J. Phys. Chem. 1995,99, 9003-9007
9003
Successive H2O Binding Energies for Fe(HZO),+ Alessandra Ricca and Charles W. Bauschlicher, Jr.* NASA Ames Research Center, Moffett Field, Califomia 94035 Received: January 26, 1995; In Final Form: March 28, 1 9 9 9
The successive H20 binding energies, computed using density functional theory (DFT), are in good agreement with experiment. The bonding is electrostatic (charge-dipole) in origin for all systems. The structures are therefore determined mostly by metal-ligand and ligand-ligand repulsion. The computed structure for FeH20+ is CZ,,where sp hybridization is important in reducing the Fe-HZO repulsion. Fe(H20)~' has D z symmetry ~ where sd, hybridization is the primary factor leading to the linear 0-Fe-0 geometry. The bonding in Fe(H20)3+ and Fe(H20)4+ is very complex because ligand-ligand and metal-ligand repulsion, both for the in-plane and out-of-plane water lone-pair orbitals, are important.
I. Introduction Trends in the successive ligand binding energies vary for different ligands and the same metal ion (atom) or for the same ligand and different metal ions (atoms). The origin of the variation in the successive ligand binding energies is due to changes in the ligand-ligand repulsion, metal-ligand repulsion, and dative bonding for both metal to ligand and ligand to metal donations. These differences are greatly affected by the metal occupation and spin state, as well as by the nature of the ligand. Thus the variation in the trends is not too surprising. Electronic structure calculations'-8 have been very useful in obtaining a detailed understanding of the nature of the bonding and how it varies with the number of ligands. The calculations'-6 have identified new bonding mechanisms and have shown some unexpected results. Because the equilibrium structures may not be those initially expected, it is important to use a method that allows the complete optimization of a reliable geometry and the calculation of the vibrational frequencies to confirm that the stationary point corresponds to a minimum. We have f ~ u n d that ~ - ~density functional theory (DFT) meets these criteria, at least for the B3LYP hybrid f u n c t i ~ n a l . ~ - 'In ~ addition, it is useful to have accurate experimental data for comparison, because if the DFT and experimental binding energies agree, one has confidence that the DFT approach has correctly described the system and has not been trapped in a local minimum or treated an excited state. In this work we report the study of Fe(H20),+. This system is chosen because there are accurate experimental results for the binding energies of the first four water molecules."-13 This system also contrasts our previous study5 of the Fe(CO),+ system; water is known to be a very different ligand from CO. For CO, the metal-ligand repulsion is localized along the MCO axis and there is an important metal 3d, to CO 2n* donation, while for H20 there is a smaller dative interaction, which involves water lone-pair donation to the empty 3d orbitals, and the metal-ligand repulsion involves both the in-plane al and out-of-plane bl oxygen lone pairs. The importance of both types of repulsion is perhaps best illustrated2 by Ni(H20),+, where-. NiH20+ has a 3 6 hole to minimize the in-plane repulsion, while Ni(H20)2+ has a 3d, hole to minimize the out-of-plane repulsion. For Ni(H20)2+ s& hybridization reduces the in-plane repulsion. The repulsion between metal and 0-H bonds is less important as the bonds are bent away from the metal. This 'Abstract published in Advance ACS Absrracts, May 15, 1995.
