Study on Estimation Method of Enthalpy of Evaporation Based on Elements and Chemical Bonds

Abstract

A new Group Contribution Method based on elements and chemical bonds was proposed to predict the enthalpy of evaporation of organic compounds at their normal boiling points. A prediction model was built using 1266 experimental data points, and the accuracy of the model estimations was evaluated using 16 experimental data points. The new method has only 42 groups, a simple way of group splitting, and a wide range of predictions with an average relative error of 5.84%. Furthermore, the inclusion of silicon elements and their chemical bonds in the group library enables the effective prediction of silicon-containing compounds with an average relative error of 2.71%. By analyzing and comparing the other three commonly used methods, it can be concluded that the new method provides accurate and reliable estimation results and has a more comprehensive application range.

1. Introduction

The design of refrigerants, fine compounds, evaporative crystallization, and chemical reactions all require knowledge of enthalpy of evaporation, which is a basic component of chemical research. A portion of the real enthalpy of evaporation data for organic compounds has been gathered by experimental techniques including the calorimetry method [1] and the vapor pressure method [2]. Yet, given the volume and diversity of substances used in business and research, these data are insufficient. With the demands of production and scientific research, new compounds are often encountered for which the enthalpy of evaporation data has not yet been determined. Methodologies that are trustworthy and precise are needed to forecast the enthalpy of evaporation for unidentified substances.

The four primary techniques for forecasting the enthalpy of evaporation of organic compounds are Correspondence State (CS), Population Contribution (PC), Topological Space (TS), and artificial neural network (ANN). The CS technique, which is popular because it can accurately capture significant atom-to-atom bonding interactions, predicts the enthalpy of evaporation using a set of atom-centered parameters and a global energy term. Based on the idea of molecular interaction energies derived from molecular orbital theory, the PC technique is a statistical mechanical approach that directly predicts enthalpy of evaporation from molecular characteristics. The TS technique, which forecasts evaporation enthalpies using topological indices and relationships, is appropriate for big molecules with intricate connectivity patterns. The ANN approach, which has enhanced accuracy and the capacity to handle massive datasets, employs a network of trained neurons to estimate enthalpies of evaporation based on molecule structure.

In conclusion, the Correspondence State technique, the Population Contribution method, the Topological Space method, and the Artificial Neural Network method are the main approaches used to forecast the enthalpy of evaporation of organic molecules. The Van der Waals equation of state and a Correspondence State equation with two or three parameters are used in the Correspondence State approach [3,4,5], a mathematical technique to simulate the properties of actual gases. Although it has been utilized in several studies, its use is restricted because of its poor prediction accuracy and the need for understanding the substance’s key properties. The topological structure of molecules is described in greater detail by Topological Space techniques [6,7], which improves the accuracy of predictions of physical attributes. Using chemical structure description codes, artificial neural network methods [8,9] have also grown in favor for their capacity to predict compound attributes. These techniques, though, are difficult and inappropriate for routine calculations.

The Group Contribution Method is regarded as the most adaptable and largely reliable approach for calculating physical attributes. With the advantages of quick estimation and suitability for everyday use, this method uses groups as the fundamental unit of contribution and derives or regresses a small number of group parameters from a large amount of physically available experimental data to predict the properties of unknown compounds. Since it was first proposed in 1923, the Group Contribution Method has undergone continuous development and improvement. Researchers have improved equations’ structural correction terms, multiplied the number of groups, and increased the complexity of models, significantly advancing our ability to predict compounds’ basic properties. Some of the methods developed for predicting the enthalpy of evaporation include the Monofunctional Group Parameter Method [10], the Bifunctional Group Parameter Method [11], the CSGC Method [12], the C. Yu Method [13], the Tertiary Functional Group Contribution Method [14], and the Second-Order Group Contribution Method [15].

