SUPPLEMENTARY MATERIAL

Experimental and theoretical thermodynamic propertiesof RS-()- and S-(+)-mandelic acids.

Vladimir N. Emel’yanenko,a,b* Vladimir V. Turovtsev,c,d Yulia A. Fedina d,e

a Department of Physical Chemistry, University of Rostock, Dr.-Lorenz-Weg 1, 18059 Rostock, Germanyb Department of Physical Chemistry, Kazan Federal University, Kremlevskaya str. 18, 420008, Kazan, Russian Federationc Department of Physics, Mathematics and Medical Informatics, Tver State Medical University, Sovetskaya 4, 170100 Tver, Russian Federationd Department of General Physics, Physics and Technical Faculty, Tver State University, Zhelyabova 33, 170100 Tver, Russian Federatione EAHS DCSD 1701 Mountain Industrial Blvd, Stone Mountain, GA 30083, USA

Table S1Provenance, purity, methods of purification and analysis of chemicals used in this work.

Compound CASWater

content,ppm

SourceInitial mole

fraction purity

Purification

method

Final mole fraction purity a

RS-()-mandelicacid 90-64-2 74.0 Alfa

Aesar 0.99vacuum

sublimation

0.999

S-(+)-mandelicacid 17199-29-0 52.0 Alfa

Aesar 0.99vacuum

sublimation

0.999

a gas chromatography.

Table S2Formula, density (T = 293 K), specific heat capacity cp (T = 298.15 K), and expansion coefficients (V/T)p of the materials used in the present study

Compounds formula cp 10-6·(V/T)p

g·cm-3 J·K-1·g-1 dm3·K-1

RS-()-mandelic acid C8H8O3 1.29 [1] 1.19 a 0.1S-(+)-mandelic acid C8H8O3 1.35 [2] 1.19 a 0.1cotton b CH1.774O0.887 1.50 [3] 1.67 [3] 0.1

a obtained according to the group additivity methodology reported in .S. Chickos, W.E. Acree, Enthalpies of vaporization of organic and organometallic compounds, 1880-2002, J. Phys. Chem. Ref. Data 32 (2003) 519-878.b Energy of combustion cu° (cotton) = -16945.2 J·g-1; u(cu°) = 4.2 J·g-1 from [3].

Table S3Results for combustion experiments at T = 298.15 K (p° = 0.1 MPa) for RS-()-mandelic acid

m (substance) /g 1.159299 1.015193 1.060403 1.093944 1.014358m'(cotton) /g 0.000974 0.000980 0.001087 0.000933 0.001009Tc /K 1.91049 1.67405 1.74899 1.80549 1.67393calor)·(-Tc) /J -28305.9 -24802.7 -25913.0 -26750.1 -24801.0cont)·(-Tc) /J -31.24 -26.76 -28.16 -29.28 -26.79Udecomp HNO3 /J 47.18 46.59 47.78 48.38 42.41Ucorr /J 22.30 19.13 20.11 20.86 19.15-m'·cu' /J 16.50 16.61 18.42 15.81 17.10cu° (cr) /(J·g-1) -24369.1 -24376.8 -24382.1 -24401.9 -24398.8

m (substance) /g 1.010329 0.997008 1.013262 1.093894m'(cotton) /g 0.000847 0.000936 0.000917 0.000933Tc /K 1.66615 1.64428 1.67155 1.80549calor)·(-Tc) /J -24685.7 -24361.7 -24765.7 -26750.1cont)·(-Tc) /J -26.61 -26.27 -26.71 -29.28Udecomp HNO3 /J 43.30 44.79 45.39 48.38Ucorr /J 19.05 18.77 19.10 20.85-m'·cu' /J 14.35 15.86 15.54 15.81cu° (cr) /(J·g-1) -24383.7 -24381.5 -24389.0 -24403.0cu° (cr) /(J·g-1) 24387.3

u(cu°) / J·g-1 3.9a The definition of the symbols are as follow: m(substance) and m'(cotton) are the mass of compound burnt and the mass of cotton thread used in each experiment, respectively, masses were corrected for buoyancy and water content; V(bomb) = 0.32 dm3 is the internal volume of the calorimetric bomb; pi(gas) = 3.04 MPa is the initial oxygen pressure in the bomb; mi(H2O) = 1.00 g is the mass of water added to the bomb for dissolution of combustion gases; Tc = Tf - Ti + Tcorr is the corrected tempera-ture rise from initial temperature Ti to final temperature Tf, with the correction Tcorr for heat exchange during the experiment; cont are the energy equivalents of the bomb contents in their initial i

cont and fi-nal states f

cont, the contribution for the bomb content is calculated with (cont)·(-Tc) =(icont)·(Ti -

