Potential energy surface and rovibrational states of the ... - IFF-CSIC

JOURNAL OF CHEMICAL PHYSICS

VOLUME 120, NUMBER 14

8 APRIL 2004

Potential energy surface and rovibrational states of the ground Ar–HI complex Rita Prosmiti,a) Sergio Lo´pez-Lo´pez, and Alberto Garcıá-Vela Instituto de Matema´ticas y Fı´sica Fundamental, C.S.I.C., Serrano 123, 28006 Madrid, Spain

共Received 26 November 2003; accepted 15 January 2004兲 A potential energy surface for the ground electronic state of the Ar–HI van der Waals complex is calculated at the coupled-cluster with single and double excitations and a noniterative perturbation treatment of triple excitations 关CCSD共T兲兴 level of theory. Calculations are performed using for the iodine atom a correlation consistent triple-␨ valence basis set in conjunction with large-core Stuttgart–Dresden–Bonn relativistic pseudopotential, whereas specific augmented correlation consistent basis sets are employed for the H and Ar atoms supplemented with an additional set of bond functions. In agreement with previous studies, the equilibrium structure is found to be linear Ar–I–H, with a well depth of 205.38 cm⫺1. Another two secondary minima are also predicted at a linear and bent Ar–H–I configurations with well depths of 153.57 and 151.57 cm⫺1, respectively. The parametrized CCSD共T兲 potential is used to calculate rovibrational bound states of Ar–HI/Ar– DI complexes, and the vibrationally averaged structures of the different isomers are determined. Spectroscopic constants are also computed from the CCSD共T兲 surface and their comparison with available experimental data demonstrates the quality of the present surface in the corresponding configuration regions. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1665467兴

experimental data by (2⫹1) REMPI 共resonance enhanced multiphoton ionization兲,22 microwave, and IR supersonic jet spectroscopy18 are available on the equilibrium structure of Ar–HI. In the preceding study18 two potential surfaces have been reported for the ground state of Ar–HI. One surface has been calculated at the MP2 level, and the other surface has been morphed by shifting and scaling the MP2 surface in order to fit the experimental data. Still, for the semiempirical morphed potential, a quite large difference is obtained in the estimated value of the dissociation energy of Ar–IH, where a value of D 0 ⫽146.43 cm⫺1 is reported in comparison with the one of 93⫾12 cm⫺1 determined from photolysis experiments by Suzuki et al.22 The need for scaling, as well as the large value for the Ar–IH dissociation energy 共as compared with the experimental value of Ref. 22兲, indicates that the level of the MP2 calculation is not sufficient to represent quantitatively the intermolecular potential energy surface. Thus, in this work, we examine the van der Waals 共vdW兲 interaction of an Ar atom with the HI molecule in its ground electronic state at the CCSD共T兲 level of theory. The aim of this study is to present high-level ab initio calculations and to obtain an accurate analytical potential energy surface for the Ar–HI complex in its ground electronic state. Bound-state calculations are carried out and the comparison with available experimental data demonstrates the quality of a pure ab initio potential. Additionally, the latter study extended to the deuterated isotopomer Ar–DI. The paper is organized as follows. In next section, together with the ab initio results, we present a parametrized functional form of the potential. Bound-state calculations on the above surface are then reported and compared with experimental data and previous ab initio studies. Conclusions constitute the closing section.

I. INTRODUCTION

The determination of the potential energy function between weakly interacting moieties has been the main goal of several theoretical and experimental studies.1– 6 Rare-gas– hydrogen-halide 共Rg–HX兲 complexes have served as prototypes for studying such intermolecular interactions. In particular the Ar–HX clusters are extensively studied using microwave, far-infrared 共far-IR兲, and IR spectroscopy, and intermolecular potentials have been constructed from spectroscopic data for Ar–HF,2,7,8 Ar–HCl,9,10 and Ar–HBr.11–13 In all three cases the potential energy surface 共PES兲 exhibits two local minima, corresponding to the Ar–H–X and Ar– X–H isomers. Structural analysis of the ground electronic state of such species turned out to be interesting in connection with the cage effect,14 and several studies have been carried out to explore it in photolysis of the H–X bond within the hydrogen-halide–rare-gas complexes.15,16 Thus, in order to understand the dynamics of such complexes, accurate potential energy surfaces are needed. This can be achieved either by fitting the potential parameters to experimental data obtained from high-resolution spectroscopic methods or by performing high-level ab initio electronic structure calculations. During last years, ab initio methods have progressed sufficiently such that the computed potentials are able to reproduce quantitatively or at least semiquantitatively the available experimental data. More recently, attempts have been made to construct PESs for weakly bound systems using morphing approaches on the ab initio calculated potentials.17–21 Such a procedure has been carried out18 for the ground Ar–HI state, where a兲

