Volume 33 Issue 3
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Chao-ying Han, Ting Jiang, Hua Zhu, Hong-jun Fan. Six-Dimensional $ab$ $ initio$ Potential Energy Surface and Bound States for He-H$ _\textbf{2} $S Complex[J]. Chinese Journal of Chemical Physics , 2020, 33(3): 319-326. doi: 10.1063/1674-0068/cjcp1907145
Citation: Chao-ying Han, Ting Jiang, Hua Zhu, Hong-jun Fan. Six-Dimensional $ab$ $ initio$ Potential Energy Surface and Bound States for He-H$ _\textbf{2} $S Complex[J]. Chinese Journal of Chemical Physics , 2020, 33(3): 319-326. doi: 10.1063/1674-0068/cjcp1907145

Six-Dimensional $ab$ $ initio$ Potential Energy Surface and Bound States for He-H$ _\textbf{2} $S Complex

doi: 10.1063/1674-0068/cjcp1907145
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  • Corresponding author: Hua Zhu.E-mail:zhuhua@scu.edu.cn; Hong-jun Fan.E-mail:hjfan@suse.edu.cn
  • Received Date: 2019-07-27
  • Accepted Date: 2019-10-16
  • Publish Date: 2020-06-27
通讯作者: 陈斌, bchen63@163.com
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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Six-Dimensional $ab$ $ initio$ Potential Energy Surface and Bound States for He-H$ _\textbf{2} $S Complex

doi: 10.1063/1674-0068/cjcp1907145
Chao-ying Han, Ting Jiang, Hua Zhu, Hong-jun Fan. Six-Dimensional $ab$ $ initio$ Potential Energy Surface and Bound States for He-H$ _\textbf{2} $S Complex[J]. Chinese Journal of Chemical Physics , 2020, 33(3): 319-326. doi: 10.1063/1674-0068/cjcp1907145
Citation: Chao-ying Han, Ting Jiang, Hua Zhu, Hong-jun Fan. Six-Dimensional $ab$ $ initio$ Potential Energy Surface and Bound States for He-H$ _\textbf{2} $S Complex[J]. Chinese Journal of Chemical Physics , 2020, 33(3): 319-326. doi: 10.1063/1674-0068/cjcp1907145
  • Van der Waals (vdW) complexes between rare-gas (Rg) atoms and nonlinear H$ _2 $X (X = O, S) molecules are of considerable interest in recent years. Such researches have been aimed at understanding the nature of the weak intermolecular potentials and dynamics of these weakly bound complexes. H$ _2 $O is one of the most significant interstellar molecules and is a key element in biological systems and collision phenomena [1-4], so considerable experimental and theoretical studies have been devoted to determining such potentials and rovibrational spectra in prototype systems formed by H$ _2 $O and Rg atoms. Compared with H$ _2 $O, H$ _2 $S also plays an equally important role in chemistry and in the spectroscopy of giant planets [5, 6]. It is intriguing to explore the difference of structure and dynamical features between the H$ _2 $S containing complexes and the H$ _2 $O containing analogues.

    Many experimental researches have been carried out concerning the Rg-H$ _2 $O complexes [7-14]. In 1988, Cohen et al. first studied the infrared spectra of the Ar-H$ _2 $O complex in the region of the H$ _2 $O asymmetric stretching $ \nu_3 $ fundamental band using a tunable infrared laser [7]. The results showed that the complex has a hydrogen bonded equilibrium structure. Subsequently, further experimental studies of microwave and infrared spectra for Rg-H$ _2 $O (Rg = Ne, Ar, Kr, Xe) were reported [8-14]. For the complexes involving H$ _2 $S, available experimental information is limited to the microwave spectra of Ar-H$ _2 $S [15, 16] and Ne-H$ _2 $S [17]. In 1997, the rotational spectra, structure, and internal dynamics of various isotopomers of the Ar-H$ _2 $S dimer has been investigated by Gutowsky et al. [16]. Later Liu et al. [17] measured the rotational spectra of 15 isotopic species and internal dynamics of Ne-H$ _2 $S. The above experimental researches revealed that these Rg-H$ _2 $S complexes have a planar T-shaped structure similar to that of the Rg-H$ _2 $O complexes.

