69th International Symposium on Molecular Spectroscopy
June 16, 2014
Rotational Analysis of
High Resolution F. T. Spectrum of
a3+ -a3 Transition of
CS Molecule
M. D. Saksena
(Retd. from Bhabha Atomic Research Centre)
INDIA
P312
ABSTRACT
ROTATIONAL ANALYSIS OF HIGH RESOLUTION F. T. SPECTRUM OF a3- a3
TRANSITION OF CS MOLECULE
MADHAV DAS SAKSENA, A-10 Basera, Off Din-Quarry Road, Deonar, Mumbai,
Maharashtra, India; K SUNANDA, Atomic and Molecular Physics, Bhabha Atomic
Research Centre, Mumbai, Maharastra, India; M N DEO, High Pressure and
Synchrotron Radiation Physics Division, Bhabha Atomic Research Centre, 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-1 using liquid nitrogen cooled InSb detector
in the region 10500 - 1800 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. For the first time seven bands of a’3- a 3
transition of CS molecule are observed lying between 8000 - 4800 cm-1 region. Rotational
analysis of these bands, viz. 7-1, 6-1, 5-0, 4-0, 3-0, 2-0, and 3-1 will be presented.
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. spinorbit, spin-spin and rotation induced interactions. The true molecular
constants can be determined only when all the perturbations involving
various states 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.
Brief history of CS
• A1 -X1+ system of CS was first reported in 1934 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 Cossart [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 d3Δ state and anomalous -doubling in 6 and 7
state by optical hetrodyne-concentration modulation abs. spectroscopy.
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.
CS Potentials from Cossart et.al.
Energy level scheme of CS
Gross spectrum of CS in the 1900-9500 cm-1 region.
BRIEF INTRODUCTION
(Steps followed for Rotational Analysis)

Using known Vibrational Constants band-positions are located and from the
molecular constants of Ground state the combination differences are
determined and the rotational analysis of various bands was carried out.

The rotational constants were obtained using the PGOPHER Program for
Simulating Rotl., Vibl. & Electronic Spectra (Colin M. Western, Bris. UK).

In the spectra of a’ 3+ - a 3 system only the =0 sub-bands appear implying
that the two states involved could be best described by 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
3
1,2 and in 1,2,3 states is very small and could not be resolved and is J
dependent.
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 inter
nuclear 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.
BRIEF INTRODUCTION
PERTURBATIONS
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
High Resolution spectrum of the a3+-a3 system of CS
2-0 band of a3+-a30 component
Observed
Simulated
Plot from the fit of the 2-0 band system
Rotational Analysis a3+ -a3 Transition of CS Molecule
First, using the Pgopher program the data of a 3 -X 1+ system was
merged with the data of CHR [1977] and the mw and ir data of Ram et. al.
[1995] with appropriate weight factor and molecular constants found.
The constants obtained for the a3 state were kept fixed in the initial
analysis of a 3 - a 3 and then released in the final fit.
Bands incorporated in the fit of a3-a3 and a3-X1+
3 -3
1
0
3 -3
1
1
3 -3
1
2
Our new data
2-0
3-0
4-0
2-0
3-0
4-0
5-0
6-1
7-1
Ref: CHR[1977]
2-0
3-0
21 bands
a3-X1+
0-0
1-0
0-1
1-1
2-1
1-2
2-2
3-2
2-3
4-3
Observations
 The overall poor fit of the bands shows that the v=0-6 levels of a3+
state are severely perturbed by the v ≥ 3 levels of a 3 state, so till
now no high resolution analysis could be attempted.
 The molecular constants of v=5, 6, 7 of a3 state are not reported as
they are perturbed and their constants can be obtained through
their interaction with the a3+ state (v=2, 3, 4, 5).
 The higher states of this system are also known only through their
perturbations with the d3Δ and A 1 states.
Matrix elements 3+ state of the Hamiltonian used keeping the molecular
constants of 3 fixed.
3
3
3
3
+
+
+
+
+
+ B*(-sqrt(2*J+2*J^2))
+ gamma*(sqrt(2*J*(J+1))/2)
+ D*((2*J+2*J^2+2)*sqrt(2*J+2*J^2))
Origin*1
B*(J+J^2)
LambdaSS*(2/3)
gamma*-1
D*(-2*J-3*J^2-2*J^3-J^4)
+
+
+
+
+
Origin*1
B*(J+J^2+2)
LambdaSS*(-4/3)
gamma*-2
D*(-8*J-9*J^2-2*J^3-J^4-4)
Molecular constants of a+ state
The molecular constants of a3 state obtained from fit of a3-a3 bands, where the
constants of a3 and X1+states are held fixed from previous fit of a3 -X1+ bands
and ir data of X1+ state.
Present work
Ref: BC (1981)
a3 state
Te (v=2)
32733.17(14)
B
0.63205(84)
1.2653(39)

D
-1.35(91)e-6
Te (v=3)
33535.00(15)
B
0.62588(73)
1.2526(38)

D
-1.05(71)e-6
Te (v=4)
34326.84(20)
B
0.6279(16)
1.044(14)

D
1.3(25)e-6
Te (v=5)
35107.02(55)
B
0.6171(44)
D
-3.5(71)e-6
Te (v=6)
35876.60(82)
35876.00(5)
B
0.607(12)
0.61038(30)
D
-8(36)e-6
1.76e-6
Te (v=7)
36636.21(30)
36636.05(5)
B
0.60356(81)
0.60426(9)
D
4.0(42)e-7
1.6e-6
Error : 0.373(Unweighted) No of observations: 2145 Parameters: 21
o Residual Fit of the a3 state from the
PGOPHER program fit.
o The residual plot shows that the R2/Q2/P2
branches in the v=2-4 are perturbed.
o Initial fit of the molecular constants
obtained excluding the perturbed
rotational lines is given below
Comparing the generated rotational
lines, line by line and improving the
effective molecular constants needs
to be carried out before
incorporating the perturbation
terms.
Summary

The v=0-6 levels of a3+ state are severely perturbed by the v ≥ 3 levels of
a3 state, so no high resolution analysis was attempted till now. The higher
states of this system are also known only through their perturbation with the
d3Δ and A 1 states.

The intense bands of CS molecule recorded in the 1900-10000 cm-1 were
recorded using the FT spectrometer at a resolution of 0.03 cm-1. This helped
in assigning new bands involving low v’s for the first time for a3+-a3
system.

The effective molecular constants of the a3+ state for the v= 2 to 7 levels are
obtained for the first time.

The perturbation terms needs to be incorporated to obtain the true constants
and the molecular constants of the v=5, 6, 7 : a3 perturbing state .
REFERENCES
•
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•
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).
•
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•
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•
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•
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•
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•
C. M. Western, PGOPHER, a Program for Simulating Rotational Structure,University of Bristol,
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