Intermolecular potential energy surface, microwave and infrared spectra

Intermolecular potential energy surface,microwave and infrared spectra of the Kr–CO 2complex from ab initio calculationsRong Chen a ,Hua Zhu a ,b ,⇑,Daiqian Xie c ,⇑aSchool of Chemistry,Sichuan University,Chengdu 610064,ChinabState Key Laboratory of Biotherapy,Sichuan University,Chengdu 610064,China cInstitute of Theoretical and Computational Chemistry,Key Laboratory of Mesoscopic Chemistry,School of Chemistry and Chemical Engineering,Nanjing University,Nanjing 210093,Chinaa r t i c l e i n f o Article history:Received 11November 2010In final form 24June 2011Available online 28June 2011a b s t r a c tWe present a new potential energy surface for Kr–CO 2which incorporates its dependence on the asym-metric Q 3normal mode with CO 2in both ground (t 3=0)and the first excited (t 3=1)states were gener-ated by integration of this potential over the Q 3coordinate.Each potential is found to have a T-shaped global minimum.The radial DVR/angular FBR method are applied to calculate the rovibrational energy levels.The calculated band origin shifts,microwave and infrared spectra are in good agreement with the available experiment values.Ó2011Elsevier B.V.All rights reserved.1.IntroductionThe weak intermolecular forces and spectroscopy for the van der Waals (vdW)complexes between rare-gas (Rg)atoms and lin-ear molecules have attracted considerable attention recently since the spectroscopy of these complexes can provide very useful infor-mation on the nature of the intermolecular potential and dynamics of these weakly bound molecules.CO 2is one of the most important absorbers of infrared radiation in the earth’s atmosphere and inter-stellar chemistry,and the Rg–CO 2complexes are prototype sys-tems for studying the intermolecular interactions between nonpolar subunits.The intermolecular interaction for Rg–CO 2has become an important object of both experimental [1–9]and theoretical [10–19]studies in recent decades.The Ar–CO 2complex was first observed in microwave spectroscopy [1],and those results showed that it has a T-shaped structure.In 1988,Randal et al.observed the infrared spectra of Ne–,Ar–,Kr–,and Xe–CO 2com-plexes in the region of the t 3fundamental vibrational transition of CO 2[2].The inertial and centrifugal distortion rotational constants for complexes formed by CO 2in its ground and first excited t 3vibrational state were determined,as well as the band origin for transitions associated with that asymmetric stretch fundamental transition.Subsequently,microwave [3]and near-infrared [4]spectra of Ne–,Ar–and Kr–CO 2complexes were observed.In 1993,Ida et al.[5]observed the microwave spectros-copy of Ne–,Ar–,Kr–CO 2complexes.In 2005,the infrared spectra of Kr–C 18O 2[9]were also determined by diode laser absorption spectroscopy of a pulsed molecular beam.Arriving at a detailed understanding of these experimental studies requires an accurate potential energy surface (PES).In 1976,Parker et al.[10]obtained an ab initio potential energy surface for He–CO 2using the elec-tron gas method.In 1996,Marshall et al.[15]reported MP2and MP4potential energy surfaces for Ar–CO 2.Subsequently,Yan et al.[17]obtained a PES for He–CO 2using MP4perturbation the-ory with a large basis set containing bond functions.The rovibra-tional energy levels,infrared spectra and spectroscopic constants were investigated using this MP4potential.A more extensive ab initio study was carried out for He–CO 2and Ne–CO 2by Negri et ing MP4theory [18].In all the above theoretical calculations,the CO 2monomer was treated as a rigid rotor,which is not sufficient for predicting the infrared spectra and the band origin shifts [19].To do so requires one to take account of the influence of intramolecular vibrational modes on the intermolecular potential energy surface and dynam-ical calculations [20–22].To date,we have successfully used this approach to construct the potentials including the dependence on the Q 3normal coordinate of the CO 2molecule,and to reproduce the infrared spectra for H 2–CO 2[23],He–CO 2[24,25],Ne–CO 2[26]and Ar–CO 2[27].Li and co-workers also reported an accurate three-dimensional potential energy surface for He–CO 2and pro-vided a good representation of the experimental results [28,29].To our best knowledge,only a few theoretical study of the Kr–CO 2complex have appeared so far.Seal et al.