EÜect of basis set on the calculated geometry of the CH4 Æ HCl complex Edmond P. F. Lee*§ and Timothy G. Wright*î Department of Chemistry, University of Southampton, High–eld, Southampton, UK SO17 1BJ The complex is studied using a variety of basis sets at the MP2 level of theory. It is found that the calculated CH4 … HCl geometry depends critically on the precise nature of the basis set used, with a particularly important ro� le played by polarization and diÜuse functions. It is established, that the ìbestœ basis sets lead to a geometry, in agreement with the conclusions reached C3v by microwave spectroscopy.The geometry is then recalculated at the MP4(SDQ) and QCISD level of theory, and the binding energy of the complex is calculated at the CCSD(T) level of theory. Introduction The complex has been studied using microwave CH4 … HCl spectroscopy by Legon et al.1 and Ohshima and Endo.2 It was found that the complex has an eÜective geometry, but that C3v it exhibits wide-amplitude motion.Craw et al.3 performed an ab initio calculation of the complex at the MP2 level of theory. It was found that the structure, obtained by standard ana- C3v lytical gradient techniques, had two imaginary frequencies, indicating that it was a saddle-point. This geometry consisted of the HCl molecule bonding along a axis, with the hydro- C3 gen atom pointing towards the centre of a face. They CH3 then allowed the H atom to move oÜ axis, and found that a new structure was obtained with an energy lower than that Cs of the stationary point ; however, this new structure was C3v not characterized, with respect to the number of real or imaginary vibrational frequencies.Other structures were also investigated, but they had energies higher than the abovementioned geometries. It was noted3 that the zero-point vibrational energy (ZPVE) (of the intermolecular librational mode) was greater than the barrier corresponding to the C3v geometry, and so the geometry was eÜectively of sym- C3v metry, in accordance with the microwave studies.Of interest, however, is that the authors3 then went on to correct the potential energy surface for basis set superposition error (BSSE) along the librational angle coordinate (this corresponds to the H atom moving oÜ the axis), by using the C3v counterpoise (CP) correction. The new surface obtained had a minimum at the geometry. The CP corrected dissociation C3v energy of the complex was 3.4 kJ mol~1 (0.8 kcal mol~1), (De) compared to a value of 4.5 kJ mol~1 (1.1 kcal mol~1) for De the structure, calculated before the CP correction was Cs applied.It is also noted that Nguyen et al.4 used the 6-311G** basis [alternatively written as 6-311G(d,p)] at the MP2 level to calculate the equilibrium geometry; however, vibrational frequencies were only calculated at the HF level. Single point calculations at the MP2/6-311G** geometry were performed at the MP4 level, using the 6-311]]G** basis set.The conclusion was that the complex had a geometry, and C3v although the calculations indicated that the complex was bound, inclusion of the CP correction led to an unbound complex (although it was noted therein that the full CP cor- § E-mail: epl=soton.ac.uk î E-mail: tgw=soton.ac.uk rection is considered by some workers as being an overcorrection to the BSSE). It has been noted5 that diÜuse polarization functions are necessary in order to describe the bonding (and hence geometry and vibrational frequencies) of weakly-bound van der Waals species, and also that at least two polarization functions per atom are required (one for the description of the dipolar eÜects, and the other for the quadrupole polarizability eÜects6), especially where dispersion eÜects are important (as they are expected to be here).Consequently, it was decided to reinvestigate the geometry of the complex in order CH4 … HCl to characterize further the and structures obtained pre- C3v Cs viously and to determine whether particular portions of the basis set might be more important than others in determining the minimum energy geometry accurately.In addition, the eÜect of higher levels of theory ought to lead to a more reliable value for the binding energy. Calculational details The calculations were performed using CADPAC7 and GAUSSIAN94.8 The majority of the basis set variation calculations were performed using the MP2 method, with the frozen