- Email: [email protected]
Accurate intermolecular ground state potential of the He–HCl van der Waals complex
Chemical Physics Letters 419 (2006) 55–58 www.elsevier.com/locate/cplett
Accurate intermolecular ground state potential of the He–HCl van der Waals complex Jose´ Luis Cagide Fajı´n, Berta Ferna´ndez
*
Department of Physical Chemistry, Avda. de las Ciencias s/n, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain Received 21 July 2005; in final form 14 November 2005 Available online 2 December 2005
Abstract We evaluate the rovibrational spectrum of the He–HCl van der Waals complex from an accurate ground state intermolecular potential, obtained from CCSD(T) interaction energies. After a systematic basis set study, we select the aug-cc-pV5Z basis set extended with midbond functions. The potential is characterized by two linear minima, i.e., He–ClH and He–HCl, with distances from the He atom to ˚ , respectively; and energies of 32.74 and 31.16 cm1, respectively. The rovibrational specthe HCl centre of mass of 3.349 and 3.832 A tra for the different isotopic species are calculated. The results are compared to those previously available. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction In previous work, we have been dealing with the study of several van der Waals complexes evaluating highly accurate intermolecular potential energy surfaces (IPESs) using the coupled cluster singles and doubles model including connected triple corrections (CCSD(T)) and augmented correlation consistent basis sets extended with a set of 3s3p2d1f1g midbond functions (denoted 33211) (see [1] and references cited therein). The results were in very good agreement with the accurate experimental data available and allowed in some cases for correction and reinterpretation of the spectra. Rare gas-hydrogen halide systems have been intensively studied both from the experimental and theoretical points of view [1,2]. The He–HCl complex was studied through scattering and collision experiments (see for example the work by Green et al. [3], Collins et al. [4,5], Held et al. [6], and Willey et al. [7]). In 1990, the near-infrared vibration–rotation spectrum of the complex was observed [8], and the results fitted to a Lennard-Jones(m, 6) empirical potential. *
Corresponding author. Fax: +34 981 595 012. E-mail address: [email protected] (B. Ferna´ndez).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.11.050
Interaction energies were evaluated using the Hartree– Fock (HF), Second order Møller–Plesset (MP2), coupled cluster singles and doubles (CCSD) and CCSD(T) methods and the augmented correlation-consistent polarized quadruple zeta basis set [9]. Recently, Murdachaew et al. [10] using symmetry-adapted perturbation theory (SAPT) and a [8s5p3d2f1g/7s3p2d1f/3s2p1d/3s2p1d] basis set (where the consecutive entries refer to Cl, He, H and midbond functions, respectively) obtained the energy levels and the rovibrational spectrum of the complex. The IPES predicts a dissociation energy of 7.74 cm1, that the authors concluded to be more accurate than the experimental value in [8]. The stationary point interaction energies were also evaluated using the CCSD(T) method with the aug-ccpVQZ basis set extended with a set of 3s2p1d midbond functions. For the rovibrational levels considerable discrepancies were found with respect to the available experimental data (even up to 23% for the lowest level). The results of all these studies are summarized in Table 1. In order to clarify the disagreement among previous results, that differ from one another considerably – absolute minimum energies between 15.5 and 47.6 cm1, discrepancies in the order of the minima and in the rovibrational levels, etc. – and clearly call for more accurate theoretical studies [8], in the present work we evaluate the
J.L. Cagide Fajı´n, B. Ferna´ndez / Chemical Physics Letters 419 (2006) 55–58
56 Table 1 IPES stationary points
This work Ref. [3] Refs. [4,5]a Ref. [7]a Exp. [8] CCSD(T) [9] SAPT [10] a
HeClH ˚) R (A
E (cm )
3.3493 3.307 3.54 3.43 3.450 3.38 3.35
32.740 D0 = 8.372 47. 60 15.5 32.8 25.0 D0 = 10.1 ± 1.2 29.5 32.81 D0 = 7.74
1
HeHCl ˚) R (A
E (cm )
Saddle point ˚) R (A
3.8321
31.159
3.7777
3.92 3.88
14.9 28.4
3.75 3.73
102.6 107.9
11.3 21.2
3.83 3.85
30.1 30.79
3.84 3.79
90.0 94.1
15.2 17.18
1
h (°) 90.0
E (cm1) 17.328
Results obtained for Murdachaew et al. [10].