All the aforementioned strategies for collective contributions, however, suffer from a limitation. While having a significant capacity for prediction, the group contribution technique with complex equations has a narrow range of applications and is challenging to divide into smaller groups. The group contribution approach with a straightforward equation provides a broad range of predictions but a somewhat limited predictive power. Moreover, several group contribution techniques have various group splitting options. The group division of some Group Contribution Methods is very complicated, and there are hundreds of groups. It is not easy to ensure that users can quickly and accurately disassemble the molecular structure without reference to the specific group structure. This means that the step of breaking down the molecules can take up a lot of valuable time for new users. In order to meet the needs of scientific research, a new method with a large prediction range, high precision, and simple operation is urgently needed.

In this paper, building on previous work [16,17], we develop an elemental and chemical bond-based model to predict the enthalpy of evaporation of organic compounds at their normal boiling points (EBH method). The EBH method employs a new approach to group splitting, which significantly reduces the difficulty of group splitting. Moreover, the new method accounts for silicon-containing groups, thus effectively predicting silicon-containing organic compounds. This method entails fewer model parameters, yet its prediction ability is reliable, with a notable improvement in its prediction range.

2. EBH Method

2.1. Methodology

According to the theory of molecular structure, the most minor component of a material is a molecule, which may exist independently and preserve the generally stable physical and chemical properties of that substance, the elements and the bonds that hold them together chemically make up molecules. Hence, the elements and chemical bonds that make up a molecule are what determine the thermodynamic properties of the molecule, such as enthalpy, entropy, and free energy. J. Hou et al. [18] published. “Topology of two-dimensional C60 domains” in the British journal Nature, which proved elements and chemical bonds really exist in the molecular. This paper also describes “the observation of images of a single C60 molecule that can distinguish chemical bonds using scanning tunneling microscopy”.

This demonstrated that the elemental and chemical bonding approach proposed by S. Xiang et al. is theoretically feasible. After nearly 20 years of development, researchers have proposed methods to predict the boiling points [19], critical properties [16] of organic compounds, and constructed the G^E-EOS model [20] using the elemental and chemical bonding method as the primary research method. In summary, the elemental and chemical bonding method has been repeatedly proven to be a reliable and accurate method for group contribution.

The EBH method uses elements and chemical bonds as the main contributing groups, where chemically bonded groups are divided into two categories depending on whether the bond is located on a ring. The method simplifies the way in which groups are split and reduces the number of groups. In the face of the surge of new substances in modern chemistry, the 42 groups in the group library of the elemental and chemical bonding method can be used to synthesize almost all organic compounds and thus estimate the enthalpy of evaporation for all types of organic compounds.

Typically, the basic substance data for organic compounds contain ten elements such as C, H, O, and N, 25 non-cyclic chemical bonds such as C-C, C-H, and O-H, and one special chemical bond which is the benzene ring, and six chemical bonds located on rings such as the ring C-C, ring C-O, and ring C-H can be accurately estimated using this method. The difficulty of the group splitting process for organic compounds is reduced due to the small number of groups in this method. The group splitting in this thesis is the same as the study by J. Li [16]. Furthermore, the EBH method has three main advantages over existing methods in terms of group splitting, as follows:

(1) The method singles out the benzene ring as a unique chemical bond and improves the accuracy of predicting the enthalpy of evaporation of compounds containing benzene rings, as the chemical bonds in benzene rings are different from the normal C-C and C=C bonds. However, existing methods for estimating the enthalpy of evaporation do not usually distinguish the benzene ring from C-C and C=C.

(2) The method improves the accuracy of predicting the enthalpy of evaporation for compounds containing a chemical bond on a ring versus those that do not. Based on the available experimental data, it can be seen that chemical bonds on rings and chemical bonds not on rings (e.g., carbon single bonds located on the main chain versus those attached to the benzene ring) contribute differently to the heat of evaporation of organic compounds, so a distinction needs to be made between them to predict data on the properties of compounds more accurately.

(3) The group libraries of the Joback [21], Gani [22], B-P [23], and Joback correction [24] methods used in the past do not involve silicon-containing groups and therefore cannot predict the enthalpy of evaporation of silicon-containing compounds. However, the present way takes complete account of the significance of studying the element silicon and its chemical bonding by including it in the range of separable groups. This allows the estimation of evaporation enthalpy data for silicon-containing compounds. This initiative provides for a more comprehensive class of predictable organic compounds.