core (FC) approximation being used, as well as the full method.The basis sets used were mostly standard, including the diÜuse and polarization functions. The variations, and the labels for the resulting basis set, are given in Table 1. Calculations were also performed using the TZ2P basis set,3 with variations systematically carried out, to try to ascertain which parts of the basis set were important in the determination of the minimum energy geometry. These variations and the labels for the resulting basis set are given in Table 2.All optimizations were performed using analytical gradient techniques, with the gradient tolerance made tight enough in each case, such that there were six unprojected frequencies very close to zero. The frequencies were calculated using analytic second derivative methods. The eÜect of including higher correlation methods was investigated by: (i) re-optimizing the geometry at the MP4(SDQ) and QCISD levels, with three basis sets being used for the MP4(SDQ) calculations. In each case, the optimization was started with a structure of symmetry; and (ii) Cs calculating the interaction energy using the CCSD(T)/aug-ccpVTZ method at the MP2/aug-cc-pVTZ geometry.The eÜect of BSSE was accounted for by the application of the full CP J. Chem. Soc., Faraday T rans., 1998, 94(1), 33»38 33Table 1 Various ìstandardœ basis sets useda basis set label notation Cl C H n-basisb (d, f)c 1 6-31G** [6631/631] [631/31]] d [31]] p 59 (6) 2 6-311]]G(2d, 2p) [631111/52111]]MspN]2d [6311/311]]MspN]2d [311]] MsN] 2p 116 (6) 3 6-311]]G(2df, 2p) [631111/52111]]MspN]2df [6311/311]]MspN]2df [311]]MsN]2p 130 (5, 7) 4 6-311]]G(3d, 2p) [631111/52111]]MspN]3d [6311/311]]MspN]3d [311]]MsN]2p 126 (5) 5 6-311]]G(3df, 2p) [631111/52111]]MspN]3df [6311/311]]MspN]3df [311]]MsN]2p 140 (5, 7) 6 Sadlej10 [63111M1N/611M1N/2M2N] [41M1N/2M2N] [41M1N/2M2N] 105 (6) 7 aug-cc-pVTZd [5s4p2d1f]] MspdfN [4s3p2d1f]]MspdfN [3s2p1d]]MspdN 211 (5, 7) 8 TZ2P3 [411111111/41111]]MspN]2d [62111/3111]]MspN]2d [311]]MsN]p 111 a Where MN indicates diÜuse functions ; [ ] indicates contracted functions, in the usual manner.b Number of basis functions for the complex. c 5 (for d) and 7 (for f) implies the use of spherical harmonics for the d and f functions. 6 implies the Cartesian d functions were used. d The uncontracted basis set which leads to the cc-pVTZ basis set has 15 and 9 primitives for the lowest three s and two p contractions, respectively, for Cl; and 8 and 3 primitives for the lowest two s and one p contractions, respectively, for C.The exponents of the diÜuse and polarization functions used in the standard basis sets are as follows. 6-311]]G**: Cl 0.75 (d), 0.0483 (sp) ; C 0.626 (d), 0.0438 (sp) ; H 0.75 (p), 0.036 (s). 6-311]]G(2d, 2p) : diÜuse functions as for 6-311]]G**, polarization functions : Cl 1.5, 0.375 (d) ; C 1.252, 0.313 (d) ; H 1.5, 0.375 (p). 6-311]]G(2df, 2p) : as for 6-311]]G(2d, 2p), except f functions are added to Cl and C, with exponents: 0.7 (Cl) and 0.8 (C). 6-311]]G(3d, 2p) : as for 6-311]]G(2d, 2p), except the two d polarization functions on Cl and C are replaced with three, with exponents: 3.0, 0.75, 0.1875 (Cl) ; 2.504, 0.626, 0.1565 (C). 6-311]]G(3df, 2p) : as for 6-311]]G(3d, 2p), but with the addition of f functions as in the 6-311]]G(2df, 2p) basis set ; aug-cc-pVTZ: Cl polarization 1.046, 0.344 (d), 0.706 (f) diÜuse 0.0591 (s), 0.0419 (p), 0.135 (d), 0.312 (f) ; C polarization 1.097, 0.318 (d), 0.761 (f) diÜuse 0.04402 (s), 0.03569 (p), 0.1 (d), 0.268 (f) ; H polarization 1.407, 0.388 (p), 1.057 (d) diÜuse 0.02526 (s), 0.102 (p), 0.247 (d).Sadlej : Cl polarization0.9528, 0.3580], [0.1250, 0.0436] (d) diÜuse 0.0696 (s), 0.0436 (p) ; C polarization [1.2067, 0.3855], [0.12194, 0.03865] (d) diÜuse 0.047 (s), 0.038 (p) ; H polarization [1.1588, 0.3258], [0.1027, 0.0324] (p) diÜuse 0.0324 (s).TZ2P]diÜ: Cl 1.2, 0.4 (d), 0.0645 (s), 0.0417 (p) ; C 0.7, 0.2 (d), 0.0450 (s), 0.0303 (p) ; H 0.8 (p), 0.0526 (s). correction of Boys and Bernardi.9 In the CP calculations, the geometry of the monomer was –xed at that obtained with the monomer basis set. Results and Discussion The results of the calculations are summarized in Tables 3 and 4. Table 3 gives the symmetry of the geometry at which the optimization was started, together with the symmetry of the resulting optimized geometry.In addition, each