[30,31]constructed a PES for Kr–CO 2at the DFT level.However,no further calculations of the bound states and spectroscopic properties have been re-ported.The purpose of this work is to present a three-dimensional Kr–CO 2ab initio PES involving the Q 3normal mode of CO 2using the supermolecular approach at the CCSD(T)level with a large0009-2614/$-see front matter Ó2011Elsevier B.V.All rights reserved.doi:10.1016/j.cplett.2011.06.067Corresponding authors.E-mail addresses:zhuhua@ (H.Zhu),dqxie@ (D.Xie).basis set plus bond functions.Fromtio PES we generated CO 2(t 3)–Kr potentials for t 3=0and 1.pling between the inter and small,these averaged potentials properties of the vdW clusters.The and Lanczos algorithm were tional energy levels.The transition and the band origin shifts were the available observed putational details 2.1.Ab initio calculationsThe geometry of the Kr–CO 2coordinates:R ,h ,Q 3.R is the CO 2center of mass.h denotes the vector and the molecular axis of CO 2.the normal mode for the t 3fined as Q 3¼ðr CO1Àr CO2Þ=ffiffiffi2p ,where r bond lengths of CO 2.The average C–O and 1states for CO 2and C 18O 2experimental rotational constants the one-dimensional Q 3potential to for the Q 3mode of the CO 2and C 18O 2scaling method [33].For the Q 3coordinate of CO 2and C 18O 2we adopt the PODVR grid points determined in our previous work for Ne–CO 2[26].Ab initio potential energies for Kr–CO 2were calculated at the coupled-cluster singles and doubles level with non-iterative inclu-sion of connected triples [CCSD(T)][34]for a total of 1700symme-try-unique points.For each of the five PODVR Q 3values,results were generated at 25–27values with R ranging from 4.0to 22.0a 0values,and 13angles ranging from h =0°to 180°in a step of 15°.We used the augmented correlation-consistent polarized va-lence triple-zeta (aug-cc-pVTZ)basis set of Woon and Dunning [35]for the C and O atoms and the uncontracted basis sets and the quasirelativistic 28-core-electron pseudopotential plus the cc-pVQZ basis for valence electron for the Kr atom [36],as well as (3s,3p,2d,1f,1g)bond functions (for 3s and 3p,a =0.9,0.3,0.1;for 2d,a =0.6,0.2;for f and g,a =0.3)[37].The bond functions are placed at the mid-point of the R vector to eliminate the need for high angular momentum functions in the atom centered basis set.The supermolecular approach was used to obtain the intermo-lecular potential energies.The full counterpoise procedure [38](FCP)was employed to correct for basis set superposition error (BSSE).The ab initio points for the Kr–CO 2complex are presented in Table S1of the supporting ing the potential points of Kr–CO 2,the potential of Kr–C 18O 2is determined from Lagrange interpolation on the Q 3coordinate.All the ab initio calculations were carried out using the MOLPRO package [39].2.2.Analytical representation of the potential energy surface The vibrationally averaged intermolecular PESs V t 3ðR ;h Þare de-fined as [40]V t 3ðR ;h Þ¼Z1À1w t 3ðQ 3ÞV ðR ;Q 3;h Þw t 3ðQ 3ÞdQ 3;ð1Þin which t 3represents the quantum number for a specific vibra-tional state of the linear CO 2molecule,and w t 3ðQ Þare the corre-sponding vibrational wavefunctions.The averaged ab initio potentials V t 3ðR ;h Þ(t 3¼0;1)were fitted to the analytical form [41,42]V ðR ;h Þ¼V sh ðR ;h ÞþV as ðR ;h Þð2ÞThe short-range part of the potential is assumed to beV sh ðR ;h Þ¼G ðR ;h Þe D ðh ÞÀB ðh ÞR ;ð3Þwhere D(h ),B(h ),G(R,h )can be expanded in terms of Legendre poly-nomial P l (cos h )D ðh Þ¼X 2l ¼2d l P l ðcos h Þ;ð4ÞB ðh Þ¼X 8l ¼0b l P l ðcos h Þ;ð5ÞG ðR ;h Þ¼RÀ1X 1i ¼0RiX 8l ¼0g i ;l P l ðcos h Þð6ÞThe term V as ðR ;h Þrepresenting the long-range part of the po-tential is expressed asV as ðR ;h Þ¼ÀX 12n ¼6X 8l ¼0f n ðB ðh ÞR Þc n ;l R Àn P l ðcos h Þð7ÞFigure 1.Contour plots (in cm À1)of the averaged intermolecular potential energy surface of Kr–CO 2for the ground state of CO 2(t 3=0).Table 1The calculated energy levels (in cm À1)for the first 10vibrational bound states of the Kr–CO 2and Kr–C 18O 2complexes for the t 3=0and 1states of CO 2.Kr–CO 2Kr–C 18O 2N Ground state t 4StateN Ground state t 4State0À197.6810À198.52390À199.2081À200.09761À167.6537À168.50501À170.6369À171.65542À165.4477À166.21742À167.6217À168.44703À141.1568À141.90373À144.2640À145.15804À140.5787À141.24334À143.7854À144.64935À135.2621À135.94495À138.3764À139.17446À121.9641À122.65036À125.0657À125.87277À121.5580À122.19967À124.6110À125.37558À111.6322À112.23618À115.7596À116.63249À109.8391À110.49379À113.1742À113.9326230where indices l and n must be even and f n ðB ðh ÞR Þis written in the Tang–Toennies form [43]f n ðx Þ¼1ÀeÀxX n k ¼0ðx Þkk !