SGC method for predicting the standard enthalpy of formation of pure compounds from their molecular structures

Thermochimica Acta 568 (2013) 46–60

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SGC method for predicting the standard enthalpy of formation of pure compounds from their molecular structures Tareq A. Albahri ∗ , Abdulla F. Aljasmi Chemical Engineering Department, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

a r t i c l e

i n f o

Article history: Received 16 February 2013 Received in revised form 14 June 2013 Accepted 18 June 2013 Available online 27 June 2013 Keywords: Standard enthalpy of formation QSPR Structure property correlation Group contribution Molecular modeling Neural networks

a b s t r a c t A theoretical method for predicting the standard enthalpy of formation of pure compounds from various chemical families is presented. Back propagation artificial neural networks were used to investigate several structural group contribution (SGC) methods available in literature. The networks were used to probe the structural groups that have significant contribution to the overall enthalpy of formation property of pure compounds and arrive at the set of groups that can best represent the enthalpy of formation for about 584 substances. The 51 atom-type structural groups listed provide better definitions of group contributions than others in the literature. The proposed method can predict the standard enthalpy of formation of pure compounds with an AAD of 11.38 kJ/mol and a correlation coefficient of 0.9934 from only their molecular structure. The results are further compared with those of the traditional SGC method based on MNLR as well as other methods in the literature. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The standard enthalpy of formation or standard heat of formation (H◦ f ) is defined as the isothermal enthalpy change of reaction to form 1 mol of a compound from its constituent elements in their standard states at 298.15 K and 1 atm. Elements in their standard states have standard enthalpy of formation of zero. The standard enthalpy of formation is one of the most important thermodynamic properties in the design and operation of industrial chemical processes to calculate the standard enthalpy change of reaction. The standard enthalpy change of a reaction is the difference between the sum of the standard heats of formation of the reactants and the sum of the standard heats of formation of the products. Chemical industries produce about 1000 new compounds each year [1]. It is extremely important to know the basic properties of these compounds such as the enthalpy of formation (or reaction). However, these properties have been experimentally measured for only a fraction of these compounds making it essential to develop accurate methods to predict them. There are many methods available in literature for estimating H◦ f of pure compounds. Detailed literature review of some of these models is presented in Gharagheizi [1] the majority of which are limited to special families of chemical compounds. Among these

∗ Corresponding author. Tel.: +965 2481 7662x7459; fax: +965 2483 9498. E-mail address: [email protected] (T.A. Albahri). 0040-6031/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2013.06.020

methods that use the molecular structure of the chemical compound are Joback and Reid [2], Benson [3], Constantinou and Gani [4], Yoneda [5] Thinh et al. [6,7], and Cardozo [8]. In these methods the property of a compound is related to the contribution of simple chemical groups that occur in the molecular structure. These methods have the advantage of giving rapid estimates without using substantial computational resources. The binary group contributions method of Benson [3] and Yoneda [5] allow for effects of next-nearest atom neighbors and yield the smallest errors but are more cumbersome. The method of Thin et al. [6,7] is also accurate but limited to only hydrocarbons. The method of Joback and Reid [2] is broadly applicable and, on the average, is slightly less accurate than Benson’s or Yoneda’s but produces large errors for some compounds. The method of Cardozo [8] is the simplest but least accurate of all. More accurate methods for estimating H◦ f use quantitative structure–property relations (QSPR) combined with advanced mathematical methods such as neutral networks, genetic algorithms, etc. to provide a relationship between the property of the compound and the molecular structure. Hu et al. [9] for example proposed a neural-network-based algorithm to reduce the inherent numerical errors caused by various intrinsic approximations of first-principles quantum mechanical calculations for the evaluation of standard enthalpy of formation for 180 small- to mediumsized organic molecules at 298 K. Although a dramatic reduction of numerical errors is clearly shown with systematic deviation being eliminated, the model was limited to only 180 organic molecules which limit its generality and applicability.

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

Vatani [10] used genetic algorithm with multivariate linear regression (MLR) to develop the following equation that can predict H◦ f for 1115 compounds: H ◦ f (kJ/mol) = 50.1688 − 80.52012nSK + 5364546SCBO − 169.21889nO − 174.75477nF − 266.57659nHM (1) R2 (squared correlation coefficient) = 0.9830, F (Fisher factor) = 10239.02, s (standard deviation) = 58.541, Q2 (squared cross validated correlation coefficient) = 0.9826. In the above equation, nSK is the number of non-H atoms, SCBO is the sum of conventional bond orders (H-depleted), nO and nF are the number of oxygen and fluorine atoms respectively and nHM is the number of heavy atoms. Similarly, Gharagheizi [1] developed an equation using the same method (genetic algorithm based on multivariate linear regression) to predict H◦ f for 1692 pure compounds. The equation below contains nine parameters. H ◦ f (kJ/mol) = 117.3219(±12.0545) + 189.0579(±4.6667)nN −263.8545(±11.1329)nHM + 2.1918(±0.0696)ZM2V −66.1868(±5.3618)BEHm3 + 177.2832(±1.9740)SEigv

(2)

−20.0659(±1.2306)RDF015m + 47.1921(±3.7695)Mor03p −63.5796(±3.4866)nHDon − 116.3568(±5.0137)C − 040

Ntraining = 1354; ntest = 338; R2 = 0.9499; Q2 Loo = 0.9481; Q2 BOOT = 0.9469; Q2 EXT = 0.9749; S = 104.03; a = 0.477; F = 2830.03. In the above equation, nN is the number of nitrogen atoms, nHM is the number of heavy atoms, ZM2V is second Zagreb index by valence vertex degrees, BEHm3 is highest Eigenvalue n.3 of burden matrix/weighted by atomic masses, SEigv is Eigenvalue sum from van der Waals weighted distance matrix, RDF015m is radial distribution function – 1.5/weighted by the atomic masses, Mor03p is 3D-MoRSE signal 03/weighted by atomic polarizabilities, nHDon is number of donor atoms for H-bonds (N and O), and C-040 is R–C( X)–X/R–C#X/X C X. Although the above correlations were able to predict H◦ f accurately enough with a correlation coefficient of 0.98 and 0.94 for Vatani’s [10] and Gharagheizi’s [1], respectively, they require intricate parameters (descriptors), that are not readily available which makes both methods inconvenient to use in practice. 2. Method The enthalpy of formation is one of the most difficult properties to estimate or correlate because of its complex dependency on the molecular structure of the molecule. Enthalpy is directly related to the bond properties. Breaking bonds of reacted elements and formation of new bonds of products results in enthalpy. The H◦ f of n-paraffins is a function of the size or number of carbon atoms in the molecule. For more complex compounds like iso-paraffins in addition to the total number of carbon atoms H◦ f depends on the type, length, and degree of branching in the molecule in addition to the presence of non-organic atoms such as oxygen, chlorine and heavy atoms. The location of the unsaturated bond along the chain and the cis- and trans-structural orientation also has an influence on H◦ f . The H◦ f of aromatics is a function of the number and type of benzene rings (condensed or non-condensed), the number of alkyl groups attached to the benzene ring, their type, length, degree of branching and to some extent their location on the ring in the ortho-, meta-, and para-positions. Cyclic compounds are the most complex because in addition to all of the above factors, their H◦ f is a function of not only the number of cyclic rings but their size as well, in addition to the number and degree of branching of the alkyl

47

groups attached to the cyclic ring, the (cis- and trans-) structural orientation and the location of the alkyl groups on the ring. This is further complicated by the coexistence of several of these groups in one molecule in addition to other functional groups for halogenated compounds, acids, ethers, ketones, aldehydes, alcohols, phenols, esters, amines, anhydrides, and sulfur compounds, which makes it difficult to formulate a model that can incorporate the behavior of all the different groups without taking into account the structure of the molecules. Such complex dependency on the molecular structure can only be adequately represented by a model that takes into account the contribution of such structures in the molecule to the H◦ f property. 2.1. Structural group contribution (SGC) method A careful examination of (H◦ f ) of hundreds of pure compounds reveals its complex dependency on the molecular structure of the substance. In this work we investigate this structural dependency of (H◦ f ) using a SGC approach which has proven to be a very powerful tool for predicting many physical and chemical properties of pure compounds. The method was successfully used to predict pure compound properties like the critical temperature, critical pressure, critical volume, boiling point, freezing point, molar volume, viscosity, surface tension, diffusivity, thermal conductivity, heat capacity, heat of combustion, entropy, and Gibbs free energy [11]. Furthermore, there are many commercial applications in the form of computer programs that estimate the properties of pure compounds from their chemical structure currently being marketed such as AIChE-Cranium and ASTM-CHETAH. There are many structural group contribution methods in the literature including, but not limited to the work of Ambrose, Joback, Fedors, Thin et al., Benson, Qrrick-Erbar, Grunberg-Nissan, and Chueh-Swanson [11]. The main differences between these are in the choice of the structural groups and the way in which they contribute to the overall property. 2.2. Technical development Enthalpy of formation is one of the macroscopic properties of compounds which are related to the molecular structure and determines the magnitude and predominant types of the intermolecular forces. The concept of structure suggests that a macroscopic property can be calculated from group contributions. The relevant characteristics of structure are related to the atoms; atomic groups, bond type etc.; to them we assign weighting factors and then determine the property, usually by an algebraic expression which sums the contributions from the molecule’s parts. Of the many SGC estimation methods available in the literature, a combination of Ambrose, Joback and Chueh-Swanson group contributions were selected on the basis of their generality and accuracy [11]. This combination was tested and then modified to account for the functional groups in the molecules which result in the best correlation coefficient and average error using Artificial Neural Networks (ANN). It was found necessary to modify the structural groups to account only for the ones that have an influence on the overall (H◦ f ) property. For example, no significant distinction in the (H◦ f ) existed for the cis- and trans-structural orientations in olefins or cyclic compounds. Hence, such distinction was avoided in the choice of the structural groups. It was also unnecessary to account for the location of the alkyl substitutions on the benzene ring in the ortho-, meta-, and para-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 location of the alkyl substitutions for naphthenes. Our attempts to enhance the model results by using

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Standard Enthalpy of Formation

Output

1 Bias

W1

Hidden

1

2

8 Bias

W2

Input

1

2

3

51

-CH3

>CH2

>CH-

>S=

Fig. 1. Schematic structure of the three-layer artificial neural network used for predicting the standard enthalpy of formation for pure compounds from their structural groups.

two sets of structural groups, one for the aromatic ring in aromatics and another for the cyclic ring in naphthenes did not result in a significant improvement in the model predictions and correlation of the experimental data. Therefore such distinctions between the structural groups in the naphthenic and aromatic rings were avoided. 2.3. SGC-based ANN model The neural network technique has been applied widely to various engineering areas. Examples in chemical engineering include the modeling of petroleum refining processes like the hydrocracker [12], and the prediction of the thermodynamic [13] and the transport [14] properties of pure compounds. The neural network method of computation has several advantages over traditional methods especially in the speed of computation, learning ability, and fault tolerance. The theoretical basis of neural computing has been reported elsewhere [15,16]. The concept of using SGC-based ANNs in predicting pure compounds properties is not new. It has been previously demonstrated to predict very accurately the thermodynamic properties of pure compounds such as the normal boiling point, the critical properties, and the acentric factor [13] in addition to the enthalpy of fusion [17]. In this work we investigate the structural dependency of (H◦ f ) using a SGC approach. For that purpose an artificial neural network model was constructed using MATLAB [18] code to test several SGC methods and atom-type structural group definitions available in literature [11]. The model was used to probe the structural groups that have significant contribution to the (H◦ f ) property of pure compounds and arrive at the final groups that provided the best correlation of the experimental data. Furthermore, the final groups arrived at were assessed for their capacity to predict the (H◦ f ) of pure compounds using the said constructed ANN model. Several ANN architectures were tried and the one that best simulate the (H◦ f ) was retained. The final ANN network structure is shown in Fig. 1 and consists of three layers: input, output, and hidden. The input layer has a number of neurons equal to the number

of the structural groups being investigated. The hidden layer is a single layer with eight neurons, and the output layer consists of one neuron representing the predicted (H◦ f ) property. A sigmoid function was selected as the transfer function for each neuron. The inputs to the network algorithm are the number of occurrences of the structural groups in the given molecule. If a certain input group in the network did not exist in a molecule an input value of zero is assigned to that group. When comparing the different SGC methods in the literature and arriving at the final list of atom-type groups, the complete data set of 584 substances were used in the ANN model as input. This probing data set was taken from the property databank of API-TDB [19]. Each one of these 584 input sets included a groupnumber vector representing the number of the structural groups in a given substance. The connection weights of the network were adjusted iteratively by the back-propagation algorithm with the generalized delta rule to minimize the mean square error between the desired and the actual outputs. During the probing course, we recorded the average absolute deviation (AAD), maximum deviation, and the correlation coefficient (R) of the predictions along with the corresponding time steps (Epochs). These were used to select (define) the atom-type structural groups that gave the best results in terms of correlation coefficient and average error. It was found that 300 epochs were sufficient to achieve the convergence, where the deviation between the actual and the desired responses has no significant change, thus the calculation was terminated at that number of time steps. Convergence was less than a minute for all cases investigated on a personal computer. To make sure the network is trained with the experimental data and does not just memorize them, the maximum number of neurons in the hidden layer is determined using the following equation for a three-layer network architecture shown in Fig. 1: H<

 (0.9 × D − 1)  I

− 2.

