Supplementary material

Ion-to-Neutral Ratios and Thermal Proton Transfer in Matrix-Assisted Laser Desorption/Ionization

I-Chung Lu,1Kuan Yu Chu,1, 2Chih-Yuan Lin,1Shang-Yun, Wu,1Yuri A. Dyakov,1Jien-Lian Chen,1Angus Gray-Weale,3Yuan-Tseh Lee,1,2 Chi-Kung Ni*1,4

  1. Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, 10617, Taiwan
  2. Also at Department of Chemistry, National Taiwan University, Taipei, 10617, Taiwan
  3. School of Chemistry, University of Melbourne, VIC 3010 Australia.
  4. Also at Department of Chemistry, National Tsing Hua University, Hsinchu, 30013, Taiwan. E-mail address: .

Chemicals

For MALDI grade materials, they were purchased from Sigma Aldrich (2,5-DHB: matrix substance for MALDI-MS, >99.0% (HPLC), 85707 Sigma; CHCA:matrix substance for MALDI-MS, ultra pure, 39468 Fluka; SA: matrix substance for MALDI-MS, ≥99%, 85429 Fluka; FA: matrix substance for MALDI-MS, ≥99.0% (HPLC), 46278 Fluka). For non-MALDI grade materials, 2,5DHB and SA were purchased from Acros Organics (2,5DHB: 99%, product code: 10127943; SA: ≥98%), CHCA and FA were purchased from Sigma Aldrich (CHCA: ≥98% (TLC), powder, C2020 Sigma; FA: 99%, D128708 Aldrich).

Calculations of temperature

The temperature-dependent heat capacity can be calculated based on the molar heat capacity of the solid matrix by using a modified Einstein model, as follows:

(S1)

where h is the Planck constant, k is the Boltzmann constant, v is the oscillatorfrequency between molecules, and vi is the vibrational frequency of the matrix. The first, second, and third terms represent the oscillation relative to neighboring molecules and the contribution from molecular rotation and vibration, respectively. The first term approaches 3R at room temperature or at a higher temperature. The second term was not included in the calculation of temperatures below the melting point because molecular rotation is restricted in the solid state. Vibrational frequencies from ab initio calculations conducted using Gaussian 09 were used to calculate the third term. The vibrational frequencies are listed in the supplementary material. Only vibrational modes with low vibrational frequencies make substantialcontributions, as shown in Equation (S1). Vibrational modes possessing high amplitudes of motion (e.g., internal rotation) typically exhibit low vibrational frequencies. However, the vibrational motions of these modes are restricted in the solid state and they are not completely free to undergo vibrational motion in the liquid phase. The number of restricted vibrational motions and rotations that occur near room temperature was derived from the fit of the calculated heat capacity to experimental measurements. The number of restricted vibrational motions and rotations gradually decreases at high temperatures.

The specific heat capacity was determined based on the relation between the specific and molar heat capacities, and, where a is the coefficient of thermal expansion and b is the isothermal compressibility. Both the isothermal compressibility and volumetric thermal expansion of thematrices in this study are not currently available. The values a = 8.5 10-4 (K-1) and b = 4.5 10-5 atm-1 (similar to the values of aniline and phenol) were used for the calculation of Cp.

Calculations of Gibbs free energy

The heats of reaction H7were calculated using ab initio methods.In the ab initio calculations, the geometries of the reactants and products were fully optimized using the hybrid density functional B3LYP method1–4 combined with the 6-31G* basis set.5 The energies of the reactants and products at the B3LYP/6-31G* optimized geometries were calculated using the G3-type computational scheme,6 specifically G3(MP2,CCSD)//B3LYP modification.7–8 Zero point energy corrections were considered by using B3LYP/6-31G* frequencies without scaling. All of the ab initio calculations were performed using the Gaussian 09 computational package.9

