J . Phys. Chem. 1989, 93, 5401-5410
5401
Effect of Counterpoise Corrections on the Components of the Interaction Energy in the Formate-, Acetate-, and Phosphate-Water Dimers. A Study of Basis Set Effects Giuliano Alagona,* Caterina Ghio, Istituto di Chimica Quantistica ed Energetica Molecolare del C.N.R., Via Risorgimento 35, I-561 26 Pisa. Italy
and Jacopo Tomasi Dipartimento di Chimica e Chimica Industriale, Universitd di Pisa, Via Risorgimento 35, I-56126 Pisa, Italy (Received: November 14, 1988) Several variants of the counterpoise procedure for the correction of the basis set superposition error in the interaction energy and in its separate components are examined for a set of six dimers formed between the formate, acetate, and phosphate anions and water along two different approaching paths, namely those giving linear and bifurcated dimers. The analysis is performed over a representative set of intermonomeric distances, using six basis sets. The counterpoise correction has a beneficial effect on the prediction of AE(R,) and %: sizable changes in these two quantities are accompanied by a noticeable reduction of the spread due to the basis set. Only the STO-3G basis set shows evident phenomena of overcorrection,whereas the smallest corrections are found for the 3-21G+ one. The most convenient basis sets for calculations on similar dimers are identified. The comparison with corresponding analyses for neutral electron donor-water dimers permits a quantitative interpretation of the nature of the interaction, giving also some suggestions on simplified computational procedures to be used on large-scale calculations.
1. Introduction Recent theoretical studies on weak molecular interactions quite often include a correction for the basis set superposition error (BSSE). In all cases the corrections are obtained by applying the Boys-Bernardi counterpoise procedure (CP)l or a variant thereof. Despite its extensive use, the C P method is still object of debate, with several contributions. The literature preceding 1987 is critically examined in a review by van Lenthe et al.,z and some more recent additions are reported in ref 3-38. The debate is (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. Adv. 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, 123, 56. (5) Gutowski, M.; van Lenthe, J. H.; Verbeek, J.; van Duijneveldt, F. B.; Chalasinski, G. Chem. Phys. Lett. 1986, 124, 370. (6) Gutowski, M.; van Duijneveldt, F. B.; Chalasinski, G.; Piela, L. Chem. Phys. Lett. 1986, 129, 325. (7) Collins, J. R.; Gallup, G. A. Chem. Phys. Lett. 1986, 129, 329. (8) Cammi, R.; Tomasi, J. Theor. Chim. Acta 1986, 69, 11. (9) Roszak, S.; Sokalski, W. A.; Hariharan, P. C.; Kaufman, J. J. Theor. Chim. Acta 1986, 70, 81. (IO) Szczesniak, M. M.; Scheiner, S. J. Chem. Phys. 1986, 84, 6328. (1 1) Gutowski, M.; van Duijneveldt, F. B.; Chalasinski, 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, 2.;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. Int. J. Quantum Chem. 1987, 32, 227. (17) Alagona, G.; Ghio, C.; Cammi, R.; Tomasi, J. In Molecules in Physics, Chemistry and Biology; Maruani, J., Ed.; Reidel: Dordrecht, 1988; Vol. 2, p 509. (1 8) Olivares del Valle, F. J.; Tolosa, S.; Ojalvo, E. A,; Espinosa, J. Chem. Phys. 1988, 127, 343. (19) Cammi, R.; Olivares del Valle, F. J.; Tomasi, J. Chem. Phys. 1988, -122. - - , 63. ~-
(20) Tolasa, S.;&perilla, J. J.; Espinosa, J.; Olivares del Valle, F. J. Chem. Phys. 1988, 127, 65. (21) Wells, B. H.; Wilson, S. Mol. Phys. 1986, 57, 21. (22) Wells, B. H.; Wilson, S. Mol.Phys. 1986, 57, 421. (23) Alagona, G.; Cammi, R.; Ghio, C.; Tomasi, J. Vestn. Slou. Kem. Drus. 1987,-34, 149. (24) Cammi, R.; Ghio, C.; Tomasi, J. Int. J . Quantum Chem. 1986, 29, c-7
J4/.
(25) Bonaccorsi, R.; Cammi, R.; Tomasi, J. In!. J. Quantum Chem. 1986, 29, 373. (26) Ghio, C.; Tomasi, J.; Weill, J.; Sillion, B. J . Mol. Struct. (THEOCHEM) 1986, 135, 299.
not centered on the basic idea of the C P method, but rather on some details, deriving from conflicting reports about the numerical results. The diverging opinions may be reduced to a few points: does the C P method give an overcorrection to the BSSE? Does the CP corrected description of the interaction energy, AE, give a reasonable description of the true interaction energy? In other words, is it worthwhile to do the little extra computational effort to compute C P corrected interaction energies? To these questions we may add one more; is it worthy to introduce C P corrections to the separate components of the interaction energy? The decomposition of AE in order to study molecular interactions is a valuable tool, extensively employed in the variational as well as in the perturbation theory approach.39 For the variational approach-the most used in actual molecular calculations-there are two methods which introduce C P corrections (Sokalski et al.,@ Cammi et al.$I) and it is pertinent to ask if the little additional computational effort gives additional insight in th: interpretation of interaction acts. The answer to these questions is not immediate, because other factors play an important role, in particular the chemical composition of the system and the specific characteristics of the basis set. For this reason we have initiated a systematic survey, of which this paper may be considered the second part. In the first we treated a representative set of neutral hydrogen-bonded dimers, using several basis sets of common use in supermolecule calculations, and considering several variants of the CP, with exami(27) Latajka, Z.; Scheiner, S. Chem. Phys. 1988, 122, 413. (28) Bulski, M.; Chalasinski, G. J . Chem. Phys. 1987, 86, 937. (29) Latajka, Z.; Scheiner, S. J . Chem. Phys. 1987, 87, 1194. (30) Kroon-Batenburg, L. M. J.; van Duijneveldt, F. B. J. Phys. Chem. 1986, 90, 5431. (31) Mathers, T. L.; Kestner, N. R. Int. J . Quantum Chem., Quantum Chem. Symp. 1985, 19, 297. (32) Bauschlicher, C. W., Jr. Chem. Phys. Lett. 1985, 122, 572. (33) Sagarik, K. P.; Ahlrichs, R.; Brode, S. Mol. Phys. 1986, 57, 1247. (34) Diercksen, G. H. F.; Kello, V.; Sadlej, A. J. Chem. Phys. 1986, 103, 55. (35) Hobza, P.; Schneider, B.; Carsky, P.; Zahradnik, R. J. Mol. Struct. (THEOCHEM) 1986, 138, 377. (36) Hobza, P.; Mehlhorn, A,; Carsky, P.; Zahradnik, R. J. Mol. Struct. (THEOCHEM) 1986, 138, 387. (37) Zahradnik, R.; Hobza, P. Int. J. Quantum Chem. 1986, 29, 663. (38) Tolosa Arroyo, S.; Garcia, J. E.; Olivares del Valle, F. J.; Requena, A. J. Mol. Struct. (THEOCHEM) 1986, 136, 99. (39) Kitaura, K.; Morokuma, K. Int. J. Quantum Chem. 1976, 10, 325. (40) Sokalski, W. A,; Roszak, S.; Hariharan, P. C.; Kaufman, J. J. Int. J . Quantum Chem. 1983, 23, 847. (41) Cammi, R.; Bonaccorsi, R.; Tomasi, J. Theor. Chim. Acta 1985,68, 271.
0022-3654/89/2093-5401$01 .50/0 0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 4. 1989
5402
STO-3G
6-31G~~
EIF.
c
0
E
\ c
0 U Y Y
W
Q LIN.
