Alkali Metal Cation Interactions with 15-Crown-5 in the Gas Phase

Quantitative interactions of the alkali metal cations with the cyclic 15-crown-5 ..... basis set for all atoms,(68) which is a triple-ζ balanced basi...
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Alkali Metal Cation Interactions with 15-Crown‑5 in the Gas Phase: Revisited P. B. Armentrout,*,† C. A. Austin,‡ and M. T. Rodgers*,‡ †

Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, United States Department of Chemistry, Wayne State University, Detroit, Michigan 48202, United States

‡

S Supporting Information *

ABSTRACT: Quantitative interactions of the alkali metal cations with the cyclic 15-crown-5 polyether ligand (15C5) are studied. In this work, Rb+(15C5) and Cs+(15C5) complexes are formed using electrospray ionization and studied using threshold collision-induced dissociation with xenon in a guided ion beam tandem mass spectrometer. The energy-dependent cross sections thus obtained are interpreted to yield bond dissociation energies (BDEs) using an analysis that includes consideration of unimolecular decay rates, internal energy of the reactant ions, and multiple ion−neutral collisions. 0 K BDEs of 175.0 ± 9.7 and 159.4 ± 9.6 kJ/mol, respectively, are determined and exceed those previously measured [J. Am. Chem. Soc. 1999, 121, 417−423] by 68 and 57 kJ/mol, respectively, consistent with the hypothesis proposed there that excited conformers had been studied. Because the analysis techniques have advanced since this early study, we also reanalyze the published data for the Na+(15C5) and K+(15C5) systems to ensure a self-consistent interpretation of all four systems. Revised BDEs for these systems are 296.1 ± 15.5 and 215.6 ± 10.6 kJ/ mol, respectively, which are within experimental uncertainty of the previously reported values. In addition, quantum chemical calculations are conducted at the B3LYP/def2-TZVPPD level of theory with theoretical BDEs in reasonable agreement with experiment. Computations are also used to explore features of the potential energy surfaces for isomerization of the M+(15C5) complexes.

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ies.15,20,21 In general, the BDEs for any particular ligand decrease as the size of the metal cation increases, consistent with electrostatic forces dominating the binding energies. Furthermore, the sums of BDEs for four DME ligands and for two DXE ligands are similar to that for 12C4 but systematically decrease across this series. This indicates that the orientations of the oxygen atoms are constrained by the backbones of the multidentate DXE and crown ligands. The independent DME ligands can optimize their bond distances from the metal cation while simultaneously orienting their local dipole moments optimally, whereas both cannot be achieved by the multidentate ligands. To understand solution-phase selectivity, it was noted that individual gas-phase M+−crown BDEs show no selectivity for particular sized crowns with particular cations; however, the combination of these quantitative BDEs and hydration energies for the alkali metal cations shows that the observed solutionphase selectivity (for instance, for K+ by 18C6) comes from the competition between hydration of the metal cation and its complexation by the crown.22 Thus, by dividing the aqueous thermochemistry into its intrinsic components, the gas-phase

INTRODUCTION Crown ether/alkali metal cation complexes are prototypical host/guest systems in molecular recognition.1−5 First characterized by Pedersen in 1967,6,7 crown ethers have found widespread applications. For example, they have been used to transport therapeutic radiation to tumors,8 as efficient carriers of amino acids and drugs across membranes,9 to develop advanced analytical methods,10 to design new materials for isotope separation,11−13 and as catalysts for phase transfer in the dissolution of metals in nonpolar solvents.14 Host/guest interactions underlie all of these applications, such that obtaining a quantitative understanding of such phenomena would be desirable. This can be achieved in the gas phase, where the intrinsic host/guest affinities can be separated from those corresponding to solvation of the separated species and their complexes. In previous work, the bond dissociation energies (BDEs) for the gas-phase complexes of five alkali metal cations with three crown ethers, 12-crown-4 (12C4 = 1,4,7,10-tetraoxacyclododecane), 15-crown-5 (15C5 = 1,4,7,10,13-pentaoxacyclopentadecane), and 18-crown-6 (18C6 = 1,4,7,10,13,16-hexaoxacyclooctadecane), were determined by More, Ray, and Armentrout.15−19 Insight into chelation effects was obtained by comparison of the crown ether results with those for simpler ligands, dimethyl ether (DME) and dimethoxyethane (DXE or diglyme),15−20 an effort aided by related theoretical stud© 2014 American Chemical Society

Special Issue: A. W. Castleman, Jr. Festschrift Received: November 26, 2013 Revised: February 21, 2014 Published: February 21, 2014 8088