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© 2004 American Institute of Physics

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J. Chem. Phys., Vol. 120, No. 14, 8 April 2004

TABLE I. Experimental and theoretical binding energies, equilibrium distances, and frequencies for the HI molecule obtained using aug-cc-pVQZ and SDB-aug-cc-pVTZ basis sets for H and I atoms, respectively. Spin– orbit effects have been approximately removed from the experimental dissociation energy using the atomic splittings of Moore 共Ref. 29兲. Property

CCSD共T兲a/MP2a

Experimentb

Binding energy (D e ) 共kcal/mol兲 Equilibrium bond length (R e ) 共Å兲 Frequency ( ␻ e ) 共cm⫺1兲

78.67/77.82 1.60049/1.60526 2354.4/2329.4

80.95 1.60916 2309.01

a

Present work. References 27 and 28.

b

II. RESULTS A. Ab initio calculations

The interaction energy of Ar–HI is calculated with the spin-restricted single- and double-excitation coupled cluster method with perturbative triples 关RCCSD共T兲兴 correlating only the valence electrons as implemented in the GAUSSIAN 98 package.23 The augmented correlation consistent quadruple-␨ basis set is used for the H 共aug-cc-pVQZ兲 and Ar 关 aug-cc-pV(Q⫹d)Z兴 atoms from EMSL library.24 For the iodine atom we use relativistic effective core potential 共RECP兲. We choose to employ the Stuttgart–Dresden–Bonn 共SDB兲 large-core energy-consistent pseudopotential25 in conjunction with an augmented correlation consistent triple-␨ 共SDB-aug-cc-pVTZ兲 valence basis set.26 This basis set is of aug-cc-pVTZ quality and has been optimized for use with the SDB pseudopotential. In order to check the performance of the above atomic basis sets we computed at CCSD共T兲 and MP2 levels several properties of the HI monomer and compared them with available experimental values27,28 共see Table I兲. It has been shown30–32 that an efficient way to saturate the dispersion energy in weakly bound systems is the use of midbond functions. Thus for a better description of the longrange interactions33,34 an additional set (3s3p2d2 f 1g) of bond functions is employed, as defined by Cybulski and Toczylowski.35 The bond functions are placed at the midpoint of the distance between Ar and the HI center of mass

for the bent configurations and at the midpoint between the Ar atom and the nearest H or I atom for the linear configurations of the complex. This procedure prevents the bond functions to get too close to the H or I atom for small bond distances. Test runs are performed using augmented correlation consistent triple-␨-type basis sets for the H and Ar atoms, as well as the above-mentioned atom-centered basis sets with and without the additional set (3s3p2d2 f 1g) of bond functions. The results of these calculations are summarized in Table II for configurations near to global and local minima. As can be seen, the use of bond functions clearly affects the interaction energies of the complex, lowering them with a lower computational cost than augmenting the whole basis set. This demonstrates their efficiency in calculations of such vdW systems. To investigate the intermolecular interaction we use the standard ab initio supermolecular approach. At a given level of theory, the interaction energy is calculated from the expression ⌬E⫽E Ar–HI⫺E BSSE⫺E Ar⫺E HI ,

where E Ar–HI , E Ar , and E HI are the energies of Ar–HI, Ar and HI, respectively. The correction E BSSE for the basis-set superposition error was calculated using the standard counterpoise method.36 The interaction energy for Ar–HI is computed on a grid of points consisting of several Ar–I distances ranging from R ArI⫽3.2 to 11 Å using a grid of equally spaced points with ⌬R ArI⫽0.1– 0.25 Å for the short and intermediate ranges of R ArI and ⌬R ArI⫽2 Å for the long-range region. The H–I–Ar angle ␾ is varied between 0° and 180° using 17 equally spaced angles by increments of ␲/16 radians, considering the HI bond fixed at its equilibrium value r e ⫽1.609 16 Å. The results for the CCSD共T兲 interaction energies of Ar–HI are listed in Table III 共Ref. 37兲. B. Analytical representation of the PESs

Given the ab initio energies computed on the abovementioned grid of points, we choose an expansion in Leg-

TABLE II. CCSD共T兲 interaction energies for Ar–HI obtained with different atomic basis sets at the indicated configurations. We denote by ‘‘bf’’ the 3s3p2d2 f 1g set of bond functions.