1.5
2.0
2.5
3.0
1.5
2.0
2.5
3.0
Figure 1. Potential energy at the SCF level (dashed line) and C P corrected level (solid line) for two approaching paths of water to H2P04(see structures 1 and 2), as described by the STO-3Gand 6-31G** basis sets. The vertical dotted lines correspond to the C P correction when the STO-3G or the 6-31G** equilibrium distances are selected.
nation of the separate components of AE.I6vi7 In the present paper, we change the chemical composition of the dimers, considering now anion-water hydrogen-bonded complexes A--H20, using again several basis sets, and examining the AE components before and after C P corrections (in several variants). Before passing to the exposition of the method and of the results, some additional comments are necessary. In most papers discussing the C P method the scrutiny is limited to a given monomer separation R . This is a risky simplification of the analysis, as ref 15 shows. Also in the present set of compounds the C P correction (even though it is always larger for smaller basis sets at every sensible distance selection) depends heavily on the distance and on the relative orientation of the partners, as can be seen by examining the potential energy curves along the linear and bifurcated approaching paths of water for the system [H2P04-H20]- reported in Figure 1. This kind of study should thus include many R values, and it should be extended also to other orientations of the partners. In neutral A-HB dimers the favored approaching channel is reasonably narrow, and so a first analysis may be limited to R values at a fixed orientation. For the anions considered, R-COO- and H2P04-, the relative orientation is of more importance, even though according to the best quality calculations, with the inclusion of C P corrections as well (in contrast with ref 42), the water complex with these anions prefers the bifurcated form 1 over the linear one 2.4247 We have
2
(42) Prasad, C. V.; Pack, G. R. J . Am. Chem. SOC.1984, 106, 8079. (43) Alagona, G . ;Ghio, C.; Kollman, P. J . Am. Chem. SOC.1983, 105, 5226.
Alagona et al. thus selected here these two arrangements, to gain some information on the effect of the C P on the orientational parameters. A second point concerns the level of the computation. Here we limit ourselves to the S C F level with BSs of moderate size (6-31G** at the maximum). The BSSE also is present in the correlation contribution to the energy, and this topic is treated in some of the above quoted papers. We consider it convenient to separate the effects, and to look at the C P on the energy components at the S C F level, because applications of ab initio methods to large molecular systems will often be limited by computational resources to the S C F approach. The interest in applications to large molecular systems has also affected our choice of the BSs employed. Larger basis sets can be used for model systems of small size, and the examination of the results may give some insight on the characteristics of the BSSE and the CP, even at the S C F level: in a forthcoming paper,48 we shall extend our analysis to larger BSs applied to smaller A-s-HB systems. Our previous results on the neutral dimers show that, with a BS of moderate size, the use of the C P gives a picture of the interaction, along the approaching path, and at the equilibrium position (AE(R,) and R,), not far from the Hartree-Fock (H-F) limit. A direct comparison with the H-F limit for our A--HB species is not possible yet, but the parallel examination of the results for the two sets of dimers gives us confidence that the H-F limit is not far from the best results we will present in one of the following sections. It must not be forgotten that there was a practical goal behind the proposal of the CP method: the need of a simple device to improve the quality of low-level and low-cost supermolecule calculations. We feel confident of having kept in mind this primary scope while setting up the present investigation.
2. Outlines of the Method The interaction energy, computed at the S C F level, is decomposed according to the Kitaura and Morokuma (KM)39decomposition scheme AEAB(R) = + EPL + E E X + ECT + EMIX (1) where the terms have well-known meanings: electrostatic interaction energy between rigid charge distributions (ES), classical polarization energy (PL), electron exchange effects (EX), charge-transfer effects (CT), and a coupling term (MIX). The correction of AE for the BSSE affects also its components. According to our decomposition scheme, the C P correction does not affect the EESand EpLterms, because these terms are computed in the Hartree approximation, where there is no enlargement of the basis set.49 After introduction of the C P correction, eq 1 becomes
+
+
A g ' , ( R ) = EES EpL Egg + E$$ + E&;x (2) The superscript C P marks the contributions to which a correction term has been added. These corrections are expressed in the following form E$' = Ex + Ax (3) where X denotes one of the components of (1) (X = EX, CT, MIX). The total C P correction, applied to AEAB, is given by ATOT
=
EAX
(4)
A further decomposition of each Ax into monomeric contributions is also introduced Ax = A: Ai (5)
+
All the Ax are positive. (44) (a) Port, G. N. J.; Pullman, A. Int. J . Quantum Chem., Quantum Biol. Symp. No. 1 1974, 32, 21. (b) Berthod, H.; Pullman, A. J. Comput. Chem. 1981, 2, 87. (45) (a) Jorgensen, W. L.; Gao, J. J . Phys. Chem. 1986, 90, 2174. (b) Gao, J.; Garner, D. S.; Jorgensen, W. L. J . Am. Chem. SOC.1986,108,4784. (46) Ikuta, S. Chem. Phys. Lett. 1983, 95, 604. (47) Lukovits, I.; Karpfen, A,; Lischka, H.;Schuster, P. Chem. Phys. Lett. 1979, 63, 151. (48) Alagona, G.; Ghio, C.; Latajka, 2.;Tomasi, J., to be published. (49) Morokuma, K. J . Chem. Phys. 1971, 55, 1236.
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989 5403
Counterpoise Corrections on Interaction Energy
-5
functional mace component
B
A
CP corrected expression
“The correction to E M l xis obtained as a difference: with AMIX = ATOT - (AEX + ACT),
AMIX
PAx = E M ~+X
The calculations of all the Ax and Gpcomponents may be performed using the method of KM39 for solving the pseudoHartree-Fock equations with partial deletion of elements in the Fock matrix F of the dimeric system, expressed in the basis of the molecular orbitals of the partners. By denoting with F X a specific partial Fock matrix, one has
FXCX = EXSXCX (6) The component E X of AE is given by the difference between EX and the reference energy p,computed for the monomeric spaces Ex = EX- @ (7) @ = E:(XA)
+ J%(xB)
(8)
The C P corrections merely consist in a modification of the reference energy in eq 7. The new reference energy is given by the monomer energy computed with an enlarged functional space
EL = EEdXL)
(9) and for every X there is a different enlargement of the functional space. The specific enlargements, and the corresponding corrections, are summarized in Table I, where x M ,&, and & denote respectively the total functional space, the occupied M O space (in the isolated monomer), and the virtual M O space for monomer M. The decomposition summarized here permits the correction for the BSSE with several variants of the original C P method. It is, in fact, sufficient to delete one or more of the A; components to obtain the results for the so-called “incomplete CP” (ICP), proposed in the literature. We quote among them the CPED corr e ~ t i o n , ’where ~ , ~ ~ the enlargement of the basis set is limited to the electron donor only. With this corrective scheme we have A E i E D= EES EpL E@A) E$;P) (10)
+
+
+
’ (CH3CO0.. .H201-
IHCOO.. .H201-
TABLE I: A Prospect of the CP Corrections to the Components of AlP
+
if the electron donor is the partner A. Other ICPs, like the correction limited to the virtual space of both monomers, CPV (see van Lenthe et aL2 and ref 16, 17, 50-52), and the recent proposal of Olivares del Valle et a1.18v20 of avoiding corrections related to the occupied subspaces and &, will be considered in more detail in another paper, which will extend the analysis to sets of molecular systems of different chemical composition. 3. Computational Details The internal geometries of the monomers have been fixed in all the calculations to the values reported in ref 53. Also the mutual orientation of the partners has been kept fixed. As stated in the Introduction, we consider here two distinct orientations corresponding, respectively, to a “bifurcated” (bif) and “linear” (lin) arrangement of the anion-water couple (see structures 1 and 2): in the linear structure the atoms 0-H-O are collinear and (50) Daudey, J. P.; Claverie, P.; Malrieu, J. P. Inr. J. Quantum Chem. 1974, 8, 1. (5 1) Morokuma, K.; Kitaura, K. In Chemical Applications of Atomic and
Molecular Elecrrosratic Potentials; Politzer, P., Truhlar, D. G., Eds.; Plenum Press: New York, 1981; p 215. (52) Magnasco, V.;Musso, G. F.; Costa, C.; Figari, G. Mol. Phys. 1985, 56, 1249. (53) Weiner, S. J.; Kollman, P. A.; Case, D. A.; Chandra Singh, U.; Ghio, C.; Alagona, G.; Piofeta, S.,Jr.; Weiner, P. J . Am. Chem. Soc. 1984, 106, 765.
