A new ab initio potential energy surface and infrared spectra for the Ar–CS2 complex Ting Yuan, Xueli Sun, Yi Hu, and Hua Zhu Citation: The Journal of Chemical Physics 141, 104306 (2014); doi: 10.1063/1.4894504 View online: http://dx.doi.org/10.1063/1.4894504 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A new ab initio intermolecular potential energy surface and predicted rotational spectra of the Kr−H2O complex J. Chem. Phys. 137, 224314 (2012); 10.1063/1.4770263 A new ab initio intermolecular potential energy surface and predicted rotational spectra of the Ar−H2S complex J. Chem. Phys. 136, 084310 (2012); 10.1063/1.3689443 A new potential energy surface and predicted infrared spectra of the Ar – CO 2 van der Waals complex J. Chem. Phys. 130, 224311 (2009); 10.1063/1.3152990 Five-dimensional ab initio potential energy surface and predicted infrared spectra of H 2 – C O 2 van der Waals complexes J. Chem. Phys. 126, 204304 (2007); 10.1063/1.2735612 A three-dimensional ab initio potential energy surface and predicted infrared spectra for the He – N 2 O complex J. Chem. Phys. 124, 144317 (2006); 10.1063/1.2189227
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THE JOURNAL OF CHEMICAL PHYSICS 141, 104306 (2014)
A new ab initio potential energy surface and infrared spectra for the Ar–CS2 complex Ting Yuan, Xueli Sun, Yi Hu, and Hua Zhua) School of Chemistry, Sichuan University, Chengdu 610064, China and State Key Laboratory of Biotherapy, Sichuan University, Chengdu 610064, China
(Received 25 April 2014; accepted 22 August 2014; published online 8 September 2014) We report a new three-dimensional potential energy surface for Ar–CS2 involving the Q3 normal mode for the υ 3 antisymmetric stretching vibration of the CS2 molecule. The potential energies were calculated using the supermolecular method at the coupled-cluster singles and doubles level with noniterative inclusion of connected triples, using augmented correlation-consistent quadruple-zeta basis set plus midpoint bond functions. Two vibrationally averaged potentials with CS2 at both the ground (υ = 0) and the first excited (υ = 1)υ 3 vibrational states were generated from the integration of the three-dimensional potential over the Q3 coordinate. Each potential was found to have a T-shaped global minimum and two equivalent linear local minima. The radial discrete variable representation /angular finite basis representation method and the Lanczos algorithm were applied to calculate the rovibrational energy levels. The calculated band origin shift of the complex (0.0622 cm−1 ) is very close to the observed one (0.0671 cm−1 ). The predicted infrared spectra and spectroscopic parameters based on the two averaged potentials are in excellent agreement with the available experimental data. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4894504] I. INTRODUCTION
In recent years, the weak intermolecular forces and spectroscopy of the van der Waals (vdW) complexes between rare-gas (Rg) atoms and a family of chromophores (CO2 , OCS, N2 O, and CO) have attracted considerable attention. The spectroscopy of these complexes can provide very useful information on the intermolecular potential energy surface (PES) and dynamics of these weakly bound molecules. Carbon dioxide complexes have been thoroughly investigated experimentally1–8 and theoretically,9–23 because CO2 is one of the most important absorbers of infrared radiation in the earth’s atmosphere and interstellar chemistry. As an analog of CO2 , carbon sulfide is also interesting because sulfur is a key element in chemistry and in the spectroscopy of giant planets.24 However, only a few studies of the complex involving CS2 have been appeared so far.25–30 Among the Rg–CO2 systems, the Ar–CO2 complex was at first studied by the microwave spectroscopy.1 Subsequently, further experimental studies of microwave and infrared spectra for Rg–CO2 (Rg = He, Ne, Ar, Kr) were reported.2, 3, 7, 8 Along with these experimental studies, a number of theoretical researches have dealt with the construction of the ab initio potential energy surface. In the previous theoretical calculations,9–17 the CO2 monomer was assumed as a rigid rotor. Although this model is generally excellent for microwave spectra, it is not sufficient for predicting the infrared spectra of the Rg–CO2 complexes. One effective way is to take into account the influence of intramolecular vibration mode on the potential energy surface and dynamical calculations.31–33 Therefore, we employed this approach to construct the potena) Electronic mail: [email protected]
0021-9606/2014/141(10)/104306/6/$30.00
tials including the dependence on the Q3 normal coordinate of the CO2 molecule and to reproduce the infrared spectra for Rg–CO2 (Rg = Ne,20, 21 Kr,22 Xe23 ). To our best knowledge, the studies of the Rg– CS2 complexes are limited both experimentally28 and theoretically.29, 30 In experiment, Mivehvar et al.28 first reported the infrared spectra of Rg–CS2 (Rg = He, Ne, Ar) in the region of the CS2 v3 fundamental band around 1535 cm−1 . In addition, the spectra of the He–CS2 complex have been measured in the v1 + v3 region (2185 cm−1 ) using a tunable diode laser. The Rg–CS2 complexes were found to have Tshaped structures similar to the Rg–CO2 complexes. The vibrational band origin shifts and inertial defects for Rg–CS2 were also presented in their paper. In theoretical field, Farrokhpour and Tozihi29 first constructed the ab initio potential energy surface of the Rg–CS2 complexes (Rg = He, Ne, Ar) using the coupled-cluster singles and doubles with noniterative inclusion of connected triple [CCSD(T)] theory with augcc-pVDZ basis set plus bond functions (3s3p2d1f1g). Lately, Zang et al.30 reported the two-dimensional PESs for the three complexes which were calculated using aug-cc-pVTZ basis set at CCSD(T) level. Based on the ab initio potential energy surfaces, they calculated the bound states, the average structural parameters, and pure rotational transition frequencies. In the above two theoretical studies, the CS2 monomer was treated as a rigid rotor. However, the shifts of the band origin in the observed infrared spectra cannot be correctly reproduced using the rigid monomer model.34, 35 In order to provide more detailed theoretical information on the dynamics of Ar–CS2 , we reported a new three-dimensional potential energy surface involving the antisymmetric Q3 normal mode of CS2 for the complex, and calculated the rovibrational energy levels, rovibrational
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transition frequencies, and transition line intensities. The potential-optimized discrete (PODVR)36, 37 grid points were employed to construct the potential energy surface. The radial discrete variable representation (DVR)/angular finite basis representation (FBR) method and Lanczos algorithm were used to calculate the bound states and rovibrational energy levels. This paper is organized as follows. Section II describes the computational details. The discussions of the features of the potential energy surface, rovibrational bound states, and the infrared spectra are presented in Secs. III–V. Section VI gives a brief conclusion.
