Chemical Physics Letters 549 (2012) 12–16

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Chemical Physics Letters

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A three-dimensional potential energy surface and infrared spectrafor the Kr–OCS van der Waals complex

Chunyan Sun, Xi Shao, Chunhua Yu, Eryin Feng ⇑, Wuying HuangDepartment of Physics, Anhui Normal University, Wuhu 241000, PR China

a r t i c l e i n f o

Article history:Received 7 July 2012In final form 28 August 2012Available online 1 September 2012

0009-2614/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.cplett.2012.08.052

⇑ Corresponding author.E-mail address: fengbf@mail.ahnu.edu.cn (E. Feng)

a b s t r a c t

The first three-dimensional potential energy surface (PES) of the Kr–OCS complex is developed at theCCSD(T) level with a large basis set plus midpoint bond functions. The potential includes explicit depen-dence on the v3 antisymmetric stretching coordinate of the OCS molecule. Two vibrationally adiabaticpotentials with the OCS molecule at both the ground and the first vibrational v3 excited states are gen-erated. The resulting potentials provide a good representation of the experimental infrared data: for66 infrared transitions the root-mean-square discrepancy is about 0.011 cm�1. The calculated infraredband origin shift, bending ground frequency, and molecular constants associated with the v3 fundamentalof OCS are all in better agreement with the experimental counterparts.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

There are considerable interests in the van der Waals (vdW)interaction between a rare-gas (Rg) atom and a linear OCS mole-cule, since OCS has proven to be an ideal probe of ultracold nano-droplets, a topic of intense recent interest in chemical physics [1].In experiments, the spectra of Rg–OCS (Rg = He,Ne,Ar,Kr) havebeen extensively investigated. For example, Harris et al. [2] re-corded the radio frequency and microwave spectrum of the Ar–OCS complex and deduced Ar–OCS has a T-shaped structure fromthe measured rotational constants and dipole moment compo-nents. Subsequently, the microwave spectra of (Ne, Ar, Kr)–OCSwere reported by Lovas and Suenran [3]. The infrared-absorptionspectra for these complexes in the antisymmetric stretching v3 re-gion of the OCS monomer were further investigated by Haymanet al. [4,5]. Xu et al. [6,7] measured the microwave spectra of iso-topically substituted He–OCS and Ne–OCS. Rotational and centrif-ugal distortion constants were determined in these works.Grebenev et al. [8,9] measured the rotationally resolved infraredspectrum of the OCS embedded in large helium droplets. A red-shift of �0.557 cm�1 was observed for the vibrational frequencycorresponding to antisymmetric stretching m3 of the OCS molecule.

On the theoretical side, much attention was devoted to the He–OCS, Ne–OCS and Ar–OCS complexes, and less to the Kr–OCS com-plex. The first He–OCS potential energy surface (PES) was obtainedby Danielson et al. [10] in 1987 by fitting total differential crosssection measurements. A more extensive ab initio study was car-ried out by Sadlej and Edwards [11] in 1993 using MP4 perturba-tion theory. The first attempt to include explicit dependence on

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.

the antisymmetric stretching vibration of the OCS molecule inthe He–OCS interaction potential was made by Gianturco andPaesani [12] in 2000. Yan et al. [13] reported the first PES for theNe–OCS complex at the MP2 electron correlation level and Zhuet al. [14] recalculated the PES for this complex at CCSD(T) level.For the Ar–OCS complex, the first ab initio calculation was limitedto Hartree–Fock (HF) level in providing short-range repulsive inter-actions [15]. Recently, Zhu et al. [16] carried out a more extensivecalculation of the PES at CCSD(T) level. The calculated pure rota-tional transition frequencies for the vibrational ground state arein good agreement with the experimental values.

In a recent work [17], we presented a PES for the Kr–OCS com-plex with bond lengths of OCS monomer fixed at the experimentalvalues. The predicted transition frequencies and spectroscopic con-stants were in good agreement with the microwave experimentalresults. Because the PES is two-dimensional in the work, it cannotbe used to interpret the infrared spectra which involve the normalmode excitation of OCS. A three-dimensional potential is thus de-manded. However, there is no report on it up to now. In this Letter,we present the ab inito determination of the PES for the Kr–OCScomplex including explicit dependence on the antisymmetricstretching vibration of the OCS molecule. The PES is then used inthe succeeding rovibrational energy levels calculations. The com-parisons of predicted transition frequencies and spectroscopic con-stants with the experimental infrared spectra are given.

