J. Phys. Chem. 1996, 100, 1605-1614
1605
Cation-Ether Complexes in the Gas Phase: Bond Dissociation Energies and Equilibrium Structures of Li+[O(CH3)2]x, x ) 1-4 Michelle B. More,† Eric D. Glendening,‡ Douglas Ray,*,‡ David Feller,*,‡ and P. B. Armentrout*,† Department of Chemistry, UniVersity of Utah, Salt Lake City, Utah 84112, and EnVironmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352 ReceiVed: August 10, 1995; In Final Form: October 18, 1995X
Bond dissociation energies, equilibrium structures, and harmonic vibrational frequencies of Li+[O(CH3)2]x, x ) 1-4, are reported. The bond dissociation energies are determined experimentally by analysis of the thresholds for collision-induced dissociation of the cation-ether complexes by xenon (measured using guided ion beam mass spectrometry) and computationally by ab initio electronic structure calculations at the RHF and MP2 levels of theory. In all cases, the primary and lowest energy dissociation channel observed experimentally is endothermic loss of one ether molecule. The cross-section thresholds are interpreted to yield 0 and 298 K bond energies after accounting for the effects of multiple ion-molecule collisions, internal energy of the complexes, and unimolecular decay rates. The experimental and theoretical bond energies are in good agreement with previous experimental results for Li+[O(CH3)2]. Agreement between experiment and theory is also good for x ) 2-4, where the bond energies calculated with a 6-31+G* basis set are larger than the experimental values by 12 ( 10, 10 ( 11, and -2 ( 14 kJ/mol, respectively. Some of these discrepancies disappear at the complete basis set limit. The equilibrium structures are determined primarily by strong electrostatic and polarization interactions. Charge transfer interactions are also important, as indicated by natural energy decomposition analysis of the calculated wave functions.
Introduction The noncovalent interactions between ions and neutral molecules are of fundamental importance to molecular recognition and related phenomena in condensed phases.1 While the importance of these interactions is widely appreciated, their subtlety is not. This subtlety is aptly illustrated by the selectivity of macrocyclic ligands (e.g., crown ethers) toward alkali cations in aqueous solution.2 Crown ether-cation complexes are interesting not only from a fundamental point of view but also because of their possible utility in advanced chemical separation methods.3 Computational methods capable of predicting ligand selectivity in a variety of condensed-phase environments would be valuable tools for the development of separation technologies. Such methods are currently under development but require accurate models of the relevant noncovalent interactions. One approach to understanding noncovalent interactions is the study of ion-molecule complexes in the gas phase. Measurements and calculations on isolated complexes allow separation of intrinsic interactions from effects due to solvation and solventinduced phenomena. Obtaining accurate data on complexes of cations with simple ethers and determining the level of theory required to accurately model these complexes are the first steps toward developing reliable models of the interaction between cations and polyethers. Experimental data and theoretical results on several ML+ complexes of alkali cations (M+) with simple ethers (L) have been obtained. Experimental results include a determination of the binding energy of the Li+-dimethyl ether complex by Woodin and Beauchamp4 as part of their study of gas-phase basicities of numerous ligands. Bond strength determinations for KL+ complexes where L was dimethyl ether and diethyl †
University of Utah. Pacific Northwest National Laboratory. X Abstract published in AdVance ACS Abstracts, December 15, 1995. ‡
0022-3654/96/20100-1605$12.00/0
ether have been reported by Davidson and Kebarle.5 Experimental determinations of the standard free energies of association of several LiL+ complexes, where L is a simple ether (dimethyl, diethyl, dipropyl, diisopropyl, dibutyl, and tert-butyl methyl ethers), have been reported by Taft et al.6 Theoretical results include ab initio calculations by Smith, Chandrasekhar, and Jorgensen on Li+ and Na+ complexes of dimethyl ether as part of their study of acid-base interactions.7 Recently, Hay and Rustad8 performed ab initio calculations on ML+ complexes of alkali and alkaline earth cations with dimethyl ether and methyl ethyl ether at the Hartree-Fock level. Glendening, Feller, and Thompson9 also performed a series of high-level ab initio calculations on the K+-dimethyl ether complex in the course of their investigation of the alkali cation complexes of 18-crown-6. There have been no published measurements or calculations on MLx+ complexes for x > 1. The present work was undertaken to extend the thermochemical database on MLx+ complexes and to test and validate the experimental and theoretical methods employed. Dimethyl ether (DME) was selected as the ligand as it may be considered the simplest functional subunit of an aliphatic polyether. Accurate experimental determinations of the bond dissociation energies of the Li+(DME)x complexes facilitate assessment of the level of ab initio theory required to accurately describe these complexes. Also, the results of the calculations (vibrational frequencies and geometries) are used to provide a more accurate analysis of the experimental data. An understanding of the thermochemical results is aided by natural energy decomposition analysis (NEDA)10 of the calculated wave functions. The work presented here represents the first step in a synergistic program to develop a predictive model of the noncovalent interactions between cations and polyethers. Work in progress extends this first investigation to other metals and more complicated ligands, such as the crown ethers. © 1996 American Chemical Society