He–HCl van der Waals complex ground state IPES and the corresponding rovibrational spectra. 2. Intermolecular potential energy surface To carry out the ab initio interaction energy calculations we select a set of 116 intermolecular geometries, described by the R and h coordinates of the He position vector with origin in the HCl center of mass. R represents the length of ˚ , and h the angle this vector makes with the the vector in A HCl molecule, taking as h = 0 the linear He–HCl configuration. The geometry of the HCl molecule is kept fixed at ˚ obtained from the microwave specthe r0 value of 1.2838 A tra [11]. The correlation between the HCl vibrational coordinate and the complex modes can be expected small. To calculate the interaction energies, we use the supermolecular model and correct for the BSSE by invoking the counterpoise method [12]. Considering the good results previously obtained, we use the CCSD(T) method and DunningÕs augmented correlation consistent polarized valence basis sets extended with the set of 33211 midbond functions centred in the middle of the van der Waals bond [1]. To obtain accurate rovibrational spectra good quality bases are essential, as we showed in the study of [13]. Considering this, we start the calculations with a systematic basis set convergence study using the aug-cc-pVXZ (X = D, T, Q, 5, 6) set of bases, with and without the 33211 set of midbond functions and additionally checking for double augmentation. We carry out the calculations at four geometries: two linear, selected close to the IPES min˚, ima available in the literature (He–HCl: R = 3.85 A ˚ , h = 180°) [10], a T-shape h = 0°; He–ClH: R = 3.35 A ˚ , h = 90°), and a geometry in the geometry (R = 3.6609 A ˚ , h = 30°). positive energy region (R = 3.250 A In order to analyze basis set convergence and considering the size of the interaction energy, we take as error limit 0.5 cm1. The presence of the midbond functions accelerates basis set convergence, and even at the quintuple zeta level these functions are relevant in the basis set. Also the relative stability of the linear configurations is altered by the presence of the midbond functions, being always the He–ClH configuration more stable than the He–HCl. In the calculations performed without midbond functions, we have to go up to the augmented quintuple zeta or the
double augmented quadruple zeta levels in order to get the convergence-limit stability. The importance of the midbond functions for getting the right He–ClH – He–HCl stability is another proof of the importance of carrying out a proper basis set selection before starting the IPES calculations (see also [10]). Within the aug-cc-pVXZ-33211 series of bases at the aug-cc-pVQZ-33211 level there is still a difference of 0.94 cm1 with respect to the aug-cc-pV5Z-33211 result for the positive geometry. On the other hand, the largest difference between the quintuple and the sextuple zeta results is 0.41 cm1, therefore, we can expect convergence (within our error limit) at the quintuple zeta level. The double augmentation is not needed, therefore, we select the aug-cc-pV5Z-33211 basis set to evaluate the IPES. We use the DALTON [14] and ACES II [15] programs. See [16] for the final results. The complex IPES is constructed by fitting the ab initio interaction energies lower than 20 cm1 to the analytic function V(R, h) [17], that has been used in similar potentials [1,18,19]. The function is the sum of two terms, the short range term Vsh and the asymptotic term Vas: V ðR; hÞ ¼ V sh ðR; hÞ þ V as ðR; hÞ;
ð1Þ
where V sh ðR; hÞ ¼ GðR; hÞeDðhÞBðhÞR
ð2Þ
and V as ðR; hÞ ¼
X7
n4 X
n¼6 l¼0;2... l¼1;3
fn ðBðhÞRÞ
C ln 0 P ðcos hÞ Rn l
ð3Þ
,..