difference in the nature of the bonding for CO and H20 leads to some interesting differences for the one ligand; for example, FeH20+ is a sextet state and FeCO+ is a quartet state. In this work we see how this difference in the ligands affects the bonding in the larger clusters. 11. Methods In this work we perform calculations analogous to our s t u d i e ~ ~of- ~ Fe(CO),+ and M(H2),+. We optimize the geometries and compute the harmonic frequencies and the binding energies using density functional theory (DFT). We use the B3LYP hybrid functional in conjunction with the fine grid option (as implemented in Gaussian 92/DFTI4). We have found that this functional performs very well for transition metal s y s t e m ~ ~ -and ~ %yields16 '~ an average absolute error of 2.22 kcal/ mol for the 55 G2 atomization energies, which is very similar to the 2.4 kcal/mol reported by Becke'O for his original hybrid functional. The fine grid is essential in optimization of the larger clusters, where convergence is greatly improved. The use of the fine grid yields very small changes with our previous resultsI5 for FeH20+, where the medium grid was used. The Fe set is an [8s4p3d] contraction of the (14s9p5d) primitive set developed by Wachters." The s and p spaces are contracted using contraction number 3, while the d space is contracted (31 1). To this basis set two diffuse p functions are added; these are the functions optimized by Wachters multiplied by 1.5. A diffuse d function'* and an f polarization function (a = 1.339) are added. The final Fe basis set is of the form (14sl lp6dlf)/[8s6p4dlfl. The hydrogen basis set is the scaled (4s)/[2s] set of Dunning and Hay,I9 supplemented with a diffuse s (0.071) and three p (1.2, 0.40, and 0.13) functions. The 0 basis set is a [4s3p] contraction of the (9s5p) primitive set optimized by Huzinaga.20 A d polarization function (0.85) is added. The s space is contracted (5211). Only the pure spherical harmonic components of the basis functions are used in all calculations. The calculations were performed using Gaussian 92/DFTI4 on the NASA Ames Central Computer Facility CRAY C90 or Computational Chemistry IBM RISC Systed6000 computers. The visualization system MOLEKEL2' has been used to represent the molecular orbitals.
111. Results and Discussion A. Preliminary Remarks on the Calculation of the Binding Energy for FeHzOf and Fe(H*O)z+. The DFT
This article not subject to U.S. Copyright. Published 1995 by the American Chemical Society
9004 J. Phys. Chem., Vol. 99, No. 22, 1995
Ricca and Bauschlicher
TABLE 1: Summary of Successive Binding Energies present work
TABLE 3: Summary of the Computed Harmonic Frequencies, in cm-l
expt"
1629(al)
3803(al)
H2O 3907(b2)
3 12(bi) 3779(b2)
347(a1)
FeH20+(6AI) 519(b>)
Taken from Dalleska et al." unless otherwise noted. The computed value for the 4 A ~state is 32.2 kcal/mol. 'From Mannelli and Squires." From Magnera er a2.I; e If spin is conserved and dissociation occurs to the 4AI state, the DOvalue would be 39.8 kcaymol.
U(bi) 546(e) 3842(e)
102(e) 1630(al)
TABLE 2: Summary of Fe Populationsa
35(b) 140(a) 362(a) 1622(a) 3770(a) 35(a) 124(a) 269(b) 369(b) 534(b) 3756(a) 3856(a)
Fe+-H20 FeH2O'-H20 Fe(H20)2+-H20 Fe(H20);+-H20
De 34.8 40.5 17.0 13.6
DO 33.46 38.5' 14.9 11.5
Do 30.6 f 1.2, 32.8 i 4,'28.8 iz 3d 39.3 i 1.0, 40.8 f 4,'38.0 f 3d 18.2 f 0.9 12.0 f 1.6
a
FeH20C6Al FeH2OfJAI Fe(H2O)z+'Al Fe(H20);+4A Fe(H20)d"A a
4s
3d,
3d,,
3d,:
3d,,
3dx2-,2
1.03 0.40 0.64 0.50 0.39
1.04 1.69 1.59 1.66 1.86
1.03 1.02 1.02 1.01 1.01
1.00 1.00 1.02 1.04 1.02
1.00 1.00 1.00 1.47 1.82
2.00 2.00 2.00 1.55 1.12
The molecular orientations are given in the text.
