Gas-phase metal–ligand bond energies can be measured by a variety of experimental techniques.
Measurements of absolute values can be made by temperature-dependent equilibrium methods,1,2,16,46,48,66–69 blackbody infrared radiative dissociation (BIRD),2–5,70–72 radiative association,73–75and the TCID method discussed in detail here. Measurements of relative thermo- chemistry can be accomplished using equilibrium methods,76,77 the kinetic method,78–81 and competitive CID82 (see Section 2.12.5.7). This review cannot include the details of all such measurements.
2.12.5.1 Introduction
Collision-induced dissociation (CID) as employed by mass spectrometrists is a powerful tool for structural elucidation.83 Although the possibility that the energy onset of CID could be a
useful means of ascertaining thermodynamic information was recognized early on, the ability to determine accurate thermochemistry is a recent development dating back to the early 1980s.
Extensive refinements allowing applications to larger molecules have been developed only since the early 1990s. TCID emerges from a simple concept involving the study of the reaction of a metal–ligand complex with a collision gas (Equation1) as a function of the kinetic energy available to the reactants.
MLxỵỵRg!MLx1ỵỵLỵRg ð1ị
Although Equation (1) refers to a cationic coordination complex, the concept also holds for anionic reactions. Neutrals could also be studied in this fashion, but the ease with which ions are accelerated to energies capable of breaking chemical bonds makes them the systems of choice for TCID work. Here we identify the collision partner as a rare gas atom (Rg), a choice discussed further below, but any species (including a surface) can be used. A broad range of metals, ligands, extent of coordination, and bond energy magnitudes (2–100 kcal mol1) have been studied using TCID experiments as illustrated in the remainder of this section. The type of TCID experiment now being performed routinely is illustrated in Figure 5 for copper bis-acetone cations colliding with Xe.84 This shows the reaction cross-section as a function of energy in the center- of-mass frame, the energy available to induce chemical processes. The reaction cross-section, , describes the probability that an ion and a neutral collide and proceed to products. Cross-sections can be converted to rate constants simply by multiplying by the relative velocity of the reactants, v, such that k(E)ẳv, which can then be averaged over a Maxwell–Boltzmann distribution to givek(T). Thus, a cross-section is a microscopic reaction probability directly related to the rate constant for reaction at a specific kinetic energy. In Figure 5, it can be seen that collisions of Cuþ(acetone)2with Xe yield no products at low energies, below those needed to cleave the metal–
ligand bond. As the energy is increased, intact acetone molecules are lost from the complex progressively to form Cuþ(acetone) and Cuþ, with more extensive decomposition occurring at higher energies. In competition with these simple CID processes are ligand exchange reactions that form XeCuỵ(acetone)x,xẳ0 and 1.
By measuring the threshold for a CID process, the BDE between MLx1þ and L can be measured, subject to several constraints. One of these is another key reason to use ions in TCID studies: the long-range attractive forces between a charged species and the ligand generally overcome barriers to dissociation typically observed in neutral systems. For coordination complexes, it is also useful to note that the bonds are generally cleaved heterolytically, i.e., with
Figure 5 Cross-sections for collision-induced dissociation of Cuþ(acetone)2with Xe as a function of kinetic energy in the center-of-mass frame (lower x-axis) and the laboratory frame (upper x-axis). Primary and secondary product CID cross-sections are shown as*and,, respectively. Primary and secondary ligand
exchange product cross-sections are shown as & and~, respectively.
Gas Phase Coordination Chemistry 151
different numbers of the bonding electrons attached to the two fragments. For such dissociations, qualitative quantum mechanical arguments show that there are no barriers in excess of the BDE along the potential energy surface.85
2.12.5.2 Instrumentation
To measure the threshold for a CID reaction, the reactant ion must be isolated and accelerated to a specific kinetic energy, undergo a collision, and the resulting products analyzed. Such studies are carried out using tandem mass spectrometers such as a guided ion beam tandem mass spectrom- eter (GIBMS), an instrument designed expressly for TCID studies.86–90 In our laboratories, this instrument utilizes a versatile source region that is capable of generating a wide variety of ions and thermalizing them so that their internal energies are known. The latter characteristic is vital to threshold studies as the energy available for dissociation must be fully characterized. An initial mass analysis device follows to select particular ions for interaction with neutral reagents in a collision cell. The use of an rf trapping field in this interaction region provides several benefits, as outlined elsewhere.91,92 Chief among these is the ability to efficiently collect product ions and to carefully define the kinetic energy of the ions. Product ions are identified using a second mass analyzer followed by a sensitive ion detector. Thus, the raw data of a reaction threshold measurement are reactant and product ion intensities as a function of the ion kinetic energy.