2. PES computation

2.1. Ab initio calculations

The geometry of the Kr–OCS complex is described with the Ja-cobi coordinates (R, h, Q3). R denotes the distance from the Kr atom

Table 1Range of the antisymmetric stretching coordinate Q3, corresponding sets of (r1, r2, r)values of the internal coordinates (in a0).

Q3 r1 r2 r

�0.5 2.86855 2.48703 5.35558�0.3 2.59494 2.67164 5.26658�0.1 2.32133 2.85626 5.177580.0 2.18452 2.94856 5.133080.1 2.04772 3.04087 5.088580.3 1.77410 3.22548 4.999580.5 1.50049 3.41009 4.91058

C. Sun et al. / Chemical Physics Letters 549 (2012) 12–16 13

to the OCS center of mass, h is the angle between R and the OCSmolecule with h = 180� referring to the linear Kr–O–C–S configura-tion, and Q3 is the normal coordinate for the v3 antisymmetricstretching vibration of the monomer OCS molecule. The geometryoptimization provides the expression for the Q3 normal modecoordinate,

Q 3 ¼ �0:511zo þ 0:857zc � 0:066zs; ð1Þ

where zo; zc; zs refer to unit vector displacements from equilibriumof O, C, and S, respectively, see Figure 1. In the calculation of the fullKr–OCS potential energy surface V(R, h, Q3) we consider seven dif-ferent values of Q3: �0.5, �0.3, �0.1, 0, 0.1, 0.3, 0.5 correspondingto extensions of the OCS molecule, with Q3 = 0 corresponding tothe equilibrium geometry. From Eq. (1), one can relate the Q3 withcorresponding actual values of r1, r2 and r (r = r1 + r2) as listed inTable 1.

For each of these seven OCS configurations the ab initio calcula-tions are then performed for 13 values of h{0, 20, 40, 60, 80, 90,100, 110, 120, 130, 150, 170, 180}�, and 19 values of R {6.0, 6.5,7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10, 10.5, 11, 11.5, 12, 12.5, 13, 15, 17,19, 20}a0. In total, we calculate 1729 points of the potential energysurface V(R, h, Q3).

The calculations are performed at the CCSD(T) level. The aug-mented correlation-consistent polarized valence triple-f (aug-cc-pVTZ) basis set of Woon and Dunning [18] is chosen for O, Cand S atoms. The quasirelativistic 10-core-electron pseudopoten-tial and augmented correlation-consistent polarized valencequadruple-f (aug-cc-pVQZ-PP) basis set is used for Kr atom [19].The set of midbond functions (3s3p2d1f) of Tao and Pan [20] (for3s and 3p, a = 0.9, 0.3 and 0.1; for 2d, a = 0.6, 0.2; for 1f, a = 0.3)are adopted with the aim of speeding up convergence of the energywith respect to the basis set size. The supermolecular approach isemployed and the full counterpoise procedure of Boys andBernardi is used to correct for basis set superposition error. Thecalculations are carried out using the MOLPRO-2006 package [21].

2.2. Construction of the three-dimensional potential energy surface

The complete three-dimensional PES V(Q3, R, h) is constructedby two steps. First, we construct seven two-dimensional PESsVðQ i

3; R; hÞ for each fixed Q i3 (i = 1–7), respectively, using the po-

tential model originally suggested by Bukowski et al. [22], and thathave been used in our previous studies [17,23–25]. The two-dimensional PES is presented by the sum of two terms, the shortrange term Vsh and the asymptotic termVas:

VðR; hÞ ¼ VshðR; hÞ þ VasðR; hÞ: ð2Þ

Here

Figure 1. Jacobi coordinates for the Kr–OCS complex employed in the ab initiocalculations.

