J . Phys. Chem. 1990, 94, 2260-2261
Sllanol as a Model for the Free Hydroxyl of Amorphous Silica: Ab Initio Calculations of the Interaction with Water P. Ugliengo,+V. Saunders,*and E. Gamone*,+ Dipartimento di Chimica Inorganica, Chimica Fisica e Chimica dei Materiali, Universitri di Torino, via P. Giuria 7 10125 Torino, Italy, and S.E.R.C. Daresbury Laboratory, Daresbury, Warrington WA4 4AD, Cheshire, England (Received: March 17, 1989; In Final Form: September I , 1989)
Literature experimental data, both vibrational and energetic, concerning the interaction of water with the isolated hydroxyl of amorphous silica are compared with the results of ab initio calculationsboth Hartree-Fock and correlated through perturbative technique (MP2). Silanol, H,SiOH, is chosen to mimic the silica free hydroxyl. Three modes of interaction are considered, envisaging water as a proton donor (I), as a proton acceptor (II), and in a bifurcated configuration. Calculated properties are the binding energy; frequencies and intensities of vibrational motion in the harmonic approximation; anharmonic SiO-H motion, including overtones; enthalpy, entropy, and free energy standard changes of reaction and related adsorption isotherm. The bifurcated configuration is very weakly bound and unstable. Structure I has a nonplanar stable configuration; structure I1 is, however, the most stable. Electrostatic, charge transfer, and dispersive contributions to the binding energy are discussed. Thermodynamicconsiderationsindicate that the former may occur as a few percent of the total coverage. Enthalpy of adsorption and vibrational features are in gross accord with the experiment; calculated adsorption isotherms are definitely in error, due to the inadequacy of the rigid-cluster model used in the computation of these latter. The behavior of silanol toward the water dimer is also discussed.
Introduction Much work has been devoted in the p a ~ t l and - ~ more r e ~ e n t l y ~ , ~ to the study of the interaction between water and silica surfaces, because such systems are of interest in adsorption, catalysis, chromatography, and also in biological studies of inhaled silica particles.l0 Depending on thermal pretreatments, silica exhibits a hydrophilic or hydrophobic behavior. Fully hydroxylated samples readily adsorb water, with an interaction energy higher than the heat of liquefaction of water; dehydroxylated samples are more reluctant, and the initial heat of adsorption is lower than the heat of liquefaction. The present paper considers the extreme aspect of the latter kind of process, i.e., the interaction of one water molecule with the isolated hydroxyl present at the surface of amorphous silica after severe outgassing. Such a system has been already investigated, from both the experimentall-'O and the t h e o r e t i ~ a l l ' - ~ ~ points of view. There was, however, the need for more work on the subject because higher quality calculations were possible, and a full comparison between calculated and experimental features has never been carried out. In general, the interaction of the SiOH group and a water molecule can be of two types, one in which H 2 0 acts as a proton donor in a H bond to the oxygen of SiOH (structures I, and Ib in Figure 1) or the other in which H 2 0 acts as a proton acceptor in a H bond to the hydrogen of SiOH (structure I1 in Figure 1). In the literature, calculations have been carried out assuming as a molecular model for the surface hydroxyl either H3SiOH (silanol) or H,O,SiOH (orthosilicic acid). An alternative termination for the cluster representative of the surface site is by means of fictitious atoms." Semiempirical calculations" have invariably indicated structure I as more stable than structure 11. Ab initio calculations indicate this order of stability only at the STO-3G level, and the reverse for any higher level of treatment.'2-'5 The best available calculation^,^^ actually a 6-31G ( d on Si only), yield interaction energies, uncorrected for basis set superposition error (hereafter BSSE) and zero-point energy, of -19.3 kJ mo1-I for structure I, and -36.0 kJ mol-' for structure 11. No attempt has been made so far to calculate the whole vibrational spectrum of the H,O/SiOH system at the required degree of sophistication, Le., ab initio techniques with large basis sets, nor to study the effect of including electron correlation. Universitl di Torino. *S.E.R.C Daresbury Laborator).
0022-3654/90/2094-2260$02.50/0
Survey of Experimental Data The energy of interaction between H 2 0and the surface of silica outgassed at high temperature has been determined by Basset et aLI6 to be 25 kJ mol-] by a heat of immersion technique, although recent microcalorimetric m e a s ~ r e m e n t s indicate '~ that it could be as low as 13 kJ mol-'. Most experimental work on the S i O H / H 2 0 system has concerned its vibrational features. The major effect in H bonding between an AH and a B molecule is the lowering in frequency of the A-H stretch, which also broadens and intensifies: indeed, the red shift AvOHof the silica hydroxyl from the unperturbed value of 3747 cm-' has been measured upon adsorption of several substance^.^ Relations between AvOH and the molar heat of interaction AHo have been proposed, among which is that advanced by Hair and Hertl:2 AHo (kJ mol-I) = 1.904Av0Hl/2- 9.6
(1)
In the case of the S i O H / H 2 0 interaction, the red shift Avo$ is not easily observed in the fundamental vOH region, because this mode probably overlaps with the modes of coordinated H,O. A
( 1 ) Peri, J. B.; Hensley, A. L., Jr. J . Phys. Chem. 1968, 72, 2926, and references cited therein. (2) Hertl, W.; Hair, M. L. Nafure 1969, 223, 1950. (3) Knozinger, H. In The Hydrogen Bond; Schuster, P., Zundel, G., Sandorfy, C., Eds.; North-Holland: Amsterdam, 1976; Vol. 111, Chapter 27, D 1263. (4) Klier, K. J . Chem. Phys. 1973, 58, 737. ( 5 ) Klier, K.; Shen, J. H.; Zettlemoyer, A. C. J . Phys. Chem. 1973, 77, -I458 (6) Kasansky, V. B.; Gritscov, A. M.; Andrew, V. M.; Zhidomirov, G. M. J . Mol. Catal. 1978, 4 , 135. (7) Anderson, J. H.; Wickersheim, K. A. Surf.Sci. 1964, 2, 252. (8) Zhdanov, S. P.; Kosheleva, L. S.; Titova, T. I . Lnngmuir 1987, 3, 960. (9) Hoffman, P.; Knozinger, E. Surf.Sci. 1987, 188, 181. (10) Fubini, B.; Bolis, V . , Giamello, E. Inorg. Chim. Acfa 1987, 138, 193. ( 1 1) Zhidomirov, G. M.; Kasansky, V. B. Adc. Cafal. 1986, 34, 131, and reference cited therein. (12) Hobza, P.; Sauer, J.; Morgeneyer, C.; Hurych, J.; Zahradnik, R. J . Phys. Chem. 1981, 85, 4061. (13) Sauer, J.; Zahradnik, R. I n f . J . Quanfum Chem. 1984, 26, 793. (14) Sauer, J.; Schroder, K. P. Chem. Phys. Letf. 1984, 107, 530. (15) Chakoumakos, 8 . C.; Gibbs, G. V . J . Phys. Chem. 1986, 90, 996. (16) Bassett, D. R.; Boucher, E. A,; Zettlemoyer, A. C. J . Colloid Interface Sci. 1970, 34, 3. ( I 7 I Fubini, B. Personal communication.
