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An ab initio study of intermolecular potential for the He–HCl complex
Journal of Molecular Structure (Theochem) 589–590 (2002) 89–93 www.elsevier.com/locate/theochem
An ab initio study of intermolecular potential for the He –HCl complex Yu Zhang, Hong-Yun Shi* Department of Chemistry, Guizhou University, Guiyang, Guizhou 550025, People’s Republic of China Received 6 January 2002; accepted 3 April 2002
Abstract The potential energy surface of the ground state of the He– HCl complex have been calculated at several levels of theory, including the single and double excitation coupled-cluster method with non-iterative perturbation treatment of triple excitation CCSD(T). Calculations have been performed using the augmented correlation-consistent polarized quadruple zeta basis set. The global minimum with a well depth of approximate 30.1 cm21 has been found for the linear He– H– Cl structure ðQ ¼ 0:08Þ ˚ . In addition to the global with the distance between the He atom and the center of mass of the HCl molecule equals 3.83 A 21 minimum, there is a secondary minimum at R ¼ 3:38 A and ðQ ¼ 1808Þ (a well depth of 29.5 cm ). We find that the results of MP2 level were contrary to the results obtained from the higher CCSD, CCSD(T) theory level and the CCSD(T) interaction energies of the two minima are almost the same. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Ab initio; Intermolecular potential; Potential energy surface
1. Introduction The rare-gas hydrogen halide (M – HX) complexes have long been studied for insights into the nature of intermolecular forces and details of inter- and intramolecular dynamics. Systematic investigations of the complexes of Xe, Kr, Ar, and lately Ne with HF, HCl, HBr and their deuterated analogs, have yielded considerable information on their structure and internal dynamics. Yet considering theoretical calculations of such van der Waals complexes, the complexes of Ar – HX (where X is a halide) have been studied frequently, whereas little is known about He – HX (where X is a halide) [1]. So, in the present paper, we perform a systematic ab initio supermolecular * Corresponding author. E-mail address: [email protected] (H.Y. Shi).
calculation for the intermolecular potential surface of the binary helium complex with the ground state molecule HCl. In comparison with the heavier rare-gas hydrogen halide complexes, the He – HCl species is expected to be relatively weakly bound. Two phenomena contribute to this effect. First, because the polarizability of helium is only half that of neon and one-eighth that of argon, the induction and dispersion forces which constitute the attractive part of the intermolecular potential are correspondingly smaller. The intermolecular potential is consequently shallower for this helium complex. Second, the small-reduced masses of the helium complex result in relatively large stretching zero-point energies. This further reduces the binding energy for the helium complexes relative to those of the heavier rare gases. In view of the small binding energy, spectroscopic
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Y. Zhang, H.-Y. Shi / Journal of Molecular Structure (Theochem) 589–590 (2002) 89–93
approach; that is, the interaction energy ðDEÞ at a given level of theory is calculated from the expression: DE ¼ EAB 2 EA 2 EB
Fig. 1. The co-ordinate system used for He –HCl; c.o.m represents the center of mass.
techniques, which were successfully applied in the studies of the complexes of the heavier rare gases are more difficult to apply to the complexes of helium. So compared to the other heavier rare gases, the experimental studies of helium are certainly delayed and the near-infrared vibration – rotation spectra of the weakly bound helium complexes was reported by Lovejoy and Nesbitt, until 1990 [2]. However, in the view of the small number of electrons, correlation effects can in principle be treated to high order. Consequently, ab initio potentials for the He –HCl complex is expected to be more reliable than those developed for the heavier M– HCl species.
