KR101267385B1 - ＳＶＲＣ Model Predicting Heat of Vaporization of Pure Organic Compound - Google Patents

Abstract

The present invention consists of up to five elements such as hydrogen (H), carbon (C), nitrogen (N), oxygen (O), and sulfur (S), and is composed of pure molecules consisting of up to 25 atoms except hydrogen. A mathematical model for predicting the heat of vaporization of organic compounds with high accuracy is provided. The above model is a scaled variable reduced coordinate (SVRC) model, and it is possible to know the value of the heat of vaporization at each temperature through the SVRC equation. Such a calculation requires values of several parameters, which are values uniquely given to each compound. In order to obtain them, the present invention is based on experimental values for the heat of vaporization of a plurality of compounds satisfying the above-mentioned conditions. Multiple linear regression and artificial neural networks were used to establish quantitative structure-property relationship (QSPR) prediction models for each parameter. Therefore, the above model predicts the heat of vaporization of a compound composed purely of this molecule, as long as the specific values of the molecular descriptors included in the model are known. As such, the present invention provides a method for predicting the value of the heat of vaporization that is reliable even for a large number of compounds of the above-mentioned conditions, in which the experimental value is unknown, thereby saving the cost and time required for the experiment, and facilitating the research and development activities of related industries. It produces such effects.

Description

SRC Model Predicting Heat of Vaporization of Pure Organic Compound

The present invention belongs to a field of physical chemistry called physical property prediction and relates to a method for predicting with high accuracy a vaporization heat which is one of several physical properties of a compound.

Knowing the exact values of the various properties of a compound specifically involves the entire process of production and consumption, such as reviewing the feasibility of the use of the substance, designing the synthesis and purification processes, and establishing methods and conditions for storage, transport, use and disposal. It is an important issue, both industrially and academically, because it is crucial for all decision making. The most accurate way of knowing the value of the property of interest of the compound of interest is also an experiment, but it is true that it is quite costly and time consuming in many aspects, including the preparation of purified samples and the construction of an environment for accurate measurements. May not be possible. Thus, as an alternative, many researchers have long been trying to predict the exact value of various properties of a compound. As such, the prediction of physical properties has a long history, and new prediction methods are constantly appearing. At present, several prediction models with different accuracy and application range coexist.

Several prediction models have been proposed to date for vaporization heat, which is a property of interest of the present invention. The heat of vaporization is the energy per mole needed to change from liquid to gas when pure material is saturated, that is, when gas and liquid co-exist in equilibrium in a closed container. Say. Previous studies on the prediction of vaporization fever have been described in Polling BE, Prausnitz JM, O'Connell JP, The Properties of Gases and Liquids (5 ed .) , New York, McGraw Hill, (2000).].

Currently known and widely used models for predicting heat of vaporization are mathematical models developed based on the principle of correspondence. The following equation, known as the Watson relation, is the most classical and widely used model [Thek RE, Stiel LI, AIChE J. , 13: 626 (1967)]. At critical temperature T _c and one reference temperature T _ref Using the heat of vaporization ΔH _ref , we can calculate the heat of vaporization for any temperature.

The value of index n is often 0.375 or 0.38. This method is known to be less accurate below the normal boiling point.

Pitzer et al. Proposed another mathematical model using critical temperature T _c and acentric factor ω [Majer V., Svoboda V., Pick J., Heats of Vaporization of Fluids, Studies in Modern Thermodynamics 9 , Elsevier, Amsterdam, (1989). This model can be approximated by the following equation in the region 0.6 <T / T _c <1.0.

On the other hand, using the information on the ΔZ difference between the saturated vapor pressure (P) and the compressibility factors of the gas and liquid state, the heat of vaporization can be calculated by the following equation [Majer V., Svoboda V. , Pick J., Heats of Vaporization of Fluids, S tudies in Modern Thermodynamics 9, Elsevier, Amsterdam, (1989).

All of the above methods have the disadvantage of requiring information on other properties of the compound in order to predict the heat of vaporization. One of the alternatives for constructing the predictive model of vaporization fever is the scaled variable reduced coordinates (SVRC) method. This method is an integrated framework that deals with the saturation properties of compounds based on the principle of the corresponding state. Shaver RD, Robinson RL Jr., Gasem KAM, Fluid Phase Equilibria , 64: 141 (1991).], But no such application has been applied to the prediction of vaporization fever. This method basically assumes that the saturation property Y of a compound is given as a function of temperature T.

Where θ and α are quantities called correlating functions and scaling indices, respectively, and ε is a kind of reduced temperature. The subscripts c and t represent the critical and triple points, respectively, where T _c and T _t represent the temperature at the critical and triple points, and α _c and α _t are the α values at the critical and triple points, respectively. _c and Y _t are the property values at the critical and triple points, respectively. In addition, A, B, and C are universal constants uniquely given to each physical property. In the present invention, in order to predict the heat of vaporization, the values are set to 1.07068, 0.325, and 0, respectively, and α _c = α _t , that is, α = It is assumed that α _c . In order to calculate the heat of vaporization through the above formula, we need to know the values of these parameters for each compound. One way to solve this problem is to establish a QSPR prediction model for each parameter.

QSPR (quantitative structure-property relationship) basically starts with the assumption that the properties of a compound are a function of the structural properties of the molecule and uses various molecular descriptors that reflect different structural properties. The number of molecular descriptors proposed to date has been thousands, and many kinds of molecular descriptors range from simple ones such as the number of carbons or hydrogens in a molecule to complex ones such as the shape, connection state, and electrochemical properties of molecules. Calculations have been developed for Todeschini R., V. Consonni V., Molecular Descriptors for Chemoinformatics : Second , Revised and Enlarged Edition : Volume I / II , Wiley-VCH, 2009]. The QSPR prediction model is presented in the form of a function that includes some of these molecular descriptors and sometimes, in addition, some of the other physicochemical properties of the compound, which are also functions of structural properties.

At this time, the most frequently adopted form of these functions is the linear combination function of the following expressions X _i , and each coefficient c ₀ , c _{i is} mainly determined from experimental data through multiple linear regression analysis.

Another way to create a QSPR model is to use an artificial neural network. Artificial neural network technology is one of the long-standing research results of human beings who want to make intelligent machines by modeling human nerve cells with intelligence, and is an information processing technology that has been applied in various fields since the mid 20th century. . 4 shows a typical example of an artificial neural network. As can be seen, the artificial neural network has an input layer for receiving input data, an output layer for producing output data, and a hidden layer located between them, each layer having one or more nodes. ) Each node in the hidden layer are connected with the input layer and the output layer nodes, each of the connection has been given a weight (weight), it called the amount w _ij, a _ij w'. Each node in the hidden and output layers receives input through these connections from the nodes in the previous stage and then processes it to produce an output value. The functions f ₁ and f ₂ , called activation functions, are applied. In order to actually use such an artificial neural network, first, the neural network is trained using a sample set in which various input values and output values corresponding to the input values are bundled together. This means optimizing the weight of each connection using a back propagation algorithm to minimize the difference. The neural network that has undergone such training does not provide the necessary rules or knowledge to solve the problem, but it establishes general rules through learning and gives valid output for unknown inputs. It is widely used as a very useful means in the field.

