General Equation to Estimate the Physicochemical Properties of Aliphatic Amines
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General Equation to Estimate the Physicochemical Properties of Aliphatic Amines
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  • Chao-Tun Cao
    Chao-Tun Cao
    Key Laboratory of Theoretical Organic Chemistry and Function Molecule, Ministry of Education, School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
    More by Chao-Tun Cao
    Orcidhttps://orcid.org/0000-0002-3390-7587
  • Shurui Chen
    Shurui Chen
    Key Laboratory of Theoretical Organic Chemistry and Function Molecule, Ministry of Education, School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
    More by Shurui Chen
  • Chenzhong Cao*
    Chenzhong Cao
    Key Laboratory of Theoretical Organic Chemistry and Function Molecule, Ministry of Education, School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
    *Email: czcao@hnust.edu.cn
    More by Chenzhong Cao
    Orcidhttps://orcid.org/0000-0001-5224-7716
Open PDFSupporting Information (1)OpenURL PEKING UNIV

ACS Omega

Cite this: ACS Omega 2023, 8, 51, 49088–49097
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https://doi.org/10.1021/acsomega.3c06992
Published December 14, 2023

Copyright © 2023 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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Changes in various physicochemical properties (P(n)) of aliphatic amines (including primary, secondary, and tertiary amines) can be roughly divided into nonlinear (P(n)) and linear (PLC(n)) changes. In our previous paper, nonlinear and linear change properties of noncyclic alkanes all were correlated with four parameters, n, SCNE, ΔAOEI, and ΔAIMPI, indicating number of carbon atoms, sum of carbon number effects, average odd–even index difference, and average inner molecular polarizability index difference, respectively. To date, there has been no general equation to express changes in the properties of substituted alkanes. This work, based on the molecular structure characteristics of aliphatic amine molecules, proposes a general equation to express nonlinear changes in their physicochemical properties, named as the “NPAA equation” (eq 12), ln(P(n)) = a + b(n) + c(SCNE) + d(ΔAOEI) + e(PEI) + f(APEI) + g(GN), and proposes a general equation to express linear changes in the physicochemical properties of them, named as the “LPAA equation” (eq 13), PLC(n) = a + b(n) + c(SCNE) + d(ΔAOEI) + e(PEI) + f(APEI) + g(GN). In NPAA and LPAA equations, a, b, c, d, e, f, and g are coefficients, and PEI, APEI, and GN represent the polarizability effect index, average polarizability effect index, and N atomic influence factor, respectively. The results show that nonlinear and linear change properties of aliphatic amines all can be correlated with six parameters, n, SCNE, ΔAOEI, PEI, APEI, and GN. NPAA and LPAA equations have the advantages of uniform expression, high estimation accuracy, and usage of fewer parameters. Further, by employing the above six parameters, a quantitative correlation equation can be established between any two properties of aliphatic amines. Using the obtained equations as model equations, the property data of aliphatic amines were predicted, involving 107 normal boiling points, 10 refractive indexes, 11 liquid densities, 54 critical temperatures, 54 critical pressures, 62 liquid thermal conductivities, 59 surface tensions, 56 heat capacities, 55 critical volumes, 54 gas enthalpies of formation, and 57 gas Gibbs energies of formation, a total of 579 values, which have not been experimentally determined yet. This work not only provides a simple and convenient method for estimating or predicting the properties of aliphatic amines but can also provide new perspectives for quantitative structure–property relationships of substituted alkanes.

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1. Introduction

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Physicochemical property data of organic compounds are indispensable in scientific research, chemical production, and practical application. Due to the huge number of organic compounds, it is an impossible task to determine the physicochemical properties of all organic compounds experimentally. So establishing a quantitative structure–property relationship (QSPR) method for organic compounds is very meaningful. (1,2) In 2021, Kontogeorgis et al., (3) after investigating the industrial requirements for thermodynamic and transport properties, reported that “In terms of models, companies ideally wish for a single universal model for all/many applications, but there is understanding that this is possibly utopian. The second major wish is the need for predictive models validated on extensive experimental databases and not only on just a few available experimental data points.” In fact, they proposed a challenging topic for molecular modeling: How to establish a single universal model for the property estimation of organic compounds, which can be expressed in Figure 1.

