DENSITY FUNCTIONAL THEORY STUDIES of OClO

DENSITY FUNCTIONAL THEORY STUDIES

OF SPECTROSCOPIC CONSTANTS

AND ANHARMONIC FORCE FIELD OF O 35ClO

ZILIANG ZHU,MEISHAN WANG *,CHUANLU YANG,

MEIZHONG MA and WENWANG LIU School of Physics and Optoelectronics Engineering

Key Laboratory of Molecular Design and Materials Synthesis of Shandong Province,Ludong University,Yantai 264025,P.R.China

*mswang1971@https://www.sodocs.net/doc/9a7476373.html,

Received 21January 2012Accepted 21September 2012Published 14December 2012

The equilibrium structure,spectroscopy constants and anharmonic force ˉeld of O 35ClO have been calculated at B3PW91and B3LYP levels of theory with two basis sets 6-311ttG(2df,2pd)and 6-311ttG(3df,3pd),respectively.The computed geometries,dipole moment,rotational constants,vibration àrotation interaction constants,vibrational band origins,anharmonic constants,quartic,and sextic centrifugal distortion constants are compared with the available experimental data.The cubic and quartic force constants are predicted.The calculated results show that the B3PW91results are in excellent agreement with experiment and represent a substantial improvement over the results obtained from B3LYP.

Keywords :Anharmonic force ˉeld;spectroscopic constant;equilibrium structure;chlorine dioxide.

1.Introduction

Chlorine-containing molecules have attracted considerable interest recently because they play important roles in the depletion of ozone in the Antarctic stratosphere.1à11The most commonly accepted mechanism involves the reaction of chlorine atoms,which are formed initially from the photodissociation of chloro°ouromethanes released into the atmosphere 1with ozone

Cl tO 3!ClO tO 2:

e1T

In the middle stratosphere,the chlorine monoxide molecule can react with oxygen atom(s)

ClO tO !Cl tO 2;

e2T

*Corresponding

author.

Journal of Theoretical and Computational Chemistry Vol.12,No.2(2013)1250117(12

pages)#c World Scientiˉc Publishing Company DOI:10.1142/S0219633612501179

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to reform chlorine atom(s),which can subsequently react with another ozone mol-ecule.Similarly,in the cold Antarctic lower stratosphere,reaction (1)is coupled with the formation and photolysis of the chlorine monoxide dimmer eClO T2,which leads to catalytic ozone loss.2à4Chlorine dioxide radical is a possible additional pathway to stratospheric polar ozone depletion.5There are two isomeric forms of the ClO 2radical and both are believed to be formed by a coupling of Cl and Br chemistry in the upper atmosphere

ClO tBrO !Br tClOO

e3T!Br tOClO :

e4T

ClOO with C s symmetry is thermodynamically more stable than OClO with C 2v symmetry by about 4kcal/mol.However,OClO is kinetically more stable than ClOO.The ClOO species is an important short-lived precursor participating in ozone destruction.ClOO is a reactive intermediate in the gas-phase photolysis reactions of Cl 2with O 2and has been implicated as a precursor to ClO,which is known to play a crucial role in the ozone destruction cycle.6à8It has been suggested that OClO radical can undergo photoisomerization to ClOO,5,9à11which could actively par-ticipate in the destruction of O 3,

OClO th )ClOO !Cl tO 2:

e5T

The importance of OClO has lead to a need to understand their chemical and physical properties.It has been the experiment subject of many spectroscopic and photochemical studies.12à32Curl and his co-workers 12à17ˉrstly investigated the microwave spectrum of chlorine dioxide and its isotopic series in the early 1960s.The measured rotational constants 12(in MHz)were:O 35ClO:A ?52072,B ?9952,C ?8332;O 37ClO:A ?50725,B ?9952,C ?8295.The structural parameters 12of chlorine dioxide were observed R ClO ?1:473?0:01#A and \OClO ?117:6 ?1 .The hyperˉne structure of the microwave spectra of O 35ClO and O 37ClO was analyzed.13In terms of the electronic structure of chlorine dioxide,the hyperˉne coupling constants obtained from the microwave spectra of chlorine dioxide were discussed.14By taking into account the e?ects of the centrifugal distortion,the microwave spectra of chlorine dioxide were reanalyzed.15The Stark and Zeeman e?ects were taken into account in the rotational spectra of OClO.16Eight rotational transitions of the 2?1state of chlorine dioxide were observed and assigned.17Employing the high-resolution infrared spectra,the B -type 1fundamental bands of chlorine dioxide were observed with the resolution of 0.06cm à1by Hamada and Tsuboi.18The ground and excited states harmonic frequencies of O 35ClO using a revised vibrational analysis were obtained by Richardson it et al 19:!001?963:5,

!002?451:7,!003?1133:0,!01?722:4,!02?296:3,and !03?780:1,all in cm à1.

