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Journal of Hazardous Materials
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j h a z m a tPrediction of autoignition temperatures of organic compounds by the
structural group contribution approach
Chan-Cheng Chen
∗, Horng-Jang Liaw, Yu-Yu Kuo
Department of Occupational Safety and Health, China Medical University, 91 Hsueh-Shih Road, Taichung 40402, Taiwan, ROC
a r t i c l e i n f o
Article history:Received 6 December 2007 Received in revised form 11 May 2008 Accepted 21 May 2008
Available online xxx Keywords:
Autoignition temperature Structural group contribution
a b s t r a c t
A model to predict the autoignition temperatures (AIT) of organic compounds is proposed based on the structural group contribution (SGC) approach. This model has been built up using a 400-compound train-ing set; the fitttrain-ing ability for these traintrain-ing data is 0.8474, with an average error of 32 K and an average error percentage of 4.9%. The predictive capability of the proposed model has been demonstrated on an 83-compound validation set; the predictive capability for these validation data is about 0.5361, with an average error of 70 K and an average error percentage of 11.0%. The proposed model is shown to be more accurate than those of other published works. This improvement is largely attributed to the modifications of the group definitions for estimating the AIT instead of the type of empirical model chosen. Through the Q2value and hypothesis testing, it was found that the empirical model should be chosen as a polyno-mial of degree 3. As compared to the known errors in experimentally determining the AIT, the proposed method offers a reasonable estimate of the AIT for the organic compounds in the training set, and can also approximate the AIT for compounds whose AIT is as yet unknown or not readily available to within a reasonable accuracy.
© 2008 Elsevier B.V. All rights reserved.
1. Introduction
The autoignition temperature (AIT) is defined as the lowest tem-perature at which a substance will ignite in the absence of a spark or flame. Based on the thermal theory of ignition and on classical reaction-rate theory, the AIT can be regarded as the temperature to which a combustible mixture must be raised so that the rate of heat evolution from the exothermic oxidation reactions of the system will just overbalance the rate at which heat is lost to the surroundings. The ability of a substance to spontaneously ignite introduces potential fire hazards for all who must handle, trans-port, or store combustible materials. Thus, risk assessment methods such as API-581 usually take the AIT of a substance as an essential input parameter to define the possible consequences of a leakage of combustible liquids[1]. Autoignition is also studied in relation to the performance of combustion engines through the phenomenon of engine knock[2].
As the AIT is the temperature at which a material will sponta-neously ignite when exposed to the atmosphere, it depends not only on the chemical and physical properties of the substance but also the method and the apparatus employed for its
determina-∗ Corresponding author. Tel.: +886 4 22076435; fax: +886 4 22076435. E-mail address:ChanCheng [email protected](C.-C. Chen).
tion, such as the test pressure, oxygen concentration, and volume and material of the vessel used. Hence, it is very common that the AIT of a specific compound is reported differently in different liter-atures; these differences may be as much as 300 K. For example, as shown inTable 1, the AIT of acetaldehyde is reported to range from 413 to 758.15 K in five different authoritative sources[3–7].Table 1 lists some compounds for which the difference in AIT is more than 100 K across separate sources. One of the important reasons that results in this uncertainty is the value of AIT reported in different databases may be conducted by different experimental method. Even in the same database, different compounds may be conducted in different experimental methods[2]. However, all databases usu-ally reported the AIT value without the information of experimental method employed. For example, there is no way to trace back the data reported in the hazardous chemical database or SAX’S dangerous properties of industrial materials. Even in the famous DIPPR®project, the data quality of AIT is still flagged as
“uneval-uated”. Since AIT is usually reported without the experimental method employed, it is not possible to account this bias by includ-ing experimental method as an additional explanatory variable or to group them by different experimental methods. In addition, because visual inspection is chosen to detect the sudden appear-ance of a flame inside the autoignition vessel, determining AIT is greatly limited by human capabilities[8]. Usually, the average error in experimentally determined AIT values is deemed to be about ±30 K in the literature[9]. Besides this problem, the determination 0304-3894/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
Table 1
Experimental AITs for selected compounds from different sourcesa
Compound name Ref.[3] Ref.[4] Ref.[5] Ref.[6] Ref.[7]
2-Butanone 677 788.71 – 788.7 778 2,4-Dimethylphenol 753 872 – – 872 Hexadecanoic acid 513 650 – – – Piperazidine 593 728.15 – – 593 1,3-Diisopropylbenzene 722 349.82 – – – Benzoyl chloride 873 358.15 – – 470.2 Methylhexanone 728 464.15 – – – 2-Methylnitrobenzene 693 578.15 – – 693 2,4-Dihydroxy-2-methylpentane 698 579 – – 579 1-Methyl-2-pyrrolidinone 518 619.15 – – 543 2-Heptanone 805 666.15 – 805.93 666 Crotonic acid 773 669.26 – – 669 1,4-Benzenedicarboxylic acid 951 769 – – 769 2,4-Dimethylpentane 598 708 – – – 1,3-Benzenedicarboxylic acid 973 769 – – – Phenol 878 988.15 988 – 988 Isobutyl formate 698 593.15 593 – – Acetaldehyde 413 758.15 448 510.93 458
aThe AIT values are in K.
of the AIT by experiment is very laborious and is not always feasible [8]. In this light, the ability to estimate AIT values by mathematical modeling will be a cost-efficient and critical aid to this discipline.
Multivariate statistical methods such as multiple linear regres-sion and principal component regresregres-sion are important approaches to predict the AITs of organic compounds. Several studies have con-sidered using the physical properties of compounds, such as the critical pressure, parachor, and molecular weight, as descriptors to predict the AIT[2,9,10–13]. Such approaches are usually known as quantitative structure–property relation (QSPR) approaches in which the molecular structures are characterized by the various physical properties of the compound. The underlying assumption in the QSPR approach is that there is some sort of relationship between the properties of interest and the molecular descriptors (i.e., the measurable physical properties). Thus, the QSPR approach involves multivariate analysis using several measurements (or descriptors) to deduce the desired property. Although the QSPR approach has been shown to estimate the properties of compounds with certain degree of success, it is applicable, however, only if the measure-ments of the molecular descriptors are available. On the other hand, the structure group contribution (SGC) method directly uses the information of the molecular structure instead of the physical prop-erties to predict the AIT. Thus, the SGC method may be a more attractive alternative as it is still applicable when the physical prop-erties of the target compound are unavailable and even if the target compound is an unknown compound.
The SGC method has recently found wide commercial applica-tion in the form of computer programs that estimate the properties of pure substances from their chemical structures, for example, the ASTM CHETAH[14]. While the SGC approach has been successfully applied to predict many of the properties of compounds, very lit-tle literature is available on predicting the AIT through the SGC approach. Albahri[15]proposed a SGC method in which a polyno-mial of degree 4 is suggested as an empirical model for predicting the AITs of 137 pure hydrocarbons with an average error percentage of 4.2% and a maximum error percentage of 31%. To consider organic compounds other than pure hydrocarbons, Albahri and George[16] developed a predictive model based on a 490-compound database in which the organic compounds include hetero-atoms such as oxy-gen, and nitrogen. In their work, they first chose a polynomial of degree 4 as the empirical model, but found that the average error percentage and maximum error percentage for such a model were 9.2% and 125%, respectively. Because of the limited success, they proposed a three-layer artificial neural network (ANN) structure
to improve the predictive performance. This ANN-SGC approach seemed to offer a significant improvement in performance, with average error percentage of 2.8% and a maximum error percentage of 20%; however, although this ANN-SGC approach exhibited bet-ter performance than that of the classical SGC approach, it usually included too many weighting parameters and was also inconve-nient for desk calculation. Thus, there is still a demand for a more accurate method to predict the AIT by the classical SGC approach.
This article is organized as follows: First, the AIT database and group definitions for this work are discussed in Section2. In Section 3, the mathematics for developing an empirical model is discussed. A brief discussion on choosing and evaluating the empirical model is provided in this section. The results of this work and some discus-sion are provided in Section4. Finally, the conclusions are presented in Section5.
