Ind. Eng. Chem. Res. 1994,33,1405-1409
1406
CORRELATIONS Group Contribution Methods for Predicting the Melting Points and Boiling Points of Aromatic Compounds Pahala Simamora and Samuel H. Yalkowsky’ Department of Pharmaceutical Sciences, College of Pharmacy, University of Arizona, Tucson, Arizona 85721
Simple methods are proposed to estimate the boiling points and the melting points of aromatic compounds from chemical structure. The transition temperatures are determined by the estimation of both the enthalpy and the entropy of transition. The enthalpies of boiling and melting are both estimated as additive constitutive properties. The entropy of boiling is assumed to be constant as described by Trouton’s rule, while the entropy of melting is estimated using a modification of Walden’s rule. The latter utilizes the nonadditive nonconstitutive molecular property, rotational symmetry.
Introduction The two physical properties of organic compounds that are most frequently measured are melting point (T,) and boiling point (Tb). These properties are of importance in the design of new organic compounds and in some industrial processes since they are the factors that primarily control solubility and vapor pressure. Despite the enormousamount of available melting point and boiling point data, there are very few useful general means for quantitatively relating the melting and/or boiling points of a compound to its chemical structure. Most of the work in the prediction of the phase transition temperature of compounds has been focused mainly on boiling point estimation (Rechsteiner, 1982;Balaban et al., 1992; Stanton et al., 1992). There are only a few methods which have been proposed to estimate melting points. Most of the methods that are available were developed mainly from small data sets and can be used to predict only certain classes of organic compounds (Deardenand Rahman, 1988;Tsakanikas and Yalkowsky, 1987;Abramowitz and Yalkowsky, 1990,1990). The work of Joback and Reid (1987)is a notable exception. Recently we proposed simple group contribution methods to predict the boiling points and melting points of rigid organic aromatics (Simamora and Yalkowsky, 1993; Simamora et al., 1993). It was found that the boiling temperatures can be estimated simply by using molecular fragment values. Melting point prediction, on the other hand, requires the aid of rotational symmetry (a nonadditive nonconstitutive property) in order to get a more accurate estimation. In the present study, we expand the applicability of the previous methods (Simamora et al., 1993) with the introduction of additional parameters from which a large variety of structurally diverse organic aromatics and heterocycles can be estimated.
Theoretical Background The thermodynamics of phase transition can be described by the following generally known equation:
* Author to whom all correspondence should be addressed. 0888-588519412633-1405$04.50/0
AG, = AH, - T,AS, (1) where AG, is the free energy of transition, AHHt,is the enthalpy of transition, Tt, is the phase transition temperature in kelvin, and AS, is the entropy of transition. The free energy of transition is equal to zero at T,, where the system is at equilibrium. Therefore, the equilibrium phase transition temperature is dependent upon the enthalpy of transition and the entropy of transition, i.e.,
Ttr = AHtrlAStI (2) For non-hydrogen bonding rigid organic compounds the entropy of vaporization follows Trouton’s rule, i.e.,
Ash = 88 J/(K mol)
(3) The entropy of melting of aromatic molecules can be calculated by the modification of Walden’s rule proposed by Dannenfelser et al. (1993). The modified Walden’s rule utilizes the rotational symmetry of the molecules, u, which is defined as the number of orientations of the molecule that are indistinguishable from some reference positions. Thus, ASm= 56.5 - R ln(u) J/(K mol)
(4)
where R is the universal gas constant, 8.314J/mol. In this study, methyl, mercapto, hydroxy, and primary amine groups are assumed to be freely rotating and radially symmetrical. Polyatomic groups such as cyano and nitro are treated as mono-substituted groups that are coplanar with the aromatic ring. It is assumed that the enthalpies of transition of the organic compounds are dependent upon the interactions between the various molecular fragments and are therefore equal to the summationof the molecular descriptor values. The molecular descriptors represent the molecular fragment values and correction factors for their interactions.
A”, = x n i b i
(5)
and
AHH,= &mi where ni is the number of times the molecular descriptor i appears in the compound, bi is the contribution of 0 1994 American Chemical Society
1406 Ind. Eng. Chem. Res., Vol. 33,No. 5, 1994
molecular descriptor i to the enthalpy of boiling, and mi is the contribution of that descriptor to the enthalpy of melting. Incorporating eqs 3 and 5 or eqs 4 and 6 into eq 2 gives
-
T,,= ),nrb, 88
(7)
and nimi 56.5 - 19.1 log(a) respectively. Some examples of melting and boiling point calculations using eqs 7 and 8 are given in the Appendix.