The technical problem to be solved by the present invention is to overcome the limitations of the various models mentioned above and to show more broad and more accurate predictive performance, hydrogen (H), carbon (C), nitrogen (N), oxygen (O) and sulfur. The SVRC model is constructed for the heat of vaporization of a pure organic compound composed of up to 5 elements including (S) and molecules having 25 or less atoms except hydrogen.

We achieved this goal by constructing QSPR models that predicted the values of the parameters in the SVRC equation, taking into account a wider variety of molecular descriptors based on more experimental data. Some of these are multilinear regression-artificial neural network hybrid models obtained by combining a combination of multiple linear regression and artificial neural network techniques. Especially, artificial neural networks have a nonlinear functional relationship between independent and dependent variables that cannot be reflected It has the advantage of being able to reflect, which makes it possible to implement a model with higher prediction performance. However, the artificial neural network has a disadvantage in that its stability is lower than that of the multiple linear regression model due to its high degree of freedom in rule setting. In the present invention, when the prediction value of the artificial neural network model and the prediction value of the multiple linear regression model show a large difference, the method of adopting the prediction value of the multiple linear regression model compensates for these shortcomings. We established an excellent prediction model that takes advantage of the neural network model.

The reason for the limitations mentioned above on the range of compounds to which the predictive model can be applied is mainly to the current state of the art, if any of the molecular descriptors used require quantum mechanical calculations to obtain their values. Is due to the fact that for compounds outside the stated range, troubles arise in terms of accuracy and calculation time. However, even within the above limitations, since there are a great many compounds and industrially important compounds are included in a large amount, it is determined that the present invention can greatly benefit human society.

Today, humans depend on a wide variety of compounds, including plastics, fibers, rubber, paints, fertilizers, medicines and fuels, and this trend is expected to intensify. According to the American Chemical Society (ACS), as of July 2010, the total number of compounds registered was over 54,000,000. In comparison, even if the physical property value is only one, the number of experimentally known compounds is only tens of thousands. The physical property value of compounds is essential for the better life of mankind, such as the development of new materials and new drugs, the optimal design of chemical plants, the improvement of the productivity of existing facilities, the development and saving of resources, the securing of safety, and the protection of the environment. In particular, the heat of vaporization is a property that commercial programs such as Aspen-Plus and Pro / II, which are well known as optimal design programs for chemical plants, are urgently requesting the exact values. However, at present, the number of compounds whose experimental values are known is only a few thousand, and depending on the compounds, the work of obtaining data through experiments may be past due to toxicity, instability, and difficulty of purification. From this point of view, the present invention, which can obtain the heat of vaporization of a large number of compounds with high accuracy only through the information on the molecule, does not only reduce the cost and time required for the experiment, but also estimates the value even when the experiment is impossible. In addition to facilitating R & D activities, it will also provide the information that is appropriate to all places that require such values, such as academia and academia, to bring about the effect of making the activities more smoothly.

1 is a flowchart illustrating a process of constructing an SVRC prediction model for a vaporization sequence provided by the present invention.
2 is a flowchart illustrating a process of constructing a multilinear regression model for α _c among parameters required for an SVRC model.
3 is a flowchart illustrating a process of constructing a multiple linear regression-artificial neural network hybrid model for ΔH _b among parameters required for an SVRC model.
Figure 4 is a view showing the structure of the artificial neural network used in the present invention.
5 to 8 illustrate, for example, a comparison of the predictive performance of the Watson model and the predictive model provided by the present invention for some compounds.
9 is a histogram plot of 29073 experimental data of the Watson model.
10 is a histogram diagram of 29073 experimental data of the SVRC model.

Figure 1 is a simplified representation of the process of building the SVRC model for the vaporization heat.

The first thing to do when building an SVRC model is to collect and review the experimental data as specified in step 1. For this invention, 125258 data were collected for 3397 compounds as a result of extensive research on all literatures and data that can be referred to through various papers, books, and Internet sites. The collected data were examined in a variety of ways to determine whether they were truly valid values that could be used to build the model.They were not experimental values, errors in data notation, or values for similar temperatures of the same compound. If the values are too reliably compared to the values, or if the values for the molecular expressions are data about a compound that is difficult to prepare immediately, then the data is corrected or deleted. Data were selected. In addition, when constructing a property prediction model, it was better to classify sample compounds separately into hydrocarbons consisting of carbon and hydrogen and nonhydrocarbons, and to model them separately. In light of this, the model was established by dividing the total data into 14,463 data sets for 433 hydrocarbons and 19,647 data sets for 673 non-hydrocarbons. In the present invention, the 'organic compound' or 'compound' is composed of five elements such as hydrogen (H), carbon (C), nitrogen (N), oxygen (O), and sulfur (S). Refers to a substance consisting of molecules with 25 or fewer atoms excluded.

The next step is to prepare the values of the molecular descriptors for these compounds. The values for various molecular descriptors totaling up to 1978 are computed in batches using a computer from files containing information on the molecules of each compound. In order to calculate the electronic structure of molecules, the Schrodinger equation is usually solved by a pure theory method to solve the electron energy. Hartree-Fock (HF) method [CCJ Roothan, Rev. Mod. Phys. 23, 69 (1951)]. This approximation introduces a fundamental error in the calculated results and adds a multidimensional theoretical perturbation term to the Post Hartree-Fock method [C. Moller and MS Plesset, Phys . Rev. 46, 618 (1934)], to obtain a more accurate solution, but require a relatively large amount of computation. In this way, it is too costly or time-consuming to calculate large molecules.

In addition, the Gaussian method that combines Hartley-Fork and Post Hartley-Fork [L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys. 94, 7221 (1991); L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, and J. A. Pople, J. Chem. Phys. 109, 7764 (1998) show very little error in energy prediction, but more computation is required because it performs energy calculations for several post-Hartley-Fork methods.

Density functional theory is used to find the ground state using the function of the total energy using the electron density function instead of the wave function with the multidimensional perturbation term to consider the correlation between the electrons of the molecules of many electrons. R. Seeger and JA Pople, J. Chem . Phys . 66, 3045 (1977). The advantage of the density functional theory is that the electron density only needs to be taken into account so that more accurate results can be obtained with comparable calculations to the Hartree-Fock method. The combination of exchange functions and correlation functions for calculating the exchange-correlation energy of the electrons is used to obtain more improved results without increasing the calculation amount.