Tanoura et al .20obtained the centrifugal distortion,spin-rotation interaction,and hyperˉne interaction constants of O 35ClO and O 37ClO using the microwave spec-troscopy of chlorine dioxide.Microwave spectra of O 35ClO and O 37ClO in the excited vibrational states, 1, 2, 3,and 2 2,were observed and the rotational,quartic

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centrifugal distortion and spin-rotation interaction constants were reduced to the equilibrium values by Miyazaki et al .21High-resolution infrared spectra of OClO were recorded by Ortigoso et al .22à24They analyzed the 1,22 2,23 3,232 1,24and e 1t 3T24bands of OClO with a Fourier transform infrared spectrometer and obtained their e?ective spectroscopic constants in terms of a rotation àspin àrotation Hamiltonian model.The rotational spectra of O 35ClO and O 37ClO in their (000),(100),(010),(001),and (020)states were reinvestigated in the selected regions between 130GHz and 526GHz.The newly derived ground state rotational and quartic centrifugal distortion constants,their vibrational changes and the sextic centrifugal distortion constants were used together with data from infrared studies in

a calculation of the quartic force ˉeld by M €u

ller et al .25The direct absorption spectra of the ~A

2A 2 ~X 2B 1transition and the photochemical dynamics of ~A 2A 2state of OClO were investigated by Richard and Vaida.26,27The photodissociation dynamics of a range of electronically excited OClO(A 2A 2)vibrational states were studied by

Davis and Lee.28Dispersed laser-induced °uorescence of the ~A

2A 2 ~X 2B 1tran-sition of OClO in solid Ne,Ar and Kr was recorded when the origin at 20991cm à1by

Liu et al .29The UV photodissociation of OClO(~A

2A 2 2>20X 2? ; ;J T!ClO eX 2? ; ;J TtO e3P J Twas studied by Delmdahl et al .30Absorption spectra of gas-phase OClO in the 325à435nm region at ˉve atmospheric temperatures between 213K and 293K were measured by Kromminga et al .31with a spectral resolution of 1.0cm à1using Fourier-transform spectroscopy.The weakly solvent dependent relaxation dynamics following photoexcitation of OClO in di?erent solvents were investigated by Brooksby et al .32

Regarding theoretical studies,Gole 9performed SCF calculations for OClO,using a constrained geometry.This work calculated the ground-and low-lying electronic states of OClO and predicted that 2B 2and 2A 1states crossed at about 120 ,which was discussed as a mechanism for photoisomerization of OClO to ClOO.Mc Crath et al .33calculated the structures,relative stabilities and vibrational spectra of OCIO and Cl 2O 2using quantitative ab initio molecular orbital method.Peterson and Werner 34calculated the near-equilibrium potential energy functions for the ˉrst four doublet electronic states of OClO employing the extensive internally contracted multireference conˉguration interaction wave functions and large basis sets.Luke 35determined the energies of ClO,two isomers of Cl 2O,two isomers of C1O 2,and three isomers of C12O 2at the G2and G2(MP2)levels of theory.Peterson and Werner 36investigated the potential energy surfaces involved in the photodissociation of OClO to Cl tO 2using the large multireference conˉguration interaction wave functions.Fern a ndez et al .37calculated the hyperˉne and nuclear quadrupole coupling tensors for the two chlorine dioxide isomers OClO and ClOO employing CCSD and CCSD(T)approaches.Aloisio and Francisco 38calculated the minimum structures,vibrational and rotational frequencies,and binding energies for the complexes of OClO with H 2O using B3LYP density functional theory method.Recently,with the develop-ment of the method of analytic second derivatives of molecular energy,it has become possible to calculate the rovibrational spectra,harmonic or anharmonic force ˉeld

Density Functional Theory Studies

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of small or middle molecules by ab initio method.39à43Employing the given force ˉeld,one can determine all spectroscopic constants of molecule,such as harmonic constants,anharmonic constants,rotational constants,centrifugal distortion con-stants,rotation àvibration interaction constants,et al .44It has been shown that spectroscopic constants from the accurate,purely ab initio anharmonic force ˉeld (such as MP2,DFT,CCSD(T)et al .)are reliable.40à43,45à48