Figure 1

Figure 1. Ideal QSPR model

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The ultimate aim in Figure 1 is a fantastic topic and also a very difficult goal to achieve owing to the complexity of molecular structures and diversity of properties of organic compounds. However, compared to the ultimate aim, the secondary aim in Figure 1 may be relatively easier to achieve. In order to investigate this challenge, Cao et al. (4) recently proposed a model (named the “NPOH equation”) to express various nonlinear (P(n), eq 1) and linear (PLC(n), eq 2) changes in the properties, of homologues, in which only two variables, carbon atom number n and the “sum of carbon number effects”, SCNE, were used, and 14 properties, including boiling point, viscosity, ionization potential, vapor pressure, etc., were involved.
ln(P(n))=a+b(n−1)+cSCNE
(1)
PLC(n)=a+b(n−1)+cSCNE
(2)
On the basis of eqs 1 and 2, a modified NPOH equation (as shown in eq 3) was proposed to express the boiling points (Tb) of 15 homologues RX (X = F, Cl, Br, I, OH, CN, NH2, CO2H, CHO, SH, C6H5, CH═CH2, C≡CH, c-C5H9, and c-C6H11). (5) It is a meaningful attempt to establish a general equation for various molecular structures, the same kind of property.
ln(Tb)=a+b(n−1)+cSCNE+d(Cg×Itg)+eμind+fCg
(3)
In eq 3, Cg is characteristic of group X and is calculated with the boiling point Tb difference between CH3CH2X and CH3CH3. Itg is the terminal effect, and its attenuation coefficient is 1/n. μind is an intramolecular charge-induced dipole, calculated with the product of parameters χX and PEI(R), as shown in eq 4.
μind=χX×PEI(R)
(4)
In eq 4, χX and PEI(R) are the electronegativity of group X and the polarizability effect index of alkyl group R, respectively. χX is calculated by using the valence electron equalized electronegativity method. (6,7) PEI(R) is calculated by using the method of Cao and Li. (8)
In 2023, Cao et al. (9) further proposed a general equation to express nonlinear changes in the physicochemical properties of noncyclic alkanes, including a total of 12 properties, named the “NPNA equation”, as shown in eq 5.
ln(P(n))=a+b(n−1)+c(SCNE)+d(ΔAOEI)+f(ΔAIMPI)
(5)
In eq 5, a, b, c, and f are coefficients and P(n) represents the nonlinear change property of the alkane with n carbon atom number. ΔAOEI and ΔAIMPI are average odd–even index difference and average inner molecular polarizability index difference, respectively.
Linear changes in the physicochemical properties PLC(n) of noncyclic alkanes can be expressed by eq 6.
PLC(n)=a+b(n−1)+c(SCNE)+d(ΔAOEI)+f(ΔAIMPI)
(6)
Equations 5 and 6 show that nonlinear and linear change properties of noncyclic alkanes can all be correlated with four parameters, n, SCNE, ΔAOEI, and ΔAIMPI, which indicates that it may be possible to establish a general model for the same kind of molecular structure-various properties.
It should be noted that eq 3 expresses the boiling point changes of homologous RX containing different functional groups, while eq 5 expresses various property changes of alkanes (including isomers) without functional groups. We want to know if a universal equation can be established for the various property changes of some substituted alkanes RX (including isomers).
In this work, we choose aliphatic amines as model compounds to investigate the general estimation model for the structure and properties of aliphatic amines. It is known that aliphatic amines have high demand and are widely used in various fields, such as chemical, daily chemical products, and medicine. Recently, Tran et al. (10) even investigated the carbon dioxide absorption of amines. On the other hand, amines are also important atmospheric environmental monitoring compounds. (11) However, it should be noted that the property data measured experimentally are severely insufficient and cannot meet the needs of scientific research and practical applications. For example, in the famous book “CRC Handbook of Chemistry and Physics”, there are only less than 90 records of the boiling point of aliphatic amines and only less than 10 records of the enthalpy of formation. (12) In the “Chemical Properties Handbook”, there are only less than 30 records of critical properties of aliphatic amines, (13) which indicates that estimating the property estimation aliphatic amines is a very meaningful work.

