J. Phys. Chem. 1991,95, 10677-10681
10677
Theoretical Study of One and Two Ammonia Molecules Bound to the First-Row Transition Metal Ions Stephen R. Langhoff,* Charles W. Bauschlicher, Jr.,* Harry Partridge, and M. Sodupe NASA Ames Research Center, Moffett Field, California 94035 (Received: June 12, 1991)
The binding energies of MNH3+and M(NH3),+ where M = (Sc-Cu) are studied using the modified coupled-pair functional (MCPF) approach. These results are compared with experiment and with previous comparable calculations performed for the water and diwater systems. In addition to the electrostatic interaction, other factors such as 4s4p or 4s3da hybridization and 4s to 3d promotion on the metal atom contribute to determining the ground state and the magnitude of the binding energy. All of the M(NH3)2+systems have linear NMN ground-state structures. However, for MII(NH~)~+, the lowest septet state has a bent structure that is only 1 kcal/mol higher than the 5Al, linear D3d ground state. In contrast, Mn(H,O),+ has a bent 'AI ground state. This difference is probably due to the greater electrostatic binding in the ammonia systems, which favors the low-spin linear state due to its much shorter bond length. We find the second ligand binding energy to be less than the first except for Cr+, Fe+, and Co+. Overall the theoretical binding energies agree with experiment to within about 6 kcal/mol, except for the first ligand binding energy for V+ and both ligand binding energies for Co'.
I. Introduction The study of the binding energies of transition metal ion systems as a function of the number of ligands is an area of intense interest. Whereas alkali metals exhibit progressively decreasing binding energies to water, ammonia, and other small molecules, transition metals have been observed to have successive binding energies that are not monotonically decreasing.I4 Previous theoretical calculations have shown that this is due to the flexibility of transition metals to undergo both hybridization and promotion to reduce repulsion, such that the binding energies are not determined entirely by electrostatics and ligand-ligand r e p u l ~ i o n . ~The magnitudes of the binding energies are therefore intimately related to the relative ordering of the d"sl and d"+l asymptotes in the transition metal positive ion. The binding energies of one and two ammonia molecules to the transition metal ions V+ through Ni+ have been estimated from the translational energy thresholds for collision-induced dissociation of the ions with an argon target gas.' The second ammonia binding energy was found to be larger than the first for the Cr+, Fe+ and Co+ ions, in analogy with the corresponding results for the metal ion-water ligand systems.'" However, there were some "visible aberrations" in the correlation between the water and ammonia binding energies that could not be accounted f0r.I For example, the second water binding energy to V+ is larger than the first, while the second ammonia is less strongly bound than the first. Thus in order to explain these differences and to compare and contrast the bonding of transition metal ions bound to ammonia and water, we have carried out calculations on the MNH3+ and M(NH3)2+systems (M = Sc-Cu) at a level comparable to previous4 calculations on the corresponding water systems.
TABLE I: Symmetry Properties of the Valence Orbitals
symmetry
metal MNH3+
e
3du, 4s, 4pu 3d6(xy,x2- y 2 ) , 3d?r(XZ,yZ), 4P?r(X,Y)
alg e8 a2u e,
M(NH3)2+ 3do, 4s 3d6(xy,x2_-y2), 3d?r(XZ,yZ) 4PO 4 ~ 4 ~ )
a,
NH3 u lone pair, NH bond NH bond
u lone pair, NH bond NH bond u lone pair, NH bond NH bond
tion.