These are converted to cross-sections as a function of the energy in the center-of-mass frame, like the data shown in Figure 5, as detailed elsewhere.86,91
Other types of tandem mass spectrometers can also be used for such experiments, e.g., commercial triple quadrupoles (QQQ) have been used occasionally, but such instruments are not designed specifically for threshold studies. The disadvantages of such instrumentation include perturbations of the ion kinetic energy induced by the quadrupole field and an ill-defined collision region.91Likewise, ion cyclotron resonance (ICR) mass spectrometers93–96and, conceivably, ion trap mass spectrometers can be used,97,98 but specification of the kinetic energy and incomplete isolation of the acceleration and reaction steps are problematic.
2.12.5.3 Data Analysis
The kinetic energy dependence of CID reactions is often modeled using a simple empirical formula (Equation (2)) for reasons reviewed recently:92
ðEị ẳ0SgiðEỵEiE0ịn=E ð2ị Here 0is an energy-independent scaling factor,E is the center-of-mass kinetic energy,E0is the reaction threshold, and n describes the shape of the energy dependence. When E<E0, the model predicts that (E)ẳ0. The sum is over all rovibrational and electronic states i of the reactants with energies Ei and populations gi, where Sgiẳ1. This requires molecular parameters (electronic, vibrational, and rotational constants) of both reactants (obtained from experimental or theoretical sources) along with information regarding the populations of these states. As noted above, a key requirement of ion sources used in TCID measurements is that the internal energy content of the reactant ions must be well characterized, so that the populations gi are known. To accurately reproduce experimental TCID data, this model must also be convoluted with the kinetic energy distributions of the reactants, using formulae found elsewhere.86,99,100
In TCID, multiple collisions between the ionic and neutral reactants lead to the same overall products but with a lowered threshold energy, because additional collisions deposit additional energy. When the dissociation kinetics are particularly slow (see Section 2.12.5.6), this extra energy can increase the probability of observing dissociation by orders of magnitude, such that TCID cross-sections are very sensitive to multiple collisions. Even at low neutral pressures, the probability of secondary collisions is finite; therefore, the acquisition of true single-collision cross-sections is achieved by measuring the pressure dependence of the cross-section and extrapo- lating to zero pressure.101
2.12.5.4 Collision Gas
The neutral reagent in TCID experiments, Rg in Equation (1), is optimally chosen to provide efficient kinetic-to-internal energy transfer during the collision. In addition, this species should not carry away extensive amounts of energy either in internal or translational modes.
Translational-to-internal energy transfer occurs most efficiently when there are long-lived collisions in which the transient (MLxþ
)(Rg) collision complex dissociates statistically. If MLx1þ or L is modestly complex, there are many more internal modes than translational modes such that statistical behavior puts most of the reactant kinetic energy into internal energy of the reactant complex. The amount of energy removed from the complex by Rg can be minimized by the use of monatomic gases, most conveniently, the stable rare gases, which have no internal modes. Of these, Xe is preferred as it has the highest polarizability, meaning that it has the strongest interaction with the MLxþ
reactant. This maximizes the probability of forming a long-lived (MLxþ)(Rg) complex. Indeed, a number of studies have demonstrated that Xe is a more efficient energy transfer reagent than the lighter rare gases.35,102–104 In some cases, however, reactions such as charge transfer (Equation (3))102 or ligand exchange (Equation (4)) (such as the minor products shown in Figure 5),31,105 can compete strongly with the desired CID process, thereby adversely affecting the ability to measure the CID threshold. In such cases, a lighter rare gas may be a better choice as a collision gas because it has a higher ionization energy and lower polarizability than Xe. In the case shown in Figure 5, the magnitude of the ligand exchange cross-sections is sufficiently small that such competition is minimal:
MLxỵỵRg!MLxỵRgỵ ð3ị
MLxỵỵRg!RgMLx1ỵỵL ð4ị
2.12.5.5 Energy Deposition Distributions Collisions between MLxþ
and Rg can be head on (allowing the possibility that all of the kinetic energy can be transferred into internal degrees of freedom of the MLxþcomplex), grazing (such that almost no energy is transferred), and everywhere in between, resulting in a broad distribution of energies transferred. For CID processes, the parameterninEquation (2)empirically describes the distribution of energies deposited in the MLxþ
reactant by the collision with Rg. A recent direct measurement found that the distribution of energy deposited,", can be described byEquation (5)
Pð"ị ẳ0nðE"ịn1=E ð5ị
Importantly, the values ofn used in Equation (2) to describe the cross-section for CID and in Equation (5)to describe the energy deposition distribution are found to be equivalent. Thus, modeling TCID cross-sections withEquation (2)and the extensions described below is physically reasonable.