0 1990 American Chemical Society
H,SiOH as Model for Free Hydroxyl of Amorphous Silica
The Journal of Physical Chemistry, Vol. 94, No. 6 , 1990 2261 TABLE I: Binding Energies of Silanol/Water Adducts and Dipolar Moment of WateP H F binding A B C D E F G H MP2 binding A H AZPE
i 066
1125
16391
I
I
III
I!
-14.77 (1.30) -15.31 -16.36 (1.30) -16.77 -11.43 (0.84) -1 1.27 -1 1.35 -1 1.39
-17.00 (1.59) -25.79 (1.46) 2.19 -17.27 -24.45 2.22 -18.35 (1.46) -25.66 (1.59) 2.25 -18.32 -25.45 2.28 -13.31 (1.00) -21.11 (1.05) 2.04 -12.97 -20.32 2.05 -13.01 -20.40 2.05 -13.06 -20.20
-20.44 (4.37) -23.04 (4.91) -31.96 (4.78) 2.1 1 -17.22 -19.09 -26.14 6.32 7.20 6.86
"Corresponding BSSE in parenthesis. AZPE = ZPE(complex) ZPE(free components). Energetic data in kilojoules per mole; dipole moments in debyes. Basis sets description: A = DZ(p,d); B = DZ+(p,d); C = TZ(p,d); D = TZ+(p,d); E = T Z ( 2 ~ , 2 d ) ;F = TZ+(2p,2d); G = TZ++(2p,2d); H = TZ1+(2p,2d). Hydrogen scale factor: 1.2, A to B; 1.0, C to H. A to B, (IOs5pld;4slp)/[3s2pId;2 ~ 1 ~ 1C, to ~ 'D, ~ (1 ls6pld;5slp)/[5s3pld;3slp];27bE to G, (1 ls6p2d;5s2p)/ [ 5 ~ 3 ~ 2 d ; 3 ~ 2H,p ]( I; ls6p2d;5~2p)/[5~4p2d;3~2p];~'~ ~~~ A to B, Si ( 1 2 ~ 8 p ) / [ 6 s 4 p ] ;C~ ~to~ G, Si ( 1 3 ~ 9 p ) / [ 6 ~ 5 pH, ] ; ~Si~ ~(12s9p)/ [ 9 ~ 6 p ] B, . ~ D, ~ ~F, G, H augmented of p diffuse on non-hydrogen atoms. G augmented of s diffuse on hydrogen atoms. A to B: d expt, 0 0.8, Si 0.45; p expt, H 1.1. C to D: d expt, 0 1.28, Si 0.388; p expt, H 1.0. E to H : d expt, 0 0.5/1.5, Si 0.25/0.9; p expt, H 0.5/1.5. Diffuse p sets: 0 0.059, Si 0.027. Diffuse s set: H 0.034.
Figure 1. Conformation of three types of water/silanol adducts: structures I, water as proton donor: (a) water molecule coplanar with Si-& H, (b) no geometric constraint; structure 11, water as a proton acceptor. Geometries calculated at HF-A level. For comparison, the geometry of free silanol and water calculated at the same level is shown in structures 111 and IV, respectively. Angles in degrees, lengths in angstroms.
way to circumvent this problem could be the use of D 2 0 ; unfortunately, rapid isotopic scrambling takes place.) According to Kasansky and co-workers,6 however, AuOHis 85 cm-l. Other a u t h o r ~ ~have - ~ ,resorted ~ to diffuse reflectance measurements in the region of overtone 2u and combination u + 6 ( 6 being the bending mode) of both SiOH and H 2 0 . Anderson and Wickersheim' have observed the SiOH v 6 combination mode to shift from 4550 to 4420 cm-l upon interaction with water; as the 6 mode is known to increase in frequency upon coordination, AuOH is 0 evaluated to be larger than 130 cm-I, ~ 2 0 cm-I. Klier and c o - ~ o r k e r have s ~ ~ measured ~ the H 2 0 u 6 and the SiOH 2v modes. Upon interaction with water, the former undergoes a red shift of some 30 cm-' only; this is clear evidence that the water molecule is acting as proton acceptor as in structure 11. The extent of the shift of the SiOH 2u overtone is some 130 cm-I; in the harmonic approximation, that of the fundamental mode is expected to be about half. In conclusion, the experimental evidence is that structure 11 is the preferred one, but there is uncertainty about the energy of interaction (1 3-25 kJ mol-') and the magnitude of Avo" (80-200 cm-I). The occurrence of structure I is however not ruled out. It is noteworthy that, according to eq 1, the uncertainty in the energy value corresponds to the uncertainty in the red shift of the fundamental SiOH stretch. No other vibrational mode has been measured. As far as the intermolecular modes are concerned, a study in the far IRI8 has assigned a band at 225 cm-' to a O.-O stretch in structure 11.
+
+
Methods To model the isolated hydroxyl of amorphous silica, we have chosen the simplest molecular model, silanol H3SiOH. Previous work1F21has shown that the known spectroscopic features of the (18) Bertoluzza, A.; Bonino, G. B.; Fabbri, G.; Lorenzelli, V. J . Chim. Phys. Phys.-Chim. Biol. 1966, 63, 395. (19) Mix, H.; Sauer, J.; Schriider, K. P.; Merkel, A. Collect. Czech. Chem. Commun. 1988, 53, 2191.