D(h), B(h), and G(R,h) are expansions in Legendre polynomials ðP 0l Þ; X5 BðhÞ ¼ bl P 0l ðcos hÞ; ð4Þ l¼0 X5 DðhÞ ¼ d l P 0l ðcos hÞ; ð5Þ l¼0 X5 GðR; hÞ ¼ g0l þ g1l R þ g2l R2 þ g3l R3 P 0l ðcos hÞ; ð6Þ l¼0 fn is the Tang–Toennies damping function, and bl, dl, gkl and C ln are adjustable parameters. The fitted values of the IPES parameters are given in Table 2. The fit of the ab initio values is characterized by a standard error of 0.0072 cm1 and a maximum error of
J.L. Cagide Fajı´n, B. Ferna´ndez / Chemical Physics Letters 419 (2006) 55–58
gives an energy barrier between the global and the local minima of 15.412 cm1. These results are close to those of the SAPT calculations in [10], and give an stability opposite to that of the previous theoretical CCSD(T) study [9]. This shows the importance of a proper basis set selection and of the inclusion of the midbond functions in the basis set. The use of midbond functions changes the position of the minima from the He–HCl linear geometry to the He–ClH linear geometry in bases with aug-cc-pVQZ quality or less. The concordance with the studies in [3–5,7,9] is bad in general. Considering the good performance showed by the CCSD(T) method and the augmented correlation consistent basis set in getting van der Waals complex IPESs, it seems that the He–HCl (semi)empirical potentials available need revision. All these results are compared in Table 1.
Table 2 Parameters of the analytic IPES Parameter
Value
Parameter
Value
b0 b1 b2 b3 b4 b5 d0 d1 d2 d3 d4 d5 g00 g01 g02 g03 g04 g05 g10 g11
13.32010238 0.34286792 0.29816363 0.29425822 0.00934684 0.03540720 2.10089330 0.01023381 0.12817719 0.01081582 0.02043170 0.00698361 4.22760910 0.22438673 1.58886495 0.31882907 0.39685627 0.17984821 2.92257112 0.25162254
g12 g13 g14 g15 g20 g21 g22 g23 g24 g25 g30 g31 g32 g33 g34 g35 C 06 C 26 C 17 C 37
1.21660466 0.11149131 0.26753161 0.08211105 0.68212733 0.08245550 0.31177458 0.00000000 0.05921384 0.00955425 0.05598598 0.00891702 0.02776035 0.00250968 0.00434989 0.00000000 0.00566357 0.00313099 0.00000000 0.00000000
57
3. Rovibrational spectra The rovibrational spectra are evaluated using the TRIAprogram [20]. The radial basis functions are chosen as Morse-type oscillator functions parameterized in terms of an equilibrium distance of 6.330582 bohr, dissociation energy of 0.00014854 Eh, and fundamental frequency of 0.000040704 Eh. The nuclear masses used are: m(4He) = 4.0026033 amu, m(H) = 1.007825 amu, m(D) = 2.014102 amu, m(35Cl) = 34.968853 amu, m(37Cl) = 36.965903 amu. To describe the intermolecular degrees of freedom we use 50 radial and 50 angular basis functions. The calculated IPES gives a D0 value of 8.372 cm1 that agrees reasonably well with the experimental determination [(10.2 ± 1.2) cm1] and improves the SAPT value of 7.74 cm1.
TOM
0.2037 cm1. A contour plot of the IPES is presented in Fig. 1. Two minima are found in the IPES, the absolute minimum has an energy of 32.740 cm1 and it is located at the He–ClH linear configuration with the He atom at a dis˚ with respect to the HCl centre of mass. tance of 3.3493 A The surface has a second minimum at the He–HCl linear ˚ with configuration, with the He at a distance of 3.8321 A respect to the HCl centre of mass and with an energy of 31.159 cm1. A saddle point with energy of ˚ and h = 90°. This 17.328 cm1 is located at R = 3.7777 A
HeHCl contour 5.5
R (Angstrom)
5
4.5
4
3.5
3 0
20
40
60
80
100
120
140
160
180
T (degrees) Fig. 1. Contour plot in Jacobi coordinates of the aug-cc-pV5Z-33211 IPES. The successive contours differ by 3 cm1.
