J. Phys. Chem. 1986, 90, 6625-6632
6625
Filling of Solvent Shells about Ions. 2. Isomeric Clusters of (H,0),(NH3)Ht Carol A. Deakyne* Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts 01 731 (Received: April 14, 1986)
Clusters of (H20),(NH3)H+,n = 2-4, and (NH3),H+, m = 43, for which the last ligand is added to an outer-shell molecule are compared to the corresponding clusters for which the last ligand is added to the inner-shell molecule. Partially optimized geometries were obtained with the use of the 3-21G and 6-31G* basis sets. The effect of diffuse functions and electron correlation on the calculated stabilization energies was determined for n = 1,2. The results indicate that (1) the MP2/6-31+G**//6-31G* dissociation energies adjusted for changes in the translational, rotational, and vibrational energies and in the PV work term are within 1-3 kcal/mol of the experimental data; (2) including diffuse functions in the basis, including electron correlation in the calculations, and converting AED into AHEL stabilize the (H20)2(NH3)H+ cluster for which the ligand is added to the H 2 0 with respect to the cluster for which the ligand is added to the NH4+; (3) the 6-31G* values can be used as an upper limit and the 3-21G values can be used as a lower limit for the relative energies of the isomeric clusters; (4) distinct solvent shells can be distinguished for (NH3),H+ but not for (H20),(NH3)H+;( 5 ) mixtures of isomeric clusters can be present at equilibrium for the (H20),(NH3)H+ ions when n = 4 and, possibly, when n = 3; (6) the electrostatic component of the stabilization energy is larger for the (H20),(NH3)Hf clusters for which the ligand is added to the outer shell, and the delocalization component is larger for the (H20),(NH3)Hfclusters for which the ligand is added to the inner shell. This compensatory effect, which is not observed for the (NH3),H+ ions, explains the smaller 6A.ED's found for the (H20),(NH3)H+ isomers.
Introduction Gas-phase ionsolvent molecule interactions have been studied both e~perimentallyl-~ and theoreticallybZo for a number of systems in recent years. Among the cluster ions investigated experimentally a r e ( N H 3 ) , H + , ( H 2 0 ) , H + , and (H20),(NH3),H+.'-5 The first two sets of ions have also been and n = l-6.8-10914,16*17 The calculated ab initio for m = l-6697J416 last set of clusters has been examined theoretically for m = 1 and = 1-5.6,ll,l6,18-20 One topic considered in many of the studies on cluster ions is whether the solvent builds up about the ion in distinct shells.1~3-5*8-10 Meot-Ner5 has developed quantitative criteria based on experimental thermochemical measurements with which one can probe this question. According to these criteria, (H,O),H+ and (NH3),H+ have distinct solvent shells. On the other hand, the criteria lead to contradictory predictions for (H20),(NH3)H+ depending upon which laboratory's experimental data are used.*5 The a b initio results agree with the experimental results for (H20),H+.8~10 However, not enough theoretical data are available for (NH3),H+ or for (HZO),(NH3)H+to make a comparison with the experimental predictions. For these clusters, only structures with the ligands added to the central NH4+ ion have been researched in detai1.6g7J1Therefore, it was of interest to carry out calculations on (H20),(NH3)H+ for n > 1 and on (NH3)mH+, m = 4 3 , where the ligands are added to an outer-shell molecule. The theoretical stabilization energies will aid in discriminating between the possible alternative structures for these complexes.8-10,12
The objectives of this research then were to determine: (1) the optimum geometries, charge distributions, total energies, and complexation energies of (H20),(NH3)H+, n = 2-4, and (NH3),H+, m = 4,5; (2) whether (H,O),(NH,)H+ and (NH3),H+ have distinct solvent shells, and if not why they differ from (H20),H+; (3) whether isomers of similar energy exist for (H20),(NH3)H+, n = 2-4, and for (NH3)mH+,m = 4,5; Le., whether clusters with completed inner shells are in equilibrium with isomers with partially filled inner and outer shells; (4) the effect of basis set size, zero-point energy corrections, and correlation energy corrections on the relative hydrogen bond energies of cluster ions with different values of n and with the same value of n. Computational Details The calculations were carried out ab initio with the Gaussian 82 programZ1on a VAX 11/780 computer. The optimum ge*Air Force Geophysics Scholar.