␾ ⫽0°

Atom/basis set

共1兲

␾ ⫽33.75° ⌬E

␾ ⫽180° ⌬E

R ArI

⌬E

R ArI

Ar/aug-cc-pV(Q⫹d)Z⫹bf I/SDB-aug-cc-pVTZ H/aug-cc-pVQZ

4.0 4.25 4.5

173.01 ⫺90.71 ⫺152.78

3.8 4.0 4.25

125.34 ⫺72.76 ⫺147.97

3.4 3.6 3.8

⫺26.10 ⫺173.30 ⫺206.17

Ar/aug-cc-pV(Q⫹d)Z I/SDB-aug-cc-pVTZ H/aug-cc-pVQZ

4.0 4.25 4.5

187.82 ⫺81.87 ⫺146.81

3.8 4.0 4.25

150.12 ⫺55.26 ⫺139.81

3.4 3.6 3.8

32.33 ⫺133.92 ⫺178.61

Ar/aug-cc-pV(Q⫹d)Z I/SDB-aug-cc-pVTZ H/aug-cc-pVTZ

4.0 4.25 4.5

206.88 ⫺71.53 ⫺141.34

3.8 4.0 4.25

166.60 ⫺47.96 ⫺133.02

3.4 3.6 3.8

39.81 ⫺128.55 ⫺174.77

Ar/aug-cc-pV(T⫹d)Z I/SDB-aug-cc-pVTZ H/aug-cc-pVTZ

4.0 4.25 4.5

227.54 ⫺58.41 ⫺132.58

3.8 4.0 4.25

198.03 ⫺22.80 ⫺116.17

3.4 3.6 3.8

83.80 ⫺99.58 ⫺156.02

R ArI


States of Ar–HI complex

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endre polynomials of the cosine of the angle ␾, as the functional form to represent the potential energy function for Ar– HI, V 共 R ArI , ␾ 兲 ⫽

兺␭ V ␭共 R ArI兲 P ␭共 cos ␾ 兲 ,

共2兲

where the corresponding V ␭ (R ArI) coefficients, with ␭ ⫽0 – 16, are obtained by a collocation method as follows. For each ␾ ( ␾ i ,i⫽1 – 17) the CCSD共T兲 ab initio data are fitted to the following analytical expression based on a Morse–van der Waals form: V 共 R ArI ; ␾ i 兲 ⫽ ␣ i0 兵 exp关 ⫺2 ␣ i1 共 R ArI⫺ ␣ i2 兲兴 ⫺2 exp关 ⫺ ␣ i1 共 R ArI⫺ ␣ i2 兲兴其 ⫺

␣ i3 ␣ i4 ⫺ 6 8 , R ArI R ArI

共3兲

with parameters ␣ i0 , ␣ i1 , ␣ i2 , ␣ i3 , and ␣ i4 and i⫽1 – 17. A nonlinear least-squares procedure was used to fit the potential function. The adjustable parameters, as well as their maximum and averaged standard deviations for each angle ␾ i , are listed in Table IV 共Ref. 37兲. A maximum standard deviation of 1.47 cm⫺1 and an averaged standard deviation of 0.45 cm⫺1 are found for the analytical representation, as compared with the ab initio points included in the fitting procedure. In addition, the accuracy of the two-dimensional fit of V(R ArI , ␾ ) is checked by calculating some extra ab initio points 共not included in the fit兲. In Table V 共Ref. 37兲 we present for the indicated geometries, selected along the minimum energy path, the ab initio CCSD共T兲 values and compare them with the corresponding V(R ArI , ␾ ) ones. The latter points are found to have an average deviation of 0.57 cm⫺1 from real ab initio values. In addition, tests using twodimensional cubic spline interpolations were also carried out: however, their accuracy was found to be worse, particularly in the regions near to the linear wells, indicating the need for more angular points. Figure 1 shows a two-dimensional contour plot of the V(R ArI , ␾ ) surface in the R ArI , ␾ plane. The potential has three wells at energies of ⫺205.38, ⫺153.57, and ⫺151.57 cm⫺1 共see Table VI兲. The linear Ar–I–H well is deeper than the bent and linear Ar–H–I ones, with the barriers between them being at energies of ⫺114.45 cm⫺1 共90.93 cm⫺1 above the global minimum兲, with R ArI⬇4.29 Å, ␾ ⬇103°, and of ⫺151.25 cm⫺1 共54.13 cm⫺1 above the global minimum兲, with R ArI⬇4.49 Å, ␾ ⬇19°, for the linear Ar–I–H↔bent Ar–H–I and bent Ar–H–I↔linear Ar–H–I isomerizations, respectively 共see Table VI兲. These potential minima and the corresponding barriers are displayed in Fig. 2, where the minimum energy path and the distance R ArI of the minimum energy are plotted as a function of the angle ␾. The equilibrium distances for the three minima are found at R e ⫽3.81 Å for the linear van der Waals Ar–I–H well, whereas R e ⫽4.39 Å for ␾ ⫽30° and R e ⫽4.56 Å for the hydrogenbonded linear Ar–H–I well. Recent MP2 calculations have estimated18 the global minimum of Ar–HI at an energy of ⫺211.54 cm⫺1 with R ⫽3.88 Å and ␾ ⫽180°, while the second minimum was