approach is biasedI5 toward states with higher 3d occupations. As a result, the 4F(3d7) state of Fe+ is 3.8 kcaVmol below the 6D(3d64s1)ground state, instead of 5.8 kcaVmol above it. This problem carriesI5 over to FeH20+ such that the 4Al state with a 3d population near 7 is below the 6A1 state with a 3d population near 6. If one computes the binding energy of the 4A1state directly with respect to the 6D state of Fe+, the resulting value is significantly larger than experiment. If however, the binding energy is computed with respect to the 4F state and corrected to the 6D asymptote using the experimental 4F-6D separation,22the 4Al De (DO) value is 1.1 (1.3) kcal/mol smaller than that for the 6A1 state. That is, after correcting for limitations in the DFT treatment of states with different 3d occupations, the ground state of FeH20+ is 6Al. Using the modified coupled pair functional (MCPF) approach yields the 6A1 state to be below the 4A1state.2 The MCPF has the opposite bias for the 3d occupations. If the MCPF result for the 4AI state is computed using the 4F asymptote and the experimental 6D-4F separation, the 6A1 state is still 0.8 kcal/mol (without zero-point effects) below the 4A1 Thus after correction for limitations in both the MCPF and D I T treatment of Fe+ states with different numbers of 3d electrons, both the DFT and MCPF method yield a 6A1 ground state with the 4A1state about 1 kcal/mol higher. Therefore we conclude that the ground state of FeH20+ is 6A1 and use that state in this work. As has been discussed previously,2 the ground state of Fe(H20)2+ is a quartet state with a 3d population near 7, not a sextet with a population near 6 like FeH20+. Thus, if the binding energy of Fe(H20)2+ was computed directly with respect to the 6A1 state of FeH20+ and HzO, the binding energy would be too large just as in the case of the 4A, state of FeH20+. Therefore we compute the binding energy of Fe(H20)2+ with respect to the 4A1 state of FeH20+ and H20 and correct this to the 6 A ~state using our 4A1-6AI separation deduced above. Using the procedures described in this section, we feel that we can compute the binding energies accurately despite the bias in the DFT approach toward states with higher 3d occupations. We note that since Fe(H20)2+, Fe(H20)3+, and Fe(H20)df all have quartet ground states and similar 3d populations, no bias is expected and the binding energies can be computed directly. B. Bonding in and Binding Energies of Fe(HZO),+, n = 1-4. The binding energies, along with experiment,"-I3 are summarized in Table 1. The Fe 4s and 3d populations are summarized in Table 2 . Since vibrational frequencies are used in interpreting some experiments, we give our harmonic
1637(al)
3687(al)
Fe(H20)2' 185(e) 163l(b2)
369(a1) 3755(b2)
485(b2) 3757(al)
57(4 270(b) 404(a) 1638(b) 3852(a)
Fe(H20)3+ 9 0 ~ 286(a) 492(b) 1642(a) 3853(b)
9603) 3 14(a) 519(b) 3755(a) 3860(b)
132(b) 343(b) 534(a) 3755(b)
49(b) 143(b) 282(a) 377(a) 1634(b) 3756(b) 3858(a)
Fe(Hz0)4+ 60(a) 204(a) 337(b) 443(a) 1634(a) 3764(b) 3859(b)
96(b) 246(b) 348(b) 455(b) 1642(a) 3765(a)
100(a) 266(a) 354(a) 506(a) 1642(b) 3855(b)
frequencies in Table 3. The optimal structures are shown in Figures 1-3, where we note the optimized bond lengths and most interesting angles. The FeH20+ system, shown in Figure 1, is planar with C2" symmetry. Let the Fe-0 bond be along the z axis. The ground state is 6 A ~which , is derived from the 6D(3d64s1)state of Fe+. The 4s orbital mixes in some 4p0 character to polarize away from the water and hence reduce the Fe-water repulsion. The 3d,, 3d,, and 3d,: orbitals are singly occupied, as this minimizes the H20 repulsion with the 3d orbitals. The 3dd-like, 3dn(a2) and 3dx2-,2(a1), orbitals have a much smaller overlap with the water, and hence the 6 A ~and 6A2 states that are derived from doubly occupying these two orbitals, respectively, are virtually degenerate. The water geometry is only slightly modified from that in free water (see Figure l), which is consistent with the bonding being electrostatic (charge-dipole) in origin. The bonding in the 4AIstate differs from that in the 6A1 state in that sd, hybridization occurs instead of sp hybridization. This difference between the 4A1 and 6A1 states is clear from the 4s and 3d, populations given in Table 2 . The Fe-0 distance is shorter for the 4A1 state-see Figure 1. Despite the shorter Fe-0 distance, the 4A1 state is above the 6A1 state, because the reduced repulsion associated with the sd, hybridization is not sufficient to overcome the promotion energy (5.8 kcal/mol) to reach the 4F state. The H20 geometry in the two states is very similar, indicating that the difference between the sp and sd, hybridization is essentially an Fe-centered effect. As discussed previously,2badding