Supporting Information
A Quantitative Approach of the Interaction between Metal Triflates and Organic Ligands Using Electrospray Mass Spectrometry (short communication)
Jean-François Gal* (), Claudio Iacobucci, Ilaria Monfardini, Lionel Massi, Elisabet Duñach, Sandra Olivero.
Institut de Chimie de Nice, Université de Nice-Sophia Antipolis, CNRS-UMR 7272, Parc Valrose, 06108 Nice Cedex 2, France.
Contents
I Detailed treatment of the ligand competition method pages S1-S5
II Experimental page S6
III Tables of relative affinities pages S7-S8
VI Evaluation of Li+ basicities (LiCB) page S9
V Additional references page S10-S11
I Detailed treatment of the ligand competition method
In this part we describe the starting hypotheses and the analysis of the ligand exchange processes leading to the relationship between the initial concentrations of the two competing ligands and the salt, and the concentrations (in solution) of the ionic species that are observed in the electrospray ionization (ESI) mass spectra. Some basic working assumptions may be already stated in the main text, but are recalled here to provide a self-sufficient document.
Empirical approach
The displacement of anions by Lewis bases on the metal center of triflate salts MTn (here T is used for the triflate anion CF3SO3-) was observed during our previous studies. For modeling the process, we assume that the strong Lewis bases A and B displace totally, by a rapid exchange in the nitromethane solution, one triflate anion of the salt by bonding two neutral ligands, either two A’s, two B’s, or (A+B) simultaneously, on the metal center of the salt MTn, n = 2, 3. Note that the model may be relevant to other salts.
If we assume complete complexation of ligands A and B, for example by working with a sufficient concentration of A and B, we can write the total displacements corresponding to the following reactions:
2 A + MTn g [M(A)2Tn-1]+ + T- (S1)
2 B + MTn g [M(B)2Tn-1]+ + T- (S2)
A + B + MTn g [M(A)(B)Tn-1]+ + T- (S3)
Our model assumes also that A and B are bonded independently on M, i.e. there are no specific and/or different interactions A/A, B/B or A/B in the adducts resulting from the displacement process. An additional assumption, independent of the model developed here, is that the observable intensities in the ESI mass spectra are proportional to the relative concentrations of the ions.
Consider the simple case for which the affinities of A and B toward the metal center are equal, with equal concentrations of A and B (CA = CB). Taking into account the assumptions stated above, the relative concentrations of [M(A)2Tn-1]+, [M(A)(B)Tn-1]+ and [M(B)2Tn-1]+ (species named respectively A2, AB and B2 in the Tables below for the sake of simplicity) are proportional to the probability of putting two ligands on the metal center. In the presence of equal concentrations of A and B (CA/(CA+CB) = CB/(CA+CB) = 1/2), the probabilities, shown in Table S1, are namely ¼, ½ and ¼, or in 1:2:1 ratios for the concentration of the ions [M(A)2Tn-1]+, [M(A)(B)Tn-1]+ and [M(B)2Tn-1]+ respectively.
Table S1. Probabilities of formation of ions [M(A)2Tn-1]+ [M(A)(B)Tn-1]+, and [M(B)2Tn-1]+ for equal affinities of A and B for the metal center and for equal concentration of A and B.
A2 / AB + BA / B2(½)2 / (½)2 + (½)2 / (½)2
This case is schematically shown on Figure S1 (a), in the form of a ESI mass spectrum, for which it is assumed that ion intensities are proportional to ion concentrations.
Figure S1. Idealized triplets of the ions [M(A)2Tn-1]+, [M(A)(B)Tn-1]+ and [M(B)2Tn-1]+ (simplified respectively as M(A)2, M(A)(B) and M(B)2 on the m/z axis) in the ESI mass spectra of a mixture of Lewis acid MTn and of ligands A and B, assuming that ion intensities reflect ion concentrations; (a) ion intensities ratios 1:2:1: equal affinities and concentrations of A and B; (b) ion intensity ratios 4:4:1: A and B of the same affinity but twice the concentration of A, or affinity of A is twofold higher than that of B, using equal concentrations. The relative intensity of the ion [M(A)2Tn-1]+ is increased by a factor four relative to the intensity of the ion [M(B)2Tn-1]+, and by a factor two relative to the intensity of the ion [M(A)(B)Tn-1]+.
If A is two times more concentrated than B (with same affinities of A and B), or if the affinity of A is twice that of B (with equal concentrations of A and B), one obtains intensity ratios 4:4:1, as detailed in Table S2, and illustrated by Figure S1 (b).
Table S2. Probabilities of formation of ions [M(A)2Tn-1]+, [M(A)(B)Tn-1]+ and [M(B)2Tn-1]+ for affinities of A for the metal center twice that of B (same concentration), or for concentration of A twice that of B (case (b) on Figure S1).
