Accurate molecular weight determination of small molecules via DOSY-NMR by using external calibration curves with normalized diffusion coefficients

We describe a novel development of MW-determination by using an external calibration curve approach with normalized diffusion coefficients.


I. Definition of ΔMW in ECC-MW-Determination
To estimate how good the MW-determination works (using for example the solvent or another molecule as internal reference) we calculate the deviation of the determined MW from the "real" MW of the compound in %, according to equation (S1): When the ΔMW is positive then the MW was determined too low and when ΔMW is negative then the MW was estimated too high.

II. Estimating the Maximum Error of logD x,norm in TOL-d 8 and THF-d 8
All measurements were performed at 25°C. All compounds have been measured in 15 mM solutions of analyte and reference in an equimolar ratio. The absolute diffusion coefficients (D x ) of all compounds are different on each NMR device. But the normalized diffusion coefficients logD x,norm shows on all devices nearly the same value with a small average standard deviation of σ = 0.0028 in TOL-d 8 and σ = 0.0020 in THF-d 8 , see S- Table 1 and S- Table 2. S- Table 1: Diffusion parameter measured on two different NMR-devices (in TOL-d 8 with ADAM as internal reference).  Figure 1: Superposition plot of two DOSY spectra measured on two different NMR devices. Left: The absolute diffusion coefficients of Si(SiMe 3 ) 4 (TTS) are uneven logD(TTS1)≠logD(TTS2) and logD(TMB1)≠logD(TMB2) due to different gradient calibrations in the NMR devices and for example diversity in viscosity and/or temperature. Right: The signal of the references has been shifted to a fixed value and the signals of TTS have been moved by the same increment of Δ1 = Δ2. With that referencing method it is possible to obtain the same diffusion values for analyte x independent of the used NMR device or changes in solution properties.

III. Overview of the Used Model Compounds for ECCs
Three dimensional models that were geometry optimized with the program Avogadro 1.1.0 have been generated. Of course the transitions between the geometries are not sharp but there are clear systematic trends that can be rationalized. S- Table 3 one can see, that compact spherical (CS) molecules have nearly the same radius in all dimensions with a highly filled space. Dissipated spheres and ellipsoids (DSE) have an elongated main-axis and a less filled space. Small annelated aromatic compounds like toluene (92 g/mol), indene (116 g/mol) or naphthaline (128 g/mol) with MW < 150 g/mol diffuse DSE-like. Also diphenylacetylene (178 g/mol) that has an elongated molecule is still in the range of a DSE geometry. The significance of one and two dimensional geometries begins approximately at MW > 178 g/mol. This is why the ECC ED for extended discs (ED) begins with anthracene that has a MW of 178 g/mol. Cyclopentane (70) THF (72) TMS (88) MTBE (88)  100 Diisopropylether (102) TMB (114) Indene (116) ADAM (136) Naphthaline (128) 1,3-Indandione (146) 2-Phenylpyridine (155) Tetramethoxypropane (164) Diphenylacetylene (178) Anthracene (178) Acridine (179) 9-Methylanthracene (192) 200

IV. Creating Calibration Curves
The power law can be linearized by taking the logarithm of both sides To obtain a linear correlation of D and MW we measured the diffusion coefficients of 28 different model compounds, aliphatics and aromatics with known MWs in a range of 70 gmol -1 (cyclopentan) to 623 gmol -1 (BINAP: (2,2'-bis(diphenylphosphino)-1,1'-binaphthyl). In TOL-d 8 we used (ADAM) and in THF-d 8 solutions we used TMB as internal standard. Plotting logD x,norm against logMW gives a linear fit that provides the values for logK and α. It is possible to calculate the MW of unknown compounds by applying their normalized diffusion coefficient logD x,norm to equation (S4).
The maximum deviation of logD x,norm was 0.0075, which is approximately the width at half maximum of a DOSY signal. This is the reason why the maximum ΔlogD x,norm was defined as 2 times 0.0075 which is reflected in the error bars in the calibration plots: a) When a compound had more than one signal in the 1 H-NMR, the average diffusion coefficient was used. b) For determining the diffusion coefficient, we used the signal of the -CH 2 groups with the highest intensity.

VII. Testing the Influence of the Temperature on ECCs
S-

VIII. Gaussian fits of the T1/T2 software of Topspin for LDA in THF-d 8 at 25°C
S- Figure 4: Gaussian fits of the internal reference PhN A) and B). The plots of LDA correspond to α-CH-C) and CH 3 protons D).   where MD W is the molar Van-der-Waals density, MW the molecular weight, V W the Van-der-Waals volume and r W the Van-der-Waals radius.

XIII. Calculation of the Molar Van-der-Vaals Density MD w S-
S- Figure 10: Weight distribution in the model compounds and molecules with heavy atoms.

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with the ECCs that are presented in this article.

XIV. ECC-MW-Determination Excel Spreadsheet
A simple Excel spreadsheet is available at http://www.stalke.chemie.uni-goettingen.de/mw_det_calc/mw_det_calc.xlsx That implements the calculation of logD x,norm described in the main text, allowing to estimate MWs of analytes from their diffusion coefficients. Please read the information on the first excel sheet.