II. COMPUTATIONAL DETAILS A. Ab initio calculations
The geometry of the Ar–CS2 complex is defined by the Jacobi coordinates (R, θ , Q3 ), where R represents the distance from the center of mass of the CS2 to the Ar atom, θ is the enclosed angle between the vector R and the molecular axis of CS2 , and the coordinate Q3 denotes the normal stretch of CS2 . Q3 is defined as mode for the υ 3 antisymmetric √ Q3 = (rcs1 − rcs2)/ 2, where rcs1 and rcs2 represent the two C–S bond lengths of CS2, respectively. The work of Le Roy and co-workers38, 39 showed that when one of the intermolecular vibrational modes of the monomer is excited, the averaged values of the other coordinates are also affected, and the authors pointed out slight equilibrium structural difference between the ground and the υ 3 excited states of CO2 may lead to more significant discrepancies in the transition frequencies. The average bond lengths of C–S in the υ = 0 and 1 states for the CS2 molecules are 2.9372 a0 and 2.9468 a0 stemmed from the experimental rotational constants.40 Therefore, we calculated the one-dimensional Q3 potential curves dependence of the sum of the two C–S bond lengths fixed at twice the observed average bond length. Both one-dimensional Q3 potential curves were computed at the CCSD(T) level41 to determine the energy levels and wave functions for the Q3 mode. A coordinate scaling method42 was used to adjust the CCSD(T) potential curve to reproduce the experimental υ 3 fundamental frequency value.40 We generated five potentialoptimized DVR (PODVR) grid points −0.24995, −0.11881, 0.0, 0.11881, and 0.24995 a0 for CS2 at the ground (υ = 0) state, and −0.24989, −0.11878, 0.0, 0.11878, and 0.24989 a0 at the first excited (υ = 1)υ 3 state. The ab initio potential energies for Ar–CS2 were computed for a total of about 1200 symmetry-unique points for each of the ground and the first excited υ 3 states of CS2 , with R ranging from 5.00 a0 to 24.00 a0 at 31 values and 13 equidistant angles from θ = 0◦ to θ = 180◦ in a step of 15◦ . The PES of Ar–CS2 was constructed at the CCSD(T) level.39 We used the augmented correlation-consistent quadruple-zeta (aug-cc-pVQZ) basis set of Woon and Dunning43 for all atoms. In order to eliminate the need for high angular momentum functions in the atom-centered basis set, bond functions (3s3p2d1f1g) (for 3s and 3p, α = 0.9, 0.3, 0.1; for 2d, α = 0.6, 0.2; for f and g, α = 0.3)44 were placed in the middle of the R vector. The supermolecular approach was adopted to produce the intermolecular potential energies. We employed
J. Chem. Phys. 141, 104306 (2014)
the full counterpoise procedure45 (FCP) to correct the basis set superposition error (BSSE). The three-dimensional potentials with CS2 at both the ground (υ = 0) and the first excited (υ = 1) υ 3 vibrational states were, respectively, integrated corresponding to the vibrational wave functions of the monomer CS2 on Q3 coordinate. Then we employed a cubic spline interpolation to obtain the potential for any arbitrary pairs of R and θ on the averaged PES Vυ (R, θ ) (υ = 0, 1). The full set of the calculated averaged potential points are available upon request. All the ab initio calculations were carried out using the MOLPRO package.46 B. Calculations of the rovibrational states
In the Jacobi coordinates, the vibrational averaged intermolecular Hamiltonian describing the nuclear motion for the Ar–CS2 complex can be written as (in atomic units)47, 48
H =−
1 ∂2 jˆ2 (Jˆ − jˆ)2 + + + Vv (R, θ ), 2μ ∂R 2 2Iv 2μR 2
(1)
where μ is the reduced mass of the complex, Iυ = ψυ (Q3 )|IQ |ψυ (Q3 ) is the vibrationally averaged rota3 tional moment of the inertia of CS2 , Jˆ and jˆ are the operators defining the angular momenta of this complex and CS2 , respectively, and Vυ (R, θ ) describes the averaged potential in a particular vibrational state υ(υ = 0, 1) of CS2 . The efficient radial DVR/angular FBR method49, 50 was used to calculate the rovibrational energy levels. In our calculations, we used 120 sine-DVR51 points for the R coordinate, 89 basis functions of associated Legendre polynomials, and 90 DVR grid points for θ . The Lanczos algorithm52 was employed to efficiently diagonalize the Hamiltonian matrix with 8000 steps. The parity-adapted rotational basis are defined in the three Euler angles (α, β, γ ) denoting the orientation of BF frame with respect to the SF frame, J∗ Jp (α, β, γ ) CKM (α, β, γ ) = [2(1 + δK0 )]−1/2 DMK J∗ + (−1)J +K+p DM−K (α, β, γ ) , p = 0, 1, (2) J DMK (α, β, γ )
where is the normalized rotational function. The total parity is given by (−1)J+P . We calculated the rovibrational energy levels with the total angular momentum J ≤ 7. III. POTENTIAL ENERGY SURFACE
The two vibrationally averaged potentials, Vυ (R, θ ) (υ = 0, 1), have very similar features. The contour plot of Vυ (R, θ ) is shown in Fig. 1. It is clear that the CCSD(T) potential is characterized by a global T-shaped minimum and two linear local minima. The global minimum is located at R = 3.66 Å and θ = 90.0◦ with a depth of 273.21 cm−1 . The two equivalent local minima with a depth well of 167.15 cm−1 occur at the linear geometry for R = 5.27 Å. However, no linear local minima were detected for the Ar–CO2 complex.19 A barrier between the two minima is located at R = 4.93 Å and
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J. Chem. Phys. 141, 104306 (2014) TABLE II. The calculated energy levels (in cm−1 ) for the first 20 vibrational bound states of the Ar–CS2 complex for the υ = 0 and 1 states of CS2 .
FIG. 1. Contour plots (in cm−1 ) of the averaged intermolecular potential energy surface for Ar–CS2 with CS2 at the ground (υ = 0) state.