As far as we know,there have been very few papers to completely report the ab initio study of spectroscopic constants and anharmonic force ˉeld of OClO.Peterson calculated the accurate three-dimensional,near-equilibrium potential energy function of the ground states of OClO using the highly correlated multi-reference conˉguration interaction wave functions with large correlation consistent basis sets.47Employing the analytical potential energy function,spectroscopic con-stants,such as the geometry,rotational,vibration àrotation,quartic centrifugal distortion constants were obtained.However,they did not discuss the sextic cen-trifugal distortion constants.In order to accurately calculate rotational spectra of molecules,it is necessary to take the spectroscopic constants into account.In the present paper,we calculate the equilibrium geometry structure and the anharmonic force ˉeld by B3PW91and B3LYP,with 6-311ttG(2df,2pd)and 6-311ttG (3df,3pd),respectively.On this base,we obtain the geometry,rotational,quartic,and sextic centrifugal distortion,vibration àrotation interaction,second-,third-,and fourth-order force constants.In addition,we compare them with the relevant experimental data.The results show that B3PW91with 6-311ttG(3df,3pd)basis set can give the reliable spectroscopic https://www.sodocs.net/doc/9a7476373.html,putational Methods

Quantum-chemical calculations are carried out at B3PW91and B3LYP levels using Gaussian 03program pakage.50B3PW91indicates a three-parameter functional using the Becke exchange functional 51and the Perdew àWang 91correlation functional.52B3LYP indicates a three-parameter functional using the Becke exchange functional 51and the LYP correlation functional.51Two di?erent high angular basis sets are employed:6-311ttG(3df,3pd)contains three sets of valence region functions,di?use functions on both heavy atoms and hydrogen atoms and multiple polarization functions:3d functions and 1f function on heavy atoms and 3p functions and 1d function on hydrogen atoms.The basis of Cl is the [7s,6p,3d,1f]contraction of a (14s,11p,3d,1f)primitive set.a The basis of O is the [5s,4p,3d,1f]contraction of a (12s,6p,3d,1f)primitive set.a 6-311ttG(2df,2pd)contains similar three sets with 6-311ttG(3df,3pd).The basis of Cl is the [7s,6p,2d,1f]contraction of a (14s,11p,2d,1f)primitive set.a The basis of O is the [5s,4p,2d,1f]contraction of a (12s,6p,2d,1f)primitive set.a

a Basis

sets were obtained from the Extensible Computational Chemistry Environment Basis Set Data-base,Version 02/02/06.

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Spherical harmonics are used throughout.Unless stated otherwise,all elections are correlated.The molecular geometries of O 35ClO (C 2v )are optimized using ana-lytic gradients as implemented in Gaussian 03.50At the computed equilibrium geometries,harmonic force ˉelds are evaluated analytically.Harmonic force con-stants without inner-shell correlation contributions are evaluated numerically from energies.The normal modes and the harmonic spectroscopic constants are obtained in the usual manner.54,55Cubic and semi-diagonal quartic normal coordinate force constants are calculated at B3PW91and B3LYP levels for the two basis sets.The anharmonic spectroscopic constants are derived from the theoretical normal coordinate force ˉelds applying standard formulas based on density functional theory.51à53

3.Result and Discussions

The theoretical results for the molecular geometries,the spectroscopic constants and the full quartic force ˉelds of O 35ClO are given in Tables 1à8.They are compared with the corresponding experimental 12,16,19,21,25or theoretical data 34,38,49whenever these are available.

The computed and experimentally derived equilibrium structures 21,25and dipole moment 16of O 35ClO are shown in Table 1.The computed bond length of O àCl by B3PW91with 6-311ttG(3df,3pd)reproduces the experimental value within 0.000468#A .The result for B3LYP with 6-311ttG(3df,3pd)is within 0.01083#A .The computed bond angle of O àCl àO by B3PW91with 6-311ttG(3df,3pd)reproduces the experimental value within 0.0334 .The result for B3LYP with 6-311ttG (3df,3pd)is within 0.0285 .The computed dipole moment by B3PW91with 6-311ttG(3df,3pd)reproduces the experimental value within 0.0256D.The best overall agreement is found at B3PW91/6-311ttG(3df,3pd),where each theoretical bond length,bond angle and dipole moment lies within the experimental uncer-tainty.From Table 1,one can ˉnd B3LYP is not good for O 35ClO and the results for 6-311ttG(3df,3pd)are all better than that of 6-311ttG(2df,2pd).The previous computed results 34,38,49are also listed in Table 1.

