# Authentication of a Painting Attributed to the Rembrandt School
## 2 The Experimental Part
### Art--FTIR Spectrometry
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type Ion** & **Theoretical Spectral** & **Peak Present in** & **Samples Analysed** \\ \cline{3-4}  & **Bands (cm\({}^{-1}\))** & **Samples (cm)\({}^{-1}\)** & **Samples Analysed** \\ \hline  & & 711.43, 1408.64 & S1 \\ \cline{3-4}  & & 738,66; 1428.92; 2306 & S2a \\ \cline{3-4}  & 670–745; 800–890; & 710.56; 1404.30 & S2b \\ \cline{3-4} Carbonate & 1040–1100; 1320–1530; & 716,51; 1377.73; 1451.35; 2385 & S3a \\ \cline{3-4}  & 2235–2925; 3405–3540 & 1378.63; 1451.98; & S3b \\ \cline{3-4}  & & 668.79; 872.87; 2924.98; 3283.56 & S7 \\ \hline  & & 607.83: 869.37; 1072.46; 1187.10; 1408.64; & \\  & & 1732.66; 3266.03 & S1 \\ \cline{3-4}  & 607–899; 1187–1732; & 599.35; 622.93; 794.07; 1069.18; 1428.92; & \\ Pb (II, III, IV) & 607–899; 1187–1732; & 1451.35; 1700.03; 3263.86 & S2a and S3a \\ \cline{3-4}  & 3000–3266 & 606.02; 803.75; 1069.84; 1404.38; & \\  & & 1626.33; 3266.38 & S2b and S3b \\ \cline{3-4}  & & 872.87; 1155.95; 1648,53; 3283.56; & S7 \\ \hline Ba(II) & 603–634; 971–1063; & 634,36, 981, 1063, 1108, 1180 & S2b and S3b \\ \cline{3-4}  & 1108–1180 & 614.40; 1101.58 & S7 \\ \hline Fe(II, III) & 523; 915; 1042; 1626; & 523, 915, 1042, 1626, 2376, 2436 & S2a and S3a \\ \hline Zn(II) & 524, 1072, 1377, & 524, 1072, 1377, 1740, 3459 & S1 (traces, weak/low peaks) \\ \hline  & & 2855.02; 2921.57; 3266.03 & S1 \\ \cline{3-4} Acvo and & & 2920.84; 3265.33; 3737.57; 3855.63 & S2a \\ \cline{3-4} hydroxocomplexes (coordination water) and & 2850–4000 & 2857.57; 2922.49; 3266.38 & S2b \\ \cline{3-4} crystallized water & & 2862.75; 2928.033263.86 & S3a \\ \cline{3-4}  & & 2858.31; 2925.58 & S3b \\ \cline{3-4}  & & 2857.96; 2924.98; 3283.56 & S7 \\ \hline  & & 1659.72 & S1 \\ \cline{3-4}  & & 1515.34; 1650.95 & S2a \\ \cline{3-4} Binder (egg protein, via & \(\sim\)1547; & 1626.13 & S2b \\ amide I and amide II) & 1621–1690 & 1664.13 & S3a \\ \cline{3-4}  & & 1652.57 & S3b \\ \cline{3-4}  & & 1553.11; 1648.53 & S7 \\ \hline  & & 1232.82; 1732.66 & S1 \\ \cline{3-4} Varnish (through ester & \(\sim\)1265; & 1794.39 & S2a \\  groups) & \(\sim\)1750 & 1700.03; 1242.91 & S3a \\ \cline{3-4}  & & 1245.26 & S3b \\ \hline  & & 605.27; 683.99; 1066.16; 1451.98; 1662.57; & \\ Anchored dirt (carbonyl, & 590–670; 1104; & 2928.03; 3263.86 & \\  carboxyl, ether, ethylenic & 1450–1620; & 605.27; 682.95; 1056.16; 1451.96; 1652.57 & S2a \\  and C-H groups) & 2930–3335; & 2925.58; 3269.29 & S3a \\ \cline{3-4}  & 3400–3512 & 596; 667; 1104; 1458.16; 1619; 2934; 3237; & \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._The cations Pb(II, III, IV), Ba(II), Fe(II, III) and Zn(II) have their oxidation states written with Roman numerals, as they are found as solid, insoluble congruents in aqueous electrolyte systems (they are in the form of cations in the atomic network and not as aqueous ions). IR vibration spectra of valence (v), symmetric (v\({}_{\rm s}\)) and antisymmetric (v\({}_{\rm ss}\)), and deformation spectra, in-plane (\(\delta\)), which can be shear (\(\delta^{\rm s}\)) and pendulum (\(\delta^{\rm ss}\)), and out-of-plane (\(\gamma\)), respectively, which in turn can be twisting (\(\gamma^{\rm ss}\)) and rocking (\(\gamma^{\rm s}\)), both in the range 500-4000 cm\({}^{-1}\) are theoretically assigned by group vibrations for white lead Pb\({}_{3}\)(OH)\({}_{2}\)(CO\({}_{3}\))\({}_{2}\) (3266, 1732, 1408, 1187, 899, 607 cm\({}^{-1}\)), BaSO\({}_{4}\) (1180, 1108, 1063, 981, 634 si 603 cm\({}^{-1}\)), Fe(II, III) (3453/3436, 2361, 1640/1636, 1042, 915, 523 cm\({}^{-1}\)), gypsum--CaSO\({}_{4}\) (3541, 3406, 2925, 2235, 1625, 1447/1451, 1135, 875/863 si 667/663 cm\({}^{-1}\)), ZnO (3450, 1740, 1380, 1090/1072, and 510 cm\({}^{-1}\)).