0022-3654/86/2090-6625$01.50/0
ometries of the (H20),(NH3)H+and (NH3),H+ clusters were obtained by utilizing the 3-21GZ2and, for selected ions, the 631G*23basis sets and the force relaxation method.24 The bond lengths were optimized to 0.001 A and the bond angles to 0.1O. Partial geometry optimizations were carried out for the complexes, whereby the geometries of the components25were held fmed and only certain bond lengths and angles between the components were varied. They are r l , r2,LA-H-B, and the orientation of the hydrogens on the electron-donating molecule with respect to the hydrogens on the proton-donating molecule. (See the diagram below for definitions.) In addition, for some complexes, the He-B-H angle was optimized. Although it would have been (1) Kebarle, P. Annu. Rev. Phys. Chem. 1977, 28, 445. (2) Keesee, R. G.; Castleman, A. W. J. Phys. Chem. Ref Data, in press. (3) Meot-Ner (Mautner), M. J. Am. Chem. SOC.1984, 106, 1265. (4) Payzant, J. D.; Cunningham, A. J.; Kebarle, P. Can. J. Chem. 1973, 51, 3242. (5) Meot-Ner (Mautner), M.; Speller, C. V., preceding article in this issue. (6) (a) Pullman, A.; Armbruster, A. M. Znt. J. Quantum Chem., Symp. 1974,8, 169. (b) Pullman, A.; Armbruster, A. M. Chem. Phys. Lett. 1975, 36, 558. (7) Hirao, K.; Fujikawa, T.; Konishi, H.; Yamabe, S. Chem. Phys. Lett. 1984, 104, 184. (8) (a) Newton, M. D.; Ehrenson, S. J. Am. Chem. Soc. 1971, 93, 4971. (b) Newton, M. D. J . Chem. Phys. 1977, 67, 5535. (9) (a) Kochanski, E. N o w . J. Chim. 1984,8,605. (b) Kochanski, E. J . Am. Chem. SOC.1985, 107, 7869. (10) Deakyne, C. A.; Meot-Ner (Mautner), M.; Campbell, C. L.; Hughes, M. G.; Murphy, S . P. J. Chem. Phys. 1986,84,4958. (11) Ikuta, S. Chem. Phys. Lett. 1983, 95, 604. (12) Hirao, K.; Yamabe, S.; Sano, M. J . Phys. Chem. 1982, 86, 2626. (1 3) Nguyen, M. T. Chem. Phys. Lett. 1985, 117, 57 1. (14) Del Bene, J. E.; Frisch, M. J.; Pople, J. A. J . Phys. Chem. 1985, 89, 3669. (15) Scheiner, S.; Harding, L. B. J . Am. Chem. SOC.1981, 103, 2169. (16) Desmeules, P. J.; Allen, L. C. J . Chem. Phys. 1980, 72, 4731. (17) Frisch, M. J.; Del Bene, J. E.; Binkley, J. S.; Schaefer, H. F., 111 J . Chem. Phys. 1986,84, 2279. (18) Bohm, H. J.; McDonald, I. R. J. Chem. SOC.,Faraday Trans. 2 1984, 80, 887. (19) Pullman, A.; Claverie, P.; Cluzan, M. C. Chem. Phys. Lett. 1985,217, 419. (20) Welti, M.; Ha, T. K.; Pretsch, E. J. Chem. Phys. 1985, 83, 2959. (21) Binkley, J. S.; Frisch, M.; Krishnan, R.;DeFrees, D. J.; Schlegel, H. B.; Whiteside, R. A.; Fluder, E. M.; Seeger, R.; Pople, J. A. Gaussian 82, release H, 1982, Carnegie-Mellon University, Pittsburgh, PA. (22) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J . Am. Chem. SOC.1980, 102, 939. (23) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 203. (24) (a) Pulay, P. Mol. Phys. 1969, 17, 197. (b) Schlegel, H. B.; Wolfe, S.; bernardi, F. J. Chem. Phys. 1975, 63, 3632. (25) Whiteside, R. A.; Frisch, M. J.; Binkley, J. S.; DeFrees, D. J.; Schlegel, H. B.; Raghavachari, K.; Pople, J. A. "Carnegie-Mellon Quantum Chemistry Archive", Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA 15123.