W Ln
W
-5 -IO -15
-70 -15 LIN.
-30 -35 -40
-15
IHzPOq.. .H201-
-
-
1.5
2.0
2,s
3.0
1.5
2.0
R[O.. .HI
2.5
3.0
1.5
2.0
8.5
3.0
rR1
Figure 2. Electrostatic contribution to the interaction energy for the two approaching paths (linear and bifurcated) of water to the anions considered, as described by the basis sets under examination.
the angle X-0-H is set equal to 120°. The scan of the potential energy hypersurface is thus limited to only a single dimension R, denoting the distance between the anionic oxygen and the water hydrogen involved in the hydrogen bond. The calculations have been performed with the following basis sets: STO-3G,S4MINI-lSS (with scale factor = l ) , 3-21G,56 4-31G,57 3-21G+,58 and 6-31G**.59 The C P algorithms for the AE decomposition analysis have been added to several ab initio molecular programs; most of the present calculations have been performed with our modified version of MONSTERGAUSS,~~ running on the GOULD 32/8705 at ICQEM (Pisa) and on the IBM 3090 at CNUCE (Pisa). 4. Results 4.1. Componentsof AE,before and after CP Correction. Since one of our aims is to compare the performance of various basis sets in describing the various components of AE, we shall make a generous use of graphic displays, to facilitate the examination of the results over a large interval of R values. Electrostatic Contribution, Em. In Figure 2 we report the E* components for all the dimers and all the basis sets. There is a wide difference in the results for the various BSs. The differences increase at small R. The STO-3G and 3-21G+ basis sets represent the two extrema. The generally shared impression that among the basis sets more widely used the STO-3G and the 4-31G ones give a sort of bracketing of the “true” electrostatic contribution is here confirmed and refined. The Em component is stronger, a t all R, in the bifurcated arrangement of all the dimers. At R = 2 A the ratio E=(bif)/Em(lin) is almost constant for all the compounds and all (54) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51, 2651. (55) Andzelm, J.; Huzinga, S.;Klobukowski, M.; Radzio-Andzelm, E.;
Sakai, Y.; Tatewaki, K.I. In Gaussian Basis Sets for Molecular Calculations, Huzinaga, S.,Ed.; Elsevier: Amsterdam, 1984. (56) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J . Am. Chem. SOC.1980, 102, 939. (57) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724. (58) (a) Clark, T.; Chandrasekhar, J.; Spitmagel, G. W.; Schleyer, P. v. R. J . Compuf.Chem. 1983,4, 294. (b) Spitmagel, G. W.; Clark, T.; Schleyer, P. v. R. J . Compur. Chem. 1987, 8, 1109. (59) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257. Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (60) Peterson, M. R.; Pokier, R. A. MONSTERGAUSS, Department of
Chemistry, University of Toronto, Toronto, Ontario, Canada.
5404
Alagona et al.
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989
TABLE 11: Ratio Ex(bif)/Ex(lin) at a Fixed Distance R = 2.0 A for the Various Complexes with Different Basis Sets complex basis set X = ES x = PL X = EX X = EXCP X = CT [HCOO...H,01STO-3G 1.556 0.669 2.360 2.371 1.724 _ . MINI-1 1.588 0.633 2.488 2.459 1.672 3-21G 1.527 0.904 2.813 2.823 1.436 4-31G 1.544 0.962 2.861 2.855 1.389 3-21G+ 1.592 1.522 2.725 2.711 1.676 ,524 1.109 2.875 ' 2.873 6-31G** 1.369 2.358 2.368 [CH,COO**.H*O]STO-3G ,554 0.674 1.716 MINI-1 2.486 2.457 ,588 0.640 1.670 ,528 0.915 2.834 2.836 3-21'3 1.414 2.874 2.862 ,545 0.976 1.382 4-31G 2.541 2.532 3-21G+ ,553 1.575 1.597 2.869 2.865 6-31G** ,523 1.117 1.373 ,540 0.707 [H2P04***H20]STO-3G 2.455 2.453 1.829 MINI-1 2.795 2.705 ,609 0.677 1.730 1.577 2.968 2.932 3-21G ,533 0.957 2.809 2.802 4-31G ,514 0.941 1.624 1.621 2.742 2.722 1.758 3-21G+ 1.573 6-3 1G** 1.576 1.176 2.908 2.891 1.673 IHCOO..
. H201-
lCH3CO0..
.H201-
IH2P04..
. H201-
IHCOO..
.H2Cl-
X = CTCP 1.722 1.655 1.436 1.394 1.656 1.394 1.713 1.652 1.409 1.383 1.566 1.396 1.821 1.707 1.513 1.582 1.749 1.692
lCH3CO0.. .H201-
.
[H2P04.. H201-
4s 40
I 30
BIF. 25 c
0 E
-u \
o
20 l5 lo
s
Y
x
W
w
15
0 '
= 30 25
LIN.
20 15 10
5 1.5
2.0
2.5
3.0
1.5
2.0
R [ O . . .HI
2.5
3.0
1.5
2.0
2.5
3.0
ri,
Figure 3. Polarization contribution to the interaction energy for the two approaching paths of water to the anions considered, as described by the
1.5
2 0
2 5
3 0
! S
2 1
R (0...HI
2 5
3 0
! 5
2 0
2 5
3 0
(iil
basis sets under examination.
Figure 4. Exchange repulsion contribution to the interaction energy for the two approaching paths of water to the anions considered, as described by the basis sets under examination.
the BSs (see Table 11). The ratios are reported in this table at a fixed value of R, in order to compare results given in graphic form in separate figures; a more detailed comparison of bif/lin values is carried out in a following section. Polarization Contribution, EPL. The EpLcomponent is reported in Figure 3. EpL is underestimated by all the basis sets employed here (information concerning this component in similar complexes evaluated with larger basis sets will be given in a forthcoming paper48). The effect of the diffuse functions present in the 3-21G+ BS is appreciable, while the improvement in passing from the 4-31G results to the 6-31G** ones is, on the contrary, modest. The ratio EPL(bif)/EPL(lin)at a given distance depends on the BS. The ratios for R = 2 8, are reported in Table 11. It may be remarked that this ratio is higher than unity only for the BSs having diffuse or polarization additional functions. In other words, such enlargements of the BS favor the bifurcated geometry in the polarization contribution to the energy. Exchange Repulsion Contribution, E E X . The E E X component is reported in Figure 4. The spread due to the basis set is remarkably smaller than for the EEs component (the energy scale is the same as in Figure 2). Such a difference between the two terms is quite reasonable, because EEXis an indirect measure of the size of the electronic cloud of the monomers: a basic feature of the electronic distribution which every basis set describes in
an almost equivalent manner at the expense, in poor basis sets, of other features of the system. The largest values in Figure 4 are given by the 3-21G+ BS, because of the presence of diffuse orbitals. The EEx term is subjected to BSSE correction in the full C P method. The Gg values have a trend hardly distinguishable from the uncorrected E E X ones, in the format selected here for the displays. We report in Figure 5 the correction AEx (remark the change of the energy scale in passing from Figure 4 to Figure 5 ) . The lowest correction is obtained with the 3-21G+ BS, the highest one with the STO-3G BS. Ninety percent or more of the AEx correction is due to A,:' with the same basis set dependence as shown for EEX. The ratio EEx(bif)/EEx(lin) at fixed R is always larger than unity. This ratio parallels the overlap between the monomeric charge distributions. The values for R = 2 A are reported in Table 11. There is a small, but noticeable, BS dependence. The table also reports the ratios after CP correction, i.e., Gg(bif)/G:(lin), at R = 2 8,. The C P correction does not alter the ratio; as will be shown later on, the effect of the C P correction on the relative weight of this component, as well as of the others, is mainly due to a shift in the equilibrium distance, of different magnitude for linear and bifurcated geometries. Charge-Transfer Contribution, Ecr. The uncorrected EcT components are reported in Figure 6 The value of this term is
Counterpoise Corrections on Interaction Energy ICH3CO0.. .H201-
IHCOO.. .H201-
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989 5405
IH2P04.. .HZOI-
BIF.
IHCOO
...H201-
ICH3CO0
...