a second water to the 6A1 state of FeH20+ does not result in a linear 0-Fe-0 structure, because the sp hybridization results in a polarization of the Fe charge away from the first water. A linear structure would result in placing the second water in an area of high electron density. Thus the lowest sextet state of Fe(H20)2+ has a bent structure with an 0-Fe-0 angle of about 90". Because sd, hybridization reduces the charge density on both sides of the Fe at the same time, the lowest quartet state is linear. With two waters sharing the cost of sd, hybridization, the ground state is ?A1 with the structure shown in Figure 1. The sharing of the cost of the hybridization results in an Fe-0 distance that is slightly shorter for Fe(H20)2+ than the 4Al state of FeH20+. The change in the bonding also results in a binding energy for the second water that is larger than that of the first water. The sd,
Successive H2O Binding Energies for Fe(H20),+
J. Phys. Chem., Vol. 99, No. 22, I995 9005
de
104.9
0.964y 105.8 n
(2.001) 2.1 02
0.973 (0.970)
(1 08.0)
9 0.969
0.967
)y
0.968
d Figure 1. Optimal DFT structures for HzO, FeHzO' (Cz,.) and , Fe(H2O)z' (&).
For FeH20' the geometrical information for the excited
106.
'AI state is given in parentheses.
2.024 108.2
Figure 3. Optimal DFT structure for Fe(Hz0)4' (Cz). B
p0.967
A
1 0 6 d . C
Figure 2. Optimal DFT structure for Fe(H20)3' (Cz).
Figure 4. Ball and stick model of Fe(H:O)J' with an isosurface of
hybridization is clearly apparent in the populations, just as for the 4A1 state of FeH20'. The optimal structure has Du symmetry with the 3dJike (3d,Z and 3d,J orbitals and one of the 3dn-like orbitals singly occupied. The staggered structure allows the H20 out-of-plane orbitals to donate to different orbitals. In addition, each of the 3dJike orbitals mixes in some 4p character to polarize away from the out-of-plane H20 orbital. Thus the bonding in Fe(H20)2' is very similar to that in the 4A1state of FeH20+. It should be noted that part of the apparent enhancement in the second binding energy is due to the change in the bonding. However, even if everything is referenced to the quartet states, FeH20'(4A~) H20 Fe+('F) 2H20, Le. Fe(H20)2' the second ligand binding energy is still 1.8 kcal/mol larger than the first. That is, sharing the cost of the sd, hybridization increases the second ligand binding energy relative to the first, in spite of a ligand-ligand repulsion of 1.1 kcal/mol. The optimal structure of Fe(H20)3+ is shown in Figure 2. This structure is unlike those previously for other systems. In Fe(CO)J+, Cu(H20)3+, and Cu(NH3)3+ the sd, hybridization is lost and the ligands are arranged'ss in a manner that minimizes the ligand-ligand repulsion; namely, the L-M-L angle is about 120". A T-shaped structure is found',' to be the most favorable for Co(H2)3+ and Co(CH&+, where two ligands have the linear L-M-L structure to retain the sd, hybridization and the third ligand bonds to the side of the ML2+ structure. For Fe(H20)3+. assume that the Fe and 0 atoms are in the y z plane and the oxygen labeled "A" is along the z axis. The water
on the z axis benefits from sd, hybridization (see the populations in Table 2), and the other two ligands have a small angle so that they also benefit somewhat from the sd, hybridization. The sd, orbital is shown in Figure 4, where it is clear that the torus about the Fe is pinched down due to the waters B and C, which suggests that the sd, hybridization is less efficient for these two waters. The small third water binding energy is consistent with this view. Two of the lobes of the singly occupied 3d,., orbital point at the in-plane lone-pair orbitals of waters B and C, and the other two lobes point at the out-of-plane lone-pair orbital of water A. The reduced water-metal repulsion associated with the singly occupied 3d, orbital probably leads to the small angle between waters B and C and hence explains the difference in the geometries of Fe(H20)3+ and Cu(H20)3+. The 3d,r,orbital is singly occupied to minimize the repulsion with the out-ofplane lone pairs on waters B and C. One 3ds-like orbital is singly occupied, as for FeH20+ and Fe(H20)2+, but unlike these smaller systems, plus and minus combinations of 3dn-like orbitals result in two 3d orbitals that are rotated by about 20" relative to the original atomic orbitals. One combination is doubly occupied and one is singly occupied. This rotation reduces the water-iron repulsion for the orientation of the waters, which is probably influenced by ligand-ligand repulsion. Thus because of the open-shell 3d orbitals on Fe and because water has significant repulsion with the metal for both the in-plane and out-of-plane lone-pair orbitals, Fe(H?0)3+ has a structure unlike anything we have found previously.