A2 / AB + BA / B2(2 ´½)2 / (2 ´ ½)(½) + (½)(½ ´ 2) / (½)2
Now suppose that the affinity of A for the Lewis acid is a times the affinity of B, Affinity(A)/Affinity(B) = a. For equimolar concentrations, the probabilities become ¼a2, ½a and ¼, or ratios a 2: 2a :1, see Table S3.
Table S3. Probabilities of formation of ions [M(A)2Tn-1]+, [M(A)(B)Tn-1]+ and [M(B)2Tn-1]+ for affinity ratio for the metal center Affinity(A)/Affinity(B) = a with same concentrations of A and B.
A2 / AB + BA / B2(a ´ ½)2 / (a ´ ½)(½) + (½)(½ ´ a) / (½)2
The important result is that the peak ratio of the [M(A)2Tn-1]+ to [M(B)2Tn-1]+ peaks varies as a2, but the [M(A)2Tn-1]+ (or [M(B)2Tn-1]+) to [M(A)(B)Tn-1]+.peaks varies linearly with a.
Similarly, the concentration dependence of the peaks intensity ratios can be related to the relative concentrations CA/(CA+CB) and CB/(CA+CB) (note however that the terms CA+CB cancels out; see Table S4). Combining the dependence of the peak intensity ratios on the concentrations and on a leads to various expressions of relative ion concentration (or intensity) ratios given in Table S4.
Table S4. Generalized probabilities of formation of the ions [M(A)2Tn-1]+, [M(A)(B)Tn-1]+ and
[M(B)2Tn-1]+ for affinity ratio for the metal center Affinity(A)/Affinity(B) = a and concentrations CA and CB.
[aCA/(CA+CB)]2 / [aCA/(CA+CB)] [CB/(CA+CB)] + [CB/(CA+CB)] [aCA/(CA+CB)] =
2a[CA/(CA+CB)] [CB/(CA+CB)] =
2a (CA CB)/(CA+CB)2 / [CB/(CA+CB)]2
[aCA]2 / 2a(CA CB) / [CB]2
[aCA/CB]2 / 2a(CA/CB) / 1
In conclusions:
- (i) The intensity ratio for the [M(A)2Tn-1]+ and [M(B)2Tn-1]+ peaks, varies as the square of the affinity ratio a2 and the square of the concentration ratio (CA/CB)2.
- (ii) The intensity ratio for the [M(A)2Tn-1]+ and [M(A)(B)Tn-1]+ peaks, or of [M(A)(B)Tn-1]+ and [M(B)2Tn-1]+ peaks, are directly proportional to the affinity ratio a and of the concentration ratio CA/CB.
Formal derivation by the Bernoulli trial method
In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent success/failure experiments, each of which yields success with probability p. Such a success/failure experiment is also called a Bernoulli experiment or Bernoulli trial.
Under the previously mentioned assumptions, our system (formation of adducts with two neutral ligands by displacement of one triflate anion) can be regarded as a Bernoulli trial. It can be statistically treated as a series of draws:
- the metal center can bind two ligands a time;
- there are two types of ligands A and B;
- the number of ligands molecules present in solution can be considered as infinite from the statistical point of view;
- the number of ligand molecules is sufficient as compared to the number of metal centers, so binding of ligands does not change the ratio between A and B.
The binomial theorem, describing the algebraic expansion of powers of a binomial, states that it is possible to expand the power (a + b)n into a sum involving terms of the form y js wt, where the exponents s and t are nonnegative integers with s + t = n and the coefficient y of each term is a specific positive integer depending on n and s.
The coefficient y in the term y js wt is known as the binomial coefficient .
If a represents the probability of binding the ligand A and b the probability of binding the ligand B, then the sum above shows all the probabilities of the k possible combinations of ligands with n binding sites on the metal center (here n = 2, with three combinations; k = 0 for two identical ligands A, k = 1 for one ligand A and one ligand B, k =2 for two identical ligands B).
· a is the probability of binding (drawing) a single ligand A in solution: it is the product of the molar fraction of ligand A and a factor a defined as the relative affinity of the ligand A (relative to the ligand B) for the metal center.
- b is the probability of binding a single ligand B in solution: it corresponds to the molar fraction of ligand B (from the definition above, the relative affinity of B is one).
Each of the three members of the last equation is equal to the intensity ratio of the peaks in the triplet. They represent the relative probability that the metal center binds (i) two ligands A, (ii) one ligand A and one ligand B, or (iii) two ligands B.
Equivalence between affinity (a) and equilibrium constant
Consider the equilibriums:
The concentration ratios of the ions [M(A)2(OTf)n-1]+, [M(A)(B)(OTf)n-1]+ and [M(B)2(OTf)n-1]+ are considered to be proportional to their intensities, respectively called I(A2), I(AB) and I(B2), with ligands concentration of A and B noted [A] and [B] respectively.