BIF.
0
0
E
E \
\
c
0 U
0 U
-
1
1 Y
W X
IU -
a LIN.
L IN.
1.5
1.0
1.5
3.0
1.5
2.0
R [ O . . .HI Figure 5. CP correction to the exchange repulsion contributions reported in Figure 4. IHCOO.
..H20 1-
ICH3CO0.
..H20 1-
IH2P04. ..H20 I-
-5 -10 -15
BIF.
-20
-25
-E 0
\
-30
-3s -40
0 U Y
v
-5
+ -10 U
w
-15
-20
-25 LIN.
-30
-3s -40
-4.5
-6-3lSu 1.5
2.0
2.5
3.0
1.5
2.0
R [ O . . .HI
2.5
3.0
1.5
2.0
2.5
3.0
[AI
Figure 6. Charge-transfer contribution to the interaction energy for the two approaching paths of water to the anions considered, as described by the basis sets under examination.
generally strongly basis set dependent and in some cases has dubious physical meaning (consider, for example, the relatively high values found in symmetric dimers, A-A, where no net charge transfer should occur61). The decomposition of EcT into monomeric components shows that in our cases the charge-transfer contribution is almost completely due to the electron donor A, as intuitively expected. The BS dependence is manifest in Figure 6. The 4-31G and 6-31G** BSs give almost coincident curves, showing that the addition of a set of polarization functions to a split valence shell of N-31G type has little influence on the charge-transfer contribution. The trend shown by these two BSs (small absolute values until the region of the equilibrium distance, followed by a sharp increase (61) Van der Avoird, A.; Wormer, P.E. S.; Mulder, F.; Berns, R.M. Top. Curr. Chem. 1980, 93, 1.
1.5
3.0
1.5
2.0
1.5
3.0
[AI
Figure 7. CP correction to the charge-transfer contributionsreported in Figure 6 .
at shorter distances) is emphasized by the 3-21G+ BS. The curves for the other BSs have different trends. The 3-21G curves differ noticeably from the other split valence shell ones; a different behavior of the 3-21G BS with respect to the 4-31G and 6-31G** BSs, in particular for the EcT, but in general for the whole AE, has been already noticed in other molecular complexes (see, e.g., Alagona et a1.I7). Even more different are the curves for two minimal BSs. It may be remarked that in all the dimers considered here the three last named BSs (3-21G, MINI-1, and STO-3G) present a sort of “isobestic point”, i.e., a crossing of the curves, in the vicinity of the equilibrium distance. The Em component slightly favors the bifurcated arrangement. The ratios EcT(bif)/Ecr(lin) are reported in Table 11. A modest effect of the BS is evident. The C P correction, ACT,is on the contrary larger in the bifurcated dimers (see Figure 7 ) making the corrected values EE! more similar in the two arrangements of the dimer; this correction is mainly responsible for the changes in the relative stabilities of the two arrangements produced by C P corrections. The Am curves of Figure 7 have a characteristic nonmonotonic trend: the occurrence of maxima in these curves is related to the characteristics of the virtual space (mainly that of the electron acceptor B, i.e., H 2 0 in our cases), as analyzed in a previous paper.17 The smaller corrections in the region of the minimum are given by the 3-21G+ and 6-31G** BSs, with values of comparable magnitude. On the whole R range, the similarity between the 6-31G** and the 4-31G curve may be remarked, in analogy with what is found in neutral dimers.I5-l7 A dissection of ACT into AgT AZT shows that the last term is almost constant over the whole R range, with values not exceeding 0.2 kcal/mol (0.02 kcal/mol for the 6-31G** and 3-21G+ BSs). To save space we do not report the G! curves; it will be sufficient to state that these corrected values are somewhat less basis set dependent, especially at large R,and that the difference between the bifurcated and linear dimers, as stated before, is reduced to a variable extent, depending on the BS. At R = 2 8, this effect is more modest, but still evident; see the ratios of EEF(bif)/ @!(lin) in Table 11. Mixing Contribution, E M = . The mixing term could be further dissected62and its components could be subjected to C P correction, using basis set extensions different from those displayed in Table I (see Cammi and Tomasi8). The E M I x terms in the present
+
( 6 2 ) Nagase, S . ; Fueno, T.; Yamabe, S . ; Kitaura, K. Theor. Chim. Acto 1978, 49, 309.
5406
Alagona et al.
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989
TABLE 111: Values of the Interaction Energya without and with CP Corrections (AE, AECP)Computed at the Equilibrium Distancesb at the SCF and CP Corrected Levels (R, and R!?) [HCOO.**H20][CH3COO.*.H20][H2P04***H20]AE ASP R, RF AE ASP R, RF AE AECP R, RZ
Bifurcated STO-3G MINI-1 3-21G 4-31G 3-21G+ 6-31G**
-25.191 -28.141 -29.994 -25.471 -22.119 -21.177
-12.340 -17.288 -18.242 -20.329 -20.500 -17.244
1.78 1.86 1.98 2.07 2.10 2.11
2.22 2.09 2.17 2.12 2.15 2.16
-24.984 -28.273 -29.726 -25.554 -22.914 -21.203
-26.862 -25.556 -26.338 -22.684 -21.021 -19.262
-12.598 -17.879 -18.426 -19.301 -19.435 -16.652
1.49 1.62 1.69 1.75 1.75 1.80
1.74 1.70 1.77 1.79 1.79 1.83
-26.735 -25.729 -26.301 -22.888 -21.784 -19.327
-12.226 -17.373 -18.399 -20.604 -20.912 -17.380
1.78 1.86 1.99 2.06 2.08 2.11
2.21 2.08 2.17 2.12 2.14 2.15
-24.997 -28.365 -26.360 -22.319 -20.716 -18.263
-16.827 -15.531 -16.654 -18.354 -18.572 -15.776
1.75 1.86 2.00 2.09 2.13 2.14
2.24 2.15 2.21 2.16 2.19 2.19
1.49 1.62 1.69 1.74 1.73 1.80
1.74 1.70 1.77 1.78 1.78 1.83
-26.059 -26.242 -22.981 -19.812 -19.699 -16.287
-11.315 -16.749 -16.650 -17.192 -17.510 -14.695
1.48 1.60 1.71 1.76 1.76 1.84
1.75 1.70 1.80 1.81 1.82 1.88
Linear STO-3G MINI-I 3-21'3 4-31G 3-21G+ 6-31GL* a
-12.507 -18.031 -18.638 -19.580 -19.890 -16.796
In kcal/mol. * I n angstroms.
