The vibrational spectroscopy of indigo: A reassessment

Vibrational Spectroscopy 50 (2009) 268–276 Contents lists available at ScienceDirect Vibrational Spectroscopy journal homepage: www.elsevier.com/locate/vibspec The vibrational spectroscopy of indigo: A reassessment John Tomkinson a,*, Mauro Bacci b, Marcello Picollo b, Daniele Colognesi c a Science and Technology Facilities Council, The ISIS Facility, The Rutherford Appleton Laboratory, Chilton, OX11 0OX, UK Istituto di Fisica Applicata ‘‘Nello Carrara’’ (IFAC-CNR), Via Madonna del Piano 10, 50019 Sesto Fiorentino (Firenze), Italy c Istituto dei Sistemi Complessi (ISC-CNR), Via Madonna del Piano 10, 50019 Sesto Fiorentino (Firenze), Italy b A R T I C L E I N F O A B S T R A C T Article history: Received 28 July 2008 Received in revised form 5 January 2009 Accepted 19 January 2009 Available online 30 January 2009 We report the neutron vibrational spectra of indigo and its model compounds thioindigo and isatin. The neutron data extend the low energy range of the vibrational spectra of these molecules. The assignments, made with the help of ab-initio calculations, give convincing fits between the observed and scaled calculated results, and correct errors in the published literature. The indigo eigenvectors are described in terms of those of its model compound isatin. Finally, candidate modes, that could be used to study indigoids in matices (e.g. ‘Maya Blue’), are selected. ß 2009 Elsevier B.V. All rights reserved. Keywords: Indigo Thioindgo Isatin Inelastic neutron scattering Maya blue 1. Introduction Indigo is a dyestuff that is not only of current commercial interest [1] but also of considerable historical importance. (The structures of indigo and the related molecules discussed in this paper are given in Fig. 1.) Since ancient times it has been widely used as a dye and a pigment [2]. It has also been found in ‘Maya Blue’, a very stable blue pigment used by the ancient inhabitants of Mexico for pottery and mural paintings. Here, the indigo chromophore is inserted in an inorganic matrix (palygorskite) [3,4,5]. Despite numerous studies of the spectroscopic behaviour of indigo it is far from being completely understood. Both electronic and vibrational spectra are very sensitive to the local environment around the indigo molecule: for instance the main absorption band in the visible region shifts from 540 nm (gas phase) to 588 nm in non-polar solvents and to 606 nm in polar solvents or in the solid state [6]. These shifts in lmax are probably related to the details of the intermolecular bonding pattern immediately around the chromophore, as has been demonstrated by the recent success in obtaining lmax from ab-initio calculations [7]. However, its vibrational spectra are even more puzzling, especially in the comparison of pure indigo and ‘Maya Blue’ [8,9,10,11]. Although the vibrational features related to the N–H group are strongly affected when indigo is inserted into clay, it is * Corresponding author. Tel.: +44 1235 44 6686; fax: +44 1235 44 5383. E-mail address: j.tomkinson@rl.ac.uk (J. Tomkinson). 0924-2031/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.vibspec.2009.01.005 still unknown if this is due to a change in the hydrogen bonding and, or, the formation of new species such as dehydro-indigo [9]. Fortunately, this spectral sensitivity to its environment offers the opportunity for a better understanding of ancient artefacts at a molecular level and hence access to the processes that were used in their creation. Central to extracting this information, and understanding ‘Maya Blue’, is a reliable appreciation of the vibrational spectroscopy of pure indigo that, until now, has been lacking. Further, the low energy spectral region of indigo and related molecules, a region that might be expected to be most sensitive to changes in the local environment, is unknown. Only one published study has addressed the entire vibrational spectrum of indigo [12], it also provides a convenient entry to earlier literature where the focus was on the vibrations of the chromophoric centre, especially n(C C) and n(C O). This work organised infrared, Raman and ab-initio calculations, to produce a complete assignment scheme. Sadly, it is marred by a chaotic mode numbering scheme and the assignment of more fundamental transitions than the theoretical maximum, 84. Some of these errors were partly addressed by more recent work [13] but it is still referenced by workers in the field and even ‘‘substantially confirmed’’ by some [14]. The magnitude of the problem can be gauged from Fig. 2, which compares this assignment scheme [12] with our new data, clearly it is inadequate. Without settling these issues, and generating a good assignment scheme, a thorough understanding of ‘Maya Blue’ as an organic-inorganic composite is unlikely to appear. As a basis for our own future work in this field we have undertaken the study of J. Tomkinson et al. / Vibrational Spectroscopy 50 (2009) 268–276 269 involving hydrogen motions and, as a consequence, direct study of the chromophore vibrations, which involve almost pure n(C C) and n(C O), is difficult. However, it has been demonstrated that the technique is ideal for the study of organic molecular crystals, especially those isolated in inorganic matrices, it is described in detail elsewhere [15]. We shall assign the vibrational spectra of two model compounds of indigo; namely, thioindigo and isatin. These assignments will then be used