J. Phys. Chem. 1994, 98, 12558-12569
12558
Binding of Polar Molecules to Li+, Na+, KS, Mg2+, and Ca2+ in Single-Ligand Adducts MSL and M2+L (L = H20, NH3, H2S, PH3) Eric Magnusson Department of Chemistry, University College (ADFA), The University of New South Wales, Canberra ACT 2600, Australia Received: June 15, 1994; In Final Form: August 29, 1994@
Electronic structure calculations show the binding of a single molecule of HzO, NH3, HzS, and PH3 to main group cations to be extremely tight (up to 40 kcal mol-’ for group 1 and up to 95 kcal mol-’ for group 2 cations); for the smallest cations the bond lengths are very short. The interactions were examined with geometry-optimized calculations at QCISD, MP2, and RHF levels using TZP and DZP basis sets; the cations were Li+, Na+, K+, Mg2+, and Ca2+ and, for comparison, H+. Averaged over all four ligands, binding to Na+ and K+ is 64% and 39% as strong, respectively, as to Li+; Ca2+ binding is 53% as strong as Mg2+ binding. Likewise, binding energies of H20, H2S, and PH3 are 86%, 68%, and 55% as great as those of NH3, invariably the most strongly bound ligand (means over all five cations). Results taken from a range of internuclear distances were used to characterize the short- and long-range metal-ligand interactions. Covalency effects explain the major departures from electrostatic behavior. They were assessed by calculations utilizing “electrostatic-only” wave functions and yielding covalency contributions of 20-50% of binding energies (Li+, MgZ+)but 10% or less for Na+, K+, and Ca2+. Relaxation of the polar molecules in the field of the cations is a small effect: it contributes from 51% of binding energy (H20, N H 3 , H2S) to 25% (PH3).
Electronic structure modeling of the metal-ligand bond is difficult at a quantitative level because the complexes are too big to handle accurately and, in any case, the experimental results are usually restricted to complexes in solution. However, the situation has been changed by new experiments conducted on small metal ion-ligand combinations in the gas phase’ and parallel computational studies.2 A feature of the results from transition metal cations bound to one or two molecules of water or ammonia is the electrostatic quality of the binding. Bauschlicher and co-workers have described the binding of water and ammonia to the monocations of the first transition series metals and describe it as largely due to ion-dipole a t t r a c t i ~ n . ~ , ~ To provide benchmarks for calculations on compounds formed by polar molecules with metals, this paper reports work carried out on group 1 and 2 cations attached to one molecule of water, ammonia, hydrogen sulfide and phosphine. The calculations center on the binding energies of the Li+, Na+, K’, Mg2+,and Ca2+ions and the polar ligands, comparing the results with proton binding energies. The work on group 1 and 2 cation binding is important for its own sake, but also for comparison with other interactions, including those with transition metal ions. A sizeable amount of literature exists on the interactions of group 1 and 2 cations with water, and it includes both the~retical~,~ and e~perimental’.~ studies. However, calculations covering other polar ligands are hardly ever mentioned and comparative data on binding energies of N, S , and P ligands do not seem to have been reported before. Other features of the binding also emerge from the study, such as the preferred orientations of the ligands, quite different for H20 and H2S. Parallel studies on substituted analogues of these ligands, on the corresponding anions (OH-, NHz-, CH30-, etc), and on halide, nitrite, and other anionic ligands important in main group metal and transition metal chemistry will be reported elsewhere? The effect on binding of adding extra, and different, ligand molecules is also being studied in order to see how to relate @
Abstract published in Advance ACS Abstracts, October 15, 1994. 0022-365419412098- 1255 8$04.5010
the results on mono-liganded species to larger clusters and to the kinds of complexes that exist in solution. Preliminary work shows that adding extra ligands will weaken the interactions and lengthen the bonds. For the case of magnesium aquo complexes, Mg(H20),2+, the average hydration energy has recently been calculated to fall from about 85 to about 45 kcal mol-’ as n rises from 1 to 6.8 To interpret either experimental or computational information about ion-ligand interactions, it is important to be able to distinguish between electrostatic and covalent binding. The distinction is not easy to make. Some steps in this direction have been made here. To start with, the total binding energy is decomposed into a covalent and electrostatic parts. Secondly, interaction potentials between each ligand and the cations are compared with the electrostatic energy of attraction of the ligands for a bare chargelo and with the highly covalent energy of attachment to a proton. Comparison of the effects of metal ions on donor ligands with the effects of the proton is important in bioinorganic chemistry, for example, in view of the observation that metals in metalloenzymes often mimic the effect of protonation of the substrate.“ An important feature of this report is that the calculations cover a range of distances between the positive ion and the ligand, not merely the distance at which the energy is a minimum. The characteristics of different types of interactions can be investigated by means of the potential energy profile, a technique which is not possible when the calculation is restricted to a single point on the curve. The information gained by the multipoint approach is of particular value in investigations of metal-ligand interactions in hindered compounds, especially metalloproteins. In cases like this the attachment of donors in amino acid side chains may be geometrically quite different from the situation in metal complexes where the ligands are free to adopt minimum energy configurations.
Computational Method Geometry-optimized calculations were carried out at fixed points over the range r(M-L) = 180-300 pm at Hartree-Fock
0 1994 American Chemical Society
J. Phys. Chem., Vol. 98, No. 48, 1994 12559
Binding of Polar Molecules
TABLE 1: Protonation Energies of HzO, NH3, HzS, and PH3 with RHF//RHF, MPUIMP2, and QCISD(T)//MP2 Theory and the 6-31+G* and 6-311+G** Basis Set&& ligand L total energy E(H+-L) orientation r(H-L);L(HAX)b binding energy AE(H+-L) hartrees (kcal mol-') level 96.06: 139.10' 0.278 98 (175.06) RHF -76.332 29 97.80; 132.4' 0.275 05 ii72.6oj MP2 -76.549 77 0.265 48 (166.59) MP2 (6-31+G*) 0.274 37 (172.17) QCISD(T) -76.560 99 as for MP2 0.344 42 (216.13) RHF -56.559 09 101.18; 180' 0.340 25 (213.51) MP2 -56.755 56 102.46; 180" MP2 (6-31+G*) 0.343 79 (215.73) 0.343 46 (215.52) QCISD(T) -56.776 95 as for MP2 MP2 0.283 31 (177.78) 134.69; 120.4' -399.130 82 0.274 31 (172.13) MP2 (6-31+G*) -399.160 32 QCISD(T) 0.287 14 (180.18) as for MP2 MP2 0.315 42 (197.93) -342.928 43 138.99; 180" MP2 (6-31+G*) 0.308 40 (193.52) 0.316 01 (198.30) QCISD(T) -342.959 89 as for MP2 Energies (hartrees), Bond Lengths (pm), and Bond Angles of the Free Ligands E(H20): -76.053 31 (94.14, 106.26') E(NH3): -56.214 67 (100.04, 108.35') E(H2S): -398.702 11 (133.08; 94.19") E(PH3): -342.477 99 (140.76; 95.67') MP2lMP2 E(H20): -76.274 72 (95.95, 103.50") E(NH3): -56.415 13 (101.33, 107.38') E(H2S): -398.847 51 (133.35,92.07") E(PH3): -342.613 01 (140.92,94.27') E(H2O): -76.286 62 (95.95, 103.50") QCISD(T)/MP2 E(NH3): -56.433 49 (101.33, 107.38') E(H2S): -398.873 18 (133.35, 92.07") E(PH3): -342.643 88 (140.92, 94.27') RHF//RHF
a All energies (in hartrees) at optimum geometries. L(HAX) refers to the angle between the H+-A axis and the major axis of the ligand (A is the ligand atom). All values refer to 6-311+G** calculations except where the 6-31+G* basis is indicated.