298.15) + (fcont)·(298.15 - Tf + Tcorr.). Udecomp HNO3 is the energy correction for the nitric acid forma-

tion. Ucorr is the correction to standard states. b Uncertainties in this table are expressed as the stan-dard deviation of the mean.

Table S4Results for combustion experiments at T = 298.15 K (p° = 0.1 MPa) for S-(+)-mandelic acid

m (substance) /g 0.980151 1.000469 1.019295 1.010429 0.992896 1.021188 1.045039m'(cotton) /g 0.000911 0.00101 0.000839 0.000905 0.001164 0.001127 0.001142Tc /K 1.61610 1.65214 1.68058 1.66769 1.63859 1.68445 1.72396calor)·(-Tc) /J -23944.1 -24478.1 -24899.5 -24708.5 -24277.4 -24956.8 -25542.3cont)·(-Tc) /J -25.74 -26.34 -26.87 -26.65 -26.08 -26.98 -27.67Udecomp HNO3 /J 43.0 37.93 45.39 43.30 45.69 39.72 45.99Ucorr /J 18.42 18.88 19.23 19.05 18.66 19.32 19.79

-m'·cu' /J 15.44 17.11 14.22 15.34 19.72 19.1 19.35cu° (cr) /(J·g-1) -24376.9 -24419.0 -24377.2 -24403.0 -24392.7 -24388.9 -24386.5cu° (cr) /(J·g-1) 24392.0

u(cu°) / J·g-1 5.6a The definition of the symbols is the same as in Table S3.

Table S5G4 calculated H298, Hartree a, and experimental gaseous enthalpy of formation, kJ·mol-1, of participants of bond separation (BS) reactions

compound H298 Δf Hm°

(g) exp

mandelic acid -535.088207 ---o-methoxybenzoic acid -535.075756 -431.91.2 [4]m-methoxybenzoic acid -535.079012 -444.91.2 [4]p-methoxybenzoic acid -535.081249 -449.51.4 [4]ethane -79.733658 -83.80.3 [5]toluene -271.370151 50.11.1 [6]lactic acid -343.453906 -615.91.3 [7]

a 1 Hartree = 2625.499 kJ·mol-1.

Table S6The experimental frequencies of mandelic acid, cm-1

IR [8] Raman [8] IR [9] Raman [9]S-(+)- RS-()- S-(+)- RS-()-

3590 (sh, w) 3531 (vw)3451(w) 3409 (m) 3442 (vw) 3397 3408

3184 (vw) 3172 (vw)3092 (vw) 3070(w) 3106 (vw) 3071 3070

3069 (vw) 3071 (vw) 3061 (m), 3052 (w)

3075(w), 3065(w) 3062 3066

3036 (vw) 3034(w) 3041 (vw) 3049 (vw)3035 (w), 3013 (vw) 3032 3024

2958(w) 2967 (w) 2982 (vw) 2999 (vw), 2973 (vw) 2970 2976

2917 (w) 2925 (vw) 2910 (w)2889 (vw) 28922717 (vw) 27182660 (vw), 2632 (vw)

1723 (vvs) 1713 (vvs) 1714 (vw) 1723 (vw) 1716 1724

1599(sh, w) 1608 (vw) 1605 (m) 1605(w), 1587 (vw) 1601, 1588 1607

1494 (vw) 1500 (w) 1500 (vw) 14981456 (w),

1434 (sh, vw) 1452 (m) 1453

1379 (vw) 13781353 (sh, vw), 1328 (sh, w) 1341 (vw) 1352 (vw)

1308 (w) 1296 (m) 1305 (vw) 1298(vw) 1300 13121268 (w) 1276 (sh) 1288 (vw)1249 (s) 1250 (vw) 1251 (vw) 1256(vw) 1264 1264