2.12.5.6 Kinetic Shifts
The CID process can be viewed as two separate steps: an energy-deposition step (Equation (6)) and a unimolecular dissociation step (Equation (7))
MLxỵỵRg! ẵMLxỵỵRg ð6ị
ẵMLxỵ!MLx1ỵỵL ð7ị
In this picture, the energized complex, [MLxþ]*, will have a lifetime that depends on its internal energy,E*, and the number of degrees of freedom it possesses. If MLxþis a small molecule, the dissociation rate is generally rapid, such that dissociation will be observed as long as the internal energy of [MLxþ]* exceeds its bond energy. However, for larger molecules, the lifetime of the complex can increase to the point that it exceeds the timescale that a particular instrument has available to observe the dissociation, , which is typically in the microsecond time regime. This
Gas Phase Coordination Chemistry 153
produces what is known as a kinetic shift, i.e., the lowest energy observation of the dissociation products (as limited by deviations in product signal from background noise levels) moves to energies higher than the thermodynamic threshold.
When kinetic shifts occur, the dissociation kinetics must be included in the analysis in order to acquire accurate thermochemistry. This is achieved by explicitly including the unimolecular dissociation probability,106–108 thereby modifyingEquation (2) to yieldEquation (8)
ðEị ẳ ðn0=EịX
i
gi Z E
E0Ei
ẵ1ekð"ỵEiịðE"ịn1dð"ị ð8ị
Here, most quantities are defined above and k("ỵEi)ẳk(E*) is the unimolecular dissociation rate constant, evaluated using modern statistical theories, such as Rice–Ramsperger–Kassel–
Marcus (RRKM) theory.109 Note that Equation (8) combines the distribution of deposited energies (Equation (5)) with the probability that the complex dissociates in time (term in square brackets), and a summation over the internal energy available to the reactants. Importantly, the integration recoversEquation (2)when the dissociation rate,k(E*), is faster than the experimental time scale, such that the term in brackets is unity.
Vibrational and rotational constants for the energized molecule, [MLxþ]*, and for the transition state (TS) leading to products are needed to evaluate kinetic shifts using RRKM theory. For the simple bond cleavages appropriate for coordination complexes, it is a good approximation to treat the TS as loose and located at the centrifugal barrier for product formation.108This makes the choice of the vibra- tional and rotational constants of the TS particularly simple as they equal those of the products.
A striking example of a large kinetic shift that has been accurately modeled involves the dissociation of a complex of Naþ with the multidentate 18-crown-6 cyclic polyether (18c6) (Figure 6).24,25 When these data are analyzed using Equation (2), a threshold of 7.370.24 eV is obtained. In contrast, when the data are analyzed usingEquation (8), the threshold obtained is 3.070.20 eV, as indicated by the arrow in Figure 6. This large kinetic shift, 4.3 eV, results from the large number of internal states available in the large and floppy 18c6 ligand combined with the strong Naþ18c6 bond. In the region above the background noise, the model ofEquation (8) reproduces the data very well. The threshold obtained including the kinetic shift agrees well with a value of 3.44 eV calculated using high-level quantum theory.110(Indeed, the agreement between
Figure 6 Zero-pressure extrapolated cross-sections for the primary collision-induced dissociation product of the Naþ(18c6) complex with Xe in the threshold region as a function of kinetic energy in the center-of mass frame (lowerx-axis) and the laboratory frame (upperx-axis). The solid line shows the best fit to the data using the model ofEquation (6)convoluted over the neutral and ion kinetic and internal energy broadening for reactants with an internal energy of 0 K. Arrows indicate the threshold values derived from this analysis
and from theory (see text).
experiment and theory is better than it first appears as this level of theory systematically over- estimates, by 128%, experimental BDEs of Naþ to one to four dimethylethers, systems that exhibit minimal kinetic shifts. For the 18c6 system, this overestimate corresponds to an increase of 0.370.25 eV in the calculated bond energy, in good agreement with the difference observed.25).