(3)

In the above equation H is the number of neurons in the hidden layer (rounded down), D is the number of experimental data points available, I is the number of input (groups) to the neural network, and 0.9 is to account for only 90% of the data points actually used for training whereas the rest 10% will be used for testing the trained network. This equation was developed based on the constraint that the number of dependent variables (weights and biases) may not be greater than the number independent variables (experimental data). Therefore, H must be rounded down to the nearest whole number. The actual number of hidden-layer neurons was arrived at by stepping down one number at a time until the best results, as indicated by the correlation coefficient, are obtained for both the training and testing data sets. After arriving at the best network architecture shown in Fig. 1, we demonstrated the predictive ability of the ANN by training it with the enthalpy of formation of 524 molecules. The trained networks were then applied to predict the enthalpy of formation of the 60 remaining molecules, which were not included in the training database. The compounds in the testing set were randomly chosen based on the abundance of their counterparts (the class of compounds they represent) in the training data set on which the neural networks were trained. This is necessary since ANN cannot predict the (H◦ f ) property of a class of compounds on which it was not trained. The accuracy of these predictions was compared with the available experimental data [19]. 2.4. SGC-based MNLR model In a traditional SGC approach, the group contributions are usually incorporated in some form of an algebraic equation relating other properties like boiling point, molecular weight, or just plain

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

constants, to estimate the desired property. Many equations have been proposed ranging from simple relations to complicated polynomials [11]. We have previously tested several equations and found the best to predict the target property in the following nonlinear form [20–22]: 2

3

˚ = a + b(˙ni ( )i ) + c(˙ni ( )i ) + d(˙ni ( )i ) + e(˙ni ( )i )

4

(4)

where a, b, c, d, and e are correlation constants to be determined by multivariable regression of experimental data, ˚ is the target property of interest, ni is the number of occurrence of each structural groups in the molecule, (φ )i is the contribution value of each ni (φ )i is the sum of the strucatom-type structural group, and ture group contributions for each molecule to the target property that are also determined from experimental data during the multivariable nonlinear regression process. 3. Results and discussion 3.1. SGC-based MNLR model Using the experimental data on H◦ f of 584 pure compounds from the API-TDB [19], the constants for Eq. (4) and the values of the various structural group contributions shown in Table 1 were calculated. An optimization algorithm based on the least square method was used for that purpose. The algorithm minimizes the sum of the difference between the calculated and experimental H◦ f using the general reduced gradient (GRG) nonlinear optimization method in the solver function of Microsoft Excel. Conversion of the above regression algorithm was achieved in less than 1 min on a desktop personal computer. The final equation obtained is: H ◦ f = 23.084 + ˙ni ( )i where H◦

(5)

f is the standard enthalpy of formation in kJ/mole, (φ )i is the atom-type structural group contribution, ni is the number of occurrences of the structural in each molecule, and ni (φ )i is the sum of the atom-type structural group contributions to the total standard enthalpy of formation. The optimal values of the constants c, d, and e in Eq. (4) were all determined to be zero making the final H◦ f equation linear. The values of the molecular contributions (φ )i for each atom-type structural group are shown in Table 1. The calculation procedure for H◦ f using the Eq. (5) and the SGC values in Table 1 is illustrated in the Appendix A for p-diethyl benzene. We have had big success in the past using the least square method and MS Excel to estimate the parameters of the traditional SGC approach for predicting such properties as octane number [20], aniline point [22] and auto ignition temperature, flash point, and upper and lower flammability limits [21] with correlation coefficients as high as 0.99. In some of these cases we have had more components and more structural groups. Therefore, using MS Excel seems to be a judicial choice for its simplicity, surprisingly faster convergence, and equal effectiveness to other optimization tools for the task in hand. The results for the traditional SGC-MNLR model predictions for H◦ f using Eq. (5) and the structural group contributions in Table 1 are summarized in row 4 of Table 2. The models predictions did not correlate very well with the experimental data as shown in Fig. 2 with a correlation coefficient of 0.90 and an absolute average deviation and error of 37.11 kJ/mol and 34.98%, respectively. The detailed results and compounds used in the SGC-MLR model are listed in Table 3. From the success we have had in the past predicting other properties [20–22] it is our conclusion that the impediment is related not to the optimization tool used but in fact to the H◦ f property which is too complex to model for various families of chemical compounds using the traditional SGC approach based on MNLR and the least square technique which

49

Table 1 Structural groups corresponding to the input nodes of the artificial neural network in Fig. 1 for the SGC-ANN model and the structural group contribution values for the SGC-MNLR model for estimating the standard enthalpy of formation of pure compounds. Serial no.

Group

( )i

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

–CH3 >CH2 >CH– >C< CH2 CH– C< C CH C– >CH2 (ring) >CH– (ring) >C< (ring) CH– (ring) C< (ring) –F –Cl –Br –OH (alcohol) –O– (nonring) >C O (nonring) O CH–(aldehyde) –COOH (acid) –COO– (ester) O –NH2 >NH (nonring) >N– (nonring) –CN –OH (phenol) –O– (ring) >C O (ring) >NH (ring) –N (ring) >N– (ring) –H >S –SH S N S –OH (acid) Na+ OH− N+ –N –O− –N+ >N

−51.2687 −19.0480 3.1420 21.8887 7.5411 31.2103 52.3869 127.7098 81.8400 109.4003 −20.9319 16.8999 56.8728 10.1903 24.5625 −184.9584 −64.9778 −7.4367 −189.5989 −133.7810 −158.6232 −144.6825 −410.1985 −34.4030 −275.0350 −24.0732 29.0316 58.8027 131.5326 −197.9590 −110.4227 −110.7879 8.6438 67.9155 0.0001 −25.8277 22.7305 37.1750 −20.0517 −13.5565 224.3873 −214.4126 −227.2361 0.0001 336.1508 −199.0195 265.1584 13.8287 0.0001

50 51

>S

214.9467 139.2612

suffers from several shortcomings. These limitations are mainly associated with using a simple correlation (Eq. 5) which is unable to capture the complex nature of the H◦ f property. In addition, as in many other iterative techniques, the method success is dependent on effectively providing appropriate initial values of the group contributions. It is our experience that minor improvement if any can be obtained using other optimization tools such as MATLAB or GAMS. 3.2. SGC-based ANN model Using the probing set of data on (H◦ f ) of 584 pure compounds [19], which included halogenated compounds, acids, ethers, ketones, aldehydes, alcohols, phenols, esters, amines, anhydrides, and sulfur compounds, several structural groups

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Table 2 Comparison of the present SGC-ANN and SGC-MNLR models with others from the literature for estimating the standard enthalpy of formation for pure components. Method

Set

AAD (kJ/mol)

Correlation coefficient

This work (SGC-ANN model) This work (SGC-ANN model) This work (SGC-ANN model) This Work (SGC-MNLR model) Vatani [10] Gharagheizi [1]

Overall (584 compounds) Training (524 compounds) Testing (60 compounds) Overall (584 compounds) Overall Overall

11.38 11.74 8.24 34.98 58.54 104.03

0.9934 0.9928 0.9979 0.90 0.983 0.94

AAD, absolute average deviation.

derived from the Ambrose, Joback and Chueh-Swanson definitions of group contributions [11] were tested and modified. During this probing stage, the correlation coefficient was used as an indication to discriminate between the SGC methods and the structural groups that have significant contribution to the (H◦ f ) property of pure compounds. It was finally arrived at the set of groups that can best represent the experimental data with a correlation coefficient of 0.9928 consisting of the 51 structural groups shown in Table 1. In addition to the above proposed structural groups, several other groups have also been investigated. Although better results were obtained with a larger number of structural groups, the improvement was not significant. The correlation coefficient and the average deviation in the predicted (H◦ f ) for all types of pure compounds ranging in (H◦ f ) from −13,614.08 to 8,701.84 (kJ/kg) are shown in Table 2 for the training, testing and overall data sets. To assess the accuracy of the models prediction, the data were then separated into training and testing data sets consisting of 524 and 60 pure compounds, respectively. The % error between the predicted H◦ f and the experimental data used in training the network was calculated. The results from the trained network are summarized in Table 2 with a correlation coefficient of 0.9934. As can be seen, the correlation of the neural network model for the training data set is very good. The predictive ability of the trained networks has been cross validated against a testing set of data of 60 compounds not originally used in the training process. The percentage error between the predicted H◦ f and the experimental data used in testing the network was calculated. The detailed results and compounds

used in training and testing the ANN are listed in Table 3 for both ANN and MNLR models. Comparing with the experimental values, we found the predictions to be comparable to the trained networks in terms of AAD and correlation coefficients as shown in Table 2. A parity plot showing the accuracy of models correlation for both training and testing is presented in Fig. 3. As can be seen, the predictions of the SGC-ANN model are excellent. Weights fitted in the ANN architecture are shown in Table 4. The method of Gharagheizi [1] is reported to give a maximum deviation greater than 100%, and is further complicated by the use of equations with intricate molecular descriptors that have to be determined manually making the method inconvenient. The method of Vatani et al. [10] is also reported to give maximum deviation greater than 156% and uses a more intricate equation than Gharagheizi [1], making the method even more difficult and less accurate to use. Our proposed method is therefore better than those of Gharagheizi [1] and Vatani et al. [10] in terms of generality, accuracy, simplicity, and convenience; requiring only the molecular structure of the compound which is always known, with no intricate molecular descriptors to be determined. Using the traditional SGC-MNLR model has previously proven to be very successful for predicting the properties of pure hydrocarbons with correlation coefficient as high as 0.99 [20–22]. However, when the method was applied in addition to other classes of compounds with various functional groups, it was not as successful with correlation coefficients ranging from 0.79 to 0.90 [23]. This is also noticed by many others [24,25]. In this work the traditional

1000

1000

R = 0.99

R = 0.90 500 Predicted ∆H0f (kJ/mole)

Predicted ∆H0f (kJ/mole)

500

0

-500

-500

Training Data Set Testing Data Set

-1000

-1000

-1500 -1500

0

-1000

-500

0

500

1000

Experimental ∆H0f (kJ/mole) Fig. 2. Parity plot showing the accuracy of the models correlation for the standard enthalpy of formation for the overall set of 584 pure compounds using the SGCMNLR model.

-1500 -1500

-1000

-500

0

500

1000

Experimental ∆H0f (kJ/mole) Fig. 3. Parity plot showing the accuracy of the models correlation for the enthalpy of formation for a training set of 524 pure compounds and prediction for a testing set for 60 compounds using the SGC-ANN model.

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Table 3 The overall set of compounds used during model development for H◦ f (kJ/mol) along with percentage errors (comparison between experimental data and correlated and calculated results for training and testing, respectively) for both SGC-ANN and SGC-MNLR models. Serial No.