Table 2lists the computed results for the rotational constants at B3PW91and B3LYP with 6-311ttG(2df,2pd)and 6-311ttG(3df,3pd),respectively,along with the available experimental 12,21,25and previous computed 38,49data for O 35ClO.The theoretical ground-state rotational constants (A 0;B 0;C 0)have been obtained from the associated equilibrium constants (A e ;B e ;C e )by taking into account the e?ects of vibration àrotation coupling.It is clear that the experimental rotational constants are reproduced well at B3PW91with 6-311ttG(3df,3pd)basis set.The deviations between the experimental values 21and the computed values at the equilibrium geometry are within 0.0513à0.069%,while the deviations at the ground-state geo-metry are within 0.0003à0.0434%.

The calculated vibration àrotation interaction constants X i eX ?A ,B ,C ;i ?1à3)are collected in Table 3,together with the corresponding experimental 21

Density Functional Theory Studies

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T a b l e 1.M o l e c u l a r e q u i l i b r i u m g e o m e t r i e s a n d d i p o l e m o m e n t o f O 35C l O .

B 3P W 91

B 3L Y P

P r e v i o u s E x p t .

P a r a m e t e r S e t A S e t B

S e t A

S e t B R e f .34R e f .38R e f .49R e f .25R e f .21R e f .16R (#A )1.4811591.4703071.490791.479221.4611.4791.47281.4698731.469839A ( T117.1443117.4303117.0188117.3748116.8117.4117.65117.3969117.4033 (D )

1.96111.8096

2.02581.86871.784

S e t A :6-311ttG (2d f ,2p d )S e t B :6-311ttG (3d f ,3p d )

T a b l e 2.R o t a t i o n a l c o n s t a n t s o f e q u i l i b r i u m a n d g r o u n d s t a t e s o f O 35C l O (M H z ).

B 3P W 91

B 3L Y P

P r e v i o u s

E x p t .

C o n s t a n t S e t A S e t B

S e t A

S e t B R e f .38R e f .49

R e f .12R e f .21

R e f .25

A e

50716.0351890.7049883.9951185.785116252040.9851864.10B e

9890.1110006.169775.8599891.79498969950.1110013.07C e

8276.1778388.5788173.9868289.77282928352.228394.19

A 0

50891.9352081.4350043.151362.8452265.825207252081.249B 0

9842.449957.4859726.5139841.3699887.1699529952.605C 0

8226.2528337.82

8122.5368237.4798292.26

83328334.220

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and previous 49computed data for O https://www.sodocs.net/doc/9a7476373.html,paring with the experimental and previous computed data,the calculations at B3PW91/6-311ttG(3df,3pd)or B3LYP/6-311ttG(3df,3pd)both well reproduce the vibration àrotation interaction constants within the acceptable error except B 2.With the basis set increasing,the results for both theory levels become better.According to B 2,there exist a big discrepancy between our computed value and the previous 49computed or experimental 21value.When we try to use other ab initio methods to investigate this

species,the predicted value of B 2is also very smaller than experimental 21

value.It is worthwhile to go on investigating this problem.It needs to point out,there is the strong Coriolis resonance between the vibrational states 2and 3or 1and 3.The values of 32; 31at B3PW91/6-311ttG(3df,3pd)are 0.9361and 0.35174,respec-tively.The corresponding results at B3LYP/6-311ttG(3df,3pd)level are 0.93517and 0.35419,respectively.The vibration àrotation interaction constants can be used to calculate the ground-state corrections to the equilibrium rotational constants using the following formula:

A ?A e àX i A i n i t1

2 :e6T

The similar expression can be easily obtained for B and C .

Table 4presents the calculated low-lying vibrational band origins for the ground state of O 35ClO,together with the corresponding experimental 19,25and previous 37,49computed data.The B3PW91calculations overestimate the vibrational band origins:the B3PW91/6-311ttG(2df,2pd)values are better than the corresponding results for B3PW91/6-311ttG(3df,3pd).The B3LYP calculations are much closer to the corresponding experimental 19,25counterparts:the B3LYP/6-311ttG(3df,3pd)values well reproduce the experimental data within 10cm à1,except for 2 3.

Table 5lists the calculated anharmonic constants x ij of O 35ClO,along with the available experimental 25and previous 49computed data.The results in Table 5show that the results of B3PW91/6-311ttG(3df,3pd)are closer to the experimental data

Table 3.Vibration àrotation interaction constants of O 35ClO (10à3cm à1).