TABLE I V Effect of the CP Correction on the Interaction Energy (kcal/mol) and on the Equilibrium Distance (A) (AAE = AEcp(G) AE(R,); %AAE AAE.lOO/AE(R,); AR, = - R,; %AR, = ARq*lOO/Rq) [HCOO**.H20][ CH3COO.*.H20][HzP04***H20]AAE %AAE AR, %ARM AAE %AAE AR, %ARM AAE %AAE AR, %AR,
Bifurcated STO-3G
MINI-I 3-21G 4-31G 3-21C+ 6-31G**
12.85 10.85 11.75 5.14 1.62 3.93
51.0 38.6 39.2 20.2 7.3 18.5
0.44 0.23 0.18 0.05 0.05 0.04
24.7 12.3 9.1 2.4 2.4 1.9
12.76 10.90 11.33 4.95 2.00 3.82
14.26 7.68 7.91 3.38 1.56 2.61
53.2 30.0 30.0 14.9 7.4 13.5
0.25 0.08 0.08 0.04 0.04 0.03
16.8 4.9 4.7 2.3 2.3 1.7
14.22 7.70 7.66 3.31 1.89 2.53
APE 3.87 3.81 5.32 1.92 0.99 1.46
%AAE 81.2 62.6 62.7 35.6 23.3 35.6
51.1 38.6 38.1 19.3 8.7 18.0
0.43 0.22 0.18 0.06 0.06 0.04
24.2 11.8 9.0 2.9 2.9 1.9
8.17 12.83 9.71 3.97 2.14 2.49
33.7 45.2 36.8 17.8 10.3 13.6
0.49 0.29 0.21 0.07 0.06 0.05
28.0 15.6 10.5 3.3 2.8 2.3
0.25 0.08 0.08 0.04 0.05 0.03
16.8 4.9 4.7 2.3 2.9 1.7
14.74 9.49 6.33 2.62 2.19 1.59
56.6 36.1 27.5 13.2 11.1 9.8
0.27 0.10 0.09 0.05 0.06 0.04
18.2 6.2 5.3 2.8 3.4 2.2
%AR, 18.1 5.8 3.5 1.4 3.4 1.3
AAE 3.26 2.45 2.95 1.17 1.41 0.66
%AAE
ARw
%AR,
54.0 29.6 28.7 13.1 15.6 10.4
0.30 0.06 0.05 0.04 0.09 0.04
10.4 2.1 1.7 1.4 3.1 1.3
Linear STO-3G
MINI-I 3-21G 4-3 1G 3-21G+ 6-31G**
HF*-HOH" STO-3G
MINI-1 3-21G 4-31G 3-21G+ 6-31G**
AR, 0.70 0.34 0.21 0.07 0.10 0.05
53.2 29.9 29.1 14.5 8.7 13.1
H20-*HOHb
%LW, APE 26.4 12.3 7.5 2.4 3.4 1.6
4.46 3.89 4.90 1.53 1.53 0.97
%AAE 69.6 46.6 45.8 19.7 19.9 17.4
AR, 0.49 0.16 0.10 0.04 0.10 0.04
H,N.**HOHC
"The 3-21G+ values are R , = 2.02 A, E = -175.130834 hartrees, AE = -4.241, R Z = 2.12 A, A S P = -3.250. bThe 3-21G+ values are R , = 1.90 A, E = -151.248485 hartrees, AE = -7.663, R q = 2.00 A, A e P = -6.137. ?The 3-21G+ values are R , = 1.95 A, E = -131.521 895 hartrees, AE = -9.034, RZp = 2.04 A, A p e = -7.623. examples are relatively small; they are negative in the region 1.5 < R < 2.5 8, with absolute values less than 8 kcal/mol (and of the order of 0-2 kcal/mol in the equilibrium region), but the positive AMIx correction brings the mixing term to positive values of the order of 0-2 kcal/mol. The 6-31G** and 3-21G+ values are similar. 4.2. Effect of CP Corrections on Stabilization Energy and Equilibrium Distance. We report in Table 111 the values of AE( R,), and A E P R,), supplemented by the corresponding values of R , and R;. The introduction of the C P correction produces a reduction of lAE(R,)( and a lengthening of R,. The range in these values due to basis set effects is noticeably reduced in each dimer by the C P correction. The mean values of these ranges are for AE, 8.73 kcal mol before correction and 6.75 kcal/mol after; for ARq,0.34 uncorrected and 0.13 8, corrected, while, with the exclusion of the STO-3G results which have a particular behavior, we obtain 8.58 kcal/mol uncorrected and 3.08 kcal/mol corrected for AE and 0.23 8, uncorrected and 0.1 1 A corrected for AR. The magnitude of the correction to AE(R,) strongly depends on the BS, in absolute as well as relative value. The largest values
i
d
of AToT are found for the STO-3G BS and the lowest for the 3-21G+ one. The ratio AmT(R,)/AE(R,) reaches 0.50 for the STO-3G BS; it is comparable for the MINI-1 and 3-21G BSs (0.36 and 0.33) as well as for the 4-31G and 6-31G** ones (0.17 and 0.14); the lowest value belongs to the 3-21G+ BS (0.09). A similar behavior is found for the correction to 4.The largest correction occurs in the STO-3G calculations, followed by the MINI-1 and 3-21G ones. (The mean values of ARq are 0.36 8, for STO-3G, 0.17 8, for MINI-I and 0.14 8, for 3-21G.) The correction for the other three BSs are comparable (0.05 8, for 4-31G, 0.04 8,for 3-21G+, and 0.05 8, for 6-31G**). Analogous trends are evident for the A R , / R g F ratios. It may be of some interest to remark that after C P correction our "best" BSs (the 3-21G+ and 6-31G** ones) give upper and lower limits for the range in AE,: the MINI-1 values, despite the minimal character of this BS, are not far from the 6-31G** ones. For R g , on the contrary, the MINI-1 BS gives the lowest estimate and the 6-31G** the largest; the 3-21G+ values are not far from the 6-31G** ones. It is interesting to compare absolute and relative changes in AEq and R , in the anion-water dimers with corresponding
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989 5407
Counterpoise Corrections on Interaction Energy TABLE V Interaction Energy (kcal/mol) and Equilibrium Distance (A) Obtained with the CP Correction Limited to the Virtual Orbitals Only
Bifurcated
STO-3G -21.447 MINI-1 -25.969 -26.331 3-21G 4-31G -24.293 3-21G+ -21.523 6-31G** -20.314
1.83 1.88 1.95 2.04 2.10 2.10
-21.253 -26.075 -26.246 -24.436 -22.234 -20.378
STO-3G MINI-1 3-21'3 4-31G 3-21G+ 6-31G**
1.51 1.63 1.67 1.75 1.76 1.81
-23.588 -24.309 -24.567 -22.124 -21.282 -18.701
c
1.83 1.88 1.96 2.04 2.08 2.09
-20.589 -25.524 -23.027 -21.176 -19.657 -17.636
1.80 1.88 1.97 2.08 2.15 2.14
1.51 1.62 1.67 1.75 1.74 1.80
-22.758 -24.505 -21.386 -19.047 -18.847 -15.788
1.49 1.60 1.70 1.78 1.78 1.86
0
E
\
c
0
-
u
Y
Linear -23.705 -24.147 -24.497 -21.900 -20.574 -18.622
quantities computed for neutral-water dimers. We report in Table IV the difference in the AEq and in the R , values, for our anion-water dimers and for a selection of neutral dimers, all computed with the same method. These last data derive from ref 15, with the exception of the 3-21G+ results computed here. The C P corrections to AE, in the neutral systems are smaller in absolute value, but larger in relative importance, than those for the anionic dimers. The changes in R , are of comparable magnitude in neutral and anionic dimers. The addition of diffuse s,p functions to the 3-21G BS noticeably modifies the C P correction to AE. The C P corrections to AE and Rq are decidedly smaller in the 3-21G+ set of results than in the 3-21G one, in the anionic as well as in the neutral dimers. We recall here the observations of Bachrach and S t r e i t w i e ~ e rabout ~~ the value of adding diffuse functions to the electron donor in order to reduce the BSSE. A question of some importance for the debate on the selection of the most convenient counterpoise procedure is whether the results examined here for the full C P correction give indications of "overcorrection". To answer this one should know the AE, and R, values at the H-F limit (we recall that experimental data are not for direct use, because the inclusion of correlation tends to increase lAEl and to lower R,, generally by an amount smaller than the C P corrections and in the opposite direction). The H-F values are not available, but the comparison with the neutral dimers given in Table IV may give us some indications. For the neutral dimers we have shown that there is no empirical evidence of overcorrection for all the split-valence-shell basis sets. The same holds for the MINI-I and the 6-31G** BSs. A macroscopic overcorrection is present in the STO-3G results, however. The similarity of the results, made evident by Table IV, suggests that the same might happen in the A--.HOH dimers: overcorrection with the STO-3G basis set, and no empirical evidence of overcorrection for the other BSs. The C P correction limited to the virtual orbitals (CPV), reported in Table V, thus seems to "undercorrect". The corrections limited to the electron donor only (CPED) run almost parallel to the full C P ones, and the difference between the two corrections is nearly independent on the BS (the STO-3G BS represents an exception; the CPED corrections are practically indistinguishable from the full C P ones). This limited C P correction may thus be used to save computational time in the study of anion-neutral complexes (as was done in ref 26). 4.3. Relative Stability of the Bifurcated and Linear Dimers. As stated in the Introduction, this comparison gives some hints of the influence of the orientational parameters in the Occurrence of the BSSE and on the effect of C P corrections. In the analysis done in section 4.1 we have brought out that the C P corrections are larger for the bifurcated than for the linear arrangement, mainly in the C T term. This observation is confirmed by the values reported in Tables I11 and IV (the mean AAE (63) Bachrach, S. M.; Streitwieser, A,, Jr. J . Am. Chem. SOC.1986, 106, 2283.