    Along with these experimental researches, a number of theoretical studies [18-30] have dealt with the construction of the ab initio potential energy surface. The first ab initio potential for Ar-H$ _2 $O [18] was reported via employing the second-order many-body perturbation theory. Subsequently, further investigations of potential energy surfaces for Rg-H$ _2 $O [22, 23] (Rg = He, Ne, Ar, Kr, Xe) were carried out at the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)] level. For the complexes involving H$ _2 $S, Oliveira et al. [24] proposed a potential energy surface which was limited to the region around equilibrium structure using MP2 method for Ar-H$ _2 $S in early time. Later, extensive ab initio calculations were carried out for Ne-H$ _2 $S [26] and Ar-H$ _2 $S [27] adopting aug-cc-pVQZ basis set at [CCSD(T)] level, the rovibrational bound states and microwave spectra for these complexes were studied based on the potential energy surfaces. In the above researches, H$ _2 $O or H$ _2 $S molecule was treated as a rigid rotor, which was sufficient for describing microwave spectra of ground-state species, but not enough for predicting the infrared spectra including the transition in the intramolecular vibrational modes. An improved approach was to construct the potential by explicitly involving the dependence of the intramolecular vibrational coordinates [31]. Up to now, the six-dimensional potential energy surfaces for Rg-H$ _2 $O (Rg = He, Ne, Ar) containing the intramolecular $ Q_1 $, $ Q_2 $, and $ Q_3 $ vibrational modes for the $ \nu_1 $ symmetric stretching vibration, $ \nu_2 $ bending vibration and $ \nu_3 $ asymmetric stretching vibration of H$ _2 $O have been presented based on this method [28-30].

    To the best of our knowledge, there is still no reliable intermolecular potential energy surface for He-H$ _2 $S which includes the intramolecular vibration modes of the H$ _2 $S monomer. The available potential for He-H$ _2 $S [25] was calculated with rigid monomer model, also not sufficient for the bound state calculations, because it was only limited to the region of the potential well. And it was only discussed on one-dimensional energy curves of the interaction energy as the function of distance $ R $ or angle $ \theta $ ($ E $-$ R $ or $ E $-$ \theta $). Recently, we have successfully constructed a full six-dimensional potential energy surface for the Ar-H$ _2 $S [32] system that explicitly depends on the three intramolecular vibrational modes of H$ _2 $S. The calculated infrared spectra for Ar-(para-H$ _2 $S) and Ar-(ortho-H$ _2 $S) are in good agreement with the experimental results. In the present work, a new six-dimensional potential for He-H$ _2 $S is presented, and is expected to be as accurate as that for Ar-H$ _2 $S. Using the obtained potential, we first predict the rovibrational spectra of He-(para-H$ _2 $S) and He-(ortho-H$ _2 $S), respectively. And we hope that the regularity of potential energy surfaces, rovibrational bound states, band origin shifts, as well as the effect of the intramolecular normal modes on the potentials and rovibrational spectra can be explored for the series of Rg-H$ _2 $S dimers.

    The six-dimensional ab initio potential for He-H$ _2 $S was constructed using [CCSD(T)]-F12a method with a large basis set plus bond functions. The $ Q_1 $, $ Q_2 $, and $ Q_3 $ normal modes for the symmetric stretching, bend and antisymmetric stretching vibration of H$ _2 $S were included in the construction of the potential. The potential optimized discrete variable representation (PODVR) [33] grid points were used to construct intermolecular potential energy surface. The combined radial discrete variable representation (DVR)/angular finite basis representation (FBR) method and Lanczos algorithm were used to calculate the rovibrational energy levels and the bound states.