Therefore, this paper is now based on the elemental and chemical bonding method to develop a model for predicting the enthalpy of evaporation of organic compounds at normal boiling points. Figure 1 shows a block diagram of the design of an evaporation enthalpy prediction model. For a problem of predicting the fundamental physical properties of organic compounds, it is first necessary to define the research needs, set the temperature range to which the model applies, the type of organic compounds, etc. Next, the model and experimental data required to calculate the enthalpy of evaporation are studied and analyzed, on the basis of which a new mathematical model is developed. The model includes feasibility equations, constraints, process parameters, calculation indicators, etc. Finally, the optimization model is solved using a specific mathematical algorithm to obtain a design solution that optimizes the specified objective function. For this model, the objective function is to minimize the prediction error of the equation when the value of the group contribution and the process parameters reach a specific set of values.

2.2. Model Development

The development of Group Contribution Methods has been very rapid. The complex Group Contribution Method has seen the emergence of third-order group contribution values as well as a variety of correction parameters And improved accuracy but is more cumbersome to use. Based on a comparison and summary of previous related equations, Equation (1) is determined by reference to the Joback method. In practice, the user only needs to know the molecular structure and normal boiling point of an organic compound in order to calculate its enthalpy of evaporation data. The equation is simple in form and involves 43 unknown parameters. Moreover, in this paper, the equation was fitted by regression using measured evaporation enthalpy data for 1266 organic species from the literature [25] by random selection. It is evident that the number of data points involved in the regression is much larger than the number of unknown parameters in the relevant equation, so the equation is well-extrapolated. The organic compounds used in the regression equation were classified into 22 categories, the detailed data of which are shown in Figure 2. The organic species that make up most of these are alkenes, alcohols, sulfur-containing compounds, and alkanes.

$$\Delta H_{vb}^{pred}=a+T_b\sum k_i\Delta H_i$$

(1)

In the initial stage of model development, we first collected a large amount of reliable molecular structure information and basic physical properties of organic compounds, such as normal boiling point, molecular weight, CAS number, etc. The molecular structures of all compounds were then decomposed according to this paper’s unique group splitting approach. Subsequent coding was performed using the Matlab software. The regression fit to Equation (1) was achieved by importing the molecular structure information of a large number of processed organic compounds into the coding program and setting the relevant program parameters. Equation (2) was obtained, where a = 19.45. The contribution values of each group received from the regression are shown in

Table 1. Contribution value of elements and chemical bonds to organic compounds obtained by regression.

No.	Groups	Contribution Value	No.	Groups	Contribution Value
1	C	0.000346	22	C-S	0.000967
2	H	0.000417	23	C-Si	−0.006890
3	O	0.006774	24	Si-Cl	0.000237
4	N	0.019124	25	Si-H	−0.003645
5	S	0.005203	26	Si-O	−0.001314
6	F	−0.005441	27	C=S	0.004262
7	Cl	0.008333	28	S-H	0.008806
8	Br	0.006728	29	S=O	0.005275
9	I	0.012826	30	C-N	−0.008837
10	Si	−0.002903	31	C=N	−0.007552
11	C-C	−0.005634	32	C≡N	0.009431
12	C=C	0.000795	33	N-H	0.004949
13	C≡C	0.013563	34	N-O	−0.006773
14	C-O	−0.003573	35	-NO2	−0.007867
15	C=O	0.008788	36 *		0.006586
16	O-H	0.024340	37	Ring C-C	−0.003089
17	C-H	0.003506	38	Ring C=C	0.006613
18	C-F	0.006218	39	Ring C-O	0.002050
19	C-CL	0.000844	40	Ring C-S	0.002989
20	C-Br	0.006728	41	Ring C-N	−0.003202
21	C-I	0.001528	42	Ring C=N	−0.004973

* Where the group serial numbers 36 to 42 are the groups attached to the ring.