2. Database and group definitions
In this work, the prediction model was developed and validated from a 483-compound database in which some of the organic com-pounds contained hydrogen, carbon, oxygen, nitrogen, or halogen atoms. In this database, there were 150 pure hydrocarbons, and the other 333 compounds included hetero-atoms. These 483 com-pounds were randomly distributed into a training set with 400 compounds and a validation set with 83 compounds. As mentioned earlier, different AIT values were reported in different literature sources, thus the value in AIChE-DIPPR was adopted as the standard in this work. However, in the case that the AIT of a compound was not available in DIPPR or the AITs reported in all the other literature sources were consistent with each other but differed from that of DIPPR, the non-DIPPR value was adopted. The corresponding AITs for all 483 compounds in this work are listed inTables A1 and A2. In these 483 data, 300 data were taken from AIChE-DIPPR and the other 183 data were taken from non-DIPPR sources.
To elucidate the classification of group definitions for estimating the AITs of organic compounds, a brief review of the mechanism of the autoignition process is provided below. Swarts and Orchin[17] reported that the autoignition mechanism proceeds by a free radical reaction and the stability of free-radical intermediates determines the ease of oxidation. Thus, the AIT of a compound is highly affected by its molecular structure because the stability of the free radicals that are formed is related directly to the molecular structure of the compound. For hydrocarbons, decreasing the chain length, addition of methyl groups, unsaturation, branching, and cyclic and aromatic
Table 2
Group contribution for estimation of the AIT
Group no. Group Remark MLR Degree 2 Degree 3 Degree 4
1 CH3 −22.6813 −29.9804 −22.8857 −23.1736 2 >CH2 −21.3527 −39.6875 −28.5961 −30.5288 3 >CH 4.0509 0.5544 1.3340 0.5424 4 >C< 56.6464 54.9627 49.7423 48.2437 5 CH2 −17.7405 −31.9088 −21.6668 −22.9287 6 CH– −39.7751 −66.2563 −46.3286 −49.5017 7 >C −31.1140 −36.4970 −32.7605 −33.1968 8 ≡CH −71.9616 −117.6474 −81.0169 −85.7134 9 ≡C −55.6234 −94.6821 −64.4957 −68.9986 10 >CH2 −24.6453 −40.1768 −28.4401 −30.1512 11 >CH −4.0091 −8.4713 −6.7179 −7.3545 12 >C< −15.3282 −62.9661 −21.7342 −26.1364 13 CH 20.5679 17.5968 19.5293 20.2876 14 >C −48.4525 −43.7461 −49.0687 −50.6287 15 CH 6.1265 2.5173 6.2350 6.1348 16 >C (Fused) 10.0809 7.8480 5.8332 4.9528 17 >C (Nonfused) 22.0000 24.2898 15.9976 14.9799 18 CH3 (Attached to at least
one halogen atom)
120.6545 82.3095 103.2738 114.6114 19 >CH2 −3.0301 −17.5437 −9.8344 −11.3142 20 >CH −23.3669 −37.6850 −24.2759 −26.4969 21 >C< 242.6675 247.3442 293.5064 287.6001 22 F (Nonring) −42.1638 −65.1907 −45.0477 −48.2274 23 Cl (Nonring) 37.8512 34.3163 33.9332 33.9492 24 Br (Nonring) −26.7706 −38.4893 −27.8628 −29.3678 25 F (Ring) 49.5353 49.8512 88.8289 90.5979 26 Cl (Ring) 27.1279 10.1433 79.4122 73.0277 27 Br (Ring) 54.0271 26.6567 53.4870 50.0560 28 -OH (Alcohol) −10.2828 −15.2847 −8.9378 −9.0980 29 OH (Phenol) 43.0417 19.8772 134.3524 135.0214 30 O (Nonring) −54.7172 −102.1454 −70.0383 −74.8046 31 O (Ring) −27.3097 −40.1570 −28.4801 −29.4928 32 >C O (Nonring) 10.3136 4.4457 8.1173 7.4529 33 >C O (Ring) 46.6977 37.5549 57.5044 58.9186 34 O CH (Aldehyde) −120.8556 −208.1346 −138.3186 −147.3836 35 COOH (Acid) 7.4758 −5.7007 4.0037 3.5463 36 -COO (Ester) 35.2785 34.2704 35.2011 35.1839 37 NH2 −17.8076 −33.4276 −17.7579 −18.9367 38 >NH (Nonring) −0.7601 1.5113 −1.8223 −1.5263 39 >NH (Ring) 22.7367 22.3273 24.5474 25.8972 40 >N (Nonring) −1.1683 −20.3543 −4.7926 −8.1033 41 >N (Ring) −42.3160 −47.2060 −49.3834 −51.0105 42 N (Nonring) −35.3780 −75.6105 −41.9897 −47.4827 43 N (Ring) 33.2611 3.5793 31.8743 24.8482 44 CN 82.0245 86.5584 80.5038 81.3197 45 NO2 −46.9847 −65.2997 −52.7670 −53.2661
structures will elevate the AIT[18]. The relationship between the AITs of lower alkanes and their corresponding alcohols and aldehy-des is in the following order: alkane > alcohol > aldehyde[17]. It has also been reported that there is no distinction in the AITs for the cis and trans structure orientations in olefins and cyclic compounds. It was found to be unnecessary to account for the location of the alkyl substitutions on the benzene ring in the para, meta, and ortho positions in aromatics; the location of the alkyl branches along the chain for iso-paraffins and iso-olefins; the location of the double bond along the chain in olefins; and the locations of the alkyl sub-stitutions and the ring size for naphthenes[15]. Albahri and George [16]also indicated that using two sets of structural groups, one for the aromatic ring in aromatics and the other for the cyclic ring in naphthenes, did not result in a significant improvement in the prediction performance.
Table 2summarizes all the group types used for estimating the AIT in this work. The group definitions in this work basically follow those in Albahri and George’s work[16]; however, some of them have been modified as follows. After carefully examining the AITs of organic compounds in our database, it was found that the condi-tion of the carbon to which the halogen group is directly attached affects the AIT of the compound. This effect may be understood from the type of chemical bonding. A carbon that bears one or
more halogen groups forms a polar covalent bond with the halo-gen group instead of the pure covalent bonds that exist between the carbon atoms; this polar covalent bond will change the ability of the carbon atom to form free radicals. InTable 2, groups 18–21 are introduced to elucidate the effect of the addition of halogen atoms to paraffins; however, the effect of adding halogen groups to organic compounds was found to be different for compounds with nonring and ring structures. It was found that adding halogen atoms increased the AIT for nonring hydrocarbons, but decreased the AIT for ring-structure compounds. Thus, the halogen atoms were divided into nonring attachment groups (groups 22–24) and ring attachment groups (groups 25–27) in this study. Finally, to include organic compounds such as 1-hexyne and hexyl acetylene, group 9 is introduced in this work to explain their structure.
3. Developing the model
The simplest empirical model to predict the AIT of an organic compound is the multiple linear regression (MLR) model:
AIT= fo+ n
i=1
where n is the number of group types defined inTable 2; vi, the
number from group i in a molecule; fi(i = 1,. . .n), the group
contri-bution for the ith defined group; and f0, the intersect of the fitting
line. For a more accurate estimation, other nonlinear models could be adopted as the empirical model. In the literature, the nonlinear form of Eq.(2)has been announced to be the most suitable form for predicting AITs[15,16].
AIT= a+ b
i vifi + c i vifi 2 + d i vifi 3 +e i vifi 4 (2)However, such a claim is debatable. First, the parameter bin Eq. (2)is a redundant parameter. It is obvious that the following Eq. (3)has the same fitting and predictive abilities as Eq.(2), but the number of unknown parameters in Eq.(3)is one less than that in Eq.(2). It is well known that solving a nonlinear regression prob-lem is usually time-consuming and can easily get bogged down at
local solutions; and a redundant parameter will aggravate these two problems. Second, it is obvious that Eq.(3)can be reasonably taken as a modified form from the conventional MLR model. So, the terms corresponding to parameters b, c, and d in Eq.(3)could be considered as the correcting terms for the MLR model, and the results of the MLR model could be then taken as the start point (i.e., all fi’s and a are taken from the MLR, and the others are set to
be zero) to solve the nonlinear regression problem of Eq.(3). For a given iterative algorithm, a good start point always decreases its possibility of being bogged at local solutions and enhance its effi-ciency, thus Eq.(3)is superior to Eq.(2)for building a model in this respect. AIT=a +
i vifi +b i vifi 2 +c i vifi 3 +d i vifi 4 (3)To demonstrate the superiority of Eq.(3), data listed inTable A1 are used to build the models of Eqs.(2)and(3), respectively. Then, data listed inTable A2are used to compare their predictive capabil-ity. The SGC groups’ definitions listed inTable 2and the linearized algorithm listed in Eq.(8)is employed to calculate the parameters
in these two equations, respectively. There are four different cases of initial conditions considered in present study, which includes: (1) case 1 – initial guesses of parameters a and fi’s are set to be
the values obtained from the results of a MLR model, and all other parameters are set to be zero; (2) case 2 – initial guesses of param-eters a and fi’s are set to be the values obtained from the results
of a MLR model, and all other parameters are set to be one; (3) case 3 – initial guesses of parameters fi’s are set to be the values
obtained from the results of a MLR model, and all other parameters (including a) are set to be zero; and (4) case 4 – initial guesses of all parameters are set to be zero.