2. Results and Discussion

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2.1. Theoretical Analysis of Factors Affecting the Property of Aliphatic Amines

Compared to the noncyclic alkane molecules, aliphatic amine molecules have the following characteristics: (i) aliphatic amine molecules have polarity due to having a polar amino group. (ii) On the same alkyl chain, amine groups can adhere to different positions in the alkyl chain to form positional isomers. In addition, when the number of carbon atoms in molecules is greater than or equal to 3, aliphatic amines can form three kinds of isomers, i.e., primary, secondary, and tertiary amines. Take C3H8 and C3H9N for examples, their molecular structures are shown in Figure 2.

Figure 2

Figure 2. Comparison of the molecular structure of C3H8 versus C3H9N: (a) propane, (b) propylamine, (c) 2-propylamine, (d) N-methyl-ethylamine, and (e) trimethylamine.

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Since the electronegativity of the nitrogen atom (N) is greater than that of the carbon atom (C), there is an intramolecular polarizability effect in the aliphatic amine molecule, and the intramolecular polarizability effect is not equal in primary amine, secondary amine, and tertiary amine with the same carbon atom number. Therefore, the factors affecting the property of aliphatic amines should involve the number of carbon atoms (descriptors n and SCNE), the terminal effect, molecular skeleton differences, polarizability of N atom to the alkyl groups attached to the N, etc. That is, the property expression of aliphatic amines should involve the main parameters in eqs 3 and 5.

2.1.1. Calculation of Molecular Structure Descriptors of Aliphatic Amines

Here, the calculation of molecular structure descriptors mainly includes the parameters related to the number of carbon atoms (carbon atom number n and the “sum of carbon number effects,” SCNE), average odd–even index difference (ΔAOEI), polarizability effect index (PEI), average polarizability effect index (APEI), and N atomic influence factor (GN).

2.1.2. Calculation of Descriptors Related to the Number of Carbon Atoms

The general formula of aliphatic amines is CnH2n+3N. According to Cao et al.’s (4) report, here, carbon atom number n and the sum of carbon number effects SCNE (SCNE=∑i=2n(1i−1)) are employed to express the effect of carbon atoms on the property of aliphatic amines.

2.1.3. Calculation of Average Odd–Even Index Difference (ΔAOEI)

Take butylamine, 2-methyl-1-propylamine, and trimethylamine as examples; they all have the same molecular formula C4H11N, but have different molecular structures, as shown in Figure 3. The calculations of their OEI, AOEI, and ΔAOEI values are re-stated briefly as follows.

Figure 3

Figure 3. Molecular skeleton diagram of (a) butylamine, (b) 2-methyl-1-propylamine, and (c) trimethylamine (numbers indicate the numbering of atoms). Molecular graphs of (d) butylamine, (e) 2-methyl-1-propylamine, and (f) trimethylamine (numbers indicate the numbering of vertexes).