  • The geometry of He-H$ _2 $S can be described by the body-fixed Jacobi coordinates ($ R $, $ \theta $, $ \varphi $, $ Q $, $ Q_2 $, $ Q_3 $): $ R $ stands for the distance from the He atom to the center of mass of H$ _2 $S, $ \theta $ denotes the angle between the $ \textbf{R} $ vector and the C$ _2 $ axis of H$ _2 $S, and $ \varphi $ is the dihedral angle between the two planes defined by $ \textbf{R} $ vector with C$ _2 $ and the H$ _2 $S molecule plane. The intramolecular coordinates $ Q_1 $, $ Q_2 $, and $ Q_3 $ represent the $ \nu_1 $ symmetric stretching, $ \nu_2 $ bending, and $ \nu_3 $ asymmetric stretching vibration of H$ _2 $S, respectively. We adopted PODVR grid points in our latest work of Ar-H$ _2 $S [32] for the three coordinates.

    The potential energies for He-H$ _2 $S were calculated with $ R $ ranging from 2.40 Å to 10.00 Å, angles $ \theta $ from 0.0$ ^{\circ} $ to 180.0$ ^{\circ} $ in a step of 15.0$ ^{\circ} $, and $ \varphi $ from 0.0$ ^{\circ} $ to 90.0$ ^{\circ} $ at intervals of 30.0$ ^{\circ} $. The calculations of potential energies were performed at the [CCSD(T)]-F12a level. The aug-cc-pVTZ basis set of Woon and Dunning [34] was employed for all atoms plus midpoint bond functions (3s3p2d1f1g) [35]. [CCSD(T)]-F12a/aVTZ can provide a remarkable description of the intermolecular interaction energies [36, 37]. The full counterpoise procedure [38] was used to correct for the basis set superposition error (BSSE). According to it, the energies of monomers are calculated using the same full basis set. All ab initio calculations were carried out using the MOLPRO package [39].

    The effective potentials $ V_{\nu _1 , \nu _2 , \nu _3 } (R, \theta , \varphi ) $ with H$ _2 $S at the vibrational ground state as well as the $ \nu_2 $ and $ \nu_3 $ excited states were acquired by averaging the six-dimensional potential over the intramolecular $ Q_1 $, $ Q_2 $, and $ Q_3 $ vibrational coordinates.

    In which vibrational wave functions in Eq.(1) and Eq.(2) were determined by calculating the two-dimensional $ V_{ \rm{H}_2 \rm{S}} $($ Q_1 $, $ Q_3 $) and one-dimensional $ V_{ \rm{H}_2 \rm{S}} $($ Q_2 $) potentials. The intramolecular potential energy surface of $ V_{ \rm{H}_2 \rm{S}} $($ Q $) governing the $ Q_1 $, $ Q_2 $, and $ Q_3 $ vibration of the isolated H$ _2 $S monomer was determined by Kozin et al. [40] from experimental spectroscopic data. The averaged intermolecular potentials $ V_{\nu_1, \nu _2, \nu_3 } (R, \theta, \varphi ) $ were fitted to a three-dimensional Morse/Long-Range (MLR) potential function employing the identical approach as Ref.[28].

  • Within the Born-Oppenheimer approximation, the vibrational averaged intermolecular Hamiltonian of He-H$ _2 $S can be expressed as [29, 32]

    where $ \mu $ is the reduced mass of He-H$ _2 $S, $ \hat J $ and $ \hat j $ are the angular momentum operators corresponding to the total and the H$ _2 $S monomer rotations, respectively, and $ \hat H_{{\rm{H}}_{\rm{2}} {\rm{S}}} $ represents the rigid rotor kinetic energy operator for H$ _2 $S.

    where $ A $, $ B $, and $ C $ are the rotational constants of H$ _2 $S [41], and $ \hat {j_ \pm } {\rm{ = }}\hat {j_x } \mp \hat {ij_y } $.