J.L. Cagide Fajı´n, B. Ferna´ndez / Chemical Physics Letters 419 (2006) 55–58
58
Table 3 Energy levels in cm1. Comparison to previous results
Acknowledgments
J
This work
SAPT [10]
Exp. [8]
0 1 2 3 4 5 6
8.3724 7.8293 6.7515 5.1563 3.0744 0.5605 2.3621
7.7438 7.2067 6.1410 4.5657 2.5143 0.0506 2.6577
10.1172 9.4975 8.2677 6.4482 4.0752 1.2117 1.9940
HeDCl
0 1 2 3 4 5 6
8.5307 7.9880 6.9108 5.3163 3.2338 0.7150 2.1289
HeH37Cl
0 1 2 3 4 5 6
8.3991 7.8584 6.7852 5.1968 3.1234 0.6182 2.2023
HeHCl
10.1467 9.5297 8.3053 6.4936 4.1301 1.2768 1.9930
The rotational energy levels for HeHCl, HeDCl, and HeH37Cl are presented in Table 3. Previously available data are also reported. Our results are similar to the SAPT [10], but closer to the experimental data [8]. Considering the accuracy we obtained in previous studies – errors in the frequencies with respect to experiment in the order of 0.6% when using the aug-cc-pV5Z-33211 basis set – [13], we can expect errors of the same magnitude for the frequencies that can be evaluated from the present results. Since for this complex and due to the difficulties encountered in the experiments, there is a considerable lack of spectroscopic data, we can expect the present results to help in dynamical studies of the complex.
This work has been supported by the NANOQUANT RTN, Contract No. MRTN-CT-2003-506842, and by the Ministerio de Educacio´n y Ciencia and FEDER (CTQ2005-01076/BQU project). References [1] J.L. Fajı´n, J.L. Cacheiro, B. Ferna´ndez, J. Chem. Phys. 121 (2004) 4599. [2] M. Jeziorka, P. Jankowski, K. Szalewicz, B. Jeziorski, J. Chem. Phys. 113 (2000) 2957. [3] S. Green, L. Monchick, J. Chem. Phys. 63 (1975) 4198. [4] L.A. Collins, N.F. Lane, Phys. Rev. A 12 (1975) 811. [5] L.A. Collins, N.F. Lane, Phys. Rev. A 14 (1976) 1358. [6] W.D. Held, E. Piper, G. Ringer, J.P. Toennies, Chem. Phys. Lett. 75 (1980) 26. [7] D.R. Willey, V.E. Choong, F.C. De Lucia, J. Chem. Phys. 96 (1992) 898. [8] C.M. Lovejoy, D.J. Nesbitt, J. Chem. Phys. 93 (1990) 5387. [9] Y. Zhang, H.Y. Shi, J. Mol. Struct.: THEOCHEM 589 (2002) 89. [10] G. Murdachaew, K. Szalewicz, H. Jiang, Z. Bacˇic´, J. Chem. Phys. 121 (2004) 11839. [11] G. Herzberg, Molecular Spectra and Molecular Structure. I Spectra of Diatomic Molecules, second edn., D. Van Nostrand Company, London, 1951. [12] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [13] C.R. Munteanu, J.L. Cacheiro, B. Ferna´ndez, J. Chem. Phys. 120 (2004) 9104. [14] T. Helgaker et al., DALTON – an Electronic Structure Program, Release 1.2, 2001. [15] J.F. Stanton et al., ACES II is a Program Product of the Quantum Theory Project, University of Florida 32611, 1996. [16] The interaction energy results can be obtained from the authors on request. [17] R. Bukowski, J. Sadlej, B. Jeziorski, P. Jankowski, K. Szalewicz, S.A. Kucharski, H.L. Williams, B.M. Rice, J. Chem. Phys. 110 (1999) 3785. [18] R.R. Toczylowski, S.M. Cybulski, J. Chem. Phys. 112 (2000) 4604. [19] T.B. Pedersen, J.L. Cacheiro, B. Ferna´ndez, H. Koch, J. Chem. Phys. 117 (2002) 6562. [20] J. Tennyson, S. Miller, C.R. Le Sueur, Comput. Phys. Commun. 75 (1993) 339.