The computational theories previously attempted to select an optimal quantum mechanical calculation method are the density ranges of the aforementioned Hartley-Fork method, various Post-Hartley-Fork methods, Gaussian (G2, G3) methods, and various combinations of functional functions. Function theory. Among them, one method of density functional theory, which is the best performance calculation time, was selected.

Therefore, in the present invention, the optimization of the molecular structure and the frequency calculation are performed by applying the calculation method of the specified density functional theory using a commercial quantum mechanical calculation program.

In the optimized structure, molecular descriptors represented by various meaningful values reflecting the properties of molecules as well as the above-described physical property information can be obtained. Some molecular descriptors can express the characteristics of two-dimensional structures, while others represent the characteristics of three-dimensional structures. Divided into 24 categories, including detailed presenters in each category. After calculating the molecular descriptor values, we picked out those that were not suitable, that is, the values were the same for all sample compounds and could not be independent variables in the model. This is because it prevents irrelevant molecular expressions from being included in the prediction model, thereby increasing the reliability of the model and reducing the computation time required to find the optimal model by reducing the number of molecular expressions.

Step 4 is followed by preparing data needed to establish a QSPR model for each parameter based on the experimental data. In order to calculate the heat of vaporization by the SVRC equation, the values of the heat of vaporization ΔH _c , ΔH _t and α _c at the critical and triple points are required. ΔH _c can theoretically be set to zero. Meanwhile, to accurately predict the temperature of the triple point is very difficult and generally entrusted well known, and therefore in the present invention, I got to the starting temperature of the heat of vaporization curve to 0.55 times (T _{0 .55b)} instead of the normal boiling point of the triple point, the sample compound The mean of these points is about the same as the mean of the triple points. Now, in order to complete the SVRC model should be established for QSPR predictive models for α _c and ΔH _{0 .55b,} which are the remaining parameters. In order to establish such a QSPR prediction model to be provided a set of the values of the various parameters for each compound, the typical curve of the first evaporation heat for ΔH _{0 .55b} rear fit to the experimental data of the compounds, in the curve It was the temperature takes the value of the point where the T _{0 .55b,} α _c for the rear from the experimental data using a numerical solution of nonlinear equations, obtaining the value α in the equation below for each temperature, the temperature in line these values forming The value of the point at which is T _c is taken.

In order to be able to obtain the value of each parameter from the experimental data of a compound to use as a data for establishing the QSPR prediction model, the experimental data of the compound is distributed evenly over a relatively wide temperature range, Since the number of compounds with relatively few experimental data satisfying these conditions exists, the number of compounds participating in the QSPR prediction model of each parameter is significantly reduced than the total number of compounds.

Step 5 is to build a QSPR model for each parameter. In the present invention, such QSPR model, the multiple linear regression models for the α _c, multiple linear regression for ΔH _{0 .55b} - adopted a hybrid artificial neural network model. 2 is a flowchart illustrating a process of constructing a multiple linear regression model, and FIG. 3 is a process of constructing a multiple linear regression-artificial neural network hybrid model. The specific detailed steps are as follows.

In detail step 1, the sample compounds are divided into two parts: the training set used to explore the predictive model, and the test set used to test the predicted performance of the determined model. Sample hydrocarbons and non-hydrocarbons were divided between 5: 5 and 8: 2, preferably 6 to 4, taking care not to distribute similar molecules on one side only.

이며 이들을 다 조사하는 것은 현실적으로 불가능하다.We then find the best multiple linear regression model based on the training set. The term 'best' is used in the sense of relative meaning that it can be obtained in a relatively short time and has a performance very close to the optimal solution in the absolute sense. The reason for not finding the optimal solution directly is because of the long computation time. For example, when there are 1700 suitable molecular representations out of 1978 molecular representations, you can choose from five different linear regression models. The total number is

It is practically impossible to investigate them all.

In order to obtain useful results within a limited time, the present invention uses a genetic algorithm [Judson, "Genetic Algorithms and Their Uses in Chemistry", Reviews in Computational Chemistry, Lipkowitz & Boyd, Eds., Vol. 10, pp. 1 -73 (VCH Publishers, NY, 1997)]. First, a population of multiple linear regression models is created by randomly drawing a certain number of molecular descriptors from a pool of molecular descriptors. For example, let's say we created a population of 1000 different polylinear regression models that were randomly drawn from 5 of the 1700 suitable molecular descriptors.

Individuals, called chromosomes, are coded by combining the numbers of extracted molecular descriptors. For example, the chromosome of the multiple linear regression model formed by the 45th, 167, 684, 1033, and 1502th molecular descriptors among 1700 molecular descriptors can be expressed as (45, 167, 684, 1033, 1502). Two parent chromosomes are selected from the populations thus generated and crossed over to generate children. In the present invention, the Roulette Wheel method is adopted as a selection method for selecting the parent chromosomes.

The Roulette Wheel method is the most commonly used selection algorithm, which allocates a roulette region to the chromosome in proportion to the fitness of each chromosome, and then rotates the roulette to select the chromosome of the corresponding region. Therefore, in this method, the higher the fit, the more likely it is to be selected. The coefficient of determination (R ² ) or average absolute error (AAE) of the regression model was used to calculate the fitness of each chromosome to determine the selection probability. In other words, the larger the coefficient of determination or the smaller the mean absolute error, the higher the probability of selection.

The single point crossover method is adopted as the breeding method. The most common breeding method is to generate a child by selecting one crossing point on the parent chromosome and exchanging chromosomal parts before and after the point. For example, if the parent chromosome is given as (24, 262, 343, 789, 1290), (38, 454, 554, 1322, 1449), and there is a crossing point between the third and fourth elements, then the child chromosomes are (24, 262, 343, 1322, 1449), (38, 454, 554, 789, 1290).

When the offspring are created, they have a chance of mutating a portion of their chromosomes, which randomly replaces several elements with completely new values. This new information does not exist in the current population. It is a process that makes it possible to search to compensate for the case where there is no proper solution in the initial set combination.

In this way, a new generation of populations are created by replacing some or all of the existing populations with newly obtained entities. Repeat this process until the number of generations reaches a pre-determined value (usually between 10 and 1000), and then select and end up the regression model with the best predictive performance.