-
+
-
the sd, hybrid orbital.
+
9006 J. Phys. Chem., Val. 99, No. 22, 1995
/'
Ricca and Bauschlicher
\
Figure 5. Ball and stick model of Fe(Hz0)4' with an isosurface of the sd, hybrid orbital.
The increase in the ligand-ligand repulsion with the addition of the third H20 (at the computed equilibrium) is 2.9 kcal/mol. The ligand-ligand repulsion is increased to only 4.4 kcal/mol, even if all three Fe-0 distances are set to those in Fe(H20)2+. Therefore, we conclude that most of the reduction in the third ligand binding energy is due to changes in the metal-ligand repulsion and not to a change in the ligand-ligand repulsion. This implies that even though the system retains sd, hybridization, it is much less efficient at reducing the metal-ligand repulsion for Fe(H20)3+ than for Fe(H20)2+. Thus both Cu(H20),l' and Fe(H20),+ show a large drop in the third binding energy even though F ~ ( H z O ) ~ retains + the sd, hybridization. For Na(H20)4* and Cu(H20)4+, the optimal structure'+23 has S4 symmetry, where the non-hydrogen atoms have T d symmetry. This is the geometry that minimizes the ligand-ligand repulsion. The optimal structure for Fe(H20)4+ is shown in Figure 3; it is between a tetrahedral and square planar structure. If one assumes that the Fe is at the origin and the 0 atoms are along the x and y axes, this structure is formed by moving two pairs of waters closer together and then distorting the opposite pairs out of the plane, one pair above and one pair below. The populations show that the 3d, orbital is doubly occupied. This orbital points out of the "plane" of the oxygen atoms-see Figure 5. It mixes in some 4s character, but unlike the sd, hybridization for the smaller clusters, where the 4s-3d, orbital has the higher occupation, the 4s 3d, orbital has the higher occupation to polarize electron density out of the plane of oxygen atoms. The 3d,v orbital is also doubly occupied, as the lobes of this orbital point in between the waters. This orbital is shown in Figure 6, where it is clear that it has polarized somewhat in response to the bending of the waters closer together. The 3d, and 3d,v orbitals would suggest a structure with D2h symmetry, where the Fe and 0 atoms are in a plane, with 0-Fe-0 angles of 90" and with H atoms of one pair of opposing H20 molecules in the plane and those of the second pair out of the plane. The ligand-ligand repulsion for this D2h symmetry species is 1.4 kcal/mol larger than that for the optimal structure. Thus the ligand-ligand repulsion favors the structure in Figure 3. However because the difference in the ligand-ligand repulsion is relatively small, we suspect that minimizing the metal-water out-of-plane lone-pair repulsion also contributes to the structure. The open-shell 3d,, orbital is shown in Figure 7; the orbital polarizes and the waters twist to reduce the Fe-water repulsion. While the orbital plots appear to confirm our analysis, the bonding is sufficiently complex that it is difficult to devise a method of completely separating changes in the ligand-ligand repulsion from changes in the metal out-of-plane lone-pair repulsion. The computed DO values are in good agreement with experiment-see Table 1. The first ligand binding energy is
+
W Figure 6. Ball and stick model of Fe(H20)4* with an isosurface of the 3d, orbital.