former are well accounted for by the latter when calculated at the appropriate level of treatment, in particular the anharmonic OH stretching modes including overtones and the S i U H bending and torsion modes. As far as the interaction with molecules is concerned, we have already shown that silanol quite satisfactorily models the isolated OH of amorphous silica in the rather weak interaction with CO;22in a separate paper, we show that silanol also represents well the isolated O H of amorphous silica in a strong interaction, that with NH3.23 Because we are dealing with a molecular complex, the calculations consist of the comparison of energy, geometry, and vibrational features of the molecules in interaction and when separated, at various levels of approximations. All the calculations have been performed at ab initio level, with the programs CADPAC4,25 and GAUSSIAN82.26 Dunning valence double-{ (DZ basis set A and B in Table I) and triple-{ (TZ basis sets C-H in Table I) plus various polarization and diffuse functions have k n adopted thro~ghout.~'Details of those basis sets are reported in Table I. Full geometry optimization has been carried out a t the Hartree-Fock (HF) level, with the A basis set only, for all structures investigated by analytical gradient techniques and with, when (20) Garrone, E.; Ugliengo, P. In Structure and Reactivity of Surfaces, Proceedings of the European Conference, Trieste 13-20 Sept 1988; Zecchina, A., Costa, G., Morterra, C., Eds.; Studies in Surface Science and Catalysis; Elsevier: Amsterdam, 1988; p 405. (21) Ugliengo, P.; Garrone, E. To be published in J . Mol. Catal. (22) Ugliengo, P.; Saunders, V. R.; Garrone, E. J . Phys. Chem. 1989, 93, 5210. (23) Ugliengo, P.; Saunders, V. R.; Garrone, E. To be published in Surf. Sci. (24) Guest, M. F.; Kendrick, J. GAMESS User Manual; Daresbury Laboratory: Warrington, U.K., 1985. (25) Amos, R. D.; Rice, J. E. CADPAC, The Cambridge Analytical Derivatives Package, 1987, Issue 4.0. (26) Binkley, J. S.; Frisch, M. J.; Defrees, D. J.; Rahgavachari, K.; Whiteside, R. A.; Schlegel, H. B.;Flufer, E. M.; Pople, J. A. GAUSSIANBI; Department of Chemistry, Carnegie-Mellon University: Pittsburgh, PA, 1982. (27) (a) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry; Schafer, H. F., 111, Ed.; Plenum Press: New York, 1977; Vol. 3, p 1. (b) Dunning, T. H., Jr. J . Chem. Phys. 1971, 55, 716. (c) McLean, A. D.; Chandler, G. S . J . Chem. Phys. 1980, 72, 5639. Ahlrichs, R.; Taylor, P. R. J . Chim. Phys. Phys.-Chim.Biol. 1981, 78, 315. (d) Huzinaga, S. Approximate Atomic Functions 11. Technical Report; University of Alberta: Edmonton, Alberta, Canada, 1971.
2262 The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
Ugliengo et ai.
TABLE 11: Harmonic Frequencies (cm-I) of the Silanol/Water Adducts Ib and 11" modes Ib I1 intermolecular 31 [31 40 [ I O O ] 49 [81 107 [I261 143 [3] 207 [ 1261 325 I1611 509 (+301;0.5) 971 (+66;0.7) 916 (-33;lO) 1779 (+21;1) 4130 (-33;9) 4225 (-25;l) 4269 (-19;2)
SiOH torsion Si-0-H bend Si-0 stretch H-0-H bend OH, stretch (s) SiO-H stretch OH, stretch (a)
111
71 [71 97 PI 104 [209] 176 [21] 191 [22] 663 (+455;0.9) 1022 ( + I 17;0.5) 957 (+8;9) 1758 (0;l) 4161 (-2;0.4) 41 16 (-134;4.5) 4283 (-5;1.6)
IV
208 [147] 905 [272] 949 [I91 1758 [I151 4163 [20] 4250 [I301 4288 [73]
"Shifts with respect to the free compounds and intensity ratio Icompler/Ifrce in parentheses. Absolute intensities in kilometers per mole in brackets. TABLE 111: Full Set of HartreeFock A//A Unscaled Frequencies for I,, I,, 11, 111 (Free Silanol), and IV (Water Monomer) (cm-') and Corresponding Intensities (km mol-') descriotion of the mode I. Ih I1 111 IV intermolecular -101 (80) 40 ( 100) 31 (3) 37 ( 1 1 ) 71 (7) 49 (8)
torsion silanol SiH, rock SiH, rock Si-0-H bend Si-0 str SiH, deformn (d) SiH3 deformn (s) SiH, deformn (d) H-0-H bend SiH, str (d) SiH3 str (s) SiH, str (d) 0-H, str (s) SiO-H str 0-H, str (d)
52 (4) 143 (3) 217 (138) 317 (106) 471 (205) 753 (67) 795 ( 1 30) 969 (173) 910 (182) 1051 (135) 1076 (170) 1097 (300) 1785 (97) 2346 (220) 2364 (141) 2410 (100) 4129 (161) 4229 (1 28) 4270 (1 50)
107 (126) 143 (3) 207 (126) 325 (161) 509 (76) 768 (113) 794 (116) 971 (194) 916 (184) 1052 ( I 32) 1076 (165) 1098 (309) 1779 (110) 2348 (215) 2365 (146) 2402 (105) 4130 (173) 4225 (147) 4269 (147)
appropriate, symmetry constraints being imposed. BSSE has k e n evaluated with the full counterpoise method.28 Harmonic normal-mode frequencies have been computed with analytical second energy derivatives being adopted and the equations of nuclear motion being solved by standard methods.29 Infrared intensities have been computed from analytical dipole moment derivatives30 as programmed in CADPAC4. The effect of anharmonicity on the stretching mode of the 0 - H bond in free silanol and in structure I1 has been investigated by determining the potential energy curve related to the 0-H distance R in the range from 0.76 to 1.26 A; when dealing with structure 11, the 0-0 intermolecular distance has been kept fixed. The resulting potential energy data have been fitted to a sixth-order polynomial. The resulting one-dimensional Schrodinger equation has been solved both variationally by means of a harmonic oscillator expansion technique3' and numerically following a Cooley discreti~ation.~~.~~ Electronic correlation has been evaluated by perturbative M~ller-Plesset technique,34 truncated at second-order (MP2), using A and H basis sets. Hereafter, any calculation is indicated by either H F or MP2 followed by the letter labeling the basis set, e.g., HF-A or MP2-H. A double slash, //, indicates the basis set at which the geometry has been optimized. The calculations have been carried out on the NAS9160 mainframe at the Turin computing center, the Rutherford Laboratory (28) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (29) Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York. . . ~1955. ~., (30) Amos, R.D. Chem. Phys. Lett. 1984, 108, 185. (31) Almlof, J . Chem. Phys. Lett. 1972, 17, 49. (32) Cooley, J. W. Math. Comput. 1961, 15, 363. (33) Lindberg, B. J . Chem. Phys. 1988, 88, 3805. (34) Maller. C.; Plesset, M. S. Phys. Reu. 1934, 46, 618. ~~
~
~~~
~
~
~
97 (2) 104 (209) 176 (21) 191 (22) 663 (136) 783 (73) 807 (181) 1022 (139) 957 (162) 1057 (138) 1085 (224) 1113 (319) 1758 (115) 2314 (257) 2335 (182) 2377 (124) 4161 (9) 4117 (586) 4283 (121)
208 (147) 737 (96) 796 (116) 905 (272) 949 (1 9) 1053 (136) 1075 (168) 1105 (324) 1758 (115) 2331 (236) 2351 (155) 2395 (113) 4163 (20) 4250 (1 30) 4288 (73) =
-- -
Figure 2. Bifurcated conformation V of the water/silanol adducts. Geometry and binding energy in kilojoules per mole calculated at HF-A as a function of the angle Si-O-.O.
