J. Phys. Chem. 1996, 100, 14899-14903
14899
Ligand Exchange Reactions in Molecular Hydrogen Complexes of Osmium(II): A Quantum Chemical Study Using Density Functional Theory Ian Bytheway,† George B. Bacskay,† and Noel S. Hush*,†,‡ School of Chemistry and Department of Biochemistry, UniVersity of Sydney, NSW 2006, Australia ReceiVed: March 20, 1996; In Final Form: May 31, 1996X
The energetics and mechanism of ligand exchange reactions in a range of molecular hydrogen complexes of Os(II), [Os(NH3)4Lz(η2-H2)](z+2)+ (where Lz ) C5H5N, CH3CN, NH2OH, NH3, (CH3)2CO, H2O, CN-, CH3COO-, and Cl-), have been studied using quantum chemical methods. Density functional theory using the BLYP functional was employed to determine the gas phase equilibrium geometries and the binding energies of H2 and the trans ligand Lz. The effects of solvation on the energetics were estimated using two variants of the self-consistent reaction field method. Thermal enthalpy and entropy contributions were also calculated, resulting in theoretical estimates of standard free energy changes for the ligand exchange reactions [Os(NH3)4H2O(η2-H2)]2+ + Lz f [Os(NH3)4Lz(η2-H2)](z+2)+ + H2O in aqueous solution which were compared with the available experimental data. A reasonable level of qualitative to semiquantitative agreement between theory and experiment is demonstrated, especially when Lz ) Cl-, CH3COO- and (CH3)2CO. In agreement with experiment, theory also predicts that [Os(NH3)4CN(η2-H2)]+ will hydrolyze, with H2O replacing H2 as a ligand with the evolution of H2 gas. The theoretical studies also suggest that ligand exchange in these systems takes place via an SN1 type mechanism, e.g., with the formation of a loosely associated [Os(NH3)4(η2-H2)]2+ and H2O as transition state. The computed free energy changes of activation are consistent with the experimentally deduced values.
Introduction Molecular hydrogen complexes of osmium(II), [Os(en)2Lz(η2-H2)](z+2)+ and [Os(NH3)4Lz(η2-H2)](z+2)+, where en is ethylenediamine and Lz is a variable trans ligand, have been of considerable interest recently and the subject of extensive experimental work, ranging from synthetic applications1 to studies of their physical and chemical properties,2,3 electrochemistry,4 X-ray and neutron crystallography,5 and isomerization reactions.6 These studies led to an understanding of the effect of the trans ligand on the properties of these complexes, in particular of the binding of the molecular hydrogen ligand. An interesting result obtained in the neutron diffraction study5 of the [Os(en)2(CH3COO-)(η2-H2)]+ complex is that the H-H separation in this complex is 1.34 Å, almost double that in free H2, although NMR data suggest that the H2 ligand is still bound in a sideways η2 fashion as molecular hydrogen, rather than as two separate hydride ligands. Electronic structure calculations on the related [Os(NH3)4(CH3COO-)(η2-H2)]+ complex7 established the important role of electron correlation that is required to reproduce the large H-H distance that is consistent with what had been observed in the neutron diffraction experiment on the related ethylenediamine complex. Hartree-Fock calculations predicted a relatively short H-H distance of 0.85 Å in the tetramine complex, but the inclusion of electron correlation using MP2 theory resulted in a considerably stretched H-H distance of 1.39 Å, in good agreement with experiment. Further studies at the correlated level of a range of [Os(NH3)4Lz)(η2-H2)](z+2)+ complexes (Lz ) C5H5N, CH3CN, NH2OH, NH3, (CH3)2CO, H2O, CN-, CH3COO-, and Cl-) have shown that the bond length of H2 varies from ∼1 to 1.4 Å, depending on the trans ligand and the level of theory used to describe electron correlation.8,9 It was †