1606 J. Phys. Chem., Vol. 100, No. 5, 1996 Experimental and Theoretical Methods Experiment. Complete descriptions of the apparatus and the experimental procedures are given elsewhere.11,12 The production of Li+-DME complexes is described below. Briefly, ions are extracted from the source, accelerated, and focused into a magnetic sector momentum analyzer for mass analysis. Massselected ions are retarded to a desired kinetic energy and focused into an octopole ion guide that radially traps the ions. The octopole passes through a static gas cell containing xenon, used as the collision gas, for reasons described elsewhere.13,14 After exiting the gas cell, product and unreacted reactant ions drift to the end of the octopole where they are focused into a quadrupole mass filter for mass analysis and subsequently detected by a secondary electron scintillation ion counter using standard pulse counting techniques. Raw ion intensities are converted to absolute cross sections as described previously.11 Absolute uncertainties in cross section magnitudes are estimated to be (30%, and relative uncertainties are (5%. Because the radio frequency used for the octopole does not trap light masses with high efficiency, the cross sections for Li+ products were more scattered and showed more variations in magnitude than is typical for this apparatus. We verified that the energy dependences (and thus the threshold analyses) of the Li+ product cross sections were not affected by these variations. Ion kinetic energies in the laboratory frame are related to center-of-mass (CM) frame energies by E(CM) ) E(lab)m/(M + m), where M and m are the ion and neutral reactant masses, respectively. All energies cited below are in the CM frame unless otherwise noted. Sharp features in the observed cross sections are broadened by the thermal motion of the neutral gas15 and the distribution of ion energies. The zero of the absolute energy scale and the full width at half-maximum (fwhm) of the ion energy distribution are measured by a retarding potential technique described elsewhere.11 The fwhm of the ion beam energy distribution was typically between 0.3 and 0.6 eV (lab) for these experiments. The uncertainty in the absolute energy scale is (0.05 eV (lab). The complexes are formed in a 1 m long flow tube12 operating at a pressure of 0.4-0.7 Torr with a helium flow rate of 40009000 standard cm3/min. Lithium ions are generated in a continuous dc discharge by argon ion sputtering of a cathode consisting of a carbon steel “boat” containing lithium metal. Complexes are formed by associative reactions with DME introduced to the flow 5 cm downstream from the dc discharge. Typical operating conditions of the discharge are 3 kV and 30 mA in a flow of 5-15% argon in helium. The flow conditions used in this source provide approximately 105 collisions between the ions and the buffer gas, which should thermalize the complexes both rotationally and vibrationally to 300 K, the temperature of the flight tube. Work from this laboratory16-20 has shown that this assumption is reasonable, and no evidence for nonthermal ions was observed in this work. Theory. Geometries and dissociation energies of the Li+(DME)x complexes were calculated by ab initio methods. Geometries were optimized at the restricted Hartree-Fock (RHF) level of theory using a modified 6-31+G* basis set.21 This basis included a single d-type polarization function on Li, C, and O and diffuse sp functions on Li and O. Previous calculations9,22 of the K+(DME) complex revealed that the diffuse functions on O reduced undesirable basis set superposition errors (BSSE) in the calculated dissociation energies. The diffuse sp functions on C, that are present in the standard 6-31+G* set, were neglected because they only marginally influenced the calculated geometrical features, dissociation
More et al. energies, and BSSE. Unless otherwise noted, all dissociation energies were corrected for BSSE through use of the counterpoise (CP) correction.23 Correlation corrections were evaluated with frozen-core, second-order Møller-Plesset perturbation theory (MP2), applied to the RHF optimized geometries. A limited number of calculations were also performed with fourth-order perturbation theory (MP4). In order to evaluate the effect of correlation recovery on geometry, the Li+(DME) and Li+(DME)2 complexes were reoptimized at the MP2 level. All optimizations were performed using the Gaussian 9224 and GAMESS25,26 programs. While previous MP2/6-31+G* results for cation-ether systems have proven remarkably reliable given the relatively small size of the basis, we wished to calibrate our present results against more extended treatments. We therefore performed benchmark RHF, MP2, and MP4 calculations of the Li+(DME) and Li+(DME)2 complexes using the correlation