CRAY-XMP/4, and the CONVEX supermini at Daresbury Laboratory.
Silanol and Water Molecules The ab initio characterization of the silanol molecule at HF-A and HF-CZ0and at the MP2-A level2' has been already published by two of us. The geometry at HF-A is illustrated in structure I11 of Figure 1 for comparison with structures I and 11. The water molecule has of course been already calculated at any desired level of accuracy.35 For comparison, we have optimized the geometry at HF-A//A level (structure IV of Figure 1).
A selection of the most relevant vibrational frequencies of both molecules are collected in Table 11. In order to compare the bonding ability of water with silanol with that of water with itself, the water dimer has been calculated, (35) Popkie, H.; Kistenmacher, H.; Clementi, E. J . Chem. Phys. 1973, 59, 1325.
H,SiOH as Model for Free Hydroxyl of Amorphous Silica TABLE I V Total Energies (hartrees) for I, (Planar Conformer of Silanol/Water-Hydrogen Donor), Ib (Nonplanar I, Conformer), and 11 (Silanol/Water-Oxygen Donor) basis sets I. Ib 11
A
H
H F Energies -442.219 579 -442.220431 -442.223 841 -442.224 595 -442.253 839 -442.254 589 -442.255 1 I4 -442.255 762 -442.271 825 -442.272 534 -442.272 902 -442.273 551 -442.272950 -442.273 589 -442.274 376 -442.275 017
-442.223 -442.227 -442.257 -442.258 -442.275 -442.276 -442.276 -442.277
MP2 Energies -442.763 926 -442.764909 -443.064 056 -443.064 766
-442.768315 -443.067 454
777 330 386 427 515 354 400 735
TABLE V Total Energies (hartrees) for 111 (Free Silanol) and IV (Water Monomer) basis sets I11 IV A
B C D E F
G H A
H
H F Energies -366.167 3 13 -366.168835 -366.191 617 -366.192024 -366.206 573 -366.206 920 -366.206936 -366.208 332
-76.046 -76.049 -76.055 -76.056 -76.060 -76.061 -76.061 -76.061
MP2 Energies -366.514 171 -366.728 359
-76.241 958 -76.329 134
642 174 985 704 893 690 690 709
following well-known workP6 at the HF-A//A level and computing the full set of harmonic frequencies and intensities (Table 111). Models for the Silanol/Water Interaction
Beside structure 11, where water behaves as a H acceptor, we have investigated three possible configurations of the water/silanol adduct in which water acts as a H donor, namely, structures I, and Ib, where interaction takes place via one H atom, and structure V (see Figure 2), where both H atoms of the water molecule evenly interact with the silanol oxygen atom (bifurcated conformation). Structures I, and Ib differ in that in the former the water molecule is constrained to be coplanar with the Si-O-H moiety. Structure I, is the one studied by Chakoumakos and Gibbs.Is We have also considered structure Ib, where none of the atoms of the water molecules lie in the Si-0-H plane. The idea was that the water hydroxyl could orient so to maximize the interaction with the oxygen lone pair of S O H . This has been suggested by the work of Millen and L e g ~ n , ~who ' showed that the spatial availability of lone pairs has a strong effect on the conformation of van der Waals complexes.38 This applies in particular to the water dimer, a case which is not too far from the present one, and involves a nonplanar structure. Structure I1 has been constrained to C, symmetry, as well as structure V. Discussion
Energy of Interaction and Basis Set Dependence. Structure I, has been studied by Chakoumakos and GibbslSusing a 6-31G ( d on Si only) basis set. The use of D Z basis set A leads to improved geometry and energy. The main result, however, is that structure I, envisaging water as the donor of one H atom, attains a lower energy by the nonplanar configuration of structure Ib. As discussed further on, structure I, is actually a transition state. Table I shows the binding energies for the structures I,, Ib, and (36) Szalewicz, K.; Cole, J. S.; Kolos, W.; Bartlett, R. J. J . Chem. Phys.
1988, 89, 3622, and references cited therein.
(37) Legon, A. C.; Millen, D. J. Chem. Reu. 1986, 86, 635. (38) Legon, A. C.; Millen, D. J. Acc. Chem. Res. 1987, 20, 39.
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2263 TABLE VI: HartreeFock Dipole Moments (debyes) (1 debye = statcoulomb cm) for I,, Ib, II, III, and IV basis sets I, Ib I1 I11 IV A
B C D E F
G
3.7604 3.7698 3.8077 3.5020 3.4993 3.4956
3.0592 3.0563 3.1604 3.1484 2.8581 2.8553 2.8531
4.2126 4.1601 4.2073 4.1549 3.9718 3.9416 3.9370
1.4693 1.5206 1.5259 1.5313 1.3591 1.3648 1.3644
2.1897 2.2155 2.2477 2.2771 2.0383 2.0471 2.0471
I1 (the total energies for structures I-IV are included in Tables IV and V). Structure V is always only slightly bound, and it is actually a transition state; optimization in C, symmetry causes the evolution of structure V to structure 11, which is illustrated in Figure 2. Although no ad hoc calculations have been carried out, the comparison with the relevant data for structures I, and Ib show that inclusion of zero-point energy and BSSE is likely to reduce the binding energy at 0 K to a meager 4 kJ mol-' in the most favorable case. As a consequence, no further investigation on structure V has been carried out. Structure I1 is definitely the one showing the largest binding energy, and for the moment, it can be proposed as the one formed in the experiment on this sole basis. As far as the role of the basis set employed is concerned, we note the following. Addition of diffuse p functions on heavy atoms cause some increase in the binding energy for structures I, and Ib (basis sets A/B, C/D), whereas a monotonic decrease is observed for structure 11. When triple-{ quality plus double polarization set is used a decrease in the binding energy is observed in all cases (basis set E/F). Diffuse sets of s function on hydrogen (basis F/G) yield a negligible increase in the binding energy. The nearly equivalent basis sets G and H yield similar results. The most important effect on the binding energy is caused by the splitting of the polarization functions into two independent sets (see Table I, basis sets E-H), characterized by exponents chosen following a well-tempered criterion.39 This allows a good description of the electronic density in the binding region, both in H F and correlative treatments of H-bonded adducts.40 In all three cases, BSSE at the H F level is rather small (5-9% of the binding energy) and shows a smooth trend along the series of basis sets A, C, E. Correlation energy has been evaluated at the MP2 level for A and H basis sets only and turns out to be 20-30% of the binding energy, in excellent agreement with the findings by Del Bene4' concerning a series of bimolecular complexes of water with firstand second-row hydrides. According to the same author4' and to Pople et al.,42 in the perturbative treatment of the same molecules, the third- and fourth-order correlation contributions are smaller than the second and tend to cancel. For these reasons and because of the computational costs involved, higher levels of correlation treatments have not been carried out. Instead, we have evaluated the BSSE at the MP2 level, which results in 20% and 15% of the binding energy for I,, Ib, and 11, respectively, showing that BSSE for correlated wave functions has to be taken into account especially when dealing with true van der Waals complexes. Zero-point energies are closely similar for structures I,, Ib, and 11. It is interesting to note that in the more delicate case of the CO/SiOH interaction, H F treatments yielded unrealistically small values of the binding energy and that electronic correlation calculations were needed to reach satisfactory results.22 The reason was probably related to the C O dipole moment, the direction of (39) Amos, R. D.; Gaw, J. F.; Handy, N. C.; Simandiras, E. D.; Somasundram, K. Theor. Chim. Acta 1987, 71, 41. (40) Hobza, P.; Zahradnik, R. Intermolecular Complexes. The Role of van Der Waals Systems in Physical Chemistry and in Biodisciplines; Studies in Physical and Theoretical Chemistry 52; Elsevier: Amsterdam, 1988. (41) Del Bene, J. E. J . Phys. Chem. 1988, 92, 2874. (42) Frisch, M. J.; Pople, J. A.; Del Bene, J. E. J . Phys. Chem. 1985.89, 3664. Frisch, M. J.; Del Bene, J. E.; Binkley, J. S.; Schaefer, H. F., 111. J . Chem. Phys. 1986, 84. 2279.
