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Basis set superposition errors in intermolecular structures and force constants
Volume 183, number 3,4
CHEMICAL PHYSICS LETTERS
30 August 1991
Basis set superposition errors in intermolecular structures and force constants Rolf Eggenberger, Stefan Gerber, Hanspeter
Huber and Debra Searles
Instirutftir Physikalische Chemie der UniversitiitBasel, Kiingelbergstrasse 80, CH-4056 Basel, Switzerland Received 10 May 1991; in final form 19 June 1991
It is now generally accepted that one has to correct the energies for the basis set superposition error in the ab initio calculation of intermolecular complexes. However, we call into question the commonly used procedure (at least for weak complexes with only small electrostatic interactions), where, after a normal gradient optimization, the energy iscorrected in a single-point calculation We investigate the influence of the counterpoise correction on the intermolecular structure and force constants in weak complexes. With a 6-3 I G** basis set, intermolecular distances may be wrong by 30 to 50 pm and frequencies by a factor of 2 to 4.
1. Introduction Two decades after recognizing the basis set superposition error (BSSE) in the supermolecule approach to intermolecular complexes, there seems to be a consensus that one has to correct for it (for a detailed discussion, see, e.g. ref. [ 1 ] ). Although there is still some controversy regarding the proper method, there is a strong tendency [ 21 to agree upon the full counterpoise correction by Boys and Bernardi [ 3 1. Some authors have developed nearly BSSE-free basis sets [ 41; however, they have only been successful for SCF calculations. Recently, Parasuk et al. [ 5 ] have shown that even in tightly bound systems, one has to consider the BSSE. Many authors (see, e.g. ref. [ 61) correct for the BSSE routinely, whereas others still prefer to neglect it. A commonly used procedure for correcting the BSSE is that the geometry is optimized without correction of the BSSE, and then the correction is evaluated in a single-point calculation (referred to as SPC hereafter) at the minimum. The advantage of this procedure is that first- and second-gradient methods can be applied. However, one might not only question whether the structure and vibrational frequencies thus obtained are correct, but also the energies obtained are dubious as they might not correspond to the real minimum. Few authors have investigated the influence of the BSSE on the structure (see, e.g.
refs. [ 7- 12 ] ) and we are aware of only one investigation of its influence on the intermolecular vibrational frequency [ 131. All but two of these studies were concerned with hydrogen-bonded complexes, where the effect might be quite different from that in weak complexes [ lo]. These studies showed that the change in equilibrium distances after applying the counterpoise correction is quite large for minimal and double-zeta basis sets. However, after inclusion of polarization functions, it becomes smaller than 5 pm (6-3 1G**) [7-l 2 1. The effect on the frequencies [ 131 is very small (about 1% for the diagonal elements of the force-constant matrix), and much smaller than the changes due to different basis sets. The two studies on nonpolar systems [ 8,9] contain few data, making a generalization difficult. Hobza et al. [ 81 find a change in the intermolecular equilibrium distance of the (H,), of only 6.4 pm with a [ 4s2p] basis set, whereas Chalasinski et al. [ 91 give data for grid points which could yield larger changes for Ar, and Mg,. The purpose of this Letter is to show, using two weak complexes without hydrogen-bonds, Ne, and (CO,),, how the change from strongly to weakly bonded complexes influences the effect of the BSSE on the intermolecular equilibrium distances and the vibrational frequencies. Furthermore, we examine the error remaining in the energy if the counterpoise correction is applied using SPC.
0009-26 14/91/$ 03.50 0 I99 I Elsevier Science Publishers B.V. All rights reserved.