. The final set of group contribution values and process parameters selected maximized the predictive power of the model relative to the other sets of parameters that were regressed simultaneously.

$$\Delta H_{vb}^{pred}=19.45+T_b\sum k_i\Delta H_i$$

(2)

In order to further analyze the consistency between literature and predicted data, the organics are classified, and the predicted data are analyzed and processed in this paper. The average absolute relative deviation percentage (AARD) of the predicted evaporation enthalpy data was calculated for each category and all organics involved in the regression. This indicator is the key indicator in this study. Of course, several other critical statistical indicators were also calculated. For example, the percentage absolute relative deviation (ARD), the absolute deviation (AD), and the average absolute deviation (AAD). These indicators are defined by Equations (3)–(6) below. The final detailed analysis data for each indicator is shown in

Table 2. Prediction error results for organic compounds involved in the regression.

No.	Type	n	AAD	ADmax	AARD	ARDmax
1	Silicon-containing compounds	10	0.74	1.31	2.71	4.43
2	Alkanes	160	1.14	5.54	3.34	29.45
3	Sulfur compounds	108	1.9	19.3	4.21	34.92
4	Iodine compounds	12	1.47	4.5	4.24	14.71
5	Cyclo alkanes	82	2.1	20.04	4.67	41.21
6	Alkenes	103	1.59	6.5	4.7	29.25
7	Aromatics	86	2.41	16.05	5.05	21.88
8	Esters	92	2.81	30.95	5.19	43.47
9	Ethers	38	1.97	4.88	5.4	17.68
10	Bromine compounds	23	2.01	9.86	5.41	23.26
11	Chlorine compounds	88	2.1	8.91	5.51	20.83
12	Aldehydes	29	2.53	7.5	6.38	19.87
13	Ketones	27	2.59	8.04	6.97	28.98
14	Others nitrogen compounds	58	2.92	9.85	7.02	39.24
15	Other oxygenated compounds	22	3.05	9.03	7.07	18.04
16	Alcohols	105	3.96	20.77	7.21	23.84
17	Amines	78	3.6	36.72	7.24	47.74
18	Alkynes	26	2.26	6.03	7.33	19.5
19	Acids	52	5.39	33.42	8.15	32.5
20	Phenols	11	5.64	14.85	9.41	20.57
21	Halogen mixtures	24	3.06	8.36	13.05	50.32
22	Fluorine compounds	32	3.22	8.05	13.94	40.92
	Total	1266	0.75	36.72	5.84	50.32

.

$$AARD=\frac{1}{n}\sum _{j=1}^n\frac{\left|\mathsf{\Delta }{H}_{vb,j}^{pred}-\mathsf{\Delta }{H}_{vb,j}^{exp}\right|}{\mathsf{\Delta }{H}_{vb,j}^{exp}}\times 100$$

(3)

$$ARD=\frac{\left|\Delta H_{vb}^{pred}-\Delta H_{vb}^{exp}||\right|}{\Delta H_{vb}^{exp}\times 100}$$

(4)

$$AD=\left|\Delta H_{vb}^{pred}-\Delta H_{vb}^{exp}||\right|$$

(5)

$$AAD=\frac{1}{n}{{\displaystyle \sum }}_{j=1}^{n\sum }\left|\Delta H_{vb}^{pred}-\Delta H_{vb}^{exp}||\right|$$

(6)

Based on the error analysis results obtained above, the method was effective in predicting the enthalpy of evaporation for a wide range of organic compounds, with an average absolute relative deviation of 5.84%. For most classes of organic compounds, the prediction of evaporation enthalpies by this method is relatively reliable. In particular, the AARD was below 5% for silicon-containing compounds, alkanes, sulfur compounds, iodine compounds, cycloalkanes, and alkenes. The AARD for the vast majority of organic compounds remains within 8%. Figure 3 shows how the predicted enthalpies of evaporation data obtained by the EBH method for 1266 organic compounds agree with the experimental data. As shown in the Figure 3a, most of the data points for the new method are on the linear equation line. This indicates that the predicted data better agrees with the experimental data. Moreover, in Figure 4, the error increases as the magnitude of the enthalpy of vaporization increases. In conclusion, the model is relatively satisfactory. This is because Equation (2) itself is straightforward in form and does not possess a complex mathematical form, not even using second-order group parameters, third-order group parameters, etc. The fact that such an equation can achieve such prediction results indicates that the method of predicting thermodynamic properties of organic compounds based on elements and chemical bonds is reliable and worthy of further study.