In equation [1], the equilibrium constant for the exchange of one A for one B, K1(AàB), is:
K1AàB=IAB.A2.IA2.B
The factor 2 comes from the equivalence of the two ligands A to be exchanged in A2.
The intensity ratio vs. the concentration ratio is therefore:
IABIA2=2 K1AàBBA
This is equivalent to the equation of the lateral vs. central peak intensity ratio I(A2)/I(AB) = ZM(A)2/M(A)(B) = ½ α[A]/[B].
From equation [2], the exchange equilibrium follows:
K2(AàB)=2.I(B2).[A]I(AB).[B]
We suppose that the affinity of A or B for the metal center is independent of the ligand already present on the metal:
K2(AB) K1(AB) = K(AB)
Here the factor 2 is applied to I(B2) because the probability applies to the species with two ligands B.
Equation [3] correspond to a double exchange, with a constant K3(2Aà2B):
K3(2Aà2B)=2.I(B2).[A]22.I(A2).[B]2=[K(AàB)]2
The intensity ratio becomes:
IB2IA2=KAàB2 BA2
equivalent to the equation using lateral peaks intensity ratio = YM(A)2/M(B)2 = α2([A]/[B])2.
The K’s appear to be equivalent to (1/a). The remarkable similarity of the experimental a values (and therefore K values) obtained from the two kinds of intensity ratios supports the hypothesis that A and B bind the metal center independently of the ligand already attached.
II Experimental
Mass spectrometry measurements were performed on a quadrupole ion trap instrument (LCQ Deca; Thermo Fisher) operated with Xcalibur (version 1.3, Thermoquest Finnigan) software package. The spectra were scanned in the m/z range from 50 to 2000. For minimizing small changes in intensity ratio associated with the m/z range, an optimization procedure carried out before each experiment was conducted on the ion [Mn+(OTf-)n-1(A)(B)]+ (n=2, 3) for which m/z is exactly the mean value of m/z of [Mn+(OTf-)n-1(A)2]+ and [Mn+(OTf-)n-1(B)2]+. By optimizing the setup in the middle of the m/z range of interest, a reasonably good compromise is achieved regarding the reliability of the relative ion intensities. For the quantitative determinations of the relative intensity of the three ions of interest, the detection region was restricted to a symmetric range of roughly 600 m/z units centered on the m/z value of [Mn+(OTf-)n-1AB]+. Under these conditions, the intensity ratios are highly repeatable, and reproducible in the long term (±10%). The spray conditions were as follows: flow rate 3 µL/min; electrospray ionization voltage: 3.1 kV; capillary temperature: 200 °C; drying and nebulizer gas: nitrogen. The capillary voltage was adjusted according to the Xcalibur tune procedure.
The helium buffer gas pressure in the ion trap was set automatically by the regulated inlet at about 2×10-3 Pa (ion gauge reading). Each spectrum was acquired with 5 micro-scans and with a maximum ion injection time of 200 ms. Confirmation of the composition of ions was obtained from isotopic simulations and tandem mass spectrometry in some cases (see Monfardini, I.; Massi, L.; Trémel, P.; Hauville, A.; Olivero, S.; Duñach, E.; Gal, J.-F. Mass spectrometric characterization of metal triflates and triflimides (Lewis superacid catalysts) by electrospray ionization and tandem mass spectrometry. Rapid Commun. Mass Spectrom. 2010, 24, 2611). Organic ligands solutions were prepared from materials of commercial origin used without further purification (nitromethane, phosphate esters, amides from Sigma-Aldrich-Fluka, Saint-Quentin-Fallavier, France, and Siccap-Emmop, Marseille, France); preliminary experiments proved that equivalent results were obtained by using nitromethane of ACS reagent grade or ReagentPlus®). Zinc and indium triflates were of commercial origin (Sigma-Aldrich-Fluka). Stock solutions of ligands and metal triflate at 3 10-3 mol/L in nitromethane were mixed to provide a final solution in the adequate concentration ratio.
III Tables of relative affinities
In the following table, α1 and α2 are the relative affinities extracted from the intensity ratios of the lateral vs. central peaks, RC, and from the intensity ratios of the lateral peaks, RL, respectively, using these equations (with concentration ratios CR):
RC = 2α1 CR
RL = (α2)2 CR2
Examples of such plots are shown in Figure S2 below.
Figure S2. Plots obtained in the case of indium triflate competitive adduct formation with N,N-diethylacetamide (DEA) and benzamide (BZ). Left: intensity ratio of the lateral peaks of the triplet vs. the squared concentration ratio; right: intensity ratio of one lateral peak to the central peak vs. concentration ratio; α values are deduced from the slopes.