(14sllp6d3f)/[8~6p4dIfl,as in the previous study of the metal-water systems. The N and H basis sets are the valence triple-{ sets of Dunning,Eaugmented with a N 3d polarization function (a = 0.8) and a H 2p polarization function (a = l.O), yielding basis sets of the form (lOs6pld)/[Ss3pld] and (5slp)/[3slp], respectively. Only the pure spherical harmonic components of the basis functions are used. The optimization of molecular geometries employed in the calculation of the binding energies were constrained somewhat due to the large number of degrees of freedom. We first fully optimized CuNH3+ at the S C F level using the above basis set, except that the metal f function was deleted and the 3s combinations of the 3d functions were included. We then fixed the ammonia geometry a t this value for the one and two ammonia calculations and optimized only the metal-nitrogen bond length at the correlated level. As in our previous study of the water and diwater systems, we included electron correlation using the modified coupled-pair functional (MCPF) a p p r ~ a c hwhich ,~ is expected to give quantitative (errors of about 3 kcal/mol for most systems) results for singly bonded systems where the bonding is predominantly electrostatic. The approximation of using a fixed ammonia geometry is expected to be valid as rather small distortions occur due to interaction with the metal ion. The MNH3+ systems have C,, symmetry and therefore the state designations in Table I are given in this symmetry, even though the calculations were actually carried out in the C,subgroup for computational convenience. The M(NH3)2+ions in a linear N M N configuration with the ammonia ligands staggered have D3d symmetry: the calculations were carried out in the c2h subgroup. The D j h symmetry eclipsed form is only slightly higher in energy; for the triplet state of Sc(NH3),+ the eclipsed is only 0.02 kcal/mol above the staggered. We also considered bent N M N geometries for
(4) Rosi, M.; Bauschlicher, C. W. J. Chem. Phys. 1990, 92, 1876; 1989, 90, 7264. ( 5 ) Wachters, A. J. H. J . Chem. Phys. 1970, 52, 1033. (6) Hay, P. J. J. Chem. Phys. 1977, 66, 4377. (7) Stewart, R. F. J. Chem. Phys. 1970, 52, 431.
(8) Dunning, T. H. J . Chem. Phys. 1971, 55, 716. (9) Chong, D. P.; Langhoff, S . R. J. Chem. Phys. 1986,84,5606. See also Ahlrichs, R.; Scharf, P.; Ehrhardt, C. J. Chem. Phys. 1985, 82, 890.
11. Methods The metal atom basis sets consist of the [8s4p3d] contraction of the (14s9pSd) primitive sets of Wachters? augmented with two diffuse p and a d function,6 as well as a three-term fit to a Slater 4f function' with exponents varying in steps of 0.4 from 1.6 for Sc to 4.8 for Cu. Thus the metal basis sets are of the form (1) Marinelli, P. J.; Squires, R. R. J . Am. Chem. SOC.1989, 1 1 1 , 4101. (2) Magnera, T. F.; David, D. E.; Michl, J. J. Am. Chem. SOC.1989, 1 1 1 , 4100.. Magnera, T. F.; David, D. E.; Stulik, D.; Orth, R. G.; Jonkman, H. T.; Mwhl, J. J. Am. Chem. Soc. 1989, 111, 5036. (3) Honma, K.; Dalleska, N. F.; Armentrout, P. B., private communica-
0022-3654191 12095-10677SO2.5010 , I
,
0 1991 American Chemical Society
10678 The Journal of Physical Chemistry, Vol. 95, No. 26, 1991 SC(NH,)~+ and MII(NH,)~+;these calculations were carried out in C2, symmetry with the ammonia ligands in the eclipsed configuration. It should be noted that for several systems we find the ground state to be a degenerate E state. In these cases we do not consider a Jahn-Teller distortion as this is expected to be quite small, since bending will adversely affect the sdu hybridization. Harmonic frequencies were computed for the CuNH3+ and Cu(NHJ2+ molecules at the SCF level using analytic second derivatives. The zero-point corrections to the successive binding energies are relatively small, being 2.9 and 2.7 kcal/mol for the first and second ligands. Following our work on the water syst e m ~ where , ~ the agreement between the computed and experimental is very good, we use these zero-point corrections for all systems. Our binding energies are expected to be too small due to limitations in the one-particle basis sets and from an underestimation of the correlation contribution to the binding energies at the MCPF level. However, the ammonia dipole moment (0.677 au) is too large at this level of theory, which leads to too large an electrostatic contribution to the bonding. Based on experience from previous calculations, we expect that these effects cancel to a large extent, thus our computed De values are, in general, quite accurate. Therefore we make no estimate for limitations in the one- and n-particle treatments and only correct our computed De values for zero-point effects. The calculations were performed using the MOLECULE-SWEDEN~O and GRADSCF~' program systems on the NASA Ames Central Computing Facility CRAY Y-MP/832 computer . 