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Volume 183, number 3,4
2. Computational methods For comparison, both complexes were calculated with the 6-3 lG** (identical to 6-3 lG*, as no hydrogens are present ) basis set as a well-known standard (no diffuse functions were therefore added ) . In addition, we used larger basis sets. For Nez, a 631G** t basis set with a diffuse sp shell and a ( 14s lop ) / [ 7s6p] basis set by Huzinaga and Klobukowski [ 141 enlarged by 4d and If was used (for details see ref. [ 151). For (CO,),, the DZP basis set used by Bone and Handy in ref. [ 161 and, for a few calculations, the contracted 5s4p2d basis of Simandiras et al. [ 171 were used. For the structure of ( C02)2, see ref. [ 181. The calculations were performed on VAX and CRAY computers with the program packages CADPAC [ 191 and GAUSSIAN 90 [ 201. Correlation was included in all calculations on different levels by Meller-Plesset (MP) perturbation theory. In the cases mentioned, the BSSE was corrected by the full counterpoise method [ 31.
3. Results and discussion Table 1 shows, the influence of the counterpoise correction on different properties of Ne, with different basis sets and levels of correlation. The table shows that for the smaller basis sets, the difference between the MP2 and MP4 (SDTQ) levels are negligible and even for the largest basis, the effects are small with the exception of the interaction energy. In contrast; the effect of the basis-set size and the counterpoise correction is huge for all three
properties. A comparison of the 6-3 1G** results, the 6-3lG**+ results and the experimental values for R, (equilibrium distance) and v (frequency) show that a counterpoise correction is meaningless if the basis set is too small. In contrast to the situation for hydrogen-bonded complexes where the change in R, is only about 5 pm [ 7, lo- 121 and the change in Y is negligible [ 13 ] (with a basis set of a quality comparable to the 6-3 IG** basis), here we have to deal with a AR, of 58 pm and v changes by more than a factor of four. This is partially due to the different physical situation (weak dispersion forces rather than strong electrostatic forces), and partially to the fact that a basis which is nearly saturated on the SCF level is, by far, not saturated if correlation is taken into account. Table 2 gives the corresponding results for (CO,),. This complex should exhibit properties between those of hydrogen-bonded complexes and rare gases, as the dispersion forces and the electrostatic forces due to the quadrupole moment are of similar importance. All calculations with the 6-3lG** and the DZP basis sets were performed within the rigid-monomer assumption (in contrast to refs. [ 18,161, where full optimizations were applied). Therefore, the results cannot be directly compared with experiment. Only in-plane frequencies were calculated. The extent to which the rigid-monomer approximation changes the frequencies is seen by comparing the noncorrected results in table 2 with previous full optimizations: for the b,, a,, a8 vibrations, the frequencies are 33, 48, 109 cm-‘, respectively, with the 6-3lG** basis [18]and22,46,99cm-‘withtheDZPbasis[16].
Table 1 Influence of the counterpoise correction on structure, frequency and interaction energy of NeZ Basis set
6-31G** &31G**cc” 6-3 I G** + 6-31G**+ ccB1 Huz4dlf Huz4dlfcc”’ exp. b,
Interaction energy (I&)
MP2
MP4(SDTQ)
MP2
MP4(SDTQ)
MP2
MP4(SDTQ)
259.0 316.6 312.9 353.2 299.5 326.1
258.7 315.8 309.8 350.3 293.9 317.5 310+5
106 23 36 13 39 21
106 23 38 14 45 25 23.4
-673.9 -53.6 -255.6 -28.8 -263.1 - 74.4
-678.1 -56.1 - 304.4 -34.1 -333.4 - 108.4 -131k5
a) cc denotes counterpoise corrected.
224
v (cm-‘)
& (pm)
‘) Ref. [21].
Volume 183, number 3,4
30 August 1991
CHEMICAL PHYSICS LETTERS
Table 2 Influence of the counterpoise correction on structure and frequencies of (CO,) 2 (slipped parallel conformation; rigid-monomer assump tion; R, is the intermolecular equilibrium distance between the carbons and Q,the angle of the monomers relative !o R,) Basis set
R. (pm)
p (deg)
b, (cm-‘)
a, (cm-‘)
a, (cm-.‘)
f%31ci** 6-3 I G** cc aJ DZP DZP cc =) 5s4pZd 5s4p2d cc a’ exp. d,
347.9 379.5 358.3 385.5 362 b’ 369 b’ 360.0
59.9 58.3 58.5 57.4 56.1 c’
32 16 18 13 18 c’
46 30 42 31 4OC’
97 68 89 66 94 =’
3222
902 I
S8.2
aJccdenotes counterpoise corrected. b1Rough optimization of R, only. ‘) From a full optimization (including intramolecular coordinates) [ IS]. d, Ref. [22].