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2.1.3.1. Odd–Even Index (OEI)
According to the report of Yuan et al., (14) the OEI value of a molecular graph is calculated by eq 7.
OEI=∑i=1m∑j≠im[(−1)Dij−1S]
(7)
In eq 7, m is the number of vertices (a total of carbon and nitrogen atoms) in the molecular graph and S indicates the derivative matrix from the distance matrix D. For the elements of S, they are the squares of the reciprocal distances (Dij)−2, that is, Sij = 1/Dij2 (when i = j, let 1/Dij2 = 0).
Following are the distance matrices D(d), D(e), and D(f) of (d), (e), and (f) in Figure 3, and their derivative matrices S(d), S(e), and S(f), respectively.
D(d)=[0123410123210123210143210],⁣D(e)=[0123210121210123210321230],⁣D(f)=[0122210111210222120221220],⁣S(d)=[01/11/41/91/161/101/11/41/91/41/101/11/41/91/41/101/11/161/91/41/10],⁣S(e)=[01/11/41/91/41/101/11/41/11/41/101/11/41/91/41/101/91/41/11/41/90],⁣S(f)=[01/11/41/41/41/101/11/11/11/41/101/41/41/41/11/401/41/41/11/41/40]
Employing eq 7, the OEI values of (d), (e), and (f) in Figure 3 are calculated. Their values are as follows. OEI(d) is 6.8194 [i.e., (−1/16) × 2 + (−1/4) × 6 + (1/9) × 4 + 1 × 8], OEI(e) is 6.4444 [i.e., (1/9) × 4 + (−1/4) × 8 + 1 × 8], and OEI(f) is 5.0000 [i.e., (−1/4) × 12 + 1 × 8].
The calculated results show that the OEI values of butylamine, 2-methyl-1-propylamine, and trimethylamine are 6.8194, 6.4444, and 5.0000, respectively.
2.1.3.2. Average Odd–Even Index AOEI and Average Odd–Even Index Differences ΔAOEI
The above calculation results show that the vertex numbers of butylamine, 2-methyl-1-propylamine, and trimethylamine are equal, while their OEI values are different from each other. Their OEI value order is butylamine (6.8194) > trimethylamine (6.4444) > 2,2-dimethylpropane (5.0000). Thus, we can employ the differences of OEI values between linear and branched aliphatic amines to express the molecular skeleton differences.
Since the OEI value is affected by vertex number of aliphatic amine, here, we use eqs 8 and 9 to calculate the average value AOEI and its difference ΔAOEI between linear and branched molecular graphs, and use AOEI and ΔAOEI to express the molecular skeleton differences.
AOEI=OEI/m
(8)
ΔAOEI=AOEIbr−AOEIlin
(9)
In eqs 8 and 9, m is the number of vertices (a total of carbon and nitrogen atoms) in molecular graphs and the subscripts br and lin represent branched molecular graph and linear molecular graph, which have equal number of vertexes, respectively. Equation 9 implies that the ΔAOEI values of aliphatic amines with linear molecular graph all are zero.
Take the calculations of the AOEI values of Figure 3d–f for example. The 3 molecular graphs all have 5 vertexes (4 carbon atoms and 1 nitrogen atom, m = 5); thus, their AOEI values are calculated. That is, AOEI(d) is 1.3639 [i.e., OEI(a)/m = 6.8194/5], AOEI(e) is 1.2889 [i.e., OEI(b)/m = 6.4444/5], and AOEI(f) is 1.0000 [i.e., OEI(c)/m = 5.0000/5].
Using the values of AOEI, we can calculate the ΔAOEI. It is known that AOEI value of butylamine is AOEI(d) = 1.3639; therefore, ΔAOEI(d) is 0.0000 [i.e., AOEI(d) – AOEI(d) = 1.3639–1.3639], ΔAOEI(e) is −0.0750 [i.e., AOEI(e) – AOEI(d) = 1.2889–1.3639], and ΔAOEI(f) is −0.3639 [i.e., AOEI(f) – AOEI(d) = 1.0000–1.3639].
The results show the ΔAOEI values of butylamine, 2-methyl-1-propylamine, and trimethylamine are 0.0000, – 0.0750, and −0.3639, respectively.
In this work, the parameter ΔAOEI is used to express the molecular skeleton difference between linear and branched molecular graphs of aliphatic amines.