and second-order Moller-Plesset (FC-MP2) levels, and singlepoint QCISD(T) calculations at the MPZoptimized geometries are also reported; all relied on the Gaussian packages.12 The main basis was the 6-311+G**,13 a triple-c set supplemented with polarization functions on all atoms and, as appropriate for the calculations on the related anions with which these results will be compared in a separate article, a single set of diffuse functions. The triple-g basis is sufficiently large to ensure that enough correlating functions are available to produce correlation corrections to the Hartree-Fock binding energies in the right sense. The K+ and Ca2+compounds utilized the Wachters 14s, 1l p basist4 in the form of a 8s, 6p contraction obtained by using the MOTTEC "Atomscf' code;15 a single d function was added to each basis ( c d = 0.039 and 0.050 for K and Ca, respectively). For the MP2 calculations on K+ adducts the relatively high energies of the 3sK and 3pK orbitals (higher than the HOMO of H20) made it necessary to correlate orbitals in these subshells as well as the valence shell orbitals. Calculations to estimate covalent contributions to binding energies were made with use of the LANLlDZ electrostatic core potentials16 provided with the Gaussian 92 package. The technique is similar to one used by Horn and Ahlrichs" and involved taking the energy difference between calculations performed with and without valence shell basis functions for the cation, taking the latter case to represent the electrostatic contribution to the binding energy. Horn and Ahlrichs' method is not practicable for all basis sets because many lack the required core-valence separation and it was modified here by using a pseudopotential for the cation and the regular 6-31 l+G** basis for the ligand (at the MP2 geometry). All energies are reported at optimum geometries. Zero-point energy corrections were not made; their influence has been estimated in calculations by del Bene et Basis set superposition energy errors, discussed at length by Latajka and Scheiner'* for systems which include some of those considered here, were not corrected for.
In addition to the MP2 calculations the interactions between selected charge-dipole pairs were for three other sets of computational conditions: calculations at Hartree-Fock and QCISD(T) levels and, separately, with the slightly smaller 6-31+G* basis set. A few of these results have been reported before but usually only at the optimum geometries; see Chattaraj and Schleyer for the most recent.Ig The comparisons here were conducted to check the severity of the differences at larger metal-ligand separations and to provide results at a standardized computational level for later comparisons.
Results Tables 1-6 provide binding energy data at various computational levels for water, ammonia, hydrogen sulfide, and phosphine computed at the optimum distances for the adducts formed with the proton, Li+, Na+, K+, Mg2+, and Ca2+ (Tables 1-6, respectively). Interaction energies over the 180-300 pm range for internuclear distance are given for Li+, Na+, and K+ (Table 7), for Mg2+ and Ca2+ (Table 8), and for H+ (Table 9). Covalent contributions to binding energies are reported in Table 10 together with overlap population data, etc. Some truncated basis results for planar and bent H20 and H2S adducts of Mg2+ appear in Table 11. For ease of comparison, some important features of the interactions are depicted in the figures. The binding potential between ammonia and Li+ is exposed in Figure l a and that between ammonia and Mg2+ in Figure 2a followed by plots for the ligands water, phosphine, and hydrogen sulfide. (The computational data plotted in the figures for single- and doublepoint charges, Z+ and Z2+, are taken from a paper dealing with electrostatic models of metal-ligand bonding.l0) Figures 3 and 4 facilitate comparison between the cations for attraction to a polar ligand. For the singly charged ions there is also the comparison with the strongly covalent H+-L interaction. The H+-ligand distance was taken down below
12560 J. Phys. Chem., Vol. 98, No. 48, 1994
Magnusson
TABLE 2: Lithium Ion-Ligand Binding Energies for L = HzO, NH3, HzS, and PH3 with RHF//RHF, MPUIMp2, and QCISD(T)//MP2 Theory and 6-31+G* and 6-311+G** Basis Set&* ligand L total energy E(Li+-L) orientation r(Li-L); L(LiAX) binding energy hartrees (kcal mol-') hE(Li+-L) level H2O -83.347 15 184.52; 180" 0.058 00 (36.40) RHF Hz0 -83.567 13 186.60; 180" 0.056 57 (34.50) MP2 0.055 76 (34.99) MP2 (6-31+G*) H20 -83.578 76 as for MP2 0.056 29 (35.32) QCISD(T) NH3 -63.515 34 197.65; 180" 0.064 83 (40.68) RHF NH3 -63.715 94 199.58; 180" 0.0064 79 (40.66) MP2 0.067 54 (42.38) MP2 (6-31+G*) NH3 -63.735 07 as for MP2 0.065 74 (41.25) QCISD(T) HzS -405.974 56 243.1; 111.9" 0.036 61 (22.97) RHF HzS -406.122 61 240.01; 109.3' 0.039 26 (24.64) MP2 0.038 93 (24.43) MP2 (6-31+G*) H2S -406.148 44 as for MP2 0.039 42 (24.74) QCISD(T) RHF PH3 -349.756 29 25 1.94; 180" 0.042 46 (26.64) PH3 -349.891 40 250.09; 180" 0.042 55 (26.70) MP2 0.043 35 (27.33) MP2 (6-31+G*) PH3 -349.921 88 as for MP2 0.042 16 (26.46) QCISD(T) a All energies in hartrees at optimum geometries. * For energies of the free ligands, see Table 1. All values refer to 6-311+G** calculations except where the 6-31+G* basis is indicated. TABLE 3: Sodium Ion-Ligand Binding Energies for L = HzO, NH3, HzS, and PH3 with MP2//MP2 Theory and the 6-311+G** Basis Set@ ligand L total energy E(Na+-L) orientation r(Na-L); L(NaAX) binding energy hartrees (kcal mol-') AE(Na+-L) H2O -237.978 36 226.60; 180" 0.039 35 (24.69) NH3 -218.125 26' 239.03; 180" 0.044 66 (28.02) H2S -560.531 77 277.67; 138.5' 0.019 97 (12.53) PH3 -504.304 96 288.79; 180" 0.027 66 (17.36)
level MP2 MP2 MP2 MP2
All energies in hartrees at optimum geometries. * For ligand energies, see Table 1.
TABLE 4: Potassium Ion-Ligand Binding Energies for L = HzO, NH3, HzS, and PH3 with MPW/MP2 Theory and the 6-311+G** Basis Serb4 ligand L total energy E(K+-L) orientation r(K-L); L(KAX) binding energy hartrees (kcal mol-') hE(K+-L) H20 -675.335 76 271.86 180" 0.027 37 (17.17) NH3 -655.478 08 289.26; 180" 0.029 10 (18.26) HIS -997.853 85 357.20; 137.4" 0.011 38 (7.14) PH3 -941.623 22 355.20; 180" 0.015 25 (9.57)
level MP2 MP2 MP2 MP2
All energies in hartrees at optimum geometries. For ligand energies, see Table 1. For the K atom basis and K electron correlation, see text.