The point-by-point frequency calculations for the 5s4d2d basis set were not feasible. Again, a large influence of the counterpoise correction on R, as well as on the frequencies can be seen and, again, the correction is not meaningful with the two smaller basis sets. Whereas the BSSE in R, seems to be small for the large 5s4p2d basis set, we might still expect an effect to be observed for the frequencies. In table 3, we compare the noncorrected interaction energy, E”, with the SPC-corrected one, Eb (the usually applied procedure) and the interaction energy corrected in the proper way, EC, i.e. the energy at minimum of the corrected potential energy surface. There can be no doubt that a correction of the BSSE is necessary (compare, e.g. with the experimental interaction energy of Ne,; an example of some interest is also the dimer of HF, which with the 63 1G** basis set and the inclusion of electron correlation through MP2 results in the slipped parallel conformation with the gradient optimization, i.e.
without correction of the BSSE!). However, it is also shown that the SPC correction (which is always larger than the proper one, as the latter is at the minimum of the corrected surface) can overshoot by a large amount, yielding even positive interaction energies in the case of pure dispersion forces. In such a case, a SPC correction is not justified even with large basis sets. Nevertheless, in complexes like (CO,),, the correction may be applied using SPC, although it overshoots by about 20%.
4. Conclusions Several conclusions can be drawn from these and previous results by other authors [7-l 31: - If a compromise due to limited computer capacity is necessary, it is clearly preferable to use a large basis set on the MP2 level than to use a small basis set on a higher level. - It is also better to stay on the MP2 level and to
Table 3 Interaction energies obtained in different ways (in p-E,,) Molecule
Basis set
Ne2
6-3 IG** 6-31G**+ Huz4dlf 6-31G** DZP
(CO,),
MP4(SDTQ) MP4(SDTQ) MP4(SDTQ) MP2 MP2
-678.1 - 304.4 - 333.4 - 2996.9 -2493.1
Ebb’
E’E,
517.7 17.9 -67.2 -832.5 -‘898.3
-56.1 - 34. I - 108.4 - 1138.2 -1107.8
a) Energy obtained at the minimum ofthe potential energy surface without counterpoise correction. b, Energy obtained as above but including the counterpoise correction with a single-point calculation (SPC). ‘) Energy obtained at the minimum of the counterpoise corrected potential energy surface.
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CHEMICAL PHYSICS LETTERS
apply the counterpoise correction than to go to the MP4( SDTQ ) level without correction. - The correction should not be applied using SPC, even with large basis sets, for very weak complexes where dispersion forces are dominant. Applying SPC is a reasonably good approximation if strong electrostatic forces are present.
Acknowledgement
This investigation is part of the Project 2029924.90 of the Schweizerischer Nationalfonds zur Fijrderung der Wissenschaften. The work was supported by the CIBA-Stiftung and by grants of computer time on the CRAY XMP at the ETH-Ziirich and the CRAY-2 at the EPFL-Lausanne and on the VAX-8840 at the University of Basel. We thank the staff of the computer centres for their assistance.