111. Results and Discussion The qualitative features of the bonding between the first-row transition metal ions (M') and H 2 0 has been described in detail by Rosi and Bauschlicher.4 The bonding between M+ and NH, is similar, except that the interaction is stronger, especially on the right-hand side of the row. We present here a brief discussion of the bonding with additional details given later when the specific systems are discussed. The magnitude of the binding energies are determined by a balance between the electrostatic interaction and Pauli repulsion. We first consider the electrostaticcontribution to the bonding. In general, there is a contraction of the metal ion with increasing 2,which leads to shorter metal-N bond distances and larger binding energies proceeding left to right in the row. In addition, Operti et al.12 have shown that the M+-L binding energies follow the same trend for M+ = Mg+, H+, C5H5Ni+,Al+, Mn+, and Cu+ with a variety of ligands. Thus the binding energies must be strongly relatedto the-electrostatic properties of the ligands. While it is ~ e l l - k n o w n 'that ~ the M+-(NH3)n binding energies are larger than those Of M+-(H20)n, this trend might seem inconsistent with the bond distance and the larger moment Of H2° cornpared with the M-N bond distance and the NH3 'pole moment* (We find the H2° dip1e moment to be larger than NH3 at the SCF level in the 'I). Togain insight into the trend, we computed the binding energy Of a point charge (3.73 Q from the heavy atom) to NH, and H 2 0 in two step. The orbitals of the ligand are first frozen in the free-ligand form and then are allowed to relax. (The first step is the same as evaluating the potential, l/r). The binding energy with NH3 is significantly larger than H 2 0 even at the frozen orbital level. Assuming Only a charge-pint dip1e bonding mechanism, the moment is found be OS2 toward effective location Of the the atoms for H2°9 but 0*7 away from the atoms for NH3. That is for the same metal-ligand distance, the dipole moment (10) MOLECULE-SWEDEN is an electronic Structure program System Written by J. AlmlBf, C. W. BauschJicher, M.R. A. Blomberg, D.P. Chong, A. Heiberg, S . R. Langhoff, P.-A. Malmqvist, A. P. Rendell, B. 0. Roos, P. E. M . Siegbahn, and P. R. Taylor. ( 1 1) GRADSCF is a vectorized SCF first- and second-derivative code written by A. Komornicki and H. King. (12) Operti, L.;Tews, E. C.;Freiser, B. S . J . Am. C h m . Sot. 1988,IIo.
3847. (13) (a) Castleman, A. W.; Keesee, R. G.Chem. Rev. 1986.86, 589. (b) Mark, T. D.; Castleman, A. W. Adu. Ai. Mol. Phys. 1985, 20, 65.
Langhoff et al.
TABLE II: A Comparison of the Binding Energies (kcal/mol) of NH3 and H20 to a Point Charge at the SCF Level" H20 NH3 N
Wb
De (frozen orbitals) 0,(relaxed orbitals)
relaxation energy
0.797 31.8 39.8
8.0
0.693 47.1 59.1 12.6
"The point charge is 3.73 a,, from the N or 0. bComputed for the free ligand.
of NH3 is 0.9 a. closer to the ion. Given that the electrostatic contribution is proportional to pZ/?, the difference in the effective distance more than compensates for the smaller dipole moment. Previously it was suggested that the larger polarizability of NH, than H 2 0 leads to the greater binding energy (see for example, the discussion in ref 13). However, as can be seen from Table 11, this relaxation enhances the NH3 binding relative to H 2 0 by only 4.6 kcal/mol. At a given bond length the electrostatic interaction is essentially independent of the orientation of the metal 3d and 4s electrons, and therefore the ordering of the states is determined primarily by Pauli repulsion. The transition metal positive ion has several mechanisms