,\')'I
wiv
Figure 7. Ball and stick model of Fe(H20)4* with an isosurface of the open-shell 3d,, orbital.
slightly larger than those of all three experiments and slightly larger than our previous best estimate of 32.5 kcal/mol. The remaining three ligand binding energies are slightly smaller than experiment, with the largest difference being 3.3 kcal/mol for Fe(H20)3+. Differences of this magnitude are consistent with the level of theory used, and hence we conclude that theory and experiment yield consistent bond energies. C. Comparison of Fe(HZO)"+and Fe(CO),+. The bonding in the Fe(H20)ni and Fe(CO),+ systems is very different. The major differences are due to the metal to CO donation and the importance of both in- and out-of-plane metal-ligand repulsion of the water. The metal to ligand donation results in FeCO+ having a quartet ground state while FeH20+ has a sextet. That is, it is important to promote the Fe+ to the 3d7 occupation to maximize the metal to CO donation; without the donation to the ligand, the promotion to 3d7 is unfavorable for FeH20+. For two ligands, the promotion becomes favorable for Fe(H20)2+, so both systems have a quartet ground state. The metal-ligand repulsion is minimized by sd, hybridization in both cases, and hence both systems have a "linear" L-M-L arrangement. For three ligands, both systems show a large reduction in the third ligand binding energy, but the structures are very different. Fe(CO)3+ has C3,, symmetry, which starts from a structure that minimizes the ligand-ligand repulsion, and the three CO molecules bend slightly out of the plane to allow some polarization of the Fe charge away from the CO molecules. This distortion significantly stabilizes Fe(CO)J+.The structure for Fe(H20)3+ is different, starting from a planar
J. Phys. Chem., Vol. 99, No. 22, 1995 9007
Successive H20 Binding Energies for Fe(H20),+ arrangement with two waters bent toward each other; this structure retains some sQ hybridization and appears to be favorable because it minimizes the sum of the in-plane and outof-plane lone-pair repulsions. With four ligands Fe(C0)4+ adopts Td symmetry that minimizes the ligand-ligand repulsion and is very favorable for metal to CO 2n* donation and minimizing the metal-CO u repulsion. The Fe(H20)4+ has a very complex bonding situation, which appears to be driven by ligand-ligand and metal in-plane and metal out-of-plane lonepair repulsion. The optimal geometry ends up as a compromise between these three effects. The third ligand binding energy drops for both systems because of the loss or reduced efficiency of sd, hybridization. For CO the fourth ligand binding energy increases, because the bonding in Fe(CO)3+ and Fe(C0)4+ are similar. As the number of CO molecules increases, the metal center becomes increasingly positive due to the metal to CO 2n* donation. This reduces the metal-CO 5a repulsion, and therefore the electrostatic bonding in M(CO),+ increases with the number of CO molecules. The ligand-ligand repulsion increases and the metal donation to an individual CO decreases with the number of CO molecules; these factors reduce the Fe-CO binding energies. Apparently for Fe(C0)4+, the factors reducing the binding energy are sufficiently small that the fourth binding energy is larger than the third. For water, there is no significant metal to ligand donation; thus, the electrostatic bonding does not increase with the number of ligands. In addition the ligand-ligand repulsion is larger for water than CO. These factors lead to a fourth ligand binding energy that is smaller than the third. This explains the different trends in the binding energies for Fe(CO),+ and Fe(H20),+.