Many such studies demonstrate that kinetic shifts must be included in the threshold analysis of CID reactions. The accuracy of the correction for the kinetic shift is limited by the models used for the kinetics, by the assumptions made regarding the TS, and by the sensitivity of the experiment. The magnitude of kinetic shifts depends on the size of the system being considered and the bond energy. Typically, systems containing fewer than about six heavy atoms dissociate rapidly enough so that kinetic shifts are minimal.
2.12.5.7 Competitive Shifts
If the MLxþ complex can dissociate by two independent pathways (for example, when two of the ligands differ from one another), competition between these channels can influence the shapes of the cross-sections and consequently the ability to accurately model the kinetic energy depend- ence of both channels. This is illustrated inFigure 7for a bis-ligated Liþcomplex.82 The kinetic energy dependence of the total cross-section is typical of simple TCID processes, but the two product cross-sections have distinct shapes. As the collision energy of the (H2O)Liþ(C2H5OH) complex increases, it first dissociates exclusively to the lowest energy channel, Liþ (C2H5OH)þH2O, yielding a rapidly rising cross-section. As the threshold for the Liþ(H2O)þC2H5OH channel is exceeded, the cross-section for the dominant channel begins to decline as some of the energized complexes now decompose to the high-energy channel.
Statistically, most complexes still dissociate to the lower-energy channel such that the cross- section for Liþ(H2O) rises more slowly but continuously as the energy is increased. This slow rise in the cross-section generally leads to a threshold (when analyzed usingEquations (2)or(8)) that is higher than the thermodynamic threshold for this channel. Further increases in the energy reduce the statistical difference between the two channels such that the magnitudes of the two cross-sections approach one another. In general, such competition leads to differences in the thresholds being overestimated when the cross-sections are analyzed independently.
Figure 7 Zero-pressure extrapolated cross-sections for the collision-induced dissociation of the (H2O)Liþ(C2H5OH) complex with Xe in the threshold region as a function of kinetic energy in the center- of mass frame (lowerx-axis) and the laboratory frame (upper x-axis). Solid lines show the best fits to the data using the model of Equation (9) 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 reactants with an internal energy of 0 K.
Gas Phase Coordination Chemistry 155
For systems that behave statistically, it is straightforward to include the effects of competition in the threshold analysis. This is achieved by modifying Equation (8) to include multiple chan- nels,82indexed by j.
jðEị ẳn0;j E
X
i
gi
Z E E0;jEi
kjðEị
ktotðEịẵ1ektotðEịðE"ịn1dð"ị ð9ị In this equation, ktotẳSkj and all rate constants are again calculated using RRKM theory. This equation introduces the competition between product channels as the ratio of dissociation rates kj/ktot.82,111,112 The analysis of the data for the (H2O)Liþ(C2H5OH) complex is typical and illustrates the power of the statistical analysis. If the two product cross-sections are analyzed independently using Equation (8), the difference in the two thresholds is found to be 0.600.10 eV. In contrast, a difference of 0.290.01 eV is obtained from an analysis of the same data using Equation (9) in which both channels are simultaneously reproduced.82 This latter analysis, shown in Figure 7, reproduces both channels and the total cross-section extremely well over an extended range of energies. Because two cross-sections must be reproduced simultan- eously, the precision in the relative thresholds from this competitive analysis is very high. To verify which interpretation of the data is more accurate, we compare these values to those obtained from direct CID measurements, 0.310.16 eV,18 and from equilibrium measurements, 0.29 eV.77 Clearly, analysis of the data without consideration of the competition does not yield accurate thermochemistry and overestimates the difference between the thresholds, whereas the statistical analysis using Equation (9) and explicit consideration of the competition provides excellent results. Recent studies show that all statistical factors, such as symmetry numbers for internal rotors, need to be included in competitive analyses in order to maintain accuracy and precision.111