available for reducing Pauli repulsion. For example, the 4s orbital can mix in 4pu character thereby allowing it to polarize away from NH3. While this mechanism occurs readily for the MNH3+ systems, when two ammonia ligands are present the ligands can reduce the repulsion by 4s4p hybridization only by forming a structure with a small N-M-N bond angle. The repulsion can be reduced by 4s3du hybridization, since the negative combination of these orbitals leads to reduced charge density along the internuclear axis. The 4s3du hybridization is especially important on the left-hand side of the row due to the similar spatial extent of the 3d and 4s orbitals. On the right-hand side of the row the 4s orbital is much larger than the 3d orbital. Therefore Fe+ with a 3d64s1occupation can reduce the metal-ligand repulsion by promoting the 4s electron into the compact 3d orbital. The actual method employed to reduce repulsion depends on the relative ordering of the atomic asymptotes of M+. An important consideration in determining the ground state is the minimization of the overlap between the metal 3d orbitals and the NH3 ligands. By considering the symmetry properties of the valence orbitals given in Table I it can be seen that the order of the overlap goes as 3du(al) > 3d7r(e) > 3d6(e) Although 3d-NH3 repulsion is an important consideration, the occupation with the lowest 3d repulsion is not always the ground state, since it may be derived from an excited asymptote of M+, In order to facilitate a comparison with water, we note that the 3d7r orbitals are contained in the bl and b2 irreducible representations, while the 3d6 orbitals are in the a l and a2 representations for the C , point group. An important consequence of this difference in symmetry will be illustrated below, where the 3d?r and 3d6 orbitals will mix in M(NH3),+, but a n n o t for the water analogues. We next consider the MNH3+ and M(NH3)2+systems for the metal ions sc through cu. The results are summarized in Table 111. In this analysis we are guided by the previous results for the corresponding water and diwater systems where all potential candidates for the ground state were considered. In this work we explore multiple states only to ensure that we have identified the ground state. Except for a few notable exceptions, M+ bonds in a similar manner to both H20 and NH3. The binding energies of all the M(NH3)"+ systems are larger than the corresponding M(H,O),,+ systems, even though the M-N distance is up to 0.2 a. larger than the M-O distance. This is consistent with the point-charge model discussed above. The 3Eground state of ScNH3+ is derived from the 3d14s1 occupation of Sc+,where the 3d electron is primarily in the 3d6(e) to the nearly orbital to minimize repulsion, ~h~ state degenerate pair of states 0Ab3A2) for ScH2O'. The Mdliken 3d population of 1.16 reflects a small contribution from the 3F(3d2)
The Journal of Physical Chemistry, Vol. 95, No. 26, 1991 10679
Binding Energies of Ammonia Complexes TABLE III:
MCPF Binding Energies (kcal/mol) for M(NH3),'
state r(M-N)(ao) D,(M '-NHJ"
( n = 1, 2)
Ti
'E 4.425 42.7
4A2
4.226 47.0
4.082 46.5
6A, 4.120 41.8
'Al 4.297 38.4
4.131 45.7
'A2 3.817 53.2
2Al
57.5
'AI 3.738 54.7
0.82 1.16 0.92 0.09
0.78 2.30 0.83 0.08
0.79 3.36 0.76 0.07
0.82 4.83 0.29 0.05
0.81 5.02 1 .oo 0.16
0.76 6.03 1 .oo 0.20
0.76 7.76 0.37 0.09
0.75 8.97 0.17 0.09
0.71 9.84 0.33 0.17
IA,;
4A2,
% 4.179
4E,
''42,
V
Cr MNH"
SE
Mn
Feb 6E
co
cu
sc
Ni 3.783
populations
charge 3d 4s 4P
state r(M-N)(ao) D,(MNH''-NH')" populations charge 3d 4s 4P
4.330 37.2 0.53 0.98 1.21 0.21
4.290 40.5 0.65 2.52 0.69 0.11
M(NHA+
%,
43.1
4.091 43.4
3.945 30.8
0.66 3.57 0.66 0.10
0.67 4.75 0.48 0.10
0.58 5.36 0.90 0.15
1
AI,
3.855 53.0
3.773 55.2
3.679 52.7
3.691 54.3
0.58 6.52 0.74 0.15
0.55 7.60 0.67 0.15
0.49 8.61 0.70 0.19
0.40 9.72 0.69 0.17
"In kcal/mol. bThe results for the 4A2state of FeNH" are re = 3.936 ao, De = 40.6 kcal/mol, charge = 0.80, 3d = 6.94,4s = 0.17,and 4p = 0.07. 'The results for the 'E state of SC(NH')~' are re = 4.468 ao, De = 36.5 kcal/mol, charge = 0.71,3d = 1.36,4s= 0.80,and 4p = 0.10. dThe 'A, state of Mn(NH,)*+ is bent with re = 4.356 ao, 8 = 89.6,De = 29.8 kcal/mol, charge = 0.68,3d = 5.04,4s = 0.96,and 4p = 0.31.