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heated to 100 °C into a radio frequency (rf) ion funnel,26,27 wherein they were focused into a tight beam. Ions exited the ion funnel and entered an rf hexapole ion guide that trapped them radially. Here the ions underwent multiple collisions (>104) with the ambient gas and became thermalized. Previous experiments25,28−32 using a source of similar design show that the ions produced generally have internal energies that are well described by a Maxwell−Boltzmann distribution of rovibrational states at 300 K. M+(15C5) complexes were extracted from the source, focused, accelerated, and mass selected using a magnetic momentum analyzer. The mass-selected ions were decelerated to a well-defined kinetic energy and focused into a rf octopole ion guide that traps the ions radially. The octopole keeps losses of the reactant and product ions that might result from scattering to a minimum.33 Once in the octopole, the ions pass through a gas cell containing xenon as the collision gas. Xe is used because it is heavy and polarizable, which leads to more efficient kinetic to internal energy transfer.34,35 Data were collected at three pressures of Xe, approximately 0.2, 0.15, and 0.10 mTorr, and the resulting cross sections extrapolated to zero pressure, which rigorously ensures that the cross sections analyzed correspond to products formed in a single collision.36 After collision, the reactant and product ions drift to the end of the octopole, are extracted and focused into a quadrupole mass filter, where they are mass analyzed. Detection of the ions is achieved using a high-voltage dynode, scintillation ion detector,37 with the signal processed using standard pulse counting techniques. Ion intensities are measured as a function of collision energy and converted to absolute cross sections using methods described previously.38 Uncertainties in relative and absolute cross sections are approximately ±5% and ±20%, respectively. The ion kinetic energy distribution is found to be Gaussian in shape with a fwhm of 0.3−0.5 eV (lab). The uncertainty in the absolute energy scale in the laboratory is approximately ±0.05 eV (lab). Laboratory frame collision energies were converted to center-of-mass (CM) frame kinetic energies using the formula, ECM = Elabm/(m + M), where M and m are the masses of the M+(15C5) and Xe reactants, respectively. In the following, all energies are reported in the CM frame. Thermochemical Analysis. Threshold regions of the CID reaction cross sections are modeled using eq 1.39−43

data provide details of the driving forces behind the host−guest interactions. These early studies found good agreement between the experimental and theoretical BDEs for all ligands bound to Li+, Na+, and K+,15−17,20,22 and for DME and 18C6 ligands to Rb+ and Cs+.18 In contrast, experimental BDEs for the multidentate 12C4 and 15C5 ligands with these two heavier metal cations were well outside of experimental uncertainty from the theoretical values.18,21 Although several possibilities for these differences were considered, the explanation most consistent with the experimental evidence was the presence of excited conformers, such that the experimental BDEs corresponded to these excited species rather than the true ground structure. This is feasible because all of the metal cation−ligand complexes were formed using a dc discharge flow-tube (DC/FT) ion source. Here, the ligands and the metal cations condense with one another in a gas flow of He and Ar, which also thermalizes the complexes formed. Such a source allows kinetic trapping of complexes in excited conformations by collisional cooling. Because the energy required for decomposition of these excited species is lower than that for the ground-state conformations, the threshold behavior observed for collision-induced dissociation (CID) of the complexes will change. Recently, we reexamined the complexes of Rb+ and Cs+ with 12C4 by generating them using an electrospray ionization (ESI) source, which should yield only ground-state species because the preformed complexes were extracted directly from solution.23 As in the earlier experiments, metal cation−12C4 binding energies were determined from analysis of the cross sections for the kinetic energy-resolved CID of these complexes with Xe. In addition, the original data for M+(12C4) complexes with M+ = Na+, K+, Rb+, and Cs+ were reanalyzed using the more advanced analysis tools available today. (The original crown ether experiments were among the earliest studies to use the phase space limit transition-state method described below.) This ensured that the thermochemical information for all four systems was self-consistent. Finally, high-level theory was used to calculate the metal cation−ligand BDEs and the complete potential energy surfaces for Na+, K+, Rb+, and Cs+ interacting with 12C4. It was found that the theoretical results (particularly B3LYP/def2-TZVPPD) agreed well with the results for Na+(12C4) and K+(12C4), both the original values and the reanalyzed results, which were within experimental uncertainty of each other, as well as with the new experimental results for Rb+(12C4) and Cs+(12C4). In the present study, we provide a parallel study by revisiting the alkali metal cation−15C5 systems.

σ (E ) = (nσ0/E) ∑ gi

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E

∫E −E (1 − e−k(E*)τ)(E − ε)n−1d(ε) 0

i

(1)

EXPERIMENTAL AND COMPUTATIONAL SECTION General Experimental Procedures. The Wayne State University guided ion beam tandem mass spectrometer, described in detail previously,24 was used to measure cross sections for CID of the rubidium and cesium cation complexes with 15C5. Experiments were conducted using an electrospray ionization (ESI) source under conditions similar to those described previously.23,25 Briefly, the ESI was operated using a 50:50 by volume H2O/MeOH solution with ∼5 × 10−4 M 15C5 and 5 × 10−4 M RbCl or CsCl (chemicals purchased from Sigma-Aldrich), which was delivered using a syringe pump at a rate of ∼1 μL/min into a 35 gauge stainless steel needle biased at ∼2000 V. Ionization occurred over the ∼5 mm distance from the tip of the needle to the entrance of the capillary, biased at ∼35 V. Ions were directed by a capillary

Here n is an adjustable parameter that describes the efficiency of collisional energy transfer,44 σ0 is an energy-independent scaling factor, E is the relative kinetic energy of the reactants, E0 is the threshold for CID of the ground electronic and rovibrational state of the reactant ion at 0 K, τ is the time available for dissociation (∼1.5 × 10−4 s), and ε is the energy transferred into the reactant ion by the collision. The summation is over the rovibrational states (i) of the reactant ions having excitation energies Ei and fractional populations gi (∑gi = 1). The energy available for dissociation is therefore E* = ε + Ei. The Beyer−Swinehart−Stein−Rabinovitch algorithm45−47 is used to evaluate the number and density of the rovibrational states, and the relative populations gi are calculated for a Maxwell−Boltzmann distribution at 300 K. The 8089