θ = 39.31◦ with height of 24.70 cm−1 , relative to the linear minimum. Table I gives a comparison of the present potential with the previous CCSD(T) PESs.29, 30 The well depth of our potential is closer to that of the potential of Ref. 29 at the global minimum than that of the potential of Ref. 30. In addition, some significant deviations do exist, for example, the well depth of our potential is about 5–6 cm−1 deeper than previous work at the local minimum and the potential barrier, and the position of the well depth is shorter at the minima and larger at the potential barrier. IV. BOUND STATES OF ROVIBRATIONAL ENERGY LEVLES
We follow Ref. 6 to label the υ 3 antisymmetric stretch of CS2 as the υ 4 vibrational mode in the Ar–CS2 complex. The energy levels for the first 20 vibrational bound states of the Ar–CS2 complex for the υ = 0 and 1 states of CS2 are listed in Table II. Because of the deep potential well, the ab initio CCSD(T) potential supports more than 100 vibrational bound states, while Ar–CO2 has 72 bound states.19 The vibrational ground state of the Ar–CS2 complex with CS2 at the ground state is bound by 240.16 cm−1 , corresponding to a zero-point energy of 33.05 cm−1 . The zero-point energy is significantly lower than the barrier height, which indicates that the ground state is mainly localized in the ground state. The calculated vibrational band origin for Ar–CS2 is
N
Ground state
υ 4 state
N
Ground state
υ 4 state
0 1 2 3 4 5 6 7 8 9
−240.1634 −215.2129 −205.4849 −190.7094 −185.3396 −174.5121 −167.5815 −164.6736 −158.8045 −149.4029
−240.1012 −215.2949 −205.4913 −190.8706 −185.4783 −174.5988 −167.7998 −164.8414 −159.0081 −149.6242
10 11 12 13 14 15 16 17 18 19
−146.4602 −144.9745 −143.5949 −140.0648 −136.9113 −132.6385 −131.5162 −131.4777 −130.3964 −125.6950
−146.6854 −145.1727 −144.3598 −140.2773 −137.1830 −132.9099 −132.1164 −132.0809 −130.6637 −126.0589
blueshifted by 0.0622 cm−1 , which agrees well with the observed value28 of 0.0671 cm−1 . However, the calculated band origin shift is larger (0.474 cm−1 ) and negative (redshift) for Ar–CO2 .19 The smaller CS2 band origin shift reveals a slight weakening of the vdW bond upon vibration excitation for Ar–CS2 . Figure 2 presents the contour plots of the wave functions for the ground and some lower excited states of Ar–CS2 with CS2 at the ground (υ = 0) state. The vdW vibrational states are defined by two quantum numbers (ns , nb ), respectively, denoting the vdW stretching and bending modes. Their assignments are loosely defined since ns and nb are not good quantum numbers and there is significant mixing between the two modes for higher excited states. Therefore, the vibrational states in Table II are labeled using numbers. Owing to the higher energy barrier, the ground states and these low-lying excited states are localized around the T-shaped global minimum. The wave functions of the higher excited vibrational states exhibit a strong mixing between the bending and stretching vibration modes. The average structures were, respectively, determined from the vibrational ground state wavefuction of the complex, R = ψ 0 |R|ψ 0 and cos 2 θ = ψ 0 |cos 2 θ |ψ 0 . The calculated average distance R for the ground state is 3.717 Å and the angle θ is 86.85◦ , the latter is a measure of the average amplitude of the bending from the 90◦ average configuration, which can be interpreted as an effect of the zero point vibrational motion of CS2 within the complex. The average θ -value of Ar–CS2 is closer to 90◦ than that of Ar–CO2 (82.90◦ ),19 indicating a smaller amplitude of zero point bending motion for Ar–CS2 . The calculated structure for Ar–CS2 is in agreement with the experimental values28 of R = 3.708 Å and θ = 86.4◦ . For the first two excited states,
TABLE I. The calculated minima and saddle point on the vibrationally averaged potentials Vυ=0 (R,θ ) and Vυ=1 (R,θ ) of Ar–CS2 together with the comparison with other ab initio PESs. The entries are given as R in angstrom, θ (deg), and V (cm−1 ).
This wok Reference 29 Reference 30
Vυ=0 Vυ=1 Vυ=0 Vυ=0
Global minimum
Local minimum
Saddle point
(3.66,90, −273.21) (3.67,90, −273.03) (3.70,90, −272.15) (3.70,90, −266.88)
(5.27,0/180, −167.15) (5.27,0/180, −168.05) (5.30,0/180, −162.52) (5.30,0/180, −161.31)
(4.93, 39.31, −142.45) (4.93, 39.12, −142.77) (4.87, 44.8, −135.99) (4.90, 40.0, −137.19)
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and 0.211 Å, and the former is close to that of the ground state, whereas the angular dispersion is 7.32◦ and 4.34◦ , and the latter is close to the value for the ground state. The rovibrational energies were assigned by the antisymmetric rotor quantum numbers JKaKc . J is the total angular momentum and Ka and Kc denote the projections of J onto the a and c axes in the principal axes of inertia. The calculated rovibrational energy levels were divided into four blocks, (even/even), (even/odd), (odd/even), and (odd/odd) for different combination parity of (j/p). In our work, we calculated the rovibrational energies for J from 0 to 7 for the vdW ground vibrational state with CS2 at both the ground (υ = 0) and the first excited (υ = 1) υ 3 vibrational states, which are available upon request.
V. INFRARED SPECTRA
FIG. 2. Contour plots of the wave functions for the lowest six vibrational states of Ar–CS2 with CS2 at the ground (υ = 0) state.