Accurate intermolecular ground state potential of the He–HCl van der Waals complex Jose´ Luis Cagide Fajı´n, Berta Ferna´ndez
*
Department of Physical Chemistry, Avda. de las Ciencias s/n, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain Received 21 July 2005; in final form 14 November 2005 Available online 2 December 2005
Abstract We evaluate the rovibrational spectrum of the He–HCl van der Waals complex from an accurate ground state intermolecular potential, obtained from CCSD(T) interaction energies. After a systematic basis set study, we select the aug-cc-pV5Z basis set extended with midbond functions. The potential is characterized by two linear minima, i.e., He–ClH and He–HCl, with distances from the He atom to ˚ , respectively; and energies of 32.74 and 31.16 cm1, respectively. The rovibrational specthe HCl centre of mass of 3.349 and 3.832 A tra for the different isotopic species are calculated. The results are compared to those previously available. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction In previous work, we have been dealing with the study of several van der Waals complexes evaluating highly accurate intermolecular potential energy surfaces (IPESs) using the coupled cluster singles and doubles model including connected triple corrections (CCSD(T)) and augmented correlation consistent basis sets extended with a set of 3s3p2d1f1g midbond functions (denoted 33211) (see [1] and references cited therein). The results were in very good agreement with the accurate experimental data available and allowed in some cases for correction and reinterpretation of the spectra. Rare gas-hydrogen halide systems have been intensively studied both from the experimental and theoretical points of view [1,2]. The He–HCl complex was studied through scattering and collision experiments (see for example the work by Green et al. [3], Collins et al. [4,5], Held et al. [6], and Willey et al. [7]). In 1990, the near-infrared vibration–rotation spectrum of the complex was observed [8], and the results fitted to a Lennard-Jones(m, 6) empirical potential. *
Corresponding author. Fax: +34 981 595 012. E-mail address: [email protected] (B. Ferna´ndez).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.11.050
Interaction energies were evaluated using the Hartree– Fock (HF), Second order Møller–Plesset (MP2), coupled cluster singles and doubles (CCSD) and CCSD(T) methods and the augmented correlation-consistent polarized quadruple zeta basis set [9]. Recently, Murdachaew et al. [10] using symmetry-adapted perturbation theory (SAPT) and a [8s5p3d2f1g/7s3p2d1f/3s2p1d/3s2p1d] basis set (where the consecutive entries refer to Cl, He, H and midbond functions, respectively) obtained the energy levels and the rovibrational spectrum of the complex. The IPES predicts a dissociation energy of 7.74 cm1, that the authors concluded to be more accurate than the experimental value in [8]. The stationary point interaction energies were also evaluated using the CCSD(T) method with the aug-ccpVQZ basis set extended with a set of 3s2p1d midbond functions. For the rovibrational levels considerable discrepancies were found with respect to the available experimental data (even up to 23% for the lowest level). The results of all these studies are summarized in Table 1. In order to clarify the disagreement among previous results, that differ from one another considerably – absolute minimum energies between 15.5 and 47.6 cm1, discrepancies in the order of the minima and in the rovibrational levels, etc. – and clearly call for more accurate theoretical studies [8], in the present work we evaluate the
J.L. Cagide Fajı´n, B. Ferna´ndez / Chemical Physics Letters 419 (2006) 55–58
56 Table 1 IPES stationary points
This work Ref. [3] Refs. [4,5]a Ref. [7]a Exp. [8] CCSD(T) [9] SAPT [10] a
HeClH ˚) R (A
E (cm )
3.3493 3.307 3.54 3.43 3.450 3.38 3.35
32.740 D0 = 8.372 47. 60 15.5 32.8 25.0 D0 = 10.1 ± 1.2 29.5 32.81 D0 = 7.74
1
HeHCl ˚) R (A
E (cm )
Saddle point ˚) R (A
3.8321
31.159
3.7777
3.92 3.88
14.9 28.4
3.75 3.73
102.6 107.9
11.3 21.2
3.83 3.85
30.1 30.79
3.84 3.79
90.0 94.1
15.2 17.18
1
h (°) 90.0
E (cm1) 17.328
Results obtained for Murdachaew et al. [10].