Experimental Section Physical Property Data Set. A data base containing melting and boiling points, molecular weight, molecular descriptors, etc. was developed in dBase I11software using an IBM PC compatible computer. The melting point data set consists of more than 1600 compounds, and the data set for the normal boiling points (measured at 1 atm) consists of more than 400 compounds. The data were compiled from several sources (Lide, 1991;Budavary et al., 1989; Aldrich catalog, 1992; Rordorf, 1989; Ultra Scientific, 1988). The compounds considered in this study are substituted aromatic including heterocyclic compounds. The substituents used are the non-hydrogen bonding and single hydrogen bonding groups that were used in the previous study (Simamora et al., 1993) (i.e., halogens, methyl (CHs), methylene (CHz), nitro (Nod, aldecyano (CN), hydroxyl (OH), primary amine (“21, hyde (CHO), amide (CONHz), and carboxyl (COOH) groups). Several new molecular fragments are added. keto (CO), carboxyl ester These are ether oxygen (01, (COO),sulfur (S),sulfoxide (SO),sulfone (Sod,mercapto (SH), secondary amine (NH), thiocyanate (SCN), and isothiocyanate (NCS). Molecular Descriptors. The fragmentation schemes for the boiling point and melting point predictions employed in this study follow the designations previously described (Simamora et al., 1993). The molecular descriptors consist of the molecular fragments and the correctionfactors. Groups attached to one or two sp2atoms are denoted by the prefix “Y” or “YY”, respectively. The prefix RYY is used to describe the YY groups which are in a ring. CBIP is assigned for carbons that are involved in non-ring sp2-sp2 and s p 2 - s ~linkages, e.g., sp2 carbon having substituents such as phenyl, nitro, aldehyde, cyano, carboxyl, amide, thiocyanate, and keto groups. Table 1 and Figure 1 summarize the different groups considered in this study and their designations. For this study CBR (bridgehead sp2 carbon) is treated as CAR (sp2 carbon). Two correction factors previously described (Simamora et al., 1993)are employed in this study. Those are IHB and OBIP correction factors. Some examples of the correction factors used in this study are shown in Figure 2. Statistical Analysis. The statistical analysis of the data was performed using the statistical analysis system (SAS)subroutine PROC REG (1985)on the University of Arizona VAX. The r (correlation coefficient) and s (standard error) values were used as a measure of correlation for the equations developed. However, in selecting the best model emphasis was placed upon reducing the standard error. The T values were used in order to determine the significanceof each group value toward the whole equation
Table 1. Description and Designation of the Molecular Descriptors description CAR CBR CHAR CBIP NAR Y-F Y-Cl Y-Br Y-I Y-CH3 Y-NO2 Y-CN Y-NCS Y-SCN Y-OH Y-NH2 Y-CONH2 Y-COOH Y-CHO Y-SH YY-O YY-s YY-so YY-so2 YY-CO YY-COO YY-NH YY-CH2 RYY-0 RYY-S RYY-SO RYY-SOz RW-CO RYY-COO RW-NH RW-CHz IHB-4 IHB-5 IHB-6 IHB-7 OBIP
designation sp2 carbon bridgehead sp2 carbon sp2 C-H carbon involved in ep2-sp2 and sp%p linkages sp2 nitrogen fluorine atom attached to an ep2carbon chlorine atom attached to an sp2 carbon bromine atom attached to an sp2 carbon iodine atom attached to an sp2 carbon methyl group attached to an sp2carbon nitro group attached to an sp2 carbon cyano group attached to an sp2carbon NCS group attached to an sp2 carbon SCN group attached to an spa carbon hydroxy group attached to an sp2 carbon amino group attached to an sp2 carbon amide group attached to an ep2 carbon carboxyl group attached to an sp2 carbon aldehyde group attached to an sp2carbon mercapto group attached to an sp2 carbon oxygen atom attached to two sp2carbons sulfur atom attached to two sp2 carbons sulfoxide group attached to two sp2 carbons sulfone group attached to two sp2 carbons keto group attached to two sp2carbons carboxyl group attached to two sp2carbons NH group attached to two sp2carbons methylene group attached to two sp2 carbons YY-O atom in a ring YY-S atom in a ring YY-SO group in a ring YY-SO2 group in a ring YY-CO group in a ring YY-COO group in a ring YY-NH group in a ring YY-CH2 group in a ring four-membered ring intramolecular hydrogen bonding five-membered ring intramolecular hydrogen bonding six-membered ring intramolecular hydrogen bonding seven-membered ring intramolecular hydrogen bonding substituent present in biphenyl at the 2,2’,6, and/or 6’positions
developed. Each T value is calculated from the ratio of the parameter estimate to the standard error. All Tvalues less than 4 are considered to be insignificant.