2. Computational details To examine the interaction of the rare-gas atom He with the HCl molecule, we use the supramolecular
where EAB is the energy of the complex, and EA and EB are the energies of monomers A and B, respectively. It is well known that for rare-gas complexes the Hartree –Fock interaction potential is repulsive and the dispersion energy is the dominant attractive intermolecular force. An adequate treatment of electron correlation is thus essential in the calculation of the intermolecular potentials of He – HCl. In our present study, the level of theory will be indicated by the superscript, e.g. DECCSDðTÞ will denote the CCSD(T) interaction energy. The most accurate are our CCSD(T) [3] results, but along the way we also obtained interaction energies at the selfconsistent field (SCF), second-order Moller – Plesset (MP2), and the single and double excitation coupledcluster (CCSD) levels of theory. Calculations have been performed using the augmented correlationconsistent polarized quadruple zeta basis set (aug-ccpVQZ) of Dunning and co-workers [4 – 6]. Our electron-correlated calculations for the He – HCl complex used frozen core approximation. The counterpoise method of Boys and Bernardi was used to avoid the basis set superposition error (BSSE) [7]. All the calculations were carried out using the GAUSSIAN 94 package [8] in the High Performance Computational Chemistry Laboratory of Guizhou University. The co-ordinate system for the He – HCl complex is shown in Fig. 1. R is the intermolecular distance from the center of mass of HCl to the rare-gas He atom, Q is the angle describing the orientation of the He atom with respect to the H – Cl bond axis. Q ¼ 08 corresponds to the He –H – Cl co-linear arrangement. The equilibrium structure of HCl in the complex remains unknown. So the H – Cl bond length was set at ˚ according to the calculation at the CCSD(T)/ 1.28 A aug-cc-pVQZ theory level and was kept constant in all calculations.
3. Results and discussion
Fig. 2. PES of the He– HCl complex. Contour is labeled in cm21.
The interaction energies at the SCF, MP2, CCSD, and CCSD(T) levels of theory obtained
Y. Zhang, H.-Y. Shi / Journal of Molecular Structure (Theochem) 589–590 (2002) 89–93 Table 1 SCF, MP2, CCSD, and CCSD(T) interaction energies (in cm21) of the He –HCl at different distances and different angles
u (8)
˚) R (A
DE HF
DE MP2
DE CCSD
DE CCSD(T)
0
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
310.9 137.5 58.9 37.9 20.9 14.9 9.0 2.8 0.3
138.0 24.8 215.5 222.8 226.1 226.2 225.0 220.9 216.5
151.1 31.3 212.2 220.4 224.4 224.7 223.9 220.1 216.0
131.1 18.0 221.1 227.7 230.1 229.7 228.0 223.0 218.0
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
241.9 108.1 47.0 30.5 17.1 12.3 7.6 2.4 0.4
94.6 10.8 218.3 223.2 224.9 224.6 223.2 219.3 215.0
102.8 14.6 215.8 221.2 223.4 223.2 222.0 218.3 214.5
86.0 3.8 223.4 227.5 228.3 227.5 225.7 220.9 216.3
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
137.7 68.7 31.4 21.0 12.4 9.2 6.0 2.4 0.8
43.9 22.0 217.3 219.6 219.9 219.4 218.2 215.0 212.0
44.3 21.8 217.0 219.3 219.6 219.0 217.8 214.6 211.6
32.9 29.7 222.6 224.0 223.4 222.4 220.7 216.8 213.2
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
117.9 57.2 27.5 19.0 11.7 9.0 6.2 2.8 1.3
35.7 0.3 212.4 214.6 215.3 215.0 214.3 212.1 29.8
33.5 20.9 212.9 214.8 215.3 215.0 214.2 211.9 29.8
24.8 27.1 217.3 218.6 218.4 217.8 216.6 213.7 210.9
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
123.1 60.5 29.6 20.7 12.9 10.0 7.1 3.4 1.6
44.0 6.1 28.4 211.3 212.7 212.8 212.4 210.8 28.9
42.2 5.1 28.9 211.5 212.9 212.8 212.4 210.7 28.7
33.9 20.8 213.1 215.1 215.7 215.4 214.6 212.3 210.0
3.20 3.40 3.60 3.70
126.8 62.3 30.5 21.3
46.5 7.5 27.6 210.7
45.4 6.8 27.9 210.8
37.0 0.9 212.1 214.4
20
40
60
80
90
91
Table 1 (continued) ˚) R (A
DE HF
DE MP2
DE CCSD
DE CCSD(T)
3.83 3.90 4.00 4.20 4.40
13.3 10.3 7.1 3.4 1.6
212.3 212.4 212.1 210.6 28.8
212.3 212.6 212.0 210.5 28.6
215.2 215.0 214.2 212.1 29.8
100
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
127.6 62.5 31.0 21.2 13.2 10.2 7.1 3.4 1.6
46.0 7.1 27.8 210.8 212.3 212.5 212.1 210.6 28.7
45.6 6.8 27.9 210.8 212.2 212.3 212.0 210.4 28.5
37.1 0.9 212.1 214.3 215.1 214.9 214.2 212.0 29.7
120
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