2.3. Model Reliability Validation

In order to check the reliability of the model, in this paper, 16 additional organics were selected from the literature [25] that were not involved in the regression fitting process to validate and evaluate Equation (2). These 16 organics belonged to different kinds. In this paper, the predictive power of Equation (2) for each class of organic compounds is reflected by calculating the indicator values. The detailed evaluation data of the enthalpy of evaporation for each of these organic compounds are shown in

Table 3. Average relative error in estimating organic compound evaporation enthalpy.

Molecular Formula	Type	Tb	$\Delta {\mathit{H}}_{\mathit{v}\mathit{b}}^{\mathit{e}\mathit{x}\mathit{p}}$	$\Delta {\mathit{H}}_{\mathit{v}\mathit{b}}^{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$	AD	ARD
C5H10O2	Esters	371.22	33.98	34.02	0.04	0.10
C4H6O	Aldehydes	341.15	29.74	29.69	0.05	0.18
C11H10	Aromatics	517.83	45.82	45.63	0.19	0.41
C8H10O	Phenols	491.14	49.88	49.58	0.30	0.61
C6H16N2	Amines	475.04	49.04	49.38	0.34	0.70
C8H18	Alkanes	383.00	32.16	32.44	0.28	0.88
CHCl3	Chlorine compounds	334.33	29.79	30.08	0.29	0.98
C4H8O2	Acids	427.85	43.88	43.18	0.70	1.60
C6H10	Alkenes	332.61	27.54	28.09	0.55	2.01
C8H11N	Azopyridine	444.00	39.51	40.32	0.81	2.05
C19H36	Alkynes	600.16	57.46	58.79	1.33	2.32
C11H24S	Sulfur compounds	530.55	49.39	47.60	1.79	3.62
C2Cl2F4	Halogen mixtures	276.92	23.15	24.02	0.87	3.78
C7H5F3	Fluorine compounds	375.20	32.89	31.58	1.31	3.99
C3H6O	Ethers	278.65	25.05	26.41	1.36	5.45
C3H8O2	Alcohols	460.75	54.48	51.34	3.14	5.76
Total: 16		AARD: 2.15

Example of group splitting: 1. Esters: 5 × C + 10 × H + 2 × O + 3 × C-C + 2 × C-O + 1 × C=O + 10 × C-H; 2. Azopyridine: 8 × C + 11 × H + 1 × N + 3 × C-C + 11 × C-H + 2 × Ring C-C + 2 × Ring C=C + 1 × Ring C-N + 1 × Ring C=N.

.

The evaluation results show that for most types of organics, the calculation errors are within the requirements. In particular, the results for esters, aldehydes, aromatics, phenols, amines, alkanes, and chlorine compounds were very accurate, with an AARD of less than 1%. The method also achieved good prediction results for most other organics. The maximum ARD is 5.76%, the minimum ARD is 0.10%, and the AARD is 2.15%. As shown in Figure 3, the experimental values of the enthalpy of evaporation for the organics not involved in the equation fitting remained almost in high agreement with the predicted values. Therefore, the fitted sets of contribution values and unknown parameter values are trustworthy.

3. Comparative Analysis of Different Methods

In order to provide a more thorough comparison between the proposed EBH method and existing methods for predicting evaporation enthalpy of organic compounds, a number of widely used Group Contribution Methods were gathered for evaluation, including the Joback method, the B-P method, and the Gani method. Following the original literature, each method is evaluated using the prescribed steps. Experimental data on the enthalpies of evaporation of organic compounds were obtained from literature sources [25] and utilized during this evaluation period.