Results The group values for the enthalpy of transition are estimated from the product of the temperatures and the entropy terms using the multiple regression analyses program in SAS (1985). The group contribution values for the enthalpies of melting and boiling, mi and bi, are summarized in Table 2. Those mi and bi having T values less than 4 are enclosed in parentheses and are considered to be insignificant. The data set used in this study consists of structurally diverse aromatic compounds ranging from simple benzene to heterocyclic compounds and polycyclic aromatics with a wide range of melting point, boiling point, and symmetry values. The results of the regression analyses for the melting point and boiling point are summarized in Table 3. The melting point regressiongives a standard deviation of 37.45 K and an r value of 0.9957 for over 1600 compounds. The boiling point regression gives a standard deviation of 17.62 K and an r value of 0.9994for over 400 compounds.
Ind. Eng. Chem. Res., Vol. 33, No. 5,1994 1407 CHAR
CBlP
I
I
CAR
I Y1 -
-F -CI - Br
I
-I
CBR CBlP
NAR
-CH3 -OH - NH2 - SH - SCN
-CHO -NCS
i i
/ I
-coo
RYY
CAR
- NO2 - COOH - CONHZ - CN
CAR YY
CBlP W
C?R
Y2 -
/
CHAR
'
-s
- CH2 - so __ - so2 - OCO - NH
'
RYY
Figure 1. Designation of the molecular fragments used in this study.
R IHM
o* An
00
00
OBlP
Figure 2. Correction factors considered in this study.
Discussion It can be seen from Table 2 that the values of mi and bj tend to increase with increasing hydrogen bonding,
Table 2. Contribution Values to the Heat of Transitions and Correction Factors (kJ/rnol) freq of use no. of compd Param CAR CHAR CBIP NAR Y-F Y-CI Y-Br Y-I Y-CHs Y-NOz Y-CN Y-NCS Y-SCN Y-OH Y-NH2 Y-CONH2 Y-COOH Y-CHO Y-SH YY-0 YY-s YY-CO YY-so YY-so2 YY-NH YY-CH2 YY-coo RYY-0 RYY-S RYY-CO RYY-SO RYY-SO2 RYY-NH RYY-CHz RYY-COO IHB-4 IHB-5 IHB-6 IHB-7 OBIP
Tm
Tb
5789 1172 8305 2083 1291 164 325 97 72 60 1424 228 490 119 167 21 752 318 631 50 37 12 1 5 4 1 238 46 240 54 16 3 155 3 34 16 3 2 18 5 10 3 51 7 6 1 8 1 11 2 18 4 5 1 166 8 21 5 146 4 2 0 6 0 8 2 46 18 17 2 42 4 182 45 154 3 24 1 199 8
Tm
Tb
mi
1619 1652 993 268 37 533 294 92 494 430 35 4
413 436 127 75 29 126 87 18 194 45 12
(0.097) 1.94 -2.14 3.46 1.95 3.40 3.90 4.44 2.60 7.28 8.20 8.78 4.61 7.11 6.52 14.97 14.69 7.73 7.73 -5.43 -3.86 2.19 (0.03) (1.16) (-1.74) -5.11 (-0.77) 2.49 2.69 4.27 7.65 10.88 6.92 2.19 8.96 3.96
5
1 1
238 241 16 156 34 3 18 10 52 6 8 11 18
46 54 3 3 16 2 5 3 7 1
5
1 8
126 19 86 2 6 8 29 17 41 146 134 21 100
1 2
4 4 3 0 0 2 9 2 4 36 3 1
8
-1.11 -1.82
-2.61 -1.19
Table 3. Regression Analysis for Boiling Point Melting Point ( Tm) estimation n r
Tb (eq 7) T, (eq 8)
444 1690
0.9994 0.9957
bi -0.704 5.67 -4.98 6.15 5.89 9.33 10.96 13.63 8.04 13.11 11.61 15.10 16.86 11.61 13.05 18.46 17.07 11.22 11.54 -9.64 -5.35 3.39 (-1.38) (2.04) -7.23 -8.77 (-0.80) 6.11 6.82 7.81 0 0 9.98 6.13 16.70 4.81 -1.42 (-0.88) (-2.36) (-1.63)
(n)and s
17.62 37.45
dipole moment, and molecular size (or polarizability) of the substituents. Hydrogen-bonding-groups tend to have higher mi and bi than the non-hydrogen-bonding substituents. The amide and carboxylic acid group have the highest mi and bi values. This is consistent with their greater ability to interact intermolecularly. Non-hydrogenbonding substituents containing nitrogen, sulfur, or oxygen, e.g., nitro, cyano, thiocyanate, or isothiocyanate, also tend to have higher enthalpic values compared to similar sized groups without those atoms. This is probably due to their large dipole moments. In the halogen series iodine possesses the highest heat of transitions followed by bromine and chlorine. Fluorine has the lowest group value. The differencesobserved in the halogen (allof series which have similar dipole moments) is likely due to the greater polarizability of the larger atoms. In general, the boiling points of organic molecules can be predicted quite well by using only additive constitutive molecular properties, i.e., molecular descriptor values. This is due to the fact that the entropy of vaporization for organic molecules is roughly constant (88J/(K mol)), and