Compound

Status

Exp.a

SGC-ANN model Calc.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

Methane Ethane Propane n-Butane Isobutane n-Pentane Isopentane (2-methylbutane) Neopentane (2,2-dimethylpropane) n-Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane (neohexane) 2,3-Dimethylbutane n-Heptane 2-Methylhexane 3-Methylhexane 3-Ethylpentane 2,2-Dimethylpentane 2,3-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane 2,2,3-Trimethylbutane (Triptane) n-Octane 2-Methylheptane 3-Methylheptane 4-Methylheptane 3-Ethylhexane 2,2-Dimethylhexane 2,3-Dimethylhexane 2,4-Dimethylhexane 2,5-Dimethylhexane (diisobutyl) 3,3-Dimethylhexane 3,4-Dimethylhexane 2-Methyl-3-Ethylpentane 3-Methyl-3-Ethylpentane 2,2,3-Trimethylpentane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 2,3,4-Trimethylpentane 2,2,3,3-TetraMethylButane n-Nonane 2-Methyloctane 3-Methyloctane 4-Methyloctane 3-Ethylheptane 2,2-Dimethylheptane 2,6-Dimethylheptane 2,2,3-Trimethylhexane 2,2,4-Trimethylhexane 2,2,5-Trimethylhexane 2,3,3-Trimethylhexane 2,3,5-Trimethylhexane 2,4,4-Trimethylhexane 3,3,4-Trimethylhexane 3,3-Diethylpentane 2,2-Dimethyl-3-ethylpentane 2,4-Dimethyl-3-ethylpentane 2,2,3,3-Tetramethylpentane 2,2,3,4-Tetramethylpentane 2,2,4,4-Tetramethylpentane 2,3,3,4-Tetramethylpentane n-Decane 2-Methylnonane 3-Methylnonane 4-Methylnonane 5-Methylnonane 2,7-Dimethyloctane 3,3,4-Trimethylheptane 3,3,5-Trimethylheptane 2,2,3,3-Tetramethylhexane 2,2,5,5-Tetramethylhexane 2,4-Dimethyl-3-Isopropylpentane

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−74.52 −83.85 −104.69 −125.65 −134.99 −146.71 −153.70 −168.07 −166.95 −174.69 −172.06 −184.68 −176.80 −187.65 −194.72 −191.33 −189.33 −205.81 −194.10 −201.67 −199.79 −204.43 −208.82 −215.35 −212.51 −211.96 −210.71 −224.60 −213.80 −219.24 −222.51 −219.99 −212.67 −212.80 −214.85 −219.95 −224.01 −218.45 −217.32 −225.73 −228.86 −235.85 −233.70 −235.21 −231.46 −246.10 −242.80 −241.42 −243.17 −253.30 −239.28 −242.55 −239.96 −235.39 −232.84 −231.29 −227.94 −237.11 −234.97 −242.26 −236.32 −249.53 −256.52 −254.39 −254.72 −254.72 −263.51 −257.74 −259.87 −257.99 −285.90 −238.86

−73.61 −83.94 −102.33 −117.87 −135.14 −136.56 −150.04 −171.61 −159.81 −169.94 −169.94 −184.75 −176.43 −182.74 −193.81 −193.81 −193.81 −197.20 −200.91 −200.91 −197.20 −201.96 −205.08 −216.95 −216.95 −216.95 −216.95 −220.78 −228.61 −228.61 −228.61 −220.78 −228.61 −228.61 −220.78 −215.20 −215.20 −215.20 −209.92 −221.46 −226.84 −239.12 −239.12 −239.12 −239.12 −237.80 −254.93 −241.41 −241.41 −241.41 −241.41 −244.90 −241.41 −241.41 −237.80 −241.41 −244.90 −244.96 −229.99 −244.96 −229.99 −248.03 −251.81 −251.81 −251.81 −251.81 −279.66 −255.92 −255.92 −269.04 −269.04 −225.43

Dev. 0.91 −0.08 2.36 7.78 −0.15 10.15 3.66 −3.54 7.14 4.75 2.12 −0.07 0.36 4.90 0.90 −2.48 −4.48 8.60 −6.81 0.76 2.58 2.47 3.74 −1.59 −4.43 −4.98 −6.23 3.82 −14.81 −9.37 −6.10 −0.79 −15.94 −15.81 −5.93 4.75 8.81 3.25 7.40 4.27 2.03 −3.27 −5.42 −3.91 −7.66 8.30 −12.13 0.01 1.76 11.89 −2.13 −2.35 −1.46 −6.02 −4.96 −10.12 −16.96 −7.85 4.98 −2.71 6.32 1.50 4.71 2.58 2.91 2.91 −16.15 1.81 3.95 −11.05 16.85 13.44

SGC-MNLR model % Error 1.22 −0.10 2.26 6.19 −0.11 6.92 2.38 −2.11 4.28 2.72 1.23 −0.04 0.21 2.61 0.46 −1.30 −2.37 4.18 −3.51 0.37 1.29 1.21 1.79 −0.74 −2.09 −2.35 −2.96 1.70 −6.93 −4.27 −2.74 −0.36 −7.49 −7.43 −2.76 2.16 3.93 1.49 3.41 1.89 0.89 −1.39 −2.32 −1.66 −3.31 3.37 −5.00 0.00 0.72 4.69 −0.89 −0.97 −0.61 −2.56 −2.13 −4.37 −7.44 −3.31 2.12 −1.12 2.68 0.60 1.84 1.01 1.14 1.14 −6.13 0.70 1.52 −4.28 5.89 5.63

Calc. −54.01 −79.45 −98.50 −117.55 −127.58 −136.60 −146.63 −160.10 −155.65 −165.68 −165.68 −179.15 −175.71 −174.69 −184.72 −184.72 −184.72 −198.20 −194.75 −194.75 −198.20 −208.23 −193.74 −203.77 −203.77 −203.77 −203.77 −217.25 −213.80 −213.80 −213.80 −217.25 −213.80 −213.80 −217.25 −227.28 −227.28 −227.28 −223.83 −240.75 −212.79 −222.82 −222.82 −222.82 −222.82 −236.29 −232.85 −246.32 −246.32 −246.32 −246.32 −242.88 −246.32 −246.32 −236.29 −246.32 −242.88 −259.80 −256.36 −259.80 −256.36 −231.84 −264.06 −264.06 −264.06 −264.06 −251.90 −265.37 −265.37 −278.85 −278.85 −271.96

Dev. 20.51 4.40 6.19 8.10 7.41 10.12 7.07 7.97 11.30 9.01 6.38 5.53 1.09 12.95 9.99 6.60 4.60 7.61 −0.66 6.91 1.59 −3.80 15.08 11.58 8.74 8.19 6.94 7.36 0.00 5.44 8.71 2.75 −1.13 −1.00 −2.39 −7.32 −3.26 −8.82 −6.51 −15.02 16.07 13.03 10.88 12.39 8.64 9.81 9.95 −4.90 −3.15 6.97 −7.04 −0.33 −6.37 −10.93 −3.45 −15.03 −14.94 −22.68 −21.38 −17.54 −20.04 17.70 −7.53 −9.67 −9.33 −9.33 11.61 −7.64 −5.50 −20.85 7.05 −33.10

% Error 27.52 5.25 5.91 6.44 5.49 6.89 4.60 4.74 6.77 5.16 3.71 2.99 0.62 6.90 5.13 3.45 2.43 3.70 0.34 3.43 0.79 1.86 7.22 5.38 4.11 3.86 3.29 3.28 0.00 2.48 3.91 1.25 0.53 0.47 1.11 3.33 1.46 4.04 3.00 6.65 7.02 5.53 4.66 5.27 3.73 3.99 4.10 2.03 1.30 2.75 2.94 0.14 2.65 4.64 1.48 6.50 6.55 9.57 9.10 7.24 8.48 7.09 2.94 3.80 3.66 3.66 4.41 2.96 2.12 8.08 2.47 13.86

52

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

Table 3 (Continued) Serial No.

Compound

Status

Exp.a

SGC-ANN model

73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

n-Undecane n-Dodecane n-Tridecane n-Tetradecane n-Pentadecane n-Hexadecane n-Heptadecane n-Octadecane n-Nonadecane n-Eicosane n-Heneicosane n-Docosane n-Tricosane n-Tetracosane n-Pentacosane n-Hexacosane n-Heptacosane n-Octacosane n-Nonacosane n-Triacontane Cyclopropane Methylcyclopropane Ethylcyclopropane cis-1,2-Dimethylcyclopropane Cyclobutane Methylcyclobutane Ethylcyclobutane Cyclopentane Methylcyclopentane Ethylcyclopentane 1,1-Dimethylcyclopentane cis-1,2-Dimethylcyclopentane trans-1,2-Dimethylcyclopentane cis-1,3-Dimethylcyclopentane trans-1,3-Dimethylcyclopentane n-Propylcyclopentane Isopropylcyclopentane 1-Methyl-1-Ethylcyclopentane cis-1-Methyl-2-Ethylcyclopentane trans-1-Methyl-2-Ethylcyclopentane cis-1-Methyl-3-ethylcyclopentane trans-1-Methyl-3-ethylcyclopentane 1,1,2-Trimethylcyclopentane 1,1,3-Trimethylcyclopentane 1,c-2,c-3-Trimethylcyclopentane 1,c-2,t-3-Trimethylcyclopentane 1,t-2,c-3-Trimethylcyclopentane 1,c-2,c-4-Trimethylcyclopentane 1,c-2,t-4-Trimethylcyclopentane 1,t-2,c-4-Trimethylcyclopentane n-Butylcyclopentane Isobutylcyclopentane 1-Methyl-1-n-propylcyclopentane 1,1-Diethylcyclopentane cis-1,2-Diethylcyclopentane 1,1-Dimethyl-2-Ethylcyclopentane n-Pentylcyclopentane n-Hexylcyclopentane n-Heptylcyclopentane n-Octylcyclopentane n-Nonylcyclopentane n-Decylcyclopentane n-Undecylcyclopentane n-Dodecylcyclopentane n-Tridecylcyclopentane n-Tetradecylcyclopentane n-Pentadecylcyclopentane n-Hexadecylcyclopentane n-Heptadecylcyclopentane n-Octadecylcyclopentane n-Nonadecylcyclopentane n-Eicosylcyclopentane Cyclohexane Methylcyclohexane

Train Test Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train

−270.16 −290.79 −311.43 −332.05 −352.69 −374.17 −393.94 −414.58 −435.21 −455.84 −435.69 −498.58 −519.28 −539.99 −560.71 −581.42 −602.10 −622.84 −643.54 −664.26 53.45 73.31 52.59 31.13 27.24 25.27 46.73 −77.24 −106.69 −127.07 −127.07 −129.54 −136.69 −135.86 −133.59 −148.07 −65.94 −78.70 −78.70 −78.70 −78.70 −78.70 −100.16 −100.16 −78.70 −100.16 −100.16 −100.16 −100.16 −100.16 −168.28 −98.07 −99.41 −99.41 −99.41 −120.88 −188.91 −209.49 −230.12 −250.70 −271.33 −291.96 −312.55 −333.17 −353.76 −374.38 395.01 −415.60 −347.19 −367.91 −388.61 −409.33 −123.13 −154.77

−268.70 −288.84 −308.49 −327.65 −346.33 −364.55 −382.30 −399.61 −416.47 −432.89 −448.89 −464.47 −479.64 −494.41 −508.79 −522.80 −536.44 −549.72 −562.67 −575.28 53.01 62.06 27.58 34.54 32.53 11.76 23.69 −38.40 −64.86 −96.46 −92.07 −85.51 −85.51 −85.51 −85.51 −126.73 −56.50 −92.07 −119.18 −119.18 −119.18 −119.18 −100.07 −100.07 −100.61 −100.61 −100.61 −100.61 −100.61 −100.61 −155.69 −89.92 −100.02 −100.02 −151.50 −137.82 −183.38 −183.38 −239.19 −259.35 −282.48 −304.59 −325.75 −345.88 −361.42 −277.26 363.60 −298.98 −402.55 −421.31 −436.71 −451.49 −93.58 −130.97

Calc.

Dev. 1.47 1.95 2.94 4.40 6.35 9.62 11.64 14.97 18.74 22.95 −13.20 34.11 39.65 45.58 51.92 58.62 65.66 73.12 80.87 88.98 −0.44 −11.24 −25.01 3.41 5.29 −13.51 −23.04 38.84 41.84 30.60 35.00 44.03 51.18 50.35 48.09 21.34 9.43 −13.37 −40.49 −40.49 −40.49 −40.49 0.09 0.09 −21.91 −0.45 −0.45 −0.45 −0.45 −0.45 12.59 8.16 −0.61 −0.61 −52.09 −16.94 5.53 26.11 −9.07 −8.65 −11.14 −12.63 −13.21 −12.71 −7.66 97.13 −31.42 116.62 −55.36 −53.41 −48.11 −42.16 29.56 23.80

SGC-MNLR model % Error 0.54 0.67 0.94 1.33 1.80 2.57 2.96 3.61 4.31 5.03 −3.03 6.84 7.63 8.44 9.26 10.08 10.91 11.74 12.57 13.39 0.82 15.34 47.55 −10.95 −19.43 53.45 49.31 50.29 39.21 24.08 27.54 33.99 37.44 37.06 35.99 14.41 14.31 −16.99 −51.44 −51.44 −51.44 −51.44 0.09 0.09 −27.84 −0.45 −0.45 −0.45 −0.45 −0.45 7.48 8.32 −0.61 −0.61 −52.39 −14.02 2.93 12.46 −3.94 −3.45 −4.11 −4.33 −4.23 −3.81 −2.17 25.94 7.95 28.06 −15.95 −14.52 −12.38 −10.30 24.00 15.38

Calc.