    The rovibrational bound states and energy levels were calculated with the effective radial DVR/angular FBR method [42, 43]. In our calculations, we used 60 sine-DVR [44] points for the $ R $ coordinate, 26 Gauss-Legendre grid points and 26 Gauss-Chebyshev quadrature points for the numerical integration over $ \theta $ and $ \varphi $. The Lanczos algorithm [45] was employed to efficiently diagonalize the Hamiltonian matrix. For the angular coordinates, the parity-adapted rotational basis function $ \Theta _{jk}^{JMK\varepsilon } $ was defined in the following form [21, 22],

    $ D_{MK}^{J^*} $ and $ D_{Kk}^{j^*} $ are the normalized rotational functions to describe the overall rotation of the complex and the rotation of the H$ _2 $S molecular, respectively.

  • The root-mean-square (rms) error between the fitted and the calculated points was found to be 0.1 cm$ ^{-1} $. The FORTRAN subroutine for generating potential energy surface of He-H$ _2 $S can be seen in the supplementary material. The 3D potentials were obtained by fitting parameters. The contour plots of the averaged potential energy surface of He-H$ _2 $S with H$ _2 $S at the vibrational ground state are shown in FIG. 1. One can see that the potential exhibits a large angular anisotropy and a strong radial-angular coupling. FIG. 1(a) presents how the minimum potential depends on $ \theta $ and $ R $ when $ \varphi $ = 0.0$ ^{\circ} $. The global minimum (point A) with the well depth of 35.301 cm$ ^{-1} $ is located at $ R $ = 3.46 Å, $ \theta $ = 109.9$ ^{\circ} $ and $ \varphi $ = 0.0$ ^{\circ} $, which is in a planar T-shape geometry with He in the H$ _2 $S molecular plane ($ \varphi $ = 0.0$ ^{\circ} $). A planar local minimum (point B) with a well depth of 26.072 cm$ ^{-1} $ occurs at $ R $ = 3.87 Å and $ \theta $ = 0.0$ ^{\circ} $. The saddle point (point C) connecting the two minima was found to be a planar structure at $ R $ = 4.18 Å and $ \theta $ = 44.2$ ^{\circ} $ with the barriers height of 14.720 cm$ ^{-1} $, relative to the global minimum. In addition, another planar first-order saddle point (point D) is located at $ R $ = 3.77 Å and $ \theta $ = 180.0$ ^{\circ} $ with the barriers height of 14.519 cm$ ^{-1} $ with respect to the global minimum. FIG. 1(b) shows the contour plot of the potential energy surface of He-H$ _2 $S with $ R $ fixed at its equilibrium value of 3.46 Å. Due to the symmetry of the system, $ \varphi $ direction is only displayed in the range from 0.0$ ^{\circ} $ to 180.0$ ^{\circ} $. A second-order saddle point is for the out-plane rotation which is hindered by a barrier of 22.598 cm$ ^{-1} $ at $ R $ = 4.15 Å, $ \theta $ = 88.4$ ^{\circ} $ and $ \varphi $ = 90.0$ ^{\circ} $, relative to the global minimum.

    Figure 1.  Contour plots of the potential energy surface for He-H$ _2 $S with H$ _2 $S at the vibrational ground state: (a) $ \varphi $ is fixed at 0.0$ ^{\circ} $, and (b) $ R $ is fixed at 3.46 Å