References [ 11P. Hobza and R. Zahradnik, Chem. Rev. 8X ( 198X) X71; J.H. van Lenthe, J.G.C.M. van Duijneveldt-van de Rijdt and F.B. van Duijneveldt, Advan. Chem. Phys. 69 (1987) 521. [ 21 M. Gutowski, F.B. van Duijneveldt, G. Chalasinski and L. Piela, Mol. Phys. 61 ( 1987) 233; G. Chalasinski and M. Gutowski, Chem. Rev. X8 ( 1988) 943, and references therein. [ 31 SF. Boys and F. Bernardi, Mol. Phys. 19 ( 1970) 553. [ 41 Z. Latajka and S. Scheiner, .I. Comput. Chem. 8 ( 1987) 663. [ 51V. Parasuk, J. Almliifand B. DeLeeuw, Chem. Phys. Letters 176 (1991) 1. [6] W. Meyer, P.C. Hariharan and W. Kutzelnigg, J. Chem. Phys. 73 ( 1980) 1880; G. Chalasinski, R.A. Kendall and .I. Simons, J. Chcm. Phys. 87 (19X7) 2965; Y. Bouteiller, C. Mijoule, M.M. Szczesniak and S. Scheiner, J. Chem. Phys. 8X ( 1988) 486 I;
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30 August 1991
B. Schneider, P. Hobza and R. Zahradnik, Theoret. Chim. Acta 73 (1988) 201; R.J. Vos, R. Hendriks and F.B. yan Duijneveldt, J. Comput. Chem. 11 (1990) 1; G. Chalasinski, M.M. Szczesniak and S. Scheiner, J. Chem. Phys.94 (1991) 2807. [ 71 M.D. Newton and N.R. Kestner, Chem. Phys. Letters 94 (1983) 198. [8] P. Hobza, B. Schneider, J. Sauer, P. Carsky and R. Zahradnik, Chem. Phys. Letters 134 ( 1987) 4 18. [9]G. Chalasinksi, D.J. Funk, J. Simons and W.H. Breckenridge, J. Chem. Phys. 87 (1987)3569. [lo] G. Alagona, C. Ghio, R. Cammi and J. Tomasi, Intern. I. Quantum Chem. 32 (1987) 207. [ 1 I ] G. Alagona, C. Ghio and J. Tomasi, J. Phys. Chem. 93 (1989) 5401. [ 121 G. Alagona, C. Ghio, 2. Latajka and J. Tomasi, J. Phys. Chem. 94 (1990) 2267. [ 131J.M. Leclercq, M. Allavena and Y. Bouteiller, J. Chem. Phys. 78 (1983) 4606. [ 141 S. Huzinaga and M. Kiobukowski, J. Mol. Struct. THEOCHEM 167 (1988) 1; T.W. Dingle, S. Huzinaga and M. Klobukowski, J. Comput. Chem. 10 (1989) 753. [ 151 R. Eggenberger, S. Gerber, H. Huber and D. Searles, Chem. Phys., to be published. [ 161 R.G.A. Bone and NC. Handy, Theoret. Chim. Acta 78 (1990) 133. [ 171 E.D. Simandiras, NC. Handy and R.D. Amos, Chem. Phys. Letters 133 ( 1987) 324. [ 181 R. Eggenberger, S. Gerber and H. Huber, Mol. Phys. 72 (1991) 433. [ 191 R.D. Amos and J.E. Rice, CADPAC: The Cambridge Analytic Derivatives Package, issue 4.0, Cambridge, 1987. [20] M.J. F&h, M. Head-Gordon, G.W. Trucks, J.B. Foresman, H.B. Schlegel, K. Raghavachari, M.A. Robb, J.S. Binkley, C. Gonzalez, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. M&us, J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart, S. Topiol and J.A. Pople, GAUSSIAN 90, Gaussian Inc., Pittsburgh, PA, 1990. [ 2 I] G.C. Maitland, Mol. Phys. 26 (1973) 513. [22 ] M.A. Walsh, T.H. England, T.R. Dyke and B.J. Howard, Chem. Phys. Letters 142 (1987) 265; K.W. Jucks,Z.S. Huang, R.E. Miller, G.T. Fraser, A.S. Pine and W.J. Lafferty, J. Chem. Phys. XX(1988) 2185.
CHEMICAL PHYSICS LETTERS
30 August 1991
Basis set superposition errors in intermolecular structures and force constants Rolf Eggenberger, Stefan Gerber, Hanspeter
Huber and Debra Searles
Instirutftir Physikalische Chemie der UniversitiitBasel, Kiingelbergstrasse 80, CH-4056 Basel, Switzerland Received 10 May 1991; in final form 19 June 1991
It is now generally accepted that one has to correct the energies for the basis set superposition error in the ab initio calculation of intermolecular complexes. However, we call into question the commonly used procedure (at least for weak complexes with only small electrostatic interactions), where, after a normal gradient optimization, the energy iscorrected in a single-point calculation We investigate the influence of the counterpoise correction on the intermolecular structure and force constants in weak complexes. With a 6-3 I G** basis set, intermolecular distances may be wrong by 30 to 50 pm and frequencies by a factor of 2 to 4.
