Caterina Fraschetti, Antonello Filippi,Maria Elisa Crestoni,Tadashi Ema, Maurizio Speranza*

Unexpected behaviour of diastereomeric ions in the gas-phase: a stimulus for pondering on ee measurements by ESI-MS.

Supplementary Material

Figure S1.Time-dependence of the overall abundance of a mixture of the [AR•H•M]+and [AS•H•M]+isobars undergoing first-order Y-to-AR (orAS) exchangereaction at rate constants k’ = 1 s-1 and k” = 0.5 s-1, respectively. The inset reports the magnification of the broken-lined section with the decay curves at various [AR•H•M]+molar fractions.

Figure S2.Time-dependent relative abundances of [pheD•H•1R]+(open circles), [pheD•H•1R•YS]+(full circles), and [YS•H•1R]+(diamonds) from the reactions between YS and the [pheD•H•1R]+ complex. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Table 1.

Figure S3. Time-dependent relative abundances of the [pheD•H•1R]+/[pheL•H•1R]+ pair (open circles), [pheD•H•1R•YR]+(full circles), and [YR•H•1R]+(diamonds) from the reactions between YR and the [pheD•H•1R]+/[pheL•H•1R]+diastereomers formed from [pheD]/[pheL] = 9:1. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Figure 4 using appropriate [pheD•H•1R]+/[pheL•H•1R]+ concentration ratios.

Figure S4. Time-dependent relative abundances of the [pheD•H•1R]+/[pheL•H•1R]+ pair (open circles), [pheD•H•1R•YR]+(full circles), and [YR•H•1R]+(diamonds) from the reactions between YR and the [pheD•H•1R]+/[pheL•H•1R]+diastereomers formed from [pheD]/[pheL] = 8:2. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Figure 4 using appropriate [pheD•H•1R]+/[pheL•H•1R]+ concentration ratios.

Figure S5. Time-dependent relative abundances of the [pheD•H•1R]+/[pheL•H•1R]+ pair (open circles), [pheD•H•1R•YR]+(full circles), and [YR•H•1R]+(diamonds) from the reactions between YR and the [pheD•H•1R]+/[pheL•H•1R]+diastereomers formed from [pheD]/[pheL] = 7:3. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Figure 4 using appropriate [pheD•H•1R]+/[pheL•H•1R]+ concentration ratios.

Figure S6. Time-dependent relative abundances of the [pheD•H•1R]+/[pheL•H•1R]+ pair (open circles), [pheD•H•1R•YR]+(full circles), and [YR•H•1R]+(diamonds) from the reactions between YR and the [pheD•H•1R]+/[pheL•H•1R]+diastereomers formed from [pheD]/[pheL] = 6:4. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Figure 4 using appropriate [pheD•H•1R]+/[pheL•H•1R]+ concentration ratios

Figure S7.Relationship between the enantiomeric composition of calibrated mixturesof D- and L-methyl mandelate (eeactual(%)) and that inferred from application of the protocol of Figure 1 of main text (eecalc(%)) (BS = (S)-N-benzoyl-2-pyrrolidinecarboxylic acid and BR* = (R)-N-(p-toluoyl)-2-pyrrolidinecarboxylic acid; ref. [8]). The correlation is shifted to the dotted line byexcludingfromthecorrelationtheconstrainsimposedbythemethod, i.e. eecalc=eeactual = 0 % (methylmandelateracemate) and 100 % (L-methyl mandelate).

Figure S8.Relationship between the enantiomeric composition of calibrated mixturesof L- and D-valinemethylester (eeactual(%)) and that inferred from application of the protocol of Figure 1 of main text (eecalc(%)) (BS = (S)-N-benzoyl-2-pyrrolidinecarboxylic acid and BR* = (R)-N-(p-toluoyl)-2-pyrrolidinecarboxylic acid; ref. [8]). The correlation is shifted to the dotted line byexcludingfromthecorrelationtheconstrainsimposedbythemethod, i.e. eecalc=eeactual = 0 % (valinemethylesterracemate) and 100 % (L-valinemethylester).