He–HCl van der Waals complex ground state IPES and the corresponding rovibrational spectra. 2. Intermolecular potential energy surface To carry out the ab initio interaction energy calculations we select a set of 116 intermolecular geometries, described by the R and h coordinates of the He position vector with origin in the HCl center of mass. R represents the length of ˚ , and h the angle this vector makes with the the vector in A HCl molecule, taking as h = 0 the linear He–HCl configuration. The geometry of the HCl molecule is kept fixed at ˚ obtained from the microwave specthe r0 value of 1.2838 A tra [11]. The correlation between the HCl vibrational coordinate and the complex modes can be expected small. To calculate the interaction energies, we use the supermolecular model and correct for the BSSE by invoking the counterpoise method [12]. Considering the good results previously obtained, we use the CCSD(T) method and DunningÕs augmented correlation consistent polarized valence basis sets extended with the set of 33211 midbond functions centred in the middle of the van der Waals bond [1]. To obtain accurate rovibrational spectra good quality bases are essential, as we showed in the study of [13]. Considering this, we start the calculations with a systematic basis set convergence study using the aug-cc-pVXZ (X = D, T, Q, 5, 6) set of bases, with and without the 33211 set of midbond functions and additionally checking for double augmentation. We carry out the calculations at four geometries: two linear, selected close to the IPES min˚, ima available in the literature (He–HCl: R = 3.85 A ˚ , h = 180°) [10], a T-shape h = 0°; He–ClH: R = 3.35 A ˚ , h = 90°), and a geometry in the geometry (R = 3.6609 A ˚ , h = 30°). positive energy region (R = 3.250 A In order to analyze basis set convergence and considering the size of the interaction energy, we take as error limit 0.5 cm1. The presence of the midbond functions accelerates basis set convergence, and even at the quintuple zeta level these functions are relevant in the basis set. Also the relative stability of the linear configurations is altered by the presence of the midbond functions, being always the He–ClH configuration more stable than the He–HCl. In the calculations performed without midbond functions, we have to go up to the augmented quintuple zeta or the
double augmented quadruple zeta levels in order to get the convergence-limit stability. The importance of the midbond functions for getting the right He–ClH – He–HCl stability is another proof of the importance of carrying out a proper basis set selection before starting the IPES calculations (see also [10]). Within the aug-cc-pVXZ-33211 series of bases at the aug-cc-pVQZ-33211 level there is still a difference of 0.94 cm1 with respect to the aug-cc-pV5Z-33211 result for the positive geometry. On the other hand, the largest difference between the quintuple and the sextuple zeta results is 0.41 cm1, therefore, we can expect convergence (within our error limit) at the quintuple zeta level. The double augmentation is not needed, therefore, we select the aug-cc-pV5Z-33211 basis set to evaluate the IPES. We use the DALTON [14] and ACES II [15] programs. See [16] for the final results. The complex IPES is constructed by fitting the ab initio interaction energies lower than 20 cm1 to the analytic function V(R, h) [17], that has been used in similar potentials [1,18,19]. The function is the sum of two terms, the short range term Vsh and the asymptotic term Vas: V ðR; hÞ ¼ V sh ðR; hÞ þ V as ðR; hÞ;
ð1Þ
where V sh ðR; hÞ ¼ GðR; hÞeDðhÞBðhÞR
ð2Þ
and V as ðR; hÞ ¼
X7
n4 X
n¼6 l¼0;2... l¼1;3
fn ðBðhÞRÞ
C ln 0 P ðcos hÞ Rn l
ð3Þ
,..