1408 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994
the boiling points are mainly affected by the enthalpic term in eq 7. Anything that can increase the enthalpic term would increase the boiling point. The additive enthalpy of boiling is responsible for the success of the various group contribution schemes (Rechsteiner, 1982). Generally, organic isomers have relatively close boiling temperatures, e.g., the boiling points of 0 - , m-, and p-dichlorobenzenes are 179,173,and 174 "C, respectively. Again, the similarity in boiling point values holds well for almost all organic isomers. Since intramolecular hydrogen bonding of a group reduces its ability to form intermolecularhydrogen bonds, it would be expected that all IHB correction factors would be negative. This is observed for IHB-5, IHB-6, and IHB-7 with the values becoming more negative with increasing ring size. As indicated above, the values enclosed in parentheses are not statistically significant. Surprisingly, the IHB-4 gives a very significant positive contribution to both the melting and boiling points. The positive contribution is due to the ability of the IHB-4 to form a reinforced intermolecular hydrogen bond; e.g., two molecules of 2-hydroxypyridine, benzoic acid, and benzamide can form a dimer held together by parallel hydrogen bonds. This type of hydrogen bonding is more favorable than the formation of a four-membered intramolecular hydrogen bonded ring. The OBIP parameter gives a significant negative contribution to the melting point, but not to the boiling point. Although the two phenyl rings of the biphenyl are planar, the presence of substituent(s) at the 2,2', 6, or 6' alters the dihedral angle of the two phenyl rings. This nonplanarity reduces the packing efficiency of the molecules in the crystal, which in turn decreases the melting point. The insignificance of the OBIP parameter to the boiling point is consistent with the larger separation between the molecules in both the liquid and the gas. Unlike boiling point, which can be predicted quite easily by simply using additive constitutive properties, melting point is difficult to estimate. This is evidenced by the fact that organic isomers generally have different melting points, e.g., 0-, m-, and p-dichlorobenzenes have melting points of -18, -24, and 56 "C, respectively. In general, it is known that the more symmetrical the organic isomer the higher its melting point. This phenomenon has been observed as early as 1882 (Carnelley, 1882). However, it was not quantitated. The difference in melting points for different isomers is due to the fact that the melting temperatures are affected not only by the enthalpy of melting but also by the entropy of melting. Therefore, there are two structure-dependent factors that affect the melting temperature (see eq 8). The enthalpy of melting like the enthalpy of boiling is additive. However, the nonconstant entropy of melting term differentiatesmelting point estimation from boiling point estimation. Since both terms have to be considered in melting point prediction, group contribution schemes reflecting only one of the terms (e.g., the enthalpy of fusion) cannot give a good estimation. Our previous study (Simamora et al., 1993)shows that the use of the nonadditive nonconstitutive property, rotational symmetry, helps in distinguishing the more symmetrical isomers which melt higher from the less symmetrical ones. The rotational symmetry, Q, as discussed by Dannenfelser et al. (1993), accounts for the statistical likehood of finding a molecule properly oriented for incorporation into the crystal. The more symmetrical the compound the higher its probability of incorporation into crystal, and the higher its melting point. Table 4 presents an interesting phenomenon observed