Figs. 1–2demonstrate the fitting abilities of the resulting mod-els of these two equations for these four different cases of initial conditions, respectively. As shown inFig. 1, the resulting models of Eq.(2)are very sensitive to the initial conditions employed, and it obviously get bogged down at the local solution in both cases 2 and 4. However, as shown inFig. 2, the resulting models of Eq. (3)are almost the same in these four cases, which means that a model of this form is more robust to initial conditions than that of Eq.(2).Table 3compares the fitting abilities and the predictive abilities of the resulting models of these two equations for these
Table 3
Comparision of robustness to initial conditions between Eqs.(2)and(3)
Initial conditions Eq.(2) Eq.(3)
R2 Q2 R2 Q2
Case 1 0.8477 0.5345 0.8477 0.5362
Case 2 0.7367 −0.3191a 0.8469 0.5336
Case 3 0.8478 0.5354 0.8472 0.5346
Case 4 0.0025 0.0018 0.8477 0.5347
aIn this case, the predictive error of the seventh compound is found to be up to
1000 K.
four different initial conditions. As shown inTable 3, the result-ing model of Eq.(2)for case 2 gives a very poor performance in prediction, although the fitting performance for this case seems to be of an acceptable value. In this case, it was found that the fitting error of the N,N-Dimethylbenzenamine in the testing set is more than 1000 K (the experimental value is 644.26 K, but the predictive value is−427.7 K), and the predictive error of this com-pound makes the Q2 to be an unreasonable negative value. This
result shows that when redundant parameters are introduced into
an empirical model, there is an increased chance for the estimation process to draw noises and other spurious phenomena from the training data into the resulting model, which always decreases the predictive capability of the resulting model.
The sum of squared errors is the usual index to evaluate the feasibility of a given model. In this study, the quantitative measure of goodness of fit is given by the explained variation in the training set (R2), whereas the predictive capability, on the other hand, is
given by the predicted variation in the validation set (Q2). These
two indices are defined as follows.
R2= 1 −
Ki=1(yi− ˆy)2
Ki=1(yi− ¯y)2
, for the training set
Q2= 1 −
K i=1(yi− ˆy) 2 K i=1(yi− ¯y)2, for the validation set
where yiis the ith sample measurement; ˆyi, the predicted value of
the ith sample; ¯y, the average of all sample measurements. Usually, the R2 and Q2 vary differently with increasing model
complex-ity (i.e., number of parameters in a model). R2is inflationary and
approaches unity as the model complexity increases. Hence, it is not sufficient to only have a high R2for a practical model. The goodness
of predictive capability Q2, on the other hand, is not inflationary and
will not automatically approach unity with increasing model com-plexity. Commencing with a very simple model, Q2 will increase
with model complexity. However, at a certain degree of complexity, Q2will reach a plateau and subsequently reduce. Usually, the point
at which Q2 reaches a plateau is the trade-off point between the
fitting and predictive capability. Besides aforementioned method, a common alternative to determine model complexity is to exam-ine the hypothesis test for a given parameter in that model. In this study, both Q2-statistics and hypothesis testing are used to
deter-mine whether the complexity of an empirical model is adequate or not.
The determination of the least-squares solution of Eq.(3)is a nonlinear regression problem. There are many different methods for solving this problem, and the solutions from different meth-ods may differ slightly. In this study, the linearized algorithm and asymptotic confidence intervals are adopted [19]. The following paragraph briefly discusses this method.
Consider the following nonlinear empirical model: yi= f (xi; ) + εi, i = 1, 2 . . . n
where yiis the AIT measurement of ith sample; n, the number of
compounds in the training set; xi∈ RK, the number of group i in
a molecule; K, the number of function groups defined inTable 2; ∈ RP, the parameter vector (includes f
i, a, b, c, and d) in the
empir-ical model; and P, the number of parameters in the model. εiis the
measurement error and is assumed to be i.i.d. N(0,2). Let us define
y ≡ [y1, y2, . . . , yn]T (4) fi() ≡ f (xi; ) i = 1, 2, · · ·, n (5) f () ≡ [f1(), f2(), . . . , fn()]T (6) F() ≡
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
∂f1() ∂1 ∂f1() ∂2 · · · ∂f1() ∂p ∂f2() ∂1 ∂f2() ∂2 · · · ∂f2() ∂p . . . ... ∂fn() ∂1 ∂fn() ∂2 · · · ∂fn() ∂p⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
=∂fi() ∂j (7)
Let * be the true value of , and ˆ, which is the convergent solution of the following iterative Eq.(8), be the estimate of . (a+1)= (a)+ (FT((a))F((a)))−1FT((a))[y − f ((a))] (8)
It has been shown in the literature that an approximate, for large n, 100(1− ˛)% confidence interval for ris as follows[19].
ˆr± t˛/2n−ps
ˆcrr (9)
where r is the rth element of ; tn−p is the t-distribution with (n− p) degrees of freedom; s is the sample standard deviation; and [(ˆcrs)]= ˆC−1with ˆC = ˆFT(ˆ)ˆF(ˆ).
4. Results and discussion
For a given model, the group contributions (fi) of different
molecular groups and the other parameters in the model were solved to minimize the squared error for the 400-compound train-ing set. Different models, includtrain-ing MLR and polynomial models of degree 2–4, were considered in this study. The parameters in the MLR model were calculated by the classical least-squares method. For nonlinear models, Eqs.(8)and(9)were used to the solve model parameters and estimate their corresponding 95% confidence inter-vals, respectively.Table 2summarizes all the group contributions for the interested models in this work, and the other parameters (i.e., a, b, c, and d) for the corresponding models are listed inTable 4. Table 5lists the 95% confidence intervals for the parameters a, b, c, and d in all the nonlinear models. The parameters inTables 2 and 4 were then used to calculate the predicted AITs of the correspond-ing model for the 83 compounds in the validation set. The fittcorrespond-ing abilities and predictive abilities of these models were then calcu-lated according to the predicted AITs. The fitting abilities of the different models for estimating AIT are summarized inTable 6, and
Table 4
Parameters for polynomial models of different degrees
Coefficients MLR Degree 2 Degree 3 Degree 4
a 731.4902 771.1828 750.3065 754.0344
b – 8.5082E−04 −8.6444E−04 −7.5627E−04
c – – −4.5604E−06 −5.0831E−06
d – – – −2.4496E−09
Table 5
95% confidence intervals for parameters a, b, c and d in different models
Model degree a− a+ b− b+ c− c+ d− d+
2 7.17984E+02 8.24381E+02 6.76307E−04 1.02534E−03 – – – –
3 7.07108E+02 7.93505E+02 −1.68051E−03 −4.83678E−05 −6.15028E−06 −2.97048E−06 – –
Table 6
Fitting ability for different types of models
Model R2 Max err (K) Avg err (K) Max err (%) Avg err (%)
MLR 0.8266 178 34 34 5.3
Degree 2 0.8361 163 33 31 5.1
Degree 3 0.8474 169 32 32 4.9
Degree 4 0.8478 168 31 32 4.9
Albahria 0.8464 166 28 31 4.2
Albahri and Georgeb 0.7900 – 58 125 9.2
a,bThese values are taken from the original papers.
Table 7
Predictive capability for different models
Model Q2 Max err (K) Avg err (K) Max err (%) Avg err (%)
MLR 0.4921 184.1 75.2 47.4 11.9
Degree 2 0.5151 189.0 72.3 45.4 11.3
Degree 3 0.5361 179.6 69.8 45.9 11.0
Degree 4 0.5349 178.5 69.7 45.5 11.0
the predicting abilities of the corresponding models are listed in Table 7.