to help assign the vibrations of indigo. Since isatin is, roughly, one half an indigo molecule (see Fig. 1), its vibrational eigenvectors are well suited to use as descriptors of the indigo vibrations. This approach addresses the inadequacy of describing molecular eigenvectors of larger molecules like indigo by the motions of a few functional groups, as has already been touched upon [13]. We shall also discuss the choice of spectral bands that can be used to determine the nature of indigoids in inorganic matrices. Fig. 1. The molecular structures of isatin (above) and indigo (below). The structure of thioindigo is that of indigo with the NH atoms replaced by sulfur atoms at the nitrogen positions. indigo, through its model compounds thioindigo and isatin, using Inelastic Neutron Scattering (INS) spectroscopy. The results we report here address, mostly, the correct assignment of these spectra and the identification of those candidate(s) in the vibrational spectrum of indigo that will allow its recognition in mixtures like Maya Blue. (Systems, like ‘Maya Blue’ itself and the Roman violet lakes, will be considered elsewhere.) Molecular vibrational spectroscopy with neutrons is a well established technique that makes use of modern spallation neutron sources to obtain spectral bandwidths similar to those obtained in the optical spectroscopy of solids, for a comparison of INS and optical spectra see [15]. INS has the advantage that its observed intensities can be simply compared to calculated spectral intensities. These intensities are obtained straightforwardly from the mean square vibrational atomic displacements that appear as output from standard ab-initio programs. This advantage is not readily available to results from optical spectroscopies and the difficulty of matching calculated and observed Raman intensities can be seen from the published literature (see especially Table 1 of Ref. [13]). The INS technique emphasises those vibrational modes Fig. 2. A comparison of the observed inelastic neutron scattering spectrum of indigo (black trace) with that calculated for the currently accepted assignment scheme (red trace), after [12]. This figure should be compared to the results shown in Fig. 7. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) 2. Molecular and crystal structures, mode numbering Isatin, see Fig. 1, crystallises in the P21/c (C2h5) space group with four molecules in the unit cell. Pairs of molecules are hydrogen bonded, head to head, into centrosymmetric dimers that interact only weakly with their neighbours [16,17]. Each dimer can be imagined to be produced from a single indigo molecule; by rupturing it at the central C C bond, translating the moieties laterally in the plane, about 2.8 Å´, and terminating both free valence, C , with an oxygen atom. The isatin molecule is planar and its 42 fundamental modes are distributed over the representation: Gvib = 29 A0 + 13 A00 . It is appropriate to note here that we shall follow the conventional approach to spectroscopic mode numbering [18]. Modes are first grouped in blocks according to their symmetry species and the mode frequencies are ordered in decreasing value within each character block. In the cases discussed here, the ordered frequency values are those given by the unscaled ab-initio calculations described below. We shall use the monomer form of isatin as our basis for its mode numbering scheme, A0 (1–29) and A00 (30–42). The isatin dimer is a planar, high symmetry (C2h), arrangement of the monomers and its 90 fundamentals are distributed over the representation: Gvib = 31 Ag + 15 Au + 14 Bg + 30 Bu. Thioindigo can be crystallised in the P21/c (C2h5) space group with two molecules in the unit cell [19] but our commercial sample is probably P21/n [20]. We shall treat the molecule as planar, C2h, with its 78 fundamental modes distributed over the representation: Gvib = 27 Ag + 13 Au + 12 Bg + 26 Bu, and its numbering scheme is; Ag (1–27), Au (28–40), Bg (41–52) and Bu (53–78), Indigo, see Fig. 1, crystallises in the P21/c (C2h5) space group with two molecules in the unit cell [21,22]. Apart from the obvious presence of intra-molecular hydrogen bonds (since the sulfur of thioindigo has been replaced by an NH group), there is also evidence of close intermolecular contacts in the crystal. These give rise to multicentred, non-linear, hydrogen bonds [22]. The molecule is planar, C2h, and its 84 fundamental modes are distributed over the representation: Gvib = 29 Ag + 14 Au + 13 Bg + 28 Bu, and its mode numbers are Ag (1–29), Au (30–43), Bg (44–56) and Bu (57–84). This numbering is in contradistinction to the confusion found in other published work, Ag (1–29), Au (28–35, 37–40), Bg (41–52) and Bu (36, 51, 56–84) with the g(NH)(Au) mode left unnumbered, Table 1 of Ref. [12]. 