116.0 56.2 27.1 18.8 12.4 9.0 6.2 2.9 1.4
34.2 0.9 211.0 213.0 213.7 213.5 212.8 210.8 28.8
35.3 1.6 210.4 212.5 213.2 212.9 212.4 210.5 28.5
26.7 24.4 214.6 216.0 216.1 215.4 214.5 212.1 29.6
140
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
89.8 42.6 20.1 13.8 8.4 6.5 4.4 2.1 1.0
11.5 210.5 216.5 216.8 216.0 215.2 214.0 211.3 29.0
13.8 28.9 215.4 215.8 215.1 214.4 213.3 210.7 28.5
5.5 214.7 219.4 219.2 217.9 216.9 215.3 212.2 29.6
160
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
62.2 28.5 13.0 8.7 5.2 4.0 2.7 1.2 0.5
211.2 221.8 222.0 220.6 218.3 217.0 215.1 211.8 29.1
28.1 219.6 220.3 219.2 217.1 215.9 214.2 211.0 28.5
216.0 225.0 224.2 222.4 219.7 218.2 216.1 212.5 29.6
180
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
50.4 22.4 9.9 6.6 3.8 2.9 1.9 0.8 0.3
220.8 226.4 224.3 222.2 219.2 217.7 215.6 212.0 29.2
217.4 224.1 222.4 220.6 217.9 216.5 214.5 211.2 28.5
225.1 229.4 226.2 223.7 220.4 218.7 216.5 212.6 29.6
u (8)
92
Y. Zhang, H.-Y. Shi / Journal of Molecular Structure (Theochem) 589–590 (2002) 89–93
Table 2 Interaction energies DE at 0, 90, and 1808
u (8)
˚) R (A
DE (cm21)
0 90 180
3.83 3.84 3.38
230.1 215.2 229.5
with the aug-cc-pVQZ basis set are reported in Table 1. We give this extensive set to allow other researchers to use the original results for developing their own model potentials. Our calculations probed the potential energy surface (PES) most extensively for intermolecular distances in the interval from 3.20 ˚ , and 11 angles in the range from 0 to 1808. to 4.40 A For 1808, calculation was performed for a additional ˚ . The PES, which is shown in Fig. 2, distance of 3.38 A could be well fitted to the analytic function described earlier [9,10]. The global minimum with a well depth of approximate 30.1 cm21 was found on the CCSD(T) surface for the linear He –H – Cl structure ðQ ¼ 0:08Þ The error due to basis set incompleteat R ¼ 3:83 A: ness is more difficult to estimate, but a comparison with the estimated complete basis set limit values of interaction energies that we obtained for He – HF suggests that it should not exceed a few percent [11]. It is clear from Table 2 that in addition to the global minimum, there is a secondary minimum at R ¼ and Q ¼ 1808 (a well depth of 29.5 cm21) 3:38 A corresponding to another linear geometry. This arises because the electron density of the HCl monomer is substantially smaller in this direction than perpendicular to the internuclear axis, so that the intermolecular repulsion at a given distance is weaker for the linear He – Cl – H structure than for a T-shaped configuration. The two minima are so close that we have to perform additional calculations for the neighboring values of R to decide the position of the global minimum. The secondary minimum is a little shallower than the global one, indicating that the He – Cl – H configuration is a little unstable with respect to the He – H – Cl configuration. A potential barrier of 15.2 cm21 separating the two minima occurs around Q ¼ 908), corresponding to the position (R ¼ 3:83 A; a T-shaped configuration. Our calculated values are in good agreement with the experimental measurements Q ¼ 0:08) [2]. (R ¼ 3:89 A; The angular dependence of the MP2, CCSD, and
Fig. 3. The angular dependence of the interaction energy at different levels of theory at R ¼ 3:83 A:
CCSD(T) supermolecule interaction energies at R ¼ is given in Fig. 3. This distance is the radial 3:83 A minimum at Q ¼ 08 and Q ¼ 908; but longer than the one at Q ¼ 1808: As can been seen in Fig. 3, each curve contains two minima, at Q ¼ 08 and Q ¼ 1808; respectively. The strength of the interaction is underestimated both at the MP2 theory level and at the CCSD level of theory, in comparison to the CCSD(T) results. It is clear from Table 1 that the global minimum of and MP2 theory level is at the point of R ¼ 3:38 A MP2 21 Q ¼ 1808 ðDE ¼ 26:5 cm Þ; indicating that the He –H – Cl configuration is unstable with respect to the He – H – Cl configuration. It is only at the higher levels of theory (CCSD and CCSD(T)) that their relative positions are reversed. The key to the understanding of this effect is the third-order correlation DEð3Þ ; whose partitioning, unfortunately, has not been implemented so far.