    The characteristic points and their corresponding energies for the effective three-dimensional potentials for He-H$ _2 $S with H$ _2 $S at the vibrational ground state as well as $ \nu_2 $ and $ \nu_3 $ excited states are listed in Table Ⅰ. The variation values of each stationary point are extremely small at different states of H$ _2 $S. FIG. 2 presents distance $ R_{\rm{m}} $ and the minimum potentials $ V_{\rm{m}} $ along the minimum potential path for He-H$ _2 $S at the ground and excited states of H$ _2 $S. It is clear that the contour plot at the ground state looks the same as that for the excited states. For comparison between He-H$ _2 $S and Ar-H$ _2 $S [32], the interaction between He and H$ _2 $S is weaker than that between Ar and H$ _2 $S, the well depth of He-H$ _2 $S is 143.939 cm$ ^{-1} $ significantly shallower than that of Ar-H$ _2 $S. In addition, there are obvious differences in the stationary points between the two complexes. For example, the distances $ R $ for all stationary geometries of He-H$ _2 $S are about 0.30 Å larger than those of Ar-H$ _2 $S, and deviations of angular coordinate $ \theta $ are about 5.0$ ^{\circ} $.

    Table Ⅰ.  Characteristic points (R in Å, θ and φ in degree) and the well depths (in cm−1) of the He-H2S with H2S at the vibrational ground and excited states.

    Figure 2.  Radial position (upper) and energy (lower) along the minimum energy path for He-H$ _2 $S with H$ _2 $S at the vibrational ground state as well as the $ \nu_2 $ and $ \nu_3 $ excited states as functions of angle $ \theta $ for optimized values of $ \varphi $ and $ R $

    The He-H$ _2 $O equilibrium structure employs a hydrogen bonded position [29], whereas an anti-hydrogen bonded orientation is adopted for He-H$ _2 $S, though the two complexes are found to have the T-shaped global geometry, and the global minimum for He-H$ _2 $S is only 1.212 cm$ ^{-1} $ deeper than that for He-H$ _2 $O. Compared with He-H$ _2 $O, the $ R $ coordinates of each stationary point for He-H$ _2 $S are about 0.40 Å larger than those of He-H$ _2 $O, which may be mainly derived from the larger atomic radius of the sulfur atom. As we all know, He-H$ _2 $O has only one planar global minimum, while He-H$ _2 $S has an additional planar local minimum, In contrast to the case of He-H$ _2 $O, the He-H$ _2 $S potential presents a local minimum in the planar configuration ($ \theta $ = 0.0$ ^{\circ} $, $ \varphi $ = 0.0$ ^{\circ} $), rather than the first-order saddle point found for the He-H$ _2 $O complex.

  • The calculated rovibrational bound states were marked with six quantum numbers ($ J, K, j, k, P, n_ \rm{s} $) in free internal rotor model, where $ J $ represents the total angular momentum number, $ K $ is the projection of total angular momentum $ J $ on the BF $ z $-axis, states with $ K $ = 0, or $ K $ = 1 are represented by Greek capital letter $ \Sigma $ or $ \Pi $ state, $ j_{k_ak_c} $ means asymmetric top level of the H$ _2 $S subunit, $ k $ denotes the projection of $ j $ on the C$ _2 $ axis of the H$ _2 $S monomer where the evenness and oddness of determine whether they belong to the He-(para-H$ _2 $S) or He-(ortho-H$ _2 $S) complex, $ P $ shows the parity $ \rm{e} $ or $ \rm{f} $ symmetry with $ P{\rm{ = ( - 1)}}^J $ or $ P{\rm{ = ( - 1)}}^{J + 1} $, and quantum number $ n_ \rm{s} $ represents the intermolecular stretching mode.