excited state of Sc+. The 4s population of 0.92 indicates that there is very little hybridization of the 4s orbital. At the state-averaged SCF level, we consider the 3E(3d6'4s'), 3E(3dr'4s'), and 3A1(3dd4s') states. The relative binding energies of 0.0, -5.0, and -18.0 kcal/mol are in the order expected based on repulsion. The ground state of Sc(NH3),+ is lAl, in D3dsymmetry. This state is computed to lie just 0.7 kcal/mol below the 3Egstate, but further improvements in the calculation may increase this separation slightly. This is different than Sc(H20)*+where the corresponding IA, state lies 1.6 kcal/mol above the nearly degenerate 3Bl, and states. The difference in ground states is due to the preferential stabilization of the singlet state in the diammonia system, because the larger electrostatic stabilization favors the state with the shorter bond length. The ground state of TiNH3+ is the 4A2state corresponding to a 3d(x ~S)(e)~4s' occupation. This state is 1.5 kcal/mol lower than the 4E state with a 3d~(e)~3d6(e)'4sl occupation. While the 4E state is derived from 100%ground state Ti+, the 4A2state has the advantage that some 3d6(e)24sl, which has the lowest overlap with the ligand, can mix into the wave function. To achieve this mixing, one must pay part of the promotion energy to reach the 4P state, as the 4A2state is derived from a mixture of 4F and 4P. For water, the 3da24s1occupation cannot mix with 3dd3d6'4s1 and thus the ground state is derived from the 3dd3d6'4s' occupation. The much smaller 3dn+l-3d"4sI separation in Ti+ than Sc+ results in more 4s to 3d promotion and 4s3da hybridization. The increased 4s to 3d promotion decreases repulsion, resulting in a stronger bond (47.0 kcal/mol in TiNH3+ compared with 42.7 kcal/mol in ScNH3+). The ground state of Ti(NH3)2+is the 4A2,(3d(?r 6)(e,)24s1) state in analogy with TiNH3+. As for the high-spin state of the Sc+ systems, there is more 4s to 3d promotion for the diligand system. The ground state of VNH3+ is the 5E state corresponding to the nearly degenerate and states of VH20+. The 3d population shows a large mixing of the 4s and 3d orbitals, even though the ground state of V+ is 5D(3d4). This illustrates the efficiency of 4s3da hybridization on the left-hand side of the row. The binding energy of VNH3+ is 10 kcal/mol larger than VH20+, and larger than the corresponding difference for the S c and Ti ions. The ground states of VNH3+ and VH20+are derived from the 3ds23d6'4s' occupation, whereas it is the 3d623dd4sl occupation that minimizes the repulsion. The former occupation is favored because it is derived from the ground state of V+, whereas the latter occupation involves mixing in of V+ excited states. For H 2 0the 5B2state, derived from the 3d623dd4sl occupation, is 1.5 kcal/mol above the ground state. For NH3, the two analogous states are separated by 5.0 kcal/mol. The ground state of V(NH3)2t is 5E,,and like VNH3+ is derived from the 3da23d6'4s1
+
+
occupation; the state derived from the 3d~S~3dd4s' occupation is 2.6 kcal/mol higher. This is different from V(H20),+ where the ground state is derived from the 3d623d~'4s'occupation, but the state derived from 3d7~~3d6~4s' is 3.2 kcal/mol higher. For both NH3 and H 2 0 , adding the second ligand favors the occupation with the lower repulsion, since the promotion energy is amortized over two ligands. However, for NH3 the effect is not large enough to reverse the order of the states. This is part of the reason that the second binding energy is about 3 kcal/mol larger than the first for H 2 0 , but about 3 kcal/mol less for NH3. The ground state of CrNH3+ is a 6A1state derived from the 9 ( 3 d 5 ) asymptote of Cr+. The Mulliken 3d population of 4.83 electrons indicates that there is only a small contribution from the 6D(3d44s') asymptote. The occupation of the 3da orbital increases the repulsion with the NH3ligand, resulting in a decrease in the binding energy as compared with VNH3+. The ground state of Cr(NH3),+ is 6Al, in analogy with the one ligand case. Like the analogous results for the water ligand systems, the second NH3 ligand binds to Cr+ more strongly than the first. This is a consequence of i n c r d 4s3da hybridization that reduces the charge density along the bond axis and thus reduces the metal-ligand repulsion. The 7Al ground state of MnNH3+is derived from the 'S(3d54s1) ground state of Mn'. There is almost no contribution from the high-lying (41.7 kcal/mol14) 5D(3d6) excited state of Mn+, as judged by the Mulliken 3d population of 5.02 electrons. The 4p population is also larger than for ScNH,' through CrNH3+, because there is increased 4s4p hybridization, as polarization is the only mechanism capable of decreasing the repulsion. The presence of electrons in both the 3do and 4s orbitals further increases the repulsion resulting in a smaller De and a longer bond length for the 'A, state of MnNH3+than for the 6A1ground state of CrNH3+. Rosi and Bauschlicher4 found that the ground state of Mn(H20)2+was a bent (0-M-O bond angle of 94O) high-spin state (7Al in C2,symmetry) derived from the ground-state asymptote. The molecule bends to reduce the repulsion between the open-shell 4s-like orbital and the l i g a n d s s e e Figure 1 of ref 4. The lowest linear state of Mn(H,O),+ was found to be the 5A, state, which is derived from a mixture of %(3d54s1)and SD(3d6). The optimal linear state was only 4.4 kcal/mol less stable. For Mn(NH3),+ we studied the corresponding linear 5A1,and bent 'A, (in C, symmetry) states. We find these two states to be very close in energy, but reversed with respect to Mn(H,O),+. That state is about 1.0 kcal/mol lower. is, in Mn(NHJ2+, the linear Since we expect that further improvements in the calculation will (14) Moore, C. E. Atomic Energy Leuels; US Natl. Bur. Stand. (US) 1949, circ. no. 467.