School of Chemistry. Department of Biochemistry. X Abstract published in AdVance ACS Abstracts, August 1, 1996. ‡
S0022-3654(96)00858-1 CCC: $12.00
also demonstrated that other properties of these complexes such as the binding energies of H2 and their dependence on the trans ligand Lz and H-D spin-spin coupling constants (JHD) could be correlated with the spectrochemical parameter10 of the trans ligand.8,9 In this paper we present further theoretical work on this series of complexes, focusing on the energetics of the trans ligand exchange reaction:
[Os(NH3)4H2O(η2-H2)]2+ + Lz f [Os(NH3)4Lz(η2-H2](z+2)+ + H2O (1) Such reactions of the related [Os(en)2Lz)(η2-H2)](z+2)+ family of complexes have been extensively studied by Li and Taube,2,3,6 measuring their equilibrium as well as rate constants. Since the experimental data are obtained in aqueous solution (as well as some other solvents), our theoretical work addresses the effects of solvation on the energetics of ligand exchange so that meaningful comparison with experiment could be made. Theoretical Details The quantum chemical calculations reported in this paper are an extension of our previous work,7-9 using techniques that have been tested extensively on the complexes of interest. The calculations were performed using density functional theory (DFT), utilizing the BLYP functional,11 in conjunction with effective core potentials and the basis sets of Stoll et al.,12 described in detail in our previous work.8,9 The quantum chemical calculations were performed using the GAUSSIAN 94 software package13 on HP700, DEC Alpha, and IBM RS 6000 computers. Solvation energies were obtained using two variants of selfconsistent reaction field (SCRF) theory, namely the selfconsistent multipole moment reaction field (SCMMRF) and the self-consistent isodensity polarizable continuum (SCIPCM) © 1996 American Chemical Society
14900 J. Phys. Chem., Vol. 100, No. 36, 1996
Bytheway et al.
TABLE 1: Ligand Binding Energies ∆E(Lz) As Defined in Eq 7 and Individual Solvation Energies Gsolv (in Water, E ) 78.54) in kcal/mol, Obtained Using the SCMMRF and SCIPCM Methods for the [Os(NH3)4Lz(η2-H2)](z+2)+ Complexes and the Free Lz Ligands -Gsolv(complex)
∆E(Lz) L
z
C5H5N CH3CN NH2OH NH3 (CH3)2CO H2O CNCH3COOCla
-Gsolv(Lz)
gas
SCMMRF
SCIPCM
SCMMRF
SCIPCM
SCMMRF
SCIPCM
expt
53.5 52.0 46.2 45.3 43.5 37.4 251.1 243.8 232.8
30.8 34.4 28.6 35.6 18.8 24.0 73.9 68.8 56.1
29.9 28.2 29.6 35.5 19.6 26.6 60.5 47.0 35.0
143.0 141.9 150.4 155.8 141.8 153.8 45.6 40.3 43.8
180.7 182.4 194.4 194.9 181.6 197.0 74.2 65.0 67.7
1.3 3.1 3.6 1.2 2.1 2.8 58.4 51.1 56.1
3.2 5.1 9.9 3.6 4.4 6.7 63.7 60.7 64.4
4.7a 3.9a
Ref 20, adjusted to conform to definition of Gsolv of ref 21.
b
Reference 21.
methods. The SCMMRF approach defines energy of solvation Esolv for a given solute as:
Esolv ) -
1 2
l
∑l m)-l ∑ Mlm0 Flm
(2)
0 0} are components of the solute’s permanent where {Mlm multipole moments (written in spherical tensor form) and {Flm} are the corresponding components of the reaction field, defined as
Flm ) glMlm
(3)
where {Mlm} are the multipole moments in the presence of the reaction field that models the solvent. An important aspect of SCRF theory is the size and shape of the cavity occupied by the solute,14 and the methods used in this work differ in their choice of cavity. Conventional SCRF and SCMMRF use a spherical cavity of radius R0 surrounding the solute, in which case
gl )
(l + 1)( - 1) 1 [(l + 1) + l] R02l+1
(4)
where is the dielectric constant of the solvent. Equations 2 and 3 are then solved iteratively15 where the components of the reaction field are obtained simply from the solute’s permanent moments and polarizabilities, e.g.
µR ) µR0 + ∑RRβFβ + ...