References

  1. Becke, A.D. Density‐functional thermochemistry. I. The effect of the exchange‐only gradient correction.J. Chem. Phys. 96, 2155-2160 (1992).
  2. Becke, A. D. Density‐functional thermochemistry. II. The effect of the Perdew-Wang generalized-gradient correlation correction. J. Chem. Phys. 97, 9173-9177 (1992).
  3. Becke, A. D. Density‐functional thermochemistry. III. The role of exact exchange. J. Chem. Phys., 98, 5648-5652 (1993).
  4. Lee, C.; Yang, W.; Parr, R.G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785-789 (1988).
  5. Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self-consistent molecular orbital methods. XII. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules. J. Chem. Phys. 56, 2257-2261 (1972).
  6. Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. Gaussian-3(G3) theory for molecules containing first and second-row atoms. J. Chem. Phys. 109, 7764-7776 (1998).
  7. Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-3 theory using density functional geometries and zero-point energies. J. Chem. Phys. 110, 7650-7657 (1999).
  8. Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Baboul, A. G.; Pople, J. A. Gaussian-3 theory using coupled cluster energies. Chem. Phys. Lett. 314, 101-107 (1999).
  9. Gaussian 09, Revision D.01, Frisch, M. J. et al. Gaussian, Inc., Wallingford CT, 2009.

Table S1. Vibrational frequencies from ab initio calculations

CHCA

375472107156183218279309

387414415427442495520551561

630647685729767786812830854

8799369819871028108011511198 1210

121712631332135313921403143014901562

161916451673182123393176319632033222

325537063743

FA

32647982129173196220223

285304355372458486487527554

572576596641705741774819 831

8618959179539541018105911461173

117711911214122712621297132113241355

137214141462148714961509155516331648

168117753027309431593177320432103216

322137663773

SA

3258647285123138159188

202215228283290309329379405

483489496537557591603620641

710740741820843882895915935

985101510641131117311741175 1181 1211

121612441267128812991342135213781414

145914851491149214961509151415371635

163916811775302830313096311631553159

317932153216322437613774

25DHB

98108228229284358374397440

457529593597614652696749752

76577979985994799511031176 1193

122412591270135313751433146915111555

164416871754318232303238337836993748

Figure S1: Relative ion intensity of MALDI grade (black) and non-MALDI grade(red) materials. Both MALDI grade and non-MALDI materials were measured from 10 samples. For each sample, we randomly chose 20 positions on the sample, and mass spectrum was accumulated for 10 laser shots for each position. Each data point represents the accumulation from 200 laser shots. Standard deviations were given for the first 5 samples.

Figure S2. The calculated heat capacities, cp, for 2,5-DHB. The blue line represents the free rotational motion and m = 0 (no restricted vibrational motion)in Equation S1. The red line represents no rotational motion and m = 7 (seven restricted vibrational motions with low vibrational frequency)in Equation S1. The solid squares are the experimental measurements. The green line represents the values used in Equation 5 for the temperature calculations. The blue dot line represents the combination of largest value of a2/b and m=0 in Equation S1. The red lot line represents the combination of smallest value of a2/b and m=7 in Equation S1. The blue and red lot lines represent the range of uncertainty of heat capacity.

Figure S3. Calculated surface temperature (black line) before desorption occurs. In the uncertainty estimation, thermal conductivity, range of the numbers of restricted vibrational modes in the solid state and the liquidphase, and ranges of thermal expansion coefficient and isothermal compressibility were taken into consideration. The gray curves represent the maximum and minimum of temperature attributable to the total uncertainty of these factors. Additional effect of decomposition on temperature was included in calculations for 2,5-DHB.

Figure S4: The geometries, relative energies (kcal/mol), and dipole moments of various conformers.

Figure S5: Dielectric constant as a function of temperature. Only the results from g =1 in Equation 11 are shown.

Figure S6: Solvation energy of neutral matrix (thick solid line), protonated matrix (thin solid line), and deprotonated matrix (dot line). Green: SA; red: FA; blue: 25DHB; black: CHCA. Only the results from g = 1 in Equation 11 are shown.