3. Calculational details Our calculations were performed in GAUSSIAN98 [23] for the isolated molecules and the isatin dimer (C2h). The molecular 270 J. Tomkinson et al. / Vibrational Spectroscopy 50 (2009) 268–276 geometries were constrained planar and, using Density Functional Theory (DFT), were optimised at the B3LYP level with the 6-31G** basis set. From this geometry the harmonic vibrational frequencies and atomic displacement vectors were produced, to be used in ACLIMAX, see below. Preparative to the DFT calculation on indigo a repeat of earlier work [12,13] was undertaken at the Hartree Fock (H-F) level, with the 3-21G basis set. The results from this calculation (when used with ViPA, see below) enabled our DFT results to be accurately correlated to the earlier assignment scheme of indigo [12] on a mode by mode basis, thus enabling us to produce Fig. 2. There are several approaches to handling the results of ab-initio calculations, some workers prefer to leave them unchanged whilst others scale the ab-initio eigenvalues according to more or less complex schemes. Such approaches have, as their objective, the aim of testing the adequacy of the different calculational schemes in reproducing the observed eigenvalues. Our approach is different, we accept the calculational scheme is adequate and stress the importance of the eigenvectors. Fortunately, eigenvectors are not very sensitive to the details of a given calculational scheme [15]. Thus, we shall assume that our calculated eigenvectors are acceptable but recognise that calculational inadequacies produce somewhat erroneous eigenvalues. If we are to fully exploit the calculated eigenvectors in understanding our observed INS spectra we must overcome the problem of poorly calculated eigenvalues. Since the eigenvectors are acceptable, if only the eigenvalues were correct the calculated INS spectrum would reproduce that observed, within the limits of theory, as would be obvious from simple visual inspection. We shall correct our eigenvalues by applying individual scaling parameters. 3.1. Spectral comparison The vibrations of structurally related molecules can be profitably compared through the form of the atomic displacements in given modes, their eigenvectors. This comparison might be attempted by inspection using commercial visualisation packages but is subjective, non-quantitative and, so, unusable. Fortunately, the comparison can be made quantitative using the ViPA program [24]. The normal modes of a given molecule are projected onto the orthonormal vector space defined by the normal modes of the reference molecule. Any one mode’s projection is then reported in terms of the percentage of each of the reference molecule’s modes. Since the vibrational displacements given by GAUSSIAN are not mass-weighted Cartesian displacement coordinates, and so not orthonormal, ViPA produces its own normal modes from the Cartesian force-fields generated by GAUSSIAN [24]. As is intuitively correct, and given by ViPA, the C–H stretching vibrations of isatin are the same as those of indigo, to better than 99%. The mode descriptions given in Tables 2a and 2b are a very condensed version of the full ViPA output and enable quantitative comparisons to be made back, from the vibrations of isatin and indigo, to the vibrations of benzene and pyrrole-2,3-dione. 4. Experimental 4.1. Samples The samples of isatin (98%) and commercial dyestuffs thioindigo and indigo (95%) were obtained from Aldrich, they were used without further treatment. 4.2. Spectrometer and data visualisation The samples, about 5 g, were wrapped in aluminium foil and held in flat sample cells. These were maintained at 20K in the neutron beam of the TOSCA spectrometer [25], at the ISIS Facility, The Rutherford Appleton Laboratory, Chilton, OX11 0QX, UK. TOSCA is a pulsed neutron, indirect geometry, low band-pass spectrometer with good spectral resolution (DEt/Et  2%) [25]. Data were collected for about 8 h and transformed into the conventional scattering law, S(Q,v) (arbitrary units), vs. energy transfer, Et (cm1), using standard programs. The INS spectra were displayed and compared with the calculated spectra from GAUSSIAN98 using ACLIMAX [26]. This free-ware program uses the GAUSSIAN output files (.LOG) to generate the TOSCA spectrum, although the output from other abinitio programs can also be used. In a simplified form; the INS intensity, S(Q,vn)l, of the mode, n, observed at the energy transfer, v, and momentum transfer, Q (determined by the neutron spectrometer), is given by X v u2 Þ (1) SðQ 1 vv Þl ¼ ðQ 2  v u2l ÞexpðQ 2 l V n where u2l, is the mean square displacement of the atom, l, in the mode, as given by GAUSSIAN. A full discussion of the details of INS intensities is given elsewhere [15]. The exponent shown in Eq. (1) is the same Debye–Waller factor that will be familiar from diffraction work and the more an atom moves the smaller will be the D–W value. Isolated molecule calculations omit those atomic displacements caused by the, external, lattice modes and to correct for this an extra term is added to the internal displacements calculated by GAUSSIAN98. X X X v u2 þ v u2 ¼ ða Þ þ ða Þ v u2 ¼ (2) l int l ext l l l v internal external A typical value for the external contribution term, (al)ext, would be that of benzene, 0.025 Å´2; for larger, or stiff, molecular systems, this will fall and for smaller, or limp, molecules it will rise [15]. 