optimized structure was characterized via its vibrational frequencies, to see whether it was a minimum or a transition state. Basis sets 1»7 are standard basis sets, with variations in the diÜuse and polarization space; basis set 8 is that used previously3 (the exponents of the polarization and diÜuse functions for these basis sets are given in the footnotes to Table 1) ; and basis sets 9»17 are variants on the basis set used previously.3 The results obtained using exactly the same basis set as that of Craw et al.3 will –rst be described.The geometry was initially optimized under symmetry, and the results were in C3v excellent agreement with those previously obtained,3 in particular that the structure was a transition state, with two C3v imaginary frequencies, see Table 3. The symmetry was then relaxed to but the Cl atom was –xed on the axis, as Cs , C3 was the case previously ;3 this yielded a minimum energy geometry that had all real vibrational frequencies, as would be expected for a minimum.It is interesting to note, however, that subsequently allowing the Cl also to move oÜ axis yielded a geometry of lower energy, but the energy diÜerence was very slight (3.4]10~6 This new geometry was also a Eh). minimum, and demonstrates that the potential energy surface is extremely —at around this region. The question arises, however, as to whether the true calculated minimum energy geometry is or remembering –rstly, that Nguyen et Cs C3v , al.4 obtained a structure of symmetry, and secondly a CP C3v correction along the librational angular coordinate of the potential energy surface yielded a minimum.3 C3v The results in Table 3 demonstrate that very few standard basis sets actually yielded a calculated minimum energy geometry of symmetry [most yielded a structure, which Cs C3v was the case whether the optimizations were started at a Cs symmetry or a symmetry (upper part of Table 3)].This is C3v in contrast to the result using the basis set of ref. 3, where a Cs structure was obtained with the basis set therein (see also Table 3). The question thus arises : what features of the basis set used previously3 can lead to the optimized geometry being rather than To this end, a systematic variation in the Cs , C3v ? basis set was also performed, with the variations used summarized in Table 2, and the results obtained summarized in the lower part of Table 3.Basis set variation at the MP2 level The TZ2P basis set3 (basis set 8), augmented with diÜuse functions, gave a optimized geometry. The underlying basis sets Cs Table 2 Variations in the TZ2P basis set of Craw et al.3 basis set label underlying basis set diÜuse region polarization regiona n-basisb 9 6-31G as ref. 3 as ref. 3 84 10 cc-pVDZ as ref. 3 but MspN on H standard 87 11 cc-pVTZ as ref. 3 but MspN on H standard 177 12 as ref. 3 except [7s5p] for Cl as ref. 3 as ref. 3 106 13 as ref. 3 except [7s5p] for Cl as ref. 3 as ref. 3 but two p for H 121 14 6-311G, but [9s5p] for Cl as ref. 3 as ref. 3 107 15 as ref. 3 as ref. 3 as ref. 3 but two p for H 126 16 as ref. 3 as ref. 3 as ref. 3 but diÜerent exponent 111 for the two C d functions 17 as ref. 3 as ref. 3 two p on H, and diÜerent exponent 141 for the two C d functions a Where the additional non-standard polarization functions mentioned in the table are as follows : H 0.388, 1.407 (p) ; C 0.318, 1.097 (d).b Number of basis functions. 34 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Table 3 Summary of the optimized geometries obtained for the Complex CH4 Æ HCl no. of starting optimized imaginary [total energy/ basis set MP2 (full)a geometry geometry frequencies Eh]500 1 N Cs C3v 0 0.571476 1 Y C3v C3v 0 0.586916 2 Y Cs C3v 0 0.748205 3 N C3v C3v 0 0.701297 4 Y C3v C3v 0 0.782489 5 N C3v C3v 0 0.707112 6 Y Cs C3v 0 0.682987 7 Y Cs C3v 0 0.787839 8 Y Cs b Cs b 0 0.835647 8 Y C3v C3v 2 0.835538 9 Y Cs C3v 0 0.636938 10 Y Cs C3v c 0 0.622507 11 Y Cs C3v 0 0.789393 12 Y Cs Cs 0 0.569773 13 Y Cs Cs 0 0.576043 14 Y Cs C3v 0 0.828518 15 Y C3v C3v 0 0.841283 16 Y C3v C3v 2 0.840241 17 Y Cs C3v 0 0.847310 a N indicates the frozen core approximation was employed; Y indicates no orbitals were frozen.b Two diÜerent structures were found, one Cs with the Cl axis –xed on the axis and one where both the H and Cl atoms moved oÜ of the axis.Neither of these had imaginary C3 C3 frequencies. The energy quoted in