Langhoff et al.
10680 The Journal of Physical Chemistry, Vol. 95, No. 26, 1991
TABLE I V Comparison of the First and Second Ligand Binding Energies of Ammonia and Water to the First-Row Transition Metal Ions (in
kcal/mol)
present work Do (M+-NH3) Do(MNH,+-NH3) A
sc
Ti
V
Cr
Mn
Fe
co
Ni
cu
39.8 34.5 -5.3
44.1 37.8 -6.3
43.6 40.4 -3.2
38.9 40.1 +1.8
35.5 28.1 -7.4
42.8 50.3 +1.5
50.3 52.5 +2.2
54.6 50.0 -4.6
51.8 51.6 -0.2
51.9 45.0 -6.9
37.4 40.8 +3.4
36.9 34.1 -2.8
38.5 48.7 +10.2
58.8 61.1 +2.3
51.2 55.1 +3.9
+3.2 +0.4 +1.2
+2.4 +7.6 +4.2
-11.4 -8.7
+3.3
+1.1 +1.8 +1.2 4-1.9
-2.9 +0.9 -4.4 +1.5
Marinelli and Squires" Do(MC-NH3) Do(MNH,+-NH3) A
difference in the successive water binding energies A( theory)*
-4.3
-3.1
A(expt). A(expt)' A(expt)d
+8.0
+8.1 +9.2
+0.5 +1.4 +4.0
Reference 1. Reference 4. Reference 3. Reference 2. favor the quintet state, the linear configuration is probably the true ground state. The reason for the reversal may be the stronger electrostatic interaction in the ammonia systems; this interaction is stronger in the quintet state where the bond length is much shorter (r(M-N) = 3.9450~)than the septet state (r(MN ) = 4 . 3 5 6 ~ ~ The ) . optimal bond angle of 89.6' is slightly less than the optimal 0-Mn-O bond angle of 93.8' in Mn(H,O),+. The ground state of FeNH3+ is the 6Estate in which the additional electron, relative to MnNH3+, is added to the 3d6(e) orbital to minimize repulsion. This state is derived entirely from the 6D(3d64s1)ground-state asymptote of Fe+ as can be seen from the populations in Table 111. The lowest quartet state (4A2),which is derived from the 4F(3d7)excited state of Fe+ with holes in the d o and the two d n orbitals, is found to lie 5.1 kcal/mol above the 6E ground state. Since this separation is comparable to the 5.8 kcal/mol 6D-4F atomic separation, this indicates that the presence of the 4s electron does not significantly increase the repulsion, as it can polarize by mixing in 4pa character. The importance of this mechanism is illustrated by the relatively large 4p population for the 6E state. However, for Fe(NH3)2+,4s4p hybridization is no longer a viable mechanism for reducing repulsion. This results in a 4Egground state for Fe(NH3)2+,which is derived from a nearly equal mixture of 6D(3d64s') and 4F(3d7)as evidenced by the Mulliken 3d population. The 'Eg state corresponds to the 4B, ground state and the nearly degenerate 'A, state of Fe(H20)>. The binding energy of the second ammonia in Fe(NH3)2+ is significantly greater than the first, because the promotion energy is now amortized over two ligands. Although the second ligand binding energy was also larger for Fe(H20)2+,the difference is greater in Fe(NH3)2+,because of the larger electrostatic stabilization for the ammonia systems and the considerably shorter bond length in the 'Eg state of Fe(NH3)2+compared with the 6E ground state of FeNH3+. The ground state of CoNH3+is the 3A2state derived from the (3d8) occupation of Co+. The binding energy is larger than for FeNH3+, because no promotion is required to reach the 3d"I atomic asymptote in Co+. Thus there is a strong electrostatic interaction and the metal-N bond length is considerably shorter than for all of the metals to the left of it in the row. The occupation of the 3d orbitals is analogous to TiNH3+,namely the two open-shell electrons are in the 3d(r + 6)(e) orbital. That is, the ground state is derived from a mixture of Co+ 3Fand 3P. As in the case of TiNH3+,we attribute the mixing of asymptotes with lowering this state