5. Results 5.1. Thioindigo The initially calculated, or unscaled, and observed spectra of thioindigo are detailed in Table 1. The two spectra are very similar, with bands of similar intensity overlapping one another (either partly or wholly). The n(CH) stretching region is remarkably sharp and structured. This structure was freely fitted to three Gaussians (at 3035, 3091 and 3152 cm1), which we identify as the n(CH) band origin and its first two phonon-wings [15]. The band origin value agrees reasonably with the average value of the n(CH), Raman, bands, 3020 cm1 [12]. The external modes are thus located below about 60 cm1 (=3091–3035) and their limit nicely corresponds to the sharp edge at 69 cm1 seen in the observed spectrum. The observed spectrum below 69 cm1 was taken as representative of the phonon-wing spectrum. A value for (al)ext (see above) was obtained, 0.008 Å´2, from the ratio of the band intensities in the n(CH) region [15]. This value is low compared to typical values for organic molecules, see above, and is a consequence of the heavy molecular mass and stiffness of thioindigo. As discussed above, we shall exploit the results from the GUASSIAN98 calculations by individually scaling the calculated eigenvalues. The process of extracting the necessary individual scaling parameters presupposes a knowledge of the optical characters of the molecular transitions as well as the calculated eigenvectors. In the case of thioindigo the Raman data was used to identify the Ag modes. (These frequencies were read directly from Fig. 3 of [12], we estimate that the frequency values are accurate to about 3 cm1.) We begin at the lowest frequencies, which has the advantage that fixing a fundamental also identifies its overtones and, 271 J. Tomkinson et al. / Vibrational Spectroscopy 50 (2009) 268–276 Table 1 A comparison of the reported infra-red and Raman spectra of thioindigo with the INS spectrum of this work, in cm1, below 2000 cm1. Both the unscaled (‘DFT’) and the scaled (‘Assigned’) eigenvalues of the GAUSSIAN98 calculations, see text, are also reported. This work DFT 29 74 78 90 137 152 203 213 230 230 270 282 305 407 425 426 445 462 487 492 [12] INS 62 90 br 99 br, sh 121 170 161 205 236 – – 280 297 392 421 414 442 462 Assigned Raman This work ir 69 88 97 95 121 170 161 205 236 227 230 270 280 297 392 421 414 445 462 480 480 502 536 594 676 691 720 489 502 536 542 605 676 691 691 703 720 750 782 794 877 877 ir 877 117 154 207 226 237 925 961 996 1022 1075 937 961 961 996 996 1022 1022 1066 1075 1075 295 1134 1138 1126 1126 932 968 1016 1026 1054 1074 1115 1126 1092 1120sh 1195 1163 1219 1228 1281 1293 1317 1321 1124 453 1140 1186 1187 1238 1243 1310 1312 1361 1361 484 532 1168 1224 1270 1290 1323 1126 1168 1168 1224 1224 1290 1290 1325 1325 601 1391sh 1402 679 691 721 1485 1486 1490 1490 1453 1467 1463 1463 1463 1463 750 1517 754 787 794 794 Raman 910 937 973 973 1002 1002 1041 1042 1066 1084 1095 803 824 882 883 Assigned 877 753 754 787 797 797 [12] INS 889 489 br 505 511 539 542 605 686 695 697 703 729 750 DFT 883 Fig. 3. A comparison of the observed inelastic neutron scattering spectrum of thioindigo (blue trace) with that calculated for the scaled ab-initio assignment scheme of Table 1 (red trace). The external mode region appears below 70 cm1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) 1574 1619 1623 1634 1639 1715 1739 1574 1619 1623 1634 1639 1715 1739 1459 1457 1467sh 1503 1523 1579 1590 1594 1656 1674 Fig. 4. A comparison of the observed inelastic neutron scattering spectrum of isatin (green trace) with that calculated for the isatin-dimer (red trace), as initially given by GAUSSIAN98 and left unscaled. (Here the contributions from the NH hydrogen atoms have been omitted from the calculated spectrum.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) 272 J. Tomkinson et al. / Vibrational Spectroscopy 50 (2009) 268–276 Table 2a A comparison of the ir, Raman, INS and unscaled calculated eigenvalues, cm1, of isatin (20 K). Results of both the monomer and dimer calculations are given. The order is given by the mode numbers of the, Cs, monomer and (A0 )g = Ag, (A0 )u = Bu, (A00 )g = Bg, (A00 )u = Au. Dimer mode numbers, therefore, occasionally appear out of sequence. Mode numbers for both the monomer, v0 , and dimer, n, are given. Calculated Monomer Observed INS This work v0 Mode Descriptions x Dimer n u 46 45 90 17 33 51 n 20 K g 31 60 30 59 62 116 ir ir [27] [29] Raman [27] 300 K 80 K 300 K A00 A00 A0 A0 A00 A0 Description, of dimer vibrations external to the monomer Antiwag of monomers Antitwist of monomers Antirock of monomers Antitranslation of monomers, along dimer Antitranslation of monomers, out of plane Antitranslation of monomers, across dimer Description, of monomer vibrations 00 42 41 40 29 28 99 140 260 270 314 44 43 42 89 88 116 143 271 275 347 59 58 57 29 28 117 143 271 275 334 A A00 A00 A0 A0 39 38 27 391 429 484 41 40 87 403 473 486 56 55 27 406 481 491 A00 A00 A0 138 167 275 273 315 334 392 459 480 26 36 37 25 24 37 35 23 546 551 514 647 658 514 731 733 86 39 553 552 85 84 36 38 83 650 675 812 734 742 26 54 51 25 24 551 553 789 648 666 53 23 734 739 A0 A00 A00 A0 A0 A00 A00 A0 550 537 627 657 657 686 717 733 34 33 32 22 768 821 879 889 37 35 34 82 767 826 887 896 52 50 49 22 766 822 887 892 A00 A00 A00 A0 768 810 879 (889) 21 31 30 20 19 944 971 998 1041 1116 81 33 32 80 79 955 971 999 1041 1116 21 48 47 20 19 954 971 999 1041 1116 A0 A00 A00 A0 A0 (944) 951 990 1008 1092 18 17 1167 1195 78 77 1178 1235 18 16 1177 1232 A0 A0 1143 1160 16 1211 76 1210 17 1210 A0 1185 15 14 13 1261 1308 1357 75 74 73 1290 1329 1365 15 14 13 1289 1332 1364 A0 A0 A0 1268 1308 1343 12 11 10 1411 1503 1516 72 71 70 1455 1503 1523 12 11 10 1466 1503 1524 A0 A0 A0 1413 1460 1480 9 8 1642 1665 69 68 1645 1663 9 8 1645 1669 A0 A0 (1606) (1621) 7 6 1816 1835 66 1818 6 7 1818 1774 A0 Ag Bu (1736) (1740) 67 1800 273 273 336 388 453 478 537 554 – 639 659 659 670 720 734 755 766 816 876 884 915 925 951 952 989 1015 1095 1111 1145 1155 1180 1189 1202 1218 1255 1267 1282 1333 1363 1377 1405 1466 1485 1538 1587 1615 1630 1677 1694 1727 1736 336 383 459 481 540 550 – 638 664 664 700 720 738 754 775 1746 140 173 257 276 335 – – 488 – – 