4. Conclusions The He –HCl CCSD(T) ab initio potential presented here provides an accurate description of the intermolecular interaction. In comparison with the experimental results, the equilibrium interaction energy that we have found, De ¼ 30:1 cm21 ; is deeper by 5.1 cm21, and the distance between the He atom and the center of mass of the HCl molecule, is shorter by 0.06 A ˚ . In addition, the R ¼ 3:83 A;
Y. Zhang, H.-Y. Shi / Journal of Molecular Structure (Theochem) 589–590 (2002) 89–93
interaction energies of linear He –Cl – H structure and linear He – Cl – H structure are almost the same. At the same time, we found that at the MP2 level the results were contrary to the results obtained from the higher CCSD, CCSD(T) theory level. The two characterizations were not found in the previous studies of Ar – HCl and Ar –FH complexes [12,13].
Acknowledgments This work was partially supported by the Science Foundation of Educational Administration of Guizhou Province and the Science Foundation of Guizhou Province, People’s Republic of China, respectively. The authors thank Prof. Y.B. Wang for computational support of our work.
References [1] S.E. Novick, Bibliography of rotational spectra of weakly
[2] [3] [4] [5] [6] [7] [8]
[9] [10] [11] [12] [13]
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bound complexes (2001). Electronic updates are available on the web at http://www.wesleyan.edu/chem/faculty/novick/ vdw.html. C.M. Lovejoy, D.J. Nesbitt, J. Chem. Phys. 93 (1990) 5387. K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1989) 479. T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007. R.A. Kendall, T.H. Dunning Jr., R.J. Harrison, J. Chem. Phys. 96 (1992) 6796. D.E. Woon, T.H. Dunning Jr., J. Chem. Phys. 98 (1993) 1358. S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. M.J. Frisch, G.W. Tnicks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. Defrees, J. Baker, J.P. Stewart, J.A. Pople, GAUSSIAN 94, Revision C, Gaussian, Inc., Pittsburgh, PA, 1992. J.M. Hutson, B.J. Howard, Mol. Phys. 43 (1981) 493. J.M. Hutson, B.J. Howard, Mol. Phys. 45 (1982) 769. Y. Zhang, H.-Y. Shi, W.-Z. Wang, Acta Physico-Chimica Sinica 11 (2001) 1013. F.-M. Tao, W. Klemperer, J. Chem. Phys. 101 (1994) 1129. G. Chalsinski, M.M. Szczesniak, B. Kukawska-Tarnawska, J. Chem. Phys. 94 (1991) 6677.
An ab initio study of intermolecular potential for the He –HCl complex Yu Zhang, Hong-Yun Shi* Department of Chemistry, Guizhou University, Guiyang, Guizhou 550025, People’s Republic of China Received 6 January 2002; accepted 3 April 2002
Abstract The potential energy surface of the ground state of the He– HCl complex have been calculated at several levels of theory, including the single and double excitation coupled-cluster method with non-iterative perturbation treatment of triple excitation CCSD(T). Calculations have been performed using the augmented correlation-consistent polarized quadruple zeta basis set. The global minimum with a well depth of approximate 30.1 cm21 has been found for the linear He– H– Cl structure ðQ ¼ 0:08Þ ˚ . In addition to the global with the distance between the He atom and the center of mass of the HCl molecule equals 3.83 A 21 minimum, there is a secondary minimum at R ¼ 3:38 A and ðQ ¼ 1808Þ (a well depth of 29.5 cm ). We find that the results of MP2 level were contrary to the results obtained from the higher CCSD, CCSD(T) theory level and the CCSD(T) interaction energies of the two minima are almost the same. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Ab initio; Intermolecular potential; Potential energy surface
1. Introduction The rare-gas hydrogen halide (M – HX) complexes have long been studied for insights into the nature of intermolecular forces and details of inter- and intramolecular dynamics. Systematic investigations of the complexes of Xe, Kr, Ar, and lately Ne with HF, HCl, HBr and their deuterated analogs, have yielded considerable information on their structure and internal dynamics. Yet considering theoretical calculations of such van der Waals complexes, the complexes of Ar – HX (where X is a halide) have been studied frequently, whereas little is known about He – HX (where X is a halide) [1]. So, in the present paper, we perform a systematic ab initio supermolecular * Corresponding author. E-mail address: [email protected] (H.Y. Shi).