Once this best multiple linear regression model has been selected, the next step is to examine its validity. If a problem is found that the t-test value of the molecular descriptors included in the model is not good, go back and look for another model. For example, if the number of sample compounds is 1005 and the selected model consists of five molecular descriptors, if the t-test for one of the molecular descriptors is 3.3 or higher, then the probability that the molecular descriptor is irrelevant to that property is 0.1 It means less than%. In the present invention, when there is a molecular presenter having a t-test value of less than about 3, the selected model is discarded and another model is found. In addition, even if the values of the molecular descriptors for the sample compounds are the same except for a few few compounds, they are not considered to be reliable models. In general, increasing the number of molecular expressions included in the model increases the predictive performance, but such problems occur. Therefore, the final model is usually obtained by repeating these steps through several trials and errors while changing the number of molecular expressions. If the problem no longer appears in the selected model, proceed to the next step.

In detail step 4, the predictive performance of the found model is evaluated using a test set that did not participate in forming the model. If a problem is found in the training set, such as a lot of poor predictive performance or a significant drop in prediction, go to detail step 1, readjust the training set and the test set, and then proceed with the detailed steps. If the difference between the training set and the test set does not exceed 20% of the absolute mean error (AAE) obtained for the training set, it is judged that the predictive performance is satisfied.

Although adoption of the parameters required for the formula parameters α _c SVRC multiple linear regression model thus establishing a final predictive model, multiple linear regression - ANN hybrid model for the ΔH _{0 .55b} adopted a final prediction model follows the Is added.

First of all, in order to construct an artificial neural network model from the already constructed multiple linear regression model, the standardization of the data of the molecular presenters and the parameter data is performed. . The entire sample thus prepared is divided into a training set, a validation set, and a test set in an approximately 6: 2: 2 ratio.

와 같이 주어지며 은닉층이 m개의 노드로 이루어져 있을 때 출력층 출력노드의 최종 출력값은

와 같이 주어진다. 여기서 T는 문턱 가중치(threshold weight)를 의미한다.We then use them to find the best artificial neural network model. At this time, the search range is limited to a neural network having a hidden layer between the input layer and the output layer as shown in FIG. 4 and having three structures connected only in a feed forward direction, that is, in a direction from the input to the output. It was. The input layer is composed of the same number of nodes that receive the values of the molecular descriptors included in the already established multilinear regression model, and the output layer is composed of one node that outputs the vaporization sequence. In addition, the sigmoid function f ₁ (x) = (1 + e ^-x ) ^-1 is adopted as the activation function of the hidden layer, and the linear function f ₂ (x) = x is adopted as the activation function of the output layer. Therefore, input values received by each node of the input layer are I ₁ , I ₂ ,... , I _l , the output value of node j of hidden layer is

When the hidden layer consists of m nodes, the final output value of the output layer output node is

As shown in Fig. Here T denotes a threshold weight.

The search proceeds from increasing the number of hidden nodes to one in order. Usually, the search proceeds to twice the number of input nodes. However, if a satisfactory model is not found, the search proceeds further. The detailed procedure is as follows. First, for each number of hidden nodes, various initial value sets (usually 1000 sets or less) of weights T, w _ij , and w´ _ij generated by using a random number generation function are prepared, and a neural network initialized with each set using a training set. Iteratively trains through the backpropagation algorithm to find the optimized values of the weights T, w _ij , w´ _ij . The judgment of the optimization is that the mean square error is minimized when the model, which is determined by the updated weights after each training, is applied to the test set. Normally this will occur within 3000 to 5000 repetitions. The optimized neural network model corresponding to each set of initial values thus obtained is applied to the training set, the test set, and the test set, respectively, to collect only those whose mean square errors are smaller than those of the multiple linear regression model. If there are several of these, choose the best model based on the coefficient of determination or the absolute absolute error.

When the artificial neural network model is selected, an overfitting prevention standard is finally set. This is a measure to improve the instability that the artificial neural network gives wrong answers to unknown inputs as a result of excessive training. For this, we set 2.3889 kcal / mol) to adopt the predictive value of the multiple linear regression model when the absolute value of the difference between the predicted values of the neural network model and the multiple linear regression model exceeds the reference value. Say that.

After this process, the QSPR model for each parameter is constructed. Next, in step 6, a test is performed to compare the entire experimental data of each compound for the heat of vaporization with the value calculated by the SVRC equation. At this time, to calculate the predicted value by SVRC equation, the normal boiling point, the critical temperature, and the value of the heat of vaporization ΔH _b at the normal boiling point are required. For this information, a value obtained by a known method or a calculation method based on the QSPR model is used. If the difference between the experimental and predicted values is greater than the acceptable level (approximately 10% more than the predicted error is greater than the experimental mean error), go back to step 5 and re-establish the QSPR model for each parameter. If it passes the test, it is adopted as the completed SVRC model.

The results for the SVRC model established through this process are summarized in Tables 1-6. Tables 1 and 2 results for SVRC model and its ability to predict the heat of vaporization of the hydrocarbon with them on will briefly describe the QSPR model for predicting the value of ΔH _{0 .55b,} α _c for each of the hydrocarbon is provided in Table 3 have. Also QSPR model for predicting the value of ΔH _{0 .55b,} α _c for non-hydrocarbons is described respectively in Tables 4 and 5. The SVRC model for predicting the heat of vaporization of non-hydrogenated hydrogen and the results of its performance are shown in Table 6.

The main contents of QSPR predictive models for hydrocarbons of ΔH _{0 .55b} Number of sample compounds 383 Number of molecular descriptors 10 Names of Molecular Presenters P ₁ : D total accessibility index / weighted by atomic electrotopological states
P ₂ : Normal boiling point
P ₃ : Radial Distribution Function-6.0 / unweighted
P ₄ : 3D molecular representation of electron diffraction-based 3D-MoRSE-signal 11 / weighted by atomic van der Waals volumes
P ₅ : Resonance integral weighted edge adjacent matrix eigenvalue 14
P ₆ : Radial Distribution Function-11.5 / weighted by atomic masses
P ₇ : Radial Distribution Function-15.0 / weighted by atomic masses
P ₈ : Relative number of rings
P ₉ : topological charge index of order 6
P ₁₀ : 3D-MoRSE-signal 10 / weighted by atomic polarizabilities Regression Model Decision Coefficients 0.9937 Regression Model AAE 0.2685 Kcal / mol Regression model

Artificial Neural Network Determination Coefficient 0.9968 Artificial Neural Network AAE 0.1832 Kcal / mol Artificial Neural Network Model