STO-3G
MINI-I
3-216
4-31G
3-216+
6-31Gu
Figure 8. Relative stability of the bifurcated and linear forms of the adducts with water of the anions considered, at the SCF level (dashed line, 0) and at the CP corrected one (solid line, A), as described by the basis sets under examination.
is 6.44 kcal/mol for bifurcated dimers and 4.56 kcal/mol for the linear ones; these averages exclude the STO-3G values). The relative stability, with and without C P corrections, as predicted by the various basis sets, is graphically displayed in Figure 8. It turns out quite clearly that the final balance is shifted in favor of the bifurcated arrangement, even if C P corrections make the energy of the two forms more comparable. The ratio Ex(bif)/Ex(lin) for the different components X of AE, as well as for AE itself, computed at the S C F and C P corrected levels, are reported in Table VI. The ratios for AE bring out, in a different form, what has been displayed in Figure 8; the C P corrected energies are more comparable; Le., the ratios are closer to unity. For the ES components there is a decrease in the ratio in passing from the S C F values to the CP corrected ones for the small basis sets, whereas for the extended basis sets there are no remarkable changes. The same holds for the PL and EX components. In this last case attention must be paid to the large reduction of the ratios at the C P level for the STO-3G basis set: this remarkable decrement is associated with the overcorrection occurring by applying the full C P to this basis set. For the C T components the introduction of C P corrections generally produces a decrease in the ratios; but considerably different values are obtained with the 3-21G+ basis set. The comparison of these ratios with those at a fixed value of R, reported in Table 11, may be of some interest. The remarkable difference in the pattern of the results confirms that the examination of C P corrections at one distance alone may lead to misleading conclusions and that a reliable appreciation of the effect of C P corrections can be reached only looking at values obtained over a large set of intermonomeric distances (and orientations). 4.4. Interpretation of the Bonding and Refinements f o r CP Corrections. The main utility of the AE decomposition schemes is that of obtaining a more detailed view of the interaction. It is again advisable to look at the results not only at a fixed R value, but over a larger range of distances. The results can be analyzed by using graphic displays, an example of which is given in Figure 9. We shall not attempt an interpretation of the interaction in the whole class of A--HB complexes, since the examples considered here are insufficient for this scope; we limit ourselves to the analysis of R, and R r .
5408
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989
Alagona et al.
TABLE VI: Ratios of the Total Interaction Energy (AE(bif)/AE(lin) = p ) and Its Components (Ex(bif)/Ex(iii)) Equilibrium Distances for the Various Complexes with Different Basis Sets X= x= complex basis set pSCF ESScF PLSCF EXSCF CTSCF pcp ESCP [ H COO.**H2 0 1 STO-3G 0.938 0.955 0.532 0.768 0.984 0.980 0.880 MINI-I 1.101 1.102 0.577 0.980 1.257 0.967 0.900 3-21G 1.139 1.082 0.664 0.850 1.233 0.990 0.992 4-31G 1.123 0.666 1.073 0.799 0.991 1.053 1.072 1.052 3-21G+ 1.075 0.832 0.863 0.631 1.055 1.072 6-31G** 1.099 1.060 0.848 0.744 0.992 1.036 1.041 [CH3COO..*H20]STO-3G 0.935 0.953 0.536 0.768 0.982 0.886 0.978 1.099 MINI-1 1.100 0.582 0.978 1.255 0.964 0.910 3-21G 1.130 1.069 0.665 0.823 1.207 0.987 0.991 4-31G 1.116 1.071 0.673 0.804 0.959 1.058 1.103 3-21G+ 1.052 1.068 0.896 0.856 0.653 1.051 1.068 6-31G** 1.097 1.058 0.749 0.847 1.035 1.051 0.980 [H2PO,*..H20]STO-3G 0.959 0.964 0.537 0.868 1.100 0.966 0.854 MINI-1 1.081 1.071 0.591 0.994 1.269 0.927 0.830 3-21G 1.147 1.082 0.697 0.919 1.279 1.000 0.983 4-31G 1.127 1.049 0.646 0.784 1.025 1.068 1.042 3-21G+ 1.044 1.026 0.798 0.781 0.613 1.057 1.032 6-31G** 1.121 1.097 0.789 0.922 1.007 1.073 1.090
x=
x=
x=
at the SCF and CP Corrected
x=
x=
x=
PLcp 0.387 0.533 0.590 0.662 0.806 0.732 0.394 0.538 0.595 0.661 0.870 0.719 0.388 0.516 0.599 0.639 0.766 0.782
EXCP
CTCP 0.448 0.882 0.872 0.906 0.535 0.924 0.461 0.896 0.856 0.872 0.557 0.927 0.443 0.780 0.816 0.924 0.505 0.959
TABLE VII: Interaction Energy and Its Components (kcal/mol) at the SCF and CP Corrected Equilibrium Distances Dimers basis set [HCOO.*.H20]-
STO-3G MINI-1 3-21G 4-31G 3-21G+ 6-31G** [CH,COO**.H20]- STO-3G MINI-1 3-21G 4-31G 3-21G+ 6-31G** [H2PO,*..H20]STO-3G MINI-1 3-21G 4-31G 3-21G+ 6-31G**
AE -25.191 -28.143 -29.994 -25.471 -22.119 -21.177 -24.984 -28.272 -29.726 -25.554 -22.914 -21.203 -24.997 -28.365 -26.360 -22.319 -20.394 -18.264
EPL
-25.167 -32.759 -26.698 -26.961 -30.815 -22.685 -25.021 -32.838 -26.646 -27.554 -3 1.807 -22.8 12 -24.576 -3 1.880 -25.391 -24.377 -26.598 -21.145
-1.032 -0.897 -1.726 -1.874 -4.127 -2.167 -1.040 -0.925 -1.773 -1.974 -5.201 -2.220 -0.966 -0.904 -1.685 -1.594 -3.290 -1.936
EEX
ECT
Bifurcated 25.754 -24.363 21.747 -15.334 11.776 -10.858 9.915 -5.060 14.362 -3.612 8.908 -4.221 25.754 -24.227 21.704 -15.267 11.510 -10.337 10.442 -4.933 15.264 -4.092 8.958 -4.111 29.682 -28.499 23.726 -18.125 12.311 -9.018 9.045 -4.379 11.558 -3.223 8.452 -3.026
It may be remarked, as an initial step in this analysis, that the strong local interaction makes the effect of adjacent chemical groups less important. Also the differences in the chemical composition of the local group (-COT and >PO;) have less influence than in similar interactions involving neutral species. The various components of AE at R , and of hEcp at R F are reported in Table VI1 (bifurcated geometries) and Table VI11 (linear geometries). The SCF results, without C P corrections (left portion of the tables), are dominated by the ES term. The next term in absolute magnitude is EX. This positive contribution is to a large extent compensated by the negative contributions CT, PL, and MIX (notice that MIX is positive with the 3-21G+ BS). The amount of compensation depends considerably on the BS, and so, according to the case, ES(R,) may result in an overestimate or an underestimate of AE(R,). In order to make this point more evident we introduce the factorf= AE(R,)/ES(R,), reported in Table IX. As remarked before, the 3-21G+ BS overemphasizes the electrostatic character of the bonding (low value off). The introduction of C P corrections increases the value of the equilibrium distance. The absolute values of ES and PL, untouched by CP corrections, are thus smaller at R F than at R,. (Compare the left-hand side portions of Tables VI1 and VI11 to the right-hand side ones.) There is at the same time a reduction of the absolute value of the stabilization energy and a different pattern of compensation among contributions of different signs. The final effect is that the resulting picture of the bonding is more shifted toward the electrostatic contribution. ES(RGp) gives in all cases an overestimate of AECP(RF): the factors pp=
0.350 0.573 0.567 0.802 0.840 0.812 0.364 0.594 0.572 0.775 0.835 0.841 0.347 0.503 0.589 0.754 0.759 0.905
(A) for the Bifurcated
EMIX
ASP
EFS
EPL
-0.383 -0.894 -2.488 -1.491 2.073 -1.012 -0.450 -0.946 -2.480 -1.535 2.922 -1.020 -0.638 -1.182 -2.577 -1.014 1.158 -0.609
-12.340 -17.288 -18.242 -20.329 -20.500 -17.244 -12.226 -17.373 -18.402 -20.605 -20.912 -17.380 -10.926 -15.530 -16.654 -18.354 -18.245 -15.776
-14.388 -23.113 -21.892 -25.553 -29.218 -21.441 -14.403 -23.450 -22.08 1 -25.8 18 -29.8 15 -21.794 -12.731 -20.456 -20.339 -22.661 -24.768 -20.000
-0.649 -0.846 -1.415 -1.778 -3.732 -2.043 -0.658 -0.870 -1.464 -1.851 -4.631 -2.117 -0.566 -0.783 -1.314 -1.483 -2.842 -1.818
@; 5.354 10.558 6.250 8.884 12.381 7.851 5.574 10.952 6.364 8.974 12.735 8.185 5.045 9.397 6.030 7.433 9.293 7.296
e&
'%l:X
-6.039 -8.789 -5.601 -3.647 -2.497 -3.171 -6.175 -8.880 -5.388 -3.537 -2.749 -3.130 -5.937 -8.764 -3.966 -2.913 -1.920 -2.196
3.382 4.902 4.417 1.764 2.567 1.561 3.437 4.875 4.168 1.627 3.548 1.475 3.263 5.076 2.935 1.270 1.992 0.942
20 10
-0 -
0
\
0
-10
Y
-20 -30
-40 1.5
2.0
2.5
3.0
1.5
2.0
2.5
3.0
R (0.. . H I [i) Figure 9. Total interaction energy and its components (3-21G+ basis set) for the linear form of the system [H2PO4--H20]-: (a) at the SCF level; (b) at the C P corrected level.