ð8ÞThe fitted potential parameters and the FORTRAN code for the averaged PESs are listed in Table S2and Code S1.2.3.Calculation of the rovibrational energy levelsWithin the Born–Oppenheimer approximation,the vibrational-ly averaged intermolecular Hamiltonian of the Kr–CO 2complex in Jacobi coordinates can be written as [44]^H ¼À12l @2@R À^j 22I t 3þð^J À^j Þ22R þV t 3ðR ;h Þð9Þwhere l is thereduced mass of the complex,and I t 3¼w t 3ðQ 3ÞD I Q 3w t 3ðQ 3Þ E ,is the vibrational averaged rotational moment of the linear CO 2molecule,^J is the total angular momentumoperators,^j is the angular momentum operator for the CO 2monomer,and V t 3ðR ;h Þis the adiabatic potential in a particular vibrational state t 3ðt 3¼0;1Þof the isolated CO 2.The efficient radial DVR/angularFBRTable 2Calculated microwave transition frequencies (in cm À1)and relative intensities for Kr–CO 2.Observed data are taken from Ref.[5].J 0K 0a K 0cÀJ 00K 00a K 00ct calt cal Àt obsIntensity 202–1010.1678À0.00140.784303–2020.2515À0.00200.673404–3030.3351À0.00270.432505–4040.4186À0.00300.236606–5050.5017À0.00400.342322–2210.2516À0.0021 1.000321–2200.2518À0.00200.953423–3220.3354À0.00270.634422–3210.3359À0.00270.563524–4230.4192À0.00340.361523–4220.4201À0.00340.409625–5240.5029À0.00400.156624–5230.5045À0.00410.129method[45]was employed to calculate the rovibrational energy lev-els.The Lanczos algorithm method[46]was performed to efficiently diagonalize the Hamiltonian matrix with5000steps.3.Results and discussion3.1.Potential energy surfaceThe root–mean–square(rms)errors of thefitted vibrationally averaged potentials for both the t3=0and1states of CO2werefound to be about0.08cmÀ1.The contour plot of V t3¼0ðR;hÞis givenin Figure1.A T-shaped global minimum is located at R=6.75a0and h=90.0°with a depth ofÀ231.70cmÀ1for V t3¼0ðR;hÞandÀ232.42cmÀ1for V t3¼1ðR;hÞ.No linear local minima were de-tected.The h=0°saddle point energies areÀ116.27cmÀ1forV t3¼0ðR;hÞandÀ117.60cmÀ1for V t3¼1ðR;hÞ,respectively,and bothoccur at R=9.05a0.It is clear from thisfigure that the PES show a fairly large angular anisotropy,which means that Kr atom is strongly hindered from free motion around the CO2molecule.3.2.Bound states of rovibrational energy levlesThe energies for thefirst ten vibrational bound states of the Kr–CO2and Kr–C18O2complexes for the t3¼0and1state of CO2are listed in Table1.The calculated vibrational band origins shifts for the Kr–CO2and Kr–C18O2complexes are found to beÀ0.8429 andÀ0.8895cmÀ1,respectively,which are close to the observed values ofÀ0.8841cmÀ1([2])andÀ0.8651cmÀ1([9]).Although the bend and the symmetric stretch of CO2may have a slight effect on the effective interaction and dynamics of the complex,the work of Li et al.[29]on He–CO2found that accurate prediction of t3 vibrational frequency shifts for this system required one to take ac-count of the difference in the average values of Q1for t3=0and1. We will examine the effect of the Q1mode on the t3band origin shifts in future work.To shed some light on the dynamics of the system,it is neces-sary to visualize the wave functions.The vdW vibrational states are defined by the two approximate quantum numbers n s and n b, respectively,denoting the vdW stretching and bending modes. Their assignments are loosely defined since n s and n b are not good quantum numbers and there is significant mixing between the two modes for higher intermolecular excited states.Therefore,the intermolecular vibrational states in Table1are labeled in order of increasing energy.Figure2presents contour plots of the wave functions for the lowest six vibrational states of Kr–CO2for the ground state of CO2(t3=0).The structures for the vibrational states of Kr–CO2consider in thisfigure are all located close to the T-shaped global minimum.The average structures were determined from the intermolecular vibrational ground stateTable3Calculated infrared transition frequencies(in cmÀ1)and relative intensities for Kr–C18O2.Observed data are taken from Ref.