the table is for the one with the both H and Cl oÜ-axis. c A geometry that was very slightly oÜ of was C3v obtained here, but the surface was extremely —at. used were the contracted basis sets of Dunning: [9s5p] for Cl; [5s,4p] for C; and [3s] for H. These are not strictly triple-zeta quality for all the atoms concerned: for Cl the p region is slightly less than triple-zeta quality and for C the p region is slightly more than triple zeta, with the s region slightly less.Thus there is an imbalance in the underlying basis set, in particular it is noted that going from 5s to 9s between C and Cl seems to emphasize the s region of Cl unduly, compared to C. In addition, as the footnotes in Table 1 show, the hydrogens really only have diÜuse s character, and one p polarization function. As noted in the Introduction, dispersion eÜects need two polarization functions, at least one of which should be diÜuse.Since the main bonding here is through the hydrogens (whether in or orientation), then it would appear that C3v Cs they ought to be described adequately (and equally with the C and Cl atoms) in order to obtain a reliable geometry. It is clear that the interactions in this complex are extremely weak, and so the balance of the basis set will be crucial to a reliable calculated geometry.In summary, there not only could be an imbalance in the underlying basis set in ref. 3, but the polarization and diÜuse regions appear better described for Cl and C than for H. Variations of the basis set used by Craw et al. were then carried out to test the above ideas. The results of Table 3 shows that it is a mixture of the polarization functions and the underlying basis set that determines the calculated geometry here. In particular, two sets of p functions are necessary in order to obtain the geometry in the main.It is clear from C3v the results using the basis sets of Table 1 (standard basis sets), and the larger of the basis sets derived from that used in ref. 3 [in particular, basis sets 11, 15 and 17 (Table 2)] that the C3v geometry is the more reliable. It may be concluded that a balanced basis set with ì sufficient œ diÜuse and polarization functions appears to lead to the ìcorrectœ description of the intermolecular interactions and, consequently a structure here.For the other basis C3v sets, it would appear that there is a delicate balance of both the underlying basis set and the added polarization and diÜuse functions, and that changing the characteristics of the basis set slightly can lead to a change in the calculated Table 4 The calculated intermolecular bond length and intermolecular harmonic vibrational frequencies for the complex CH4 Æ HCl (C3v minima only) vibrational frequencies/cm~1 basis MP2 set (full)a r(CwCl)/” a1 symmetry e symmetry 1 N 3.9121 73.8 79.4, 124.1 1 Y 3.9017 75.1 79.9, 127.0 2 Y 3.7746 80.8 81.8, 110.1 3 N 3.7731 83.4 88.5, 110.8 4 Y 3.7638 89.1 111.3, 161.4 5 N 3.7749 87.1 105.7, 182.5 6 Y 3.6667 109.6 167.0, 294.4 7 Y 3.6603 105.2 124.0, 181.7 9 Y 3.8252 85.4 112.2, 174.6 10 Y 3.8719 75.8 81.0, (82.3/89.5)b 11 Y 3.7494 88.0 114.1, 187.5 14 Y 3.8511 75.4 29.3, 124.4 15 Y 3.8030 83.7 49.4, 104.8 17 Y 3.7924 79.2 75.1, 129.8 a N indicates that the frozen-core approximation was used; Y indicates that no orbitals were frozen.b A geometry very slightly oÜ of was C3v obtained here. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 35geometry. A more sensitive test of the intermolecular bonding is the intermolecular bond length and the vibrational frequencies, and these are now considered. Intermolecular bond length and vibrational frequencies. The general trend for the intermolecular bond length (Table 4) is that the more polarization and diÜuse functions added, the shorter the bond length.In particular, the shortest bond lengths are obtained with the aug-cc-pVTZ and Sadlej basis sets (ca. 3.667 and 3.660 respectively), where the aug-cc- Aé , pVTZ basis set is the largest one used here with a signi–cant quantity of diÜuse and polarization functions (in particular, diÜuse polarization functions), and the Sadlej basis set is also rich in diÜuse polarization functions, and is designed for the study of molecular electrical properties.10 The increase in the size of the basis set between these two is considerable (105» 211 basis functions) and when compared to the modest decrease in