AEP(R:)/ES(R:p), reported in Table IX, are more homogeneous than theffactors. In other words, the introduction of CP corrections makes the analysis of the bonding energy less basis set dependent. One could ask whether this analysis may be exploited to get approximate, but less costly, estimates of the bond strengths. The evaluation of ES is surely less costly than the evaluation of AE; there are numerous analyses and recipes allowing a fairly good
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989 5409
Counterpoise Corrections on Interaction Energy 19,
19 1 i
1
J
h
18-
h
0
&
c
p!
5a
17-
PI
16-
c
le:
2
17-
v
w“ a I
1
a PI
w“ a
15-
I
16-
.
15-
1 14
15
16
- AE(6-31G**)
17
18
14
15
16
17
Ta
- AE(6-31G**)
Figure 10. Total interaction energy A&, (kcal/mol) as produced by the empirical mean factor (fp)kES(Rc) versus M P (kcal/mol) at the 6-31G** level: (a) k = 4-31G; (b) k = 3-21G+. TABLE VIII: Interaction Energy and Its Components (kcal/mol) at the SCF and CP Corrected Equilibrium Distance (A) for the Linear Dimers basis set AE E, EpL E,, EcT EMIx AI??’ E, EpL G!
Linear [HCOO.*.H20]-
[CH3COO...H20]-
[H2PO,*..H20]-
STO-3G MINI-1 3-21G 4-31G 3-21G+ 6-31G** STO-3G MINI-1 3-21G 4-31G 3-21G+ 6-31G**
-26.862 -25.556 -26.3 38 -22.684 -21.021 -19.262 -26.735 -25.729 -26.301 -22.888 -21.784 -19.328 STO-3G -26.059 MINI-1 -26.242 -22.980 3-21G -19.8 12 4-31G 3-21G+ -19.534 6-31G** -16.288
-26.366 -29.737 -24.676 -25.125 -28.675 -21.405 -26.263 -29.850 -24.929 -25.734 -29.777 -21.566 -25.486 -29.761 -23.467 -23.236 -25.921 -19.276
TABLE I X Numerical Values of the Factors f and Text
-1.940 -1.555 -2.599 -2.8 13 -4.959 -2.91 1 -1.942 -1.590 -2.665 -2.935 -5.806 -2.965 -1.798 -1.529 -2.416 -2.468 -4.122 -2.453
33.546 22.190 13.850 12.404 16.642 10.510 33.528 22.181 13.977 12.982 17.830 10.579 34.185 23.868 13.400 11.531 14.798 9.169
Defined in the
[HCOO***H20]- [CH3COO**.H,O]-
f
f’
f
1.001 0.859 1.123 0.945 0.718 0.934
0.858 0.748 0.863 0.796 0.702 0.804
Bifurcated 0.999 0.861 1.116 0.927 0.720 0.929
STO-3G 1.019
0.770 0.696 0.835 0.810 0.713 0.810
1.018 0.862 1.055 0.889 0.732 0.896
STO-3G MINI-1 3-21G 4-31G 3-21G+ 6-31G**
f’ 0.849 0.741 0.833 0.798 0.701 0.797
1.017 0.890 1.038 0.916 0.767 0.864
0.858 0.759 0.819 0.810 0.737 0.789
0.769 0.700 0.836 0.802 0.712 0.810
1.022 0.882 0.979 0.853 0.754 0.845
0.759 0.680 0.805 0.790 0.719 0.801
Linear MINI-1 3-21G 4-31G 3-21G+ 6-31G**
0.859 1.067 0.903 0.733 0.900
appreciation of ES even for partners of large size, without making use of the full wave function of the monomersu The appreciation of ES depends, however, on the ab initio description of the interacting chemical groups and is, consequently, basis set dependent. The reduced dependence on the BS brought out for C P corrected results could facilitate the task of finding simple recipes. Let us define a mean value of the aforementioned factor,fCP, for all the species we have examined, with a fixed BS k: P p ) k (k stands for the basis set employed: M I N I - 1 , 3-21G, etc.), and let us use this factor together with the ES(RF), values re orted in Tables VI1 and VI11 to get an appreciation of APp(R$) for our set of compounds. Because the H-F limiting values of the stabilization energies are not available, we compare AEapp(k)= @P)kES(R:)k with the corresponding counterpoise corrected
e
(64) Bonaccorsi, R.; Ghio, C.; Tomasi, J. 26, 637.
Znt.
J . Quantum Chem. 1984,
-24.766 -12.199 -8.807 -5.106 -5.726 -4.255 -24.678 -12.161 -8.565 -5.146 -6.262 -4.193 -25.901 -14.281 -7.049 -4.274 -5.260 -3.004
-7.336 -4.255 -4.106 -2.044 1.697 -1.201 -7.380 -4.309 -4.119 -2.055 2.230 -1.183 -7.059 -4.539 -3.448 -1.365 0.971 -0.724
-12.598 -17.879 -18.426 -19.301 -19.435 -16.652 -12.507 -18.031 -18.638 -19.579 -19.890 -16.797 -11.315 -16.750 -16.650 -17.191 -17.254 -14.696
-16.357 -25.680 -22.068 -23.839 -27.256 -20.588 -16.263 -25.770 -22.292 -24.404 -27.925 -20.740 -14.916 -24.633 -20.692 -21.757 -24.011 -18.342
-1.675 -1.587 -2.400 -2.685 -4.632 -2.791 -1.670 -1.618 -2.459 -2.800 -5.323 -2.843 -1.458 -1.516 -2.195 -2.321 -3.710 -2.324
15.315 18.435 11.028 11.079 14.738 9.668 15.296 18.426 11.127 11.585 15.260 9.728 14.548 18.699 10.230 9.855 12.250 8.063
-13.470 -9.960 -6.425 -4.026 -4.668 -3.431 -13.405 -9.913 -6.291 -4.057 -4.933 -3.378 -13.387 -1 1.242 -4.862 -3.152 -3.802 -2.290
3.588 0.913 1.438 0.170 2.384 0.490 3.535 0.843 1.277 0.096 3.032 0.437 3.899 1.943 0.870 0.184 2.019 0.197
6-31G** interaction energies: A@p(Rg)6slG... A couple of examples are shown in Figure 10. The good correlation found with this simple recipe (the regression coefficient is r = 0.97 in both cases) is a manifestation of the reduction of the BS dependence produced by the C P correction. Notice that the “experimental” values (Le., the 6-3 1G** ones in this example) have not been employed as an empirical calibration for data obtained with other BSs: the (fP)kES(R$)k values depend on the BS k alone. A similar situation has been found for neutral hydrogen-bonded dimers. Other recipes, including also empirical calibrations, are possible. The numerical data given in the preceding tables are sufficient for the interested reader to explore other definitions. Despite the relatively large strength of the interaction, the inclusion of the polarization contribution into the recipes for the approximate values of AE does not improve noticeably the quality of the results; from this point of view anion-water and neutralwater dimers behave in the same manner. The approximate evaluation of the interaction strength based on the @P)kES requires a separate evaluation of the equilibrium distance. There are no big changes in Rg in the set of the bifurcated dimers (as well as of the linear ones) when the anion is changed, at least in the present set of compounds. It should be possible thus to define an empirical value for R,, on the basis of a few values obtained employing BSs of good quality. Such an empirical value may be introduced under the form of a step function, or of a repulsive function with an exponential decay: the C P correction modifies the exponent of this function. A single-exponential function gives, in general, a very good description of E,,(R) and G ; ( R ) , with regression coefficient r = 1 .oo.