Table 4. Comparison between mi Values of the Ring and Non-Ring Grows environment mOUD YY RYY diff, kJ/mol -5.43 2.49 7.92 0 -3.86 2.69 6.55 S (-1.74) NH 6.92 8.66 (0.03) 7.65 7.62 so (1.16) 10.88 9.72 so2 -5.11 2.19 7.30 CH2 (-0.77) 8.96 9.73 coo 2.19 co 4.27 2.08 Table 5. Comparison of Melting and Boiling Point Estimations std error n Joback and Reid (1987) this studv T, 1660 69.32 37.52 Tb 440 42.80 17.62 ~
~~~~
in this study. It is noticed that the difference between the mi values for most groups is roughly 8.2 kJ/mol (ranging from 6.55 kJ/mol for sulfur to 9.73 kJ/mol for COO). Interestingly, the difference in mi between RYY-CO and YY-CO for the carbonyl group is only 2.08 kJ/mol. The difference in mi values between the RYY and the YY groups results from the different environment for which the groups are located. The groups that are in the ring (RYY)are part of a somewhat planar and rigid system. Such molecules tend to pack efficiently in the crystal and have high melting points. On the other hand, compounds which have YY groups that are sp3 hybridized are usually flexible and comparatively low melting. The small difference in mi between RYY-CO and YYCO is believed to be due to the fact that aromatic rings on the same carbonyl group are in resonance with each other and are thus likely to be coplanar and relatively rigid. Since the rigidity and flexibility of the YY-CO compounds and of the RYY-CO compounds are somewhat similar, it is reasonable that the mi values for these groups are similar. Just as the difference in mi values of the ring and non-ring carbonyl groups is smaller than for the others, the difference between the mi values for the ester group is larger than the average. This is because the two aromatic groups joined to a non-ring ester group are separated by two atoms which gives them a greater degree of flexibility than the aromatic rings connected to a single atom. Interestingly, the net dipole moment does not play an important role in determining the melting point. It would be expected that the higher the dipole moment of an isomer the higher its melting point since dipole moment is one of the factors directly controlling the melting point. In fact,p-dichlorobenzene, which has zero net dipole moment, melts higher than its less symmetrical isomers, which have greater net dipole moments. Apparently, the sum of the local dipole moments has a more pronounced effect than the net dipole moment on melting point. This is due to the close distance between molecules in the crystal. The molecular interactions taking place are mostly due to the interaction between local dipole moments of neighboring atoms or groups. Table 5 presents the comparison between the proposed methods and those of Joback and Reid (1987) to estimate T, and Tb. The compounds employed in the data set for comparison are from the data set used in this study excluding Y-SCN, Y-NCS, SO, and SO2 groups. These groups were excluded because Joback does not have values for them. It is clear from Table 5 that our methods give better
Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 1409 estimates. There are several reasons for this: (1)the data set used in this study consists of only aromatic compounds; (2) we distinguish the environment for which the group is attached, i.e., Y, YY, and RYY; (3)the use of rotational symmetry in the melting point prediction enables the technique to recognize the more symmetrical molecules. The effect of sp3 environment (aliphatic compounds) on the melting and boiling points will be discussed in a forthcoming report.