It is very possible that a model fits well for training data but gives poor predictive performance for testing data. Thus, when develop-ing a suitable model for prediction, there is a need to balance the fitting ability and predictive capability of the model. The fitting abil-ity measures the abilabil-ity to mathematically reproduce the data of the training set, and the predictive capability gauges the reliability of the predicted outcomes of other experiments. Usually, this com-promise is achieved through the model complexity. Both R2 and
Q2for different models are plotted against their model complexity
inFig. 3. It was found that the predictive capability (Q2) reached a
maximum for a model with a polynomial of degree 3, and the fit-ting ability (R2) for a polynomial of degree 4 was only a little better
than that for a polynomial of degree 3. Thus, the nonlinear model suggested by Albahri, a polynomial model of degree 4, might be an overfitting model for predicting the AITs of organic compounds. Moreover, as shown inTable 5, the 95% confidence interval for parameter d in the polynomial model of degree 4 contains the zero value. This implies that we cannot reject the hypothesis d = 0 with 95% confidence, and also indicates that the model of degree 4 is an overfitting model. For a model of degree 3, although the estimate of c is a very small number (−4.5604 × 10−6), the 95% confidence
inter-val of c does not include the zero inter-value; and the hypothesis c = 0 will
Fig. 3. Adequacy of model complexity.
be rejected with 95% confidence in this case. Thus, from the method of hypothesis testing, it was also concluded that the most adequate model is a polynomial of degree 3.Figs. 4–7show the experimen-tal AITs vs. the predicted values for all the interested models in both the training and validation sets. It could be found in these fig-ures that the drawing at lower experimental AIT part become more and more flat as the model complexity increases. This means that the compounds with large fitting errors will tend to concentrate on the compounds with the lower experimental AIT as the model complexity increases. Usually, the occurring of a specific pattern of fitting errors is an evidence to indicate that the corresponding model is possibly overfitting; thus, the empirical model of degree 4 is possibly an overfitting model. It should be noted that this phe-nomenon that the fitting errors tend to concentrate on a specific region was also found in Albahri and George’s original work[16]. From all aforementioned facts, it is then concluded by us that a model of degree 3 is more adequate than a model of degree 4 for predicting the AIT of an organic compound.
A comparison of the fitting ability between this study and the other two studies in the literature is also listed in Table 6. In
Fig. 5. Parity plot for the polynomial model of degree 2: (a) training set; (b) validation set.
Fig. 6. Parity plot for the polynomial model of degree 3: (a) training set; (b) validation set.
Albahri’s work, the R2 of their empirical model (of degree 4) is
0.846[15]. However, that empirical model was conducted from 137 pure hydrocarbons, and hence, such a model cannot be applied to the case of organic compounds containing hetero-atoms. Albahri and George’s work explored 490 organic compounds containing hetero-atoms and the R2 of the corresponding empirical model
(of degree 4) is 0.790[16]. In present work, the results are drawn from 483 organic compounds containing hetero-atoms, and the R2 of the proposed method is 0.847—which is better than that
of Albahri and George’s work and is comparable with that of the Albahri’s work for only pure hydrocarbons. Moreover, the aver-age error and maximum error of the proposed model are 4.9% and 32%, respectively; and these two values are 9.2% and 125% for the model proposed by Albahri and George. Since AIT is a safety related parameter, the improvement in maximum error should be notified.
As it was shown in Table 6, the R2 of the MLR model in
present work is 0.827, which is also better than that of Albahri and George’s work; thus, it was deemed by us that much of the improvement in this work is attributed to the revised group def-initions instead of the type of empirical model chosen. In fact, we also attempted to use many other types of empirical mod-els to improve the prediction performance, but the improvement was limited. However, as the database in present study is different from that in Albahri and George’s work, aforementioned conclu-sion that much of the improvement in this work is attributed to the revised group definition still needs more evidences to support it. To make a more objective comparison, the group definitions and pre-dictive equation of Albahri and George’s work have been applied to our database to obtain the corresponding predictive AIT value for all compounds. Because the predictive equation proposed by Albahri and George is obtained from their own database, some pretreatments in our database are needed to avoid this possible bias. First, the compounds that could not be decomposed accord-ing to their group definitions are excluded out; and thus, there are each three compounds dropped from the training set and valida-tion set, respectively. Second, as Albahri and George announced that the maximum error is 125% and the average error is 9.2% in their training set, the compounds of which the absolute predic-tive error are larger than 150 K by their predicted equation are also dropped from the database to let the overall performance of the predicted results meets aforementioned two requirements. Thus, we delete, according to this criterion, 10 compounds from
our training set and 9 compounds from our validation set, respec-tively. With these pretreatments, the average errors of Albahri and George’s model for the trimmed training set and the trimmed val-idation set are 7.20% and 9.40%, respectively; and the maximum errors are 26.95% and 26.73%, respectively.Fig. 8shows the fitting performance of Albahri and George’s model for both the trimmed training set and the trimmed validation set. It could be found that the drawings are of two flat parts at the lower experimental AIT zone and higher experimental AIT zone. As this phenomenon was also found in their original work, the fitting results for these two trimmed sets are of similar characteristics with their origi-nal work[16]. With above efforts, it is then assumed by us that the effects of the bias of establishing the model parameters from different database have been moderated. With aforementioned pretreatment, the fitting performance, i.e., the R2 value, of their
models are 0.7094 and 0.6609 for the trimmed training set and the trimmed validation set, respectively. It is obvious that the resulting fitting performance in both trimmed sets is still infe-rior to that of the MLR case in present study. Thus, our previous conclusion that much of the improvement in present study is attributed to the revised group definitions is supported by these results.
To assess whether a model is capable of predicting AITs or not, the number of compounds in the validation set is very important. In many commercial softwares, it is a common practice that the num-bers of observations in the validation set should be at least one-fifth the numbers of observations in the training set to avoid underesti-mating the predictive error[20]. However, this ratio is only 20/470 in Albahri and George’s work, which is deemed to be too small to derive a reasonable conclusion about the predictive performance of their model. To show this point, we take 2-hydroxy-1-ethylaziridine ( ) as an example to explain the case of underestimating the predictive error for their model. By using their group definitions and predictive model, the estimated AIT for 2- hydroxy-1-ethylaziridine is about 1630 K, but the reported experimental value is only 607 K. Thus, the prediction error is more than 1000 K in this example, which means that if this compound is included in their validation set, the predictive capability of their model will drastically decrease. So, it is obvious that the predictive error is possibly underestimated in their work.
As shown inTable 7, the Q2, average error and maximum error
for the present work are 0.5361, 11.0% and 45.9%, respectively. A rule of thumb for developing a practical model is: the difference
between R2and Q2must not be too large and preferably not
exceed-ing 0.2–0.3. Moreover, a Q2> 0.5 is regarded as good and a Q2> 0.9
as excellent[21]. In this study, the Q2value for the 83-compound
validation set was 0.5361 and the R2value for the 400-compound
training set was 0.8474; thus, the proposed method coincides with this rule of thumb and can be taken as a reasonable model for esti-mating the AIT of an unavailable or unknown compound in practical applications.
5. Conclusions
A predictive model for AITs was proposed based on the SGC approach. The proposed equation to predict AITs may be expressed as Eq.(10). This model includes 45 molecular function groups and is a polynomial of degree 3. This model was deduced from a 400-compound training set. The fitting ability of the proposed model is about 0.8474, with an average error of 32 K and an average error percentage of 4.9%. The predictive capability of the model was demonstrated on 83 compounds which were not included in the original training set. The predictive capability of the proposed model is about 0.5361, with average error 70 K and an average error percentage of 11.0% AIT= 750.3065 +
i vifi − 8.644 × 10−4× i vifi 2 − 4.5604 × 10−6× i vifi 3 (10)As compared to Albahri and George’s work, the proposed model exhibits better performance in terms of R2. It was also found that
much of the improvement may be attributed to the modification of the group definitions and not the type of empirical model cho-sen. As mentioned earlier, the addition of halogen atoms to nonring hydrocarbons and ring-structure compounds has different effects on their AITs. Thus, in this study, 14 new groups were introduced to discriminate this effect for halogen compounds.
In this work, the average fitting error for the 400-compound training set was 32 K, and the average prediction error was 70 K for the 83-compound validation set. Because the average experimental error in measuring the AIT is deemed to be greater than 30 K in the literature, the proposed method could offer a reasonable estimate of the AIT value for the organic compounds in the training set and could also approximate the AITs of compounds that were unknown or whose AITs were not readily available to within a reasonable degree.
Acknowledgements
The authors would like to thank both the National Science Coun-cil and China Medical University of the ROC for supporting this study financially under grant #NSC 96-2221-E-039-001 and #CMU 96-152, respectively.
Appendix A
SeeTables A1 and A2.