the average distance is 3.773 Å and 3.760 Å, respectively, and the angle is 82.68 and 85.67◦ , respectively. One can see from Fig. 2 that the first vibrational excited state can be attributed to the intermolecular bending mode with a frequency of 24.95 cm−1 , while the second vibrational excited state is due to the intermolecular stretching mode with a frequency of 34.68 cm−1 . The radial dispersion and angular dispersion suggest a similar trend. The radial dispersion and angular dispersion is 0.092 Å and 3.15◦ for the ground state, respectively. For the first two excited states, the radial dispersion is 0.098 Å
The rovibrational energy levels for J ≤ 4 were fitted to a Watson asymmetric top Hamiltonian53 using the a-type reduction in the Ir representation. The fitted molecular spectroscopic constants are given in Table III together with the experimental28 and previous theoretical30 result. It is clear that our calculated constants agree well with the experimental values. From the rotational constants, the inertial defect 0 in the ground state of Ar–CS2 was calculated to be 2.95 amu Å2 , whereas for the Ar–CO2 complex 0 is 2.39 amu Å2 ,2 which quantifies the extent to which the former complex is less rigid than the latter. On the other hand, the Ar–CO2 complex is nearer the symmetric prolate top limit than the Ar–CS2 complex. This can be seen from the asymmetry parameter, κ = (2B − A − C)/(A − C) (equal to −1 for the symmetric prolate top). The asymmetry parameter κ is −0.635 and −0.942 for the Ar–CS2 and Ar–CO2 complexes, respectively. The details regarding calculation of the transition intensities can be found in Ref. 35. The calculated rovibrational transition frequencies and the relative intensities at the temperature of T = 7 K for Ar–CS2 with their deviations from the observed infrared spectra are given in Table IV. One can see that the calculated transition frequencies are in excellent agreement with the experimental values. Most of the calculated frequencies are within 0.007 cm−1 of the observed values, and the root mean squares error of the 69 calculated
TABLE III. Spectroscopic constants (in cm−1 ) and the inertial defects 0 (in amu Å2 ) for the Ar–CS2 complex at both the ground and J Ka Kc − J Ka Kc states. Observed data are taken from Ref. 28. Ground state Experiment A B C K JK J δK δJ 0
0.109901 0.047067 0.032765 −1.234 × 10−6 1.705 × 10−6 1.891 × 10−7 1.418 × 10−6 4.937 × 10−8 2.95
This work 0.109873 0.046687 0.032578 −1.770 × 10−6 1.627 × 10−6 1.841 × 10−7 1.197 × 10−6 5.591 × 10−8 2.95
υ cal state Reference 24 0.110215 0.046419 0.032493 −3.700 × 10−6 2.090 × 10−6 7.792 × 10−7 1.418 × 10−6 4.937 × 10−8 2.69
Experiment 0.109188 0.047046 0.032691 −1.361 × 10−6 1.708 × 10−6 1.828 × 10−7 1.321 × 10−6 4.937 × 10−8 2.95
This work 0.109140 0.046670 0.032504 −1.778 × 10−6 1.631 × 10−6 1.842 × 10−7 1.198 × 10−6 5.617 × 10−8 2.96
Reference 24 0.109305 0.046304 0.032368 −2.830 × 10−6 1.743 × 10−6 0.659 × 10−6 2.874 × 10−6 4.937 × 10−8 2.52
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TABLE IV. Calculated infrared transition frequencies (in cm−1 ) and relative intensities for Ar–CS2 . Observed data are taken from Ref. 28. JKa Kc − JKa Kc 331 –440 330 –441 615 –726 514 –625 413 –524 432 –441 634 –643 533 –542 431 –440 532 –541 616 –707 312 –423 212 –321 633 –642 734 –743 211 –322 717 –726 515 –606 111 –220 616 –625 110 –221 414 –505 515 –524 414 –423 313 –404 313 –322 716 –725 615 –624 312 –321 514 –523 413 –422 111 –202 312 –303 734 –725 313 –202
υ cal
υ cal − υ obs
Intensity
JKa K − JKa Kc
υ cal
υ cal − υ obs
Intensity
1534.6026 1534.6028 1534.7900 1534.8341 1534.8807 1534.9229 1534.9230 1534.9234 1534.9243 1534.9287 1534.9312 1534.9322 1534.9375 1534.9381 1534.9543 1534.9902 1534.9950 1535.0022 1535.0391 1535.0474 1535.0554 1535.0767 1535.0934 1535.1320 1535.1556 1535.1627 1535.1838 1535.2197 1535.2373 1535.2386 1535.2432 1535.3243 1535.5387 1535.6825 1535.6835
−0.0051 −0.0049 −0.0033 −0.0035 −0.0039 −0.0072 −0.0071 −0.0067 −0.0058 −0.0069 −0.0016 −0.0034 −0.0023 −0.0077 −0.0081 −0.0045 −0.0024 −0.0022 −0.0053 −0.0034 −0.0058 −0.0024 −0.0035 −0.0049 −0.0026 −0.0052 −0.0030 −0.0043 −0.0061 −0.0048 −0.0053 −0.0036 −0.0056 −0.0033 −0.0060
0.521 0.521 0.467 0.422 0.382 0.153 0.339 0.262 0.153 0.263 0.857 0.348 0.226 0.343 0.407 0.302 0.309 0.755 0.271 0.317 0.303 0.633 0.325 0.309 0.477 0.260 1.000 0.753 0.420 0.726 0.604 0.140 0.538 0.821 0.449
633 –624 615 –606 532 –523 414 –303 431 –422 330 –321 331 –322 432 –423 716 –707 533 –524 515 –404 634 –625 615 –524 735 –726 616 –505 716 –625 717 –606 651 –642 652 –643 550 –541 551 –542 432 –321 431 –322 533 –422 532 –421 634 –523 735 –624 550 –441 551 –440 652 –541 651 –542 753 –642 752 –643 770 –661
1535.7010 1535.7037 1535.7226 1535.7385 1535.7415 1535.7541 1535.7641 1535.7691 1535.7773 1535.7787 1535.7931 1535.7943 1535.7949 1535.8170 1535.8497 1535.8935 1535.9087 1536.0249 1536.0256 1536.0278 1536.0280 1536.0742 1536.0858 1536.1412 1536.1757 1536.1988 1536.2467 1536.4286 1536.4286 1536.5075 1536.5077 1536.5859 1536.5867 1536.8502
−0.0028 −0.0086 −0.0029 −0.0064 −0.0034 −0.0035 −0.0041 −0.0039 −0.0086 −0.0042 −0.0064 −0.0052 −0.0099 −0.0048 −0.0067 −0.0099 −0.0073 −0.0029 −0.0022 −0.0028 −0.0026 −0.0056 −0.0061 −0.0059 −0.0069 −0.0058 −0.0058 −0.0056 −0.0056 −0.0064 −0.0062 −0.0073 −0.0065 −0.0064
0.590 0.397 0.468 0.581 0.338 0.192 0.138 0.320 0.785 0.411 0.717 0.464 0.319 0.479 0.839 0.432 0.296 0.244 0.244 0.143 0.143 0.467 0.457 0.441 0.410 0.417 0.541 0.672 0.672 0.614 0.614 0.557 0.554 0.611
transitions is only 0.005 cm−1 . The relatively most intense line is the transition from 716 to 725 at 1535.1838 cm−1 . Although good agreements between the calculated and observed infrared spectra confirm the high quality of our new potentials, the bend and symmetric stretch of CS2 are not considered in this work, which could have a slight effect on the potential and spectroscopic properties of Ar–CS2 in the υ 3 region of the CS2 molecule.
rms error
0.005
and the Lanczos algorithm. The calculated spectroscopic constants and infrared spectra are in good agreement with the available observed values. The experimental band origin shift in the infrared spectra is reproduced very well. It is expected that the accurate descriptions of the new potential should be useful for further studies of the structures and spectroscopy of the ArN –CS2 clusters. ACKNOWLEDGMENTS
VI. CONCLUSION
We have presented a three-dimensional PES for the Ar– CS2 complex including the Q3 normal mode of CS2 at the CCSD(T) level with a large basis set plus bond functions. The intermolecular potential was calculated over five PODVR grid points for the Q3 normal mode. Based on the ab initio potential points, two vibrationally averaged PESs of the complex were generated. Each PES has a T-shaped global minimum and two equivalent local minima of linear geometry. The bound rovibrational energy levels of Ar–CS2 were obtained by employing the radial DVR/angular FBR method
This work was supported by the National Natural Science Foundation of China (Grant No. 21373139). 1 J.