Summary We have proposed methods to predict the melting and boiling points of organic compounds from their chemical structures. The boiling points can be predicted simply by the additive constitutive molecular fragment values. The melting point estimation is accomplished by the addition of the nonadditive nonconstitutive property, rotational symmetry. The melting point point equation is developed from a data set containing 1690aromatic compounds which gives a standard error of 37.45 K. The boiling point equation has been shown to estimate the boiling points of 444 compounds with a standard error of 17.62 K. Acknowledgment Financial support for this research was provided by the Environmental Protection Agency (EPA), Grant No. R817475-01. The contents of this paper do not necessarily reflect the views and policies of the EPA. Appendix Some examples to illustrate the estimation of melting point and boiling point using the methods developed in this study are presented below. The group values are taken from Table 3 and then substituted in eqs 7 and 8 to get the boiling point and melting point in kelvin. 1. p-Dichlorobenzene: a=4 CHAR = 4 CAR = 2 Y-c1= 2 calculated T, = [(4 X 1940) + (2 X 97) + (2 X 3400)1/ [56.5 - 19.1 l0g(4)] = 327.9 K observed T, = 326.1 K
error = 1.8 K
+
calculated Tb = [(4 X 5670) - (2 X 704) (2 X 9330)1/88 = 453.8 K observed Tb= 448 K 2. 2-Chlorobiphenyl:
error = 5.8 K
a = l
CHAR = 9 CAR = 1 CBIP = 2 Y-c1= 1 OBIP = 1 calculated T, = [(9 X 1940) + (97) - (2 X 2140) + (3400) - (1190)]/[56.5 - 19.1 l0g(1)] = 274.1 K
observed T, = 307 K calculated Tb = [(g
X
error = 32.8 K
+
5670) - (704) - (2 X 4980) (9330) - (1630)]/88 = 546.2 K
observed Tb= 547 K
error = 0.8 K
Supplementary Material Available: Tables containing all compounds with their symmetry numbers, observed/calculated boiling and melting point values (in kelvin), and residues (46 pages). Ordering information is given on any current masthead page. Literature Cited Abramowitz, R.; Yalkowsky, S. H. Melting Point, Boiling Point, and Symmetry. Pharm. Res. 1990a, 7,942-947. Abramowitz, R.; Yalkowsky, S. H. Estimation of Aqueous Solubility and Melting Point of PCB Congeners. Chemosphere 1990b,21, 1221-1229. Aldrich: Catalog Handbook of Fine Chemicals; Aldrich Chemical Co.: Milwaukee, WI, 1992. Balaban, A. T.; Kier, L. B.; Joshi, N. Correlations Between Chemical Structure and Normal Boiling Points of Halogenated Alkanes C1C4. J . Chem. Znf. Comput. Sci. 1992,32,233-237. Budavary, S., ONeil, M. J., Smith, A., Heckelman, P. E., Eds. The Merck Index: An Encyclopedia of Chemicals, Drugs, and Biologicals; Merck and Co., Inc.: Rahway, NJ, 1989. Carnelley, T. Chemical Symmetry, or The Influence of Atomic Arrangement on the Physical Properties of Compounds. Philos. Mag. 1882,13,112-130. Dannenfelser, R. M.; Surendren, N.; Yalkowsky, S. H. Molecular Symmetry and Relatad Properties. SAR QSAR Enuiron. Res. 1993,1,213-292. Dearden, J. C.; Rahman, M. H. QSAR Approach To the Prediction of Melting Points of Substituted Anilines. Math. Comput. Model. 1988,11,843-846. Joback, K. G.; Reid, R. C. Estimation of Pure-Component Properties From Group-Contributions. Chem.Eng. Commun. 1987,57,233243. Lide, D. R. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1991. Rechsteiner, Jr., C. E. Boiling Point. In Handbook of Chemical Property Estimation Techniques; Lyman, W. J., Reehl, W.F., Rosenblatt, D. H., Eds.; McGraw-Hill: New York, 1982;Chapter 12. Rordorf, B. F. Prediction of Vapor Pressures, Boiling Pointa and Enthalpies of Fusion for Twenty-Nine Halogenated Dibenzo-PDioxins and Fifty-Five Dibenzofurans by A Vapor Pressure Correlation Method. Chemosphere 1989,18,183-788. SAS User's Guide: Statistics, Version 5 Edition; SAS Institute: Cary, NC, 1985. Simamora, P.; Yalkowsky, S. H. Quantitative Structure Property Relationship In The Prediction of Melting Point and Boiling Point of Rigid Non-Hydrogen Bonding Organic Molecules. SAR QSAR Environ. Res. 1993,1, 293-300. Simamora, P.; Miller, A. H.; Yalkowsky, S. H.Melting Point and Normal Boiling Point Correlations: Applications To Rigid Aromatic Compounds. J. Chem.Znf. Comput. Sci. 1993,33,437440. Stanton, D. T.; Egolf, L. M.; Jure, P. C. Computer-Aeaisted Prediction of Normal Boiling Points of Pyrans and Pyrroles. J. Chem. Znf. Comput. Sci. 1992,32,306-316. Tsakanikas, P. D.;Yalkowsky, S. H. Estimation of Melting Point of Flexible Molecules: Aliphatic Hydrocarbons. Toricol. Enuiron. Chem. 1987,17,19-33. Ultra Scientific: PCB Congener Solutions; Ultra Scientific: Kingstown, RI, 1988.
Received for review December 2, 1993 Revised manuscript received February 24, 1994 Accepted March 10, 1994. Abstract published in Advance ACS Abstracts, April 15, 1994.