Vsh ¼ GðR; hÞeBðhÞ�DðhÞR; ð3Þ

VasðR; #Þ ¼X10

n¼6

Xn�4

l ¼ 0;2 . . .

l ¼ 1;3 . . .

fnðDðhÞRÞ �Cnl

Rn P0l ðcos hÞ; ð4Þ

where fn(x) is the Tang-Toennies damping function [26]. D(h), B(h)and G(R, h) are further expanded in terms of Legendre polynomialsP0

l ðcos hÞ. The expansion coefficients and Cnl parameters are deter-mined by a two-step nonlinear least squares fitting procedure[17,23–25]. Those configurations with energy more than 500 cm�1

are excluded from the fit.Next, the seven two-dimensional PESs are used to construct the

three-dimensional PES by interpolating along Q3 using a six-orderpolynomial:

VðQ i3;Rj; hkÞ ¼

X6

n¼0

Ai;nanðRj; hkÞ; ð5Þ

where Ai;n ¼ ðjQ i3Þ

n. For a given values of (Rj, hk), the an (n = 0,. . ..6) isthus determined from seven two-dimensional PESs VðQi

3;R; hÞ bysolving a 7-variables linear equations,

anðRj; hkÞ ¼X6

i¼0

½Ai;n��1VðQ i3;Rj; hkÞ; ð6Þ

where Qi3 = (�0.5, �0.3, �0.1, 0.0, 0.1, 0.3, 0.5), respectively. The an’s

are then used to calculate the VðQi3;Rj; hkÞ according to Eq. (5).

The total root-mean-square (rms) error is 0.158 cm�1 and themaximum absolute deviation is 1.027 cm�1 for 1443 fitting config-urations. In order to test the accuracy, we also compare the inter-action energies predicted by our three-dimensional PES with the abinitio values additionally calculated at Q3 = �0.2, +0.2 in a total of423 configurations. The total test rms error is 0.356 cm�1, andthe maximum absolute deviation is 5.14 cm�1. The comparisonsare list in Table 2. We see that our PES agrees well with the ab initiocalculation, indicating that our surface is a faithful representationof the CCSD(T) potential energy.

Table 2Comparison of our three-dimensional surface with ab initio CCSD(T) computations.The Dmax is the maximum absolute deviation, and the Drms is the root-mean-squaredeviation. All the deviations are reported in cm�1.

Energy range(cm�1)

Fitting points Testing points

No. ofpoints

Dmax Drms No. ofpoints

Dmax Drms

500–0 79 0.323 0.179 23 5.14 1.36�20–0 897 1.027 0.187 140 0.135 0.04<�20 467 0.5523 0.072 260 0.582 0.21

2 4 6 8 10 12 14 16 18

-200

-100

0

100

200

v20

v10

v21

v22

v11

Ene

rgy

(cm

-1)

R (a 0)

v00

Figure 3. Vibrational matrix elements of the three-dimension PES as a function of Rfor h = 90�.

Table 3The calculated energy levels (in cm�1) for some lowest bound states of the 84Kr–OCScomplexes for v3 = 0 and v3 = 1 vibrational states of the OCS molecule. ns and nb,respectively, denote the vdW stretching and bending mode.

14 C. Sun et al. / Chemical Physics Letters 549 (2012) 12–16

3. Rovibrational energy levels calculation

3.1. Vibrationally averaged potentials and bound state calculations

Some previous works [12,27,28] showed that the vibrationallyadiabatic potential provides a good explanation for the experimen-tal results. It is because that the vibrational motion of OCS is usu-ally fast compared to the other motions in the Rg–OCS system. Thevibrationally averaged matrix elements of Kr–OCS three-dimen-sional potential can be expressed as:

Vv3v 03ðR; hÞ ¼ vv3

ðQ 3ÞD ���VðQ 3;R; hÞ vm03

ðQ3Þ��� E

; ð7Þ

where m3 is the quantum number for the antisymmetric stretchingvibrational state of isolated OCS monomer, and vv3

ðQ3Þ is the corre-sponding vibrational wave function. vv3

ðQ3Þ is obtained by solvingthe following one-dimensional Schrödinger equation:

� 12M

d2

dQ23

þ VOCSðQ3Þ" #

vv3ðQ3Þ ¼ Ev3vv3

ðQ 3Þ; ð8Þ

where M is the OCS reduced mass along the Q3 normal coordinateand VOCS(Q3) is the corresponding potential energy curve. TheVOCS(Q3) is calculated by CCSD(T) method at 37 values of Q3 rangingfrom +0.5 to �0.5. The discrete variable representation (DVR) gridmethod is used to solve the Eq. (8). Clearly, the diagonal matrix ele-ments with v3 ¼ v 03 correspond to the vibrationally adiabatic poten-tial. The off-diagonal matrix elements describe nonadiabatic effectsthrough which the OCS molecule can undergo changes of its vibra-tional state during the interaction with the Kr partner.