TABLE 5: Magnesium Ion-Ligand Binding Energies for L = HzO, NH3, HzS, and PH3 with RHJ? and MP2 Theory and the 6-31+6* and 6-311+G** Basis Set&* ligand L total energy E(MgZ+-L) geometry r(Mg-L); L ( M g A X ) binding energy hE(MgZ+-L) hartrees (kcal mol-') level H20 -275.003 01 193.9; 180' 0.126 71 (79.51) RHF H20 -275.222 67 195.84; 180" 0.124 96 (78.41) MP2 0.127 44 (79.97) MP2 (6-31+G*) H20 -275.233 88 as for MP2 0.124 27 (77.98) QCISD(T) NH3 -255.187 83 206.06; 180" 0.150 17 (94.23) RHF 3" -255.389 36 207.79; 180" 0.151 06 (94.79) MP2 0.157 33 (98.57) MP2 (6-31+G*) NH3 -255.408 06 as for MP2 0.151 58 (95.12) QCISD(T) HzS -597.640 13 246.42; 107.9" 0.115 03 (72.18) RHF H2S -597.789 69 246.12; 104.1" 0.119 19 (74.79) MP2 0.121 76 (76.41) MP2 (6-31+G*) H2S -597.816 36 as for MP2 0.120 19 (75.42) QCISD(T) PH3 -541.440 81 255.65; 180" 0.139 83 (87.74) RHF PH3 -541.574 62 255.08; 180" 0.138 62 (86.99) MP2 0.142 45 (89.39) MP2 (6-31+G*) PH3 -541.605 04 as for MP2 0.138 17 (86.70) QCISD(T) All energies (in hartrees) at optimum geometries. For isolated ligand energies, see Table 1. All values refer to 6-311+G** calculations except where the 6-31+G* basis is indicated. the equilibrium OH, NH, SH, and PH distances in the H30+, N&+, H3St and P b + ions but the other interactions were not computed below 160-180 pm. For all ligands the PE profile for the interaction with the point charges Z+, Z2+ curves sharply downward as the separation is reduced, becoming unrealistically large at distances below about 180 pm. The profile has no minimum because the point charge has no inner shell electrons with which to repel the neutral molecule at small separations.
As the data in Table 9 show, MP2 level calculations of the H+-NH3 interaction energy over the r(H+-N) range from 100 to 300 pm show no sign of converging at large separations to the values calculated for Z+-NH3, as they do at RHF level. The problem arises because the dissociation of a proton from N&+ is complicated by the preferred dissociation to H and NH3+ and the two configurations of [H-NH# both contribute to the MP2 wave function at large H-N distances. (The
Binding of Polar Molecules
J. Phys. Chem., Vol. 98, No. 48, 1994 12561
TABLE 6: Calcium Ion-Ligand Binding Energies for L = H20, NH3, HzS, and PH3 with MP2 Theory and the 6-31+G* Basis Set@& ligand L total energy E(Ca2'-L) geometry r(Ca-L); L(CaAX) binding energy AE(Ca2+-L) hartrees (kcal mol-') level HzO -752.413 03 245.68; 180" 0.073 44 (46.08) MP2 NH3 -732.580 25 253.18; 180" 0.095 58 (59.98) MP2 HzS - 1074.97099 303.54; 87.9" 0.053 51 (33.58) MP2 0.064 18 (40.27) MP2 PH3 -1018.744 84 311.60; 180" All energies (in hartrees) at optimum geometries. For isolated ligand energies, see Table 1. For the Ca atom basis, see text. TABLE 7: Lithium, Sodium, and Potassium Ion Attraction Energies for M+L adducts (L = HzO, NH3, HzS, PH3) at RHF and MP2 Levels and the 6-311+G** Basis Serb" ion-ligand distance (pm) 180 200 220 240 300 level -0.057 76 -0.056 00 -0.050 34 -0.043 93 -0.028 48 RHF MP2 -0.056 08 -0.055 14 -0.049 97 -0.043 80 -0.028 45 -0.055 97 -0.055 02 -0.049 87 -0.043 73 -0.028 43 MP2 (unrelaxed) -0.055 83 -0.054 82 -0.049 62 -0.043 47 -0.028 12 QCISD(T) -0.060 92 -0.064 78 -0.061 32 -0.055 12 -0.036 16 RHF MP2 -0.060 20 -0.064 78 -0.061 93 -0.056 13 -0.037 34 MP2 (unrelaxed) -0.059 27 -0.064 21 -0.061 57 -0.055 89 -0.037 22 MP2 -0.039 25 -0.029 14 -0.022 68 -0.036 13 +0.010 83 MP2 (unrelaxed) +0.011 58 -0.022 34 -0.035 91 -0.039 10 -0.029 08 MP2 -0.035 08 -0.041 90 -0.034 61 $0.028 64 -0.015 31 MP2 (unrelaxed) +0.030 18 -0.013 26 -0.032 77 -0.039 58 -0.032 92 ion-ligand distance (pm) level 200 220 240 260 300 Na+-H20 -0.032 33 -0.039 05 -0.038 47 -0.035 29 -0.027 81 MP2 Na+-NH3 -0.028 99 -0.041 94 -0.044 65 -0.042 80 -0.034 93 MP2 K+-H20 +0.030 83 -0.021 87 -0.026 83 -0.025 65 MP2 K+-NH3 +0.063 34 -0.014 77 -0.025 36 -0.028 8 1 MP2 All energies (in hartrees) at fully optimized geometries except for those designated MP2 (unrelaxed), which were calculated at the MP2//MP2 geometry of the isolated ligand. For isolated ligand energies, see Table 1. For K basis and K electron correlation, see text.
TABLE 8: Magnesium and Calcium Ion Attraction Energies for M2+LAdducts (L = H20, NH3, H S , PH3) at RHF and MP02 Levels and the 6-311+G** Basis Sel?J'c ion-ligand distance (pm) 180 200 220 240 300 level MgZ+-H20 -0.121 48 -0.125 96 -0.116 70 -0.103 03 -0.065 35 RHF -0.116 72 -0.066 66 MP2 -0.118 39 -0.124 63 -0.103 94 MgZf-HzO Mg2+-Hz0 -0.117 68 -0.124 03 -0.116 15 -0.103 41 -0.066 42 MP2 (unrelaxed) Mg2+-Hz0 -0.117 72 -0.123 94 -0.116 02 -0.103 21 -0.065 85 QCISD(T) MgZ+-NH3 -0.131 84 -0.149 43 -0.147 17 -0.136 27 -0.093 66 RHF Mg2+-Nh3 -0.131 45 -0.149 91 -0.148 93 -0.139 46 -0.100 60 MP2 Mg2+-NH3 -0.128 32 -0.148 31 -0.148 15 -0.139 08 -0.100 26 MP2 (unrelaxed) MgZ+-H2S f0.011 32 -0.071 62 -0.107 61 -0.118 70 -0.100 18 MP2 Mg2+-HzS +0.013 72 -0.070 45 -0.106 82 -0.118 -0.099 90 MP2 (unrelaxed) Mg2+-PH3 +0.027 73 -0.070 37 -0.117 19 -0.135 52 -0.123 83 MP2 Mg2+-PH3 +0.034 34 -0.061 88 -0.107 37 -0.124 80 -0.112 17 MP2 (unrelaxed) Ca2+-H20 -0.025 88 -0.060 62 -0.073 01 -0.071 37 -0.057 74 MP2 Ca2+-NH3 -0.079 25 -0.093 66 -0.095 19 -0.083 93 MP2 a All energies (in hartrees) at fully optimized geometries except for those designated MP2 (unrelaxed), which were calculated at the MP2//MP2 geometry of the isolated ligand. For isolated ligand energies, for Table 1. For Ca basis, see text.