IV. Conclusions The computed successive H20-Fef binding energies are in good agreement with experiment. The calculations find the bonding to be electrostatic in origin. The optimal structures are determined by minimizing the metal-ligand and ligandligand repulsions. For Fe(H20)2+, the ligand-ligand repulsion is small and the increase in the binding energy relative to the first is a result of a change in the spin state from sextet to quartet. The metal-ligand repulsion is reduced by sQ hybridization in Fe(H20)2+. For FeH20+ this mechanism is unfavorable because it requires a promotion of the Fe+ to the 4F(3d7)excited state. For Fe(H20)3+, the ligand-ligand repulsion is increased, but it represents only a small fraction of the decrease in the third ligand binding energy. Most of the reduction in the binding energy comes from the fact that sd, hybridization is much less efficient at reducing the metal-ligand repulsion for three waters than for two. The bonding in Fe(H20)4+ is very complex, resulting
in an optimal structure with C2 symmetry. The ligand-ligand repulsion is minimized for a structure where the heavy atoms have Td symmetry. If only the Fe in-plane water lone-pair repulsion was important, the Fe occupation would appear to favor a structure with D2h symmetry. Ligand-ligand repulsion slightly favors the C2 structure over the D2h one. This leads to the suggestion that ligand-ligand and metal-ligand repulsions, both for the in-plane and out-of-plane water lone-pair orbitals, are all important in determining the optimal structure. The Fe(H20)n+ results are found to be very different from those for Fe(CO),+, which are attributed to the important dative (metal to CO 2n* donation) interaction for CO that is absent for water. Acknowledgment. A.R. would like to acknowledge an NRC fellowship. References and Notes (1) Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H. J . Chem. Phys. 1991, 94, 2068.
(2) (a) Rosi, M.; Bauschlicher, C. W. J. Chem. Phys. 1989, 90, 7264. (b) Rosi, M.; Bauschlicher, C. W. J. Chem. Phys. 1990, 92, 1876. (3) Bauschlicher, C. W.; Maitre, P. J. Phys. Chem. 1995, 99, 3444. (4) Maitre, P.; Bauschlicher, C. W. J. Phys. Chem., in press. ( 5 ) Ricca, A.; Bauschlicher, C. W. J. Phys. Chem. 1994, 98, 12899. (6) Ricca, A.; Bauschlicher, C. W. J. Phys. Chem., in press. (7) Haynes, C. L.; Armentrout, P. B.; Perry, J. K.; Goddard, W. A. J . Phys. Chem., submitted. (8) Blomberg, M. R. A,; Siegbahn, P. E. M.; Lee, T. J.; Rendell, A. P.; Rice, J. E. J. Chem. Phys. 1991, 95, 5898. (9) Stevens, P. J.; Devlin, F. J.; Chablowski, C. F.; Frisch, M. J. J . Phys. Chem. 1994, 98, 11623. (10) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (1 1) Dalleska, N. F.; Honma, K.; Sunderlin, L. S.;Armentrout, P. B. J . Phys. Chem. 1993, 97, 596. (12) Marinelli, P. J.; Squires, R. R. J. Am. Chem. SOC. 1989, 111,4101. (13) Magnera, T. F.; David, D. E.; Stulik, D.; Orth, R. G.; Jonkman, H. T.; Michl, J. J . Am. Chem. SOC. 1989, 111, 5036. (14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A,; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, Revision G.2; Gaussian, Inc.; Pittsburgh, PA, 1993. (15) Ricca, A,; Bauschlicher, C. W. Theor. Chim. Acta, in press. (16) Bauschlicher, C. W.; Partridge, H. J . Chem. Phys., in press. (17) Wachters, A. J. H. J. Chem. Phys. 1970, 52, 1033. (18) Hay, P. J. J. Chem. Phys. 1977, 66, 4377. (19) Dunning, T. H.; Hay, P. J. In Methods of Electronic Structure Theory; Schaefer, H. F., Ed.; Plenum Press: New York, 1977; pp 1-27. (20) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. (21) Fliikiger, P. F. Development of the Molecular Graphics Package MOLEKEL and its Application to Selected Problems in Organic and Organometallic Chemistry. Ph.D. Thesis 2561, University of Geneva, 1992. (22) Moore, C. E. Atomic energy levels. Natl. Bur. Stand. Circ. (US.) 1949, 46. (23) Bauschlicher, C . W.; Langhoff, S. R.; Partridge, H.; Rice, J. E.; Komomicki, A. J . Chem. Phys. 1991, 95, 5142.
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