551 Antitwist, Bz against Py Antiwag (butterfly), Bz against Py Bz[33(20), 10(4)]: Py[51(24)] Antirock, Bz against Py Bz[–]: Py[92(17)] Bz[54(20)]: Py[52(23), 14(20)] Bz[48(20)]: Py[27(22), 17(21), 14(20)] Antitranslation, Bz against Py – 736 Bz[13(20)]: Py[26(13), 21(16),14(15)] Bz[39(20), 22(8)]: Py[37(21)] g(NH) Bz[61(18)]: Py[46(16), 11(13)] Bz[34(18)]: Py[55(15), 12(21), 11(14)] g(NH) Bz[60(8), 20(4)]: Py[29(18), 16(21)] Bz[33(18), 11(14)]: Py[36(14), 16(10), 11(2)] – – – 886 Bz[42(11), 41(4)]: Py[–] Bz[48(11)]: Py[70(19), 12(20)] Bz[53(11), 30(19), 12(2)]: Py[–] Bz[38(7)]: Py[31(11), 18(13)] – – 950 – 1016 1100 Bz[19(6), 15(14), 15(17),10(10)]: Py[30(14), 27(12)] Bz[83(19), 16(11)]: Py[–] Bz[61(2), 38(19)]: Py[–] Bz[61(14), 24(6)]: Py[–] Bz[45(14), 23(17), 18(7)]: Py[18(8), 11(7)] 1152 Bz[20(17), 18(10), 11(6)]: Py[34(12)] Bz[33(10), 27(17)]: Py[21(12), 14(9)] 1192 1208 1220 – 1266 1302 1338 – – 1424 1466 Bz[46(17), 18(7)]: Py[12(9)] 1606 1621 1735 1740 Bz[16(17), 14(14), 11(7)]: Py[24(11), 21(10), 18(8)] Bz[28(3), 26(9)]: Py[31(9)] Bz[44(9),39(3)]: Py[12(8), 10(9)] Bz[24(9)]: Py[34(7), 12(8), 11(2)] Bz[81(13)]: Py[38(6)] Bz[80(13)]: Py[–] Bz[94(16)]: Py[31(6), 19(2)] Bz[74(16)]: Py[37(3), 24(7)] Bz[–]: Py[95(5)] Bz[–]: Py[96(4)] Our mode descriptions of the internal vibrations of the monomer are taken from the GAUSSIAN98 output and given with respect to the modes of the parent cycles benzene and pyrrole-2,3-dione, after [24]; Bz[x(y)] implies that this isatin mode has x% of the benzene mode number y [30], similarly for pyrrole-2,3-dione, Py, see Table 2b below (only contributions greater than 10% are shown). 273 J. Tomkinson et al. / Vibrational Spectroscopy 50 (2009) 268–276 so, prevents strong overtones being mistaken for fundamentals. Then, taking the lowest calculated frequency, we search for nearby observed transitions, not only of similar INS intensity but also which possess an appropriate optical character. Thus, for example, if the optical character of the transition identifies it as an Ag mode it can only be associated with a calculated Ag eigenvector. The observed band is thus assigned to a specific ab-initio eigenvector and eigenvalue, we then scale the calculated eigenvalue to equal the observed value, thus each transition has its individual scaling parameter. Above about 1200 cm1 the INS features weaken and become undifferentiable, consequently, in this region, our assignment scheme is mostly dependant on the optical data previously published [12]. The resulting scaled spectrum clearly agrees very well with observation, see Fig. 3, and adds support to the assignments of Table 1. 5.2. Isatin The observed INS spectrum of isatin was compared with the, unscaled, calculated spectrum of the dimer using ACLIMAX, a working value for the (al)ext parameter was found, 0.025 Å´2, which is more typical of organic systems, see above. As was the case for thioindigo, the overall distribution of the calculated bands corresponded well with the observed spectrum. Except, that is, for two strong features calculated at 789 and 812 cm1, these had no immediate counterparts in the observed spectrum. The calculated eigenvectors of both modes showed them to be, predominantly, the out-of-phase and in-phase components of the out-of-plane N–H vibration, g(NH). To emphasise this in ACLIMAX, the N–H hydrogen’s neutron scattering cross-section was set to zero and the observed and calculated spectra again compared. Whilst several features suffered minor intensity loss the 789 and 812 cm1 bands were almost completely eliminated. This left most of the remaining calculated features in convincing register with the observed spectrum. This is shown in Fig. 4 and detailed in Table 2. Working as outlined above, for thioindigo, the calculated frequencies were scaled to those of nearby observed INS features of the same intensity and appropriate optical characters [27]. The scaled results reported in Table 2 are unambiguously assigned, at least below 1200 cm1, and constitute the first reliable assignment scheme for isatin. At the end of this process two observed bands remain to be assigned, at 627 and 686 cm1, these are known to be out-of-plane, A00 , modes from optical work [27] and the region is typical for Fig. 5. A comparison of the observed inelastic neutron scattering spectrum of isatin (green trace) with that calculated for the scaled ab-initio assignment scheme of Table 2 (red trace), NH contributions included. The external mode region appears below 120 cm1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) g(NH) modes. Indeed, the earliest optical work assigned g(NH) at 742 cm1 (misprinted as 724 cm1 in the original table) [28]. This was challenged by latter work, where it was assigned at 670 cm1 (at 300 K), increasing to 690 cm1 (at 110 K) [27] but more recent work has these positions as 681 cm1 (at 300 K), and 700 cm1 (at 80 K) [29]. Clearly the positions of these bands, unlike all other spectral features of isatin, are rather sample dependant and we assign our calculated ungerade g(NH) 812 cm1 band to the observed INS feature at 686 cm1. The discrepancy between the ab-initio g(NH) band position and that observed is due to the overly short N. . .O length found in the dimer calculation. Consequently, the g(NH) frequency should be less than that calculated in the dimer (where it has an average of 801 cm1) but more than in the, non-H-bonded, monomer (where it was calculated at 514 cm1). Correspondingly, the calculated