calculation for the intermolecular potential surface of the binary helium complex with the ground state molecule HCl. In comparison with the heavier rare-gas hydrogen halide complexes, the He – HCl species is expected to be relatively weakly bound. Two phenomena contribute to this effect. First, because the polarizability of helium is only half that of neon and one-eighth that of argon, the induction and dispersion forces which constitute the attractive part of the intermolecular potential are correspondingly smaller. The intermolecular potential is consequently shallower for this helium complex. Second, the small-reduced masses of the helium complex result in relatively large stretching zero-point energies. This further reduces the binding energy for the helium complexes relative to those of the heavier rare gases. In view of the small binding energy, spectroscopic
0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 - 1 2 8 0 ( 0 2 ) 0 0 2 4 8 - 8
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Y. Zhang, H.-Y. Shi / Journal of Molecular Structure (Theochem) 589–590 (2002) 89–93
approach; that is, the interaction energy ðDEÞ at a given level of theory is calculated from the expression: DE ¼ EAB 2 EA 2 EB
Fig. 1. The co-ordinate system used for He –HCl; c.o.m represents the center of mass.
techniques, which were successfully applied in the studies of the complexes of the heavier rare gases are more difficult to apply to the complexes of helium. So compared to the other heavier rare gases, the experimental studies of helium are certainly delayed and the near-infrared vibration – rotation spectra of the weakly bound helium complexes was reported by Lovejoy and Nesbitt, until 1990 [2]. However, in the view of the small number of electrons, correlation effects can in principle be treated to high order. Consequently, ab initio potentials for the He –HCl complex is expected to be more reliable than those developed for the heavier M– HCl species.
2. Computational details To examine the interaction of the rare-gas atom He with the HCl molecule, we use the supramolecular
where EAB is the energy of the complex, and EA and EB are the energies of monomers A and B, respectively. It is well known that for rare-gas complexes the Hartree –Fock interaction potential is repulsive and the dispersion energy is the dominant attractive intermolecular force. An adequate treatment of electron correlation is thus essential in the calculation of the intermolecular potentials of He – HCl. In our present study, the level of theory will be indicated by the superscript, e.g. DECCSDðTÞ will denote the CCSD(T) interaction energy. The most accurate are our CCSD(T) [3] results, but along the way we also obtained interaction energies at the selfconsistent field (SCF), second-order Moller – Plesset (MP2), and the single and double excitation coupledcluster (CCSD) levels of theory. Calculations have been performed using the augmented correlationconsistent polarized quadruple zeta basis set (aug-ccpVQZ) of Dunning and co-workers [4 – 6]. Our electron-correlated calculations for the He – HCl complex used frozen core approximation. The counterpoise method of Boys and Bernardi was used to avoid the basis set superposition error (BSSE) [7]. All the calculations were carried out using the GAUSSIAN 94 package [8] in the High Performance Computational Chemistry Laboratory of Guizhou University. The co-ordinate system for the He – HCl complex is shown in Fig. 1. R is the intermolecular distance from the center of mass of HCl to the rare-gas He atom, Q is the angle describing the orientation of the He atom with respect to the H – Cl bond axis. Q ¼ 08 corresponds to the He –H – Cl co-linear arrangement. The equilibrium structure of HCl in the complex remains unknown. So the H – Cl bond length was set at ˚ according to the calculation at the CCSD(T)/ 1.28 A aug-cc-pVQZ theory level and was kept constant in all calculations.
3. Results and discussion
Fig. 2. PES of the He– HCl complex. Contour is labeled in cm21.