Dev.

−250.89 −269.93 −288.98 −308.03 −327.08 −346.13 −365.17 −384.22 −403.27 −422.32 −441.37 −460.41 −479.46 −498.51 −517.56 −536.61 −555.65 −574.70 −593.75 −612.80 −39.71 −53.15 −72.20 −66.59 −60.64 −74.08 −93.13 −81.58 −95.01 −114.06 −106.31 −108.45 −108.45 −108.45 −108.45 −133.11 −143.14 −125.36 −127.50 −127.50 −127.50 −127.50 −119.74 −119.74 −121.89 −121.89 −121.89 −121.89 −121.89 −121.89 −152.16 −162.19 −144.40 −144.40 −146.55 −138.79 −171.20 −190.25 −370.40 −228.35 −247.40 −266.44 −285.49 −304.54 −323.59 −342.64 −361.68 −380.73 −399.78 −418.83 −437.88 −456.92 −102.51 −115.94

19.28 20.86 22.45 24.02 25.61 28.04 28.77 30.36 31.94 33.52 −5.68 38.16 39.82 41.48 43.15 44.81 46.45 48.14 49.79 51.46 −93.16 −126.46 −124.79 −97.71 −87.88 −99.35 −139.86 −4.34 11.68 13.01 20.76 21.09 28.24 27.41 25.15 14.96 −77.20 −46.66 −48.80 −48.80 −48.80 −48.80 −19.58 −19.58 −43.19 −21.72 −21.72 −21.72 −21.72 −21.72 16.13 −64.11 −44.99 −44.99 −47.13 −17.92 17.71 19.24 −140.28 22.36 23.94 25.52 27.05 28.63 30.17 31.75 −756.70 34.86 −52.59 −50.92 −49.27 −47.59 20.63 38.82

% Error 7.14 7.17 7.21 7.24 7.26 7.49 7.30 7.32 7.34 7.35 1.30 7.65 7.67 7.68 7.70 7.71 7.71 7.73 7.74 7.75 −174.30 −172.50 −237.28 −313.91 −322.63 −393.14 −299.27 5.62 10.95 10.24 16.34 16.28 20.66 20.17 18.82 10.11 117.09 59.28 62.00 62.00 62.00 62.00 19.55 19.55 54.88 21.69 21.69 21.69 21.69 21.69 9.58 65.37 45.26 45.26 47.41 14.82 9.37 9.19 60.96 8.92 8.82 8.74 8.66 8.59 8.53 8.48 −191.56 8.39 15.15 13.84 12.68 11.63 16.75 25.08

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

53

Table 3 (Continued) Serial No.

Compound

Status

Exp.a

SGC-ANN model Calc.

Dev.

% Error

Calc.

Dev.

147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221

Ethylcyclohexane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane cis-1,3-Dimethylcyclohexane trans-1,3-Dimethylcyclohexane cis-1,4-Dimethylcyclohexane trans-1,4-Dimethylcyclohexane n-Propylcyclohexane Isopropylcyclohexane n-Butylcyclohexane iso-butylcyclohexane sec-butylcyclohexane tert-butylcyclohexane 1-Methyl-4-Isopropylcyclohexane n-pentylcyclohexane n-Hexylcyclohexane n-Heptylcyclohexane n-Octylcyclohexane n-Nonylcyclohexane n-Decylcyclohexane n-Undecylcyclohexane n-Dodecylcyclohexane n-Tridecylcyclohexane n-Tetradecylcyclohexane n-Pentadecylcyclohexane n-Hexadecylcyclohexane n-Heptadecylcyclohexane n-Octadecylcyclohexane n-Nonadecylcyclohexane n-Eicosylcyclohexane Cycloheptane Cyclooctane Cyclononane Ethylcycloheptane Bicyclohexyl cis-Decahydronaphthalene (cis-decalin) trans-Decahydronaphthalene (trans-decalin) Ethylene (ethene) Propylene (propene) cis-2-Butene trans-2-Butene 2-methylpropene (Isobutene) 1-Pentene cis-2-Pentene trans-2-Pentene 2-Methyl-1-butene 3-Methyl-1-butene 2-Methyl-2-butene 1-Hexene cis-2-Hexene trans-2-Hexene cis-3-Hexene trans-3-Hexene 2-Methyl-1-pentene 3-Methyl-1-pentene 4-Methyl-1-pentene 2-Methyl-2-pentene cis-3-Methyl-2-Pentene trans-3-Methyl-2-pentene cis-4-Methyl-2-pentene trans-4-Methyl-2-pentene 2-Ethyl-1-Butene 2,3-Dimethyl-1-Butene 3,3-Dimethyl-1-Butene 2,3-Dimethyl-2-Butene 1-Heptene cis-2-Heptene trans-2-Heptene cis-3-Heptene trans-3-Heptene 2-Methyl-1-hexene 3-Methyl-1-hexene 4-Methyl-1-hexene 5-Methyl-1-hexene

Test Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train

−171.75 −181.00 −172.17 −180.00 −184.76 −176.56 −176.65 −184.60 −193.30 −93.81 −213.17 −136.74 −114.52 −125.94 −135.98 −233.80 −254.39 −275.02 −295.60 −316.23 −336.85 −357.44 −378.07 −398.65 −419.28 −439.91 −460.49 −375.06 −395.76 −416.48 −437.19 −119.04 −125.69 −133.89 −36.11 −272.01 −169.24 −182.17 52.28 19.71 −6.99 −11.17 −16.90 −20.92 −28.07 −31.76 −36.32 −28.95 −42.55 −41.67 −48.37 −52.55 −48.37 −52.55 −56.73 −46.11 −48.78 −62.59 −59.92 −59.92 −55.48 −59.66 −54.06 −61.84 −59.62 −66.57 −62.30 −69.20 −73.81 −68.70 −73.01 −76.23 −63.60 −70.67 −70.67

−156.86 −179.58 −162.28 −162.28 −162.28 −162.28 −162.28 −162.28 −181.57 −129.37 −205.17 −157.57 −157.57 −119.45 −155.30 −227.73 −249.30 −269.94 −289.71 −308.66 −326.85 −344.33 −361.15 −377.34 −392.93 −407.23 −407.33 −381.52 −421.64 −433.82 −446.54 −124.42 −133.76 −127.38 −193.07 −215.72 −204.48 −204.48 37.12 3.26 −10.95 −10.95 −20.19 −11.97 −28.18 −28.18 −32.39 −26.30 −41.08 −36.57 −52.24 −52.24 −52.24 −52.24 −51.29 −43.46 −43.46 −57.09 −57.09 −57.09 −61.84 −61.84 −51.29 −64.89 −76.15 −66.13 −61.07 −74.54 −74.54 −74.54 −74.54 −75.13 −68.95 −68.95 −68.95

14.90 1.42 9.89 17.71 22.48 14.28 14.36 22.31 11.73 −35.57 8.00 −20.83 −43.05 6.49 −19.32 6.07 5.09 5.08 5.89 7.57 10.00 13.10 16.92 21.31 26.35 32.68 53.16 −6.46 −25.88 −17.34 −9.35 −5.38 −8.07 6.51 −156.96 56.29 −35.24 −22.31 −15.17 −16.45 −3.97 0.22 −3.29 8.95 −0.10 3.58 3.93 2.66 1.47 5.11 −3.87 0.31 −3.87 0.31 5.45 2.65 5.33 5.50 2.83 2.83 −6.36 −2.18 2.77 −3.05 −16.53 0.44 1.23 −5.34 −0.73 −5.84 −1.52 1.11 −5.35 1.72 1.72

8.67 0.78 5.74 9.84 12.17 8.09 8.13 12.09 6.07 −37.91 3.75 −15.23 −37.59 5.15 −14.20 2.60 2.00 1.85 1.99 2.39 2.97 3.67 4.47 5.35 6.28 7.43 11.54 −1.72 −6.54 −4.16 −2.14 −4.52 −6.42 4.86 −434.69 20.69 −20.82 −12.25 29.01 83.44 −56.76 1.95 −19.44 42.80 −0.36 11.28 10.81 9.18 3.46 12.25 −8.00 0.60 −8.00 0.60 9.60 5.75 10.92 8.79 4.72 4.72 −11.47 −3.65 5.13 −4.94 −27.73 0.66 1.97 −7.71 −0.99 −8.49 −2.09 1.45 −8.42 2.43 2.43

−134.99 −127.24 −129.38 −129.38 −129.38 −129.38 −129.38 −129.38 −154.04 −164.07 −173.09 −183.12 −183.12 −196.59 −177.51 −192.14 −211.18 −230.23 −249.28 −268.33 −287.38 −306.42 −325.47 −344.52 −363.57 −382.62 −401.66 −420.71 −439.76 −458.81 −477.86 −123.44 −144.37 −165.30 −155.92 −152.43 −110.57 −110.57 38.17 −13.10 −17.03 −17.03 −19.53 −27.53 −36.08 −36.08 −38.57 −37.56 −47.12 −46.58 −55.13 −55.13 −55.13 −55.13 −57.62 −56.61 −56.61 −66.17 −66.17 −66.17 −65.16 −65.16 −57.62 −67.65 −70.08 −77.22 −65.63 −74.18 −74.18 −74.18 −74.18 −76.67 −75.66 −75.66 −75.66

36.76 53.76 42.79 50.62 55.38 47.18 47.27 55.22 39.26 −70.26 40.09 −46.38 −68.60 −70.65 −41.53 41.67 43.21 44.78 46.32 47.90 49.48 51.01 52.59 54.13 55.71 57.29 58.83 −45.66 −44.00 −42.32 −40.66 −4.40 −18.68 −31.41 −119.82 119.58 58.67 71.60 −14.12 −32.81 −10.04 −5.86 −2.62 −6.61 −8.01 −4.32 −2.26 −8.61 −4.57 −4.90 −6.76 −2.58 −6.76 −2.58 −0.89 −10.50 −7.82 −3.58 −6.26 −6.26 −9.68 −5.49 −3.56 −5.81 −10.46 −10.65 −3.32 −4.97 −0.37 −5.47 −1.16 −0.43 −12.06 −4.99 −4.99

SGC-MNLR model % Error 21.40 29.70 24.85 28.12 29.98 26.72 26.76 29.91 20.31 74.90 18.80 33.92 59.91 56.10 30.54 17.82 16.98 16.28 15.67 15.15 14.69 14.27 13.91 13.58 13.29 13.02 12.78 12.17 11.12 10.16 9.30 3.70 14.86 23.46 331.82 43.96 34.67 39.30 −27.00 −166.48 143.75 52.46 15.51 31.59 28.52 13.62 6.21 29.73 10.75 11.77 13.98 4.91 13.98 4.91 1.56 22.77 16.04 5.72 10.44 10.44 17.45 9.21 6.59 9.40 17.54 16.00 5.34 7.19 0.50 7.97 1.59 0.57 18.96 7.05 7.05

54

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

Table 3 (Continued) Serial No.