dimer gerade g(NH) mode at 789 cm1, is assigned to the INS band at 627 cm1. The final, scaled, spectrum clearly agrees very well with observation, see Fig. 5, and adds support to the assignments of Table 2. Finally, each vibrational eigenvector of isatin was correlated to its equivalent mode in thioindigo, using ViPA. This result will be Table 2b The mode numbers, n, unscaled calculated eigenvalues, cm1, and brief description of the vibrations of pyrrole-2,3-dione, for use in conjunction with Table 2a. n A0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Calculated frequency (cm1) 3659 3280 3242 1846 1806 1621 1428 1353 1248 1127 1084 1040 794 740 616 555 313 Description n (NH) n (CH) in-phase n (CH) anti-phase n (C(2) O) n (C(3) O) n (C C) d (CH) in-phase, d (NH) anti-phase d (CH), d (NH) – all in-phase n (HC–CO), n (OC–CO), n (OC–N), d (C C–C) d (CH) anti-phase, d (NH) n (C(5)–N), d (CH) n (C(2)–N), d (CH) d (C C–C) n (OC–CO), d (C C–C) d (ring) d (C O) in-phase d (C O) anti-phase n: stretching vibrations; d: in-plane angle bending vibrations; g: out-of-plane vibrations. n Calculated frequency (cm1) Description A00 18 19 20 21 22 23 24 956 827 734 537 454 283 139 g (CH) anti-phase g (C O) anti-phase, g (CH) in-phase g (CH) in-phase g (C O) in-phase g (NH) g (ring), g (NH) g (ring) 274 J. Tomkinson et al. / Vibrational Spectroscopy 50 (2009) 268–276 Table 3 A comparison of the reported infra-red and Raman spectra of indigo with the INS spectrum of this work, in cm1, below 2000 cm1. The mode numbers, n, and results of the GAUSSIAN98 calculations (both DFT and H-F, see text) are also reported. The DFT are unscaled and the H–F values have been scaled by 0.89 [12]. The scaled DFT values, see text, are given under ‘Assigned’. (Where they differ from our assignment, the characters of the optical transitions are given immediately following their wavenumber value.). v0 n x 6 8 8 9 9 7 7 10 10 11 11 12 12 13 14 6 62 7 63 8 9 64 65 10 66 11 67 12 13 69 13 14 15 68 14 15 Ag Bu Ag Bu Ag Ag Bu Bu Ag Bu Ag Bu Ag Ag Bu Bu Bu Ag Ag 15 17 16 16 17 18 18 70 16 17 71 72 18 73 Bu Ag Ag Bu Bu Ag Bu Optical results This work Observed INS Raman ir Raman [12] [12] [13] 1701 1701 1627 1625 1625 1614 1582 1571 1582 1574 1585 1483 1482 1483 1505 1463 1464 1365 1356 1462 1460 1408 1400 1365 1392 1317 1299 1310 1248 1295 1310 1248 1257 1220 1224 1190 1224 1190 1199 1174 1147 74 19 75 Bu Ag Bu 20 20 30 30 21 31 31 20 76 44 30 21 31 45 Ag Bu Bg Au Ag Au Bg 22 22 32 32 33 33 23 23 34 34 35 25 35 24 37 37 24 25 36 26 77 22 32 46 47 33 78 23 34 48 49 79 35 24 36 50 80 25 51 81 Bu Ag Au Bg Bg Au Bu Ag Au Bg Bg Bu Au Ag Au Bg Bu Ag Bg Bu 36 26 27 37 26 82 Au Ag Bu 1182 1147 1128 1121 21 19 19 1220 1139 1128 1105 1096 1097 Bg 1097 Bg 1074 1038 1015 Ag 1090 1012 Bg 1011 1005 989 979 964 970 966 947 940 921 940 921 934 879 868 862 858 797 854 797 765 758 760 788 746 747 699 674 675 716 682 646 637 635 598 597 566 633 600 591 559 588 538 544 542 544 508 508 Assigned DFT H–F 1701 1627 1625 1614 1582 1574 1585 1505 1505 1464 1464 1400 1400 1356 1356 1748 1668 1675 1636 1635 1619 1617 1534 1532 1508 1507 1465 1432 1398 1352 1746 1586 1592 1559 1559 1677 1694 1471 1470 1448 1452 1396 1364 1315 1297 1295 1295 1384 1372 1288 1234 1243 1197 1284 1272 1234 1237 1221 1203 1198 1234 1225 1196 1161 1140 1122 1073 1108 1138 1136 1014 1080 1082 1049 1045 1032 1031 965 998 998 991 987 1056 1056 918 1022 1023 904 883 904 902 822 820 788 780 789 788 753 730 725 698 655 643 613 624 587 582 867 840 933 912 943 865 805 737 805 818 780 692 752 679 643 618 593 606 586 563 577 564 528 535 549 508 g(NH)0-2 1220 1220 1182 1182 1160 1145 1130 – – 1108 1092 1092 – 1005 1005 974 974 965 933 933 – 904 883 856 856 788 788 774 772 748 748 718 718 683 684 655 643 601 630 592 555 – 546 539 505 Table 3 (Continued ) v0 n x Optical results This work Observed ir Raman [12] [12] [13] 38 38 52 38 Bg Au 467 39 39 29 40 29 53 39 27 54 83 28 40 29 41 55 56 42 84 43 Bg Au Ag Bg Bu Ag Au Ag Au Bg Bg Au Bu Au 401 40 41 41 INS Raman 466 427 420 310 275Ag 266 464 424 400 387 312 286 252 244 236 175 129 102 87 72 Assigned 463 424 – 397 384 313 289 280 260 247 236 180 174 129 101 87 71 DFT H–F 484 447 514 449 425 397 312 300 291 255 249 231 170 166 114 88 69 36 428 404 296 294 277 240 250 222 169 163 105 88 71 35 Two mode numbers are given; in the first column, v0 , are the mode numbers of the isatin monomer eigenvectors (see, Table 2) that most nearly correspond to the indigo mode, as numbered in the second column, n. N.B. not all indigo modes have corresponding eigenvectors in the isatin monomer. used, after the assignment of indigo, to correlate isatin eigenvectors to those of indigo. 