The interaction energies at the SCF, MP2, CCSD, and CCSD(T) levels of theory obtained
Y. Zhang, H.-Y. Shi / Journal of Molecular Structure (Theochem) 589–590 (2002) 89–93 Table 1 SCF, MP2, CCSD, and CCSD(T) interaction energies (in cm21) of the He –HCl at different distances and different angles
u (8)
˚) R (A
DE HF
DE MP2
DE CCSD
DE CCSD(T)
0
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
310.9 137.5 58.9 37.9 20.9 14.9 9.0 2.8 0.3
138.0 24.8 215.5 222.8 226.1 226.2 225.0 220.9 216.5
151.1 31.3 212.2 220.4 224.4 224.7 223.9 220.1 216.0
131.1 18.0 221.1 227.7 230.1 229.7 228.0 223.0 218.0
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
241.9 108.1 47.0 30.5 17.1 12.3 7.6 2.4 0.4
94.6 10.8 218.3 223.2 224.9 224.6 223.2 219.3 215.0
102.8 14.6 215.8 221.2 223.4 223.2 222.0 218.3 214.5
86.0 3.8 223.4 227.5 228.3 227.5 225.7 220.9 216.3
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
137.7 68.7 31.4 21.0 12.4 9.2 6.0 2.4 0.8
43.9 22.0 217.3 219.6 219.9 219.4 218.2 215.0 212.0
44.3 21.8 217.0 219.3 219.6 219.0 217.8 214.6 211.6
32.9 29.7 222.6 224.0 223.4 222.4 220.7 216.8 213.2
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
117.9 57.2 27.5 19.0 11.7 9.0 6.2 2.8 1.3
35.7 0.3 212.4 214.6 215.3 215.0 214.3 212.1 29.8
33.5 20.9 212.9 214.8 215.3 215.0 214.2 211.9 29.8
24.8 27.1 217.3 218.6 218.4 217.8 216.6 213.7 210.9
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
123.1 60.5 29.6 20.7 12.9 10.0 7.1 3.4 1.6
44.0 6.1 28.4 211.3 212.7 212.8 212.4 210.8 28.9
42.2 5.1 28.9 211.5 212.9 212.8 212.4 210.7 28.7
33.9 20.8 213.1 215.1 215.7 215.4 214.6 212.3 210.0
3.20 3.40 3.60 3.70
126.8 62.3 30.5 21.3
46.5 7.5 27.6 210.7
45.4 6.8 27.9 210.8
37.0 0.9 212.1 214.4
20
40
60
80
90
91
Table 1 (continued) ˚) R (A
DE HF
DE MP2
DE CCSD
DE CCSD(T)
3.83 3.90 4.00 4.20 4.40
13.3 10.3 7.1 3.4 1.6
212.3 212.4 212.1 210.6 28.8
212.3 212.6 212.0 210.5 28.6
215.2 215.0 214.2 212.1 29.8
100
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
127.6 62.5 31.0 21.2 13.2 10.2 7.1 3.4 1.6
46.0 7.1 27.8 210.8 212.3 212.5 212.1 210.6 28.7
45.6 6.8 27.9 210.8 212.2 212.3 212.0 210.4 28.5
37.1 0.9 212.1 214.3 215.1 214.9 214.2 212.0 29.7
120
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
116.0 56.2 27.1 18.8 12.4 9.0 6.2 2.9 1.4
34.2 0.9 211.0 213.0 213.7 213.5 212.8 210.8 28.8
35.3 1.6 210.4 212.5 213.2 212.9 212.4 210.5 28.5
26.7 24.4 214.6 216.0 216.1 215.4 214.5 212.1 29.6
140
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
89.8 42.6 20.1 13.8 8.4 6.5 4.4 2.1 1.0
11.5 210.5 216.5 216.8 216.0 215.2 214.0 211.3 29.0
13.8 28.9 215.4 215.8 215.1 214.4 213.3 210.7 28.5
5.5 214.7 219.4 219.2 217.9 216.9 215.3 212.2 29.6
160
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
62.2 28.5 13.0 8.7 5.2 4.0 2.7 1.2 0.5
211.2 221.8 222.0 220.6 218.3 217.0 215.1 211.8 29.1
28.1 219.6 220.3 219.2 217.1 215.9 214.2 211.0 28.5
216.0 225.0 224.2 222.4 219.7 218.2 216.1 212.5 29.6
180
3.20 3.40 3.60 3.70 3.83 3.90 4.00 4.20 4.40
50.4 22.4 9.9 6.6 3.8 2.9 1.9 0.8 0.3
220.8 226.4 224.3 222.2 219.2 217.7 215.6 212.0 29.2
217.4 224.1 222.4 220.6 217.9 216.5 214.5 211.2 28.5
225.1 229.4 226.2 223.7 220.4 218.7 216.5 212.6 29.6
u (8)
92
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Table 2 Interaction energies DE at 0, 90, and 1808
u (8)
˚) R (A
DE (cm21)
0 90 180
3.83 3.84 3.38
230.1 215.2 229.5