In accordance with the available literature, the Joback method employs 41 groups including those containing halogens and a variety of groups containing the elements C, N, O, and S on the ring and not on the ring, respectively. The enthalpy of evaporation of a compound at normal boiling point is calculated by the Joback method using Equation (7), which is simple in form and incorporates only first-order groups and their corresponding contribution values. The B-P method presents 73 group contributions, as seen in Equation (8), which can cover a variety of organic compounds. The group contribution of the B-P method includes a certain number of alkanes, aromatics, and other substituents. The Gani method equation, shown in Equation (9), is more complex in form and employs a three-level calculation process with 125 first-order, 112 second-order, and 22 third-order groups. This method introduces molecular structure information, which improves the reliability of the prediction. Additionally, the notable number of groups in the Gani method extends the range of molecular characterization.

$$\Delta H_{vb}=15.30+\sum k_i\Delta H_i$$

(7)

$$\Delta H^V=A\left(1-T_r{)}^{\alpha }\exp (-\alpha T_r\right)$$

(8)

$$\Delta H_V\left(T_b\right)=h_b+{{\displaystyle \sum }}_{i=1}^{n_b}{N}_{h_b,i}{C}_{h_b,i}+\omega {{\displaystyle \sum }}_{j=1}^{m_b}{M}_{h_b,j}{D}_{h_b,j}+z{{\displaystyle \sum }}_{k=1}^{o_b}{O}_{h_b,k}{E}_{h_b,k}$$

(9)

The present study evaluates the predictive power of three methods, namely the Joback method, the B-P method, and the Gani method, using the following procedures. Firstly, the Joback method is applied to identify the organic compounds that can be split based on the range of group libraries of the Joback method. The organic compounds are tn dided into respective molecular structures using the corresponding group splitting methods. Based on the obtained group contribution values, the enthalpy of evaporation of organic compounds is calculated using Equation (2). A comprehensive statistical analysis is conducted to compare the experimental and predicted data. The evaluation results are tabulated in

Table 4. Classification and summary of prediction results by Joback method.

No.	Type	n	AAD	ADmax	AARD	ARDmax
1	Alkanes	137	0.97	11.20	3.58	137.30
2	Sulfur compounds	62	2.06	11.24	4.77	23.25
3	Iodine compounds	12	1.79	4.17	5.01	15.49
4	Cycloalkanes	59	1.34	5.67	3.10	12.02
5	Alkenes	130	1.51	25.85	4.09	49.67
6	Aromatics	75	2.41	48.57	4.51	86.71
7	Esters	86	4.23	34.99	8.86	69.68
8	Ethers	50	2.47	11.17	5.67	21.79
9	Bromine compounds	23	2.43	6.26	6.40	15.25
10	Chlorine compounds	89	2.72	10.93	7.37	34.53
11	Aldehydes	32	2.52	19.23	7.42	87.44
12	Ketones	23	2.14	9.00	6.08	34.07
13	Other nitrogen compounds	31	4.60	24.55	10.83	75.15
14	Other oxygenated compounds	21	4.67	22.73	10.18	41.97
15	Alcohols	76	3.51	13.13	5.94	26.43
16	Amines	106	4.71	47.41	10.93	133.62
17	Alkynes	27	1.40	8.26	3.69	25.43
18	Acids	53	8.23	37.68	12.80	59.49
19	Phenols	19	3.97	11.00	7.25	17.44
20	Halogen mixtures	26	2.22	7.44	9.51	47.41
21	Fluorine compounds	34	4.14	39.97	18.52	172.38
	Total	1171	2.92	39.97	6.90	172.38

,

Table 5. Classification and summary of prediction results by B-P method.