B3PW91

B3LYP

Previous Expt.Constant Set A Set B Set A Set B Ref.49Ref.21 A 1 1.766744

1.906692

2.304055 2.34775 2.224872 1.799578 A 2à29.1427à30.7803à28.7568à30.4591à3

3.0128à31.9511 A 315.6412716.1491315.8381516.298915.6975216.06545 B 1 1.677101 1.710399 1.696813 1.735698 2.021398 2.002051 B 20.0470990.0822580.0793220.1069790.3702560.296739 B 3 1.456057 1.45448 1.515847 1.521408 1.82126 1.820926 C 1 1.535244 1.558184 1.571158 1.595077 1.79791 1.783901 C 20.6555180.6701570.6839870.6938110.8205680.798552 C 3

1.139812

1.157761

1.177269

1.199812

1.400969

1.429656

Density Functional Theory Studies

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than the values of B3LYP/6-311ttG(3df,3pd).It needs to point out,the present and previous 49results for X 23are close to each other,however,both of them are bigger almost twice than the corresponding experimental values.

Table 6contains the equilibrium quartic centrifugal distortion constants (S reduction 56)calculated from two quadratic force ˉelds (B3PW91and B3LYP)and compares them with the experimental 25and previous 49counterparts of O 35ClO.The discrepancies of the ˉrst fourth constants between the calculated equilibrium values at B3PW91/6-311ttG(3df,3pd)and the observed values are less than 6%.The results are in well agreement with the previous 49corresponding counterparts,it shows that the calculated equilibrium values are reliable at this level.It is worth noting that the present and previous 49value for D JK is smaller about 100KHz or 150KHz than the experimental counterpart.When we try to use other ab initio methods to investigate this species,the predicted value of D JK is also smaller about 100KHz than the experimental value.

The equilibrium sextic centrifugal distortion constants (S reduction 56)calculated from the B3PW91and B3LYP cubic force ˉelds are shown in Table 7,along with the

Table 4.Selected calculated vibrational band origins of O 35ClO (cm à1).

B3PW91

B3LYP Previous Expt.Constant Set A Set B Set A Set B Ref.38

Ref.49Ref.25

Ref.19!1982.6101001.448946.018966.038960.2963.5!2455.277459.898445.738450.681455.6451.7!31131.8681158.4381089.0401117.4151127.91133.0

1967.602985.942930.797950.714968940.8945.592 2451.337455.902441.552446.643451449.9447.702 31112.6621139.3391069.6131098.6051119

1105.71110.106

2 11928.7391965.0171855.0431894.6431872.118822 2902.408911.584882.714893.005898.78962 3

2215.3272268.8052129.1942187.5592200.12208 2t 11415.9301438.6571369.2781394.2191386.51389 3t 12066.1912111.1881986.1402035.3772029.32038

3t 2

1559.660

1590.878

1506.644

1540.875

1549.9

Table 5.

Anharmonicity constants X ij of O 35ClO (cm à1).

B3PW91

B3LYP

Previous Expt.Constant Set A Set B Set A Set B Ref.49Ref.25X 11à3.23311à3.43315à3.27530à3.39219à4.49à4.335X 12à3.00881à3.18737à3.07085à3.13799à4.06à3.993X 13à14.0741à14.0922à14.2702à13.9419à16.71à16.765X 22à0.133015à0.110335à0.195113à0.140882à0.48à0.15X 23à4.33977à4.36262à4.52068à4.37384à5.46à2.4X 33

à4.99913

à4.93603

à5.01571

à4.82594

à5.55

à5.61

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Table 6.Equilibrium quartic centrifugal distortion constants of O 35ClO (KHz).

B3PW91

B3LYP

Previous Expt.Constant Set A Set B Set A Set B Ref.49Ref.25D J 7.8989167.96068.0583158.1079838.538.5173D K à103.131656à107.9920à100.661603à106.018610à107à112.638D JK 1816.1397301908.82461804.1585511908.46644219502051.84d 1à2.167450à2.1827à2.195320à2.205003à2.21à2.3045d 2

à0.120404

à0.1189

à0.124649

à0.122444

à0.12

à0.1388

Table 7.Sextic centrifugal distortion constants of O 35ClO (Hz).