0 1986 American Chemical Society
6626 The Journal of Physical Chemistry, Vol. 90, No. 25, 1986 preferable to fully optimize the structures of the complexes, this was not feasible due to the size and lack of symmetry of some of the ions.
Several isomers were examined for the cluster ions considered. They are illustrated here for the (H,O),(NH,)H+ system. (The numbering refers to Figures 1 and 2; see Results and Analysis H
n-
. H
H
\
(1)
9 I
H'
n
"'
d \H H
= ET((B),AH+) - ET((B),,AH+) - ET(B) = -AED
H
A
H
of the clusters with large values of n, the energies of all of the ions were calculated also at the 4-31G basis set leveLZ8The 4-3 1G basis yields more accurate energetics than the 3-21G.10,29 Electron correlation was included in the calculations by carrying out single-point computations employing second-order (MP2) and third-order (MP3) Moller-Plesset perturbation theory.30 The frozen-core approximation was used to compute the correlation energy. Frisch et al.I7 have reported that single-point calculations give reasonable dissociation energies. Del Bene and ~ o - w o r k e r s ~ ~ ~ ~ ~ have shown that the largest component of the electron correlation contribution to the binding energies of the dimers they investigated is obtained at MP2. The third-order and full fourth-order components tend to cancel each Overall, they reduce the second-order contribution ~ l i g h t l y . l ~ , ~ ~ The stabilization energies were obtained from the following equation: AE,,,,
(Vlll)
H
Deakyne
-
H
(XI (XI) of Results.) The isomers differ by the number of ligand molecules bonded to the core ion and by the identity of the core ion, Le., whether it is NH4+, H 3 0 + , or NH3-.H+.-H20. The complexes can be categorized as either branched or straight-chain molecules. For example, VI11 and XI have branched structures while IX and X have straight chains. Although several other isomers are plausible for (H20)4(NH3)H+,only the ones corresponding to those given for (H20),(NH3)H+were studied. Newton and Ehrensons have shown that cyclic structures become competitive for the (H20),H+ ions as n becomes larger. They are currently under investigation for the (H20),(NH,)H+ ions, and the results will be reported in a later article. The structures of (H20),(NH3)H+, n = 1-4, and (NH3),H+, m = 2-5, where all of the ligands are added to the central ion, have been studied previously by Ikuta" and Hirao et al.,7 respectively. Hirao et aL7 optimized the structures completely at the 3-21G ( m = 2-5) and 6-31G** ( m = 2 and 3) basis set levels. In Ikuta's work," the geometries of the complexes were fully optimized with the 3-21G basis ( n = 1-4) and partially optimized with the 6-31G* basis ( n = 1-3). The n = 4 cluster with one of the water ligands bonded to an outer-shell water was examined by Ikuta," also, but the completely optimized fragments (HzO),(NH,)H+ and H 2 0were utilized to compute rl and r2 for the additional hydrogen bond. In order to have a consistent set of stabilization energies and to determine the effect of the limited optimizations on the stabilization energies, the geometries of all the clusters have been reoptimized with the method employed in this work. The effect of adding polarization functions to the basis set was probed by calculating the total energies and complexation energies with the 6-31G* and 6-31G** bases. The change in these energies caused by adding diffuse functions to the basis was determined by computing them with the 6-31+G** basis set.26 It has been shown that reliable relative hydrogen bond energies are obtained with these bases, especially with the 6-31+G** set.14,'7,27Since these basis sets were too big to be utilized to evaluate the stabilities (26) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J . Comput. Chem. 1983, 4, 294. (27) Frisch, M. J.; Pople, J. A.; Del Bene, J. E. J . Am. Chem. SOC.1985, 89, 3664. (28) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724.