preference arises because the ionization energy of NH3 (8.5 eV) is less than that of the hydrogen atom (13.6 ev).) Because of the influence of the singlet [H-NH3] configuration, the MP2 optimum geometry of the NH3 fragment is almost planar, contrasting with the pyramidal shape of the molecule as calculated by the restricted Hartree-Fock method, it being impossible for dissociation to two radicals to occur within the restricted formalism. The problem has been discussed by Kaldor, Roszak, Hariharan and KaufmanZoand, for similar cases involving dications, by Gill and Radom,21and the MP2 results should be ignored at r(N-H) values above about 250 pm. The problem recurs in various ways for other interactions of the proton considered here such as with H20, HzS, and PH3 ( E s 10.8, 11.7, and 8.6 eV, respectively), these three molecules also being easier to ionize than the hydrogen atom. Unlike the MP2
binding energies, RHF binding energies converge appropriately to zero energy at large separations, the bad dissociation behavior for which SCF theory is famed being avoided because the restricted Hartree-Fock method forces dissociation of cations like NH4+ to the closed shell species H+ and NH3. A similar problem occurs for the interaction between Mg2+ and NH3, where dissociation to Mg+ and NH3+ occurs at large separations in the MP2 level calculations. To facilitate discussion of the contribution to binding energies from relaxation of the ligands, Table 7 contains data calculated for Li+ and MgZf in interaction with the four ligands over distances from r = 180 to 300 pm but with the ligand molecules fixed in their isolated molecule geometries (see the entries designated MP2(unrelaxed)]. As a compatability check with literature values, binding
12562 J. Phys. Chem., Vol. 98, No. 48, 1994
Magnusson
TABLE 9: Proton Attraction Energies for H+L Adducts (L = Hz0, NH3, H2S, PH3) with RHF//RHF, MW/MP2, QCISD(T)//MP2 Theory and the 6-311+G** Basis Serb proton-ligand distance (um) 100 150 200 250 300 H+-H20 -0.277 59 -0.177 12 -0.094 38 -0.050 43 -0.030 01 H+-H20 -0.274 64 -0.189 09 -0.112 75 -0.066 03 -0.037 75 H+-H20 -0.257 81 -0.190 68 -0.115 23 -0.074 85 -0.066 17 H+-NH3 -0.344 30 -0.247 93 -0.160 67 -0.092 89 -0.061 69 H+-NH3 -0.339 75 -0.264 70 -0.180 28 -0.130 21 -0.104 51 H+-H2S -0.168 10 -0.274 26 -0.202 42 -0.143 61 -0.109 53 H+-PH3 -0.175 32 -0.310 65 -0.240 09 -0.172 95 -0.132 05 ~
and
~~~~~~
level RHF
MP2 QCISD(T) RHF MP2 MP2 MP2
'All energies (in hartrees) at optimum geometries. For isolated ligand energies, see Table 1. TABLE 10: Covalent Contributions (AE,,,) to Binding Eneriges for Li+, Na+, K+, Mg2+,and Ca2+Adducts (L = H20, NH3, HzS, PH3); Energies in Hartreeeb ion-ligand distance (pm) 180 200 220 240 300 Li(H20)+ BE -0.0578 -0.0560 -0.0503 -0.0439 -0.0285 -0.0144 -0.0062 -0.0030 -0.0017 -0.0005 AE(Li+-Z+)c +0.0252 +0.0110 +0.0045 +0.0015 -0.0002 PMOd 0.350 0.278 0.194 0.130 0.036 Li(NH# BE -0.0578 -0.0560 -0.0503 -0.0439 -0.0285 AECOV -0.0144 -0.0062 -0.0030 -0.0017 -0.0005 AE(Li+-Z+)' +0.0252 f0.0110 f0.0045 +0.0015 -0.0002 PMOd 0.350 0.278 0.194 0.130 0.036 Mg(Hz0)" BE -0.12148 -0.12596 -0.11670 -0.10303 -0.06535 &OV -0.0299 -0.0173 -0.0119 -0.0092 -0.0042 AE(Mg2+-Z2+) +0.0841 +0.0366 +0.0134 +0.0026 -0.0031 0.396 0.342 0.286 0.126 DM0 0.444 ion-ligand - distance (um) .~ . 200 220 240 260 300 Na(HzO)+ BE -0.0323 -0.0391 -0.0385 -0.0353 -0.0278 AE,,, -0.0074 -0.0030 -0.0013 -0.0007 -0.0003 pMod 0.010 0.022 0.024 0.022 0.014 Na(NH# BE -0.0419 -0.0290 -0.0447 -0.0428 -0.0349 AEcov -0.0214 -0.0106 -0.0053 -0.0029 -0.0011 mod 0.027 0.042 0.042 0.030 0.025 K(Hz0)' BE -0.0308 -0.0219 -0.0268 -0.0267 A.Ecov -0.0060 -0.0013 -0.0007 -0.0003 p ~ o -0.151 -0.039 -0.019 0.004 K(NH3)+ BE -0.0633 -0.0148 -0.0254 -0.0288 -0.0051 -0.0026 -0.001 1 AE,,, -0.0193 -0.060 -0.041 -0.040 PMO 0.0 Ca(H20)2+ BE -0.0204 -0.0583 -0.0742 -0.0727 -0.0599 AEcov -0.0059 -0.0024 -0.0011 -0.0006 -0.0003 PMO 0.4 Ca(NH#+ BE -0.0793 -0.0937 -0.0952 -0.0839 AEcov -0.0112 -0.0062 -0.0044 -0.0031 PMO 0.4 Calculated with the CEP-31* basis (Li, Mg), LANLlDZ basis (Na, K, Ca), and the 6-311+G** basis (other atoms). RHFUMP2 level results for comparison with entries in Table 1-3 and 6. AE(Mn+Z"+) is the energy difference between cation-ligand and bare charge-ligand binding energies (Tables 4 and 6, respectively). dpWo is the metal-oxygen bond order (RHF overlap population). ~
C
O
V
energy results for H30+ and Li(H20)+ may be compared with results at a generally similar level from del Bene et al.,5 who report 0.273 78 hartree (MP4 level) and 0.056 10 hartree (MP3 level), respectively. Adding zero-point energies calculated
TABLE 11: Covalent Contributions (AEcov)to Binding ~+ in Planar Energies for Mg(HzO)2+and M ~ ( H z S ) Adducts and Bent Geometrieeb MAX angle' 90" 120" 150' 180" M~(HZO)~+ (r(Mg-0) = 200 pm) BE 0.0791 0.1089 0.1216 0.1246 mcov 0.0295 0.0233 0.0189 0.0173 PMs-0 0.392 0.398 0.394 0.396 M~(HZS)~+ (r(Mg-S) = 238.2 pm) BE 0.1163 0.1164 0.1063 0.1004 m c o v 0.1733 0.1775 0.1683 0.1549 PMg-S 0.734 0.704 0.702 0.722 ~
~~~
Calculated using the CEP effective core potential for Mg and the 6-31l+G** basis for the other atoms and for the valence shell functions of the metals. RHF calculations at the MP2-optimized geometries. MAX refers to the angle between the Mg-A bond and bisector of the HAH angle; it is 180" for the planar conformation. A is the ligand atom. from RHF frequencies, APV terms, etc., yields M g 8= -0.262 63 hartree for Hf/H20 binding (exptl value -0.263 42 f 0.002 87)22 and M g 8 = -0.054 50 hartree for Li+/H20 binding (exptl value -0.054 18 f 0.003 19).23 When converted to enthalpies in the same way, the MP2//6-311+G** level binding energies reported here lie within 2 kcal mol-' of the experimental values. In addition to the binding energy data, Figures 1 and 2 also include several other plots. The curve labeled Z+-H20 in Figure l b represents the attraction of a bare charge for H20. This model of cation-ligand binding is discussed elsewhere.24 AE(Li+-Z+) represents the difference between the Li+ ion attraction to the ligand and that of a bare charge; for separations below about 250 pm the difference can be large. It is usually positive because it is mainly due to the repulsion between the ligand and the inner shell electrons which the cations possess but which the bare charge Zn+ does not possess. However, the difference can also be partly due to covalent binding, here estimated from truncated basis calculations and plotted separately as AE,,,.