1231 (m) 1223 (vw) 1228 12321189 (m) 1191 (m) 1199 (vw) 1194(w) 1193 1196

1178 (vw) 1180(vw) 11671148 (vw) 1157 (vw)1138 (vw)

1098 (m) 1106 (vw) 1093 (vw)1079(vw) 1078

1063 (vs) 1061(vs) 1063 (vw) 1058 (vw) 1064 10621027 (w) 1029(w) 1028 (w) 1028(w) 1030 1033

1001 (sh, vw) 1001 (vw), 990 (vw) 1004 (vvs) 1004 (vvs) 1004 1007

936(m) 944(s) 941 (vw) 934(vw) 941 940908 (sh, vw) 891(s) 908 (vw) 910(vw) 891 880

855 (m) 853 (m) 863 (w) 861 (w) 857 852840 (vw) 842(vw)

770 (w) 768(w) 758 (vw) 769 (vw) 768724 (s) 732(vs) 732 (w) 737(w) 733 736

691 (s) 695(vs), 679(s)

718 (sh, vw) 680 (vw) 698, 686

643 (m) 647 (vw)614 (m) 610(s) 619 (vw) 619 (vw) 617, 609 620592 (w)525 (w) 529(m) 527 (vw)495 (m) 493(m) 497 (vw) 504 (vw) 496 504463 (w) 465(w) 462 (vw) 481 475

389 (vw)347 (vw) 337 (vw) 345326 (vw) 279 (vw) 288

246 (w)192 (w) 220 (vw) 208

169 (w)d) 154(w)124 (vs)117 (vs)

Table S7The anharmonic (anharm) and harmonic (harm) vibrational frequencies of mandelic acid’s conformations (I-V), obtained via B3LYP/6-311++g(3df,3pd) (anharm) and B3LYP/aug-cc-pVTZ (harm), cm–1

I II III IV Vanharm harm anharm harm anharm harm anharm harm anharm harm

3547 3736 3621 3795 3668 3815 3635 3815 3628 38063519 3710 3586 3743 3460 3654 3576 3741 3555 37353076 3194 3066 3198 3062 3192 3053 3191 3056 31923062 3186 3063 3188 3044 3183 3051 3184 3052 31863047 3176 3050 3179 3036 3175 3046 3176 3045 31773039 3166 3046 3170 3030 3168 3043 3167 3035 31683008 3159 3007 3162 3007 3163 3006 3160 3002 31612873 3008 2921 3071 2906 3042 2889 3017 2902 30341766 1792 1790 1814 1811 1842 1799 1830 1776 18031605 1642 1603 1641 1607 1643 1602 1641 1603 16401597 1627 1591 1624 1593 1626 1593 1625 1594 16251510 1529 1502 1529 1501 1530 1499 1528 1495 15281465 1488 1461 1483 1469 1490 1467 1489 1467 14891377 1426 1385 1416 1348 1381 1377 1414 1365 14041344 1372 1335 1361 1333 1368 1356 1377 1349 13771326 1349 1315 1346 1318 1355 1309 1349 1330 13601315 1344 1294 1328 1314 1350 1274 1317 1313 13491284 1307 1255 1287 1268 1304 1270 1301 1271 13011226 1255 1251 1272 1215 1250 1209 1238 1211 12461187 1207 1196 1207 1189 1214 1195 1206 1190 12071176 1197 1177 1191 1185 1205 1182 1200 1172 11991169 1182 1167 1183 1173 1185 1177 1183 1171 11831130 1166 1112 1153 1117 1146 1115 1144 1120 11471098 1120 1091 1109 1094 1110 1089 1108 1091 11121067 1090 1073 1078 1065 1057 1084 1079 1058 10761043 1050 1058 1051 1030 1045 1054 1050 1051 10501041 1022 1042 1021 1030 1022 1041 1022 1038 10221000 1019 1015 1020 1007 1021 1031 1021 1006 1021980 999 997 1005 982 1000 995 1003 981 1003938 952 948 954 942 950 946 954 937 953873 894 866 875 869 887 871 888 858 877856 871 854 869 850 864 861 867 852 867844 862 854 865 847 860 860 864 851 863768 770 759 756 787 781 788 782 775 780733 729 738 738 733 733 741 738 735 746714 715 733 719 721 716 735 717 735 718646 661 649 656 641 698 663 671 660 668628 633 648 634 636 643 648 633 634 634604 626 607 614 623 626 616 622 611 613