the bond length, it might be assumed that the basis set eÜect is saturated.The intermolecular vibrational frequencies (Table 4) suggest that this is not quite so clear cut, however, as one of the degenerate e vibrational modes changes from 181.7 to 294.4 cm~1 between these two basis sets : note, however that the 6-311]]G(3df, 2p) basis set (140 basis functions) yields similar results to the aug-cc-pVTZ basis set.In fact these, together with the results of the MP2/6- 311G(3d, 2p) calculation indicates that it is the three d functions that are giving the higher values of the frequency for this mode (and do not change the intermolecular bond length signi–cantly). An analysis of the normal coordinates for this vibration show that it is in fact the librational motion, corresponding to a movement of the HCl moiety oÜ-axis»the description of the potential energy in this direction is therefore very sensitive to the d orbital space.Looking at these results, and that obtained with the Sadlej basis set, it appears clear that it is the most diÜuse d function that is critical. It seems that at the MP2 level, the aug-cc-pVTZ basis set gives the best picture of the bonding in this complex, where there is a large underlying basis set, and also diÜuse s, p, d and f functions. The TZ2P basis set used previously3 does not have a and so is not included in Table 4; however, the C3v minimum, variants on the basis set, which led to a minimum, are.It C3v may be seen that the intermolecular bond lengths are ca. 0.2 Aé longer than the aug-cc-pVTZ basis set, not that unreasonable, but the intermolecular vibrational frequencies show a very large scatter. In line with some of the observations made above, it is felt that this is due to imbalances present in this basis set, and even very modest changes in the basis set are leading to large changes in the calculated frequencies.A point about the MP2 energies ought to be mentioned at this juncture : it can be seen (Table 3) that the basis set used previously gives a very low MP2 total energy compared to some of the large basis sets (even lower than the aug-cc-pVTZ basis set) ; however, this is not the case at the HF level, where the calculated energies follow the expected ordering as indicated by the size of the basis set.Some attempt to shed light on this oddity was made, in particular, the energy of the isolated HCl moiety was calculated and it was found that the same sudden lowering occurred at the MP2 level, and not at the HF level. In addition, even when the underlying basis is changed to 6-311G for C and H, but is left as [9s5p] for Cl (basis set 14), the dramatic lowering in energy is still present. Thus, there is some peculiarity here, caused by the use of the Cl [9s5p] basis set in the MP2 procedure, but no further attempts were made to isolate the problem further. Calculated geometry at higher levels of theory Higher level calculations were performed in order to ascertain the eÜects of higher-order electron correlation eÜects on the calculated geometry.This proved to be more problematical than anticipated : at both the MP4(SDQ) and QCISD levels, the surface is so —at that although the energy gradient converged fairly straightforwardly, the displacement criterion did not (this implies that the energy changes are very small for relatively signi–cant changes of the geometry around the minimum).Table 5 shows the angle of the HCl to the axis C3 at the last geometry obtained when the very —at potential energy region was encountered, i.e. where the energy changes between successive points near the minimum were \10~6 Eh . The MP4(SDQ) calculations were carried out with three basis sets : 6-311]]G**, 6-311]]G(2d, 2p) and 6-311]]G(3df, 2p).The smallest basis set led to an unconverged geometry, when after 28 optimization steps, the energy gradient was still rather large and so the optimization was halted. For the second basis set, the initial optimization led to a geometry with the HCl oÜ-axis by B3.5° [both for the MP4(SDQ) and QCISD methods]. For the MP4(SDQ) method, the convergence criteria for the wavefunction and the gradient were then tightened and this led to an angle of only 0.7°.Similarly, with the largest of the basis sets the tight criterion led to an angle of only 0.2°, with the energy changing by \10~6 at Eh this point. At the point that the QCISD/6-311]]G(2d, 