    The calculated rovibrational energy levels within $ J $$ \leq $4 for He-(para-H$ _2 $S) and He-(ortho-H$ _2 $S) with H$ _2 $S at the vibrational ground state as well as $ \nu_2 $ and $ \nu_3 $ excited states are listed in Table Ⅱ. One can see the rovibrational energy levels of the three states are almost identical. Our potentials support only one vibrational bound state for both He-(para-H$ _2 $S) and He-(ortho-H$ _2 $S). The lowest vibrational energy of $ - $7.161 cm$ ^{-1} $ for He-(para-H$ _2 $S) with H$ _2 $S at the vibrational ground state corresponds to the zero-point energy of 28.140 cm$ ^{-1} $, which is about 80% of the well depth (35.301 cm$ ^{-1} $). The zero-point energy is distinctly higher than the in-plane barrier height of 14.720 and 14.519 cm$ ^{-1} $. With such lower barriers, the minima are not able to trap the He atom very well, leading to a delocalized angular distribution. In the case of He-(ortho-H$ _2 $S), the energy level for a bound state of the complex is that the total rovibrational energy minus the rotational energy for the free H$ _2 $S molecule. The asymptote for ortho-H$ _2 $S with $ j_{k_a k_c } $ = 1$ _{01} $ had the energy of 13.749 cm$ ^{-1} $ [46], which was calculated from the sum of the rotational constants $ B $+$ C $ of H$ _2 $S. As seen in Table Ⅱ, the lowest vibrational energy is 5.702 cm$ ^{-1} $, corresponding to the truly bound state energy of $ - $8.047 cm$ ^{-1} $, so the zero-point energy is 27.254 cm$ ^{-1} $ for He-(ortho-H$ _2 $S), which is about 1 cm$ ^{-1} $ lower than that of He-(para-H$ _2 $S). Table Ⅲ presents the energy levels on the lowest two states $ \Sigma \left( {0_{00} } \right)^ \rm{e} $ and $ \Sigma \left( {1_{01} } \right)^ \rm{e} $ for He-H$ _2 $S with H$ _2 $S at the vibrational ground state as well as $ \nu_2 $ and $ \nu_3 $ excited states. The predicted vibrational band origins are blue-shifted by 0.025 cm$ ^{-1} $ and 0.031 cm$ ^{-1} $ for He-(para-H$ _2 $S) in the $ \nu_2 $ and $ \nu_3 $ region of H$ _2 $S, respectively. For the He-(ortho-H$ _2 $S) complex, the predicted vibrational band origins are also blue-shifted by 0.034 cm$ ^{-1} $ and 0.060 cm$ ^{-1} $ with H$ _2 $S at the $ \nu_2 $ and $ \nu_3 $ states, respectively. The smaller H$ _2 $S band origin shifts reveal a slight weakening of the vdW bond upon vibration excitation for He-H$ _2 $S. Compared with He-H$ _2 $S, the shifts for Ar-H$ _2 $S [32] are larger ($ - $0.38 and $ - $0.63 cm$ ^{-1} $). The shifts of the two complexes are consistent with a common trend that the lighter, less-polarizable partner He tends to induce positive (blue-shifted), while the heavier, polarizable partner Ar tends to move these shifts to the red.

    Table Ⅱ.  The calculated energy levels for He-H$ _2 $S with H$ _2 $S at the vibrational ground and excited states (labeled with $ K $($ j_{k_ak_c} $)$ ^{J+P} $). The $ ^* $ means resonance states.

    Table Ⅲ.  The rovibrational energy comparison for He-H$ _2 $S on the $ \Sigma $(0$ _{00} $)$ ^ \rm{e} $ and $ \Sigma $(1$ _{01} $)$ ^ \rm{e} $ states with H$ _2 $S at the vibrational ground and excited states (in cm$ ^{-1} $).