Compound

Status

Exp.a

222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296

2-Methyl-2-hexene cis-3-Methyl-2-hexene trans-3-Methyl-2-hexene cis-4-Methyl-2-hexene trans-4-Methyl-2-hexene cis-5-Methyl-2-Hexene trans-5-Methyl-2-hexene cis-2-methyl-3-hexene trans-2-Methyl-3-hexene cis-3-Methyl-3-hexene trans-3-Methyl-3-hexene 2-Ethyl-1-Pentene 3-Ethyl-1-Pentene 3-Ethyl-2-Pentene 2,3-Dimethyl-1-pentene 2,4-Dimethyl-1-pentene 3,3-Dimethyl-1-pentene 3,4-Dimethyl-1-pentene 4,4-Dimethyl-1-pentene 2,3-Dimethyl-2-pentene 2,4-Dimethyl-2-pentene cis-3,4-Dimethyl-2-pentene trans-3,4-Dimethyl-2-Pentene cis-4,4-Dimethyl-2-pentene trans-4,4-Dimethyl-2-pentene 3-Methyl-2-ethyl-1-butene 2,3,3-Trimethyl-1-butene 1-Octene cis-2-Octene trans-2-Octene cis-3-Octene trans-3-Octene cis-4-Octene trans-4-Octene 2-Methyl-1-heptene 3-Methyl-1-Heptene 4-Methyl-1-Heptene trans-6-Methyl-2-Heptene trans-3-Methyl-3-heptene 2-Ethyl-1-Hexene 3-Ethyl-1-Hexene 4-Ethyl-1-Hexene 2,3-Dimethyl-1-hexene 2,3-Dimethyl-2-hexene cis-2,2-Dimethyl-3-hexene 2,3,3-Trimethyl-1-pentene 2,4,4-Trimethyl-1-pentene 2,4,4-Trimethyl-2-pentene 1-Nonene 1-Decene 1-Undecene 1-Dodecene 1-Tridecene 1-Tetradecene 1-Pentadecene 1-Hexadecene 1-Heptadecene 1-Octadecene 1-Nonadecene 1-Eicosene Propadiene 1,2-Butadiene 1,3-Butadiene 1,2-Pentadiene cis-1,3-Pentadiene trans-1,3-Pentadiene 1,4-Pentadiene 2,3-Pentadiene 3-Methyl-1,2-Butadiene 2-Methyl-1,3-Butadiene (isoprene) 2,3-Dimethyl-1,3-Butadiene 1,2-Hexadiene 1,5-Hexadiene 2,3-Hexadiene 3-Methyl-1,2-Pentadiene

Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Test Train Train Train Train Train Train Test Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train

−87.95 −110.21 −88.75 −83.31 −83.31 −95.27 −95.27 −81.55 −81.55 −87.16 −87.16 −75.44 −69.83 −87.95 −85.73 −84.94 −78.08 −78.53 −82.22 −78.54 −95.69 −102.09 −95.69 −94.73 −94.73 −83.18 −95.69 −82.93 −94.51 −95.30 −93.71 −94.60 −93.72 −94.60 −96.94 −128.70 −102.00 −158.94 −118.34 −97.00 −105.39 −103.68 −103.01 −162.25 −109.70 −133.88 −110.40 −104.90 −103.51 −124.14 −144.77 −165.36 −185.98 −206.52 −227.23 −247.82 −268.40 −289.03 −310.04 −330.24 191.53 163.29 110.30 140.69 82.78 75.84 106.38 133.07 129.08 75.75 42.34 −65.82 84.44 213.82 68.54

SGC-ANN model Calc. −90.95 −90.95 −90.95 −86.50 −86.50 −86.50 −86.50 −86.50 −86.50 −90.95 −90.95 −75.13 −68.95 −90.95 −85.38 −85.38 −89.58 −70.52 −89.58 −89.64 −93.55 −93.55 −93.55 −94.55 −94.55 −85.38 −97.41 −84.98 −98.01 −98.01 −98.01 −98.01 −98.01 −98.01 −98.64 −93.90 −93.90 −110.68 −113.37 −98.64 −93.90 −93.90 −110.15 −129.49 −107.99 −110.32 −110.32 −115.84 −108.28 −131.00 −153.17 −174.79 −195.90 −216.49 −236.57 −256.16 −275.26 −293.88 −312.03 −329.71 196.31 158.25 127.57 135.04 83.08 83.08 117.97 134.40 129.15 92.59 55.81 −62.76 92.20 213.97 69.73

Dev. −3.00 19.26 −2.20 −3.20 −3.20 8.77 8.77 −4.95 −4.95 −3.79 −3.79 0.31 0.88 −3.00 0.36 −0.44 −11.51 8.02 −7.36 −11.10 2.14 8.54 2.14 0.17 0.17 −2.20 −1.72 −2.05 −3.50 −2.71 −4.30 −3.41 −4.29 −3.41 −1.70 34.79 8.10 48.26 4.97 −1.65 11.49 9.77 −7.15 32.76 1.71 23.56 0.07 −10.94 −4.77 −6.86 −8.40 −9.44 −9.92 −9.96 −9.34 −8.34 −6.86 −4.85 −1.99 0.53 4.78 −5.04 17.27 −5.66 0.29 7.24 11.58 1.33 0.07 16.83 13.47 3.06 7.77 0.16 1.19

SGC-MNLR model % Error −3.41 17.48 −2.48 −3.84 −3.84 9.20 9.20 −6.08 −6.08 −4.35 −4.35 0.42 1.26 −3.41 0.42 −0.52 −14.74 10.21 −8.96 −14.13 2.23 8.37 2.23 0.18 0.18 −2.64 −1.80 −2.47 −3.70 −2.85 −4.58 −3.61 −4.58 −3.61 −1.76 27.03 7.94 30.37 4.20 −1.70 10.90 9.43 −6.94 20.19 1.56 17.60 0.07 −10.43 −4.60 −5.53 −5.80 −5.71 −5.33 −4.82 −4.11 −3.37 −2.55 −1.68 −0.64 0.16 −2.50 3.09 −15.66 4.02 −0.35 −9.55 −10.89 −1.00 −0.05 −22.22 −31.80 4.64 −9.20 −0.07 −1.74

Calc.

Dev.

−85.22 −85.22 −85.22 −84.21 −84.21 −84.21 −84.21 −84.21 −84.21 −85.22 −85.22 −76.67 −75.66 −85.22 −86.70 −86.70 −89.13 −85.69 −89.13 −96.26 −95.25 −95.25 −95.25 −97.68 −97.68 −86.70 −100.17 −84.67 −93.22 −93.22 −93.22 −93.22 −93.22 −93.22 −95.72 −94.70 −94.70 −103.26 −104.27 −95.72 −94.70 −94.70 −105.75 −115.31 −116.73 −119.22 −119.22 −127.77 −103.72 −122.77 −141.82 −160.87 −179.91 −198.96 −218.01 −237.06 −256.11 −275.15 −294.20 −313.25 165.88 138.28 100.59 119.23 72.99 72.99 81.54 110.68 108.18 70.49 40.40 100.18 62.49 91.63 89.14

2.73 24.99 3.52 −0.90 −0.90 11.07 11.07 −2.66 −2.66 1.94 1.94 −1.23 −5.82 2.73 −0.97 −1.76 −11.05 −7.15 −6.91 −17.73 0.44 6.84 0.44 −2.95 −2.95 −3.52 −4.48 −1.75 1.29 2.07 0.49 1.37 0.49 1.37 1.22 33.99 7.30 55.69 14.07 1.28 10.69 8.97 −2.74 46.94 −7.03 14.66 −8.83 −22.88 −0.21 1.37 2.95 4.49 6.07 7.56 9.22 10.76 12.30 13.88 15.84 16.99 −25.66 −25.02 −9.71 −21.46 −9.80 −2.85 −24.85 −22.39 −20.90 −5.26 −1.94 166.00 −21.95 −122.19 20.60

% Error 3.10 22.68 3.97 1.08 1.08 11.61 11.61 3.26 3.26 2.22 2.22 1.63 8.34 3.10 1.13 2.07 14.16 9.11 8.41 22.57 0.46 6.70 0.46 3.12 3.12 4.23 4.68 2.10 1.36 2.17 0.52 1.45 0.53 1.45 1.26 26.41 7.15 35.04 11.89 1.32 10.14 8.66 2.66 28.93 6.41 10.95 8.00 21.81 0.20 1.10 2.04 2.72 3.26 3.66 4.06 4.34 4.58 4.80 5.11 5.15 −13.40 −15.32 −8.81 −15.26 −11.83 −3.76 −23.35 −16.83 −16.19 −6.94 −4.58 252.20 −25.99 −57.15 −30.05

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

55

Table 3 (Continued) Serial No.

Compound

Status

Exp.a

297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371

2-Methyl-1,5-Hexadiene 2-Methyl-2,4-Hexadiene 2,6-Octadiene 2,6-Dimethyl-1,5-Heptadiene 3,7-Dimethyl-1,6-Octadiene Cyclopentene 1-Methylcyclopentene 1-Ethylcyclopentene 3-Ethylcyclopentene 1-n-Propylcyclopentene Cyclohexene 1-Methylcyclohexene 1-Ethylcyclohexene Cyclopentadiene Dicyclopentadiene alfa-Pinene Beta-Pinene Acetylene (Ethyne) Methylacetylene (Propyne) Dimethylacetylene Ethylacetylene (1-butyne) Vinylacetylene 1-Pentyne 2-Pentyne 3-Methyl-1-Butyne 1-Hexyne 1-Heptyne 1-Octyne 1-Nonyne 1-Decyne Benzene Toluene Ethylbenzene o-Xylene m-Xylene p-Xylene n-Propylbenzene Isopropylbenzene (cumene) o-Ethyltoluene m-Ethyltoluene p-Ethyltoluene 1,2,3-Trimethylbenzene (hemimellitene) 1,2,4-Trimethylbenzene (pseudocumene) 1,3,5-Trimethylbenzene (mesitylene) n-Butylbenzene Isobutylbenzene sec-Butylbenzene tert-Butylbenzene 1-Methyl-2-n-propylbenzene 1-Methyl-3-n-propylbenzene 1-Methyl-4-n-Propylbenzene o-Cymene m-Cymene p-Cymene o-Diethylbenzene m-Diethylbenzene p-Diethylbenzene 1,2-Dimethyl-3-ethylbenzene 1,2-Dimethyl-4-Ethylbenzene 1,3-Dimethyl-2-Ethylbenzene 1,3-Dimethyl-4-ethylbenzene 1,3-Dimethyl-5-ethylbenzene 1,4-Dimethyl-2-ethylbenzene 1,2,3,4-Tetramethylbenzene 1,2,3,5-Tetramethylbenzene 1,2,4,5-Tetramethylbenzene n-Pentylbenzene n-Hexylbenzene n-Heptylbenzene n-Octylbenzene n-Nonylbenzene n-Decylbenzene n-Undecylbenzene n-Dodecylbenzene n-Tridecylbenzene

Train Train Train Train Test Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train

101.84 62.72 46.19 9.45 −72.59 32.93 85.82 −22.43 −43.77 −44.48 −5.36 −36.32 −56.23 130.80 126.02 28.30 38.70 226.75 184.51 146.31 165.18 304.63 144.35 128.87 136.40 123.64 103.01 82.42 61.80 41.21 82.93 50.17 29.79 19.00 17.32 18.03 7.90 3.93 1.30 −1.80 −3.20 −9.50 −13.80 −15.90 −13.14 −20.34 −16.90 −21.63 −19.78 −24.14 −23.14 −22.67 −28.70 −27.74 −15.73 −21.00 −20.37 −25.65 −32.09 −26.23 −30.80 −35.40 −32.18 −33.05 −40.54 −44.56 −33.90 −54.60 −75.30 538.81 −116.80 −137.50 −158.31 −179.00 −199.70

SGC-ANN model Calc. 81.94 51.28 42.24 7.14 −49.25 36.23 88.93 −28.11 −44.34 −24.87 −2.20 −57.53 −82.32 83.34 114.89 24.39 42.75 226.72 182.32 140.65 170.34 307.30 146.68 135.04 131.94 123.72 101.77 80.74 60.54 41.07 70.77 51.65 25.38 22.27 22.27 22.27 8.54 3.29 −3.23 −3.23 −3.23 −11.11 −11.11 −11.11 −15.34 −16.31 −16.31 −22.55 −28.00 −28.00 −28.00 −8.09 −8.09 −8.09 −28.00 −28.00 −28.00 −34.80 −34.80 −34.80 −34.80 −34.80 −34.80 −41.57 −41.57 −41.57 −49.65 −70.13 −5.98 518.64 −110.95 −130.13 −152.99 −173.11 −192.57

Dev. −19.90 −11.43 −3.95 −2.31 23.35 3.31 3.11 −5.69 −0.57 19.61 3.16 −21.22 −26.09 −47.45 −11.13 −3.91 4.04 −0.03 −2.19 −5.67 5.16 2.67 2.33 6.18 −4.46 0.08 −1.24 −1.68 −1.26 −0.14 −12.16 1.48 −4.41 3.28 4.95 4.24 0.64 −0.64 −4.53 −1.43 −0.03 −1.61 2.68 4.78 −2.20 4.03 0.59 −0.93 −8.22 −3.86 −4.86 14.58 20.61 19.65 −12.27 −7.00 −7.63 −9.15 −2.71 −8.57 −4.00 0.60 −2.62 −8.52 −1.03 2.99 −15.75 −15.53 69.32 −20.17 5.85 7.37 5.32 5.89 7.13

SGC-MNLR model % Error 19.54 18.23 8.56 24.45 32.16 −10.04 −3.62 −25.37 −1.30 44.09 58.91 −58.42 −46.39 36.28 8.83 13.81 −10.45 0.01 1.19 3.87 −3.12 −0.88 −1.62 −4.79 3.27 −0.06 1.21 2.04 2.03 0.34 14.66 −2.95 14.81 −17.24 −28.58 −23.52 −8.10 16.36 348.47 −79.41 −0.91 −17.00 19.46 30.09 −16.74 19.82 3.49 −4.28 −41.55 −15.99 −21.00 64.32 71.81 70.84 −77.98 −33.32 −37.45 −35.69 −8.46 −32.69 −13.00 1.68 −8.15 −25.78 −2.54 6.71 −46.47 −28.45 92.06 3.74 5.01 5.36 3.36 3.29 3.57

Calc.