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term k(E*) is the unimolecular rate constant for dissociation of the energized molecule (EM) as defined by Rice-RamspergerKassel-Marcus (RRKM) theory,48−51 eq 2, k(E*) = Nvr †(E* − E0)/hρvr (E*)

effective core potentials (ECPs) and valence basis sets of Hay and Wadt64 (equivalent to the LANL2DZ basis set) with single d polarization functions added.65 Relative energies were determined using single point energies determined at the B3LYP and MP2(full) levels using the HW*/6-311+G(2p,2d) basis set. Previous work on the BDEs for Rb+ and Cs+ interacting amino acids66,67 and 12C423 found that the Hay− Wadt ECP/valence basis sets do not yield values in very good agreement with experimental values. Therefore, calculations were repeated using the def2-TZVPPD basis set for all atoms,68 which is a triple-ζ balanced basis set that includes two polarization and diffuse functions with ECPs on rubidium and cesium developed by Leininger et al.69 The def2-TZVPPD basis set was obtained from the EMSL basis set exchange library.70,71 The B3LYP/def2-TZVPPD approach was used to determine geometry optimizations and vibrational frequencies, with zero point energies being scaled by 0.98. Single point energies using MP2(full)/def2-TZVPPD with the B3LYP geometries were also calculated. The MP2 results including counterpoise corrections were systematically high by 9 ± 6% with a mean absolute deviation (MAD) of 14 ± 8 kJ/mol. The best agreement between experiment and theory for the M+(12C4) complexes was found for the B3LYP/def2-TZVPPD results, 1 ± 3% deviation with a MAD = 5 ± 5 kJ/mol. Hence the present study focuses on this latter approach. In our previous study of the M+(12C4) complexes, basis set superposition errors (BSSEs) were estimated for all BDEs using the full counterpoise method.72,73 Such corrections were critical for the MP2 single-point energies, where the BSSE ranged from 14 to 25 kJ/mol, whereas for the B3LYP single-point energies, BSSE corrections were less than 2 kJ/mol for all structures examined there. Similar results are found here for the M+(15C5) complexes, with BSSE corrections contributing between 3.0 and 0.4 kJ/mol.

(2)

where h is Planck’s constant, Nvr†(E* − E0) is the sum of rovibrational states of the transition state (TS) at an energy E* − E0, and ρvr(E*) is the density of rovibrational states of the EM at the available energy, E*. This equation accounts for the fact that the complexes examined in the present study are sufficiently large that their dissociation lifetime near the dissociation threshold can be comparable to the experimental time-of-flight. To evaluate the rate constant in eq 2, vibrational frequencies and rotational constants for the EM and TS are required. Because the metal cation−ligand interactions in the complexes studied here are mainly long-range electrostatic interactions (ion−dipole, ion−quadrupole, and ion−induced dipole interactions), the most appropriate model for the TS is generally a loose association of the ion and neutral ligand fragments,52−57 even for multidentate ligands.16−18,23,28 Therefore, the TSs are treated as product-like, such that the TS frequencies are those of the dissociated products. The transitional frequencies are treated as rotors, a treatment that corresponds to a phase space limit (PSL), as described in detail elsewhere.41,42 The 2-D external rotations are treated adiabatically but with centrifugal effects included.58 In the present work, the adiabatic 2-D rotational energy is treated using a statistical distribution with an explicit summation over all possible values of the rotational quantum number.41 Notably, the utilization of a PSL approach for analyzing the CID cross sections for heterolytic bond dissociations,59 such as those discussed here, have advanced since the early applications described in the previous M+−15C5 work. To ensure that the present results for Rb+ and Cs+ are self-consistent with the previous work, the previous data for Na+ and K+ are reanalyzed using the same methods. The model cross sections of eq 1 are convoluted with the kinetic energy distribution of the reactants, as described elsewhere in detail,38 and compared to the data. A nonlinear least-squares analysis is used to provide optimized values for σ0, n, and E0. The uncertainty associated with E0 is estimated from the range of threshold values determined from different data sets, along with variations in the parameter n, variations in vibrational frequencies (±10% for all frequencies), changes in dissociation time by factors of 2, and the uncertainty of the absolute energy scale, 0.05 eV (lab). In deriving the final optimized BDEs at 0 K, two assumptions are made. First, there is no activation barrier in excess of the endothermicity for the loss of the ligand, which is generally true for ion−molecule reactions and for the heterolytic noncovalent bond dissociations considered here.59 Second, the measured threshold E0 values for dissociation are from ground reactant ion to ground ion and neutral ligand products. Given the relatively long experimental time frame (∼1.5 × 10−4 s), incipient products should be able to rearrange to their low-energy conformations after collisional excitation. Computational Details. All theoretical calculations were performed using the Gaussian09 suite of programs.60 In our recent study of the analogous M+(12C4) systems,23 several levels of theory were applied including geometry and frequency calculations at the B3LYP/HW*/6-311+G(2d,2p) level,61−63 where HW* indicates that Rb and Cs were described using the

