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J. Phys. Chem. 1992, 96,8827-8832 (25) Maple, Reference Manual; Symbolic Computation Group, Department of Computer Science, University of Waterloo: Waterloo, Ontario, Canada, 1989. (26) Beckert, D.; Schneider, G. Chem. Phys. 1987, 116, 421. (27) Plato, M.; Lubitz, W.; MBbius, K. J. Phys. Chem. 1981, 85, 1202.
(28) Rao, P. S.; Hayon, E. J . Phys. Chem. 1973, 77, 2274. (29) Beckert, D. Dissertation B, Akademie der Wissenschaften, Leipzig, 1986. (30) Wong, S . K.; Sytniyk, W.; Wan,J. S.K. Can. J . Chem. 1972, 50, 3052.
Calculatlon of Mg+-Llgand Relative Binding Energies Harry Partridge* and Charles W. Bauschlicher, Jr.* NASA Ames Research Center, Moffett Field, California 94035 (Received: April 3, 1992)
The calculated relative binding energies of 16 organic molecules to Mg+ are compared with experimental results where available. The geometries of the ligands and the Mg+-ligand complexes are optimized at the self-consistent field (SCF) level using a 6-31G* basis set. The Mg+ binding energies are evaluated using second-order perturbation theory and basis sets of triple-f quality augmented with two sets of polarization functions. This level of theory is calibrated against higher levels of theory for selected systems. The computed binding energies are accurate to about 2 kcal/mol.
Introduction Operti, Tews, and Freiserl (OTF) have measured the relative gas-phase AGZ9*values for the binding of 12 organic molecules to Mg+ by determining the equilibrium constant of various exchange reactions. The relative AG298values are believed to be accurate to fO.l kcal/mol, based upon the mutual agreement of the results for various pairs. Because of the similar bonding mechanism for all the systems, OTF suggested that the relative AG298values should be nearly equivalent to the relative binding energies. While the measured rate constants for the ligand exchange reactions are expected to yield excellent relative AG298 values (or binding energies), the absolute binding energies could not be determined in this manner. Photodissociation experimentsl on MgMeOH+ and MgMqCO+ were used to obtain the absolute binding energies. Unfortunately, these photodissociation experiments only establish an upper bound, because it is not known how high the dissociative state lies above the ground-state asymptotes-see, for example ref 2. Freiser suggested3 that ab initio calculation could help establish absolute binding energies, and such calculations (employing the modified coupled-pair functional (MCPF) method) were reported in a previous manuscript.‘ One observation of this work was that the self-consistent field (SCF) binding energies in a large basis set were in fairly good agreement with those from a high-level correlation treatment. However, the addition of correlation in a large basis set was required to compute accurate relative binding energies. Unfortunately, this leads to prohibitively large MCPF calculations for many of the organic ligands that were included in the experimental study. In this work electron correlation is included using second-order Maller-Plesset (MP2) perturbation theory. The advantage of this approach is that a direct implementation5 is available which can be applied to all of the ligands studied in the experiment. For the smaller ligands the MP2 absolute binding energies are in good agreement with the MCPF re~ults.49~ Overall the MP2 results are in better agreement with experiment than are the SCF results, but even this level of theory is only capable of about 2.0 kcal/mol accuracy in the relative binding energies for the alcohols, aldehydes, and ethers considered in this work.
Metbods The geometries and vibrational frequencies are computed at the self-consistent field (SCF) level using analytic first- and second-derivative techniques. The eigenvalues of the Hessian confirm that the optimized structures correspond to a minimum. The geometry of the ligand was optimized, and then the metalligand structure was optimized using this ligand structure with
the Mg ion bound to the oxygen of the organic ligand. As discussed below, the optimization strategy is important because of the possibility of local minimum resulting from rotations of the side chains. A 6-31G* basis set’ is employed for the geometry optimizations. The d exponents are Mg (0.175), C (0.80),and 0 (0.90). The binding energies are then evaluated using the MP2 approach with a triple-t plus two sets of polarization functions (TZ2P) basis set at the 6-3 lG* optimized geometries. The Mg set is the (12s 9p)/[6s 4p] basis developed by McLean and Chandler8 with two 3d functions added (a = 0.4 and 0.16). The C and 0 sets are the (10s 6p)/[5s 3p] contraction of Dunning9 with two 3d functions added (a = 1.6 and 0.6 for oxygen and CY = 1.40 and 0.4 for carbon). The hydrogen basis is the (5s)/[3s] set of Dunningg with two 2p polarization functions added (a = 1.25 and 0.45). For selected systems the MP2 approach is calibrated by comparing with results employing the nearly size-consistent MCPF method.I0 We also calibrate the TZ2P basis sets by comparing with calculations employing the much larger atomic natural orbital (ANO) basis sets” described in previous work.4v6 The Mg basis is (20s 15p 6d)/[(5 1)s (4 1)p 2d] where the notation m+n specifies that m ANOs are used and the n most diffuse functions are uncontracted. The C and 0 A N 0 basis sets are of the form (13s 8p 6p lf)/[4s 3p 2d lfl, and the hydrogen set is of thdform (8s 6p 4d)/[4s 2p Id]. In order to compare with experiment we compute AS using the rigid rotor and harmonic oscillator approximations. We use the SCF 6-3 1G* geometries and the scaled (0.89) vibrational frequencies. While this treatment is somewhat qualitative, the differential effect of AS is small, and the relative AG values are expected to be accurate. The scaled SCF vibrational frequencies are also used to compute the zero-point corrections. All functions are included in the SCF geometry optimizations, but only the pure spherical harmonic components of the basis functions are using in the MP2 and MCPF calculations. The calculations were performed using the MOLECUL.ESWEDEN,*2 DISCO,” and GRADSCFI4 program systems.
+
+
Calibration Calculations For all systems the Mg+ is bound to the oxygen of the organic ligand. We believe that the error in our approximations probably vary more with the functional groups at the Mg+ binding site than with the length of the hydrocarbon chain. Therefore we use two alcohols, two aldehydes, and one ether for calibration. For MeCHO, MeOH, and H2C0, the SCF binding energies computed with the TZ2P basis set at the 6-3 1G* geometries differ by only
This article not subject to US.Copyright. Published 1992 by the American Chemical Society
8828 The Journal of Physical Chemistry, Vol. 96, No. 22, 1992
Partridge and Bauschlicher
TABLE I:
Calibration Calculationsc
TZ2P MP2
MeOH
EtOH H2CO Me20
MeCHO
37.0 39.3 32.1 39.3 38.7
AN0
MCPF 36.9 39.1 32.3 38.9 38.9
MCPF 36.7' 32.8b 39.0 39.7
From ref 4. Further expansion of the basis set increases the binding energy to 37.0 kcal/mol. bReference4.