FIG. 1. Contour plots of the Ar–HI potential energy surface V(R ArI , ␾ ) 关Eq. 共2兲兴 in the (R ArI , ␾ ) plane. The HI distance is fixed at 1.609 16 Å. Contour intervals 共solid lines兲 are of 25 cm⫺1 and for energies from ⫺200 to ⫺25 cm⫺1. Dashed lines correspond to the energies of the two isomerization barriers.

found at ⫺166.06 cm⫺1 for R⫽4.57 Å and ␾ ⫽0°, and a third one with an energy of ⫺163.94 cm⫺1 at R⫽4.27 Å and ␾ ⫽44° 共see Table VI兲. A modified scheme has been introduced18 to adjust the ab initio calculation to the experimental observations: by scaling in energy and shifting in the R coordinate the MP2 surface 共see Table VI兲, the energy TABLE VI. Well depths, equilibrium distances, and isomerization barriers for the Ar–HI complex as predicted by the CCSD共T兲 surface in comparison with previous studies. MP2 calculations for the two linear structures using the same basis sets as in CCSD共T兲 calculations are reported in the second column. Energies in cm⫺1 and distances in Å. CCSD共T兲a/MP2a MP2b/MP2 scaledb Linear Ar–I–H structure De R eArI ␾

205.38/260.77 3.81/3.74 180

211.54/220.0 3.88/3.79 180

Bent Ar–H–I structure De R eArI ␾

151.57 4.39 30

163.94/170.5 4.27/4.18 44

Linear Ar–H–I structure De R eArI ␾

153.57/196.2 4.56/4.48 0

166.06/172.7 4.57/4.49 0

Isomerization barriers

a

E* * R ArI ␾

⫺114.45 4.29 103

⫺126.4/⫺131.5 4.31/4.22 98

E* * R ArI ␾

⫺151.25 4.49 19

– – –

Present work. Reference 18.

b

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For a given total angular momentum J and a parity of total nuclear coordinates inversion, p, the corresponding Hamiltonian is represented as a product of radial 兵 f n (R) 其 p) and angular 兵 ⌰ (JM 其 basis functions. For the R coordinate a j⍀ discrete variable representation 共DVR兲 basis set is used based on the particle in a box eigenfunctions.39 The expression for the 兵 f n (R) 其 functions is given by f n共 R 兲 ⫽

2

N

兺冑L 共 N⫹1 兲 k⫽1

sin

k␲n k ␲ 共 R⫺R 0 兲 sin , L N⫹1

共5兲

where N is the total number of DVR functions, L⫽R max ⫺R0 is the size of the box, and the DVR points in the R coordinate are given by R n⫽ FIG. 2. 共a兲 Minimum energy V m in cm⫺1 and 共b兲 distance of minimum m , from Ar to I, as a function of ␾. The energy levels for J⫽0 of energy, R ArI n⫽0 and n⫽1 vibrational vdW states are also displayed.

nL ⫹R 0 , N⫹1

for n⫽1,...,N.