Table A1
Experimental values and predicted values of the compounds in the training set
Compound name Exp. value Reference MLR Degree 3
1 Butane 645 [11] 643.42 643.16 2 Pentane 538 [11] 622.07 614.17 3 Hexane 513 [11] 600.72 586.71 4 Heptane 486 [11] 579.36 561.42 5 2-Methylpropane 733.15 [3] 667.50 680.46 6 2-Methylbutane 693.15 [3] 646.14 650.46 7 3-Methylpentane 551.15 [3] 624.79 621.19 8 2,2-Dimethylpropane 723.15 [3] 697.41 707.33 9 2,2-Dimethylbutane 678 [4] 676.06 677.22 10 2,3-Dimethylpentane 610.37 [3] 627.51 628.30 11 2,2,3-Trimethylbutane 685 [11] 678.78 684.64 12 1-Pentene 571 [11] 608.59 598.09 13 1-Heptene 536 [11] 565.88 548.06 14 1-Octene 523 [4] 544.53 527.50 15 1-Decene 508.15 [3] 501.82 498.46 16 1,3-Pentadiene 613 [11] 571.74 565.84 17 2-Methyl-1-pentene 579 [11] 594.57 589.28 18 2,4,4-Trimethyl-1-pentene 693 [3] 627.20 620.88 19 Cyclopentane 593 [11] 608.26 603.74 20 Methylcyclopentane 602.04 [3] 606.22 602.61 21 Ethylcyclohexane 535.37 [3] 560.22 551.89 22 n-Propylcyclohexane 521.15 [3] 538.87 530.74 23 trans-1,2-Dimethylcyclohexane 577.15 [3] 579.53 575.08 24 Dicyclohexyl 518.15 [3] 477.02 496.27 25 Decalin 541 [11] 526.31 522.96 26 Hydrindane 569 [11] 641.38 629.21 27 Cyclopentene 668.15 [3] 698.69 702.65 28 Cyclohexene 583.15 [3] 674.04 672.68 29 Benzene 771 [4] 768.25 786.27 30 Toluene 755 [11] 761.44 774.02 31 Ethylbenzene 705.37 [3] 740.09 745.98 32 n-Propylbenzene 729.15 [3] 718.74 716.63 33 n-Butylbenzene 685.37 [3] 697.38 686.60 34 1,3-Dimethylbenzene 800.93 [3] 754.63 761.36 35 1,4-Diethylbenzene 703.15 [3] 711.93 702.89 36 Biphenyl 813.15 [3] 836.76 833.13 37 Naphthalene 813 [11] 800.66 807.52
Table A1 (Continued )
Compound name Exp. value Reference MLR Degree 3
38 1-Methylnaphthalene 802.04 [3] 793.86 796.18 39 Anthracene 828 [11] 833.08 826.77 40 Ethanol 673 [11] 677.17 687.74 41 1-Propanol 644.26 [3] 655.82 657.66 42 1-Butanol 616 [3] 634.47 628.16 43 2-Butanol 663 [4] 658.54 665.04 44 tert-Butanol 733 [11] 709.81 721.88 45 Cyclohexanol 573.15 [3] 593.97 588.85 46 Benzyl alcohol 709.26 [3] 752.49 759.86 47 1-Hexanol 558 [3] 591.76 573.45 48 Allyl alcohol 643 [11] 642.34 640.51 49 Dimethyl ether 623.15 [3] 631.41 629.99 50 Dibutyl ether 467.59 [3] 503.29 499.77
51 Methyl vinyl ether 560.15 [3] 596.58 586.01
52 Diphenyl ether 891.15 [3] 782.04 774.04 53 Propylene oxide 738.15 [3] 652.84 660.27 54 Propionaldehyde 500 [11] 566.60 560.55 55 Butyraldehyde 503.15 [3] 545.25 538.18 56 Acetophenone 833 [11] 771.76 781.65 57 2-Butanone 677 [11] 675.09 681.59 58 2-Pentanone 725.15 [3] 653.74 651.57 59 Cyclohexanone 693.15 [3] 654.96 662.18 60 Acetic acid 737 [11] 716.28 731.15 61 Butyric acid 718 [11] 673.58 671.24 62 Pentanoic acid 673.15 [3] 652.23 641.39 63 Acrylic acid 711.15 [3] 681.45 683.97 64 Dipropylamine 572.15 [3] 599.96 585.03 65 Diphenylamine 907.04 [3] 836.00 831.82 66 2-Aminoethanol 673 [11] 660.69 663.03 67 1-Chlorobutane 523 [11] 700.92 692.42 68 Acetyl chloride 663.15 [3] 756.97 769.12 69 Chlorobenzene 863 [4] 811.25 853.79 70 1-Bromobutane 538 [4] 636.30 627.99 71 Bromobenzene 838.15 [3] 838.15 837.56 72 Ethyl formate 708 [11] 722.73 733.82 73 Ethyl acetate 700 [3] 700.05 710.09 74 Propyl acetate 708 [11] 678.70 679.99 75 Butyl acetate 653 [11] 657.35 650.00 76 Isobutyl acetate 696 [3] 681.42 687.42 77 Methyl propionate 728 [11] 700.05 710.09 78 Ethyl propionate 718 [11] 678.70 679.99 79 Methyl butyrate 728 [11] 678.70 679.99 80 Methyl benzoate 783 [4] 796.72 805.78 81 Ethyl benzoate 763.15 [3] 775.37 780.24 82 Butyl benzoate 708 [11] 732.66 723.49 83 Ethyl acrylate 655.93 [3] 665.22 662.62 84 2-Methylpentane 579.26 [3] 624.79 621.19 85 2,2,4-Trimethylbutane 680 [11] 654.71 647.27 86 trans-2-Hexene 528 [11] 563.87 555.74 87 trans-2-Pentene 558 [3] 585.22 580.42 88 1,3-Hexadiene 593 [11] 550.39 542.81 89 1,5-Hexadiene 618 [11] 573.75 557.74 90 2-Methylpropene 738.15 [3] 637.27 646.02 91 3-Methyl-1-butene 638.15 [3] 632.66 633.43 92 4-Methyl-1-pentene 577 [11] 611.31 604.88 93 2-Ethyl-1-butene 597 [11] 594.57 589.28 94 2,3-Dimethyl-1-butene 633.15 [3] 618.64 623.97 95 2,3,3-Trimethyl-1-butene 656 [11] 648.56 650.14 96 2,4,4-Trimethyl-2-pentene 581 [3] 603.84 602.22 97 Ethylcyclopentane 533.5 [3] 584.87 575.97 98 Propylcyclopentane 542.15 [3] 563.51 551.77 99 n-Hexylcyclopentane 501 [11] 499.46 500.15 100 Isopropylcyclohexane 556 [4] 562.94 557.60 101 Butylcyclohexane 519.15 [3] 517.52 513.30 102 Isobutylcyclohexane 547 [11] 541.59 535.63 103 sec-Butylcyclohexane 550 [11] 541.59 535.63 104 tert-Butylcyclohexane 615 [11] 592.86 579.68 105 trans-1,3-Dimethylcyclohexane 579 [3] 579.53 575.08 106 trans-1,4-Dimethylcyclohexane 577 [3] 579.53 575.08 107 1,3,5-Trimethylcyclohexane 587 [11] 577.48 574.04 108 4-Isopropyl-1-methylcyclohexane 579 [11] 560.90 556.64 109 Cyclodecane 508 [11] 485.04 500.89 110 Isobutylbenzene 700.93 [3] 721.46 723.95 111 sec-Butylbenzene 690.93 [3] 721.46 723.95 112 tert-Butylbenzene 723.15 [3] 772.73 777.77
Table A1 (Continued )
Compound name Exp. value Reference MLR Degree 3