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THE JOURNAL OF CHEMICAL PHYSICS 141, 104306 (2014)
A new ab initio potential energy surface and infrared spectra for the Ar–CS2 complex Ting Yuan, Xueli Sun, Yi Hu, and Hua Zhua) School of Chemistry, Sichuan University, Chengdu 610064, China and State Key Laboratory of Biotherapy, Sichuan University, Chengdu 610064, China
(Received 25 April 2014; accepted 22 August 2014; published online 8 September 2014) We report a new three-dimensional potential energy surface for Ar–CS2 involving the Q3 normal mode for the υ 3 antisymmetric stretching vibration of the CS2 molecule. The potential energies were calculated using the supermolecular method at the coupled-cluster singles and doubles level with noniterative inclusion of connected triples, using augmented correlation-consistent quadruple-zeta basis set plus midpoint bond functions. Two vibrationally averaged potentials with CS2 at both the ground (υ = 0) and the first excited (υ = 1)υ 3 vibrational states were generated from the integration of the three-dimensional potential over the Q3 coordinate. Each potential was found to have a T-shaped global minimum and two equivalent linear local minima. The radial discrete variable representation /angular finite basis representation method and the Lanczos algorithm were applied to calculate the rovibrational energy levels. The calculated band origin shift of the complex (0.0622 cm−1 ) is very close to the observed one (0.0671 cm−1 ). The predicted infrared spectra and spectroscopic parameters based on the two averaged potentials are in excellent agreement with the available experimental data. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4894504] I. INTRODUCTION
In recent years, the weak intermolecular forces and spectroscopy of the van der Waals (vdW) complexes between rare-gas (Rg) atoms and a family of chromophores (CO2 , OCS, N2 O, and CO) have attracted considerable attention. The spectroscopy of these complexes can provide very useful information on the intermolecular potential energy surface (PES) and dynamics of these weakly bound molecules. Carbon dioxide complexes have been thoroughly investigated experimentally1–8 and theoretically,9–23 because CO2 is one of the most important absorbers of infrared radiation in the earth’s atmosphere and interstellar chemistry. As an analog of CO2 , carbon sulfide is also interesting because sulfur is a key element in chemistry and in the spectroscopy of giant planets.24 However, only a few studies of the complex involving CS2 have been appeared so far.25–30 Among the Rg–CO2 systems, the Ar–CO2 complex was at first studied by the microwave spectroscopy.1 Subsequently, further experimental studies of microwave and infrared spectra for Rg–CO2 (Rg = He, Ne, Ar, Kr) were reported.2, 3, 7, 8 Along with these experimental studies, a number of theoretical researches have dealt with the construction of the ab initio potential energy surface. In the previous theoretical calculations,9–17 the CO2 monomer was assumed as a rigid rotor. Although this model is generally excellent for microwave spectra, it is not sufficient for predicting the infrared spectra of the Rg–CO2 complexes. One effective way is to take into account the influence of intramolecular vibration mode on the potential energy surface and dynamical calculations.31–33 Therefore, we employed this approach to construct the potena) Electronic mail: [email protected]
0021-9606/2014/141(10)/104306/6/$30.00
tials including the dependence on the Q3 normal coordinate of the CO2 molecule and to reproduce the infrared spectra for Rg–CO2 (Rg = Ne,20, 21 Kr,22 Xe23 ). To our best knowledge, the studies of the Rg– CS2 complexes are limited both experimentally28 and theoretically.29, 30 In experiment, Mivehvar et al.28 first reported the infrared spectra of Rg–CS2 (Rg = He, Ne, Ar) in the region of the CS2 v3 fundamental band around 1535 cm−1 . In addition, the spectra of the He–CS2 complex have been measured in the v1 + v3 region (2185 cm−1 ) using a tunable diode laser. The Rg–CS2 complexes were found to have Tshaped structures similar to the Rg–CO2 complexes. The vibrational band origin shifts and inertial defects for Rg–CS2 were also presented in their paper. In theoretical field, Farrokhpour and Tozihi29 first constructed the ab initio potential energy surface of the Rg–CS2 complexes (Rg = He, Ne, Ar) using the coupled-cluster singles and doubles with noniterative inclusion of connected triple [CCSD(T)] theory with augcc-pVDZ basis set plus bond functions (3s3p2d1f1g). Lately, Zang et al.30 reported the two-dimensional PESs for the three complexes which were calculated using aug-cc-pVTZ basis set at CCSD(T) level. Based on the ab initio potential energy surfaces, they calculated the bound states, the average structural parameters, and pure rotational transition frequencies. In the above two theoretical studies, the CS2 monomer was treated as a rigid rotor. However, the shifts of the band origin in the observed infrared spectra cannot be correctly reproduced using the rigid monomer model.34, 35 In order to provide more detailed theoretical information on the dynamics of Ar–CS2 , we reported a new three-dimensional potential energy surface involving the antisymmetric Q3 normal mode of CS2 for the complex, and calculated the rovibrational energy levels, rovibrational
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transition frequencies, and transition line intensities. The potential-optimized discrete (PODVR)36, 37 grid points were employed to construct the potential energy surface. The radial discrete variable representation (DVR)/angular finite basis representation (FBR) method and Lanczos algorithm were used to calculate the bound states and rovibrational energy levels. This paper is organized as follows. Section II describes the computational details. The discussions of the features of the potential energy surface, rovibrational bound states, and the infrared spectra are presented in Secs. III–V. Section VI gives a brief conclusion.