共6兲

p) In turn, the angular 兵 ⌰ (JM 其 basis functions are eigenfuncj⍀ tions of the parity, JM p 兲 JM 兲 JM 兲 ⫽ 关 2 共 1⫹ ␦ ⍀0 兲兴 ⫺1/2关 ⌽ 共j⍀ ⫹ p 共 ⫺1 兲 J ⌽ 共j⫺⍀ ⌰ 共j⍀ 兴 , 共7兲

minima were corrected to be at energies of ⫺220.0, ⫺172.7, and ⫺170.5 cm⫺1, respectively. Note that the results of the unscaled MP2 surface reported in Ref. 18 are very close to those predicted by the CCSD共T兲 surface presented here, especially for the Ar–I–H linear well. However, we should stress that MP2 overestimates the interaction energy for Ar– HI. We carried out MP2 calculations for the two potential minima at the linear structures of Ar–HI, using the same basis sets as in the CCSD共T兲 calculations, and the results are reported in the second column of Table VI. It is found that the MP2 well depths are by 55 and 40 cm⫺1 deeper than their corresponding CCSD共T兲 values for the Ar–I–H and for the Ar–H–I configurations, respectively 共see Table VI兲. This result is in accord with previous calculations,38 where differences of 30 cm⫺1 were found between MP2 and CCSD共T兲 energies for the Ar–HI complex, using smaller basis sets than the ones employed in the present study. This outlines the importance of correlation effects and fully justifies the use of a higher-level approximation and larger basis sets. C. Bound-state calculations

The rovibrational states of Ar–HI are calculated using a two-dimensional atom–rigid-diatom Hamiltonian expressed in Jacobi coordinates, ˆ ⫽⫺ H

ˆj 2 ˆl 2 ប2 ⳵2 ⫹ ⫹ ⫹V 共 r e ,R, ␪ 兲 , 2 ␮ 1 ⳵ R 2 2 ␮ 2 r 2e 2 ␮ 1 R 2

共4兲

where R is the intermolecular distance of the Ar atom from the center of mass of HI, r is the bond length of HI, and ␪ is ⫺1 the angle between the R and r vectors. ␮ ⫺1 1 ⫽m Ar ⫹(m H ⫺1 ⫺1 ⫺1 ⫺1 ⫹m I) and ␮ 2 ⫽m H ⫹m I are the reduced masses, m H⫽1.007 94 amu, and mI m Ar⫽39.948 amu, ⫽126.904 47 amu are the atomic masses of 40Ar, 1H, and 127 I isotopes and ˆl and ˆj are the angular momenta associated with the vectors R and r, respectively, leading to a total angular momenta Jˆ ⫽ ˆl ⫹ ˆj . Here r e is fixed at the equilibrium H–I bond length and the potential for an Ar–HI complex in 共R, ␪兲 coordinates.

with JM 兲 ⫽ ⌽ 共j⍀

冑

2J⫹1 J * DM ⍀ 共 ␾ R , ␪ R ,0兲 Y j⍀ 共 ␪ , ␾ 兲 , 4␲

共8兲

M is the projection of J on the space-fixed z axis, ⍀ being its projection on the body-fixed z axis, which is chosen here along the R vector. The DJM*⍀ ( ␾ R , ␪ R ,0) are Wigner matrices and Y j⍀ ( ␪ , ␾ ) are spherical harmonic functions,40 with ␪ R and ␾ R being the space-fixed polar angles defining the direction of R, while ␪ and ␾ are the polar angles of the r vector in the body-fixed system. All matrix elements of the Hamiltonian involving angular functions are given in Ref. 41. A basis set of 120 DVR functions over the range from R⫽2 to 15 Å and up to 40 values of the diatomic rotation j are used. Depending on the values of J and the parity p, the size of the Hamiltonian matrix ranges from 4800 to 14 040. By diagonalizing the Hamiltonian the eigenfunctions and the corresponding energies are obtained for a total angular momentum up to J⫽2 for even ( p⫽⫹1) and odd (p⫽⫺1) parity symmetries. The rotational constants for HI and DI used here are ប 2 /2␮ HIr 2e ⫽6.510 274 9 cm⫺1 and ប 2 /2␮ DIr 2e ⫽3.283 638 3 cm⫺1 , respectively, being r e ⫽1.609 16 Å, the same equilibrium distance as that used in Ref. 18. The reduced masses for Ar–HI and Ar–DI are 30.449 39 and 30.506 07 amu, respectively. In this way, a convergence of 2⫻10⫺9 cm⫺1 is achieved in the bound-state calculations. In Fig. 3 we plot the angular and radial probability distributions for the lowest J⫽0 vdW eigenfunctions of the Ar–HI complex. As can be seen 共see Fig. 3 and Table VII兲, there are groups of states that are localized in the van der Waals and hydrogen-bonded linear wells. For example, the n⫽0 state is localized in the linear vdW Ar–I–H well and the n⫽1 corresponds to the linear Ar–H–I configuration, while the n⫽2 state mainly exhibits a vdW linear structure and n⫽3 is associated to a hydrogen-bonded linear isomer. Vibrationally averaged structures with R⫽4.059 89 Å and ␪ ⫽140.81° and R⫽3.979 31 Å and ␪ ⫽156.25° are obtained for the Ar–I–H and Ar–I–D isomers, respectively. The