The vibrationally averaged ground state PES (V00 surface) ischaracterized by a global T-shaped minimum and one local collin-ear minimum. The global minimum energy is �271.23 cm�1 atRe = 7.152a0 and he = 103.5�, which is slightly different from(�270.73 cm�1, 7.146a0, 105.0�) predicted by our recently con-structed two-dimensional potential surface [17]. It results fromthe minor difference in bond lengths of the adiabatic Q3 vibrationalground state and equilibrium values of the OCS monomer. Strongeranisotropy is shown in the global minimum region, which meansthat the Kr atom is much hindered from moving freely aroundthe OCS molecule and localized near the C atom in a T-shapedgeometry. The second minimum with a depth of �195.15 cm�1

locates at R = 9.17a0, h = 0.0�, corresponding to the collinearKr–S–C–O structure.

Figure 2. Computed energy differences between vibrationally adiabatic V00 and V11

PES’s (in cm�1).

The difference contours between the adiabatic potentials V00

and V11 are shown in Figure 2. There are only little changes inthe region of potential minimum, since the coupling acts mostlywithin the short-range, repulsive region of the interaction. It indi-cates that the structure of the Kr–OCS complex does not changesignificantly on excitation of the v3 vibration of OCS. The corre-sponding behavior of the nonadiabatic, off-diagonal matrix ele-ments at h = 90� is presented in Figure 3 along with the diagonalones. It can be seen that the diabatic couplings are important onlyin regions that are inaccessible to the bound states. When the rel-ative distances between partners move away from the repulsivewalls, the excitation coupling essentially dies out. The adiabaticsurfaces V00 and V11 are therefore employed to calculate the boundstates for the Kr–OCS complex. A FORTRAN subroutine for generatingboth the full three-dimensional PES and the vibrational matrix ele-ments is available on request.

(ns, nb) Ground state (v3 = 0) Excited state (v3 = 1)

0, 0 �239.0998 �239.96550, 1 �213.9441 �214.90461, 0 �206.3386 �207.15850, 2 �190.7387 �191.71762, 0 �183.6880 �184.60201, 1 �177.6478 �178.4365

Table 4The calculated spectroscopic constants (in cm�1) for the 84Kr–OCS complex togetherwith the observed values.

Ground state (v3 = 0) Excited state (v3 = 1)

Cal. Obs.a Cal. Obs.a

A 0.222266 0.221631 0.221560 0.220759B 0.032423 0.032971 0.032438 0.032929C 0.028167 0.028571 0.028167 0.028586DJ 1.128 � 10�7 1.157 � 10�7 1.128 � 10�7 �DJK 1.001 � 10�6 1.031 � 10�6 9.983 � 10�7 �DK 5.243 � 10�6 4.945 � 10�6 5.226 � 10�6 �dJ 1.716 � 10�8 1.780 � 10�8 1.723 � 10�8 �dK 1.208 � 10�6 1.234 � 10�6 1.183 � 10�6 �

a Data converted from Refs. [3,5].

C. Sun et al. / Chemical Physics Letters 549 (2012) 12–16 15

In the vibrationally adiabatic approximation, the nuclear mo-tions of the Kr–OCS are thus described by (in atomic units),

H ¼ � 12l

@2

@R2 þðJ � jÞ2

2lR2 þ bv3 j2 þ Vv3v3 ðR; hÞ; ð9Þ

where l is the reduced mass of the complex, J and j are the rota-tional angular momentum operators corresponding to the totaland the OCS monomer. Vv3v3 ðR; hÞ is the adiabatic potential in a par-ticular vibrational state v3 (v3 = 0,1) of the OCS and bv3 is the corre-sponding rotational constant. The method used to solve the Eq. (9)has been described in detail in our previous papers [17,23–25].