Discussion Discussion of the calculated interaction energies of five positive centers with the four neutral ligands will be mainly directed at the MP2//MP2 results because (a) the QCISD(T) results are insufficiently different in interactions of this kind to lead to any clear-cut differences in interpretation of the overall computational trends and (b) Hartree-Fock results are quite different from those from the correlated calculations at several important points. Exceptions are the results for protonmolecule interactions at large distances, a phenomenon already discussed; in these cases the MP2 results are much less satisfactory than the QCISD(T) level results.
J. Phys. Chem., Vol. 98, No. 48, 1994 12563
Binding of Polar Molecules 0.2
0.05
---
b . AE(LI+-Z+) 0
VI
0.1 0
I
e,
5
~;,
-0.05 BE
e
m
@-'C-,,
-0.1
.-
u)
F
Q
Q
0.05
c
.-
0
e
E
-
0
e
-0.05 -0.1
A
t
\. 100
150
200
.
I
100
300
250
I
150
200
250
300
r(M-L)
r(M-L)
0.2
i
Mg2+-PH3
', ,
0.1
0
0
-
-0.05
0
-0.1
t
m
f.
-0.1
.-F u)
.-VI
-0.2
F
0.05
c c
0.1 0
-0.05 -0.1 -0.2
-0.3 100
150
200
250
300
350
400
r(M-L)
Figure 1. Binding energies (BE) between the Li+ ion and a single ligand molecule L for (a) ammonia, (b) water, (c) phosphine, and (d) hydrogen sulfide, calculated at separations from 180 to 400 pm at the MP2//MP2 level and using the 6-311+G** basis set. Covalent contributions to bonding (A&,,,),bare charge-ligand attractions (Z+L), and the difference between lithium ion and bare charge attraction (AE(Li+-Z+) are also plotted.
Bond Lengths. The optimum metal-ligand bond lengths in Tables 2-6 and obtained at the MP2/6-311+G** level of calculation are much more readily compared with experimental results for water as ligand than for the other molecules. Two important sources are the recent compilation of Ohtaki and RadnaiZ5 and the earlier ones by Friedman and Lewis and Shannon.26 As expected for singly coordinated species the values obtained here for the adducts of monovalent and divalent
100
150
200
250
300
350
400
r(M-L)
Figure 2. Binding energies (BE) between the Mg2+ion and a single ligand molecule L for (a) ammonia, (b) water, (c) phosphine, and (d) hydrogen sulfide and at separations from 180 to 400 pm calculated as in Figure 1. Covalent contributions to bonding (AEcov),bare chargeligand attractions (Z*+L),and the difference between magnesium ion and bare charge attraction (AE(Z2+-Mg+) are also plotted. cations lie a little below the lower ends of the ranges quoted by these authors for tetra-coordinated species and even further below the hexa-coordinated species in crystals. Although transition metal ion adducts show exception^,^.^ this is normal behavior for main group cations;6 the addition of extra ligands always lengthens the bond and weakens the interaction. It is useful to compare the optimum bond lengths calculated here for adducts of H20 with the Ohtaki and Radnai values.25 These workers made estimates of the geometries of
Magnusson
12564 J. Phys. Chem., Vol. 98, No. 48, 1994 0
0.05
-0.01
0
-0.05
-0.02
-0.1
-0.03 -0.04
-0.15 '
-0.05
i
-0.06
-0.25 BE (Mn*..NH3)
0 -0.01
-0.02 -0.03 -0.04 -0.05
[ ,p* I
-0.2
-
,
-0.06
0
-0.01
L
O b
-0.02
-0.05 /
-0.03
1
-0.04
-0.1
-0.15 1
-0.2 -0.25
1
1
."
.*-.
-0.06
I
:(c)
*
-0.05
1
0
.
-0.02 -0.04
-0.06 -0.08
-0.1 -0.12 -0.14 0 BE (Mn+..H2S)
-0.02 -0.04
100
150
200
250
300
350
400
W-L)
Figure 3. Binding energies between a single molecule of (a) ammonia, (b) water, (c) phosphine, and (d) hydrogen snlfide and the ions Li+, Na+, K+,Mg2+, and CaZ+(full curves) and H+ (dotted curves) at separations frdm 100 to 400 pm and calculated as in Figure 1.
4-, 6-, and 8-coordinate complexes of the group 1 and 2 cations from a large number of experimental results, not all of which were concordant: horangez5
cation Li+ Na+
K+ Mg2+ Ca2+
coord no. 4-6 4-8 8 6 6
(pm) 200-213 240-250 271-286 200-212 244-246
present work (pm) 187 239 272 196 246
Note that one water molecule is bound some 10%closer to Li+ ~RCI MP+ ions than four or six water molecules but that the contraction almost disappears in binding to the larger cations.
-0.06 -0.08
-0.1
-D 12 -0.44 -0.16 100
150
200
250
300
350
400
r(M.L)
Figure 4. Binding energies calculated as in Figure 1 between Li+ (a), Na+ (b), K+ (c), Mg2+(d), and Caz+(e) and a single ligand molecule L (L = NH3, HzO,PH3, H S ) at separations from 180 to 400 pm. The optimized bond distances obtained here may also be campared with the distances predicted from the ionic radii (of the cations) and the covalent radii (of the ligands). In all cases the comparison shows the ligand to be binding at a radius which is not constant but lies somewhere between the covalent and van der Waals radii of the donor atom. (The K+ adducts formed with HzS and PH3 are exceptions; both bind at distances greater
J. Phys. Chem., Vol. 98, No. 48, I994 12565
Binding of Polar Molecules
H20
NH3
H2S
PH3
Figure 5. Optimized bond distancesfor LPL, Na+L, and K+L (upper) and Mg2+Land Ca2+L(lower) for L = NH3, H20, PH3, and H2S. The ionic radii of the cations are shown (shaded) to reveal the residual “binding radii” of the ligands (unshaded).