B3PW91

B3LYP

Expt.Constant Set A Set B Set A Set B Ref.25H J 0.014570.014400.014770.014600.01301H K à0.3318à0.3217à0.3429à0.3344à0.2945H JK à14.4635à15.6223à14.6121à15.8559à17.056H KJ 213.4288231.6281213.7939234.3013241.32h 1á1037.64287.5764637.7902497.72107.038h 2á1030.95580.94640040.99330.97860.986h 3á103

0.4005

0.399326

0.4160

0.4126

0.414

Table 8.Quadratic,cubic and quartic force constants of O 35ClO in normal coordinates (cm à1).

B3PW91

B3LYP Constant Set A Set B Set A Set B !1982.6101001.448946.018966.038!2455.277459.898445.738450.681!31131.8681158.4381089.0401117.415111à237.034à243.975à234.148à241.164211à28.152à28.470à26.986à27.7062217.4198.150 4.980 5.911222à41.260à43.571à41.624à43.615331à284.650à289.437

à281.177à286.342332à8.9168.066à9.970à9.544111146.95347.55947.35649.375211113.01515.29213.86715.9182211à11.215à11.999à10.809à11.1872221 5.238 6.455 5.495 6.7452222 4.612 5.671 3.643 5.133331156.74558.83057.57761.1403321 2.883 4.679 3.714 5.9563322à21.456à21.872à21.303à21.0703333

66.132

69.386

67.898

73.426

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J . T h e o r . C o m p u t . C h e m . D o w n l o a d e d f r o m w w w .w o r l d s c i e n t i f i c .c o m b y 218.56.38.228 o n 03/24/13. F o r p e r s o n a l u s e o n l y .

experimental 25counterparts of O 35ClO.With the basis set increasing,the results of B3PW91and B3LYP are both close to the experimental counterparts.The values at B3PW91/6-311ttG(3df,3pd)are better than the corresponding results at B3LYP/6-311ttG(3df,3pd).The discrepancies of sextic centrifugal distortion constants between the computed values at B3PW91/6-311ttG(3df,3pd)and the exper-imental counterparts are less than 10%.

Table 8lists the complete ab initio quartic force ˉelds in normal coordinates for O 35ClO.It includes the results of B3PW91and B3LYP with 6-311ttG(2df,2pd)and 6-311ttG(3df,3pd)basis sets,respectively.By deˉnition,the quadratic normal coordinate constants correspond to the harmonic wave numbers.The results at B3PW91/6-311ttG(3df,3pd)and B3LYP/6-311ttG(3df,3pd)are closer to each other,they can provide the reliable values of the force constants of O 35ClO.

4.Conclusion

The complete quartic force ˉelds and spectroscopic constants of O 35ClO have been computed at B3PW91and B3LYP theory employing 6-311ttG(2df,2pd)and 6-311ttG(3df,3pd)basis sets,respectively.These calculations make use of analytic B3PW91and B3LYP second derivatives,which are di?erentiated numerically in reduced normal coordinates.The B3PW91results are in excellent agreement with the available experimental data for O 35ClO,so that the B3PW91predictions for spectroscopic constants of O 35ClO,yet unknown,are expected to be reliable.B3PW91/6-311ttG(3df,3pd)a?ords a marked improvement over B3LYP/6-311ttG(3df,3pd)in the calculation of rotational constants,vibration àrotation interaction constants,and anharmonic constants.Our calculation also shows that basis set enhancement can lead to major improvements in the computed anharmonic properties and that 6-311ttG(3df,3pd)basis sets should be su±cient in such applications.

As an asymmetric top molecule,the e?ective Hamiltonian in S reduction 56can be written as:

^H S ?A K J 2z tA J J 2t12

a eJ 2ttJ 2àTàD K J 4z àD JK J 2J 2z àD J J 4tH K J 6z tH KJ J 2J 4z tH JK J 4J 2z tH J J 6td 1J 2eJ 2ttJ 2

àT

td 2eJ 4ttJ 4àTth 1J 4eJ 2ttJ 2àTth 2J 2eJ 4ttJ 4àTth 3eJ 6ttJ 6àT:e7T

In the above equation,A K ?A àeB tC T=2,A J ?eB tC T=2,a ?eB àC T=2,?; t

represents the positive commutator.Submitting the parameters in Tables 6and 7into the above equation,one can obtain the computed rotational energy of molecule in the study,which is necessary to assign the observed rotational energy of molecules.

Z.Zhu et al.

J . T h e o r . C o m p u t . C h e m . D o w n l o a d e d f r o m w w w .w o r l d s c i e n t i f i c .c o m b y 218.56.38.228 o n 03/24/13. F o r p e r s o n a l u s e o n l y .

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos.11074103and 10974078).All calculations for the present study were carried out at Shuguang Computer Center of Ludong University.References

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