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RESULTS Cross Sections for Collision-Induced Dissociation of Rb+(15C5) and Cs+(15C5). Figure 1 shows the kinetic energydependent experimental cross sections obtained for the interaction of Xe with M+(15C5), where M+ = Rb+ and Cs+. The pressure dependence of these cross sections is small but observable in both cases; therefore, zero pressure extrapolated data are analyzed in both cases. For both complexes, the only dissociation pathway observed was the loss of the intact 15C5 ligand in the collision-induced dissociation (CID) reaction (3). M+(15C5) + Xe → M+ + 15C5 + Xe

(3)

Figure 1 includes the previously published results for both systems19 and clearly shows higher thresholds for the present ESI data. The lower cross section magnitudes observed here (by about an order of magnitude) are also a direct result of the different energetics because a higher threshold energy is expected to yield less efficient dissociation. The model of eq 1 (including lifetime effects) and eq 1 without lifetime effects (eq 1 with the term containing the rate constant removed) were used to analyze zero pressure extrapolated cross sections for reaction 3 for both M+(15C5) systems. Figure 2 shows that both experimental cross sections are reproduced by eq 1 over a large range of energies (>3 eV) and magnitudes (∼2 orders of magnitude). The optimized fitting parameters of eq 1 are provided in Table 1 and were obtained utilizing molecular parameters for the lowest energy species taken from the B3LYP/def2-TZVPPD calculations; see 8090

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Figure 2. Cross sections for collision-induced dissociation of Rb+(15C5) and Cs+(15C5) produced by ESI (parts a and b) with xenon as a function of kinetic energy in the center-of-mass frame (lower x-axis) and the laboratory frame (upper x-axis). Solid lines show the best fit to the data using the model of eq 1 convoluted over the neutral and ion kinetic and internal energy distributions. Dashed lines show the model cross sections in the absence of experimental kinetic energy broadening for reactant ions with an internal energy of 0 K.

Figure 1. Comparison of dc discharge flow-tube ion source (DC/FT) data from the literature19 with the present ESI data for collisioninduced dissociation of M+(15C5) where M+ = Rb+ (part a) and Cs+ (part b) with Xe as a function of energy in the center-of-mass frame (lower x-axis) and the laboratory frame (upper x-axis). In both cases, the DC/FT data have been scaled down by a factor of 10.

below. If alternative low-energy conformers for either the M+(15C5) complex or 15C5 product were used instead, changes in fitting parameters were quite small and less than 0.02 eV for the threshold energies. Kinetic shifts are large (1.0−1.1 eV) commensurate with the relatively large size of the complexes. Values of ΔS†1000, the entropy of activation at 1000 K, which gives some idea of the looseness of the transition states, are also listed in Table 1 and are in the range determined by Lifshitz74 for simple bond cleavage dissociations. This is reasonable considering that the TSs are assumed to lie at the centrifugal barrier for the association of M+ + 15C5. Reanalysis of the Cross Sections for Collision-Induced Dissociation of M+(15C5). The implementation of our phase space limit (PSL) approach to the analysis of heterolytic bond cleavage reactions has been refined since the early DC/FT data were taken.19 Hence, we reanalyze the older data here to ensure that comparison between the old and new experimental results and between the experimental results and new theoretical results are self-consistent. Table 2 compares the previous analysis for all four metal cation complexes19 with that performed here using molecular parameters calculated here using B3LYP/def2-TZVPPD. The models of the data are comparable to those published previously19 and reproduce the data well, in some cases over a somewhat larger energy range.

The thresholds obtained here are similar in all four cases to the previous PSL thresholds with differences well within the experimental uncertainties. Some of these changes are reflections of the differences in the entropies of activation, which lead to changes in the kinetic shifts. The present activation entropies are more consistent from metal to metal, which is probably more reasonable given the similarity of the dissociation processes. Conversion from 0 to 298 K. Conversion from 0 K bond energies to 298 K bond enthalpies and free energies is accomplished using the rigid rotor/harmonic oscillator approximation with rotational constants and vibrational frequencies calculated at the B3LYP/def2-TZVPPD level. The resulting ΔH298 and ΔG298 values along with the conversion factors and 0 K enthalpies measured here for ground-state conformers of all four M+(15C5) complexes are reported in Table 3. The uncertainties listed are determined by scaling all of the vibrational frequencies by ±10%, except for the metal− ligand frequencies, which are scaled by a factor of 2. Theoretical Results for 15C5. Hill and Feller have comprehensively looked at the conformations of the free 15-crown-5 ligand, describing in detail 16 low-energy variations 8091

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Table 1. Fitting Parameters for Eq 1, Threshold Dissociation Energies at 0 K, and Entropies of Activation at 1000 K of M+(15C5) Complexes Produced by ESIa M+ +

Rb Cs+ a

σ0b

nb

E0c (eV)

E0(PSL)b (eV)

kinetic shift (eV)

ΔS†(PSL)b (J mol−1 K−1)

5.6 (1.4) 2.9 (0.5)

1.6 (0.2) 1.1 (0.2)

2.92 (0.10) 2.64 (0.10)

1.81 (0.10) 1.65 (0.10)

1.11 0.99

71 (2) 62 (2)

Uncertainties are listed in parentheses. bAverage values for loose PSL TS. cNo RRKM lifetime analysis.