2p) calculation was halted, it had started to change symmetry from to the calculation was then restarted under Cs C1; C1 symmetry, but again the gradient converged, while the geometry was still changing signi–cantly. Nontheless, the energy diÜerence between the structure (Table 5) and the Cs structure was \10~6 indicating the surface is —at in C1 Eh , more than one direction at this level of theory.Despite this slightly diÜerent behaviour between the MP4(SDQ) and QCISD methods using the 6-311]]G(2d, 2p) basis set, they lead to broadly similar results. Dissociation energy. The calculated dissociation energy at the MP2 level employing the two largest basis sets is shown in Table 6. It may be seen that the CP correction is of the order of 1 kcal mol~1, indicating that the basis sets are close to saturation ; however, the dissociation energy is so small that the BSSE is a signi–cant percentage of the dissociation energy.It is a philosophical point as to whether an in–nite basis set would lead to a zero BSSE as calculated by the full CP approach, especially at the correlated level. From the experience of a large number of calculations, a BSSE of ca. 0»1 kcal mol~1 appears to indicate merely that the basis set is very close to saturation.The higher level CCSD(T) single point calculation indicates that the MP2 result, as far as the CP-corrected energy is concerned, is fairly reliable. The ZPVE correction destabilizes the complex slightly. These calculations suggest that at the low temperatures in a molecular beam the complex is stable, as is seen experimentally, but that at even moderate temperatures the complex will be unstable. It is noted that Craw et al.3 calculated the complex to be stable at the MP2 level (both with and without CP correction, yielding values of 0.81 and Table 5 Calculated geometry at higher levels of theory [total energy] level of theory 500/Eh r/” last ha/degrees MP4(SDQ)/ 0.699979 3.8576 0.73 6-311]]G(2d, 2p) MP4(SDQ)/ 0.704967 3.8498 0.21 6-311]]G(3df, 2p) QCISD/ 0.700371 3.8813 3.48 6-311]]G(2d, 2p) a This was the last angle in the optimization before the energy changes were insigni–cant (\10~6 The MP4(SDQ) calculation Eh).had a tighter convergence criterion than the QCISD: the MP4(SDQ)/ 6-311]]G(2d, 2p) optimization was also performed with this less stringent criterion, and gave, then, an angle of 3.5° (see text). 36 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Table 6 Calculated dissociation energies MP2(full)/6-311]]G(3df, 2p) MP2(full)/aug-cc-pVTZ CCSD(T) (FC)/aug-cc-pVTZ//MP2(full)/aug-cc-pVTZ *Ee/kcal nol~1 [1.500 [2.374 » *Ee(CP)/kcal mol~1 [0.970 [0.153 [0.985 *Ee(CP)] [0.067 [0.163 ]0.005 ZPVE/kcal mol~1 *H298(CP)/kcal mol~1 [0.017 [0.177 [0.009 *S/ cal mol~1 K~1 [15.477 [16.56 » 1.1 kcal mol~1, respectively ; but the ZPVE was not included), as do Nguyen et al.4 (best value is 1.0 kcal mol~1).The latter authors also calculated the dissociation energy at the MP4 level, and obtained a value of 1.0 kcal mol~1. It was noted, however, that the complex was unbound when the CP correction was employed.4 The CCSD(T) calculations in the present work (including CP and ZPVE corrections) are the highest level to date, and do seem to imply that the complex is stable at very low temperatures, in agreement with the observation of the complex in molecular beams.Isotopic substitution and comparison with the experimental values The vibrational frequencies and the rotational constants were calculated for some isotopically substituted complexes, and the results are shown in Table 7. The two microwave spectroscopy experiments1,2 derived rotational constants for the ground vibrational level giving results in fairly good agreement with those obtained here, which are equilibrium values. Similar trends between the variations of these constants are observed in the experiment and calculations.As an example, for the isotopomer the vibrational ground state CH4 Æ H35Cl value was observed to be B2.9 GHz (0.097 cm~1), compared with a calculated value of 3.36 GHz (0.112 cm~1) obtained here. This agreement might not be as close as it could be as the complex is extremely —oppy, even with only the ZPVE present,2 and so it is probable that the geometry diÜers sig- re ni–cantly from the structure.r0 There is only a limited amount of information on the intermolecular vibrational frequencies