No.	Type	n	AAD	ADmax	AARD	ARDmax
1	Alkanes	113	1.17	7.94	3.29	24.33
2	Sulfur compounds	47	1.81	8.36	3.82	14.84
3	Iodine compounds	11	2.56	11.10	6.79	26.91
4	Cycloalkanes	65	1.53	7.71	3.38	15.71
5	Alkenes	76	1.23	5.71	3.29	13.03
6	Aromatics	72	1.85	6.61	3.81	10.82
7	Esters	76	2.24	13.58	4.75	19.39
8	Ethers	41	2.02	9.38	4.82	17.35
9	Bromine compounds	22	1.21	4.30	3.20	10.10
10	Chlorine compounds	72	1.95	12.15	5.06	24.55
11	Aldehydes	29	2.15	5.79	5.13	15.45
12	Ketones	21	1.76	6.39	4.41	12.90
13	Other nitrogen compounds	22	2.72	10.00	6.26	18.04
14	Other oxygenated compounds	6	2.38	3.79	6.54	12.45
15	Alcohols	60	8.06	113.79	11.63	85.48
16	Amines	84	4.55	39.30	8.61	52.44
17	Alkynes	19	3.57	13.90	9.21	24.78
18	Acids	36	8.83	25.13	14.45	29.57
19	Phenols	22	4.95	29.62	8.33	41.03
20	Halogen mixtures	18	4.67	14.38	17.63	45.19
21	Fluorine compounds	26	1.96	12.84	9.53	59.04
	Total	938	2.84	113.79	6.02	85.48

and

Table 6. Classification and summary of prediction results by Gani method.

No.	Type	n	AAD	ADmax	AARD	ARDmax
1	Silicon-containing compounds	6	1.83	5.35	5.64	15.25
2	Alkanes	135	1.45	4.55	4.09	16.29
3	Sulfur compounds	94	1.76	9.50	3.59	17.98
4	Iodine compounds	12	1.92	4.75	5.40	17.70
5	Cycloalkanes	66	1.53	8.97	3.19	15.47
6	Alkenes	108	1.21	6.39	3.29	14.44
7	Aromatics	85	2.59	8.13	5.35	15.99
8	Esters	81	2.49	45.24	5.00	64.62
9	Ethers	50	1.97	7.96	4.64	13.01
10	Bromine compounds	22	2.46	6.75	6.59	15.93
11	Chlorine compounds	72	1.84	34.40	4.13	53.94
12	Aldehydes	29	2.32	6.07	4.91	11.98
13	Ketones	17	1.57	3.08	4.40	7.67
14	Other nitrogen compounds	24	2.48	7.59	5.90	14.14
15	Other oxygenated compounds	16	2.18	7.62	4.63	13.32
16	Alcohols	72	3.18	16.01	5.35	15.69
17	Amines	81	2.18	11.98	4.42	15.39
18	Alkynes	26	1.06	4.71	2.95	8.05
19	Acids	32	5.10	20.16	8.86	91.67
20	Phenols	17	3.30	11.56	6.11	21.21
21	Halogen mixtures	22	1.46	4.73	5.60	15.00
22	Fluorine compounds	24	1.22	2.93	5.97	15.43
	Total	1091	2.05	45.24	4.58	91.67

. The state of agreement between the predicted and experimental data is shown in Figure 4.

The EBH method is followed and compared with the three commonly used methods above. Several vital indicators are listed as a basis for comparison. For example, application range, percentage of average relative deviation, the percentage value of maximum absolute relative deviation, and number of ARD values greater than 50%. The specific data analyzed are shown in

Table 7. Summary of estimation results of organic compounds evaporation enthalpy at normal boiling point.

Methods	n	AARD	ARDmax	m
EBH	1282	5.84	50.32	1
Joback	1171	6.90	172.38	8
B-P	938	6.02	82.50	5
Gani	1091	4.58	91.67	3

.

It can be seen from the comparison results that THE estimation range of the EBH method is the widest, AARD is 5.84%, absolute error is 50.32, and there is only one data point with a relative error over 50%. The Joback method has a wide prediction range and low prediction accuracy, and the relative error of individual data points is large. At the same time, there are as many as 8 data points with a relative error of more than 50%. The low prediction range of B-P and Gani methods is due to the lack of certain groups and the inability to characterize all organic compounds in the database. As a third-order Group Contribution Method, the Gani method has the most accurate prediction ability in terms of prediction ability. The AARD of the B-P method is slightly lower than that of the EBH method, perhaps because the training set of 307 data points is only used in fitting the equation, leading to the ineffectiveness of group contribution value in predicting some complex organic compounds.