FIG. 3. Angular 共a兲, 共b兲 and radial 共c兲, 共d兲 probability distributions for the indicated n C vdW levels of Ar–HI for J⫽0 calculated using the CCSD共T兲 potential. C is H or W for hydrogen-bonded and van der Waals configurations, respectively.

above values are consistent with the ones determined by the microwave analysis18 for these species. In particular, for Ar– I–H a structure with R⫽3.9975 Å and ␪ ⫽149.33° has been assigned, while for Ar–I–D R⫽3.9483 Å and ␪ ⫽157.11°. It is interesting to note that small differences 共0.06 and 0.03 Å兲 are found in the R average values for both isotopomers, whereas a larger difference from the experiment is obtained in the ␪ average value for the Ar–I–H isomer.

For all J values (J⫽0,1,2) the results of our calculations on Ar–HI and Ar–DI are summarized in Table VII, in comparison with previous theoretical data using the morphed MP2 potential.18 The energy levels are labeled as J Cp , where J is the total angular momentum, p is the parity under total nuclear coordinates inversion 共⫹ for even, ⫺ for odd兲, and C is W or H for vdW and hydrogen-bonded linear configurations, respectively. The l-type doubling splittings q for ⌸ states are also given in Table VII, computed from the energy difference between the J⫽1 states of odd and even parity. For J⫽0, the lowest states of Ar–HI are found at energies of ⫺127.567, ⫺121.831, ⫺105.743, and ⫺100.207 cm⫺1 共see Table VII兲, whereas for Ar–DI they are at ⫺140.833, ⫺126.667, ⫺116.701, and ⫺107.769 cm⫺1. The main difference with the morphed MP2 results18 is the value of the binding energy D 0 for the Ar–HI and Ar–DI isotopomers. The CCSD共T兲 potential predicts a D 0 value of 127.567 cm⫺1 for Ar–HI and 140.833 cm⫺1 for Ar–DI, while the morphed MP2 surface estimate is 146.43 and 158.87 cm⫺1, respectively. These latter values are much deeper than ours, approximately by 20 cm⫺1, and almost 55 cm⫺1 lower than the value of 93⫾12 cm⫺1 determined from the photolysis experiments by Suzuki et al.22 As we discussed above, the MP2 calculations overestimate the interaction energy of the Ar–HI cluster in comparison with the CCSD共T兲 results 共see Table VI and Ref. 38兲. Without using additional information 共like experimental data兲 for the cluster dissociation energy, the morphing MP2 procedure essentially keeps a similar overestimate as the original MP2 surface.18

TABLE VII. Calculated energy levels for Ar–HI using the CCSD共T兲 potential in comparison with previous MP2 data. The energy levels are labeled as n, J Cp , where J is the total angular momentum with n as an ordering number of each level, p is the parity under total nuclear coordinates inversion 共⫹ for even, ⫺ for odd兲, and C is H or W for hydrogen-bonded and vdW linear configurations, respectively. The l-type doubling splitting q for ⌸ states is also given in the last column. Energies 共in cm⫺1兲 are relative to n⫽0 state for J⫽0. Isomer

n,J Cp

CCSD共T兲a

MP2 scaledb

Ar–I–H

D0 ⫹ 0,0W 1,0H⫹ ⫹ 2,0W 3,0H⫹ ⫹ 4,0W 5,0H⫹ ⫺ 1,1W 4,1H⫺ ⫺ 7,1W ⫺ 1,2W D0 ⫹ 0,0W 1,0H⫹ ⫹ 2,0W 3,0H⫹ ⫹ 4,0W 5,0H⫹ ⫺ 1,1W 4,1H⫺ ⫺ 6,1W ⫺ 1,2W

127.5673 0.0 5.7368 21.8242 27.3605 40.0986 45.2473 0.06726 24.3694 42.5349 0.2018 140.8328 0.0 14.1654 24.1322 33.0639 42.2502 48.0951 0.06940 27.6139 35.7768 0.2082

146.43 0.0 7.89 23.09 29.85

Ar–I–D

a


b

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⌺ ⌺ ⌺ ⌺ ⌺ ⌸ ⌸ ⌺ ⌺ ⌺ ⌺

⌸ ⌸

– 26.71 42.67 – 158.87 0.0 15.19 25.18 34.35

28.85 34.69 –

q (10⫺2 )