than the van der Waals radii would imply.) The actual radii, obtained by subtracting the standard ionic radius of the cation from the metal-ligand distance obtained by optimization, are shown in bar graph form in Figure 5. These results have important implications for attempts at electrostatic modeling of the interactions. Strangely, the optimized metal-ligand distances are smaller for the lithium than for the magnesium adducts, even though the ionic radius for Mg2+ is consistently quoted as the ~ m a l l e r . I ~This *~~ comment applies to all ligands, the differences being less for H2S and PH3 than for water and ammonia, and it suggests that partial covalency in the bonding may be responsible. If so, this is consistent with the fact that the bond distances are within the range expected for partly covalent binding. Note the reversal of the order of sizes if covalent radii are used for the prediction (rcov(Li)= 134 pm .C rcov(Mg)= 145 pm) compared with qon(Li) = 90 pm > rcov(Mg)= 86 pm. The bar graphs in Figure 5 show each optimized bond length value as the sum of the standard ionic radius of the cation (upper bar) and a highly variable bond radius for the ligand (lower bar). For Li+, Na+, and K+ the residual “binding radius’’ increases in parallel with the size of the cation. For bonds from Li+, Na+, and K+ to water the ligand radii are 97, 111, and 120 pm, respectively, yielding about the same relative increments as those for the other three ligands. These results may be rationalized simply by noting the chargehadius ratios for the three cations. For Mg2+ and Ca2+ adducts this explanation for the residual binding radii of the ligands is impossible. Water adducts do indeed yield residual radii in the expected order for these two ions, but for the other three ligands the order is reversed; they are greater by some 10 pm for Mg2+ than for Li+ adducts for all four ligands. With a deforming power more than double that of Li+, the Mg2+ ion would have been predicted to bind much closer to the ligand. Instead of this, the binding radii of
NH3, H2S, and PH3 with Mg2+ are about the same as those with Na+, not Li+. The only explanation is that covalency is interfering with predictions based on electrostatic binding, and, on this basis, the magnesium adducts are anomalous (because they show the highest covalency contributions),not the calcium compounds. Consistent with this is the fact that the anomalous behavior occurs not for water but for the three ligands which show the greatest degree of geometrical distortion when bound to Mg2+ (see below). Strengths of Binding. The interaction energies plotted in the figures are broadly similar, and the patterns are easily described. The figures contain MP2 level results; the differences between these results and the higher level QCISD(T) numbers are generally less than 0.0005 au (0.3 kcal m-l). The latter were calculated for the Li+ and Mg2+ minimum energy MP2 geometries only and appear in Tables 1, 2, 5, and 7-9. Taking water as an example, the order of binding strengths of the ions and charges to the neutral molecule is predictable (see Figure 3b). Because of the strong covalent component, the binding energy of the proton to H20 is much greater than that of a bare charge to distances beyond 300 pm.Io However, by 400 pm the attraction of H+ to H20 is only as great as that of a bare charge and the H+-H20 and Z+-H20 curves merge. When the H+ to H20 bond is stretched this far, the binding is entirely electrostatic. Covalent binding and polarization are the two mechanisms likely to produce a difference from purely electrostatic behavior, but a separation of 400 pm is so far beyond the binding range for so small a species as H+ that covalency effects cannot exist. Polarization of the unbound H’ ion is impossible because there are no inner shell electrons. In spite of the strength of the covalent 0-H bond, the H+-OH2 interaction energy is much smaller than the Mg2+-OH2 energy and smaller by far than the attraction between water and a dipositive point charge. In turn, all of these interactions are only a fraction of the electrostatic attraction between two single but opposite point charges. These relativities will be taken up elsewhere in a parallel report on cation binding to N, 0, P, and S anions.9 In spite of the fact that the optimum Mg2+-ligand separations are greater than the corresponding Li+-ligand distances the binding energy of water for Mg2+ is much more than twice as strong as that for Li+. This is true over the whole range of separations for which the interaction energies were calculated. For example, at 200 pm the binding energies are 0.066and 0.182 hartree (Li+ and Mg2+). For the H2S and PH3 adducts the disparity is even more stark, the Mg2+ binding energies being more than 3 times as great as those due to Li+. The relationships are much different for the larger cations, which are much less strongly bound to neutral ligands than Li+ and Mg2+. Comparisons of Binding to H20, NH3, HzS, and PH3. The relative strengths of binding of the four ligands are most easily viewed in Figures 1, 2, and 4. Generalizations are difficult to make because the larger ligands bind at greater distances and their binding energies decline at larger separations than those for water and ammonia. The order in which the ligand binding energies fall (kcal mol-’) is summarized below:
H+
NH, 213.5
Li+
>
PH,
> H2S >
H20
197.9
177.8
172.6
NH, > H20> PH, > H2S 40.2
35.5
26.7
24.6
12566 J. Phys. Chem., Vol. 98, No. 48, 1994 Na+
NH, > H 2 0 > PH, 28.0
24.7
Magnusson these characteristics occurs for the binding of Mg2+ to H2S and PH3; here the BE and Zz+-L curves are disparate even out beyond 400 pm. For the same reason, the AE(Z2+-Mg2+)curve drops below the zero energy line. Strengths of binding, as determined relative to the two strongest binding ions, are
> H2S
17.4
12.5
K+
NH, < H 2 0 > PH, > H2S 18.3 17.2 9.6 7.1
Mg2+
NH, > PH, > H,O > H2S 94.8 87.0 78.4 74.8
Ca2+
NH, > H 2 0 > PH,
relative binding strengths for Li+ Na+ K+ Mg2+ CaZ+
> H2S
60.0 46.1 40.3 30.1 In spite of binding more weakly than ammonia, water always binds at shorter range than ammonia, behavior mimicked by H2S and PH3. Relative to ammonia, always the strongest ligand bound, binding strengths of the four polar ligands are relative binding strength of NH3 H20 PH3 H2S meansoverallcations standard deviations
100%
86% 6%
68% 15%
55% 16%
This pattern of the binding of the four ligands is the least variable feature of the calculations. Of all the metal ions it is disturbed only by Mg2+ and then only to a small extent. Covalency emerges as an important difference between the small ligands and the larger H2S and PH3 molecules, as the AEc,, curves show in Figures 1 and 2. The size of this contribution is enough to offset the strong repulsion to inner shell electrons in the cations and produce unexpectedly small values for AE(Li+-Z+) and AE(Mg2+-Z2+) at the optimum separations. By comparison, these quantities for H20 and NH3 binding are dominated by inner shell repulsion and are large and positive. Comparison of Binding to Li+, Na+, K+, Mg2+,and Ca2+. Metal ion comparisons are most easily made from Figure 3 and the reasons for them in Figures 1 and 2. They provide no support for easy generalizations about bond strengths. For H2S and PH3, for example, proton binding is everywhere stronger than cation binding, whether monovalent or divalent. Again, for ammonia, the distinction between monovalent and divalent ion binding is clear, but it becomes progressively blurred for H20, H2S, and PH3. Ammonia stands out as the ligand best adapted to discriminate between different cations. As argued later, the separate effects of covalency, size, charge, and inner shell repulsion combine in different ways to award each metal its own character. As is obvious from Figure 5 , the uniqueness is expressed in bond lengths as well as bond strengths; neither is easy to predict from simple electrostatic arguments. The attraction of water for lithium ion is smaller than the Z+-H20 attraction out to distances beyond 400 pm, at which point the two become identical. [AE(Z+- Li+)] is repulsive below 250 pm but faintly attractive for a small part of the distance range beyond that. Covalency is small at separations as large as 300 pm but still of a size to produce this small stabilizing interaction (0.005 hartree = 3 kcal mol-' = 13 kJ mol-'). It is also present, of course, at smaller separations but does not show because it is swamped by the repulsive component. Although taken up separately later, comparisons between the various reasons for strong and weak binding may start with the covalent contributions displayed in Figures 1 and 2 . Bonds to water contain the least covalency. In addition, the covalency decays quickly with increasing separation, so the binding energy curves (BE) to water depart least from the behavior of a molecule attracted to the point charge Zz+. The reverse of both