II. COMPUTATIONAL DETAILS A. Ab initio calculations
The geometry of the Ar–CS2 complex is defined by the Jacobi coordinates (R, θ , Q3 ), where R represents the distance from the center of mass of the CS2 to the Ar atom, θ is the enclosed angle between the vector R and the molecular axis of CS2 , and the coordinate Q3 denotes the normal stretch of CS2 . Q3 is defined as mode for the υ 3 antisymmetric √ Q3 = (rcs1 − rcs2)/ 2, where rcs1 and rcs2 represent the two C–S bond lengths of CS2, respectively. The work of Le Roy and co-workers38, 39 showed that when one of the intermolecular vibrational modes of the monomer is excited, the averaged values of the other coordinates are also affected, and the authors pointed out slight equilibrium structural difference between the ground and the υ 3 excited states of CO2 may lead to more significant discrepancies in the transition frequencies. The average bond lengths of C–S in the υ = 0 and 1 states for the CS2 molecules are 2.9372 a0 and 2.9468 a0 stemmed from the experimental rotational constants.40 Therefore, we calculated the one-dimensional Q3 potential curves dependence of the sum of the two C–S bond lengths fixed at twice the observed average bond length. Both one-dimensional Q3 potential curves were computed at the CCSD(T) level41 to determine the energy levels and wave functions for the Q3 mode. A coordinate scaling method42 was used to adjust the CCSD(T) potential curve to reproduce the experimental υ 3 fundamental frequency value.40 We generated five potentialoptimized DVR (PODVR) grid points −0.24995, −0.11881, 0.0, 0.11881, and 0.24995 a0 for CS2 at the ground (υ = 0) state, and −0.24989, −0.11878, 0.0, 0.11878, and 0.24989 a0 at the first excited (υ = 1)υ 3 state. The ab initio potential energies for Ar–CS2 were computed for a total of about 1200 symmetry-unique points for each of the ground and the first excited υ 3 states of CS2 , with R ranging from 5.00 a0 to 24.00 a0 at 31 values and 13 equidistant angles from θ = 0◦ to θ = 180◦ in a step of 15◦ . The PES of Ar–CS2 was constructed at the CCSD(T) level.39 We used the augmented correlation-consistent quadruple-zeta (aug-cc-pVQZ) basis set of Woon and Dunning43 for all atoms. In order to eliminate the need for high angular momentum functions in the atom-centered basis set, bond functions (3s3p2d1f1g) (for 3s and 3p, α = 0.9, 0.3, 0.1; for 2d, α = 0.6, 0.2; for f and g, α = 0.3)44 were placed in the middle of the R vector. The supermolecular approach was adopted to produce the intermolecular potential energies. We employed
J. Chem. Phys. 141, 104306 (2014)
the full counterpoise procedure45 (FCP) to correct the basis set superposition error (BSSE). The three-dimensional potentials with CS2 at both the ground (υ = 0) and the first excited (υ = 1) υ 3 vibrational states were, respectively, integrated corresponding to the vibrational wave functions of the monomer CS2 on Q3 coordinate. Then we employed a cubic spline interpolation to obtain the potential for any arbitrary pairs of R and θ on the averaged PES Vυ (R, θ ) (υ = 0, 1). The full set of the calculated averaged potential points are available upon request. All the ab initio calculations were carried out using the MOLPRO package.46 B. Calculations of the rovibrational states
In the Jacobi coordinates, the vibrational averaged intermolecular Hamiltonian describing the nuclear motion for the Ar–CS2 complex can be written as (in atomic units)47, 48
H =−
1 ∂2 jˆ2 (Jˆ − jˆ)2 + + + Vv (R, θ ), 2μ ∂R 2 2Iv 2μR 2
(1)
where μ is the reduced mass of the complex, Iυ = ψυ (Q3 )|IQ |ψυ (Q3 ) is the vibrationally averaged rota3 tional moment of the inertia of CS2 , Jˆ and jˆ are the operators defining the angular momenta of this complex and CS2 , respectively, and Vυ (R, θ ) describes the averaged potential in a particular vibrational state υ(υ = 0, 1) of CS2 . The efficient radial DVR/angular FBR method49, 50 was used to calculate the rovibrational energy levels. In our calculations, we used 120 sine-DVR51 points for the R coordinate, 89 basis functions of associated Legendre polynomials, and 90 DVR grid points for θ . The Lanczos algorithm52 was employed to efficiently diagonalize the Hamiltonian matrix with 8000 steps. The parity-adapted rotational basis are defined in the three Euler angles (α, β, γ ) denoting the orientation of BF frame with respect to the SF frame, J∗ Jp (α, β, γ ) CKM (α, β, γ ) = [2(1 + δK0 )]−1/2 DMK J∗ + (−1)J +K+p DM−K (α, β, γ ) , p = 0, 1, (2) J DMK (α, β, γ )
where is the normalized rotational function. The total parity is given by (−1)J+P . We calculated the rovibrational energy levels with the total angular momentum J ≤ 7. III. POTENTIAL ENERGY SURFACE
The two vibrationally averaged potentials, Vυ (R, θ ) (υ = 0, 1), have very similar features. The contour plot of Vυ (R, θ ) is shown in Fig. 1. It is clear that the CCSD(T) potential is characterized by a global T-shaped minimum and two linear local minima. The global minimum is located at R = 3.66 Å and θ = 90.0◦ with a depth of 273.21 cm−1 . The two equivalent local minima with a depth well of 167.15 cm−1 occur at the linear geometry for R = 5.27 Å. However, no linear local minima were detected for the Ar–CO2 complex.19 A barrier between the two minima is located at R = 4.93 Å and
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J. Chem. Phys. 141, 104306 (2014) TABLE II. The calculated energy levels (in cm−1 ) for the first 20 vibrational bound states of the Ar–CS2 complex for the υ = 0 and 1 states of CS2 .
FIG. 1. Contour plots (in cm−1 ) of the averaged intermolecular potential energy surface for Ar–CS2 with CS2 at the ground (υ = 0) state.