⫺0.6897 ⫺0.5362

⫺0.0703 ⫺0.2363

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TABLE VIII. Predicted spectroscopic constants obtained from CCSD共T兲 potential in comparison with previous MP2 and experimental data. Note that values in parentheses in the third column are obtained for comparison reasons using rotational constants for HI and DI from Ref. 18. Parameter

CCSD共T兲a

MP2b/MP2 scaledb

Experiment/uncert.b

Ar–I–H

B 0 (10⫺2 cm⫺1 ) D J (10⫺7 cm⫺1 ) 具 P 1 „cos(␪)…典具 P 2 „cos(␪)…典 D ␪ (10⫺6 cm⫺1 )

3.363共3.373兲 3.561共3.207兲 ⫺0.7750共⫺0.7937兲 0.5832共0.5974兲 ⫺76.2共⫺66.3兲

3.292/3.454 3.43/3.54 ⫺0.799/⫺0.817 0.585/0.603 ⫺45.8/⫺40.6

3.449/0.01 3.53/0.01 – 0.610/0.004 ⫺44.3/1.5

Ar–I–D

B 0 (10⫺2 cm⫺1 ) D J (10⫺7 cm⫺1 ) 具 P 1 „cos(␪)…典具 P 2 „cos(␪)…典 D ␪ (10⫺6 cm⫺1 )

3.470共3.471兲 1.652共1.645兲 ⫺0.9153共⫺0.9165兲 0.7696共0.7725兲 ⫺12.6共⫺12.3兲

3.345/3.505 2.09/2.34 ⫺0.909/⫺0.912 0.754/0.761 ⫺11.3/⫺11.2

3.510/0.01 2.33/0.03 – 0.771/0.004 ⫺15.5/1.5

Isomer

a


b

As a result, the morphed MP2 surface predicts larger dissociation energies for Ar–HI/Ar–DI than the CCSD共T兲 surface. The present CCSD共T兲 D 0 value for Ar–HI is consistent with the trend of increasing D 0 values with increasing mass of the halogen atom in the Ar–HX series (X⫽F, Cl, and Br兲 of complexes. The dissociation energies given in the literature for these complexes are 101 cm⫺1 for Ar–HF,8 115 cm⫺1 for Ar–HCl,3 and 121 cm⫺1 for Ar–HBr.3 However, in contrast to Ar–HF, Ar–HCl, and Ar–HBr the Ar–I–H structure is predicted to be the most stable isomer, in agreement with the previous potential of Ref. 18. In turn, for higher vdW levels smaller differences, by about 2 cm⫺1, are obtained, and in particular the energy difference between the Ar–I–H and Ar–H–I isomers is found to be 5.737 cm⫺1, in comparison with 7.89 cm⫺1 for the MP2 morphed surface 共see Table VII兲. We should note that transitions associated with the Ar–H–I/Ar–D–I isomer, not yet observed, would contribute to evaluate further the CCSD共T兲 potential. For both Ar–I–H and Ar–I–D isomers, spectroscopic constants are calculated from the CCSD共T兲 potential and are listed in Table VIII together with the available theoretical and experimental data. In the present calculation, spectroscopic constants, such as rotational, B 0 , and centrifugal distortion, D J , are determined from the energy difference between the J⫽0 and J⫽1 levels and second differences between calculations for J⫽0, 1 and 2 states, respectively, for the vibrational state concerned.9 Angular expectation values 具 P 1 „cos(␪)…典 and 具 P 2 „cos(␪)…典 are obtained by averaging over the corresponding wave functions, while the centrifugal distortion constant for 具 P 2 „cos(␪)…典 , D ␪ , is calculated by evaluating 具 P 2 „cos(␪)…典 for J⫽0 and 1 states.42 It should be noted that the rotational constants for HI and DI used in the present calculations are somewhat different to those used in Ref. 18 共6.341 965 and 3.223 077 2 cm⫺1 for HI and DI, respectively兲, despite the fact that the monomer equilibrium distance r e is the same. The differences are probably due to slightly different masses used for I, H, and D. We carried out calculations using the rotational constants of Ref. 18, and the results are shown in parentheses in Table VIII for the sake of comparison. In general, small differences are found from the results obtained with the present HI and DI