D(h), B(h), and G(R,h) are expansions in Legendre polynomials ðP 0l Þ; X5 BðhÞ ¼ bl P 0l ðcos hÞ; ð4Þ l¼0 X5 DðhÞ ¼ d l P 0l ðcos hÞ; ð5Þ l¼0 X5 GðR; hÞ ¼ g0l þ g1l R þ g2l R2 þ g3l R3 P 0l ðcos hÞ; ð6Þ l¼0 fn is the Tang–Toennies damping function, and bl, dl, gkl and C ln are adjustable parameters. The fitted values of the IPES parameters are given in Table 2. The fit of the ab initio values is characterized by a standard error of 0.0072 cm1 and a maximum error of
J.L. Cagide Fajı´n, B. Ferna´ndez / Chemical Physics Letters 419 (2006) 55–58
gives an energy barrier between the global and the local minima of 15.412 cm1. These results are close to those of the SAPT calculations in [10], and give an stability opposite to that of the previous theoretical CCSD(T) study [9]. This shows the importance of a proper basis set selection and of the inclusion of the midbond functions in the basis set. The use of midbond functions changes the position of the minima from the He–HCl linear geometry to the He–ClH linear geometry in bases with aug-cc-pVQZ quality or less. The concordance with the studies in [3–5,7,9] is bad in general. Considering the good performance showed by the CCSD(T) method and the augmented correlation consistent basis set in getting van der Waals complex IPESs, it seems that the He–HCl (semi)empirical potentials available need revision. All these results are compared in Table 1.
Table 2 Parameters of the analytic IPES Parameter
Value
Parameter
Value
b0 b1 b2 b3 b4 b5 d0 d1 d2 d3 d4 d5 g00 g01 g02 g03 g04 g05 g10 g11
13.32010238 0.34286792 0.29816363 0.29425822 0.00934684 0.03540720 2.10089330 0.01023381 0.12817719 0.01081582 0.02043170 0.00698361 4.22760910 0.22438673 1.58886495 0.31882907 0.39685627 0.17984821 2.92257112 0.25162254
g12 g13 g14 g15 g20 g21 g22 g23 g24 g25 g30 g31 g32 g33 g34 g35 C 06 C 26 C 17 C 37
1.21660466 0.11149131 0.26753161 0.08211105 0.68212733 0.08245550 0.31177458 0.00000000 0.05921384 0.00955425 0.05598598 0.00891702 0.02776035 0.00250968 0.00434989 0.00000000 0.00566357 0.00313099 0.00000000 0.00000000
57
3. Rovibrational spectra The rovibrational spectra are evaluated using the TRIAprogram [20]. The radial basis functions are chosen as Morse-type oscillator functions parameterized in terms of an equilibrium distance of 6.330582 bohr, dissociation energy of 0.00014854 Eh, and fundamental frequency of 0.000040704 Eh. The nuclear masses used are: m(4He) = 4.0026033 amu, m(H) = 1.007825 amu, m(D) = 2.014102 amu, m(35Cl) = 34.968853 amu, m(37Cl) = 36.965903 amu. To describe the intermolecular degrees of freedom we use 50 radial and 50 angular basis functions. The calculated IPES gives a D0 value of 8.372 cm1 that agrees reasonably well with the experimental determination [(10.2 ± 1.2) cm1] and improves the SAPT value of 7.74 cm1.
TOM
0.2037 cm1. A contour plot of the IPES is presented in Fig. 1. Two minima are found in the IPES, the absolute minimum has an energy of 32.740 cm1 and it is located at the He–ClH linear configuration with the He atom at a dis˚ with respect to the HCl centre of mass. tance of 3.3493 A The surface has a second minimum at the He–HCl linear ˚ with configuration, with the He at a distance of 3.8321 A respect to the HCl centre of mass and with an energy of 31.159 cm1. A saddle point with energy of ˚ and h = 90°. This 17.328 cm1 is located at R = 3.7777 A
HeHCl contour 5.5
R (Angstrom)
5
4.5
4
3.5
3 0
20
40
60
80
100
120
140
160
180
T (degrees) Fig. 1. Contour plot in Jacobi coordinates of the aug-cc-pV5Z-33211 IPES. The successive contours differ by 3 cm1.