2264
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
Ugliengo et al. TABLE VII: Atomic Coordinates for the Hartree-Fock A//A Optimized Dimer of Water and Conformers of Structures I and II’ (a) Water Dimer 1 H -0.059471 1.157376 0.0 2 0 0.009 352 2.948 146 0.0 3 H -1.676674 3.525237 0.0 4 5 6
-180
-197
_.-
I
CT 60013
I 2 3 4 5 6 7 8 9
0 H H
0.009 352 0.793 256 0.793 256
-2.683 663 -3.399236 -3.399 236
0.0 -1.435 125 1.435 125
(b) Conformer I1 (Silanol/Water-Oxygen Donor) H 0.000000 1.540693 0.709 228 0 0.000000 1.626021 0.000000 SI -2.720402 0.189834 0.000000 -4.696734 2.139053 0.000000 H H -3.047675 -1.432363 -2.247332 H -3.047675 -1.432363 2.247332 0 4.539402 -1.483 167 0.000000 H 5.510904 -1.892032 -1.440232 5.510904 -1.892032 1.440232 H
(c) Conformer Ib (Silanol/Water-HydrogenDonor; Nonplanar
Conformation)
-217
‘-121
Figure 3. Mulliken population analysis for structures I,, I,, and I1 and the component molecules. Bare numbers, net charges; bracketed numbers, difference in net charge induced by adduct formation; CT = total electron. charge transfer. Unit =
1 2 3 4 5 6 7 8 9
H 0
SI H H H H
0 H
0.164749 0.18 1 707 2.794491 2.158 438 3.687753 4.809 985 -3.516277 -5.252790 -5.858860
2.946475 1.247 089 -0.445318 -2.955 940 -0.629113 0.704 040 0.015222 -0.393283 -0.676674
0.394496 -0.145 358 0.017069 -0.958 783 2.644619 -1.5 16 709 0.065088 0.216341 -1.435546
(d) Conformer I, (Silanol/Water-Hydrogen Donor; Planar Conformation) which is only computed correctly after allowing for electron 1 H -0.061 928 3.228238 0.0 correlation. In the present case, the dipole moment of water is 0.0 1.446898 0.0 2 0 calculated satisfactorily at the H F level. Dipole moments cal3 SI 2.748959 -0.030271 0.0 culated with the various basis sets are reported in Table I and 4 H 2.188292 -2.737744 0.0 are compared with the experimental value of 1.855 D (the H F 5 H 4.226 98 0.657 406 -2.2544 dipole moments of structures I-IV are given in Table VI). It 6 H 4.226 98 0.657406 2.2544 is noteworthy that the binding energies roughly parallel the 7 H -3.417316 -0.535231 0.0 8 0 -4.920679 -1.507786 0.0 calculated dipole moments of water, in agreement with the 9 H -6.283003 -0.359 I75 0.0 well-known importance of electrostatic interactions in H bonding.40 Another aspect of H bonding, which has been long d i s c ~ s s e d , ~ ~ ~ ~“Data in bohr. is electron transfer from the proton-acceptor molecule to the 3.03 and 2.92 8, values). The changes in bond lengths brought proton-donor one. Chakoumakos and Gibbs’* have shown the occurrence of electron transfer by the use of difference electron about by adduct formation are those expected on the basis of Gutmann rules.44 In particular, the 0-H bond of the H donor density maps. We have evaluated the electron transfer occurring molecule lengthens while the adjacent bond (0-H in the case of upon interaction through the Mulliken population analysis obtained at the HF-A//A level, of the adducts and the component molewater, Si-0 for silanol) shrinks. The intermolecular O.-O distance is found to be shorter, the larger the binding energy (3.03, 3.01, cules; the results are shown in Figure 3. We note that Mulliken and 2.92 8, vs -14.8, -17.0, and -25.8 kJ mol-’ for I,, Ib, and 11, absolute data are not very reliable, being very basis set dependent, but the comparison between closely related structures is certainly respectively). It is noteworthy that in the two stable conformers I b and 11, the H atom involved in H bonding does not lie in the meaningful. A net flow of charge from silanol to water occurs plane Si-0-H or H-0-H, respectively, but it is approximately in structures I and the reverse in structure 11. The absolute value oriented to better interact with the oxygen lone pair. This is in of the electron transfer parallels the energy of interaction (-7 x agreement with the already cited rules of Millen and L e g ~ n . ~ ~ , ~ * -9 X and +13 X electrons versus -14.8, -17.0, However, rather large intermolecular movements are possible with and -25.8 kJ mol-] for structures I,, Ib, and 11, respectively; see a very small decrease in binding energy, as shown above for Table I). Data in Figure 3 also illustrate the polarization of the structures I, and Ib, or for different conformations of structure charge distribution within the component molecules brought about V (see Figure 2). by the adduct formation. It is noteworthy that in structure I1 the The full set of harmonic frequencies has been calculated for 0-H moiety of the hydrogen donor group silanol is more polarized structures I,, Ib, and 11 at the HF-A//A level. Table I1 shows than the corresponding 0-H moiety of water in structures I, and Ib, due to the larger interaction energy. a selection of the vibrational frequencies for structures I b and 11 Geometry and Vibrational Features. HF-A//A geometries of only. The vibrational features of structure I, are close to those structures I,, Ib, and 11 are shown in Figure 1, together with the of structure the only significant difference is one imaginary geometries optimized at the same level for water and silanol (Table intermolecular frequency, demonstrating that it is a transition state as already mentioned. VI1 shows the atomic coordinates for the water dimer and conformers I,, Ib, and 11). Comparison of our structures I, and 11 Data in Table I1 allow a clear cut discrimination between with those calculated by Chakoumakos and Gibbs” shows that structures I b and 11. Indeed, (i) the highest intermolecular frethe absence of polarization functions in their basis set leads to quency is somewhat larger for Ib than for 11, and considerably anomalously short intermolecular 0--0distances (2.9 1 and 2.74 more intense; (ii) the shift in the Si-0-H torsion mode parallels 8, for I, and 11, respectively, to be compared with our HF-A//A (43) Kollman. P. A.; Allen, L. C. J . Am. Chem. Soc. 1971, 93, 4991.