4. Results and Discussion

The results of this study show that the EBH method for predicting the enthalpy of evaporation is a relatively simple and efficient method that provides a reasonable degree of accuracy in its predictions. Our comparison with three other prediction methods suggests that the EBH method can meet the needs of scientific research to a certain extent. However, further research is needed to improve the accuracy of the predictions, particularly for organic compounds with more complex structures. Additionally, it should be noted that while the EBH method is relatively simple, it requires a significant amount of experimental data for accurate predictions, and may not be suitable for all applications. Overall, the EBH method provides a valuable alternative for predicting the enthalpy of evaporation in a wide range of organic compounds.

Firstly, the EBH method can accurately and extensively predict silica-containing compounds, which is the most prominent advantage over the other methods. The accuracy of the method’s predictions is high, with an AARD of 2.71%. The prediction range covers almost all organic compounds containing elemental silicon. Of the three methods, only the Gani method can predict a fraction of the silicon-containing compounds, and its prediction accuracy is slightly lower than that of the EBH method. The Gani method is limited in its ability to characterize silicon-containing compounds due to the lack of a comprehensive range of silicon-containing groups, such as >(SiH)−, >SiH2, −SiH3, etc.

Secondly, the EBH method has a relatively high prediction accuracy, with an AARD value of 5.84%. The error is slightly higher than that of the third-order Group Contribution Method, but overall, the new method greatly improves the prediction range and accuracy. Compared with the B-P method, the EBH method has little difference in error. Because the B-P method lacks the groups required for certain kinds of compounds, it does not apply to all compounds in our database. The B-P method lacks the contribution of sulfonyl groups, diazo groups, and some polycyclic aromatic groups. However, the group library of the EBH method is relatively complete, and it is relatively accurate in predicting the enthalpy data of silicon-containing compounds, sulfur compounds, alkanes, iodine compounds, cyclo alkanes, alkenes, and aromatics.

Finally, by comparing the ease of group splitting and the number of groups, it is easy to see that the Gani method and the B-P method have some more complex group structures and a far greater number of groups than the EBH method. The formulae for both methods are also more complex. As a result, the bulk splitting of organics takes up more time and effort for the user. However, the EBH method has only 42 groups, which are not only easy to disassemble but also very easy to remember. It is easy for the user to accurately disassemble the molecular structure of an organic compound without reference to the structure of the groups. The simplicity and ease of use of the EBH method are ensured to a great extent.

Surprisingly, when the EBH method was used to predict the enthalpy of evaporation for halogen mixtures and fluorinated compounds, the AARD values for these substances were 13.05% and 13.94%. This is not an ideal prediction result. The analysis of the study revealed the following main reasons for the accuracy of the prediction results. Firstly, as fluorine is too electronegative, it tends to form C-F bonds with high binding energy and strong stability. Therefore, the new method is not suitable for predicting the enthalpy of evaporation of fluorine-containing compounds. Secondly, as the method cannot distinguish between cis and trans isomers, it produces some intermediate values in the regression of the group contribution values. Therefore, the true molecular structure cannot be perfectly realized, resulting in a more significant error in the calculation of a class of organic compounds containing isomers.

In the following study, we will fully recognize the shortcomings of the present method itself and try to improve it. Efforts will be made to improve the prediction accuracy and speed up the regression equation by increasing the complexity of the equation, adding correction parameters for the structure of the relevant groups, and using some optimization algorithms [26] to improve the programming process of regression fitting equations.

5. Conclusions

The new method proposed in this study for predicting the enthalpy of evaporation of organic compounds at normal boiling points, based on the elemental and chemical bonding method, was demonstrated to be effective. By developing a new equation based on the Joback method, the EBH method achieves an AARD of 5.84%, making it a more accurate and efficient alternative to other evaporation enthalpy prediction methods. The results show that the EBH method can accurately predict silicon-containing compounds and has a broader range of predictions, with an easier and faster method of grouping. However, to build even more accurate models, increasing the complexity of the equations and adding correction factors for the structure of relevant groups should be a top priority. Overall, the EBH method is a reliable and superior method for predicting the enthalpy of evaporation data for organic compounds, with potential for further development and improvement.