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Ind. Eng. Chem. Res. 2004, 43, 7618-7621
GENERAL RESEARCH Estimation of Melting Points of Organic Compounds Akash Jain,* Gang Yang, and Samuel H. Yalkowsky College of Pharmacy, University of Arizona, 1703 E. Mabel Street, Room 441, Tucson, Arizona 85721
A combination of additive group contributions and nonadditive molecular parameters is employed to estimate the normal melting points of 1215 organic compounds. The melting points are calculated from the ratio of the total phase change enthalpy and entropy of melting. The total phase change enthalpy of melting is calculated from the enthalpic group contributions, whereas the total phase change entropy of melting is estimated using a semiempirical equation based on only two nonadditive molecular parameters. The average absolute error in estimating the melting points of these organic compounds is 33.2 K. This is a relatively low value considering the wide range of pharmaceutically and environmentally relevant organic compounds included in this data set. Introduction
∆Hm )
Melting point is one of the most widely used fundamental physical properties. It finds applications in chemical identification, purification, and calculation of a number of other physicochemical properties such as vapor pressure and aqueous solubility. A quick estimation of the melting point can be a useful tool in the absence of experimental data. A number of methods have been used for the estimation of melting points. These methods are based on either group contribution methods1-3 or physical and structural molecular parameters such as molecular cohesiveness, bulkiness, hydrogen-bonding parameters, and geometric factors.4-7 Recently, Katritzky et al.8 discussed a variety of melting point correlation and prediction methods. Zhao and Yalkowsky9 applied a combined approach of group contribution and nonadditive molecular parameters to estimate the melting points of aliphatic compounds. In this study, a similar combined approach is applied to predict the melting points for a database of more complex organic compounds. Theory
∑nimi
(II)
where ni is the number of times a group i appears in a compound and mi is the contribution of group i to the enthalpy of melting. The entropy of melting of an organic molecule is the sum of its positional, rotational, and conformational entropies. During the process of melting, the total entropy of melting mainly consists of the rotational and conformational components, with the positional entropy change being insignificant because of a very small increase (10-15%) in volume. Dannenfelser and Yalkowsky10 found that two nonadditive molecular parameters can be used to account for the rotational and conformational entropies. The rotational entropy is related to the rotational symmetry number (σ), whereas the conformational entropy is related to the molecular flexibility number (Φ) of a compound. The total entropy of melting, ∆Sm (J/K‚mol), can be estimated by the semiempirical equation of Dannenfelser and Yalkowsky:10
∆Sm ) C - R ln σ + R ln Φ
(III)
The free energy of transition is equal to zero at equilibrium. The transition temperature is therefore related to the enthalpy (∆Htr) and entropy of transition (∆Str) by the following relationship:
where σ represents the number of positions into which a molecule can be rotated that are identical with a reference position and Φ indicates the molecular flexibility. The molecular flexibility is an exponential function of the chain length and can be calculated by
Ttr ) ∆Htr/∆Str
Φ ) 2.435SP3+0.5SP2+0.5RING-1
(I)
The enthalpy of melting of an organic molecule is assumed to be dependent upon the interactions between its molecular fragments and therefore can be calculated by the summation of its constituent group values.9 The total phase change enthalpy of melting, ∆Hm (kJ/mol), can be calculated by * To whom correspondence should be addressed. Fax: (520) 626-4063. E-mail:
[email protected].
(IV)
where SP3 is the number of nonring, nonterminal sp3 atoms such as CH2, CH, C, NH, N, O, and S, SP2 is the number of nonring, nonterminal sp2 atoms such as dCH, dC, dN, and CdO, and RING represents the number of single or fused aromatic ring systems.11 For aliphatic cyclic compounds such as cyclopentane and cyclohexane, the flexibility was estimated by
Φ ) 2.435SP3+0.5SP2-3
10.1021/ie049378m CCC: $27.50 © 2004 American Chemical Society Published on Web 10/13/2004
(V)
Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7619 Table 1. Group Contribution Values (mi) and Occurrence (n) for the Enthalpy of Melting (kJ/mol)a molecular fragments
mi(X)
freq
mi(Y)
freq
mi(YY)
1.183 3.000 0.636 1.39 0.924 (0.673) -1.064
-OH -O-
4.619 2.133
252 6.086 80 4.118
84 74 2.484
-CHO >CdO >CdS -C(dO)O-C(dO)OH
5.815 4.571 10.118 5.962 9.487
9 25 3 55 129
4.174 2.599
3 10 4.789
7.391 11.931
53 60
-NH2 -NH>NdN-CN >N-C(dO)H -NO -NO2 -NHC(dO)NH2 -NHC(dO)NH-NC(dO)NH2
5.157 5.106 2.579 5.331 6.005 9.065 (-2.189) 4.768 17.686 18.043 18.538
5.8 4.687 3.202 1.464 5.333
66 21 4.189 40 (1.319) 15 16
-F -Cl
0.38 2.484
-SH -S>SdO -S(dO)dO-S(dO)(dO)O-
1.815 3.488 7.531 9.762 (0.471)
22 (3.779) 44 4.741 1 5 2.503 2
-PO4 -P(dS)O3 -P(dS)SO2 -P(dO)O2-
5.828 7.128 3.583 8.32
1 10 5 3
a
25 12 9 9 27 1 6 88 7 5 2
2.688 2.365 (0.695) 1.111
309 267 104 62
2.147 -4.207
81 4
4.896
101
141 2.134 146 3.279
88 385
molecular fragments
Carbon Increments tCH 2.834 19 tC(0.454) 17 dCd -3.021 20 Car Cbp CHar (-0.0721) 16 Cbr
-CH3 -CH2>CH>C< dCH2 dCHdC
NC(dO)NH8 >NC(dO)N< 6 -C(dO)NHCdO-C(dO)(N-)CdO-CH(dN)>CdN-CHdNOH >CdNOH Nar NHar
14.733 7.335 11.173 10.239 7.396 1.49 10.622 (3.977) 2.58 8.636
Halogen Increments -Br -I
4.125 5.877
55 3.751 4 4.473
Sulfur Increments -SSdO10 -SO2NH2 -SO2NH-SC(dO)N< Sar
9.465 8.49 5.993 11.083 2.915
1 3 5 2 20
Phosphorus Increments -P(dS)O2-P(dS)SO-P(dO)