(44) Gutmann, V. The Donor-Acceptor Approach to Molecular Interactions; Plenum: New York, 1978. Gutmann, V.; Resch, G.; Linert, W. Coord. Chem. Rev. 1982, 43, 133.
H,SiOH as Model for Free Hydroxyl of Amorphous Silica
a l
TABLE VIII: Equilibrium OH Bond Length R , (A), Harmonic Frequency Y,,, Fundamental Mode woI, First Overtone wO2, w, and Anharmonicity Constant w,x, for Free Silanol 111 and the Silanol/Water Adduct I1 (Vibrational Data in cm-I)"
Free Silanol
AE
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2265
I
III(HF) R,
III(MP2) 0.9598 4012 3844 7527 4005 81
0.9418 4250 4091 8031 4243 75
WO,
w O ~
we w,x,
II(HF) 0.9485 (0.007) 4121 (-129) 3937 (-154) 7692 (-339) 4119 (-124) 91 (+16)
II(MP2) 0.9698 (0.01) 3818 (-194) 3610 (-234) 7014 (-513) 3817 (-188) 103 (+22)
Differences with respect to silanol alone at the same level of treatment in parentheses. SCHEME I /H O\H
75
.95
R' -~
b
A€ I
135 ~
1.3 7
~
H,
0
K.
I T Si,
H/ H ",)
Silanol /water structure I1
I
I
m / /
75
Figure 4. Potential energy curves for SiO-H stretching motion: dashed curves, HF-A; solid curves, MP2-A; (a) free silanol; (b) silanol/water structure 11. Vibrational levels shown as horizontal bars; vertical arrows are corresponding transitions. Energy in hartree, 0-H distance in angstroms.
the binding energies (-17.0 and -25.8 kJ mol-' vs 301 and 455 cm-' for Ib and 11, respectively) (the large computed blue shift suggests that this mode should become detectable in the I R region); (iii) the shift in the S i - G H bend is +117 cm-l for structure 11, which is roughly twice the value for Ib; (iv) the shift in the Si-0 stretch is -33 and +8 cm-l for Ib and 11, respectively, in agreement with the corresponding lengthening and shortening of this bond upon coordination of water; (v) as to the modes of molecular water, no significant changes are computed for structure 11, in agreement with the whereas significant blue shift of the bending mode, red shift, and intensification of the 0-H stretches are found for structure Ib (for the water dimer, the corresponding values are very close to the present ones, +27, -47, and -23 cm-I for bend, symmetric and antisymmetric stretches, respectively; intensification of one order of magnitude for the symmetric stretch is also calculated; (vi) the SiO-H stretch shows a marked red shift of -134 cm-l for I1 in sharp contrast with the small red shift of -26 cm-l for 1, (sizeable intensity increase is only computed for structure 11). Because structure I1 is the one most likely formed in the experiment, a more detailed analysis has been carried out for both the intermolecular 0-0 stretch mode and the SiO-H stretch, which are the experimentally available feature^.^.^.'^ MP2-A optimization of the 0-0 distance, keeping the rest of the geometry fixed at the HF-A//A level, has led to an optimum O--O value shorter by the relatively large amount of 0.1 A with respect to
I
+
Kb b
H3SiOH
Si H/
\**H
H
1
KS C
the H F value; the corresponding harmonic frequency is 224 cm-l in probably fortuitous coincidence with the experimental value of 225 cm-I.I8 The potential energy of the proton motion has been calculated at the HF-A//A and MP2-A levels, keeping the 0--0distance fixed to the HF-A//A and MP2-A optimized values, respectively. The resulting curves are reported in Figure 4b whereas Figure 4a illustrates for comparison the case of silanol alone. In both cases, it is seen that electron correlation alters the H F curves substantially in the direction of increased anharmonicity. A further definite increase in anharmonicity is observed upon adduct formation, as noted by Kasansky and mworkers both experimentally6 and in calculations of lower quality." Figure 4 also shows the vibrational energy levels Ei (i = 0, 1, 2), from which one calculates the basic vibrational features, namely, the fundamental mode woI, the first overtone wO2,we, and the anharmonicity constant wexe: ~ 0 = 1
2w,xe =
El - Eo
2W0,
- wo2
~ 0 = 2
E2 - Eo
we = w01
+ 2W&
The relevant data are reported in Table VIII. Both H F and MP2 data show a 20% increase in the anharmonicity constant upon adduct formation. The shift on wol is -154 and -234 cm-' at H F and MP2-A levels, respectively, whereas the shift on the harmonic frequency uh was -129 (in good agreement with the harmonic value of 134 cm-I computed with standard methods) and -194 cm-I, respectively. This means that taking into account anharmonicity varies AuoH by =20% but has however less effect on the 0 - H stretch mode than the electron correlation, which alters AuOHby 50%. As discussed above, the comparison with the experiment is not straightforward. The adequacy of those calculations may be checked, however, in closely related SiOH/NH3, where the best datum of -582 cm-l (MP2-A anharmonic treatment) still slightly underestimates AuoH. In the present case, the calculations seem to suggest values definitely larger than found in the experimental literature for both the AvoH fundamental and the shift in the first overtone, which is found to be as large as -513 cm-', whereas the proposed experimental value is only -1 30 cm-1.495 Thermodynamic Considerations
The possible reaction equilibria involving a single water molecule with the silica hydroxyl group are reported in Scheme I, in which K, = K b / K , and AG, = AGb - AGa. Gas-phase water aggregates in dimers at room temperature to a very small extent45 according to reaction d in Scheme 11.
2266 The Journal of Physical Chemistry, Vol. 94, No. 6,1990
Ugliengo et al.