meansoverallligands standard deviations
100%
64% 9%
39% 9%
100%
53% 9%
Relaxation of the Ligands. As frequently noted, the geometries of ligand molecules are altered in the presence of an ion or a point charge and the size of the change affects the bond strength. The optimized geometries of the water molecule in the fields of H+, Li+, and Mg2+ ions are given below together with hErelax, the energy lowering obtained when the water molecule relaxes in this way. Interference with bonding in the H20 fragment is strongest when the foreign charge is H+ (because it forms a strong covalent bond) or Mg2+ (because of the severity of the perturbation). The deformations follow unusual patterns. For example, in several cases the approach of the charge produces a change in one direction, which is reversed as the charge gets closer to the ligand. separation (pm) H+
r(0-H) L(H0H) AEreiax (kcal mole-') Li' r(0-H) L(H0H) AEnlax(kcal mole-') Mg2+ 40-H) L(H0H) AEnlax(kcal mole-')
180 98.1 106.7" 0.8 96.5 104.7' 0.06 97.2 103.6' 0.4
200 98.1 106.2' 0.7 96.2 105.1' 0.06 97.6 105.2' 0.4
300 96.2 105.2' 0.1 96.0 102.8' 96.7 105.9' 0.1
= 96.0 103.5" 96.0 103.5' 96.0 103.5'
Changes in the geometry of ligand when confronted by an ion or a point charge do not represent the whole change which the ligand molecule experiences; the electronic distribution is also polarized. The change in electronic structure more than compensates for the effects of the geometry change, which, if imposed on the molecule in the absence of the ion, would be unfavorable. The figures for the metal ion adducts below are calculated with the water molecules fixed at their field-free optimum geometries and the results compared with the fully optimized energies to yield AEE~,Mn++(H20).Calculations of the effect of the same change imposed on a free water molecule show the cost of deforming the water geometry. For these five cations it is about the same magnitude as the net improvement in binding energy in the adduct, which shows that the gross benefit of the electronic rearrangement must be about double the cost. AEre1axM"+(H20) (kcal mole-') Li+(H20) Na+(H20) K'(H20) Mg2+(Hz0) CaZ+(H20)
-0.07 -0.03 -0.01 -0.38 -0.26
A&e1ax(H20) (kcal mole-') +0.07 +0.04 f0.01 +0.41 +0.24
The data below allow a comparison of the relaxation contributions to binding energy in the four ligands. The AErela, values at the optimum separations show the strong dependence on the charge on the ion and the softness of the ligand with
J. Phys. Chem., Vol. 98, No. 48, 1994 12567
Binding of Polar Molecules unexpectedly high values for phosphine adducts: Li(H20)+ Li(NH3)+ Li(HZS)+ Li(PH3)+ AEElax(kcal mole-')
m r e a ix (kcal
-0.1
-0.4
-0.2
-1.3
Mg(HzO)'+
Mg(NH#+
Mg(HzS)'+
Mg(PH#+
-0.4
-0.8
-0.4
-7.2
mole-')
The Orientational Dependence of Ion-Dipole Binding. NH3, like PH3, has only one lone pair, and it points along the dipolar axis of the molecule. So, if either of these molecules forms a covalent bond, it will probably be aligned with the lone pair and have the same geometry as if the binding were due to the ion-dipole attraction only. HzO and H2S have two lone pairs, neither of which coincides with the direction of the dipole. As a result, the orientation of a water or hydrogen sulfide donor molecule in the neighborhood of a cation is unpredictable. Apart from the strong preference for a pyramidal conformation for the strongly covalent H+-H20 and H+-H2S interactions, the dependence of the water and hydrogen sulfide binding energies on ligand orientation found in these results would have been very difficult to guess. The orientation of water as a ligand is often discussed; Friedman has collected crystallographic data for a compilati~n.~' For H2O the preferred approach of a proton lies along a curve drawn through the density maximum of one of the lone pairs, covalent bonding being dominant. At the bottom of the well the bond angles for the symmetrical pyramidal H30+ structure are %112", but by the time a proton has been withdrawn to a distance of 400 pm its interaction with the water molecule is almost entirely electrostatic and the 0-H+ bond lies only 5" away from the HOH plane. The structures calculated for the water adducts of Li+ and Mgz+ are planar at all separations. This may not be the case for coordination of four or six water molecules, and neutron diffraction results are said to indicate tilt angles varying from 40" to 70" for LiCl solutions.25 Also from neutron diffraction experiments, the atomic positions reported for the three unique water molecules in the Mg2+(H20)6 entity in magnesium hydrogen maleate show tilt angles of 10.5", 5.9". and 10.3"; this result, however, is obtained from a crystal exhibiting hydrogen bonding between maleate anions and all the water molecules bound to magnesium.?* In constrast to HzO the calculated minimum energy path for interaction with H2S is never in the molecular plane. At a separation of about 240 pm the preferred angle of approach for the positive center is almost perpendicular to the direction of the H2S dipole for Li+, Mg2+,Z+, and Z2+ as well as H+. This result implies that as the M-S axis bends out of the H2S plane, some new component of the metal-sulfur bond energy more than compensates for the loss in ion-dipole attraction. It would be tempting to call this new component the covalent component were it not for the fact that it is also prominent in one of the cases where a covalent bond cannot be formed, the noncovalent ZZ+-SH2 interaction!'O Presumably the effect of the q = +2 bare charge on the H2S electron distribution is sufficient perturbation to create a lower energy approach path than the one along the dipolar axis. For both the Z2+ bare charge and the Mg2+ ion the minimum energy approach path is about 100" from the H2S plane. For the Mg2+ ion this angle is maintained even at distances as large as 400 pm, whereas for a bare charge at this distance the minimum energy conformation is almost planar. Although the lowest energy approach of Li+ and Mg2+ to H2S is almost perpendicular to the HSH plane, the softer cations
Na+ and K+ bind to H;?Sin the direction of the dipole and Caz+ binds only 3" away from it. The explanation must lie in either the lower deforming power of the larger cations or the lack of appreciable covalence in the M-S bond. The clearest hint of what causes the conformational preferences comes from the data about the covalent contributions to the binding energies of Mg(HzO)?+ and Mg(HzS)2+ in Table 11. Both sets of data show the covalent contribution dropping as the Mgz+ ion moves from a 90" inclination toward planarity, as expected. In the Mg(H20)2+ case the electrostaticcomponent (strongest for the planar conformation) swamps the covalent component; for HzS the opposite holds. The energy to force the H30+ and H3S+ molecules into the planar conformation is not small, even out to quite large H+-L distances; some values of this quantity (designated AEpl,) for this and other adducts are given below. Note that this deformation energy AJZpl, is even greater for H2S than for HzO. Although AEph is smaller in the MgZfSH2adduct than in H3S+, where the covalent component is clearly responsible for the preference for the nonplanar conformation, it is still sizeable: r(H+-L) (pm) 150 200 300