θ = 39.31◦ with height of 24.70 cm−1 , relative to the linear minimum. Table I gives a comparison of the present potential with the previous CCSD(T) PESs.29, 30 The well depth of our potential is closer to that of the potential of Ref. 29 at the global minimum than that of the potential of Ref. 30. In addition, some significant deviations do exist, for example, the well depth of our potential is about 5–6 cm−1 deeper than previous work at the local minimum and the potential barrier, and the position of the well depth is shorter at the minima and larger at the potential barrier. IV. BOUND STATES OF ROVIBRATIONAL ENERGY LEVLES
We follow Ref. 6 to label the υ 3 antisymmetric stretch of CS2 as the υ 4 vibrational mode in the Ar–CS2 complex. The energy levels for the first 20 vibrational bound states of the Ar–CS2 complex for the υ = 0 and 1 states of CS2 are listed in Table II. Because of the deep potential well, the ab initio CCSD(T) potential supports more than 100 vibrational bound states, while Ar–CO2 has 72 bound states.19 The vibrational ground state of the Ar–CS2 complex with CS2 at the ground state is bound by 240.16 cm−1 , corresponding to a zero-point energy of 33.05 cm−1 . The zero-point energy is significantly lower than the barrier height, which indicates that the ground state is mainly localized in the ground state. The calculated vibrational band origin for Ar–CS2 is
N
Ground state
υ 4 state
N
Ground state
υ 4 state
0 1 2 3 4 5 6 7 8 9
−240.1634 −215.2129 −205.4849 −190.7094 −185.3396 −174.5121 −167.5815 −164.6736 −158.8045 −149.4029
−240.1012 −215.2949 −205.4913 −190.8706 −185.4783 −174.5988 −167.7998 −164.8414 −159.0081 −149.6242
10 11 12 13 14 15 16 17 18 19
−146.4602 −144.9745 −143.5949 −140.0648 −136.9113 −132.6385 −131.5162 −131.4777 −130.3964 −125.6950
−146.6854 −145.1727 −144.3598 −140.2773 −137.1830 −132.9099 −132.1164 −132.0809 −130.6637 −126.0589
blueshifted by 0.0622 cm−1 , which agrees well with the observed value28 of 0.0671 cm−1 . However, the calculated band origin shift is larger (0.474 cm−1 ) and negative (redshift) for Ar–CO2 .19 The smaller CS2 band origin shift reveals a slight weakening of the vdW bond upon vibration excitation for Ar–CS2 . Figure 2 presents the contour plots of the wave functions for the ground and some lower excited states of Ar–CS2 with CS2 at the ground (υ = 0) state. The vdW vibrational states are defined by two quantum numbers (ns , nb ), respectively, denoting the vdW stretching and bending modes. Their assignments are loosely defined since ns and nb are not good quantum numbers and there is significant mixing between the two modes for higher excited states. Therefore, the vibrational states in Table II are labeled using numbers. Owing to the higher energy barrier, the ground states and these low-lying excited states are localized around the T-shaped global minimum. The wave functions of the higher excited vibrational states exhibit a strong mixing between the bending and stretching vibration modes. The average structures were, respectively, determined from the vibrational ground state wavefuction of the complex, R = ψ 0 |R|ψ 0 and cos 2 θ = ψ 0 |cos 2 θ |ψ 0 . The calculated average distance R for the ground state is 3.717 Å and the angle θ is 86.85◦ , the latter is a measure of the average amplitude of the bending from the 90◦ average configuration, which can be interpreted as an effect of the zero point vibrational motion of CS2 within the complex. The average θ -value of Ar–CS2 is closer to 90◦ than that of Ar–CO2 (82.90◦ ),19 indicating a smaller amplitude of zero point bending motion for Ar–CS2 . The calculated structure for Ar–CS2 is in agreement with the experimental values28 of R = 3.708 Å and θ = 86.4◦ . For the first two excited states,
TABLE I. The calculated minima and saddle point on the vibrationally averaged potentials Vυ=0 (R,θ ) and Vυ=1 (R,θ ) of Ar–CS2 together with the comparison with other ab initio PESs. The entries are given as R in angstrom, θ (deg), and V (cm−1 ).
This wok Reference 29 Reference 30
Vυ=0 Vυ=1 Vυ=0 Vυ=0
Global minimum
Local minimum
Saddle point
(3.66,90, −273.21) (3.67,90, −273.03) (3.70,90, −272.15) (3.70,90, −266.88)
(5.27,0/180, −167.15) (5.27,0/180, −168.05) (5.30,0/180, −162.52) (5.30,0/180, −161.31)
(4.93, 39.31, −142.45) (4.93, 39.12, −142.77) (4.87, 44.8, −135.99) (4.90, 40.0, −137.19)
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and 0.211 Å, and the former is close to that of the ground state, whereas the angular dispersion is 7.32◦ and 4.34◦ , and the latter is close to the value for the ground state. The rovibrational energies were assigned by the antisymmetric rotor quantum numbers JKaKc . J is the total angular momentum and Ka and Kc denote the projections of J onto the a and c axes in the principal axes of inertia. The calculated rovibrational energy levels were divided into four blocks, (even/even), (even/odd), (odd/even), and (odd/odd) for different combination parity of (j/p). In our work, we calculated the rovibrational energies for J from 0 to 7 for the vdW ground vibrational state with CS2 at both the ground (υ = 0) and the first excited (υ = 1) υ 3 vibrational states, which are available upon request.
V. INFRARED SPECTRA
FIG. 2. Contour plots of the wave functions for the lowest six vibrational states of Ar–CS2 with CS2 at the ground (υ = 0) state.
the average distance is 3.773 Å and 3.760 Å, respectively, and the angle is 82.68 and 85.67◦ , respectively. One can see from Fig. 2 that the first vibrational excited state can be attributed to the intermolecular bending mode with a frequency of 24.95 cm−1 , while the second vibrational excited state is due to the intermolecular stretching mode with a frequency of 34.68 cm−1 . The radial dispersion and angular dispersion suggest a similar trend. The radial dispersion and angular dispersion is 0.092 Å and 3.15◦ for the ground state, respectively. For the first two excited states, the radial dispersion is 0.098 Å