113 1,2-Dimethylbenzene 737.04 [3] 754.63 761.36 114 1,4-Dimethylbenzene 802.04 [3] 754.63 761.36 115 1,2,3-Trimethylbenezene 743.15 [3] 747.83 748.34 116 1,2,4-Trimethylbenezene 788.15 [3] 747.83 748.34 117 1-Methyl-2-ethylbenzene 721 [11] 733.28 732.64 118 1-Methyl-3-ethylbenzene 753.15 [3] 733.28 732.64 119 1-Methyl-4-ethylbenzene 748.15 [3] 733.28 732.64 120 1,2-Diethylbenzene 677 [11] 711.93 702.89 121 1,3-Diethylbenzene 723.15 [3] 711.93 702.89 122 1-Methyl-3,5-diethylbenzene 734 [11] 705.12 689.07 123 2-Ethylbiphenyl 722 [11] 808.60 799.87 124 2-Propylbiphenyl 725 [11] 787.24 773.77 125 2-Butylbiphenyl 706 [11] 765.89 745.72 126 Diphenylmethane 759 [11] 815.40 811.02 127 1-Ethylnaphthalene 754 [11] 772.50 769.76 128 Tetralin 657.04 [3] 618.28 611.97 129 Methanol 728 [4] 698.53 717.75 130 3-Pentanol 638 [11] 637.19 635.34 131 2-Methyl-1-butanol 658.15 [3] 637.19 635.34 132 2-Propanol 672.04 [3] 679.90 695.16 133 2-Methyl-1-propanol 678 [11] 658.54 665.04 134 3-Methyl-1-butanol 623.15 [3] 637.19 635.34 135 2-Pentanol 616.48 [3] 637.19 635.34 136 2-Methyl-2-butanol 708 [11] 688.46 691.92 137 2,2-Dimethyl-1-propanol 693 [11] 688.46 691.92 138 4-Methyl-2-pentanol 613 [11] 639.91 642.58 139 1-Heptanol 555 [3] 570.41 549.52 140 4-Heptanol 568 [11] 594.48 579.75 141 2-Octanol 538 [11] 573.13 555.15 142 2-Ethyl-1-hexanol 560.93 [3] 573.13 555.15 143 1-Nonanol 533 [11] 527.70 511.71 144 1-Decanol 523 [11] 506.35 499.12 145 Ethylene glycol 673.15 [3] 668.22 672.30 146 1,2-Propanediol 694.26 [3] 670.94 679.72 147 Glycerol 673 [11] 661.99 664.30 148 2-Ethyl-1,3-hexanediol 633 [11] 588.25 572.95 149 2,2-Dimethyl-1,3-propanediol 672 [3] 679.50 676.48 150 3,5-Dimethylphenol 828 [11] 813.55 867.67 151 2,4-Dimethylphenol 872 [3] 813.55 867.67 152 2,4-Dimethyl-3-pentanol 668 [11] 642.64 649.88 153 Methoxybenzene 748 [4] 706.72 703.18 154 Dipentyl ether 444 [4] 460.59 489.67
155 Butyl vinyl ether 528 [11] 532.52 519.46
156 Ethylene oxide 702.04 [3] 654.89 661.48 157 1,2-Epoxyethylbenzene 811 [11] 728.16 733.63 158 Isobutyraldehyde 534 [11] 569.32 566.52 159 2-Propenal 573 [11] 553.12 547.25 160 Crotonaldehyde 553 [11] 508.40 515.34 161 2-Ethylcrotonaldehyde 523 [11] 473.03 498.22 162 3-Pentanone 725.37 [3] 653.74 651.57 163 Propionic acid 713 [11] 694.93 701.37 164 Isobutyric acid 733 [11] 697.65 708.76 165 Isopentanoic acid 689.15 [3] 676.30 678.66 166 Hexanoic acid 653.15 [3] 630.87 612.48 167 2-Methylpentanoic acid 651 [11] 654.95 648.68 168 Heptanoic acid 571 [3] 609.52 585.14 169 Decanoic acid 570 [3] 545.46 518.90 170 Dodecanoic acid 503 [11] 502.76 494.32 171 Tetradecanoic acid 508 [11] 460.05 491.37 172 Hexadecanoic acid 513 [11] 417.35 515.16 173 o-Phthalic acid 863 [11] 814.95 810.35 174 2,2-Dimethylpropionic acid 723 [11] 727.57 735.22 175 2-Ethylbutyric acid 663 [11] 654.95 648.68 176 2-Aminobiphenyl 725 [11] 834.82 827.27 177 1,2-Propanediamine 689 [11] 655.89 661.17 178 DL-1-Amino-2-propanol 647.04 [3] 663.42 670.43 179 Diisopropanolamine 647 [11] 630.20 625.75 180 Triisopropanolamine 593 [11] 579.52 567.12 181 2-Diethylaminoethanol 593 [11] 589.27 574.26 182 Benzyl chloride 858.15 [3] 818.94 815.54 183 1,1,1-Trichloroethane 810.15 [3] 799.00 801.62 184 Trichloroethylene 693 [11] 774.15 772.52 185 Bis(2-ethoxyethyl)ether 478 [11] 393.86 521.09 186 n-Hexyl Cellosolve 553 [11] 494.34 495.07 187 Methyl formate 729.26 [3] 744.09 762.48
Table A1 (Continued )
Compound name Exp. value Reference MLR Degree 3
188 Propyl formate 708 [11] 701.38 704.10 189 n-Butyl formate 595.37 [3] 680.03 673.98 190 lsopropyl formate 713 [11] 725.46 741.00 191 Methyl acetate 748 [11] 721.41 739.65 192 lsopropyl acetate 698 [11] 702.78 717.44 193 Pentyl acetate 633.15 [3] 636.00 620.75 194 lsopentyl acetate 653 [11] 660.07 657.35 195 Hexyl acetate 528 [11] 614.64 592.88 196 tert-Butyl acetate 708 [11] 732.69 743.67 197 sec-Butyl acetate 683 [11] 681.42 687.42 198 n-Decyl acetate 488 [11] 529.23 508.03 199 Vinyl acetate 698 [11] 686.57 692.73 200 Allyl acetate 647.04 [3] 665.22 662.62 201 Phenyl acetate 858 [11] 796.72 805.78 202 n-Propyl propionate 703 [11] 657.35 650.00 203 Isopropyl propionate 698 [11] 681.42 687.42 204 Butyl propionate 658 [11] 636.00 620.75 205 Isobutyl propionate 708 [11] 660.07 657.35 206 Ethyl butyrate 713 [11] 657.35 650.00 207 Propyl butyrate 693 [11] 636.00 620.75 208 1-Hexyne 536 [4] 517.17 515.16 209 3-Hexyn-2,5-diol 553 [4] 562.42 560.40 210 Ethyne 578.15 [3] 587.57 584.98 211 1,2,4-Triethenyl-Cyclohexane 543 [4] 472.98 493.21 212 4-Fluorobenzyl chloride 863 [4] 863.00 861.47 213 1,1-Difluoro-1-chloroethane 905 [3] 905.00 880.03 214 Fluoroethene 658.15 [3] 631.81 632.80 215 Amyl nitrite 478 [4] 576.41 560.35 216 Tetrahydropyrrole 618 [4] 655.65 657.45 217 1-Octanamine 538 [4] 541.53 523.05 218 N-Ethyl-N,N-diisopropylamine 513 [4] 603.66 600.89 219 2-Amino-2-ethylhexane 538 [4] 565.61 548.13 220 N-Butyl-1-butanamine 533 [4] 557.25 537.62 221 N,N-Dimethylacetamide 627.15 [3] 672.59 682.56 222 2-Butoxime 588 [4] 588.00 588.66 223 2-Hydroxy-1-ethylaziridine 607 [4] 586.90 575.59 224 1-Benzazine 753.15 [3] 811.82 814.86 225 Nitrocarbol 652.15 [3] 661.82 671.68 226 Aminomethane 703.15 [3] 691.00 708.54 227 Ethylamine 657 [3] 669.65 678.44 228 N,N-Dimethylamine 673.15 [3] 685.37 701.25 229 Piperazidine 728.15 [3] 678.38 683.26 230 Azabenzene 823 [4] 867.59 855.42 231 Tetrafluorethene 473.15 [3] 500.61 520.06 232 Imidole 823 [4] 836.50 838.93 233 Triacetaldehyde 510.93 [3] 569.49 573.94 234 3-Picoline 810 [3] 775.89 786.84 235 Butane nitrile 761 [4] 748.13 750.73 236 Cyanoacetic ester 733 [4] 783.41 784.63 237 2-Picoline 810.93 [3] 775.89 786.84 238 1,1-Dimethylcyclohexane 577 [3] 547.57 544.64 239 2,3,3-Trimethyl-1-Pentene 504 [4] 627.20 620.88 240 Isoprene 493.15 [3] 602.44 600.74 241 ␣-Methylstyrene 847.59 [3] 712.59 719.51 242 Butyl butyrate 623 [11] 614.64 592.88 243 Propylamine 591 [3] 648.30 648.47 244 ␣-Pinene 528.15 [3] 562.92 560.17 245 trans-2-Butene 597.04 [3] 606.58 607.41 246 1-Dodecanol 548.15 [3] 463.65 489.73 247 1,3-Butanediol 667.04 [3] 649.59 649.73 248 Isobutyl acrylate 613.15 [3] 642.54 638.83 249 Dimethyl terephthalate 843.15 [3] 825.19 823.65 250 1,7-Octadiene 493 [4] 531.05 517.32 251 1,3-Diisopropylbenzene 722 [4] 717.37 717.63 252 Benzoyl chloride 873 [4] 832.29 829.41 253 1,4-Dioxane 453.15 [3] 578.29 577.08 254 2-Ethylhexanal 463.15 [3] 483.91 496.49 255 Methylhexanone 728 [4] 635.11 629.39 256 2-(2-Methoxyethoxy)ethanol 488 [4] 503.68 500.18 257 2-Methoxyethyl ether 463 [4] 436.57 493.03 258 1,2-Dimethoxyethane, 473 [4] 533.99 521.67