Dev.

32.40 15.30 7.29 −25.29 −43.33 −19.33 −56.23 −75.28 −51.82 −73.39 −40.26 −77.16 −96.21 42.91 110.89 −57.05 −48.50 186.76 163.06 139.35 144.01 253.08 124.96 120.30 114.93 105.91 86.86 67.82 48.77 29.72 84.23 47.33 28.28 10.43 10.43 10.43 9.23 −0.80 −8.61 −8.61 −8.61 −26.46 −26.46 −26.46 −9.81 −19.85 −19.85 63.34 −27.66 −27.66 −27.66 −37.69 −37.69 −37.69 −27.66 −27.66 −27.66 −45.51 −45.51 −45.51 −45.51 −45.51 −45.51 −63.36 −63.36 −63.36 −28.86 −47.91 −66.96 −86.01 −105.05 −124.10 −143.15 −162.20 −181.25

−69.44 −47.42 −38.90 −34.75 29.27 −52.26 −142.05 −52.85 −8.05 −28.91 −34.91 −40.84 −39.97 −87.88 −15.13 −85.35 −87.20 −39.98 −21.45 −6.97 −21.18 −51.55 −19.39 −8.57 −21.47 −17.73 −16.15 −14.61 −13.03 −11.49 1.29 −2.84 −1.51 −8.56 −6.89 −7.60 1.33 −4.73 −9.91 −6.81 −5.41 −16.96 −12.66 −10.56 3.33 0.49 −2.95 84.97 −7.88 −3.52 −4.52 −15.02 −8.99 −9.95 −11.93 −6.66 −7.29 −19.86 −13.42 −19.28 −14.71 −10.11 −13.33 −30.31 −22.82 −18.80 5.04 6.69 8.34 −624.82 11.75 13.40 15.15 16.81 18.45

% Error −68.19 −75.61 −84.21 −367.51 40.32 −158.70 −165.52 235.67 18.39 65.01 651.73 112.46 71.09 −67.19 −12.00 −301.57 −225.31 −17.63 −11.63 −4.76 −12.82 −16.92 −13.43 −6.65 −15.74 −14.34 −15.67 −17.72 −21.08 −27.89 −1.56 −5.66 −5.07 −45.08 −39.77 −42.13 −16.88 −120.26 −762.70 378.50 169.13 178.58 91.78 66.45 25.31 2.43 17.43 392.86 39.85 14.60 19.55 66.26 31.34 35.87 75.84 31.72 35.80 77.43 41.82 73.50 47.76 28.56 41.42 91.72 56.28 42.19 14.86 12.25 11.08 −115.96 10.06 9.75 9.57 9.39 9.24

56

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

Table 3 (Continued) Serial No.

Compound

Status

Exp.a

SGC-ANN model Calc.

Dev.

372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446

n-Tetradecylbenzene n-Pentadecylbenzene n-Hexadecylbenzene Cyclohexylbenzene Styrene cis-1-Propenyl benzene trans-1-Propenyl benzene 2-Propenyl benzene 1-Methyl-2-ethenyl benzene 1-Methyl-3-Ethenyl Benzene 1-Methyl-4-Ethenyl Benzene 1-Methyl-4-(trans-1-n-Propenyl)Benzene 1-Ethyl-2-Ethenyl Benzene 1-Ethyl-3-Ethenyl Benzene 1-Ethyl-4-Ethenyl Benzene 2-Phenyl-1-Butene Biphenyl 1-Methyl-2-Phenylbenzene 1-Methyl-3-Phenylbenzene 1-Methyl-4-Phenylbenzene 1-Ethyl-4-Phenylbenzene 1-Methyl-4(4-Methylphenyl)-Benzene Diphenylmethane 1,1-Diphenylethane 1,2-Diphenylethane 1,2-Diphenylpropane cis-1,2-Diphenylethene trans-1,2-Diphenylethene Phenylacetylene Diphenylacetylene 1,2-Diphenylbenzene (o-terphenyl) 1,3-Diphenylbenzene (m-terphenyl) 1,4-Diphenylbenzene (p-terphenyl) Naphthalene 1-Methylnaphthalene 2-Methylnaphthalene 1-Ethylnaphthalene 1,2-Dimethylnaphthalene 1,4-Dimethylnaphthalene 1-n-Propylnaphthalene 2-n-Propylnaphthalene 1-n-Butylnaphthalene 2-n-Butylnaphthalene 1-n-Pentylnaphthalene 1-n-Hexylnaphthalene 2-n-Hexylnaphthalene 1-n-Heptylnaphthalene 1-n-Octylnaphthalene 1-n-Nonylnaphthalene 2-n-Nonylnaphthalene 1-n-Decylnaphthalene 1,2,3,4-Tetrahydronaphthalene 1-Methyl-[1,2,3,4-Tetrahydronaphthalene] 1-Ethyl-[1,2,3,4-Tetrahydronaphthalene] 2,2-Dimethyl-[1,2,3,4-Tetrahydronaphthalene] 2,6-Dimethyl-[1,2,3,4-Tetrahydronaphthalene] 6,7-Dimethyl-[1,2,3,4-Tetrahydronaphthalene] 1-n-Propyl-[1,2,3,4-Tetrahydronaphthalene] 6-n-Propyl-[1,2,3,4-Tetrahydronaphthalene] 1-n-Hexyl-[1,2,3,4-Tetrahydronaphthalene] 1-n-Heptyl-[1,2,3,4-Tetrahydronaphthalene] 1-n-Octyl-[1,2,3,4-Tetrahydronaphthalene] 1-n-Nonyl-[1,2,3,4-Tetrahydronaphthalene] 1-n-Decyl-[1,2,3,4-Tetrahydronaphthalene] indene 1-Methylindene 2-Methylindene Indan (2,3-dihydroindene) 1-Methyl-2,3-Dihydroindene 2-Methyl-2,3-Dihydroindene 4-Methyl-2,3-Dihydroindene 5-Methyl-2,3-Dihydroindene Acenaphthalene (Acenaphthylene) Acenaphthene Fluorene

Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train

−220.40 −241.21 −261.91 −20.92 147.36 121.33 117.15 112.97 118.41 115.48 114.64 106.61 106.52 85.81 85.81 105.43 182.09 73.68 137.86 137.86 148.20 137.86 154.00 116.00 143.00 116.11 245.19 241.00 84.77 430.11 276.57 276.57 276.57 150.58 116.86 116.11 323.89 73.43 61.21 61.21 −58.91 85.67 85.67 29.33 7.28 29.33 −80.96 −14.77 −47.50 −14.77 −68.20 26.61 −36.82 −16.19 −38.24 −18.20 −46.69 −75.73 −79.75 −110.25 −130.96 −151.67 −173.89 −192.63 163.28 90.25 125.36 149.96 33.22 5.27 5.27 −1.13 259.59 155.00 186.90

−211.46 −229.78 −247.55 −24.17 154.88 124.80 124.80 127.78 123.09 123.09 123.09 99.61 96.88 96.88 96.88 91.81 173.70 139.92 139.92 139.92 116.82 116.82 135.05 148.12 123.63 122.87 255.39 255.39 85.44 429.73 271.61 271.61 271.61 162.37 126.87 126.87 100.91 91.04 91.04 75.74 75.74 51.36 51.36 27.77 4.94 4.94 −17.15 −18.51 −59.01 −19.01 −74.35 28.00 −35.04 −20.83 −43.60 −17.94 −40.62 −55.53 −58.88 −123.59 −144.44 −164.47 −183.73 −202.25 150.03 110.70 101.81 82.11 8.71 8.71 2.15 2.15 226.23 168.21 201.47

8.95 11.43 14.36 −3.25 7.52 3.46 7.65 14.81 4.68 7.61 8.45 −6.99 −9.64 11.07 11.07 −13.63 −8.39 66.24 2.05 2.05 −31.38 −21.04 −18.95 32.12 −19.36 6.77 10.21 14.39 0.67 −0.38 −4.96 −4.96 −4.96 11.79 10.01 10.76 −222.98 17.61 29.83 14.53 134.65 −34.31 −34.31 −1.56 −2.34 −24.39 63.81 −3.74 −11.51 −4.24 −6.14 1.39 1.78 −4.64 −5.35 0.26 6.08 20.20 20.87 −13.34 −13.48 −12.80 −9.84 −9.62 −13.25 20.45 −23.55 −67.85 −24.51 3.44 −3.12 3.28 −33.36 13.21 14.57

SGC-MNLR model % Error 4.06 4.74 5.48 −15.55 −5.10 −2.85 −6.53 −13.11 −3.95 −6.59 −7.37 6.56 9.05 −12.90 −12.90 12.93 4.61 −89.89 −1.49 −1.49 21.17 15.26 12.31 −27.69 13.54 −5.83 −4.16 −5.97 −0.79 0.09 1.79 1.79 1.79 −7.83 −8.57 −9.27 68.85 −23.98 −48.73 −23.73 228.56 40.04 40.04 5.33 32.18 83.17 78.82 −25.33 −24.24 −28.73 −9.01 −5.22 4.84 −28.66 −14.00 1.43 13.01 26.67 26.17 −12.10 −10.30 −8.44 −5.66 −4.99 8.12 −22.66 18.78 45.25 73.78 −65.28 59.12 290.93 12.85 −8.52 −7.80

Calc.

Dev.

−200.29 −219.34 −238.39 10.84 137.35 109.75 109.75 118.30 100.45 100.45 100.45 72.85 81.41 81.41 81.41 88.21 174.11 137.22 137.22 137.22 118.17 118.17 134.68 125.99 136.02 106.94 236.53 236.53 289.84 392.91 264.00 264.00 264.00 153.73 116.84 116.84 97.79 79.94 79.94 78.74 78.74 59.69 59.69 40.64 21.60 21.60 2.55 −16.50 −35.55 −35.55 −54.60 −27.66 15.81 −3.24 4.51 −21.09 −44.55 −22.29 −76.32 −79.43 −98.48 −117.53 −136.58 −155.63 112.42 98.98 75.52 50.17 36.74 36.74 13.28 13.28 202.86 140.61 181.93

20.11 21.86 23.52 31.76 −10.01 −11.58 −7.40 5.33 −17.95 −15.02 −14.19 −33.75 −25.12 −4.40 −4.40 −17.22 −7.98 63.53 −0.65 −0.65 −30.03 −19.70 −19.31 9.99 −6.98 −9.17 −8.66 −4.47 205.07 −37.20 −12.57 −12.57 −12.57 3.15 −0.02 0.73 −226.10 6.51 18.73 17.53 137.65 −25.98 −25.98 11.31 14.32 −7.74 83.51 −1.73 11.95 −20.78 13.61 −54.27 52.63 12.95 42.75 −2.89 2.14 53.44 3.43 30.81 32.48 34.14 37.31 37.01 −50.86 8.73 −49.83 −99.78 3.52 31.47 8.01 14.41 −56.74 −14.39 −4.97

% Error 9.12 9.06 8.98 151.81 −6.79 −9.55 −6.32 −4.72 −15.16 −13.01 −12.38 −31.66 −23.58 −5.13 −5.13 −16.34 −4.38 −86.23 −0.47 −0.47 −20.26 −14.29 −12.54 −8.61 −4.88 −7.90 −3.53 −1.86 −241.91 −8.65 −4.54 −4.54 −4.54 −2.09 −0.02 −0.63 −69.81 −8.86 −30.59 −28.63 233.65 −30.33 −30.33 −38.56 −196.65 −26.38 103.15 11.74 25.16 140.68 19.95 −203.95 142.93 79.98 111.79 15.87 4.59 70.57 4.30 27.95 24.80 22.51 21.46 19.21 −31.15 −9.68 −39.75 −66.54 −10.59 −597.05 −151.94 1,276.62 −21.86 −9.28 −2.66

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

57

Table 3 (Continued) Serial No.