3.2. Results and comparison with experiments

A self-written FORTRAN code is used to calculate the rovibrationalenergy levels and wave functions of the Kr–OCS. In the calculation,the values of the OCS rotational constants used in the calculationsis fixed at the experimental values [29] (b0 = 0.202856 cm�1 andb1 = 0.202251 cm�1). The rotational energies of Kr–OCS are as-signed by the conventional notation JKaKc

. J is the total angularmomentum and Ka and Kc denote the projections of J onto the aand c axes in the principal axes of inertia. From the rotational ener-gies computed for the Kr–OCS complexes with the OCS molecule inboth v3 = 0 and v3 = 1 antisymmetric stretching vibrational states,one then calculate the rovibrational transition frequency accordingto,

m ¼ m0 þ Ev3¼1J;Ka ;Kc

� Ev3¼0J0 ;Ka0 ;Kc0

; ð10Þ

Table 5Calculated infrared transition frequencies (in cm�1). For observed values, thenumbers in parentheses indicate the residuals.

TransitionJKaKc

J0K 0a K 0c

Calc. (O–C) TransitionJKaKc

J0K 0aK 0c

Calc. (O–C)

717–808 2060.9955(0.0006) 514–505 2061.5608(0.0086)707–716 2061.0777(0.0102) 615–606 2061.5755(0.0082)000–111 2061.0850(0.0119) 111–000 2061.5851(0.0113)606–615 2061.0954(0.0095) 716–707 2061.5934(0.0085)505–514 2061.1099(0.0106) 101,9–100,10 2061.6691(0.0124)404–413 2061.1215(0.0108) 808–717 2061.6752(0.0188)403–312 2061.1305(0.0112) 313–202 2061.6957(0.0112)202–211 2061.1371(0.0111) 111,10–110,11 2061.7025(0.0123)101–110

a 2061.1412(0.0116) 414–303 2061.7480(0.0118)414–505 2061.2049(0.0034) 515–404 2061.7984(0.0116)101–202

b 2061.2141(0.0113) 826–817 2061.8486(0.0017)660–661 2061.3101(0.0035) 624–615 2061.8695(0.0050)661–660 2061.3101(0.0035) 523–514 2061.8795(0.0051)761–762 2061.3102(0.0034) 422–413 2061.8885(0.0061)762–761 2061.3102(0.0034) 321–312 2061.8961(0.0061)862–863 2061.3104(0.0032) 221–212 2061.9148(0.0075)863–862 2061.3104(0.0032) 322–312 2061.8958(0.0316)550–551 2061.3178(0.0069) 423–414 2061.9299(0.0071)551–550 2061.3178(0.0069) 524–515 2061.9407(0.0068)651–652 2061.3179(0.0068) 818–707 2061.9405(0.0134)652–651 2061.3179(0.0068) 625–616 2061.9537(0.0064)752–753 2061.3181(0.0067) 725–717 2061.9778(�0.0009)753–752 2061.3181(0.0067) 827–818 2061.9865(0.0088)440–441 2061.3242(0.0096) 919–808 2061.9858(0.0155)441–440 2061.3242(0.0096) 928–919 2062.0062(0.0080)541–542 2061.3243(0.0096) 221–110 2062.0275(0.0093)542–541 2061.3243(0.0096) 220–111 2062.0318(0.0093)642–643 2061.3244(0.0095) 101,10–909 2062.0307(0.0163)643–642 2061.3244(0.0095) 11210–11111 2062.0526(0.0096)505–414 2061.4656(0.0195) 322–211 2062.0838(0.0100)110–101 2061.5288(0.0095) 321–212 2062.0969(0.0101)211–202 2061.5332(0.0087) 423–312 2062.1381(0.0091)413–404 2061.5490(0.0089) 422–313 2062.1646(0.0119)

a Misprinted as 110–110 in Ref. [5].b Misprinted as 110–202 in Ref. [5].

where m0 is the antisymmetric stretching vibrational frequency ofthe free OCS (fixed at the experimental value of 2062.2012 cm�1

[30]), and Ev3J;Ka ;Kc

are the rotational levels computed with vibration-ally adiabatic potentials. The energies Ev3

J;Ka ;Kcare thus calculated rel-

ative to the dissociation limit of the completely separated Kr atomand OCS molecule, with the latter in the corresponding vibrationalstate v3.