259 Ethyl vinyl ether 451 [4] 575.22 560.78
260 2-(2-Ethoxyethoxy) ethanol 477.15 [3] 482.33 492.09
261 Pentanal 495.15 [3] 523.90 519.29
Table A1 (Continued )
Compound name Exp. value Reference MLR Degree 3
263 1,1-Diethoxyethane 503.15 [3] 515.36 509.67 264 2-Methyl-2-propenal 507.15 [3] 539.10 540.20 265 2-Ethoxyethanol 508.15 [3] 579.75 562.35 266 1-Nonene 510 [3] 523.18 510.75 267 Methylal 510.35 [3] 555.34 541.08 268 2-Butoxyethanol 511.15 [3] 537.05 520.58 269 Butylcyclopentane 523.15 [3] 542.16 530.64 270 trans-Decahydronaphthalene 528 [4] 526.31 522.96 271 beta-Pinene 528 [3] 522.65 525.46 272 1-Hendecanol 550 [3] 485.00 491.58 273 1-Nonanol 550 [3] 527.70 511.71 274 Methyl acetylacetate 623 [4] 710.37 718.56
275 Propanoic acid anhydride 558 [3] 609.33 589.86
276 2-Methoxyethanol 558.15 [3] 601.10 587.73 277 2-Pentene 561 [3] 585.22 580.42 278 cis-2-Methylcyclohexanol 569.15 [3] 591.93 587.77 279 cis-4-Methylcyclohexanol 570.15 [3] 591.93 587.77 280 cis-1,4-Dimethylcyclohexane 577 [3] 579.53 575.08 281 cis-1,2-Dimethylcyclohexane 577.15 [3] 579.53 575.08 282 2-Methylnitrobenzene 693 [4] 730.33 731.32 283 2,4-Dihydroxy-2-methylpentane 698 [4] 682.23 683.91 284 cis-1,3-Dimethylcyclohexane 579 [3] 579.53 575.08 285 1-Butanamine 585 [3] 626.94 619.27 286 2-Furancarboxaldehyde 588.71 [3] 596.58 589.39 287 Hexahydro-1H-azepine 603.15 [3] 606.36 599.98 288 Acetylene tetrabromide 608.15 [3] 632.51 637.16 289 2,4-Pentanedione 613.15 [3] 638.67 639.32 290 Propyl ac rylate 615 [3] 643.87 632.98 291 1-Methyl-2-pyrrolidinone 619.15 [3] 639.25 646.13 292 1-Methoxy-2-propyl acetate 627.15 [3] 626.71 614.97 293 1,4-Butanediol 630 [3] 625.51 613.48 294 2-(2-Ethoxyethoxy)ethyl acetate 583 [4] 505.21 497.60 295 Nitroethane 633.15 [3] 640.47 641.83 296 2-Methyt-1-butene 638 [3] 615.92 616.92 297 2-Aminoethylethanolamine 641 [3] 617.23 603.06 298 Allylamine 647.04 [3] 634.81 631.47 299 1,3-Propylene glycol 651 [3] 646.87 642.43 300 2-Ethoxyethyl acetate 652.59 [3] 602.63 580.99 301 Ethylenediamine 658.15 [3] 653.17 653.80 302 1-Methyl-3-nitrobenzene 713 [4] 730.33 731.32
303 Acetic acid anhydride 603 [4] 652.04 646.66
304 2-Furanmethanol 664.15 [3] 685.80 691.87 305 2-Heptanone 666.15 [3] 611.03 594.31 306 Crotonic acid 669.26 [3] 636.73 634.34 307 Ethyl 2-hydroxypropanoate 673.15 [3] 693.82 702.11 308 1,3,5-Trioxacyclohexane 683 [4] 575.63 577.05 309 Hexanedioic acid 678 [4] 661.03 639.64 310 Ethylene chlorohydrin 698.15 [3] 734.68 736.73 311 Cyclobutane 700 [3] 632.91 632.07 312 Tartaric acid 700.93 [3] 733.98 743.06 313 3-Isopropyltoluene 709 [3] 736.00 739.83 314 3-Methyl-2-butanol 710 [3] 661.27 672.44 315 1,2-Epoxybutane 643 [4] 631.49 630.69 316 N,N-Dimethylformamide 683 [4] 564.10 561.31 317 N-Phenylacetoacetamide 725.15 [3] 759.96 760.32 318 Methyl formate 729.26 [3] 744.09 762.48 319 1,1-Dichloroethane 731.15 [3] 761.14 770.60 320 trans-1,2-dichloroethylene 733 [3] 727.64 725.05 321 1,1,2-Trichloroethane 733.15 [3] 818.65 812.62 322 Acetonitrile 797 [4] 790.83 804.18 323 Vinyl chloride 745 [3] 711.83 715.42 324 Ethylphenylamine 752.15 [3] 739.33 744.14 325 Acrylonitrile 754.26 [3] 756.00 762.67 326 3-Aminotoluene 755.15 [3] 759.51 766.35 327 4-Aminotoluene 755.15 [3] 759.51 766.35 328 Nitrobenzol 753 [4] 737.14 744.69 329 1-Bromopropane 763.15 [3] 657.66 657.49 330 3-Hydroxypropionitrile 767.59 [3] 760.53 764.49 331 1,4-Benzenedicarboxylic acid 769 [3] 814.95 810.35 332 Ethyl bromide 784.26 [3] 679.01 687.56 333 o-Nitroaniline 794.15 [3] 735.20 736.57 334 N-Phenylacetamide 803.15 [3] 771.00 779.95 335 4-Picoline 810 [3] 775.89 786.84 336 Hexanedinitrile 823.15 [3] 810.13 794.59 337 Dichlorofluoromethane 825.15 [3] 741.66 748.85
Table A1 (Continued )
Compound name Exp. value Reference MLR Degree 3
338 1,2-Dichloropropane 830 [3] 758.11 761.07 339 Benzoic acid 805 [4] 791.60 798.61 340 1,3,5-Trichlorobenzene, 850 [3] 897.25 845.55 341 p-Nitroaniline 773 [4] 735.20 736.57 342 Phthalic anhydride 857.04 [3] 866.08 862.51 343 Hexachlorobutadiene 883.15 [3] 834.14 816.57 344 Methyl chloride 905 [3] 890.00 859.46 345 1,4-Dichlorobenzene 920 [3] 854.25 880.02 346 1,2-Dichlorobenzene 913 [4] 854.25 880.02 347 2-Methylnaphthalene 802 [3] 793.86 796.18 348 cis-1,2-Dichloroethylene 733 [3] 727.64 725.05 349 Ethylene 723.15 [3] 696.01 705.72 350 Ethyl chloride 792 [3] 743.63 751.52 351 Ethane 745 [3] 686.13 703.16 352 Acetone 738 [4] 696.44 711.67 353 Propane 723 [3] 664.77 673.03 354 Chloroprene 593.15 [3] 662.97 658.21 355 cis-2-Butene 598.15 [3] 606.58 607.41 356 Diethylamine 585.15 [3] 642.66 641.28 357 Cyclopentadiene 913.15 [3] 789.12 797.29 358 2-Methyl-2-butene 563 [3] 592.56 598.40 359 p-Hydroquinone 788.7 [3] 886.08 826.80 360 2-Methyl-1,3-butadiene 493 [3] 557.72 558.01 361 2-Hexanone 697.04 [3] 632.38 622.27 362 m-Cresol 832.04 [3] 820.36 872.41 363 o-Cresol 872.04 [3] 820.36 872.41 364 2,4-Dimethylpentane 610 [3] 627.51 628.30 365 Isopropyl butyrate 708 [3] 660.07 657.35 