1. Introduction Two decades after recognizing the basis set superposition error (BSSE) in the supermolecule approach to intermolecular complexes, there seems to be a consensus that one has to correct for it (for a detailed discussion, see, e.g. ref. [ 1 ] ). Although there is still some controversy regarding the proper method, there is a strong tendency [ 21 to agree upon the full counterpoise correction by Boys and Bernardi [ 3 1. Some authors have developed nearly BSSE-free basis sets [ 41; however, they have only been successful for SCF calculations. Recently, Parasuk et al. [ 5 ] have shown that even in tightly bound systems, one has to consider the BSSE. Many authors (see, e.g. ref. [ 61) correct for the BSSE routinely, whereas others still prefer to neglect it. A commonly used procedure for correcting the BSSE is that the geometry is optimized without correction of the BSSE, and then the correction is evaluated in a single-point calculation (referred to as SPC hereafter) at the minimum. The advantage of this procedure is that first- and second-gradient methods can be applied. However, one might not only question whether the structure and vibrational frequencies thus obtained are correct, but also the energies obtained are dubious as they might not correspond to the real minimum. Few authors have investigated the influence of the BSSE on the structure (see, e.g.
refs. [ 7- 12 ] ) and we are aware of only one investigation of its influence on the intermolecular vibrational frequency [ 131. All but two of these studies were concerned with hydrogen-bonded complexes, where the effect might be quite different from that in weak complexes [ lo]. These studies showed that the change in equilibrium distances after applying the counterpoise correction is quite large for minimal and double-zeta basis sets. However, after inclusion of polarization functions, it becomes smaller than 5 pm (6-3 1G**) [7-l 2 1. The effect on the frequencies [ 131 is very small (about 1% for the diagonal elements of the force-constant matrix), and much smaller than the changes due to different basis sets. The two studies on nonpolar systems [ 8,9] contain few data, making a generalization difficult. Hobza et al. [ 81 find a change in the intermolecular equilibrium distance of the (H,), of only 6.4 pm with a [ 4s2p] basis set, whereas Chalasinski et al. [ 91 give data for grid points which could yield larger changes for Ar, and Mg,. The purpose of this Letter is to show, using two weak complexes without hydrogen-bonds, Ne, and (CO,),, how the change from strongly to weakly bonded complexes influences the effect of the BSSE on the intermolecular equilibrium distances and the vibrational frequencies. Furthermore, we examine the error remaining in the energy if the counterpoise correction is applied using SPC.
0009-26 14/91/$ 03.50 0 I99 I Elsevier Science Publishers B.V. All rights reserved.
223
30 August 199 I
CHEMICAL PHYSICS LETTERS
Volume 183, number 3,4
2. Computational methods For comparison, both complexes were calculated with the 6-3 lG** (identical to 6-3 lG*, as no hydrogens are present ) basis set as a well-known standard (no diffuse functions were therefore added ) . In addition, we used larger basis sets. For Nez, a 631G** t basis set with a diffuse sp shell and a ( 14s lop ) / [ 7s6p] basis set by Huzinaga and Klobukowski [ 141 enlarged by 4d and If was used (for details see ref. [ 151). For (CO,),, the DZP basis set used by Bone and Handy in ref. [ 161 and, for a few calculations, the contracted 5s4p2d basis of Simandiras et al. [ 171 were used. For the structure of ( C02)2, see ref. [ 181. The calculations were performed on VAX and CRAY computers with the program packages CADPAC [ 191 and GAUSSIAN 90 [ 201. Correlation was included in all calculations on different levels by Meller-Plesset (MP) perturbation theory. In the cases mentioned, the BSSE was corrected by the full counterpoise method [ 31.
