Rotational Analysis of High Resolution F. T. Spectrum of a 3  + -a 3  Transition of CS Molecule 69 th International Symposium on Molecular Spectroscopy June 16, 2014 M. D. Saksena (Retd. from Bhabha Atomic Research Centre) INDIA

P312 ABSTRACT ROTATIONAL ANALYSIS OF HIGH RESOLUTION F. T. SPECTRUM OF a 3  - a 3  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 cm -1. Intense spectrum of CS radical was excited by DC discharge of mixture of CS 2 (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 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. spin- orbit, 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.

A 1  -X 1  + system of CS was first reported in 1934 in the near ultraviolet region by Crawford et.al.. Later perturbations in the A 1  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 3 Δ i 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 3 Δ- a 3  + system was done by Bergeman and Cossart [1981]. Fourier Transform spectrum of d 3 Δ - 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 3 Δ state and anomalous  -doubling in 6 and 7 state by optical hetrodyne-concentration modulation abs. spectroscopy. Brief history of CS

CS Potentials from Cossart et.al.  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 CS 2 (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 d 3  –a 3  and a  + –a 3  system.  LN 2 cooled InSb Detector. Recording of CS radical Spectra in the cm -1 Subject of this talk

Energy level scheme of CS

Gross spectrum of CS in the 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  1,2 and in 3  1,2,3 states is very small and could not be resolved and is J dependent.

The molecular Hamiltonian consists of the following terms H = H ev + H rot + H so +H ss + H sr For unperturbed electronic states the effective Hamiltonian consists of H ev [T e ] Vibronic part and H rot [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 : H SO is the spin-orbit, H SS [ ] the spin-spin, H SR [  ] 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 [A d ] respectively. A d 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  * (a 3 , A 1  states) interact with the vibronic levels of the second excited configuration  3  2  * (a 3  +, d 3 Δ, e 3  -, A 1  +, 1  -, 1 Δ 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 ± │ 3 Δ/ 3 , v   =0    3 ,v│B(R)L ± │ 3 Δ/ 3 , v  A   3 ,v│A L ± S ± │ 1 Δ / 1  ±,v   =±1 BRIEF INTRODUCTION

High Resolution spectrum of the a 3  + -a 3  system of CS 2-0 band of a 3  + -a 3  0 component Observed Simulated Plot from the fit of the 2-0 band system

Rotational Analysis a 3  + -a 3  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 a 3  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  -a 3  and a 3  -X 1  + 31-3031-30 31-3131-31 31-3231-32 a 3  -X 1  + Our new dataRef: CHR[1977] bands4-3

33 33 33 + Origin*1 + B*(J+J^2) + LambdaSS*(2/3) + gamma*-1 + D*(-2*J-3*J^2-2*J^3-J^4) + 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)) 33 + Origin*1 + B*(J+J^2+2) + LambdaSS*(-4/3) + gamma*-2 + D*(-8*J-9*J^2-2*J^3-J^4-4)  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 a 3  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 d 3 Δ and A 1  states. Matrix elements 3  + state of the Hamiltonian used keeping the molecular constants of 3  fixed. Observations

The molecular constants of a 3  state obtained from fit of a 3  -a 3  bands, where the constants of a 3  and X 1  + states are held fixed from previous fit of a 3  -X 1  + bands and ir data of X 1  + state. a 3  state Present workRef: BC (1981) T e (v=2) (14) B (84)  (39) D-1.35(91)e-6 T e (v=3) (15) B (73)  (38) D-1.05(71)e-6 T e (v=4) (20) B (16)  1.044(14) D1.3(25)e-6 T e (v=5) (55) B0.6171(44) D-3.5(71)e-6 T e (v=6) (82) (5) B0.607(12) (30) D-8(36)e-61.76e-6 T e (v=7) (30) (5) B (81) (9) D4.0(42)e-71.6e-6 Error : 0.373(Unweighted) No of observations: 2145 Parameters: 21 Molecular constants of a  + state

o Residual Fit of the a 3  state from the PGOPHER program fit. o The residual plot shows that the R 2 /Q 2 /P 2 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 a 3  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 d 3 Δ and A 1  states.  The intense bands of CS molecule recorded in the 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  + -a 3  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 : a 3  perturbing state.

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, 2978 (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,