Overconformity Prevention Criteria 0.7167 Kcal / mol

Highlights of QSPR Prediction Model for Hydrocarbon α _c Number of sample compounds 383 Number of molecular descriptors 10 Names of Molecular Presenters P ₁ : highest occupied molecular orbital-1 energy (HOMO-1 energy) P ₂ : R--CR--R number of functional groups (R--CR--R) P ₃ : antidepressant of Ghose-Viswanadhan-Wendoloski (Ghose-Viswanadhan-Wendoloski antidepressant-like index at 80%) P ₄ : leverage-weighted autocorrelation of lag 6 / Weighted by atomic masses P ₅ : Moran autocorrelation-lag 6 / Weighted by atomic masses P ₆ : ΔH _b / ΔH _0.55b , ΔH _b is the heat of vaporization at normal boiling point P ₇ : Number of non-terminal sp carbons (number of non-terminal C (sp)) P ₈ : highest eigenvalue n. 6 of Burden matrix / weighted by atomic Sanderson electronegativities P ₉ : R maximum autocorrelation order R / maximal autocorrelation of lag 1 / Weighted by atomic masses P ₁₀ : Dipole moment weighted edge adjacent matrix eigenvalue 12 Coefficient of determination 0.2758 Mean Absolute Error 0.04594 model

Highlights of the SVRC Prediction Model for Hydrocarbons Number of sample compounds 433 Number of experiment data 14463 Coefficient of determination 0.992 Mean Absolute Error 0.2423 Kcal / mol model

The main contents of QSPR predictive models for ΔH _{0 .55b} of the non-hydrocarbon Number of sample compounds 645 Number of molecular descriptors 15 Names of Molecular Presenters P ₁ : presence of phase distance 5 OO coupling
P ₂ : presence of phase distance 10 CC coupling
P ₃ : relative number of nitrogen atoms
P ₄ : Moran autocorrelation-lag 1 / Weighted by atomic masses
P ₅ : Minimum Net Atomic Charge
P ₆ : Minimum net atomic charge of hydrogen atom
P ₇ : Radial Distribution Function-7.0 / unweighted
P ₈ : Normal boiling point
P ₉ : Eigenvalues of edge diagram weighted edge adjacency matrix 15
P ₁₀ : minimum partial charge of hydrogen atom
P ₁₁ : area-weighted surface charge of hydrogen bond-dependent hydrogen bond base atoms (HA dependent HDCA-2)
P ₁₂ : presence of phase distance 3 OO coupling
P ₁₃ : total number of quaternary sp3 carbons
P ₁₄ : area-weighted surface area fraction of hydrogen bond-dependent hydrogen bond base atoms (HA dependent HDSA-2 / TMSA)
P15: Average electrophilic response index of oxygen atom Regression Model Decision Coefficients 0.9603 Regression Model AAE 0.5746 Kcal / mol Regression model

Artificial Neural Network Determination Coefficient 0.9704 Artificial Neural Network AAE 0.4983 Kcal / mol Artificial Neural Network Model

Overconformity Prevention Criteria 2.3889 Kcal / mol

Main Contents of QSPR Prediction Model for α _c in Unhydrogenated Hydrogen Number of sample compounds 507 Number of molecular descriptors 15 Names of Molecular Presenters P ₁ : R maximal autocorrelation of lag 2 / Weighted by atomic van der Waals volumes
P ₂ : 1st component accessibility directional WHIM index / weighted by atomic polarizabilities
P ₃ : Presence / absence of O-O at topological distance 07
P ₄ : R max autocorrelation order 4 / unweighted
(R maximal autocorrelation of lag 4 / Unweighted)
P ₅ : Presence of phase distance 5 OO coupling
(presence / absence of O-O at topological distance 05)
P ₆ : 3D molecular structure representation based on electron diffraction-order 8 / weighted
(3D-MoRSE-signal 08 / unweighted)
P ₇ : Dielectric moment weighted edge adjacent matrix eigenvalue 7
P ₈ : Sum of geometric distances between O..S
(sum of geometrical distances between O..S)
_{P 9: ΔH b / ΔH 0} .55b, ΔH b is the heat of vaporization from the normal boiling point
P ₁₀ : minimum nucleophilic response index of oxygen atom
P ₁₁ : H autocorrelation of lag 6 / Weighted by atomic masses
P ₁₂ : number of secondary alcohols
P ₁₃ : Total point-charge component of the molecular dipole
P ₁₄ : R # N / R = N- number of functional groups (R # N / R = N-)
P ₁₅ : Frequency of O-O at topological distance 06 Coefficient of determination 0.4532 Mean Absolute Error 0.1073 model

Main Contents of SVRC Prediction Model for Unhydrogenated Hydrogen Number of sample compounds 673 Number of experiment data 19647 Coefficient of determination 0.9688 Mean Absolute Error 0.4379 kcal / mol model

In order to show that the present invention is superior to the existing technology, the predictive performance of the Watson model described above was compared with the SVRC model of the present invention and 29073 experimental data of 1067 compounds as one of the widely used conventional models. As a result, the Watson model showed a coefficient of 0.872981 and an average absolute error value of 1.9211kcal / mol, whereas the SVRC model of the present invention showed a remarkably superior value of 0.98489 and an average absolute error of 0.3219kcal / mol. I learned. 5 to 8 are examples for comparing the predictive performance of each model for some compounds. From these drawings, it can be seen that the SVRC model has better performance than the existing model. Meanwhile, FIGS. 9 and 10 illustrate the histogram of the error between the experimental value and the predicted value for 29073 experimental data. These figures demonstrate that the SVRC model is more accurate, showing that the Watson model has a probability of 81.73% and the SVRC model has a probability of 99.88% within 3 kcal / mol of error.

The present invention is not limited to the above-described embodiments, and any person having ordinary skill in the art to which the present invention pertains may make various modifications without departing from the gist of the present invention as claimed in the claims. Such changes are intended to fall within the scope of the claims.

Claims (30)

A first step of inputting experimental data of hydrocarbon series among collected sample organic compounds;
A second step of preparing a molecular descriptor value for the heat of vaporization of the hydrocarbon-based organic compound of the sample compounds and examining the suitability of the molecular descriptor for removing the molecular descriptor that cannot be an independent variable;
A third step of obtaining the parameters required for the SVRC equation described in equation (1) below:

[Where ΔH is the heat of vaporization, ΔH _0.55b is the heat of vaporization at a temperature T _{0.55b that} is 0.55 times the normal boiling point, α _c is the scaling index, T is the temperature, and T _c is the critical temperature];
A fourth step of constructing a QSPR model for the heat of vaporization, α _c , at a temperature of 0.55 times the normal boiling point of the parameter obtained in the third step;
A fifth step of testing predictive performance with the experimental data;
When satisfying the test of the fifth step, the hydrocarbon-based organic compound by the SVRC model including the sixth step of adopting the vaporization heat prediction value of the searched model as the vaporization heat value and not satisfied, repeating the fourth and fifth steps. To get the heat of vaporization.
The method of claim 1, wherein the method for obtaining a QSPR model for the heat of vaporization at a temperature of 0.55 times the normal boiling point in the fourth step is
Step 4-0 of extracting optimal molecular descriptors for each of the heat of vaporization and α _c at a temperature of 0.55 times the normal boiling point;
Step 4-1 separating the experimental data into a training set and a test set;
Step 4-2 of searching for an optimal multiple linear regression model for the training set;
Steps 4-3 to review the validity of the selected model;
Step 4-3, if the validity in step 4-3, and repeats step 4-2, step 4-3, and if valid, step 4-4 of testing the predictive performance of the model against the test set;
If the performance does not meet the criteria in the 4-4 test for the test set, repeat steps 4-2 to 4-4, and if the performance satisfies the criteria, separate the data into three sets after sample standardization. 4-5 steps;
Step 4-6 of dividing the entire sample into three sets and searching for an optimal artificial neural network model;
The vaporization heat prediction value at a temperature of 0.55 times the normal boiling point obtained by the optimal multiple linear regression model satisfying the performance test in steps 4-5 and the optimal artificial neural network model found in steps 4-6. A fourth step of comparing the absolute value of the difference in the estimated heat of vaporization at a temperature of 0.55 times the normal boiling point with a preset overfit prevention reference value;
If the difference is greater than the reference value for preventing overfitting, the estimated heat of vaporization at the temperature of 0.55 times the normal boiling point by the multiple linear regression model obtained in steps 4-5 is adopted as the heat of vaporization at the temperature of 0.55 times the normal boiling point. If it is smaller than the sum prevention reference value, steps 4-8 of adopting the predicted vaporization heat value at a temperature of 0.55 times the normal boiling point by the artificial neural network model detected in steps 4-6 as the vaporization heat value at a temperature of 0.55 times the normal boiling point. Including,
The method of obtaining the QSPR model for α _c in step 4-0 is
If the performance does not meet the criteria in the above-described steps 4-1 to 4-4 and the test set 4-4 for the test set, the steps 4-2 to 4-4 are repeated, and the performance is the standard. Step 4-5-1 to determine the optimal multiple linear regression model if satisfied;
Method for obtaining the heat of vaporization of the hydrocarbon-based organic compound by the SVRC model comprising the step 4-6-1 to obtain the α _c value through the linear regression model that satisfies the performance test in the step 4-5-1.
3. The method of claim 2, wherein the optimal molecular descriptor in step 4-0 is an independent molecular descriptor whose values are not the same for all sample compounds. .
The method of claim 2, wherein the training set and the test set are divided by a ratio of 5: 5 to 8: 2 in step 4-1.
3. The hydrocarbon-based method of claim 2, wherein the multilinear regression model is searched for a linear regression model by applying a genetic algorithm to the training set in step 4-2. How to find the heat of vaporization of organic compounds.
The method of claim 5, wherein the genetic algorithm generates a population composed of a plurality of multiple linear regression models randomly drawn from a predetermined number of molecular expressions in a pool of molecular expressions. Making; Encoding each individual by combining the numbers of the extracted molecular presenters; Selecting two parent chromosomes from the created population by the Roulette Wheel method and generating offspring by a single point crossover method; Obtaining the heat of vaporization of hydrocarbon-based organic compounds by the SVRC model comprising the step of mutating a portion of the chromosome of the generated offspring with a certain probability and then replacing a part of the existing population with them to generate a new population. Way.
The method of claim 2, wherein the step 4-2 is to obtain the heat of vaporization of the hydrocarbon-based organic compound by the SVRC model comprising determining the predictive performance by the coefficient of determination or the mean absolute error of the regression model.
The method of claim 2, wherein the validity in the step 4-3 is to determine the heat of vaporization of the hydrocarbon-based organic compound by the SVRC model to determine the validity by the t-test value.
3. The method of claim 2, wherein in step 4-5, if the difference between the training set and the test set does not exceed 20% of the absolute mean error (AAE) obtained for the training set, the multiple linear regression model is determined. If the difference is more than 20% of the absolute mean error (AAE) obtained for the training set, then the heat of vaporization of the hydrocarbon-based organic compound is obtained by the SVRC model that reclassifies the training set and the test set.
[4] The SVRC model of claim 2, wherein the search range by the artificial neural network in step 4-6 has one hidden layer between the input layer and the output layer and is connected only in a feed forward. A method of obtaining the heat of vaporization of a hydrocarbon-based organic compound by
The method of claim 10, wherein the activation function of the hidden layer is a sigmoid function to obtain a heat of vaporization of a hydrocarbon-based organic compound by an SVRC model.
According to claim 2, wherein the overfit prevention reference value for the heat of vaporization at the temperature of 0.55 times the normal boiling point in the step 4-7 is 0.7167 kcal / mol characterized in that the heat of vaporization of the hydrocarbon-based organic compound by the SVRC model How to obtain.
According to claim 2, wherein in the step 4-0 molecular expression extracted for the heat of vaporization at a temperature of 0.55 times the normal boiling point
P ₁ : D total accessibility index / weighted by atomic electrotopological states,
P ₂ : normal boiling point,
P ₃ : Radial Distribution Function-6.0 / unweighted,
P ₄ : 3D-MoRSE-signal 11 / weighted by atomic van der Waals volumes
P ₅ : Eigenvalue 14 from edge adjacency matrix weighted by resonance integrals,
P ₆ : Tokyo Distribution Function-11.5 / Radial Distribution Function-11.5 / weighted by atomic masses,
P ₇ : radial distribution function-15.0 / weighted by atomic masses,
P ₈ : Relative number of rings,
P ₉ : topological charge index of order 6 and
P ₁₀ : includes electron diffraction-based three-dimensional molecular structure representation-order 10 / atomic polarization weighting (3D-MoRSE-signal 10 / weighted by atomic polarizabilities),
The molecular expression extracted for the α _c is
P ₁ : highest level occupied molecular orbital-1 energy (HOMO-1 energy),
P ₂ : R--CR--R number of functions (R--CR--R),
P ₃ : Ghose-Viswanadhan-Wendoloski antidepressant-like index at 80%,
P ₄ : leverage-weighted autocorrelation of lag 6 / Weighted by atomic masses,
P ₅ : Moran autocorrelation-lag 6 / Weighted by atomic masses,
P ₆ : ΔH _b / ΔH _0.55b , ΔH _b is the heat of vaporization at the normal boiling point,
P7: number of non-terminal C (sp),
P8: highest eigenvalue n. 6 of Burden matrix / weighted by atomic Sanderson electronegativities,
P9: R maximal autocorrelation of lag 1 / Weighted by atomic masses,
P10: A method of obtaining the heat of vaporization of a hydrocarbon-based organic compound by an SVRC model, comprising an Eigenvalue 12 from edge adjacency matrix weighted by dipole moments.
A computer-readable storage medium having recorded thereon a program for executing on a computer a method for obtaining vaporization heat of a hydrocarbon-based organic compound according to any one of claims 1 to 13.
A first step of inputting non-hydrocarbon-based experimental data among collected sample organic compounds;
Preparing a molecular presenter value for the heat of vaporization of the input sample organic compounds;
Third step of obtaining parameters required for SVRC equation described in Equation (2) below