In order to compare a calculated dissociation energy AED with an experimental AH', the computed energy must be adjusted for (1) the differences in zero-point energies (ZPE) between reactants and products, (2) the change in the PV work term, and (3) the temperature corrections for the vibrational, rotational, and translational energies between reactants and products. Normal-mode harmonic vibrational frequencies3I were determined for (H20),(NH3)H+, n = 1,2, and (NH3)2H+using their fully optimized 3-21G structures. The frequencies were utilized to calculate the zero-point vibrational energies and the contribution to the binding energy of the low-lying vibrational modes at 298 K.32 Hartree-Fock ZPE corrections appear to be reliable for clusters with asymmetric hydrogen bonds.I7 Entropies were computed for H 2 0 , NH4+,(H,O)(NH,)H+ (V), (H20)2(NH3)H+(VI), and (H,O),(NH,)H+ (VII) with the use of the 3-21G basis set.31 The translational, rotational, and vibrational contributions were included in the calculations. NO corrections were made for the basis set superposition error (BSSE) for the following reasons: (1) The BSSE for (H20)(NH3)H+is small (0.8 kcal/mol) when a double-{ basis set is employed and becomes smaller (0.4 kcal/mol) as the size of the basis set increases.20 (2) The BSSE for different isomers ,~ will be similar in magnit~de.~,(3) Schwenke and T r ~ h l a r have found from their study of BSSE in calculated HF-HF interaction energies that the counterpoise c~rrection,~ neither systematically reduces the spread in the uncertainty in the complexation energy for a given set of basis sets nor systematically improves the accuracy obtained with small basis sets. Therefore, they concluded that in general the extra expense of correcting for BSSE is not warranted. The better approach is to use the maximum basis set size possible for non-counterpoise-correctedc a l c ~ l a t i o n s . ' ~ ~ ~ ~ Results and Analysis of Results
Geometries. The 3-21G and 6-3 lG* (underlined) equilibrium structures of (H20),(NH3)H+, n = 1-4, (V-XV), (NH3),H+, m = 2-5 (XVI-XXII) are displayed in Figures 1 and 2. Those isomers whose 4-31G//3-21G energies are within - 3 kcal/mol of each other were investigated at the 6-31G* basis set level (Table I). Only the bond lengths and bond angles optimized in the ~~
(29) Latajka, Z.; Scheiner, S. J . Chem. Phys. 1985,82, 4131. (30) (a) Moller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618. (b) Pople, J. A.; Binkley, J. S.; Seeger, R. Int. J . Quant. Chem., Symp. 1976, 10, 1 . (31) (a) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. In?.J . Quantum Chem., Symp. 1979, 13, 325. (b) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A,; Hout, R. J.; Hehre, W. J. Ibid. 1981, 15, 269. (32) Pitzer, K. S. Quantum Chemistry; Prentice Hall: Englewod Cliffs, NJ, 1961. (33) The counterpoise correction3' for the 3-21G basis set is 4.5, 4.2, and 4.5 kcal/mol for (H,0)(NH3)Hf (V), (H20),(NH3)H+(VI), and (H20)2(NH3)H+(VII), respectively. (34) Schwenke, D. W.; Truhlar, D. G . J . Chem. Phys. 1985, 82, 2418 (35) Boys, S . F.; Bernardi, F. Mol. Phys. 1970, 19, 558.
Filling of Solvent Shells about Ions. 2
The Journal of Physical Chemistry, Vol. 90, No. 25, 1986 6627
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