Compound

Status

Exp.a

447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521

Anthracene Phenanthrene Pyrene Fluoranthene Chrysene (1,2-benzophenanthrene) Formic Acid Acetic Acid Propionic Acid n-Butyric Acid 2-Methylpropionic Acid n-Pentanoic Acid 2-Methylbutyric Acid 3-Methylbutyric Acid n-Hexanoic Acid Methanol Ethanol n-Propanol Isopropanol n-Butanol Isobutanol sec-Butanol tert-Butanol 1-Pentanol 2-Pentanol 2-Methyl-1-Butanol 2-Methyl-2-Butanol 3-Methyl-2-Butanol 2,2-Dimethy-1-Propanol 4-Methyl-2-Pentanol Phenol o-Cresol m-Cresol p-Cresol Formaldehyde Acetaldehyde n-Propionaldehyde n-Butyraldehyde Acrolein trans-Crotonaldehyde Methacrolein Methylamine Ethylamine n-Propylamine Isopropylamine n-Butylamine Isobutylamine sec-Butylamine tert-Butylamine Urea Nitric Oxide Nitrous Oxide Nitrogen Dioxide Nitrogen Tetroxide Sodium Hydroxide Acetonitrile Morpholine Pyridine Aniline Indole Quinoline Dibenzopyrrole Acridine Methyl Formate Methyl Acetate Ethyl Formate Ethyl Acetate n-Propyl Formate Vinyl Acetate Methyl n-Butyrate n-Propyl Acetate Isopropyl Acetate n-Butyl Acetate n-Pentyl Acetate Dimethy Ether Methyl Ethyl Ether

Train Train Train Train Test Train Train Train Train Train Train Train Test Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Test Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Test Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Test Train Train Train

230.10 207.10 225.00 288.90 262.90 −378.65 −432.24 −453.56 −470.31 −484.16 −490.36 −497.99 −514.69 −513.61 −200.66 −234.44 −256.42 −272.44 −274.67 −283.21 −292.87 −312.41 −298.74 −313.80 −302.09 −329.71 −314.22 −319.08 −342.43 −96.40 −128.57 −132.30 −125.35 −115.91 −166.18 −186.00 −206.07 −81.00 −103.60 −112.72 −22.97 −46.02 −72.38 −83.80 −92.05 −98.80 −104.19 −119.88 −245.62 90.26 82.04 33.10 9.08 −197.77 74.04 −156.00 140.16 86.86 156.60 222.30 209.60 291.04 −352.39 −409.15 −388.31 −442.95 −404.41 −315.73 −450.69 −464.79 −481.69 −485.31 −505.52 −184.06 −216.46

SGC-ANN model Calc. 231.41 231.41 219.69 288.03 298.87 −378.64 −429.74 −457.77 −471.70 -489.04 −491.33 −503.12 −503.12 −511.02 −201.65 −236.89 −255.52 −267.74 −255.52 −288.20 −288.20 −312.13 −300.25 −312.28 −312.28 −324.50 −311.38 −324.50 −340.66 −96.73 −128.63 −128.63 −128.63 −115.90 −165.55 −183.97 −208.79 −77.56 −105.03 −114.60 −22.81 −51.88 −67.53 −82.47 −91.11 −98.56 −98.56 −122.43 −242.07 90.23 82.01 33.08 9.08 −197.80 74.05 −155.97 140.59 92.86 156.29 221.16 209.88 291.76 −364.35 −406.00 −374.67 −436.80 −379.63 −369.59 −462.35 −462.35 −430.75 −488.23 −514.57 −187.08 −213.68

Dev. 1.31 24.31 −5.31 −0.87 35.97 0.01 2.50 −4.22 −1.39 −4.89 −0.98 −5.13 11.57 2.59 −0.99 −2.45 0.90 4.70 19.16 −5.00 4.67 0.28 −1.51 1.53 −10.18 5.20 2.84 −5.42 1.77 −0.34 −0.06 3.67 −3.28 0.01 0.63 2.04 −2.72 3.43 −1.43 −1.88 0.17 −5.86 4.85 1.33 0.95 0.25 5.63 −2.55 3.55 −0.03 −0.03 −0.02 0.01 −0.02 0.01 0.03 0.43 5.99 −0.31 −1.14 0.28 0.72 −11.96 3.15 13.64 6.14 24.78 −53.86 −11.66 2.44 50.94 −2.92 −9.05 −3.01 2.78

SGC-MNLR model % Error −0.57 −11.74 2.36 0.30 −13.68 0.00 0.58 −0.93 −0.30 −1.01 −0.20 −1.03 2.25 0.50 −0.49 −1.05 0.35 1.73 6.97 −1.76 1.59 0.09 −0.51 0.49 −3.37 1.58 0.90 −1.70 0.52 −0.35 −0.05 2.77 −2.62 0.01 0.38 1.09 −1.32 4.24 −1.38 −1.67 0.73 −12.73 6.70 1.59 1.03 0.25 5.40 −2.13 1.45 0.04 0.04 0.06 −0.06 −0.01 −0.02 0.02 −0.31 −6.90 0.20 0.51 −0.13 −0.25 −3.39 0.77 3.51 1.39 6.13 −17.06 −2.59 0.53 10.58 −0.60 −1.79 −1.64 1.28

Calc. 223.24 223.24 210.12 272.36 292.74 −412.94 −438.38 −457.43 −476.48 −486.51 −495.53 −505.56 −505.56 −514.57 −217.78 −236.83 −255.88 −265.91 −255.88 −284.96 −284.96 −298.43 −293.98 −304.01 −304.01 −317.48 −314.04 −317.48 −333.08 −99.36 −136.26 −136.26 −136.26 −147.43 -172.87 −191.91 −210.96 −82.85 −110.45 −112.94 −52.26 −71.31 −90.35 −100.38 −109.40 −119.43 −119.43 −132.91 −183.69 84.20 75.67 27.04 3.33 −204.15 67.66 −162.42 141.95 74.53 142.00 211.46 211.50 280.96 −88.42 −113.86 −107.46 −132.90 −100.68 −23.84 −151.95 −151.95 −161.98 −171.00 −190.05 −213.23 −232.28

Dev. −6.86 16.14 −14.88 −16.54 29.84 −34.29 −6.15 −3.87 −6.17 −2.35 −5.17 −7.57 9.13 −0.97 −17.13 −2.39 0.54 6.53 18.80 −1.75 7.92 13.98 4.77 9.80 −1.91 12.23 0.19 1.60 9.34 −2.96 −7.69 −3.96 −10.91 −31.51 -6.69 −5.91 −4.89 −1.85 −6.85 −0.22 −29.28 −25.29 −17.97 −16.58 −17.35 −20.63 −15.25 −13.03 61.94 −6.06 −6.38 −6.06 −5.75 −6.38 −6.38 −6.42 1.79 −12.34 −14.61 −10.84 1.90 −10.08 263.98 295.29 280.85 310.04 303.72 291.89 298.74 312.84 319.71 314.31 315.47 −29.17 −15.82

% Error −2.98 −7.79 −6.61 −5.72 −11.35 9.06 1.42 0.85 1.31 0.49 1.05 1.52 1.77 0.19 8.54 1.02 0.21 2.40 6.84 0.62 2.70 4.47 1.60 3.12 0.63 3.71 0.06 0.50 2.73 3.07 5.98 2.99 8.70 27.19 4.02 3.18 2.37 2.28 6.61 0.20 127.48 54.94 24.83 19.79 18.85 20.88 14.63 10.87 25.22 −6.72 −7.77 −18.32 −63.31 3.22 −8.61 4.12 −1.27 −14.20 −9.33 −4.88 −0.91 −3.46 74.91 72.17 72.33 70.00 75.10 92.45 66.28 67.31 66.37 64.76 62.41 15.85 7.31

58

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

Table 3 (Continued) Serial No.

Compound

Status

Exp.a

SGC-ANN model

522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584

Diethyl Ether Methyl-tert-Butyl Ether Tetrahydrofuran Bromine Hydrogen Bromide Hydrogen Chloride Hydrogen Cyanide Hydrogen Fluoride Hydrogen Sulfide Carbon Dioxide Sulfur Dioxide Chlorotrifluoromethane Dichlorodifluoromethane Trichlorofluoromethane Carbon Tetrachloride Carbon Tetrafluoride Chlorodifluoromethane Dichlorofluoromethane Chloroform Trifluoromethane Dichloromethane Methyl Chloride Methyl Fluoride Vinyl Chloride 1,1,1-Trichloroethane 1,1,2-Trichloroethane 1,1,1-Trifluoroethane 1,1-Dichloroethane 1,2-Dichloroethane 1,1-Difluoroethane Ethyl Chloride Ethyl Fluoride 1,2-Dichloropropane Acetone Methyl Ethyl Ketone Diethyl Ketone Methyl-n-Propyl Ketone Methyl-n-Butyl Ketone Methyl Isobutyl Ketone Carbon Disulfide Methyl Mercaptan 2,3-Dithiabutane Dimethyl Sulfide Ethyl Mercaptan 2-Thiabutane n-Butanethiol tert-Butanethiol 3-Thiapentane 1-Pentanethiol Water Sulfuric Acid Furfural 1,2-Propylene Glycol Diethylene Glycol Tetraethylene Glycol Monoethanolamine Diethanolamine Methyl Diethanolamine Triethanolamine N,N-Dimethylformamide N-Methyl-2-Pyrrolidone Dimethyl Sulfoxide Sulfolane

Test Train Test Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Test Train Train Train Train Train Train Train Train Test Train Train Test Train Train Test Train Test Train Test Train

−252.12 −292.88 −184.19 30.91 −36.44 −92.31 135.17 −272.60 −20.63 −393.53 −296.85 −707.95 491.61 −288.70 −95.98 −933.16 −481.59 −283.25 −103.18 −693.25 −95.52 −81.96 −237.64 28.45 −142.30 −145.60 −745.58 −130.12 −129.79 −493.72 −112.25 −263.18 −165.69 −217.15 −238.38 −258.39 −259.19 −279.83 −288.49 117.07 −22.60 −23.60 −37.20 −46.02 −74.38 −88.07 −109.29 −83.47 109.79 −241.82 −735.12 −151.05 −409.80 −571.11 −882.34 −210.18 −396.90 −379.99 −562.09 −191.69 −195.39 −209.16 −390.02

−253.77 −290.29 −184.18 31.30 −36.69 −95.02 135.12 −273.33 −20.65 −393.45 −296.86 −704.42 491.71 −288.70 −51.89 −914.89 −482.17 −178.22 −104.35 −692.39 −93.65 −82.54 −237.72 26.95 −140.60 −181.44 −748.09 −143.81 −130.58 −495.71 −103.75 −261.54 −185.51 −217.27 −238.76 −269.92 −269.92 −265.72 −284.16 117.07 −24.26 −23.26 −37.24 −32.81 −75.87 −103.25 −109.34 −82.22 109.00 −241.74 −735.12 −151.11 −421.54 −561.27 −881.50 −211.31 −396.90 −391.53 −561.99 −191.78 −195.40 −209.19 −390.04

Calc.

SGC-MNLR model

Dev. −1.65 2.59 0.01 0.39 −0.25 −2.71 −0.04 −0.73 −0.01 0.08 −0.01 3.53 0.10 0.01 44.09 18.28 −0.57 105.03 −1.17 0.86 1.87 −0.58 −0.08 −1.50 1.70 −35.84 −2.51 −13.68 −0.79 −1.99 8.51 1.64 −19.82 −0.12 −0.38 −11.52 −10.72 14.11 4.33 0.00 −1.66 0.34 −0.05 13.21 −1.49 −15.18 −0.04 1.25 −0.79 0.08 0.00 −0.06 −11.73 9.85 0.84 −1.12 −0.01 −11.54 0.10 −0.09 −0.01 −0.03 −0.02

% Error −0.65 0.88 0.01 −1.26 −0.69 −2.94 0.03 −0.27 −0.07 0.02 0.00 0.50 −0.02 0.00 45.94 1.96 −0.12 37.08 −1.13 0.12 1.96 −0.70 −0.03 5.27 1.19 −24.62 −0.34 −10.52 −0.61 −0.40 7.58 0.62 −11.96 −0.05 −0.16 −4.46 −4.14 5.04 1.50 0.00 −7.35 1.42 −0.13 28.71 −2.00 −17.23 −0.04 1.49 0.72 0.03 0.00 −0.04 −2.86 1.72 0.10 −0.53 0.00 −3.04 0.02 −0.05 0.00 −0.01 0.00

Calc.