366 3-Methylhexane 553.15 [3] 603.44 593.30 367 2,6-Xylenol 872.04 [3] 813.55 867.67 368 Vinylcyclohexene 543 [3] 547.51 543.44 369 3,4,4-Trimethyl-2-pentene 598 [3] 603.84 602.22 370 Isobutyl isobutyrate 705.15 [3] 662.79 664.73 371 Benzyl acetate 734 [3] 775.37 780.24 372 Glyceryl triacetate 706 [3] 730.63 731.12 373 Dicyclopentadiene 783.15 [3] 748.43 744.65 374 Diethyl phthalate 730.15 [3] 782.49 774.10 375 Phenyl benzoate 833 [3] 872.03 855.43 376 2-(2-Butoxyethoxy)ethanol 477.59 [3] 439.62 493.46 377 Diglycolic acid 503 [3] 649.02 626.52 378 1-Hendecene 510 [3] 480.47 491.28 379 cis-Decahydronaphthalene 523.15 [3] 526.31 522.96 380 Tetrahydro-2-furancarbinol 555.37 [3] 594.60 588.67 381 trans-2-Methylcyclohexanol 569.15 [3] 591.93 587.77 382 Morpholine 583.15 [3] 628.34 628.07 383 3,3-Dimethylpentane 610 [3] 654.71 647.27 384 4-Methyl-3-penten-2-one 617.59 [3] 602.87 606.24 385 Vinyl ether 633.15 [3] 561.74 547.47 386 Ethanamine 657 [3] 669.65 678.44 387 4-Hydroxynitrobenzene 729 [4] 730.33 731.32 388 Isocrotonic acid 669 [3] 636.73 634.34 389 Isopropylamine 675.15 [3] 672.37 685.86 390 2-Methoxy-2-methylpropane 708 [4] 642.69 634.03 391 2-Propenoic acid 688 [4] 686.57 692.73 392 2-Aminotoluene 755.15 [3] 759.51 766.35 393 Ethylene diacetate 755.15 [3] 713.98 716.99 394 Allyl chloride 663 [4] 708.80 705.13 395 1,3-Benzenedicarboxylic acid 769 [3] 814.95 810.35 396 Methyl bromide 810.37 [3] 825.37 818.85 397 1,2-Dimethyl phthalate 829 [3] 825.19 823.65 398 1,2,4-Trichlorobenzol 844.26 [3] 897.25 845.55 399 m-Nitroaniline 794 [4] 735.20 736.57 400 Dichloromethane 878 [4] 804.16 804.54 Table A2
Experimental values and predicted values of the compounds in the validation set
No. Compound name Exp. value Reference MLR Degree 3
1 1-Hexene 538 [4] 587.24 571.80 2 1-Hexadecene 513.15 [3] 373.71 554.21 3 2,3-Dimethyl-2-butene 673.7 [3] 578.54 589.59 4 Cyclohexane 533.15 [3] 583.62 577.15 5 Methylcyclohexane 558.15 [3] 581.57 576.11 6 Isopropylbenzene 697.04 [3] 742.81 753.03 7 1,3,5-Trimethylbenzene 823.15 [3] 747.83 748.34
Table A2 (Continued )
No. Compound name Exp. value Reference MLR Degree 3
8 1-Pentanol 573.15 [3] 613.12 599.87 9 1-Octanol 555 [3] 549.06 528.73 10 Phenol 878 [11] 827.16 876.07 11 Diisopropylamine 588.71 [3] 648.11 655.90 12 1,2-Dichloroethane 711 [11] 779.78 769.54 13 Isobutyl formate 593.15 [3] 704.10 711.48 14 2,3-Dimethylbutane 669 [11] 648.87 657.81 15 1,3-Cyclohexadiene 633 [11] 764.47 771.11 16 2-Methylbiphenyl 775 [11] 829.95 823.38 17 Dipropyl ether 488 [4] 546.00 529.93 18 Dihexyl ether 458.15 [3] 417.88 504.76 19 Octanoic acid 570 [3] 588.17 560.00 20 Hexylacetylene 498 [4] 474.46 492.79 21 Isopentyl nitrite 481 [4] 600.49 592.09 22 Cyclopropane 770.93 [3] 657.55 661.53 23 1-Propyne-3-ol 388.15 [3] 572.27 566.27 24 Dibutyl sebacate 638.15 [3] 457.75 494.43 25 Ethoxy ethane 433.15 [3] 588.71 575.05 26 1-Dodecene 528.15 [3] 555.54 516.29 27 1-Chloropentane 533.15 [3] 679.57 662.31 28 Ethyl acetylacetate 568.15 [3] 689.01 688.55 29 trans-4-Methylcyclohexanol 570.15 [3] 591.93 587.77 30 Ethyleneimine 593.15 [3] 704.94 717.22 31 Triethylene glycol 644 [3] 473.37 490.09 32 2-Isopropyltoluene 650 [3] 736.00 739.83 33 2-Methyl-1-propanamine 651.15 [3] 651.02 655.80 34 1-Nitropropane 694.15 [3] 619.12 612.90 35 3,5,5-Trimethyl-2-cyclohexane-1-one 733.15 [3] 617.64 626.44 36 Acetaldehyde 758.15 [3] 587.95 585.74 37 Phenylacetylene 763 [3] 656.54 647.94 38 1-Chloropropane 793.15 [3] 722.28 722.37 39 Vinylidene chloride 843 [3] 758.34 763.58 40 cis-1-Propenylbenzene 848 [3] 681.89 679.35 41 2,3-Dimethylphenol 872 [3] 813.55 867.67 42 3,4-Dimethylphenol 872.04 [3] 813.55 867.67 43 Formic acid 874.26 [3] 738.97 754.30 44 Aniline 813 [2] 766.32 778.86 45 Propylene 728.15 [3] 651.29 655.71 46 Maleic anhydride 749.82 [3] 838.71 853.23 47 1,3-Butadiene 702.04 [3] 616.46 609.80 48 1-Butene 657.04 [3] 629.94 626.27 49 1,5-Pentanediol 608.15 [3] 604.16 586.06 50 cis-2-Hexene 526 [3] 563.87 555.74 51 Ethylcyclobutane 483 [3] 609.51 602.46 52 p-Cresol 832.04 [3] 820.36 872.41 53 2-Methylhexane 566 [4] 603.44 593.30 54 n-Butyl acrylate 565.93 [3] 622.51 604.45 55 Styrene 763.15 [3] 726.61 729.15 56 Isopentyl propionate 698 [3] 638.72 627.85 57 p-Cymene 709.26 [3] 736.00 739.83 58 2-Ethylhexyl acrylate 530.93 [3] 561.18 536.87 59 1,1-Diphenylethane 713.15 [3] 818.13 816.76 60 Dibutyl phthalate 675.15 [3] 697.07 656.62
61 Ethyl methyl ether 463.15 [3] 610.06 601.61
62 Peroxyacetic acid 473.15 [3] 654.12 652.72
63 Cyclohexenylethylene 543 [3] 637.17 624.75
64 Butanoic acid anhydride 552.59 [3] 566.63 541.44
65 Cyclohexanamine 566.15 [3] 586.45 580.73 66 Tetraethylenepentamine 594 [4] 522.77 507.17 67 Nonanoic acid 589 [3] 566.82 537.71 68 Tetrahydrofuran 594.26 [3] 605.60 603.70 69 Diethylenetriamine 631 [3] 609.70 594.61 70 N,N-Dimethylbenzenamine 644.26 [3] 737.59 746.91 71 2-Butanamine 651 [3] 651.02 655.80 72 1,2,3,4-Tetramethylbenzene 700 [3] 741.02 735.04 73 2-Nitropropane 698 [4] 643.19 649.12 74 Diisopropyl ether 678 [4] 594.15 587.86
75 2-Hydroxybenzoic acid methyl ester 728 [3] 855.64 879.58
76 4-Methyl-2-pentanone 721 [4] 656.46 658.93 77 Propionitrile 785 [3] 769.48 778.49 78 2-Hydroxybenzoic acid 818.15 [3] 850.51 878.66 79 trans-1-Methylstyrene 848 [3] 681.89 679.35 80 2-Chloropropane 863 [4] 700.61 713.28 81 2,5-Dimethylphenol 872 [3] 813.55 867.67 82 4-Hydroxy-4-methyl-2-pentanone 876.48 [3] 698.77 700.47 83 1,3-Dichlorobenzene 920 [3] 854.25 880.02
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