5. Conclusions The analysis of the interaction energy for some anion-water dimers performed in parallel without and with C P corrections to
J. Phys. Chem. 1989, 93, 5410-5414
5410
the BSSE has confirmed the results obtained in our previous studies on neutral hydrogen-bonded dimers. The picture of the interaction resulting after C P corrections is less basis set dependent for the interaction along the approaching path as well as for the quantities having the status of observables, Le., R , and hE(R,). The modifications introduced by C P corrections give more emphasis to the electrostatic character of the interaction, at the expense of other contributions. The approximation of using the electrostatic component to get an estimate of AE in noncovalent dimers was proposed many years and successively tested on many systems. In more recent times, this approximation has been proposed again66 and cor-
roborated by a number of examples. This approximation is not invalidated by C P corrections; on the contrary there is numerical evidence that artifacts due to the basis set dependence of Em may be reduced to a noticeable extent, making it easier to model H-bond interactions for large molecular systems.
Acknowledgment. We are grateful to the CNUCE Institute for a generous grant of computer time that allowed us to carry out the computations with the 3-21G+ and 6-31G** basis sets on the carboxylate- and phosphate-water complexes. Registry No. HCOO-,71-47-6; CH,COO-, 71-50-1 ; H2P0Lr 14066-20-7; H20, 7732-18-5.
~
(65) Bonaccorsi, R.; Petrongolo, C.; Scrocco, E.; Tomasi, J. Theor. Chim. Acra 1971, 20, 331.
(66) Buckingham, A. D.; Fowler, P. W. J. Chem. Phys. 1983, 79, 6426.
Influence of Solvent Polarity on the Excited Triplet States of Nonphosphorescent 1,P-Naphthoquinone and Phosphorescent 8,lO-Phenanthrenequinone: Time-Resolved Triplet ESR and CIDEP Studies Hirami Shimoishi? Shozo Tero-Kubota,t**Kimio Akiyama,t and Yusaku Ikegami*.t Chemical Research Institute of Non-Aqueous Solutions, Tohoku University, Katahira 2-1 -1. Sendai 980, Japan, and Coordination Chemistry Laboratories, Institute for Molecular Science, Okazaki 444, Japan (Received: November 17, 1988; In Final Form: February 28, 1989)
The excited triplet states of 1,2-naphthoquinone and 9,lO-phenanthrenequinonewere observed in several glassy matrices at low temperatures by time-resolved ESR method. Notable solvent effects on the zfs parameters were observed, indicating the small energy separation between 3nr* and 3rr*states in these o-quinones. It was found that the TI state has dominantly rr* character in ethanol while it is an n r * in nonpolar solvents. CIDEP spectra of the semiquinone radicals produced by photoinduced hydrogen abstraction from the solvent reflect the electronic character of the T1states.
Introduction Photochemistry of quinones has been extensively studied, and in particular, recent CIDEP (chemically induced dynamic electron polarization) studies in this field made a fundamental contribution to our understanding of the reaction mechanism of pquinones.14 It has been well established that the excited state taking part in the hydrogen abstraction and electron-transfer reactions of pquinones is the triplet (TI) state, and the ODMRS and time-resolved ESR (TRESR)6*7studies assigned the TI state to be n r * in character. In contrast to the case of p-quinones, there have been only a few studies on the electronic structure and photochemistry of o-quinones. It is known that several o-quinones are photoreactive in the presence of hydrogen donors.*-1° From the phosphorescence measurements, the TI state of 9,lO-phenanthrenequinone (9,lO-PQ) is identified as nr*." However, no information has been obtained for 1,2-naphthoquinone (1,2-NQ) because of its nonphosphorescent character. TRESR technique is a powerful tool for investigating the short-lived and nonphosphorescent TI states.l2-I4 In our recent work,15 anion radicals of several o-quinones were detected for the electron-transfer reactions of amines in acetonitrile. The CIDEP spectra were emissive for 1,2-NQ and 9,lO-FQ and absorptive for acenaphthenequinone in polar solvent. This result induced us to do a detailed study on the o-quinone triplet states. This paper deals with the influence of solvent polarity on the TI states of 1,2-NQ and 9,lO-PQ (Figure 1). The observed Present address: RI Laboratory, Fukushima Medical College, Hikarigaoka 1, Fukushima 960-12. Japan. 'Tohoku University. f Institute for Molecular Science.
0022-3654/89/2093-5410$01.50/0
zero-field splitting (zfs) parameters in some glassy matrices are discussed in terms of na*-ar* interaction. Photoinduced hydrogen abstraction of these o-quinones in several solvents afforded the CIDEP spectra, which also provided information for confirming the nature of the TI states.
Experimental Section Commercial 1,2-NQ, 9,1O-PQ, and 1,4-NQ were carefully purified by sublimation after recrystallization from ethanol. Solvents were purified by distillation after dehydration by pre(1) Wan, J. K.; Wong, S.-K.; Hutchinson, D. A. Acc. Chem. Res. 1974, 7, 58. (2) Wan, J. K. S.; Elliot, A. J. Acc. Chem. Res. 1977, 10, 161. (3) Wong, S. K. J. Am. Chem. SOC.1978, 100, 5488. (4) Primer, T.; Dobbert, 0.;Dinse, K. P.; van Willigen, H. J. Am. Chem. SOC.1988, 110, 1622. (5) Kinoshita, M.; Iwasaki, N.; Nishi, N. Appl. Spectrosc. Rev. 1981, 17, 1. (6) Murai, H.; Hayashi, T.; I'Haya, Y. J. Chem. Phys. Lett. 1984, 106, 139. (7) Murai, H.; Minami, M.; Hayashi, T.; I'Haya, Y. J. Chem. Phys. 1985, 93, 333. (8) Rubin, M. B.; Zwitkowits, P. J . Org. Chem. 1964, 29, 2362. (9) Maruyama, K.; Otsuki, T.; Naruta, Y. Bull. Chem. SOC.Jpn. 1976, 49, 791. (10) Takuwa, A,; Soga, 0.;Maruyama, K. J. Chem. SOC.,Perkin Trans. 2 1985, 409. (11) Kuboyama, A,; Yabe, S. Bull. Chem. SOC.Jpn. 1967, 40, 2475. (12) Akiyama, K.; Ikegami, Y.; Tero-Kubota, S.J. Am. Chem. Soc. 1987, 109, 2538. (13) Tero-Kubota, S.;Migita, K.; Akiyama, K.; Ikegami, Y. J. Chem. Soc., Chem. Commun. 1988, 1067. (14) Hirota, N.; Yamauchi, S.;Terazima, M. Rev. Chem. Intermed. 1987, 8, 189. (15) Shimoishi, H.; Akiyama, K.; Tero-Kubota, S.; Ikegami, Y. Chem. Lerr. 1988, 251.
0 1989 American Chemical Society