AEPim(H+-H20) AEpim(H+-HzS) AEpim(Mg2+-HzS) (kcal mole-') (kcal mole-') (kcal mole-') 49 29 16
70 36 38
4 16
The Nature of the Bonding. Five different ways of calculating the attraction between a metal ion and a polar molecule have been used in this project. Two, the all-electron calculations and the truncated basis calculations, are described here and the three simplified models of ion-dipole interaction in a separate paper (ref 10). The models frequently fail to predict important features of the binding, but they do have some value for determining the relative contributions to the binding from covalent and ionic interactions and from effects originating from the shape, size, and deformability of ligand and metal ion. Covalency is considered first. The data are in Table 10 where the AJZ,,, values and the metal-ligand overlap populations for the metal-oxygen and metal-nitrogen interactions are tabulated against m. At the actual optimum metal-ligand separations the estimated covalency contributions to binding are (in hartrees, with a percent figure indicating the fraction of the binding energy) Li(NH3)+
Li(H20)+ AEcov AECOV
AEcov AECOV
AECO"
AEmv AEcov
-0.0105 (18%)
-0.0169 (26%)
Na(HZO)+
Na(NHs)+
-0.0023 (6%)
-0.0054 (12%)
K(HzO)+
K(NH3)+
-0.0005 (2%)
-0.0013 (5%)
Mg(HzO)'+
Mg(NH3)"
-0.0192 (15%)
-0.0341 (23%)
Ca(H20)'+
Ca(NH#+
-0.00074 (10%)
-0.0050 (5%)
Li(HzS)+
Li(PH3)+
-0.0121 (41%)
-0.0201 (47%)
Mg(HzS)Z+
Mg(PH3)"
-0.0586 (51%)
-0.0709 (51%)
The main trends which these figures disclose are due to changes in the hardsoft mismatch between the cation and the base. Thus, for water and ammonia, the strength of the binding and the size of the covalent contribution diminish very rapidly from Li+ Na+ K+ and from Mg2+ Ca2+. Likewise, for all metals, the covalency fraction of the binding increases in the order H20 NH3 HzS PH3. The obverse of the truncated basis calculation is the information it provides about the electrostatic part of the metal-ligand
- - - -
12568 J. Phys. Chem., Vol. 98, No. 48, 1994 binding energy. A bond without covalency is weaker and longer, just how much so being indicated by the positions of the energy minima calculated with the “electrostatic-only’’wave functions. The metal-ligand separations calculated in this way are located beyond those obtained with the ordinary basis sets by Hartree-Fock or MP2 procedures:
Magnusson Mean binding energies of the Na+ and K+ adducts maintain a fairly constant ratio to Li+ binding energies, as do Ca2+ binding energies to those of Mg2+:
meansoverallligands wave function Li+-NH3 Li+-H20 Li+-PH3 Li+-H2S Na+-NH3 Na+-H20 Mg2+-NH3 Mg2+-H20 Mg2+-PH3 Mg2+-H2S
r(M-L)opl MP2 199.6 186.6 250.1
240.0 239.0 226.6 207.8 195.8 255.1 246.1
r(M-UoPl electrostatic only 223.0 204.4 277.9 215.9 242.8 227.1 221.9 206.3 273.3 272.3
For Na+, K+, and Ca2+ the difference is noticeable but small; for Li+ and Mgz+ it is very large, with average lengthenings of 10%. Adducts of water, the hardest base considered, are affected least (average lengthening 5%). Overlap contributions, inspected for the trends they disclose rather than for absolute values, are instructive (see Table 10). The covalent energy contributions follow the movement in the overlap populations even down to small metal-ligand distances, where AE,,, rapidly increases in size. AE,,, passes through no minimum because it contains no contribution from the repulsion between the lone pair and the core of the cation; the repulsive term appears in the ionic part of the binding energy. The Li-0 and Mg-0 overlap densities (PLiO, a g o ) fall quickly but are still quite significant at 300 pm, as expected for the rather diffuse metal 2s and 3s orbitals. Naturally, maximum binding energies of ions with the secondrow molecules H2S and PH3 occur at much larger separations than with H20 and NH3. There is also a readily noticeable difference between the behavior of the two pairs of ligands. The binding curves for Li+ and Mg2+ do not merge with the Z+ and Z2+ curves until well beyond the region where this occurs for H20 and NH3 (I x 300 pm). This means that the binding does not become purely electrostatic until the bonds are stretched well beyond separations of 400 pm. In H2S and PH3 adducts of both metal ions the covalent contribution to the binding makes a much larger fraction of the total binding energy than in the H20 and NH3 cases; the contributions in the latter cases are in the 15-25% range compared with 40-50% for H2S and PH3. The covalent contributions are still strong at separations where the electrostatic contribution has weakened, which leaves the ratio between the two qualitatively quite different from what is found for the binding of water and ammonia. The long-range binding is especially pronounced for the binding to magnesium. The Mg2+-H2S and Mg2+-PH3 binding curves drop well below the Z2+ binding curves for a considerable distance beyond r = 300 pm (see Figures 3 and 4). These data are consistent with geometry optimization data discussed earlier.
Conclusions Binding energy data calculated for single molecules of H20, NH3, HzS, and PH3 bound to H+, Li+, Na+, K+, Mg2+, and Ca” ions over a range of separations provide benchmarks for ion-dipole binding by transition metal ions and other iondipole interactions, but they have intrinsic interest as well.
relative binding energies for Li+ Na+ K+ Mg2+ CaZ+ 100% 64% 39% 100% 53%
Similarly, the relative binding energies of HzO, PH3, and H2S, compared with the most strongly bound ligand, NH3, are calculated to be
meansoverallcations
relative binding energies for NH3 H20 PH3 H2S 100% 86% 68% 55%
Bond distances for Li+ and Mg2+ water adducts are calculated to be some 10% shorter than is found by experiment for more highly coordinated complexes. At such close range the binding is very strong and covalency much higher than predicted for 4and 6-coordinated complexes. For Na+, K+, and Ca2+ the shortening is less than the uncertainties in the reported experimental bond distances. Ligands other than water display much more covalency in the binding, and similar bond length shortening is expected; a paucity of experimental results precludes any comparisons. Total ligand binding energies (at the MP2/6-31 l+G** energy minima) fall in the same order for all ions except Mg2+: H+,Li+,Na+,K+,Ca2+:
Mg2+:
NH3 > H 2 0 > PH, > H2S
NH, > PH3 > H2S > H 2 0
Truncated basis calculations of the covalent fraction of the total binding energy yield values of 20-50% for Li+ and Mg2+ adducts at their optimum geometries and 10% or less for Na+, K+, and Ca2+adducts. Covalency is an explanation for metalligand bonds shorter than ionic radii would suggest and for the fact that the Mg2+-ligand bonds are longer than the Li+ counterparts; ionic radii alone predict the opposite. Taken as a whole, the bond lengths are anomalous and cannot be predicted from standard radii for the metal ions and ligand atoms. Although not restricted to them, the anomalies are greatest for magnesium adducts, the compounds in which the ligands are most severely deformed. Consistent with these observations is the fact that the Mg2+(NH3), Mg2+(PH3), and Mg2+(HzS) adducts depart most from simple charge-dipole behavior; the adducts formed by the monovalent ions depart least, especially those containing water. The Li+ and Mg2+ ions distinguish between the ligands better than the larger, softer Na+, K+, and Ca2+ions. The two larger ligands discriminate between the monovalent and divalent cations much less effectively than H20 and NH3. Thus, Ca2+ binding energies are only marginally larger than the values for Li+. The energies required to deform the ligands to the geometries they adopt when bound to Li+ and Mg2+ fall in the range 0.0002-0.01 hartree (0.1-7 kcal mol-’). Relative to each other the deformation energies are H20 H2S < NH3