[9].J0K0a K0c ÀJ00K00aK00ct cal t calÀt obs Intensity J0K0a K0cÀJ00K00aK00ct cal t calÀt obs Intensity937–10462310.17870.00210.321413–4042313.5124À0.00520.845 936–10472310.17900.00240.315514–5052313.5247À0.0055 1.000 836–9452310.25720.00170.425615–6062313.5399À0.00580.968 835–9462310.25730.00180.411716–7072313.5582À0.00620.715 735–8442310.33580.00100.387111–0002313.5656À0.00580.393 734–8452310.33590.00110.385817–8082313.5798À0.00670.715 634–7432310.4138–0.00030.713918–9092313.6050À0.00700.539 633–7442310.41450.00040.7191019–100102313.6340À0.00800.568 533–6422310.4930–0.00020.792212–1012313.6400–0.00610.293 532–6432310.4930À0.00020.78111110–10112313.6671À0.00780.359 432–5412310.5722À0.00070.53112111–120122313.7046À0.00770.128 431–5422310.5722À0.00070.5381139–122102313.71310.00180.091 533–5422310.9678À0.00540.301313–2022313.7120À0.00570.394 532–5412310.9678À0.00540.31113112–130132313.7465À0.00820.535 634–6432310.9680À0.00520.298414–3032313.7817À0.00550.735 633–6422310.9681À0.00510.2931037–112102313.85000.00810.435 735–7442310.9684À0.00480.305515–4042313.8492À0.00340.634 734–7432310.97330.00010.310616–5052313.9146À0.00370.630 836–8452310.9687À0.00450.307717–6062313.9781À0.000370.615 835–8442310.9690À0.00420.312818–7072314.0402À0.00800.495 937–9462310.9693À0.00380.301919–8082314.1003À0.00760.511 936–9452310.9697À0.00350.29710110–9092314.1596À0.00760.498 1038–10472310.9700À0.00320.30811111–100102314.2180À0.00720.310 1139–11482310.9707À0.00240.31112112–110112314.2759-0.00710.291 1037–10462310.9707À0.00240.30413113–120122314.3336À0.00760.263 1138–11472310.97550.00230.31114114–130132314.3914À0.00820.131 10110–11292311.20330.00720.79515115–140142313.4495À0.00890.085 919–10282311.31690.00650.68516116–150152314.52350.00600.131 13112–142132311.34080.00440.615936–9272314.6995À0.00010.217 12111–132122311.39090.00370.591431–4222314.7136À0.00240.532 818–9272311.42560.00520.620634–6252314.72820.00220.413 1019–112102311.49700.00320.776533–5242314.7143À0.00170.412 918–10292311.55310.00210.723735–7262314.7145À0.00150.408 817–9282311.61140.00210.813330–3212314.7143À0.00170.394 616–7252311.62960.00310.709432–4232314.7144À0.00160.421 817–7262312.9550À0.00110.315331–3222314.7146À0.00140.398 515–6062312.98090.00360.735836–8272314.7151À0.00090.415 918–8272313.0540À0.00960.412937–9282314.71610.00010.397 414–5052313.07040.00150.6311038–10292314.71760.00160.399 313–4042313.15820.00070.430331–2202314.9521À0.00010.396 1019–9282313.1550À0.01120.103330–2212314.9512À0.00010.413 110–1012313.4910À0.00450.358432–3212315.0308À0.00290.213 211–2022313.4957À0.00460.585431–3222315.0311.À0.00260.214 312–3032313.5007À0.00680.891rms error0.005232R.Chen et al./Chemical Physics Letters511(2011)229–234wavefunction of the complex,h R i ¼w 0h j R w 0j i andh cos 2h i ¼w 0h j cos 2h w 0j i :The calculated average distance R for the ground state is 6.95a 0and the angle h is 83.8°,the latter is a mea-sure of the average amplitude of the bending from the 90°average configuration,which can be interpreted as the zero-point vibra-tional motion of CO 2within the complex.The calculated average structure is close to the effective structure [2]R =6.85a 0and h =83.28°determined from the observed infrared spectra [2].For the first two intermolecular excited states,the average distance and corresponding dispersion are 7.01±0.48,7.09±0.57a 0respec-tively,while the average angle and corresponding dispersion are 81.6±6.9°,80.2±7.2°,respectively.These values indicate the com-plex in the first two intermolecular excited states is less rigid than in the ground state.From Figure 2we also find that the first inter-molecular excited state can be attributed to the intermolecular bending mode with a frequency of 30.027cm À1,while the second intermolecular excited state is due to the intermolecular stretching mode with a frequency of 32.233cm À1.For the t 3=1state of CO 2,the calculated average distance R and angle h are 6.94a 0and 83.7°and the energy of the first intermolecular excited state is 30.019cm À1.A comparison of the wave functions of Kr–CO 2with those of He–CO 2,Ne–CO 2and Ar–CO 2indicates significant differences.Our results show that the