[Where ΔH is the heat of vaporization, ΔH _0.55b is the heat of vaporization at a temperature T _{0.55b that} is 0.55 times the normal boiling point, α _c is the scaling index, T is the temperature, and T _c is the critical temperature];
A fourth step of constructing a QSPR model for the heat of vaporization, α _c , at a temperature of 0.55 times the normal boiling point of the parameter obtained in the third step;
A fifth step of testing predictive performance with the experimental data;
If the test of the fifth step is satisfied, the vaporized heat prediction value is adopted by the SVRC model including the sixth step of repeating the fourth step and the fifth step by adopting the vaporization heat prediction value of the searched model as the vaporization heat value. A method of obtaining the heat of vaporization of a compound.
The method of claim 15, wherein the method for obtaining a QSPR model for the heat of vaporization at a temperature of 0.55 times the normal boiling point in the fourth step is
Step 4-0 of extracting optimal molecular descriptors for each of the heat of vaporization and α _c at a temperature of 0.55 times the normal boiling point;
Step 4-1 separating the experimental data into a training set and a test set;
Step 4-2 of searching for an optimal multiple linear regression model for the training set;
Steps 4-3 to review the validity of the selected model;
Step 4-3, if the validity in step 4-3, and repeats step 4-2, step 4-3, and if valid, step 4-4 of testing the predictive performance of the model against the test set;
If the performance does not meet the criteria in the 4-4 test for the test set, repeat steps 4-2 to 4-4, and if the performance satisfies the criteria, separate the data into three sets after sample standardization. 4-5 steps;
Step 4-6 of dividing the entire sample into three sets and searching for an optimal artificial neural network model;
The vaporization heat prediction value at a temperature of 0.55 times the normal boiling point obtained by the optimal linear regression model satisfying the performance test in steps 4-5, and the optimal artificial neural network model found in steps 4-6. Steps 4-7 of comparing the absolute value of the difference in the predicted heat of vaporization at a temperature of 0.55 times the normal boiling point with a preset overfit prevention reference value;
If the difference is greater than the reference value for preventing overfitting, the estimated heat of vaporization at the temperature of 0.55 times the normal boiling point by the multiple linear regression model obtained in steps 4-5 is adopted as the heat of vaporization at the temperature of 0.55 times the normal boiling point. If it is smaller than the sum prevention reference value, steps 4-8 of adopting the predicted vaporization heat value at a temperature of 0.55 times the normal boiling point by the artificial neural network model detected in steps 4-6 as the vaporization heat value at a temperature of 0.55 times the normal boiling point. Including,
The method of obtaining the QSPR model for α _c in step 4-0 is
If the performance does not meet the criteria in the above-described steps 4-1 to 4-4 and the test set 4-4 for the test set, the steps 4-2 to 4-4 are repeated, and the performance is the standard. Step 4-5-1 to determine the optimal multiple linear regression model if satisfied;
Method for obtaining vaporization heat of non-hydrocarbon-based organic compound by SVRC model including step 4-6-1 to obtain α _c value through the multiple linear regression model satisfying the performance test in step 4-5-1
17. The method of claim 16, wherein in step 4-0, the optimal molecular descriptors are independent molecular descriptors whose values are not the same for all the sample compounds. Way.
17. The method of claim 16, wherein the training set and the test set are divided by a ratio of 5: 5 to 8: 2 in step 4-1.
17. The method of claim 16, wherein in step 4-2, the multiple linear regression model is searched for by the SVRC model by searching for the multiple linear regression model by applying a genetic algorithm to the training set. Method for obtaining heat of vaporization of hydrocarbon-based organic compounds.
20. The method of claim 19, wherein the genetic algorithm generates a population consisting of a plurality of multiple linear regression models randomly drawn from a pool of molecular presenters. Making; Encoding each individual by combining the numbers of the extracted molecular presenters; Selecting two parent chromosomes from the created population by the Roulette Wheel method and generating offspring by a single point crossover method; The vaporization heat of the non-hydrocarbon-based organic compound is generated by the SVRC model, which comprises generating a new population by mutating a portion of the chromosomes of the generated offspring with a certain probability and then replacing a part of the existing population with them. How to obtain.
17. The method of claim 16, wherein the step 4-2 is to determine the heat of vaporization of the non-hydrocarbon-based organic compound by the SVRC model comprising determining the predictive performance by the regression model crystal coefficient or the mean absolute error.
17. The method of claim 16, wherein the validity in the step 4-3 is to obtain the heat of vaporization of the non-hydrocarbon-based organic compound by the SVRC model to determine the validity by the t-test value.
17. The method of claim 16, wherein in step 4-5, if the difference between the training set and the test set does not exceed 20% of the absolute mean error (AAE) obtained for the training set, the multiple linear regression model is determined. If the difference exceeds 20% of the absolute mean error (AAE) obtained for the training set, the heat of vaporization of the non-hydrocarbon-based organic compound is obtained by the SVRC model that reclassifies the training set and the test set.
17. The SVRC model according to claim 16, wherein in step 4-6, the search range by the artificial neural network has one hidden layer between the input layer and the output layer and is connected only in a feed forward. To obtain the heat of vaporization of non-hydrocarbon organic compounds.
25. The method of claim 24, wherein a function of sigmoid function is used as the activation function of the hidden layer.
17. The method of claim 16, wherein the overfit prevention reference value for the heat of vaporization at the normal boiling point in steps 4-7 is 2.3889 kcal / mol.
The method of claim 16, wherein the molecular expression extracted for the heat of vaporization at a temperature of 0.55 times the normal boiling point
P ₁ : Presence / absence of O-O at topological distance 05,
P ₂ : Presence / absence of C-C at topological distance 10
P ₃ : Relative number of N atoms,
P ₄ : Moran autocorrelation-lag 1 / Weighted by atomic masses,
P ₅ : minimum net atomic charge,
P ₆ : Min net atomic charge for a H atom,
P ₇ : Radial Distribution Function-7.0 / unweighted,
P ₈ : normal boiling point,
P ₉ : Edgevalue 15 from edge adjacency matrix weighted by edge degrees,
P ₁₀ : Min partial charge for a H atom,
P ₁₁ : area-weighted surface charge of hydrogen bond-dependent hydrogen bond base atoms (HA dependent HDCA-2),
P ₁₂ : presence of presence / absence of O-O at topological distance 03,
P ₁₃ : number of total quaternary C (sp3),
P ₁₄ is the area-weighted surface area fraction (HA dependent HDSA-2 / TMSA) of hydrogen bond-dependent hydrogen bond base atoms;
P ₁₅ : contains average electrophilic reaction index for a O atom,
The molecular expression extracted for the α _c is
P ₁ : R maximal autocorrelation of lag 2 / Weighted by atomic van der Waals volumes,
P ₂ : 1st component accessibility directional WHIM index / weighted by atomic polarizabilities,
P ₃ : Presence / absence of O-O at topological distance 07
P ₄ : R maximal autocorrelation of lag 4 / Unweighted,
P ₅ : Presence / absence of O-O at topological distance 05,
P ₆ : 3D molecular structure representation based on electron diffraction-order 8 / unweighted (3D-MoRSE-signal 08 / unweighted),
P ₇ : Eigenvalue 09 from edge adjacency matrix weighted by dipole moments,
P ₈ : sum of geometrical distances between O..S,
₉ P: _b ΔH / ΔH _{0 .55b,} ΔH is a heat of vaporization at the normal boiling point _b,
P ₁₀ : Min nucleophilic reaction index for a O atom,
P ₁₁ : H autocorrelation of lag 6 / Weighted by atomic masses,
P ₁₂ : number of secondary alcohols,
P ₁₃ : Total point-charge component of the molecular dipole,
P ₁₄ : R # N / R = N- number of functional groups (R # N / R = N-) and
P ₁₅ : Phase distance 6 A method for obtaining the heat of vaporization of a non-hydrocarbon-based organic compound by an SVRC model comprising a frequency of O-O at topological distance 06.
A computer readable storage medium having recorded thereon a program for executing on a computer a method for obtaining the heat of vaporization of a non-hydrocarbon based organic compound according to any one of claims 15 to 27.
About SVRC model described in following formula (3)