TABLE IX: Standard Thermodynamic Quantities and Equilibrium Constants for Reactions a-e (See Schemes I and 11)" AE~ -19.09 -26.14 -7.05 -19.66 -6.48
a b C
d e
AZPEc
AH,,d
AHo
7.03 6.61 -0.42 9.16 -2.55
-0.24
-12.30 -19.42 -7.12 -1 2.37 -7.05
+o. 1 1 0.35 -1.87 I .98
TAS -33.1 -32.5 0.6 -24.8 -7.7
A G O
Ks4
20.80 13.08 -7.72 12.43 0.65
2.3 X IO4 5.1 x 10-3 2.3 X 10 6.7 X 7.6 X IO-'
"Standard states at 1 atm (101 325 Pa) and 298 K. Energetic data in kilojoules per mole and KCgin atm-'. bAE = energy differences between products and reactants. CAZPE= zero-point correction to AE. dAH,h= thermal correction to AE.
TABLE X: Thermodynamic Quantities Computed at 298 K Different Systems in the Rigid-Cluster Approach' H,O H,O*.*H,O 111 Ih Hvib 0.002 1.924 0.653 2.966 0.888 0 0 H,,, 0.888 1.480 0 0 H,,,, 1.480 4.294 0.653 2.966 H,,, 2.311 23.88 38.99 29.05 ZPE 13.43 Svib S,,,
S,,,, S,,,
0.007 10.340 34.590 44.940
12.20 21.15 36.70 69.99
3.45 0 0 3.45
21.99 0 0 21.99
for
I1 3.051 0 0 3.05 1 38.89 22.40 0 0 22.40
'Heats in kilocalories per mole; entropies in calories per mole per Kelvin. The intramolecular frequencies scaled by 0.92; the intermolecular frequencies unscaled. ZPE in kilocalories per mole.
SCHEME I1
$ (H20-H20), (H20-.H20), + (H3SiO-H), $ (H3SiO-H-.H20), 2(H20),
+ (H,O),
According to Hobza et a1.,12 however, it is instructive to consider also reaction e between the dimer and the isolated surface hydroxyls because the dimer can be taken as the simplest model of H-bonded water in aqueous systems, in which K, = Kb/& and AGc = AGb.-.AG,j. For simplicity, only structure I1 is considered to be competitive with the water dimer. Table IX reports the relevant thermodynamic data of such reactions calculated, assuming that the molecules modeling surface species (silanol, adducts Ib and 11) are only allowed to have harmonic vibrational degrees of freedom (rigid-cluster model'2), whereas water (both monomeric and dimeric) is treated in the rigid-rotor-harmonic oscillator ideal gas approximation. The binding energies entering the calculations are MP2-H, geometries (for moments of inertia) are HF-A//A as well as are the vibrational data. For the water dimer, the best available binding energy36has been adopted. For all intramolecular frequencies, a scale factor of 0.92 was used, which produces the best agreement between experimental and HF-A//A frequencies of the water monomer and the OH stretching mode of SiOH, whereas unscaled intermolecular values were used (see Table X). The lower value of AGO indicates that reaction b leading to structure 11 is favored over reaction a leading to structure Ib. It is interesting that corrections for ZPE, thermal corrections, and entropic terms do not alter appreciably the difference in energy of Ib and 11, which remains =8 kJ mol-,. Data in Table IX actually allow the calculation of the relative populations of species I b and 11. With 8,and 82 defined as the coverage of Ib and 11, respectively (e,+ 02= 8 = overall coverage), and assuming that all silica hydroxyls are equivalent and noninteracting, the equilibrium constant of reaction c may be simply written as K, = 8,/8,, from which we find el/e = ] / ( I + KJ
the presence of species Ib cannot be entirely ruled out. For the sake of simplicity, however, we will in the following neglect 8, with respect to 8. As a first consequence, the heat of SiOH/H20 interaction will coincide with the enthalpy of formation of structure 11, which at 298 K is -19.42 kJ mol-' (Table IX). Such value falls well within the proposed range 13-25 kJ mol-' of experimental value^.^^^^^ With the same assumption, it is possible to calculate the equilibrium constant of reaction b as from which A Langmuir isotherm is arrived at, as it is implicit in the as-
l/Kb represents the water pressure at sumptions made. p l which half of the sur!ac:hydroxyls are engaged in a H bond with water and is thus representative of the range of pressure in which the adsorption takes place. It results pllz= 2 X lo7 Pa. Such value is exceedingly large because the experiment shows that a few kilopascals (vapor pressure at temperatures around the amb i e r ~ t )are ~ sufficient to have extensive interaction. In our opinion, this poor result reflects an inadequacy of the rigid-cluster model adopted. Indeed, the calculations of the gas-phase reaction, e.g., reaction d of the water dimerization, lead to satisfactory agreement with the e ~ p e r i m e n t .O~n~ the other hand, similar calculations in the rigid-cluster model on the SiOH/NH3 systemz3also show poor agreement with the experiment, in that a much higher p I l 2value is again calculated. Possible causes for this will be discussed elsewhere;23we anticipate that, in our opinion, the flaw is to be sought in the evaluation of the zero-point and entropic terms, in which are not included the perturbations caused by adsorption, of vibrational modes of the solid. Such a criticism does not at all apply to reaction c between the two conformers. As to reaction e, we note that the equilibrium constant calculated by us is close to that reported by Hobza et al.'* and that, on this ground, it can be stated that silanol competes with water for the association with water itself. If account is taken that most probably the same criticism advanced above (incorrect evaluation of the entropic term) also applies to reaction e, it is realized that the equilibrium is probably definitely shifted toward the formation of S i O H / H 2 0 adducts. This is in agreement with the well-documented fact that the isolated hydroxyl of silica is definitely more acidic than water and accordingly more prone to undergo H bonding as a H donor. Solution pKBkare about 7 and 14, re~pectively;~ theoretical deprotonation energies in the gas phase are 1475 and 1635 kJ mol-], r e ~ p e c t i v e l y . ~The ~ higher acidity of silanol with respect to water is also reflected in the definitely higher enthalpy of reaction b (adduct I1 formation) with respect to reaction d (water dimer formation). Conclusions
The coverage of species Ib is a constant fraction of the total coverage and is calculated to be 4.2%. Although a minor feature,
Although the experimental evidence concerning the SiOH/HzO interaction is not as firm as for the interaction of other molecules (CO, NH3) with silica, the calculations we have carried out corroborate the main conclusions from experiment. Water mainly interacts with SiOH as a hydrogen acceptor, as in structure 11: structure 1 (actually the nonplanar version Ib) has to be considered at the most a minor feature and other possible forms (e.g., structure V) do not occur.