553 573 531 576 603 607 573 586 578 596486 501 487 486 517 519 497 499 497 501458 465 448 453 486 489 450 452 450 458408 418 426 417 411 415 422 416 412 416391 410 400 383 353 358 351 357 356 365351 357 382 328 325 334 295 302 275 290301 311 314 280 290 249 194 246 214 255223 232 251 250 264 227 184 225 189 227211 215 203 199 210 199 124 193 182 19980 95 116 111 84 93 108 93 87 9253 55 80 59 36 62 79 47 23 50-19 29 64 28 -43 16 72 33 14 33

Table S8The recommended vibrational frequencies of mandelic acid’s conformations, composed from experimental and calculated spectra, cm-1

I II III IV V3531 3621 3668 3635 36283519 3590 3451 3590 35903071 3066 3062 3061 30613062 3062 3041 3052 30523049 3052 3036 3049 30493036 3049 3032 3041 30353013 3013 3013 3013 29992889 2925 2910 2889 29101723 1790 1811 1799 17761605 1601 1607 1601 16051599 1588 1599 1599 15991500 1500 1500 1498 14941456 1456 1469 1467 14671378 1379 1352 1378 13791341 1341 1328 1353 13521328 1312 1318 1308 13281312 1296 1312 1276 13121288 1256 1268 1268 12681228 1250 1223 1209 12111189 1196 1189 1194 11911178 1178 1180 1180 11721167 1167 1178 1178 11711138 1106 1117 1106 11201098 1093 1093 1093 10931064 1079 1064 1079 10581058 1058 1029 1058 10511033 1042 1028 1033 10331001 1007 1007 1030 1007

990 1001 990 990 990936 944 941 944 936880 863 863 863 857857 855 852 861 852842 853 847 861 852768 758 787 788 770733 737 733 737 736718 732 724 736 736647 649 643 663 660620 647 643 647 643609 609 620 617 610553 529 609 573 578493 481 525 497 497462 448 481 450 450408 426 411 422 412389 400 347 347 347347 389 326 295 279288 279 288 194 246220 246 246 192 208208 208 192 124 19280 117 84 117 8753 59 62 47 5029 28 16 33 33

Table S9Thermodynamic properties of conformation (I) of mandelic acid

T, K HT0 −H0

0 S0 GT0−H 0

0 C p0

298.15 28 419 -97 161300 29 420 -97 161400 47 473 -142 208500 70 524 -192 247600 96 572 -247 278700 125 617 -306 303800 157 658 -370 322900 190 697 -438 3381000 224 734 -509 3511100 260 767 -584 3621200 296 799 -663 3711300 334 829 -744 3791400 372 858 -829 3851500 411 884 -916 391

HT0 −H0

0, GT

0−H 00 - kJmol-1, C p

0 and S in JК-1mol-1

Table S10Thermodynamic properties of conformation (II) of mandelic acid a

T, K HT0 −H0

0 S0 GT0−H 0

0 C p0

298.15 28 412 -95 163300 28 413 -96 164400 47 467 -140 211500 70 518 -189 251600 97 567 -243 283700 126 613 -302 309800 158 655 -366 330900 192 695 -433 3471000 228 732 -505 3621100 264 767 -580 3741200 302 800 -658 3841300 341 832 -740 3931400 381 861 -824 4011500 422 889 -912 408

а HT0 −H0

0, GT

0−H 00, Δf HT

0, Δf GT

0 - kJmol-1, C p

0 and S

0- JК-1mol-1

Table S11Thermodynamic properties of conformation (III) of mandelic acid a

T, K HT0 −H0

0 S0 GT0−H 0

0 C p0

298.15 28 422 -97 160300 29 423 -98 161400 47 475 -143 207500 70 526 -193 246600 96 574 -248 279700 125 619 -308 305800 157 661 -372 326900 190 700 -440 3431000 225 737 -512 3581100 262 772 -587 3701200 299 805 -666 3811300 338 835 -748 3901400 377 865 -833 3971500 417 892 -921 403