[Where ΔH is the heat of vaporization, ΔH _0.55b is the heat of vaporization at a temperature (T _0.55b ) that is 0.55 times the normal boiling point, α _c is the scaling index, T is the temperature, and T _c is the critical temperature.
Molecular expression extracted for the heat of vaporization at a temperature of 0.55 times the normal boiling point
P ₁ : D total accessibility index / weighted by atomic electrotopological states,
P ₂ : normal boiling point,
P ₃ : Radial Distribution Function-6.0 / unweighted,
P ₄ : 3D-MoRSE-signal 11 / weighted by atomic van der Waals volumes
P ₅ : Eigenvalue 14 from edge adjacency matrix weighted by resonance integrals,
P ₆ : Radial Distribution Function-11.5 / weighted by atomic masses
P ₇ : radial distribution function-15.0 / weighted by atomic masses,
P ₈ : Relative number of rings,
P ₉ : topological charge index of order 6 and
P ₁₀ : includes electron diffraction-based three-dimensional molecular structure representation-order 10 / atomic polarization weighting (3D-MoRSE-signal 10 / weighted by atomic polarizabilities),
The molecular expression extracted for the α _c is
P ₁ : highest level occupied molecular orbital-1 energy (HOMO-1 energy),
P ₂ : R--CR--R number of functions (R--CR--R),
P ₃ : Ghose-Viswanadhan-Wendoloski antidepressant-like index at 80%,
P ₄ : leverage-weighted autocorrelation of lag 6 / Weighted by atomic masses,
P ₅ : Moran autocorrelation-lag 6 / Weighted by atomic masses,
P ₆ : ΔH _b / ΔH _0.55b , ΔH _b is the heat of vaporization at the normal boiling point,
P ₇ : number of non-terminal C (sp),
P ₈ : highest eigenvalue n. 6 of Burden matrix / weighted by atomic Sanderson electronegativities,
P ₉ : R maximal autocorrelation of lag 1 / Weighted by atomic masses and
P ₁₀ : A method for obtaining the heat of vaporization of a hydrocarbon-based organic compound by an SVRC model, comprising a dipole moment weighted edge adjacency matrix eigenvalue 12 (Eigenvalue 12 from edge adjacency matrix weighted by dipole moments).
About SVRC model described in following formula (4)

[Where ΔH is a heat of vaporization, ΔH _{0 .55b} is 0.55 times the heat of vaporization at a temperature (T _{0 .55b)} of the normal boiling point, α _c is a scaling factor, T is the temperature, T _c is the critical temperature;
Molecular expression extracted for the heat of vaporization at a temperature of 0.55 times the normal boiling point
P ₁ : Presence / absence of O-O at topological distance 05,
P ₂ : Presence / absence of C-C at topological distance 10
P ₃ : Relative number of N atoms,
P ₄ : Moran autocorrelation-lag 1 / Weighted by atomic masses,
P ₅ : minimum net atomic charge,
P ₆ : Min net atomic charge for a H atom,
P ₇ : Radial Distribution Function-7.0 / unweighted,
P ₈ : normal boiling point,
P ₉ : Edgevalue 15 from edge adjacency matrix weighted by edge degrees,
P ₁₀ : Min partial charge for a H atom,
P ₁₁ : area-weighted surface charge of hydrogen bond-dependent hydrogen bond base atoms (HA dependent HDCA-2),
P ₁₂ : presence of presence / absence of O-O at topological distance 03,
P ₁₃ : number of total quaternary C (sp3),
P ₁₄ is the area-weighted surface area fraction (HA dependent HDSA-2 / TMSA) of hydrogen bond-dependent hydrogen bond base atoms;
P ₁₅ : contains the average electrophilic reaction index for a O atom,
The molecular expression extracted for the α _c is
P ₁ : R maximal autocorrelation of lag 2 / Weighted by atomic van der Waals volumes,
P ₂ : 1st component accessibility directional WHIM index / weighted by atomic polarizabilities,
P ₃ : Presence / absence of O-O at topological distance 07
P ₄ : R maximal autocorrelation of lag 4 / Unweighted,
P ₅ : Presence / absence of O-O at topological distance 05,
P ₆ : 3D molecular structure representation based on electron diffraction-order 8 / unweighted (3D-MoRSE-signal 08 / unweighted),
P ₇ : Eigenvalue 09 from edge adjacency matrix weighted by dipole moments,
P ₈ : sum of geometrical distances between O..S,
₉ P: _b ΔH / ΔH _{0 .55b,} ΔH is a heat of vaporization at the normal boiling point _b,
P ₁₀ : Min nucleophilic reaction index for a O atom,
P ₁₁ : H autocorrelation of lag 6 / Weighted by atomic masses,
P ₁₂ : number of secondary alcohols,
P ₁₃ : Total point-charge component of the molecular dipole,
P ₁₄ : R # N / R = N- number of functional groups (R # N / R = N-) and
P ₁₅ : Phase distance 6 A method for obtaining the heat of vaporization of a non-hydrocarbon-based organic compound by an SVRC model comprising a frequency of O-O at topological distance 06.

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