consistent series of basis sets.27-29 This series includes sets of approximate double-, triple-, and quadruple-zeta quality (denoted cc-pVxZ, x ) D, T, Q) in the valence space that permit one to systematically approach the complete basis set (CBS) limit. We also employed the augmented double- and triple-zeta sets (denoted aug-cc-pVxZ, x ) D, T) that include an extra diffuse shell of each type of angular momentum function. Calculations with the still larger aug-cc-pVQZ basis, which would have entailed 577 functions on Li+(DME), were judged to be beyond the capabilities of the available computational resources. Full geometry optimizations were performed at each level of theory, except for the calculations with the cc-pVQZ basis set. The RHF and MP2 geometries for these latter calculations were performed by first using Gaussian 92 to fully optimize the complex with the g functions deleted from the C and O basis sets. Subsequent numerical optimizations of the Li‚‚‚O distance, CO bond length, and COC bond angle with the g functions included were performed with the SUPERMOLECULE30 program. Conventional MP2 calculations with the 400-basis function, cc-pVQZ set are prohibitively expensive. We therefore employed the RI-MP231,32 technique, which was found to yield excellent agreement with the MP2 dissociation energy and geometry for K+(DME) with the smaller aug-ccpVDZ basis set.9 The nature of the RI-MP2 approximation is such that this method converges to conventional MP2 as the size of the basis set increases. Previous studies33-36 have shown that the energies and geometrical parameters calculated with the correlation consistent basis sets tend to converge exponentially with increasing basis set size to the CBS limit. By fitting the computed values with a simple function of the form f(x) ) aCBS + b exp(-cx), x ) 2, 3, and 4 for cc-pVDZ, cc-pVTZ, and cc-pVQZ (or the augcc-pVxZ series), we are able to obtain an approximate result (given by the parameter aCBS) that is more reliable than any that can be explicitly computed. A comparison of the 6-31+G* basis set results and CBS limits for Li+(DME) dissociation energies allows us to assess the accuracy of the lower level 6-31+G* approach. Natural energy decomposition analysis (NEDA)10,37 of the Li+(DME)x complexes was performed. NEDA partitions the energy change [∑Ee(x)] for the complete dissociation of the complexes, i.e., reactions 1,
Li+(DME)x f Li+ + xDME
(1)
into electrostatic (ES), polarization (POL), charge transfer (CT), exchange (EX), deformation (DEF), and distortion (DIS)
Cation-Ether Complexes in the Gas Phase
J. Phys. Chem., Vol. 100, No. 5, 1996 1607
Figure 1. Threshold for CID of Li+(DME)x, x ) 1-4 as a function of kinetic energy on the center-of-mass frame (lower x axis) and the laboratory frame (upper x axis). Open circles show the primary cross sections extrapolated to zero pressure of the Xe reactant. The best fits to the data using the model of eq 4 are shown as dashed lines. Solid lines show these results convoluted over the neutral and ionic kinetic energy distributions. Filled triangles and open diamonds show secondary and tertiary products, respectively.
components, namely,
Experimental Results
∑Ee(x) ) ES + POL + CT + EX + DEF(Li) +
Experimental cross sections are shown in Figure 1 for the collision-induced dissociation (CID) of the Li+[O(CH3)]x, x ) 1-4, ion-molecule complexes. The sequential loss of intact DME molecules and ligand exchange with xenon are the major processes observed in these systems over the collision energy range studied, typically 0-10 eV. The cross sections for ligand exchange were small and thus neglected in data collection. The primary (both the lowest energy and most important) process for all complexes is the loss of a single DME ligand in reaction 3.
xDEF(DME) + xDIS(DME) (2)
ES arises from the classical electrostatic interaction of the unperturbed fragment (Li+ and DME) charge distributions. POL is the extra electrostatic stabilization that occurs when the fragment charge distributions polarize in the field of the neighboring fragments. CT results from the delocalization of electrons from the donor orbitals of one fragment into the acceptor orbitals of neighboring fragments. EX arises from the exchange interactions between the occupied molecular orbitals of the Li+ and DME fragments. DEF is the energy penalty for deformation of the fragment charge distribution from that calculated at infinite separation to that of the complex. This deformation arises from polarization induced by the adjacent fragments and, for small fragment separations, from Pauli repulsions as the fragment wave functions maintain orthogonality. DIS is the energy penalty for distorting the DME geometry from that of the isolated molecule to that of the complex. Dipole moments of the ligands in the Li+(DME)x complexes were evaluated as expectation values of the intermediate fragment wave functions calculated by the NEDA method. Atomic charges were also calculated using natural population analysis.38
Li+(DME)x + Xe f Li+(DME)x-1 + DME + Xe (3) Results for the interaction of Li+(DME) with xenon are shown in Figure 1a. The major product is Li+, which has an apparent threshold near 1.5 eV and a maximum cross section of 2.5 Å2. Two minor products, CH3OLi+ and CH2OLi+, are produced at higher energies (>6 eV) and have small cross sections (