(5)
R,β
where {RRβ} are components of the dipole polarizability. The multipole moments up to hexadecapole were used in conjunction with the dipole polarizability R. This method represents a simplification of conventional SCRF theory16,17 where the multipole moments {Mlm} are obtained by the self-consistent solution of the appropriate Schro¨dinger equation with the perturbed Hamiltonian
H ˆ )H ˆ0 - ∑ l
l
∑
M ˆ lmFlm
(6)
m)-l
The SCMMRF method has been tested for a variety of molecules at different levels of theory, with a range of basis sets. Close agreement between the SCMMRF results and those obtained using the conventional approach was found.15 The SCIPCM technique is based on Tomasi’s polarizable continuum model.14 The reaction field is obtained in terms of a surface integral over the charge density on the cavity surface, and in the SCIPCM model, which is implemented in the
c
4.3b 1.9a 6.3b 70.5c 87.2c 81.2c
Reference 22.
GAUSSIAN 94 software package, the solute cavity is defined by an electron density isosurface. The recommended value18 for the charge density isosurface of 0.0004 e Å-3 was used in this work. Application of the SCIPCM method has, however, necessitated doing all-electron calculations as in previous work of ours.9 These were performed at the ecp-optimized geometries, representing the core orbitals of each atom by Huzinaga’s minimal basis sets.19 Results and Discussion Binding Energies of Lz. The calculated solvation energies of the [Os(NH3)4Lz(η2-H2)](z+2)+ complexes and of the free ligands Lz are given in Table 1 along with the binding energies in each complex, in gas phase and solution, defined as the energy change ∆E(Lz) associated with the reaction: ∆E(Lz)
[Os(NH3)4(η2-H2)Lz](z+2)+ 98 [Os(NH3)4(η2-H2)]2+ + Lz (7) Comparison of the solvation energies as predicted by the SCMMRF and SCIPCM methods indicates that while the differences are fairly substantial they are systematic, and the two methods agree with respect to the trends in solvation energies as Lz varies. The SCIPCM values are consistently larger in magnitude than those from SCMMRF, as expected, given that in the former method the cavity closely hugs the solute molecule, i.e., containing effectively less “empty” space. In the case of the free ligands the quality of the theoretical predictions can be assessed by comparison with experimental free energies of hydration.20-22 The agreement between theory and experiment is remarkably good, especially in the case of neutral molecules. For charged ligands the discrepancies are of course larger, commensurate with the very much larger solvation energies. As the data in Table 1 show, solvation significantly reduces the magnitude of the binding energy of the trans ligand Lz. The reduction is of course most dramatic in the case of charged ligands, since solvation of a dissociated ion pair cancels much of the Coulomb energy that is present in the (associated) complex. H2O/Lz Exchange Reactions. The energetics of the ligand exchange reactions given in eq 1 were calculated from the data in Table 1 and are summarized in Table 2. To facilitate comparison with the available experimental data the Gibbs free energies of the reactions were also estimated on the basis of the rotational and translational entropy contributions of the appropriate products and reactants in eq 1. (Unfortunately, the calculation of vibrational frequencies was found to be too costly to be carried out routinely, since the force constant matrix is
Molecular Hydrogen Complexes of Osmium(II)
J. Phys. Chem., Vol. 100, No. 36, 1996 14901
TABLE 2: Enthalpy, Entropy, and Gibbs Free Energy Changesa (kcal mol-1) for the Lz/H2O Ligand Exchange Reactions (1) in Gas Phase and Aqueous Solution (at 298.15 K Unless Indicated Otherwise) Lz
∆Hgas (0 K)
T∆Sgas
∆Ggas
C5H5N CH3CN NH2OH NH3 (CH3)2CO
-16.1 -14.6 -8.8 -7.9 -6.1
-4.3 -2.1 -2.2 -1.1 -3.8
-11.8 -12.5 -6.6 -6.8 -2.3
CNCH3COOClCl- d
-213.7 -206.4 -195.5 -197.1
-0.4 -3.9 2.8 1.2
-213.3 -202.5 -198.3 -198.3
∆G° ∆G° (SCMMRF) (SCIPCM) -2.5 -0.2 -2.4 -10.4 9.0 8.5c -49.5 -40.8 -34.9 -34.9
0.9 0.5 -7.1 -7.8 10.8 9.9c -33.7 -16.5 -11.3 -11.3
∆G° (obs)b