structure distributions for the nine lowest levels are localized close to the global minimum,while that for the tenth is spread somewhat more widely and those for higher vibrational states are delocalized more widely towards larger an-gles.The theoretical research on He–CO 2[24]found that only the structure distribution for the ground state was localized near the global minimum,while for Ne–CO 2[26]and Ar–CO 2[27]the distri-butions for the lowest three and six lowest states,respectively,are localized there.These differences mainly reflect the different effects of zero-point energy of these complexes.The zero-point energy of 33.89cm À1for Kr–CO 2is only about one-seventh of the global well depth,while the zero-point energy of 32.41cm À1for He–CO 2[24]is nearly two-thirds of the global well depth,thezero-point energy of29.71cmÀ1for Ne–CO2[26]is about one-third of the global well depth,and the value of36.67cmÀ1for Ar–CO2 [27]is about one-sixth of the global well depth.The rovibrational energies were assigned by the antisymmetric rotor quantum numbers JK a K c.J is the total angular momentum and K a and K c denote the projections of J onto the a and c principal axes of inertia.According to our previous research[24],the rotational energy levels were divided into four blocks,(even/even),(even/ odd),(odd/even),and(odd/odd)for different combination parity of(j/p).The calculated rovibrational energies for Kr–CO2and Kr–C18O2complexes are presented in Table S3.3.3.The microwave and infrared spectraDetails regarding calculation of the transition intensities can be found in our recent review[47].The calculated pure rotational transition energies and intensities at T=4K for Kr–CO2,and the deviations of the former from the microwave spectra are given in Table2.It is clear that our calculated frequencies agree well with the observed values,with a root mean square deviation of 0.003cmÀ1.The transition from322to221is found to be the stron-gest.In this Letter,we label the t3asymmetric stretch of CO2as the t4vibrational mode in the Kr–CO2complex.The calculated infrared transition are defined as the differences between the appropriate rovibrational energies on the upper(t3=1)and lower(t3=0)2D surface,plus the experimental CO2t3band origin energy[2,9]. The calculated infrared transition frequencies and line intensities of Kr–C18O2in the t3range of CO2at the rotational temperature of T=4K are given in Table3.One can see that most of the calcu-lated frequencies are within0.005cmÀ1of the observed frequen-cies and the root-mean-square error is0.005cmÀ1.Overall,the calculated transition frequencies are in excellent agreement with the experimental values.The fundamental infrared spectra for Kr–C18O2contain only b-type(D K a=±1)transitions,and the stron-gest transition is found to be from514to505.Figure3plots a portion of the simulated infrared spectra,which is consistent with the observed spectra of Ozaki[48].Although agreement between the calculated and observed values demonstrates the accuracy of the new PES,higher quality results on Kr–CO2would be obtained using basis set extrapolation.4.ConclusionWe have presented a three-dimensional PES for the Kr–CO2 complex including the Q3normal mode of CO2at the CCSD(T)level with a large basis set plus bond functions.The intermolecular potential was calculated overfive PODVR grid points for the Q3 normal mode.Based on the ab initio potential points,two vibra-tionally averaged PESs of the complex were generated.Each PES has a T-shaped global minimum,and no linear minima are de-tected.The bound rovibrational energy levels of Kr–CO2were obtained by employing the radial DVR/angular FBR method and the Lanczos algorithm.The experimental band origin shifts in the infrared spectra of Kr–CO2and Kr–C18O2are reproduced very well. In addition,the calculated microwave and infrared spectra are in good agreement with the available experiment values.AcknowledgmentsThis work was supported by the National Natural Science Foun-dation of China(Grant Nos.20973117and20725312)and by the Ministry of Science and Technology(2007CB815201).Appendix A.Supplementary dataSupplementary data associated with this Letter can be found,in the online version,at doi:10.1016/j.cplett.2011.06.067. 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