Table 2. Fitting Parameters Taken from the Literature and Reanalysis of M+(15C5) CID Cross Sections: Threshold Dissociation Energies at 0 K and Entropies of Activation at 1000 Ka previous analysis M

+ +

Na K+ Rb+ Cs+

b

E0 (eV) 6.11 3.95 1.71 1.47

(0.39) (0.25) (0.08) (0.10)

−1

ΔS (PSL) (J mol

E0(PSL) (eV) 3.05 2.12 1.18 1.04

reanalysis †

(0.19) (0.15) (0.07) (0.06)

−1

ΔS†(PSL)c (J mol−1 K−1)

c

E0(PSL) (eV)

K )

92 51 44 33

3.07 2.23 1.11 1.06

(0.16) (0.11) (0.08) (0.09)

69 72 74 64

(2) (2) (2) (2)

a

Analysis of DC/FT data taken from ref 19 and parameters taken from the same reference. Uncertainties are listed in parentheses. bNo RRKM lifetime analysis. cAverage values for loose PSL TS obtained using eq 1 and molecular parameters from B3LYP/def2-TZVPPD calculations.

Table 3. Conversion of 0 K Threshold Energies to 298 K Enthalpies and Free Energies of Dissociation for M+(15C5) M+ +

Na K+ Rb+ Cs+

ΔH0a (kJ/mol) 296.1 215.6 175.0 159.4

ΔH298 − ΔH0b (kJ/mol)

(15.5) (10.6) (9.7) (9.6)

3.0 2.3 1.8 1.1

ΔH298 (kJ/mol)

(1.0) (1.0) (0.9) (0.9)

299.1 217.9 176.8 160.5

TΔSb (kJ/mol)

(15.5) (10.6) (9.7) (9.6)

41.7 40.7 40.2 38.5

(5.1) (5.0) (5.1) (5.1)

ΔG298 (kJ/mol) 257.4 177.2 136.6 122.0

(16.3) (11.8) (11.0) (10.9)

a

Values from Tables 1 (Rb+ and Cs+) and 2 (Na+ and K+). bCalculated using standard formulas and the rigid rotor/harmonic oscillator approximations. Uncertainties are obtained by varying all frequencies by ±10% except for 2-fold variations in the metal−ligand frequencies.

Table 4. Sequences, Average Bond Distances (Å), and Theoretical Relative Energies (kJ/mol) at 0 K of 15C5 Conformations conformer

sequences about CC, CO, OC dihedral anglesa

average r(CC)/r(CO)

0 1 11

−+0/00+/−0−/−00/+00 +00/−+0/000/−+0/+00b,d −+0/++−/+0+/−0−/+00b −+0/+−0/−+−/−0−/+00d +00/−+0/00+/+− −/+00b,d

8

d

MP2/6-31+G(d)b

MP2/6-31+G(d)c

B3LYP/def2-TZVPPD

1.517/1.416 1.516/1.417 1.516/1.419

0.1 0.0

4.4 (4.8) 0.1 (0.2) 0.0 (0.0)

0.0 2.3 4.7

1.519/1.418

2.3

2.8 (3.1)

6.7

The sequence of dihedral angles is designated according to the nomenclature of Hill and Feller75 by the ∠OCCO, ∠CCOC, and ∠COCC dihedral angles, where + indicates angles between 0° and 120°, 0 indicates angles from 120° to 240°, and − indicates angles between 240° and 360°. bHill and Feller using a hybrid basis set, see text.75 cPresent calculations with MP2/6-31+G(d) (MP2/def2-TZVPPD) zero point energy corrections. d Sequence calculated here. a

out of 34 low-energy conformers located.75 They used MP2 theory with a hybrid basis set of 6-31+G(d) on the oxygen and 6-31G(d) on carbon and hydrogen atoms, which is referred to here as 6-31+G(d). Zero point energy corrections were determined at the RHF/6-31+G(d) level. At this level of theory, they found 15 conformers within 12 kJ/mol of the lowest conformer with another at 20.5 kJ/mol. Here, we use B3LYP/def2-TZVPPD theory to reproduce their three lowest energy structures, denoted 1, 11, and 8, which they found had relative energies of 0.1, 0.0, and 2.3 kJ/mol, respectively. Our calculations find that 1 lies below 11 by 2.3 kJ/mol with 8 another 2.1 kJ/mol higher, Table 4. (Although an examination of the structure of 11 shows it to be identical to that of Hill and Feller, we obtain different dihedral angles, as indicated in Table 4.) In the process of locating these conformers, we also found a competitive structure that does not appear to be among those located by Hill and Feller (but is similar to their structures 9 and 15). Named 0 here, this conformer lies 2.3 kJ/mol below 1 at the B3LYP/def2-TZVPPD level. This species is shown in Figure 3 and compared to the other structures in Table 4.