а HT0 −H0

0, GT

0−H 00, Δf HT

0, Δf GT

0 - kJmol-1, C p

0 and S

0- JК-1mol-1

Table S12Thermodynamic properties of conformation (IV) of mandelic acid a

T, K HT0 −H0

0 S0 GT0−H 0

0 C p0

298.15 29 422 -97 155300 29 423 -98 156400 47 474 -143 197500 68 522 -193 232600 93 567 -247 262700 120 609 -306 286800 150 648 -369 307900 181 686 -436 3241000 215 721 -506 339

1100 249 753 -580 3521200 285 784 -657 3631300 322 814 -736 3721400 359 842 -819 3811500 398 868 -905 388

а HT0 −H0

0, GT

0−H 00, Δf HT

0, Δf GT

0 - kJmol-1, C p

0 and S

0- JК-1mol-1

Table S13Thermodynamic properties of conformation (V) of mandelic acid a

T, K HT0 −H0

0 S0 GT0−H 0

0 C p0

298.15 30 425 -97 170300 30 426 -98 171400 49 481 -143 216500 73 534 -194 253600 100 583 -250 284700 129 628 -310 308800 161 671 -375 328900 195 710 -444 3441000 230 747 -517 3561100 266 782 -594 3661200 303 814 -673 3751300 341 844 -756 3821400 379 873 -842 3871500 418 900 -931 392

а HT0 −H0

0, GT

0−H 00, Δf HT

0, Δf GT

0 - kJmol-1, C p

0 and S

0- JК-1mol-1

Figure S1. The melting curve for RS-()-mandelic acid

Figure S2. The melting curve for S-(+)-mandelic acid

Figure S3. The stable conformations of mandelic acid, gas phase.

References

[1] H.A. Rose, Crystallographic data. 61. dl-Mandelic acid, Anal. Chem. 24 (1952) 1680–1681. DOI: 10.1021/ac60070a065.[2] A.O. Patil, W.T. Pennington, I.C. Paul, D.Y. Curtin, C. E. Dykstra, Reactions of crys-talline (R)-(-)- and (S)-(+)-mandelic acid with amines. Crystal structure and dipole moment of (S)-mandelic acid. A method of determining absolute configuration of chiral crystals, J. Am. Chem. Soc. 109 (1987) 1529-1535.[3] S.P. Verevkin, Thermochemistry of phenols: quantification of the ortho-, para-, and meta-interactions in tert-alkyl substituted phenols, J. Chem. Thermodyn. 31 (1999) 559-585.[4] S.P. Verevkin, Dz.H. Zaitsau, V.N. Emel’yanenko, E.N. Stepurko, K.V. Zherikova, Ben-zoic acid derivatives: Evaluation of thermochemical properties with complementary experi-mental and computational methods, Thermochim. Acta 622 (2015) 18–30.[5] B. Pedley, R.D. Naylor, S.P. Kirby, Thermochemical data of organic compounds, Springer Netherlands, 1986.[6] M.V. Roux, M. Temprado, J.S. Chickos, Y. Nagano, Critically evaluated thermochemical properties of polycyclic aromatic hydrocarbons, J. Phys. Chem. Ref. Data 37 (2008) 1855-1996.[7] V.N. Emel'yanenko, S.P. Verevkin, C. Schick, E.N. Stepurko, G.N. Roganov, M.K. Georgieva, The thermodynamic properties of S-lactic acid, Russ. J. Phys. Chem. A 84 (2010) 1491-1497. [8] H.M. Badawi, W. Förner, Analysis of the infrared and raman spectra of phenylacetic acid and mandelic (2-hydroxy-2-phenylacetic) acid, Spectrochim. Acta 78 (2011) 1162-1167.[9] H.W. Badawi, W. Förner, S.A. Ali, A Study of the solvent dependence of the structures and the vibrational, 1H and 13C NMR spectra of l- and dl-mandelic acid and l- and dl-3-phenyllactic acid, J. Mol. Struct. 1093 (2015) 150-161.