(45) Curtiss, L. A,; Frurip, D. J.; Blander, M. Chem. Phys. Lett. 1978, 54, 575.
80, 60.
(46) Heidrich, D.; Volkmann, D.; Zurawski, B. Chem. Phys. Leu. 1981,
J . Phys. Chem. 1990, 94, 2261-2213 The energy of interaction is within the experimental range; all calculated spectroscopic features are quite reasonable although the shift of stretching mode of silica hydroxyl upon water coordination appears larger than what was measured. The model adopted for the SiOH f H20system appears to be inadequate, however, when considering the entropy and the free enthalpy of interaction on the basis of a rigid-cluster model. As a consequence,
2267
unrealistic values of the equilibrium constant are calculated.
Acknowledgment. We are grateful to CSI Piemonte and to SERC for allowance of computer resources. P.U. also thanks the Daresbury Laboratory for kind hospitality and in particular Dr. Julia Rice for kind help in the use of the C A D P A C ~program; we are also grateful to Dr. J. Sauer for stimulating discussions.
Basis Set Superposition Errors and Counterpoise Corrections for Some Basis Sets Evaluated for a Few X-***M Dimers Giuliano Alagona,* Caterina Ghio, Istituto di Chimica Quantistica ed Energetica Molecolare del CNR, Via Risorgimento 35, I-561 26 Pisa, Italy
Zdzislaw Latajka,+and Jacopo Tomasi Dipartimento di Chimica e Chimica Industriale, Universitii di Pisa, Via Risorgimento 35, I-561 26 Pisa, Italy (Received: May 26, 1989; I n Final Form: August 30, 1989)
SCF calculations of the interaction energy AE along the approaching path of an anion to a neutral molecule (general formula of the system considered: H,OF) have been carried out using several basis sets (MINI-1, 4-31G, 3-21G+, 6-31G**, 6-3 l G * * + V P , 6-31G**+VP(2d)S). The AE decomposition has been analyzed and subjected to counterpoise corrections. The last two basis sets are almost unaffected by BSSEs, whereas the others show different behaviors: the addition of diffuse functions to the 3-21G basis set produces a beneficial effect on the description of the interaction energy of the systems considered (bifurcated and linear structures of H 2 0 - - F and HO-n-HF, with the four atoms collinear). On the contrary, the addition of polarization functions to the N-31G basis sets (as in the 6-31G** one) slightly affects the trend of the curves, which are generally similar to those obtained with the 4-31G basis set. Simple approximate formulas, able to give an estimate of the interaction energy from the electrostatic energy component only, are proposed.
Introduction The search for a viable procedure to lower the basis set superposition error (BSSE) in the analysis of molecular interactions has been the object of numerous studies in the past years. Attention has been primarily paid to the examination of the validity of the counterpoise procedure (CP) in its original version’ as well as in several variants, and to the perusal of the results of the interaction energy decomposition after C P corrections. The literature prior to 1986 is surveyed in a review by van Lenthe et al.,* to which refs 3-38 add information about more recent developments. A second point of attack on the BSSE problem has been the elaboration of new basis sets (BS) for which the C P corrections were not necessary. In principle, near-complete BSs should produce a very small, and practically negligible, BSSE. A mere increase in the number of functions used to describe the atomic orbitals is not sufficient, however, to ensure better performances. A careful selection of the basis functions must be made, taking into account also that practical reasons prevent an unlimited and excessive enlargement of the functional space. Basis sets having the required characteristics have been proposed by Latajka and Scheiner.I3 The scope of the present paper is to test the performances of two BSs addressed to the minimization of the BSSE in the description of the components of the interaction energy AE. The decomposition of AE is a versatile analytical tool available in several versions (the most currently used one, employed also in the present paper, is due to Kitaura and Morokuma (KM)39)and it is very useful for the interpretation and comparison of molecular interaction acts. Several examples in the literature (see, e.g., ref 40) show that large, not well balanced, basis sets give a confused ‘Institute of Chemistry, University of Wroclaw, 14 F. Joliot-Curie Street, 50383 Wroclaw. Poland.
0022-3654 f 90f 2O94-2261$02.50f 0
TABLE I: Scaling Factor (sf) of the Inner and Outer Shells and Orbital Exponents a for the +Vp(2dS) Basis Set F,Oa H F OH-
sf(2spi) s f ( 2 ~ ~ 0 )a s p “d sf(ls,) sf(ls,) ap 1.007 1.074 0.133 0.850 1.610 1.008 1.085 0.098 1.431 0.209 1.265 1.309 0.940
“The scaling factors of the 1s shell were unchanged (=1) after opti-
mization. description of molecular interactions, useless for interpretative purposes. (1) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (2) Van Lenthe, J. H.; van Duijneveldt-van de Rijdt, J. C. M.; van Duijneveldt, F. B. Adu. Chem. Phys. 1987, 69, 521. (3) Olivares del Valle, F. J.; Tolosa, S.; Ojalvo, E. A,; Esperilla, J. J. J . Chem. Phys. 1986.85, 3448. (4) Collins, J. R.; Gallup, G. A. Chem. Phys. Lett. 1986, Z23, 56. (5) Gutowski, M.; van Lenthe, J. H.; Verbeek, J.; van Duijneveldt, F. B.; Chalasibski, G. Chem. Phys. Lett. 1986, 124, 370. (6) Gutowski, M.; van Duijneveldt, F. B.; Chalasibski, G.; Piela, L. Chem. Phys. Lett. 1986, 129, 325. (7) Collins, J. R.; Gallup, G. A. Chem. Phys. Left. 1986, 129, 329. (8) Cammi, R.; Tomasi, J. Theor. Chim. Acta 1986, 69, 1 I . (9) Roszak, S.; Sokalski, W. A,; Hariharan, P. C.; Kaufman, J. J. Theor. Chim. Acta 1986, 70, 81. (10) SzczgSniak, M. M.; Scheiner, S. J . Chem. Phys. 1986, 84, 6328. (1 I ) Gutowski, M.; van Duijneveldt, F. B.; Chalasiiiski, G.; Piela, L.Mol. Phys. 1987, 61, 233. (12) Sokalski, W. A.; Roszak, S. Int. J . Quantum Chem. 1987, 32, 279. (13) Latajka, Z.; Scheiner, S. J . Comput. Chem. 1987, 8, 663. (14) Latajka, Z.; Scheiner, S. J . Comput. Chem. 1987, 8, 674. (15) Alagona, G.; Ghio, C.; Cammi, R.; Tomasi, J. Int. J . Quantum Chem. 1987, 32, 207. (16) Alagona, G.; Ghio, C.; Cammi, R.; Tomasi, J. In?. J . Quantum Chem. 1987, 32, 227.
0 1990 American Chemical Society