3. Results and discussion Table 1 shows, the influence of the counterpoise correction on different properties of Ne, with different basis sets and levels of correlation. The table shows that for the smaller basis sets, the difference between the MP2 and MP4 (SDTQ) levels are negligible and even for the largest basis, the effects are small with the exception of the interaction energy. In contrast; the effect of the basis-set size and the counterpoise correction is huge for all three
properties. A comparison of the 6-3 1G** results, the 6-3lG**+ results and the experimental values for R, (equilibrium distance) and v (frequency) show that a counterpoise correction is meaningless if the basis set is too small. In contrast to the situation for hydrogen-bonded complexes where the change in R, is only about 5 pm [ 7, lo- 121 and the change in Y is negligible [ 13 ] (with a basis set of a quality comparable to the 6-3 IG** basis), here we have to deal with a AR, of 58 pm and v changes by more than a factor of four. This is partially due to the different physical situation (weak dispersion forces rather than strong electrostatic forces), and partially to the fact that a basis which is nearly saturated on the SCF level is, by far, not saturated if correlation is taken into account. Table 2 gives the corresponding results for (CO,),. This complex should exhibit properties between those of hydrogen-bonded complexes and rare gases, as the dispersion forces and the electrostatic forces due to the quadrupole moment are of similar importance. All calculations with the 6-3lG** and the DZP basis sets were performed within the rigid-monomer assumption (in contrast to refs. [ 18,161, where full optimizations were applied). Therefore, the results cannot be directly compared with experiment. Only in-plane frequencies were calculated. The extent to which the rigid-monomer approximation changes the frequencies is seen by comparing the noncorrected results in table 2 with previous full optimizations: for the b,, a,, a8 vibrations, the frequencies are 33, 48, 109 cm-‘, respectively, with the 6-3lG** basis [18]and22,46,99cm-‘withtheDZPbasis[16].
Table 1 Influence of the counterpoise correction on structure, frequency and interaction energy of NeZ Basis set
6-31G** &31G**cc” 6-3 I G** + 6-31G**+ ccB1 Huz4dlf Huz4dlfcc”’ exp. b,
Interaction energy (I&)
MP2
MP4(SDTQ)
MP2
MP4(SDTQ)
MP2
MP4(SDTQ)
259.0 316.6 312.9 353.2 299.5 326.1
258.7 315.8 309.8 350.3 293.9 317.5 310+5
106 23 36 13 39 21
106 23 38 14 45 25 23.4
-673.9 -53.6 -255.6 -28.8 -263.1 - 74.4
-678.1 -56.1 - 304.4 -34.1 -333.4 - 108.4 -131k5
a) cc denotes counterpoise corrected.
224
v (cm-‘)
& (pm)
‘) Ref. [21].
Volume 183, number 3,4
30 August 1991
CHEMICAL PHYSICS LETTERS
Table 2 Influence of the counterpoise correction on structure and frequencies of (CO,) 2 (slipped parallel conformation; rigid-monomer assump tion; R, is the intermolecular equilibrium distance between the carbons and Q,the angle of the monomers relative !o R,) Basis set
R. (pm)
p (deg)
b, (cm-‘)
a, (cm-‘)
a, (cm-.‘)
f%31ci** 6-3 I G** cc aJ DZP DZP cc =) 5s4pZd 5s4p2d cc a’ exp. d,
347.9 379.5 358.3 385.5 362 b’ 369 b’ 360.0
59.9 58.3 58.5 57.4 56.1 c’
32 16 18 13 18 c’
46 30 42 31 4OC’
97 68 89 66 94 =’
3222
902 I
S8.2
aJccdenotes counterpoise corrected. b1Rough optimization of R, only. ‘) From a full optimization (including intramolecular coordinates) [ IS]. d, Ref. [22].