5.3. Indigo The INS spectrum of indigo is detailed in Table 3. As could be anticipated, the INS spectra of indigo and thioindigo are rather similar (with the exception that bands involving the indigo NH are absent from thioindigo). The same strong features occur in both spectra, typically to within about 30 cm1 of each other. Below about 600 cm1 the thioindigo features appear to lower frequency than the corresponding indigo transitions and above 600 cm1 they appear to higher frequency. Above about 1000 cm1, the influence of the sulfur substitution has lost its impact and the corresponding transitions from the two systems appear in close proximity. This comparison of the two spectra exposed extra intensity in the indigo spectrum at 646 cm1, at 1257, 1352 and 1397 cm1. The first of these corresponds to g(NH)(0–1), which would give rise to a harmonic overtone at about 1292 cm1 (=646  2) but observed here at 1257 cm1. The other features are associated with the in-plane deformation, d(NH), clearly in line with other work [9], where an ir band, about 1394 cm1, was shown to disappear upon indigo’s incorporation into inorganic matrices. The stretching mode region of the indigo spectrum, about 3000 cm1, is quite sharp and strong but is unstructured and a direct analysis, as was done for thioindigo, was not possible. We estimated a value for (al)ext about 0.01 Å´2, similar to, but slightly larger than the heavier thioindigo. The observed spectrum below 50 cm1 was taken as representative of the phonon-wing spectrum. Unfortunately, the unscaled ab-initio INS spectrum of indigo does not compare to the observed spectrum nearly as straightforwardly as did the results for thioindigo and isatin. Attempts to determine scaling factors directly from the comparison were difficult and an indirect approach was adopted. Here, the model compounds’ spectra were used as a guide. Since the INS spectra of indigo of thioindigo are so very similar, we compared the scaled ab-initio spectrum of thioindigo (from Fig. 3) to the INS of indigo, see Fig. 6. This figure enables us to associate an observed band in J. Tomkinson et al. / Vibrational Spectroscopy 50 (2009) 268–276 Fig. 6. A comparison of the observed inelastic neutron scattering spectrum of indigo (black trace) with that calculated for the scaled ab-initio assignment scheme of thioindigo (red trace), Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) the indigo spectrum with candidate eigenvalues in its model compound, thioindigo, and, hence, to candidates in the unscaled ab-initio spectra of indigo. (Candidate eigenvectors were also checked to be consistent with those of isatin.) The final assignment is made by comparing the symmetry of the calculated indigo candidate eigenvector with the optical character of the indigo transition; as was done, above, in the assignments of thioindigo and isatin. In this manner, each indigo transition is associated with a calculated eigenvector (and eigenvalue) and scaling parameters can then be extracted. This rather drawn out process was unambiguous up to 1000 cm1, where two calculated u-g pairs are candidates for two indigo transitions observed at 970 and 1005 cm1. Unfortunately, here, and only here, the optical studies [12,13] have conflicting assignments of the character of the transition about 1014 cm1 (our 1005 cm1 INS band). We have opted to assign this to an in-plane mode. This is in agreement with the earlier optical work [12], consistent with the thioindigo assignments (above) and in best agreement with the distribu- Fig. 7. A comparison of the observed inelastic neutron scattering spectrum of indigo (black trace) with that calculated for scaled ab-initio assignment scheme of Table 3 (red trace). Note the over intense g(NH)(0–1) and (0–2) transitions in the calculated spectrum, which are not reflected in the observed spectrum, see text for details. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) 275 tion of INS intensities. The remaining assignments are given in Table 3. (We disagree with the assigned optical character of only two Raman features, observed at 275 and 1097 cm1, these were assigned Ag [12] and Bg [12,13] respectively but we have them as Bg and Ag.) Above about 1200 cm1 the observed INS features are too indistinct to be reasonably assigned according to their strengths and, here, our assignment scheme relies on the published optical data [12,13]. The INS spectrum of indigo can now be compared directly to its scaled ab-initio spectrum, shown in Fig. 7. The good fit shown in the figure supports the assignments of Table 3. So far we have ignored the N–H vibrations and, as can be seen from Fig. 6, one strong feature of the observed spectrum remains to be assigned. Quite fortuitously, we believe, the calculated g(NH), ca 650 cm1, fall almost exactly on the strong INS band at 646 cm1. The relatively low frequency calculated for g(NH) stems from a hydrogen bonding environment of rather modest strength. The intra-molecular contacts, the only contributions to our ab-initio calculations, show a long N. . .O distance, 2.917 Å´ compared with isatin, 2.876 Å´. This is compounded by a severely non-linear geometry, the N–H. . .O bond is bent at 120.08 (c.f. 168.28 in isatin). In the crystal other hydrogen bonding contacts are present [22] but cannot be as important as the intra-molecular bond. Where the intermolecular contacts are important, however, is in the way they subtly change the atomic displacements involved in the g(NH) mode. As calculated, the eigenvector for this mode is almost purely a hydrogen motion (i.e. an oscillator mass about 1.0 amu), with little movement of other atoms, and it is strong in the calculated spectrum. Its observed strength, about half that of the calculated value, shows that the intermolecular contacts have coupled displacements of other atoms into g(NH). This is also mirrored in the weakness of the observed (0–2) compared with that calculated. From the reduced intensity of the fundamental and the ratio of the fundamental to overtone intensities [15], we estimate the effective oscillator mass to be about 3 amu. The intensities of the in-plane deformation modes, d(NH) about 1375 cm1, are reasonably calculated since they are always found mixed with heavy atom displacements. 