of this complex. Ohshima and Endo2 estimated the intermolecular stretch frequencies for various isotopomers, from the values of the centrifugal distortion constants for each of the methane internal rota- (DJ), tional levels.Values of 57»58 cm~1 were obtained, in general, which compared rather poorly with the calculated stretch vibrational frequency values here (Table 4, under a1 symmetry). Given that the experimental value is obtained using a pseudodiatomic picture, and that the complex is very —oppy, perhaps this poor agreement is not entirely unexpected. Internal rotational states were also calculated elsewhere, 2 but a de–nitive value for the parameter was not V3 able to be obtained, thus also not allowing an accurate picture of the internal rotor levels to be deduced.Two internal rotational axes, which were assumed in ref. 2, were labelled s and h: [s corresponded to motion around a axis, whilst h cor- C3v responded to movement away from the intermolecular axis (see Fig. 2 of ref. 2)]. Analysis of the normal modes calculated in this work indicate that this is a simplistic picture : although both the stretch and the h internal rotation are relatively clear from the normal modes calculated here, the other internal rotation (s) is not so clear. There does not appear to be any more experimental information on the intermolecular vibrational modes of this complex.Of note is that the higher of the two intermolecular e modes, second lowest vibrational frequency of e symmetry overall, (assigned to the librational motion of the HCl moiety), is particularly sensitive to deuteration of the HCl, as would be expected.Other modes also show strong isotopic dependences. Of note here, however, is that the intermolecular stretch (lowest vibrational frequency of symmetry) is only weakly isotope dependent. a1 Finally, the microwave studies derived values for the CwCl distance of B3.94 (and these compare quite favourably with ” the calculated values ofB3.66 at the MP2 level, using large re ” basis sets remembering that these will be values). r0 Conclusions The eÜect of the basis set on the calculated equilibrium geometry of the complex has been studied at the CH4 Æ HCl MP2 level of theory.It is found that the resulting geometry can depend on some quite subtle eÜects of the basis set. The most important feature for this complex appeared to be the provision of two sets of p polarization functions on the hydrogen atoms. The intermolecular vibrational frequencies Table 7 Calculated rotational constants and vibrational frequencies for some isotopomers of the complex (values obtained at the CH4 Æ HCl MP2(full)/aug-cc-pVTZ level of theory) CH4 Æ H35Cl CD4 Æ H35Cl CD4 Æ D35Cl CD4 Æ H37Cl CH4 Æ H37Cl CH4 Æ D37Cl equilibrium 158.7418 79.4319 79.4319 79.4319 158.7418 158.7418 rotational 3.3565 2.8366 2.8366 2.7961 3.3004 3.2999 constants/GHz 3.3565 2.8366 2.8366 2.7961 3.3004 3.2999 vibrational a1 symmetry 105.2 91.5 97.1 96.8 104.4 104.0 frequencies/cm~1 1367.4 1033.1 1033.1 1033.1 1367.4 1367.3 3040.4 2175.2 2172.5 2175.2 3038.2 2178.1 3076.2 2368.7 2183.1 2368.7 3076.1 3074.9 3201.2 3041.1 2368.7 3039.4 3201.2 3021.1 e symmetry 124.1 88.5 88.5 88.4 124.0 123.8 181.7 181.5 129.6 181.5 181.6 129.9 1365.7 1031.7 1031.6 1031.7 1365.7 1365.7 1601.2 1132.9 1132.6 1132.9 1601.2 1601.0 3193.8 2364.7 2364.7 2364.7 3193.8 3193.7 J.Chem. Soc., Faraday T rans., 1998, V ol. 94 37appeared to be sensitive to the basis set as well, with the librational mode (bending of HCl oÜ the axis) being particu- C3 larly so. A good description of the potential energy surface along this coordinate appeared to need three d functions on the non-hydrogen atoms, and it was concluded that the most diÜuse d function was having the greatest eÜect.The complex was computed to be bound at the levels of theory used here, even when BSSE and ZPVE had been accounted for. Finally, it is noted that at higher levels of theory [MP4(SDQ), QCISD], the surface appears to become even —atter than at the MP2 level. This complex is clearly a challenge to ab initio methods.authors are grateful to the EPSRC for the award of com- The puting time at the Rutherford Appleton Laboratories, and to Dr J. Altmann for technical support. E.P.E.L. is grateful to the Hong Kong Polytechnic University for support during this work. 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