with the aug-cc-pVQZ basis set are reported in Table 1. We give this extensive set to allow other researchers to use the original results for developing their own model potentials. Our calculations probed the potential energy surface (PES) most extensively for intermolecular distances in the interval from 3.20 ˚ , and 11 angles in the range from 0 to 1808. to 4.40 A For 1808, calculation was performed for a additional ˚ . The PES, which is shown in Fig. 2, distance of 3.38 A could be well fitted to the analytic function described earlier [9,10]. The global minimum with a well depth of approximate 30.1 cm21 was found on the CCSD(T) surface for the linear He –H – Cl structure ðQ ¼ 0:08Þ The error due to basis set incompleteat R ¼ 3:83 A: ness is more difficult to estimate, but a comparison with the estimated complete basis set limit values of interaction energies that we obtained for He – HF suggests that it should not exceed a few percent [11]. It is clear from Table 2 that in addition to the global minimum, there is a secondary minimum at R ¼ and Q ¼ 1808 (a well depth of 29.5 cm21) 3:38 A corresponding to another linear geometry. This arises because the electron density of the HCl monomer is substantially smaller in this direction than perpendicular to the internuclear axis, so that the intermolecular repulsion at a given distance is weaker for the linear He – Cl – H structure than for a T-shaped configuration. The two minima are so close that we have to perform additional calculations for the neighboring values of R to decide the position of the global minimum. The secondary minimum is a little shallower than the global one, indicating that the He – Cl – H configuration is a little unstable with respect to the He – H – Cl configuration. A potential barrier of 15.2 cm21 separating the two minima occurs around Q ¼ 908), corresponding to the position (R ¼ 3:83 A; a T-shaped configuration. Our calculated values are in good agreement with the experimental measurements Q ¼ 0:08) [2]. (R ¼ 3:89 A; The angular dependence of the MP2, CCSD, and
Fig. 3. The angular dependence of the interaction energy at different levels of theory at R ¼ 3:83 A:
CCSD(T) supermolecule interaction energies at R ¼ is given in Fig. 3. This distance is the radial 3:83 A minimum at Q ¼ 08 and Q ¼ 908; but longer than the one at Q ¼ 1808: As can been seen in Fig. 3, each curve contains two minima, at Q ¼ 08 and Q ¼ 1808; respectively. The strength of the interaction is underestimated both at the MP2 theory level and at the CCSD level of theory, in comparison to the CCSD(T) results. It is clear from Table 1 that the global minimum of and MP2 theory level is at the point of R ¼ 3:38 A MP2 21 Q ¼ 1808 ðDE ¼ 26:5 cm Þ; indicating that the He –H – Cl configuration is unstable with respect to the He – H – Cl configuration. It is only at the higher levels of theory (CCSD and CCSD(T)) that their relative positions are reversed. The key to the understanding of this effect is the third-order correlation DEð3Þ ; whose partitioning, unfortunately, has not been implemented so far.
4. Conclusions The He –HCl CCSD(T) ab initio potential presented here provides an accurate description of the intermolecular interaction. In comparison with the experimental results, the equilibrium interaction energy that we have found, De ¼ 30:1 cm21 ; is deeper by 5.1 cm21, and the distance between the He atom and the center of mass of the HCl molecule, is shorter by 0.06 A ˚ . In addition, the R ¼ 3:83 A;
Y. Zhang, H.-Y. Shi / Journal of Molecular Structure (Theochem) 589–590 (2002) 89–93
interaction energies of linear He –Cl – H structure and linear He – Cl – H structure are almost the same. At the same time, we found that at the MP2 level the results were contrary to the results obtained from the higher CCSD, CCSD(T) theory level. The two characterizations were not found in the previous studies of Ar – HCl and Ar –FH complexes [12,13].
Acknowledgments This work was partially supported by the Science Foundation of Educational Administration of Guizhou Province and the Science Foundation of Guizhou Province, People’s Republic of China, respectively. The authors thank Prof. Y.B. Wang for computational support of our work.
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