Search of the maximum value of the slope of the curves of Figure 1.

KineticEquations.

Table S1.

Figure S1.Time-dependence of the overall abundance of a mixture of the [AR•H•M]+and [AS•H•M]+isobars undergoing first-order Y-to-AR (orAS) exchangereaction at rate constants k’ = 1 s-1 and k” = 0.5 s-1, respectively. The inset reports the magnification of the broken-lined section with the decay curves at various [AR•H•M]+molar fractions.

Figure S2. Time-dependent relative abundances of [pheD•H•1R]+(open circles), [pheD•H•1R•YS]+(full circles), and [YS•H•1R]+(diamonds) from the reactions between YS and the [pheD•H•1R]+ complex. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Table 1.

Figure S3. Time-dependent relative abundances of the [pheD•H•1R]+/[pheL•H•1R]+ pair (open circles), [pheD•H•1R•YR]+(full circles), and [YR•H•1R]+(diamonds) from the reactions between YR and the [pheD•H•1R]+/[pheL•H•1R]+diastereomers formed from [pheD]/[pheL] = 9:1. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Figure 4 using appropriate [pheD•H•1R]+/[pheL•H•1R]+ concentration ratios.

Figure S4. Time-dependent relative abundances of the [pheD•H•1R]+/[pheL•H•1R]+ pair (open circles), [pheD•H•1R•YR]+(full circles), and [YR•H•1R]+(diamonds) from the reactions between YR and the [pheD•H•1R]+/[pheL•H•1R]+diastereomers formed from [pheD]/[pheL] = 8:2. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Figure 4 using appropriate [pheD•H•1R]+/[pheL•H•1R]+ concentration ratios.

Figure S5. Time-dependent relative abundances of the [pheD•H•1R]+/[pheL•H•1R]+ pair (open circles), [pheD•H•1R•YR]+(full circles), and [YR•H•1R]+(diamonds) from the reactions between YR and the [pheD•H•1R]+/[pheL•H•1R]+diastereomers formed from [pheD]/[pheL] = 7:3. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Figure 4 using appropriate [pheD•H•1R]+/[pheL•H•1R]+ concentration ratios.

Figure S6. Time-dependent relative abundances of [phe*•H•1R]+(open circles), [pheD•H•1R•YR]+(full circles), and [YR•H•1R]+(diamonds) from the reactions between YR and the [phe*•H•1R]+diastereomers formed from [pheD]/[pheL] = 6:4. The continuous lines represent the relative abundance of reactants and products calculated from the exact rate expressions for the reaction mechanisms reported in Figure 4 using appropriate [pheD•H•1R]+/[pheL•H•1R]+ concentration ratios.

Search of the maximum value of the slope of the curves of Figure 1.

Expression of the time-dependent reaction extent of two isobaric species (molar fraction  and 1-, respectively) which undergo first-order decay by reaction with a suitable reactant at the corresponding rate constants k’ and k” (Figure S1):

(S1)

Expression of the slope of the curves of Figure 1 :

(S2)

Search of the maxima and the minima of eq. S2 as a function of the reaction time t:

(S3)

Expression of the tmax (insert of Figure 1) :

(S4)

Kinetic equations

For the kinetic scheme of [pheD•H•1R]+:

If [B]0 = [C]0 = 0:

(S5)

(S6)

(S7)

For the kinetic scheme of [pheL•H•1R]+:

If [C]0 = 0:

(S8)

For the [pheD•H•1R]+/[pheL•H•1R]+ isobaric mixture:

(S9)

(S10)

Table S1. Effect of the presence of a chiral molecule (1R) on nano-ESI of calibrated pheD/pheLmixtures.

[pheD•H•1R]0+ molar fraction /  / a = [pheD•H•1R]0+/([pheL•H•1R]0+ / b = [pheD]/([pheL] / Ratio b/a
0.60 / 0.9 / 1.50 / 9.00 / 6.0
0.42 / 0.8 / 0.74 / 4.00 / 5.4
0.31 / 0.7 / 0.45 / 2.33 / 5.1
0.21 / 0.6 / 0.27 / 1.50 / 5.6