The rovibrational energy levels for J ≤ 4 were fitted to a Watson asymmetric top Hamiltonian53 using the a-type reduction in the Ir representation. The fitted molecular spectroscopic constants are given in Table III together with the experimental28 and previous theoretical30 result. It is clear that our calculated constants agree well with the experimental values. From the rotational constants, the inertial defect 0 in the ground state of Ar–CS2 was calculated to be 2.95 amu Å2 , whereas for the Ar–CO2 complex 0 is 2.39 amu Å2 ,2 which quantifies the extent to which the former complex is less rigid than the latter. On the other hand, the Ar–CO2 complex is nearer the symmetric prolate top limit than the Ar–CS2 complex. This can be seen from the asymmetry parameter, κ = (2B − A − C)/(A − C) (equal to −1 for the symmetric prolate top). The asymmetry parameter κ is −0.635 and −0.942 for the Ar–CS2 and Ar–CO2 complexes, respectively. The details regarding calculation of the transition intensities can be found in Ref. 35. The calculated rovibrational transition frequencies and the relative intensities at the temperature of T = 7 K for Ar–CS2 with their deviations from the observed infrared spectra are given in Table IV. One can see that the calculated transition frequencies are in excellent agreement with the experimental values. Most of the calculated frequencies are within 0.007 cm−1 of the observed values, and the root mean squares error of the 69 calculated
TABLE III. Spectroscopic constants (in cm−1 ) and the inertial defects 0 (in amu Å2 ) for the Ar–CS2 complex at both the ground and J Ka Kc − J Ka Kc states. Observed data are taken from Ref. 28. Ground state Experiment A B C K JK J δK δJ 0
0.109901 0.047067 0.032765 −1.234 × 10−6 1.705 × 10−6 1.891 × 10−7 1.418 × 10−6 4.937 × 10−8 2.95
This work 0.109873 0.046687 0.032578 −1.770 × 10−6 1.627 × 10−6 1.841 × 10−7 1.197 × 10−6 5.591 × 10−8 2.95
υ cal state Reference 24 0.110215 0.046419 0.032493 −3.700 × 10−6 2.090 × 10−6 7.792 × 10−7 1.418 × 10−6 4.937 × 10−8 2.69
Experiment 0.109188 0.047046 0.032691 −1.361 × 10−6 1.708 × 10−6 1.828 × 10−7 1.321 × 10−6 4.937 × 10−8 2.95
This work 0.109140 0.046670 0.032504 −1.778 × 10−6 1.631 × 10−6 1.842 × 10−7 1.198 × 10−6 5.617 × 10−8 2.96
Reference 24 0.109305 0.046304 0.032368 −2.830 × 10−6 1.743 × 10−6 0.659 × 10−6 2.874 × 10−6 4.937 × 10−8 2.52
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TABLE IV. Calculated infrared transition frequencies (in cm−1 ) and relative intensities for Ar–CS2 . Observed data are taken from Ref. 28. JKa Kc − JKa Kc 331 –440 330 –441 615 –726 514 –625 413 –524 432 –441 634 –643 533 –542 431 –440 532 –541 616 –707 312 –423 212 –321 633 –642 734 –743 211 –322 717 –726 515 –606 111 –220 616 –625 110 –221 414 –505 515 –524 414 –423 313 –404 313 –322 716 –725 615 –624 312 –321 514 –523 413 –422 111 –202 312 –303 734 –725 313 –202
υ cal
υ cal − υ obs
Intensity
JKa K − JKa Kc
υ cal
υ cal − υ obs
Intensity
1534.6026 1534.6028 1534.7900 1534.8341 1534.8807 1534.9229 1534.9230 1534.9234 1534.9243 1534.9287 1534.9312 1534.9322 1534.9375 1534.9381 1534.9543 1534.9902 1534.9950 1535.0022 1535.0391 1535.0474 1535.0554 1535.0767 1535.0934 1535.1320 1535.1556 1535.1627 1535.1838 1535.2197 1535.2373 1535.2386 1535.2432 1535.3243 1535.5387 1535.6825 1535.6835
−0.0051 −0.0049 −0.0033 −0.0035 −0.0039 −0.0072 −0.0071 −0.0067 −0.0058 −0.0069 −0.0016 −0.0034 −0.0023 −0.0077 −0.0081 −0.0045 −0.0024 −0.0022 −0.0053 −0.0034 −0.0058 −0.0024 −0.0035 −0.0049 −0.0026 −0.0052 −0.0030 −0.0043 −0.0061 −0.0048 −0.0053 −0.0036 −0.0056 −0.0033 −0.0060
0.521 0.521 0.467 0.422 0.382 0.153 0.339 0.262 0.153 0.263 0.857 0.348 0.226 0.343 0.407 0.302 0.309 0.755 0.271 0.317 0.303 0.633 0.325 0.309 0.477 0.260 1.000 0.753 0.420 0.726 0.604 0.140 0.538 0.821 0.449
633 –624 615 –606 532 –523 414 –303 431 –422 330 –321 331 –322 432 –423 716 –707 533 –524 515 –404 634 –625 615 –524 735 –726 616 –505 716 –625 717 –606 651 –642 652 –643 550 –541 551 –542 432 –321 431 –322 533 –422 532 –421 634 –523 735 –624 550 –441 551 –440 652 –541 651 –542 753 –642 752 –643 770 –661
1535.7010 1535.7037 1535.7226 1535.7385 1535.7415 1535.7541 1535.7641 1535.7691 1535.7773 1535.7787 1535.7931 1535.7943 1535.7949 1535.8170 1535.8497 1535.8935 1535.9087 1536.0249 1536.0256 1536.0278 1536.0280 1536.0742 1536.0858 1536.1412 1536.1757 1536.1988 1536.2467 1536.4286 1536.4286 1536.5075 1536.5077 1536.5859 1536.5867 1536.8502
−0.0028 −0.0086 −0.0029 −0.0064 −0.0034 −0.0035 −0.0041 −0.0039 −0.0086 −0.0042 −0.0064 −0.0052 −0.0099 −0.0048 −0.0067 −0.0099 −0.0073 −0.0029 −0.0022 −0.0028 −0.0026 −0.0056 −0.0061 −0.0059 −0.0069 −0.0058 −0.0058 −0.0056 −0.0056 −0.0064 −0.0062 −0.0073 −0.0065 −0.0064
0.590 0.397 0.468 0.581 0.338 0.192 0.138 0.320 0.785 0.411 0.717 0.464 0.319 0.479 0.839 0.432 0.296 0.244 0.244 0.143 0.143 0.467 0.457 0.441 0.410 0.417 0.541 0.672 0.672 0.614 0.614 0.557 0.554 0.611
transitions is only 0.005 cm−1 . The relatively most intense line is the transition from 716 to 725 at 1535.1838 cm−1 . Although good agreements between the calculated and observed infrared spectra confirm the high quality of our new potentials, the bend and symmetric stretch of CS2 are not considered in this work, which could have a slight effect on the potential and spectroscopic properties of Ar–CS2 in the υ 3 region of the CS2 molecule.
rms error
0.005
and the Lanczos algorithm. The calculated spectroscopic constants and infrared spectra are in good agreement with the available observed values. The experimental band origin shift in the infrared spectra is reproduced very well. It is expected that the accurate descriptions of the new potential should be useful for further studies of the structures and spectroscopy of the ArN –CS2 clusters. ACKNOWLEDGMENTS
VI. CONCLUSION
We have presented a three-dimensional PES for the Ar– CS2 complex including the Q3 normal mode of CS2 at the CCSD(T) level with a large basis set plus bond functions. The intermolecular potential was calculated over five PODVR grid points for the Q3 normal mode. Based on the ab initio potential points, two vibrationally averaged PESs of the complex were generated. Each PES has a T-shaped global minimum and two equivalent local minima of linear geometry. The bound rovibrational energy levels of Ar–CS2 were obtained by employing the radial DVR/angular FBR method
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