relative to those which have a smaller repulsion. The 4s3do hybridization, which reduces the a repulsion, is evident in the populations. However, it should be noted that other states are very low-lying, for example the 3Estate with holes in the 3da and 3d6 orbitals is only 0.5 kcal/mol higher. The ground state of Co(NH,),+ is 3A2g,which corresponds to two electrons in the 3d(x + 6)(e) orbital. Thus the ground-state occupation is analogous to that found for CoNH3+ as well as that found for Ti( NH3)2+. The ground state of NiNH3+ is the 2Al state derived from the Ni+ 3d9 occupation with the hole in the 3do orbital to minimize
""
c
9co
3
o 0.06
0.05
re
m
0.07
-2M-Na 0-2)
Figure 1. The experimental (triangles) and theoretical (circles) Dovalues for the first ligand plotted against the theoretical l/rz values. The solid and dashed lies are least-squares fits to the theoretical and experimental
data, respectively. The theoretical and experimental values for the same ion are connected by a dotted line. Note the experimental Dovalues for Co+ and V+ are not used in the least-squares fit. repulsion. This state has the smallest repulsion, which results in the largest 0, value for MNH3+ of all of the first-row metals. The ground state of Ni(NH3)2+is the *E, state arising from a hole in the 3 d r orbital. The 3ds4s' occupatlon reduces the o repulsion by 4s3da hybridization and the hole in the 3 d r orbital reduces the r repulsion. The large promotion energy does not allow this occupation to contribute in the single ligand case. However, the two ligands can share the promotion energy and so the occupation of the ground-state changes. This change in the ground state with the second ligand is the same as found for Ni(H20)"+. The ground state of CuNH3+is the 'A, state derived from the 3dI0 ground state asymptote of Cu'. As can be seen from the Mulliken populations there is some 4s3da hybridization to reduce the repulsion. For two ammonia ligands the degree of hybridization is greater, since the promotion energy to the 3d94s' asymptote is amortized over two ligands. Since we have extensively studied the Cu(NH3),+ (n = 1-4) systems previously, we refer the reader to ref 15 for further discussion of the nature of the bonding in these systems. While the binding energy of Cu+ with one ammonia has not been measured, Clemmer and Armentrout16 have deduced that its binding energy should be very similar to that of Co+, and that is what we find. Most of the computed Dovalues are expected to be accurate to about 3 kcal/mol. Thus in those cases where there are two or more low-lying states the identification of the ground state is tentative. For those systems where 4s to 3d promotion is critical to the bonding, for example the second ammonia binding energy to Mn+ or Fe+, our estimate of Domight be as much as 6 kcal/mol too low. This is consistent with a comparison of theory and (15) Bauschlicher, C . W.; Langhoff, S . R.; Partridge, H. J . Chem. Phys. 1991, 94. 2068. (16) Clemmer, D. E.: Armentrout, P. B. J . Phys. Chem. 1991,95, 3084.
J. Phys. Chem. 1991,95, 10681-10688
Figure 2. The experimental (triangles) and theoretical (circles) Dovalues for the second ligand plotted against the theoretical l / r : values. The solid and dashed lines are least-squares fits to the theoretical and experimental data, respectively. The theoretical and experimental values for the same ion are connected by a dotted line. Note the Mn+ Dovalues are not included in the least-squares fit as they are derived from a different bonding mechanism.