The energy levels for the pure vdW vibrational bound states ofKr–OCS for v3 = 0 and v3 = 1 states of OCS are obtained and the sixlowest levels are listed in Table 3. The states are labeled by twoquantum numbers (ns, nb), respectively, denoting the stretchingand bending modes. Their wavefunctions reveal rather regularnode structure and spread around the global minimum approxi-mately corresponding to a series of the states of increasing energy:(ns, nb) = (0,0), (1,0), (0,1), (2,0), (0,2) and (1,1). The assignments areusually loosely defined since there is significant mixing betweentwo vibrational modes of higher excited states. The states inv3 = 1 mode of OCS are slightly stronger bound than correspondingv3 = 0 states. The predicted frequency of vdW bending vibration forground state (v3 = 0) is 25.2 cm�1, which is close to the experimen-tally estimated value of 26.1 cm�1 [3]. The calculated vibrationalband origin shift, which is �0.8657 cm�1, also agrees well withthe observed value of �0.8554 cm�1 [5].

We further fit the rotational energy levels of Kr–OCS in both theground and the excited states for J up to 12 to the conventionalWatson asymmetric top Hamiltonian using the A-type reductionin the Ir representation [31]. In Ref. [3] the experimentally ob-served transition spectra lines were fitted with the formulation de-scribed by Kirchhoff while in Ref. [5] the spectroscopic constantsfor 84Kr–OCS are given in Watson S-type reduction. In order tofacilitate the comparison, a conversion is first performed for thedata in Refs. [3,5]. The fitted spectroscopic constants are given inTable 4 together with those converted experimental values. Therelative error is about 0.3% for rotational constant A and less than2% for the constants B, and C. In spite of the fairly large errors sur-mised by the experiment for the higher order potential parameters,the calculated values are always of the same order of magnitude asthem. This overall agreement indicates that the present potentialenergy surface accurately describes the interaction between theOCS molecule and the Kr atom. The rotational constants A > B � Cindicate that the Kr–OCS complex is a prolate near-symmetric ro-tor. In addition, the rotational constants of excited state are onlydifferent slightly with corresponding values of ground state. Itindicates that the excitation of the v3vibration of OCS makes no sig-nificant changes to the structure of the Kr–OCS complex, which canbe comprehended from Figure 2.

Finally, a comparison of the calculated transition frequencieswith experimentally observed results is given in Table 5. It revealsour theoretical results are again in better agreement with experi-mental data [5] with a total rms error of 0.011 cm�1 for the 66spectra lines. The experimental data are slightly bigger than thetheoretical results in general. By the way, there are two misprintsin Table III of Ref. [5] for the transitions listed as 110–110 and110–202 because these transitions are parity forbidden ones. Thecorrect transitions should be 101–110 and 101–202.

4. Summary

We have presented an accurate calculation of the Kr–OCS po-tential energy surface. The potential includes explicit dependenceon the v3 antisymmetric stretching coordinate Q3 of the OCS mol-ecule. The calculations are performed by CCSD(T) method with alarge basis set plus (3s3p2d1f) midbond functions. The three-dimensional PES is constructed via a two-step procedure. In thefirst step, an analytical two-dimensional model potential is

16 C. Sun et al. / Chemical Physics Letters 549 (2012) 12–16

presented to fit numerically to the computed single point energiesat each of seven fixed Q3 values. The seven two-dimensionalpotentials are then used to construct the three-dimensional PESby interpolating along Q3 using a six-order polynomial. The totalroot-mean-square error is 0.158 cm�1 and the maximum absolutedeviation is 1.027 cm�1 for 1443 configurations, indicating our sur-face is a faithful representation of the CCSD(T) potential energy.

Based on the three-dimensional PES, two vibrational averagedPESs of the complex are generated by averaging over the Q3 normalcoordinate. Each potential is characterized by a global T-shapedminimum and a local collinear minimum. The two vibrational adi-abatic surfaces are further used to calculate the bound rovibra-tional states and the infrared spectrum of the Kr–OCS complex.The theoretical results, including the red-shift from the OCS mono-mer origin, bending ground frequency, molecular constants andtransition spectra, are all in better agreement with the experimen-tal counterparts. These findings suggest that the present potentialis rather accurate, and may be very useful in the computation ofother observable quantities like scattering cross sections, interac-tion second virial coefficients and the simulating the quantum sol-vation of OCS in a krypton clusters.

Acknowledgments

This work is supported by the National Natural Science Founda-tion of China (Grant No. 10874001) and Natural Science Founda-tion of Anhui province (Grant No. 1208085MA08).

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