J.L. Cagide Fajı´n, B. Ferna´ndez / Chemical Physics Letters 419 (2006) 55–58
58
Table 3 Energy levels in cm1. Comparison to previous results
Acknowledgments
J
This work
SAPT [10]
Exp. [8]
0 1 2 3 4 5 6
8.3724 7.8293 6.7515 5.1563 3.0744 0.5605 2.3621
7.7438 7.2067 6.1410 4.5657 2.5143 0.0506 2.6577
10.1172 9.4975 8.2677 6.4482 4.0752 1.2117 1.9940
HeDCl
0 1 2 3 4 5 6
8.5307 7.9880 6.9108 5.3163 3.2338 0.7150 2.1289
HeH37Cl
0 1 2 3 4 5 6
8.3991 7.8584 6.7852 5.1968 3.1234 0.6182 2.2023
HeHCl
10.1467 9.5297 8.3053 6.4936 4.1301 1.2768 1.9930
The rotational energy levels for HeHCl, HeDCl, and HeH37Cl are presented in Table 3. Previously available data are also reported. Our results are similar to the SAPT [10], but closer to the experimental data [8]. Considering the accuracy we obtained in previous studies – errors in the frequencies with respect to experiment in the order of 0.6% when using the aug-cc-pV5Z-33211 basis set – [13], we can expect errors of the same magnitude for the frequencies that can be evaluated from the present results. Since for this complex and due to the difficulties encountered in the experiments, there is a considerable lack of spectroscopic data, we can expect the present results to help in dynamical studies of the complex.
This work has been supported by the NANOQUANT RTN, Contract No. MRTN-CT-2003-506842, and by the Ministerio de Educacio´n y Ciencia and FEDER (CTQ2005-01076/BQU project). References [1] J.L. Fajı´n, J.L. Cacheiro, B. Ferna´ndez, J. Chem. Phys. 121 (2004) 4599. [2] M. Jeziorka, P. Jankowski, K. Szalewicz, B. Jeziorski, J. Chem. Phys. 113 (2000) 2957. [3] S. Green, L. Monchick, J. Chem. Phys. 63 (1975) 4198. [4] L.A. Collins, N.F. Lane, Phys. Rev. A 12 (1975) 811. [5] L.A. Collins, N.F. Lane, Phys. Rev. A 14 (1976) 1358. [6] W.D. Held, E. Piper, G. Ringer, J.P. Toennies, Chem. Phys. Lett. 75 (1980) 26. [7] D.R. Willey, V.E. Choong, F.C. De Lucia, J. Chem. Phys. 96 (1992) 898. [8] C.M. Lovejoy, D.J. Nesbitt, J. Chem. Phys. 93 (1990) 5387. [9] Y. Zhang, H.Y. Shi, J. Mol. Struct.: THEOCHEM 589 (2002) 89. [10] G. Murdachaew, K. Szalewicz, H. Jiang, Z. Bacˇic´, J. Chem. Phys. 121 (2004) 11839. [11] G. Herzberg, Molecular Spectra and Molecular Structure. I Spectra of Diatomic Molecules, second edn., D. Van Nostrand Company, London, 1951. [12] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [13] C.R. Munteanu, J.L. Cacheiro, B. Ferna´ndez, J. Chem. Phys. 120 (2004) 9104. [14] T. Helgaker et al., DALTON – an Electronic Structure Program, Release 1.2, 2001. [15] J.F. Stanton et al., ACES II is a Program Product of the Quantum Theory Project, University of Florida 32611, 1996. [16] The interaction energy results can be obtained from the authors on request. [17] R. Bukowski, J. Sadlej, B. Jeziorski, P. Jankowski, K. Szalewicz, S.A. Kucharski, H.L. Williams, B.M. Rice, J. Chem. Phys. 110 (1999) 3785. [18] R.R. Toczylowski, S.M. Cybulski, J. Chem. Phys. 112 (2000) 4604. [19] T.B. Pedersen, J.L. Cacheiro, B. Ferna´ndez, H. Koch, J. Chem. Phys. 117 (2002) 6562. [20] J. Tennyson, S. Miller, C.R. Le Sueur, Comput. Phys. Commun. 75 (1993) 339.