The point-by-point frequency calculations for the 5s4d2d basis set were not feasible. Again, a large influence of the counterpoise correction on R, as well as on the frequencies can be seen and, again, the correction is not meaningful with the two smaller basis sets. Whereas the BSSE in R, seems to be small for the large 5s4p2d basis set, we might still expect an effect to be observed for the frequencies. In table 3, we compare the noncorrected interaction energy, E”, with the SPC-corrected one, Eb (the usually applied procedure) and the interaction energy corrected in the proper way, EC, i.e. the energy at minimum of the corrected potential energy surface. There can be no doubt that a correction of the BSSE is necessary (compare, e.g. with the experimental interaction energy of Ne,; an example of some interest is also the dimer of HF, which with the 63 1G** basis set and the inclusion of electron correlation through MP2 results in the slipped parallel conformation with the gradient optimization, i.e.
without correction of the BSSE!). However, it is also shown that the SPC correction (which is always larger than the proper one, as the latter is at the minimum of the corrected surface) can overshoot by a large amount, yielding even positive interaction energies in the case of pure dispersion forces. In such a case, a SPC correction is not justified even with large basis sets. Nevertheless, in complexes like (CO,),, the correction may be applied using SPC, although it overshoots by about 20%.
4. Conclusions Several conclusions can be drawn from these and previous results by other authors [7-l 31: - If a compromise due to limited computer capacity is necessary, it is clearly preferable to use a large basis set on the MP2 level than to use a small basis set on a higher level. - It is also better to stay on the MP2 level and to
Table 3 Interaction energies obtained in different ways (in p-E,,) Molecule
Basis set
Ne2
6-3 IG** 6-31G**+ Huz4dlf 6-31G** DZP
(CO,),
MP4(SDTQ) MP4(SDTQ) MP4(SDTQ) MP2 MP2
-678.1 - 304.4 - 333.4 - 2996.9 -2493.1
Ebb’
E’E,
517.7 17.9 -67.2 -832.5 -‘898.3
-56.1 - 34. I - 108.4 - 1138.2 -1107.8
a) Energy obtained at the minimum ofthe potential energy surface without counterpoise correction. b, Energy obtained as above but including the counterpoise correction with a single-point calculation (SPC). ‘) Energy obtained at the minimum of the counterpoise corrected potential energy surface.
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CHEMICAL PHYSICS LETTERS
apply the counterpoise correction than to go to the MP4( SDTQ ) level without correction. - The correction should not be applied using SPC, even with large basis sets, for very weak complexes where dispersion forces are dominant. Applying SPC is a reasonably good approximation if strong electrostatic forces are present.
Acknowledgement
This investigation is part of the Project 2029924.90 of the Schweizerischer Nationalfonds zur Fijrderung der Wissenschaften. The work was supported by the CIBA-Stiftung and by grants of computer time on the CRAY XMP at the ETH-Ziirich and the CRAY-2 at the EPFL-Lausanne and on the VAX-8840 at the University of Basel. We thank the staff of the computer centres for their assistance.
References [ 11P. Hobza and R. Zahradnik, Chem. Rev. 8X ( 198X) X71; J.H. van Lenthe, J.G.C.M. van Duijneveldt-van de Rijdt and F.B. van Duijneveldt, Advan. Chem. Phys. 69 (1987) 521. [ 21 M. Gutowski, F.B. van Duijneveldt, G. Chalasinski and L. Piela, Mol. Phys. 61 ( 1987) 233; G. Chalasinski and M. Gutowski, Chem. Rev. X8 ( 1988) 943, and references therein. [ 31 SF. Boys and F. Bernardi, Mol. Phys. 19 ( 1970) 553. [ 41 Z. Latajka and S. Scheiner, .I. Comput. Chem. 8 ( 1987) 663. [ 51V. Parasuk, J. Almliifand B. DeLeeuw, Chem. Phys. Letters 176 (1991) 1. [6] W. Meyer, P.C. Hariharan and W. Kutzelnigg, J. Chem. Phys. 73 ( 1980) 1880; G. Chalasinski, R.A. Kendall and .I. Simons, J. Chcm. Phys. 87 (19X7) 2965; Y. Bouteiller, C. Mijoule, M.M. Szczesniak and S. Scheiner, J. Chem. Phys. 8X ( 1988) 486 I;
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