Notably, if these four low-energy conformers are recalculated at the MP2 level using the 6-31+G(d) basis set on all atoms (along with zero point energies calculated at the same level and scaled by 0.9676 or using the def2-TZVPPD frequencies), we reproduce the energy ordering of Hill and Feller for 1, 11, and 8, and also find that 0 lies 4.4−4.8 kJ/mol above 11, Table 4. The isotropic polarizabilities of all four 15C5 conformers were calculated at the PBE1PBE/def2-TZVPPD level of theory, a density functional that has been shown to yield polarizabilities that are in good agreement with measured values.76 We find all four conformers yield nearly identical polarizability volumes with that for conformer 0 being 21.8 Å3. Theoretical Results for M+(15C5). Structures of complexes of the alkali metal cations with 15C5 have been examined by Paulson and Hay77 using molecular mechanics (MM3) and then using quantum chemical methods (MP2/ 6‑31+G*) by Hill and Feller,75 where the Hay−Wadt effective core potential64 was used for potassium, rubidium, and cesium augmented with an additional polarization function.65 Both studies compared their results to crystal structures found in the 8092

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Table 5. Theoretical Metal−Oxygen Bond Distances (Å), Metal−Dipole Angles (deg), and Relative Energies (kJ/mol) at 0 K of M+(15C5) Conformations energy M

conformer

r(M−O)

∠MμO

Na

1(O5)

2.340, 2.355, 2.330, 2.350, 2.351 2.383, 2.423, 2.380, 2.395, 2.411 2.315, 2.418, 2.439, 2.313, 2.494 2.340, 2.261, 3.785, 2.257, 2.323 2.279, 2.238, 4.003, 3.811, 3.864 2.788, 2.774, 2.740, 2.773, 2.762 2.758, 2.741, 2.742, 2.703, 2.723 2.805 (5) 2.791, 2.689, 4.170, 2.656, 2.730 2.742, 2.713, 4.252, 4.345, 2.695 2.995, 2.950, 2.909, 2.969, 2.930 2.984 (5) 2.951, 2.943, 2.937, 2.873, 2.923 3.013, 2.891, 4.354, 2.847, 2.918 3.045, 2.996, 4.571, 4.639, 2.970 3.199, 3.111, 3.067, 3.155, 3.087 3.152 (5) 3.129, 3.118, 3.121, 3.027, 3.096 3.210, 3.084, 4.491, 3.019, 3.094 3.148, 3.100, 4.716, 4.696, 3.069

50, 42, 48, 46, 46 45, 46, 43, 44, 45 0, 49, 50, 8, 54 60, 16, 165, 36, 43 22, 13, 165, 155, 135 51, 39, 40, 35, 40 34, 62, 35, 40, 54 39 (5) 67, 9, 155, 31, 33 69, 9, 175, 148, 18 54, 37, 37, 32, 37 36 (5) 31, 66, 32, 37, 55 71, 6, 152, 30, 29 73, 6, 173, 143, 13 57, 34, 34, 30, 34 35 (5) 29, 67, 29, 34, 58 73, 4, 147, 29, 27 74, 5, 173, 142, 11

2(O5) 4(O5) O4 O2 K

2(O5) 1(O5) 4(O5) O4 O3

Rb

2(O5) 4(O5) 1(O5) O4

Figure 3. Structures of the lowest energy conformation of 15-crown-5 (0) and all conformers of Cs+(15C5) calculated at the B3LYP/def2TZVPPD level of theory. Other metals exhibit similar structures for analogous species.

O3 Cs

2(O5) 4(O5) 1(O5)

Cambridge Structural Database (CSD).78 Here we adopt the nomenclature of Hill and Feller, such that each structure is labeled as M-n where M indicates the metal and n is adopted from the labeling convention of Paulson and Hay. We also add a designation of the number of oxygens coordinated to the metal cation (O5). For the four metal cations studied here, there are three low-energy structures in which all five oxygens have comparable M−O bond distances: 1(O5), 2(O5), and 4(O5). These can be differentiated using the ∠OCCO, ∠CCOC, and ∠COCC dihedral angles as detailed in Table S1 of the Supporting Information. Guided by these results, we calculated these low-energy structures for all four metal cations at the B3LYP/def2-TZVPPD level with results compared to the literature in Table 5. It should also be noted that there are enantiomers corresponding to the mirror images in all cases (inversion of all + and − signs) and therefore have identical energies. Such enantiomers will not be discussed further. For all four metal cations, our results parallel those of Hill and Feller with only slight differences in the relative energies but the same overall order, Table 5. Structure 2(O5) is the ground conformer for K+−Cs+, whereas the Na+ complex adopts structure 1(O5). Figure 3 shows structures for all conformers found for the Cs+(complex), whereas Figure 4 shows the ground-state structures for all four metal complexes. Structure 4(O5) generally has C5 symmetry but undergoes a distortion for the smaller Na+ cation. For all four metal cations, structure 1(O5) has the lowest average metal−oxygen distance, 2.345, 2.733, 2.925, and 3.098 Å for Na+−Cs+, respectively, with structure 2(O5) having slightly longer average distances by 0.054, 0.034, 0.026, and 0.026 Å, respectively. Structure

O4 O3 a

a

a

B3LYPa

MP2b

0.0

0.0

9.3

10.5

27.5

34.1

66.5 202.6 0.0

0.0

5.3

6.4

7.4 62.1

9.7

117.4 0.0

0.0

4.7 7.9

5.6 10.3

61.1 111.0 0.0

0.0

3.8 9.1

3.2 12.4

59.9 105.5

Calculated at the B3LYP/def2-TZVPPD level here. 6‑31+G(d) values from Hill and Feller.75

b

MP2/

4(O5) has generally slightly longer metal−oxygen distances still by 0.041, 0.032, and 0.028 Å for K+−Cs+, respectively, with the average distances for Na-2(O5) and Na-4(O5) being nearly equivalent. The increases in the bond lengths roughly track with increases in the metal cation radii: 0.98, 1.33, 1.49, and 1.69 Å for Na+, K+, Rb+, and Cs+, respectively.79 The fact that the lowest average metal−oxygen distance does not always predict the lowest energy structure indicates that the orientation of the local dipole of each oxygen atom also contributes to the electrostatic interaction with the metal cations in determining the relative energies. This is verified by examining the angle between the metal cation and the local dipole moment of the oxygen atoms, ∠MμO, where 0° indicates alignment, Table 5. The smallest average angle is found for structure 4(O5), followed by 2(O5), with 1(O5) having the largest value for all four metal cations. For a given structure, the angles tend to be smaller for the larger cations except for Na-4(O5) (which no longer has C5 symmetry as for the other metal cations). In the M+(15C5) complexes, the bond distances of the crown are not greatly distorted from the free ligand. For the 8093