    To further research the properties of the vibrational states, it is necessary to visualize the wave functions. FIG. 3 and FIG. 4 present the contour plots of wave functions for some lower rovibrational energy levels of He-(para-H$ _2 $S) and He-(ortho-H$ _2 $S) with H$ _2 $S at the vibrational ground state, respectively. It is clear that these states spread over the entire range of angles. For comparison between the wave functions of He-(para-H$ _2 $S) and those of He-(ortho-H$ _2 $S), the variation of wave functions of $ \theta {\rm{ - }}\varphi $ is very small along $ \varphi $ coordinate for He-(para-H$ _2 $S), while the variation of wave functions of $ \theta {\rm{ - }}\varphi $ is remarkable along $ \varphi $ coordinate for He-(ortho-H$ _2 $S). For He-(para-H$ _2 $S), the analysis of the wave functions indicated that $ \Pi \left( {1_{11} } \right)^ \rm{e} $ is a resonance state, and the $ \Pi $-contributions of $ \Pi \left( {1_{11} } \right)^ \rm{f} $ state accounts for 58%, 57%, 43%, and 71% for $ J $ = 1, 2, 3 and 4, respectively, while the $ \Pi \left( {1_{11} } \right)^ \rm{f} $ state has 99% of $ \Pi $-contribution for $ J $ = 1$ - $4. For He-(ortho-H$ _2 $S), the wave function on the $ \Sigma \left( {1_{01} } \right)^ \rm{e} $ state only exhibits a clear node along coordinate, the wave functions on the $ \Pi\left( {1_{01} } \right)^ \rm{e} $ and $ \Pi \left( {1_{01} } \right)^ \rm{f} $ states also show the clear nodal structure along $ \theta $ and $ \varphi $ coordinates, and the two states display strong coupling between $ \theta $ and $ \varphi $ coordinates.

    Figure 3.  The wave functions for the lower energy levels of He-(para-H$ _2 $S): (left panel) as a function of $ R $ and $ \theta $, (right panel) as a function of $ \theta $ and $ \varphi $, respectively.

    Figure 4.  The wave functions for the lower energy levels of He-(ortho-H$ _2 $S). Left panel: as functions of $ R $ and $ \theta $, right panel: as functions of $ \theta $ and $ \varphi $, respectively.

  • In this work, an accurate six-dimensional potential energy surface for He-H$ _2 $S which explicitly involves the intramolecular $ Q_1 $, $ Q_2 $ and $ Q_3 $ normal coordinates for the $ \nu_1 $ symmetric stretching vibration, $ \nu_2 $ bending vibration and $ \nu_3 $ asymmetric stretching vibration of H$ _2 $S was presented. The intermolecular potential was calculated over five PODVR grid points for the $ Q_1 $, $ Q_2 $, and $ Q_3 $ normal modes, respectively, employing the [CCSD(T)]-F12a method with aug-cc-pVTZ basis set plus bond functions placed at the mid-point on the intermolecular axis. Three vibrationally averaged potential energy surfaces of He-H$ _2 $S with H$ _2 $S at the vibrational ground state as well as the $ \nu_2 $ and $ \nu_3 $ excited states were generated from averaging of the six-dimensional potential over the $ Q_1 $, $ Q_2 $, and $ Q_3 $ coordinates. It was found that each averaged potential energy surface has a T-shaped global minimum, a planar local minimum, two in-plane saddle points and an out-plane saddle point. Based on the ab initio potentials, rovibrational energy levels were calculated using the radial DVR/angular FBR method for He-(para-H$ _2 $S) and He-(ortho-H$ _2 $S) with H$ _2 $S at different states. Our potentials support only one vibrational bound state for He-(para-H$ _2 $S) and He-(ortho-H$ _2 $S), respectively. In addition, we predicted that the band origins were blue-shifted (0.025 cm$ ^{-1} $ and 0.031 cm$ ^{-1} $) and (0.041 cm$ ^{-1} $ and 0.060 cm$ ^{-1} $) for He-(para-H$ _2 $S) and He-(ortho-H$ _2 $S) with the H$ _2 $S molecule at the $ \nu_2 $ and $ \nu_3 $ states, respectively. It is expected that the potential energy surfaces and rovibrational bound states should be useful for further theoretical and experimental studies for the He-H$ _2 $S complex.

    Supplementary materials: The FORTRAN subroutine, which generates potential energy surfaces of He-H$ _2 $S can be found.

  • This work was supported by the National Natural Science Foundation of China (No.21973065) and Sichuan Science and Technology Program (No.2018JY0172).

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