experiment for the water systems.'-4 The successive binding energies of the M(NH3)2+systems are compared with experiment in Table IV. Except for the f m t ligand binding energy to V+ and both ligand binding energies to Co+, agreement with experiment is very good. The difference for the second ligand binding energy to Mn+ is also relatively large, but in this case our value may be somewhat low. We analyze the difference between theory and experiment by making use of the fact that the bonding is primarily electrostatic, and therefore a correlation is expected between l/r(M - N)z and the binding energy. To illustrate that this is the case we have plotted our Do values and those of Marinelli and Squires for the first and second binding energies of M(NH3)z+against l/r(M - N)z in Figures 1 and 2, respectively. Although there are exceptions, the binding energies generally display a linear relationship with 1/$. For the single ligand case, there is a much larger variation from linear for both experiment and theory. This probably represents the greater diversity in the bonding mechanisms. However, the plot
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suggests that the experimental values1 for VNH3+ and CoNH3+ are too high. The second ligand binding energies show a much more linear behavior, excluding Mn+, which is exceptional because the 5A,, ground state is derived from a highly excited asymptote. This results in a short bond distance, but a relatively small Do value because of the large promotion energy required to reach the excited atomic asymptote. From this plot it is clear that the experimental value for Co(NH3)2+is much too large, and the value for V(NH3)2+is probably a little large. The binding energies of the ammonia systems are larger than the corresponding water systems in all cases, but the differences tend to increase from left to right in the transition row. For example, in the single ligand case, the difference increases from 5.3 kcal/mol for Sc+ to 14.5 kcallmol for Cu+. This reflects the larger electrostatic contribution to the bonding on the right side of the row as a result of the smaller getal-N bond lengths. This in turn results from the contraction of the 3d orbitals and the increasing stability of the 3d"I asymptote with respect to 3d"4s1. As discussed above the origins of the changes in bonding between the first and second ligand are similar to those for the transition metal-water systems. This results in a t least a qualitative similarity in the successive binding energies for the ammonia and water systems (see Table IV).
IV. Conclusions The successive binding energies in M(NH3)2+have been computed for the metals Sc through Cu at the MCPF level of correlation treatment. While the bonding is predominantly electrostatic, the ground state is dictated primarily by minimizing the Pauli repulsion. Using a point-charge model we show that for a given m e t a l 4 or metal-N distance, the dipole moment of ammonia is effectively much closer to the metal than is that of water. Thus the binding energies of the ammonia complexes are all larger than the corresponding water complexes even without allowing ligand polarization, which further increases the ammonia binding energy relative to water.
Acknowledgment. M. Sodupe gratefully acknowledges a Fulbright fellowship. Registry NO. NH,, 7664-41-7.
Pulsed Laser Induced Photoelectrochemistry of Polypyridinic Ru( I I)Complexes in Water and in Acetonitrile Katrin Karlsson and And& Kirsch-De Mesmaeker* Chimie Organique et Chimie Organique Physique, Facultd des Sciences, Universitd Libre de Bruxelles, CP 160, 50 Avenue F. D. Roosevelt, 1050 Brussels, Belgium (Received: February 28, 1991; In Final Form: June 26, 1991) The photoelectrochemistry (PEC) of a series of complexes Ru(bpy),(tap),-,2+ (bpy, 2,2'-bipyridine; tap, 1,4,5,8-tetraazaphenanthrene) is examined on a transparent SnO, electrode under pulsed laser illumination. The kinetics of the photoinduced open-circuit photopotentials in long time domains extending to a few milliseconds,are analyzed as a function of various parameters such as the nature of the solvent, the complex, and the oxygen concentration. Different SnOZphotosensitization processes are shown to occur, and some of them are explained on the basis of the bulk photochemistry. Biphotonic (or bimolecular) photoelectron transfers that generate long-lived reducing and oxidizing electroactive intermediates in the bulk solution are mainly responsible for the SnO, sensitization in long time domains; they give rise to electron injection into, or electron ejection from, the electrode, according to the experimentalconditions and the complex. The measurement of the laser-induced open-circuit photopotentials as a function of time is shown to be a very useful method for studying these photosensitization mechanisms and may also be regarded as a technique complementary to the classical flash photolysis for the examination of photoinduced charge-transfer processes.
Introduction In the past 10 years considerable attention has focused on kinetic studies of pulsed laser induced photopotentials or photocurrents *To whom correspondence should be addressed.
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at different "semiconductor/solution" interfaces in short time domains. In a first approach, the semiconductor itself is irradiated and the separation of the photoinduced electron-hole pairs and the subsequent charge-transfer reactions at the interface are studied 0 1991 American Chemical Society