Dev.

−251.33 −293.88 −171.07 8.21 −10.18 −67.72 128.79 −187.70 −5.84 −399.28 −302.60 −574.88 −454.90 −334.92 −694.86 −214.94 −415.75 −288.69 −175.79 −535.73 −136.64 −170.65 −290.63 −3.14 −201.23 −187.76 −561.17 −155.00 −144.97 −394.96 −112.21 −232.19 −174.05 −238.08 −257.12 −276.17 −276.17 −295.22 −305.25 110.69 8.99 −33.99 −56.72 −10.06 −75.77 −48.15 −71.66 −94.82 −67.20 −162.35 −740.86 −176.89 −423.29 −566.09 −909.84 −228.68 −403.27 −400.56 −601.20 −165.33 −201.77 −215.23 −395.77

0.79 −1.00 13.13 −22.70 26.26 24.59 −6.38 84.90 14.79 −5.75 −5.75 133.07 −946.51 −46.21 −598.88 718.23 65.84 −5.43 −72.61 157.52 −41.12 −88.68 −52.98 −31.59 −58.93 −42.16 184.41 −24.88 −15.18 98.76 0.04 30.99 −8.35 −20.92 −18.75 −17.78 −16.98 −15.39 −16.76 −6.38 31.59 −10.39 −19.53 35.96 −1.39 39.92 37.63 −11.35 −176.99 79.47 −5.75 −25.84 −13.48 5.03 −27.50 −18.50 −6.38 −20.57 −39.11 26.36 −6.38 −6.06 −5.75

% Error 0.31 0.34 7.13 −73.43 72.07 26.64 −4.72 31.14 71.69 1.46 1.94 18.80 −192.53 16.01 623.97 76.97 13.67 1.92 70.37 22.72 43.05 108.19 22.30 −111.04 41.42 28.96 24.73 19.12 11.69 20.00 0.04 11.78 5.04 9.64 7.86 6.88 6.55 5.50 5.81 −5.45 139.78 44.05 52.50 78.15 1.87 45.32 34.43 13.60 −161.21 32.86 0.78 17.10 3.29 0.88 3.12 8.80 1.61 5.41 6.96 13.75 3.26 2.90 1.47

SGC-ANN model: AAD = 11.38, average absolute error = 12.32%, correlation coefficient = 0.9934. SGC-MNLR model: AAD = 34.98, average absolute error = 37.11%, correlation coefficient = 0.900. a Standard heat of formation property range from −933.16 to 538.81 kJ/mol.

SGC-MNLR method was able to correlate the experimental data with a correlation coefficient of 0.90 which is not accurate enough, and therefore an ANN method had to be used [23]. ANN has consistently provided better alternative with a high accuracy in all cases [23–25]. ANN method negates the inconveniences and inaccuracies or the limitations of least square fitting and offers a

promising alternative to modeling for a number of reasons. ANNs are able to capture the non-linearity in the system behavior very effectively. Once properly trained, ANNs offer predictions quickly and accurately on a personal computer. Furthermore, the connection weights and network architecture make predictions possible using a spreadsheet.

T.A. Albahri, A.F. Aljasmi / Thermochimica Acta 568 (2013) 46–60

59

Table 4 Parameters (weights and biases) of the hidden layer for the ANN architecture described in Fig. 1 for predicting the standard enthalpy of formation using the SGC-MNLR model. W1

Hidden neuron

Input neuron

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

0.5688 0.0977 0.3664 0.2876 −0.2037 0.6225 −0.2552 −0.5339 0.6342 −0.3329 0.2346 0.4510 −0.4038 0.1742 0.6025 0.2869 −0.2627 0.4407 0.2304 −0.2256 0.6956 0.6458 0.0276 0.6247 −0.1430 −0.3815 0.4984 0.5496 0.5135 0.2386 0.4098 0.6239 −0.1258 0.4285 −0.2701 0.2286 0.4548 0.0870 0.0864 −0.4297 −0.1684 −0.0409 0.5172 −0.5215 0.5774 −0.2841 0.0802 0.5784 0.2461 0.2722 −0.5684

−0.0765 −0.0613 0.7030 0.0345 −0.7048 0.3155 −0.1955 0.0346 −0.3301 0.7808 −0.5768 0.1893 0.1596 0.2905 0.2793 0.1289 0.2160 0.6381 0.5994 −0.0529 −0.1980 −0.4816 −0.4809 −0.2578 −0.2213 0.2834 −0.4996 0.5721 0.1057 0.4253 0.0213 −0.5471 −0.1566 0.3091 0.5867 0.1823 −0.2849 −0.0710 0.2381 0.4488 −0.2640 −0.4646 0.7673 −0.4395 −0.7700 0.2695 −0.0225 0.6599 0.6675 −0.0943 −0.1603

0.4355 −0.0782 0.0829 0.6192 0.3652 0.4973 0.5261 −0.5477 0.5561 −0.4119 −0.5787 0.0861 0.1501 0.2537 −0.6088 0.0132 0.6959 −0.4915 −0.3259 0.5918 0.0449 −0.5561 0.3085 −0.0896 −0.3071 0.2372 −0.6688 −0.3515 0.6872 −0.1719 −0.4102 −0.1654 0.0079 −0.0545 0.4795 0.2648 0.1254 0.5792 0.3900 0.1696 0.0058 0.1139 0.0056 −0.5643 0.1269 0.6268 0.6468 −0.6962 −0.2234 0.2875 −0.2384

0.4607 −0.5775 −0.6805 0.2989 0.5531 −0.4073 −0.1791 0.3781 −0.5581 −0.0022 −0.6796 −0.3586 0.2234 0.5279 −0.6014 −0.5963 0.0040 −0.5293 −0.1129 −0.3802 −0.4464 0.0911 −0.3493 −0.0404 0.5164 −0.5117 0.3277 0.0973 0.4088 −0.0818 −0.5555 −0.2647 −0.4632 −0.5847 −0.2338 0.0142 −0.5180 −0.3052 −0.5517 −0.6787 0.0904 0.2332 0.1808 −0.5023 0.0590 −0.2197 −0.3755 0.3748 0.1324 0.1537 0.6223

−0.4466 −0.0756 0.1287 −0.3639 −0.2862 −0.0601 −0.5705 −0.1672 −0.5817 −0.2804 −0.2834 0.4309 −0.4237 −0.6519 −0.6532 −0.4105 0.5991 0.3515 −0.3841 0.4845 0.0026 0.6279 0.5806 −0.4693 0.1692 −0.6390 0.0489 −0.4560 −0.4649 −0.0227 −0.4586 −0.4436 0.0331 0.4292 0.5095 0.2863 −0.3287 −0.5821 −0.6677 0.5231 0.3576 0.2366 0.3916 −0.0576 0.2055 0.0843 −0.0286 0.5987 0.1545 −0.2678 0.4531

−0.1614 −0.2033 0.4809 −0.0766 −0.3784 −0.6372 −0.4565 0.4918 −0.4041 0.2627 0.4817 −0.3601 0.2077 −0.2884 −0.4150 −0.1831 0.4989 0.3373 −0.7063 0.2382 −0.1183 −0.7244 −0.5518 −0.5538 −0.3937 −0.3617 −0.3406 0.1435 0.5065 0.1644 −0.1407 0.6033 0.2148 −0.4669 −0.0309 0.0231 0.4609 −0.0356 0.0635 0.3980 0.4257 0.6730 −0.0781 0.4382 −0.2838 −0.5796 0.0403 0.4765 −0.7553 0.5415 −0.3674

0.0259 −0.2464 0.5953 −0.4090 0.5400 0.4381 −0.5622 −0.5657 0.5404 0.5715 0.6058 0.3165 −0.4114 0.3482 0.0203 −0.2790 0.5210 0.1892 −0.5226 0.4881 0.2002 0.4620 0.0270 0.0406 0.5966 −0.4785 −0.1641 −0.2108 −0.3845 −0.4043 −0.1151 −0.2212 −0.6037 −0.0682 0.0759 0.1321 0.2094 0.6036 −0.6154 0.5079 −0.0198 0.3371 0.0304 −0.2732 −0.3355 −0.4130 0.3653 0.5289 0.6015 −0.4841 −0.5704

0.2809 0.4530 −0.3581 0.6037 −0.4752 0.0799 0.0859 0.1261 −0.5625 0.3432 −0.6215 0.2056 0.0510 −0.2481 −0.0538 0.3488 −0.4982 0.3271 0.4514 −0.0153 0.2236 −0.6092 0.5089 0.2907 0.1809 −0.5546 −0.6272 0.2042 0.1790 −0.6412 −0.5760 0.3013 0.4337 −0.6271 0.1492 0.6009 −0.6263 0.5438 −0.0627 0.3329 0.3891 0.3057 −0.4230 −0.3544 −0.1081 −0.2847 −0.3953 −0.3876 0.5144 −0.2684 −0.6362

Bias Out 0.6318

1 −2.9165

2 2.0832

3 −1.2499

4 −0.4166

5 −0.4166

6 −1.2499

7 2.0832

8 2.9165

Hidden neuron connection to output neuron 2 3 1 0.4878 0.6137 0.1488

4 0.2751

5 −0.4975

6 −0.7114

7 0.3031

8 0.8922

W2

Finally, this work demonstrates that the complex property, H◦ f , can be modeled by back-propagation artificial neural network models. Considering the difficulty and complexity of developing a first principles mechanistic model of H◦ f involving the kinetics and dynamics of formation reactions, neural networks can be an effective alternative. The H◦ f property has a number of intrinsic physical parameters associated to the molecular structure such as group interactions, structural orientations, skew, hindrance, steric, resonance, inductive, and chiral effects that are usually unknown and have to be determined through a parameter estimation methodology. Neural networks can learn about these inherent relationships among various structural groups and their contribution to the overall H◦ f property of the molecules.

4. Conclusion and future outlook The neural network based structural group contribution model presented here proves to be a powerful technique for accurately predicting the enthalpy of formation (H◦ f ) of pure substances from their molecular structure alone. The correlation coefficient was 0.9934 which is better than other models in the literature. The method offers advantages to other methods in terms of simplicity, generality and accuracy without the need to calculate additional parameters (or molecular descriptors). Another major advantage is the ability of the ANNs to probe the structural groups that have significant contribution to the overall (H◦ f ) of pure compounds which is very difficult and time consuming to perform with the

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Fig. 4. Molecular structure of p-diethyl benzene.

traditional SGC approach using multivariable nonlinear regression (MNLR). We are currently making efforts to obtain and use a more comprehensive data set as part of our future outlook to improve both ANN and MNLR models using binary structural groups that require more data which was not possible at this point of time. Appendix A. Example: Prediction of the standard enthalpy of formation for p-diethyl benzene The molecular structure for p-diethyl benzene, shown in Fig. 4, consists of the following structural groups obtained from Table 1 for estimating H◦ f ; two (–CH3 ), two (>CH2 ), four ( CH– (ring)), and two (>C (ring)). Calculating the overall structural group contributions: ˙( )i = 2(−CH3 ) + 2(> CH2 ) + 4( CH − (ring)) + 2(> C (ring)) = 2(−51.2687) + 2(−19.048) + 4(10.1903) + 2(24.5625) = −50.7472



Substituting into Eq. (5), H◦ f = 23.084 + ( )i = 23.084 + (−50.7472) = −27.66 kJ/mol Which is 7.3 kJ/mol less than the experimental value of 20.4 kJ/mol. Appendix B. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tca.2013.06.020. References [1] F. Gharagheizi, Prediction of the standard enthalpy of formation of pure compounds using molecular structure, Aust. J. Chem. 62 (2009) 376–381. [2] K.G. Joback, R.C. Reid, Estimation of pure-component properties from group contributions, Chem. Eng. Commun. 57 (1987) 233–243. [3] S.W. Benson, Thermochemical Kinetics, Wiley, New York, 1968. [4] L. Constantinou, R. Gani, New group contribution method for estimating properties of pure compound, AIChE J. 40 (1994) 1697.

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