6. Discussion The mode numbering scheme of indigo, n, is given in Table 3. Also given there are those mode numbers, v0 , of the isatin monomer whose eigenvectors most nearly correspond to the eigenvectors of indigo. (Several different modes of isatin correlate, to a greater or lesser degree, with any given indigo mode but this information has been severely condensed in Table 3, where only the leading terms are retained, the v0 .) By referring back to Table 2, where the eigenvectors of isatin are described in detail, the approximate form of the indigo eigenvectors can be determined. Those indigo modes which imply little, or no, deformation of the isatin unit correspond to low energy vibrations involving the displacement of isatin monomers against one another. Otherwise, as could be expected, each u–g pair of indigo modes represents the in- and out-of-phase vibrations of a common isatin ‘root’ mode. The indigo mode n44 corresponds to the in-phase vibration of the isatin mode v030 , with indigo n30 corresponding to the out-of-phase vibrations of the same isatin mode (the isatin v030 is defined in Table 2). Thus n30 and n44 involve mostly ‘ring-breathing’ displacements of the benzenoid motifs in indigo (mode ‘2’ is the ring-breathing mode of benzene [30]). In searching for candidate vibrations of indigo that can be used in INS spectroscopy to identify the chemical species present in inorganic matrices (like Maya Blue), two criteria present themselves: the modes must be easily observable and sensitive to different environments. Certainly the INS region above 1200 cm1 276 J. Tomkinson et al. / Vibrational Spectroscopy 50 (2009) 268–276 is not a good frequency range for strong transitions, candidates in this region may be discounted. Transitions at low frequencies can also be rejected, their eigenvalues are likely to be too much influenced by external forces. Such that, in a non-homogenous system like Maya Blue, very broad features are the most likely result. However, ease of observation is not limited to the domain of intense transitions. As can be seen in all the figures there are several strong features about 1100 cm1 but they have strong bands nearby and frequency changes in any one of these features may be masked by its becoming accidentally degenerate with its neighbours. Strong features separated from other strong features would represent better candidates. The assigned spectrum of indigo shows two good candidates in the mid-frequency range, the g(NH) mode and the band at ca. 750 cm1. (The 750 cm1 band is the degenerate composite of the u and g components of a g(C–H) mode of the benzene motif. This is itself a 1:1 mixture of the benzene modes ‘4’ and ‘11’ [30], see Table 2). The g(C–H) and g(NH) bands are both strong and yet isolated from other strong features in the region. However, the g(C–H) mode involves atoms somewhat distanced from the part of the molecule that interacts with its environment. Even if the band were observed it would give little further information than we have at present. This is definitely not the case with the g(NH) mode, so much so, that if dehydro-indigo is the chemical species in Maya Blue [9] then g(NH) will be completely absent and the presence of dehydro-indigo could only be implied rather than observed. However, the two bands, g(C–H) and g(NH), could be used in conjunction to demonstrate and quantify the presence of an indigoid, through g(C–H), and how it interacts with its environment, through g(NH). Any variations in the g(NH) frequency and, or, intensity can then be exploited to study the interaction of the incorporated indigo with its environment. In all probability, the intra-molecular hydrogen bond of indigo will retain some of its character in the matrix and variations in the intensity of g(NH) will indicate how the matrix environment differs from that of its crystal. In the event that the intra-molecular hydrogen bond is ruptured indigo may bond directly, or through water, to the matrix. The modes of intermolecular hydrogen bonds are known to be rather sensitive to the local bonding environment, increasing in frequency as the hydrogen bond length falls [31]. Under these circumstances it is even possible that the g(NH) mode intensity could increase, as the involvement of heavy atoms in the eigenvector is reduced. In contrast, the g(C–H) band will remain almost unchanged by inclusion into the matrix, it will act as an internal standard. Its strength will be a clear indicator of the experimental statistics allowing, say, a judgement to be made as to the statistical relevance of the non-observation of a g(NH) band. These results clearly show that INS spectroscopy will be singularly advantaged in the study of Maya Blue since it, alone of all the molecular vibrational techniques, can readily observe the g(C–H) and g(NH) modes. 7. Conclusions Using inelastic neutron scattering techniques and ab-initio methods, we have extended the measured spectra of isatin, thioindigo and indigo down to the lowest frequencies. We have revised previous calculations and provided sound spectral assignments, below 1200 cm1. We have described the vibrational eigenvectors of indigo in terms of those of its model compound isatin and identified a g(C–H) and the g(NH) modes, used in conjunction, as the best candidates for vibrational features that could be used to determine the nature of the organic residue in Maya Blue and how it might interact with the inorganic matrix. 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