, J. Mol. Spectrosc –303 (1977).
D. Cossart, J. Phys –502 (1980) .
D. Cossart and T. Bergeman, J. Chem. Phys. 65, 5462 (1976).
T. Bergeman, D. Cossart, J. Mol. Spectrosc –195 (1981).
J.I. Choe, Y.M Rho, S.M. Lee, A.C. LeFloch, S.G. Kukolich, J. Mol. Spectrosc –213 (1991).
C. L. Li, L. H. Deng, Y. Zhang, L. Wu, X. H. Yang, and Y. Q. Chen, J. Phys. Chem. A 115, (2011).
C. L. Li, L. H. Deng, Y. Zhang, L. Wu, and Y. Q. Chen, J. Phys. Chem (2012).
C. L. Li, L. H. Deng, J Zhang, X Qiu, J Wei, and Y. Q. Chen, J. Mol. Spectrosc. A , (2013).
R.S. Ram, P.F. Bernath, S.P. Davis, J. Mol. Spectrosc –157 (1995).
C. M. Western, PGOPHER, a Program for Simulating Rotational Structure,University of Bristol,

21. New Laser transitions discovered
Diatomics Studied BO
AlO
AlCl
MgCl
GaO
GaCl/GaI
Se2
InO/InO+
InCl/InBr CS
InCl+
New Laser transitions discovered
GaCl
GaBr
InBr

22. I had privilege of working with a number of persons : From India :
SPECTROCHEMICAL ANALYSIS TEAM :
B. R. Vengsarkar, G. S. Ghodgaonkar, L. C. Chandola, N. P. Karanjikar,  S. V. Grampurohit, P. S. Murthy,  V. S. Dixit, V. N. P. Kaimal and S. K. Kapoor 
MOLECULAR SPECTROSCOPY TEAM :
Mahavir Singh, V. B. Kartha, V. A. Job, G. Lakshminarayana, T. K. Balasubramanian, G. L. Bhale,  G. Krishnamurthy, S. Gopal, M. N. Deo, Sunanda K., Saraswathy P., R. V. Subramanian, H. A. Khan, B. J. Shetty,  K. S. Chandrasekar;  
S. H. Behere, Ashok Jadhav, and C. T. Londhe;
K.N. Uttam, Renu Singh, Pavitra Tandon and Shipra Tiwari .
From Abroad :
W. J. Balfour, R. F. Barrow, J. M. Brown, I. D. Malcolm, Andrew. M. James, Orson L. Bourne, Benoit Simard, Jonathan P. Towle, and K. Kawaguchi

23. Thank You