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conformers, although they did find excited conformations of M+(15C5) lying only 16 − 21 kJ/mol above the ground state.75 Theoretical Results for Interconversion of M+(15C5) Conformations. In addition to these stable species, we also characterized the transition states (characterized by a single imaginary frequency) connecting the M-O4 structures with lower energy M-O5 species for all four metal cations, TS(M-O4/5). Transition-state barriers above the M-O4 species are highest for Na+ at 3 kJ/mol, decrease to 0.3 kJ/mol for K+, and decrease further as the metal cation gets larger such that with zero point energies included, TS(Rb-O4/5) and TS(Cs-O4/5) lie below M-O4. These trends mirror the calculated imaginary frequencies, which are associated with motion of the nonbonded oxygen toward the metal cation center: 135, 67, 33, and 26 cm−1, respectively (unscaled). As the DC/FT experiments clearly show that excited conformers of Rb+(15C5) and Cs+(15C5) can be stabilized, either the M-O4 structures here are not representative of the actual structures formed experimentally or theory is underestimating the height of the barrier for interconversion. Nevertheless, the present theoretical results suggest that there are no appreciable differences in the potential energy surfaces for interconversion of excited conformers as a function of the different metal cations.

■

COMPARISON OF THEORETICAL AND EXPERIMENTAL BOND DISSOCIATION ENERGIES The theoretical BDEs for the M+(15C5) complexes, where M+ = Na+, K+, Rb+, and Cs+, calculated here are compared to the new experimental values in Table 6. The latter include Table 6. Bond Dissociation Enthalpies (kJ/mol) of M+(15C5) Complexes at 0 K

Figure 4. Structures of the lowest energy conformations of Na+(15C5) Na-1(O5), K + (15C5) K-2(O5), Rb + (15C5) Rb-2(O5), and Cs+(15C5) Cs-2(O5) calculated at the B3LYP/def2-TZVPPD level of theory. M−O bond distances are shown in Å.

B3LYPb M

+

Na+ K+ Rb+ Cs+ MADf

free 15C5 ligand, the average carbon−oxygen and carbon− carbon bond lengths for the lowest four conformers are rCO = 1.417 ± 0.005 Å and rCC = 1.517 ± 0.003 Å. In the ground conformers for all four metal cation complexes, the average carbon−carbon bond distances are very similar, 1.515 ± 0.004 Å. The average carbon−oxygen bond distances increase compared with the free ligand and increase more the smaller the metal cation: 1.428, 1.426, 1.425, and 1.424 ± 0.002 Å for Na+−Cs+. These changes are consistent with some electron transfer from the ligand to the metal cation. Because the DC/FT results for Rb+ and Cs+ were postulated to involve a high-energy conformer, we also located highenergy structures for each metal cation complexed with 15C5, including structures with four (M-O4), three (M-O3), and two (M-O2) short metal−oxygen interactions, Table 5. No comprehensive attempt to look for all such structures was made, but rather these act as representative examples of families of such structures. The Cs-O4 and Cs-O3 structures for the case of Cs+(15C5) are included in Figure 3, and analogous structures for the other metals are similar. In all cases, because the number of metal−oxygen interactions is smaller than the ground conformers, these species lie considerably higher in energy, Table 5. Loss of one oxygen interaction raises the energy by a surprisingly uniform 60−66 kJ/mol, with two lost interactions raising the energy by another 43−55 kJ/mol, increasing with decreasing metal cation size. Interestingly, Hill and Feller looked for but did not locate such excited

a

De

D0d

(15.5) (10.6) (9.7) (9.6) (2.8)g

328.0 230.0 196.7 173.5 21 (8)

319.7 223.8 191.4 168.7 14 (7)

TCID 296.1 215.6 175.0 159.4 11.3

MP2c D0(cp)

d,e

317.9 220.8 191.0 168.3 13 (7)

D0 323/323 246/239 207/204 178/157 27 (6)/20 (12)

a

Results from Table 3. Uncertainties are listed in parentheses. Calculated at the B3LYP/def2-TZVPPD level of theory. cMP2/ 6‑31+G(d)//MP2/6-31+G(d) including counterpoise corrections and MP2/aug-cc-pVDZ//MP2/6‑31+G(d) (in italics) results from Hill and Feller.75 dIncluding ZPE corrections with the B3LYP/def2TZVPPD frequencies scaled by a factor of 0.98. eIncluding counterpoise corrections. fMean absolute deviation. gAverage experimental uncertainty. b

those from the new data for the rubidium and cesium systems, Table 1, and the reanalysis of the DC/FT data for sodium and potassium, Table 2. For all four metal cations, B3LYP/def2TZVPPD calculations yield 0 K BDEs after counterpoise corrections in reasonable agreement with experiment, lying 21.8, 5.2, 16.0, and 8.9 kJ/mol higher in energy for Na+−Cs+, respectively. On average, these theoretical values are 6 ± 3% higher, which is comparable to the average experimental uncertainty of 5%. Our theoretical results can also be compared favorably to those of Hill and Feller, calculated at the MP2/ 6‑31+G(d)//MP2/6-31+G(d) and MP2/aug-cc-pVDZ// MP2/6-31+G(d) levels,75 Table 6, which generally lie somewhat higher than our theoretical results. The comparison 8094