rotational constants, with the quantities given in parentheses being somewhat closer to the experimental values. A good agreement is found between the present calculations and the previous ones using ab initio MP2 and morphed MP2 potential surface.18 The CCSD共T兲 results lie between the ab initio MP2 ones and those predicted by the scaled MP2 potential surface. A similar trend has been observed for other weakly bound vdW systems like Ne–HF 共Ref. 17兲 and He–ClF 共Ref. 43兲. A general good accord is also found between the CCSD共T兲 and the experimental measurements 共see Table VIII兲. In particular, the B 0 constant is underestimated by about 0.0008 and 0.0004 cm⫺1 for the Ar–I–H and Ar–I–D states, respectively, while the 具 P 2 „cos(␪)…典 values are lying very close to the corresponding experimental values and for Ar–I–D within the given uncertainty. The estimated D J constant for Ar–I–H is also close to the experimental one, as well as the D ␪ term for Ar–I–D. Larger differences, by about 30⫻10⫺6 and 0.68 ⫻10⫺7 cm⫺1 , are obtained for the D ␪ and D J values for Ar–I–H and Ar–I–D, respectively. The larger value of D ␪ for Ar–I–H is consistent with the differences found above in the vibrationally averaged structure for this isomer from the experimental one. We should stress here that particular attention has been paid in the convergence criteria for both eigenvalues and eigenfunctions in our bound-state calculations, in order to achieve the required accuracy in the computation of the above-mentioned spectroscopic terms. Thus part of the small deviations obtained from the experiment can be attributed to the lack of r dependence in the potential form,43 as well as to the level of calculation and the fitting procedure. The quantitative agreement obtained with the available experimental data suggests that pure 共without any morphing procedure兲 CCSD共T兲 ab initio calculations can provide results effectively converged. However, for a global evaluation of the CCSD共T兲 surface further experimental information, involving transitions from higher rovibrational states on the Ar–HI ground electronic state surface, is needed. III. CONCLUSIONS

The ground potential energy surface is calculated for the Ar–HI complex at the CCSD共T兲 level of theory. As in other


studies of this complex, the existence of two relatively isolated linear minima is established. The Ar–I–H structure is found to be the most stable isomer with a binding energy of D 0 ⫽127.567 cm⫺1 , while the linear Ar–H–I isomer is predicted to lie 5.737 cm⫺1 above the ground state of the system. Bound-state calculations 共up to J⫽2) are carried out using the above CCSD共T兲 surface. Vibrationally averaged structures with (R⫽4.059 89 Å, ␪ ⫽140.81°) and (R ⫽3.979 31 Å, ␪ ⫽156.25°) are determined for Ar–I–H and Ar–I–D isomers, respectively, and they compare very well with the experimental ones. Spectroscopic constants are also evaluated for both Ar–I–H and Ar–I–D isotopomers, and by comparing our results with the experimentally determined ones,18 the quality of the CCSD共T兲 potential is tested. A general very good accord is found between the values obtained from the CCSD共T兲 surface and the experimental ones. There is no need of scaling or shifting the present potential surface to achieve the quantitative agreement reported here. Comparison with previous MP2 and MP2 morphed PESs is also presented. The main discrepancy with the MP2 morphed surface is found for the binding energy D 0 of Ar–I–H and Ar–I–D isomers and attributed to the overestimation of the well depths of the complex in the MP2 calculations. Our calculated D 0 value for Ar–I–H lies between the experimental value of 93⫾12 cm⫺1 found by Suzuki et al.22 and the value of 146.4 cm⫺1 obtained from the morphed/ semiempirical surface based on a combination of MP2 calculations and microwave and near IR supersonic jet spectroscopy.18 Additionally, the D 0 value reported here follows the general trend of increasing D 0 for the Ar–HX series (X⫽F, Cl, Br兲 of complexes. These findings, in combination with the limited experimental information available on the systems under study, demonstrate that CCSD共T兲 calculations provide an alternative way of constructing reliable potential surfaces for modeling the rovibrational ground-state dynamics of such vdW complexes. ACKNOWLEDGMENTS

The authors wish to thank the Centro Tećnico de Informa´tica 共CTI兲, CSIC, the Centro de Supercomputacioń de Galicia 共CESGA兲, and the Grupo de SuperComputacioń del CIEMAT 共GSC兲 for allocation of computer time. This work has been supported by CICYT, Spain, Grant No. BFM 20012179 and by a European TMR network, Grant No. HPRNCT-1999-00005. S.L.-L. acknowledges C.I.C.Y.T. for a predoctoral fellowship, and R.P. acknowledges a contract from the Comunidad Autońoma de Madrid, Spain. 1 2

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