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explanation for the different behavior of the smaller and larger alkali metal cations was proposed that relies on the kinetics for stabilization of the M+(12C4) complexes made by three-body association of M+ + 12C4 in the flow-tube ion source previously used. Because the M + −12C4 bond energies decrease dramatically for larger cations, the internal energies of the complexes initially formed vary considerably as M+ changes. Thus, stabilization of these complexes requires fewer collisions with the bath gases present for the larger cations. Furthermore, the weaker binding of the larger alkali metal cations leads to lower metal−ligand frequencies, increasing the density of states of these complexes, which would decrease the rate of dissociation leading to a longer lifetime. The longer lifetime allows three-body collisional stabilization of the excited conformation before rearrangement to lower energy conformations. Clearly, a similar explanation would also be viable for the M+(15C5) analogues.

between the new experimental BDEs and the B3LYP/def2TZVPPD results is also shown in Figure 5, along with previous results for the analogous M+(12C4) complexes,23 where it can be seen that the agreement is quite reasonable.

■

CONCLUSIONS The present reexamination of the alkali metal cation complexes with the polyether 15-crown-5 have shown that the structures formed are sensitive to the mode of ion formation, as also demonstrated in other systems.23,29,80−83 Electrospray ionization clearly forms ground-state conformations with no evidence (to better than 1 part in 1000) for the excited conformers formed in a flow-tube source by condensation of Rb+ and Cs+ with 15C5.19 An examination of the potential energy surfaces suggests this is not a result of distinctive barriers between the conformers but rather is related to the kinetics of the association process. Reexamination of the previous data for Na+(15C5) and K+(15C5) demonstrates that the data analysis methods used are robust. Overall, the present experiments for Rb+(15C5) and Cs+(15C5) along with a reanalysis of the data for Na+(15C5) and K+(15C5) provide reliable thermochemistry for these complexes, as demonstrated convincingly by comparison with high-level quantum calculations, Figure 5.

Figure 5. Comparison of the experimental TCID bond energies for M+−12C4 (blue circles, values from ref 23) and M+−15C5 (red triangles, values from Table 6) for M+ = Na+, K+, Rb+, and Cs+ with those calculated at the B3LYP/def2-TZVPPD level of theory. The diagonal line shows perfect agreement between experiment and theory.

As discussed in the Introduction, the low BDEs found previously for Rb+(15C5) and Cs+(15C5) were hypothesized to be a result of excited conformations.19 This suggestion can be tested by a comparison of the previous and current BDEs along with the theoretical calculations. As discussed above, a reanalysis of the previous data for CID of Rb+(15C5) and Cs+(15C5) yields 0 K thresholds of 1.11 ± 0.08 and 1.06 ± 0.09 eV, respectively, which lie 0.70 ± 0.13 and 0.59 ± 0.13 eV below the values obtained from the ESI data. Equating these differences with excitation energies suggests the presence of M-O4 tetradentate conformers, which have calculated energies relative to the M-2(O5) pentadentate ground states of 0.63 and 0.62 eV for M+ = Rb+ and Cs+, Table 5. Previously,19 the low threshold energies for the larger metal cation 15C5 complexes were rationalized on the basis of kinetic trapping of higher energy conformers. It was conjectured that this occurred because the barriers between the higher energy conformers and the ground conformer of the complexes varied appreciably with the metal cation identity as a consequence of the different charge densities. Thus, a lower barrier for the smaller metal cations was hypothesized, thereby allowing the initially formed complexes to readily rearrange to the ground conformers, whereas the higher barrier for larger cations allowed these higher energy conformers to be collisionally trapped in the DC/FT source. In contrast to this hypothesis, the present calculations of the transition states between the M-O4 and M-O5 conformers indicates that these barriers are small for all metal cations: 3 kJ/mol for Na+, 0.3 kJ/mol for K+, and lower than the M-O4 conformer once zero point energies are included for Rb+ and Cs+. These results parallel those from a recent study of the M+(12C4) analogues where the entire potential energy surface for interaction of M+ with 12C4 could be conducted theoretically. Again it was found that there are no appreciable distinctions in the energies of the transition states for interconversion of different M+(12C4) conformers as a function of the metal cations.23 Instead, an alternative

■

ASSOCIATED CONTENT

S Supporting Information *

Tables giving approximate dihedral angles for the various M+(15C5) species and transition states connecting them, along with Cartesian coordinates of the ground states of 15C5 and M+(15C5) complexes. This information is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work is supported by the National Science Foundation, CHE-0911191 (M.T.R.) and CHE-1049580 (P.B.A.). Grants of computer time from the Center for High Performance Computing at the University of Utah and the C&IT at Wayne State University are gratefully acknowledged.

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REFERENCES

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