2.1.4. Calculation of Polarizability Effect Index (PEI)

2.1.4.1. Polarizability Effect Index PEI of Alkyl Groups Attached to the N Atom
Aliphatic amines are polar molecules due to the electronegativity of the N atom being greater than that of the C atom. An intramolecular charge-induced dipole μind will be generated between N atom and alkyl R, which can be expressed by eq 4. (5) In aliphatic amines, the χN of N atom is fixed, thus their μind values can be expressed by only using PEI(R) values of alkyl groups R.
The PEI(R) values are calculated by using the method of Cao et al. (8) That is, PEI(R) = ΣΔPEI(i), in which the ΔPEI(i) value is the PEI increment of the ith carbon atom in the alkyl R. Table 1 lists the PEI values of some normal alkyl R.
Table 1. PEI Values of Normal Alkyl H(CH2)n and the ΔPEI Values of the ith Carbon Atom (ni) in Alkyl
nPEIniΔPEInPEIniΔPEInPEIniΔPEInPEIniΔPEI
11.000011.0000061.235060.00905111.2551110.00238161.2625160.00107
21.140520.1405371.241470.00639121.2571120.00197171.2634170.00094
31.188730.0481381.246180.00475131.2587130.00166181.2642180.00084
41.212240.0235091.249890.00367141.2602140.00142191.2650190.00075
51.226050.01380101.2527100.00292151.2614150.00123201.2657200.00067
Take Figure 3a-c for example; they are butylamine, 2-methyl-1-propylamine, and trimethylamine, respectively, and their molecules have one butyl, one 2-methyl-propyl, and three methyl attached to the N atom, respectively. Thus, their PEI(R) values are calculated. The obtained values are as follows. PEI(R)(a) is 1.2122, PEI(R)(b) is 1.2368 (i.e., 1.1887 + 0.04813), and PEI(R)(d) is 3.0000 (i.e., 1.0000 × 3).
2.1.4.2. Average Polarization Effect Index (APEI)
The average polarizability effect index (APEI) represents the proportion of intramolecular charge-induced dipole μind in the whole aliphatic amine molecules, which can be calculated by eq 10.
APEI=PEI(R)/n
(10)
where n is the carbon atom number in aliphatic amine molecules.
Take Figure 3a-c for example; their carbon atom numbers n all are 5, and PEI(R)(a) = 1.2122, PEI(R)(b) = 1.2368, and PEI(R)(d) = 3.0000. Thus, APEI(a), APEI(b), and APEI(d) are 1.2122/5 = 0.2442, 1.2368/5 = 0.2474, and 3.0000/5 = 0.6000, respectively.
In this work, parameters PEI(R) and APEI are used to express intramolecular charge-induced dipole differences in aliphatic amine molecules.

2.1.5. Calculation of N Atomic Influence Factor (GN)

The N atomic influence factor (GN) is like the terminal effect (Itg). (5) It means that the influence of the N atom on the property of aliphatic amine gradually decreases with the increase of the number of carbon atoms, resulting in the property of aliphatic amine being close to that of alkane. Therefore, the influence of N atom on the property of aliphatic amine also is considered to be related to the number of carbon atom (n), as shown in eq 11.
GN=1/n
(11)
Take 3-methyl-1-hexylamine for example, its carbon atom number n = 7, thus its GN = 1/n = 1/7 = 0.1429.

2.1.6. General Equation Expressing the Properties of Aliphatic Amines

Based on eqs 1 and 3 and employing the molecular descriptors calculated in Section 2.1.1, we propose eq 12 to express nonlinear changes in the properties of aliphatic amines and use eq 13 to express linear changes in the properties of aliphatic amines. For convenience, eqs 12 and 13 are named the “NPAA equation” and “LPAA equation”, respectively (i.e., the abbreviations of “Nonlinear Properties of Aliphatic Amines equation” and “Linear Properties of Aliphatic Amines equation” respectively).
ln(P(n))=a+b(n)+c(SCNE)+d(ΔAOEI)+e(PEI)+f(APEI)+g(GN)
(12)
PLC(n)=a+b(n)+c(SCNE)+d(ΔAOEI)+e(PEI)+f(APEI)+g(GN)
(13)
In eqs 12 and 13, a, b, c, d, e, f, and g are coefficients.

2.2. Applicability of NPAA and LPAA Equations

2.2.1. Correlation with the Properties of Aliphatic Amines

In order to test the applicability of NPAA and LPAA eqs 12 and 13, quantitative correlation analysis was conducted using various physicochemical properties of aliphatic amines. First, the ΔAOEI, PEI, APEI, and GN values were calculated with the methods described in Section 2.1.1, and the SCNE values were taken from Cao et al. report. (4) Then, using eqs 12 and 13 as model equations, we performed regression analysis of the nonlinear change properties P(n) and linear change properties PLC(n) of aliphatic amines. The results are given in Table 2. These properties, P(n) and PLC(n), used in Table 2 are experimental data collected from the literature, (12,13,15,16) and the detailed data can be seen in the Supporting Information.
Table 2. Correlation Equations of Nonlinear Change and Linear Change Properties for Aliphatic Amines (CnH2n+3N) (Model Equations: ln(P(n)) = a + b(n) + c(SCNE) + d(ΔAOEI) + e(PEI) + f(APEI) + g(GN); PLC(n) = a + b(n) + c(SCNE) + d(ΔAOEI) + e(PEI) + f(APEI) + g(GN))
   ln(P(n)) = a + b(n) + c(SCNE) + d(ΔAOEI) + e(PEI) + f(APEI) + g(GN)      
no.propertyarange of nbabcdefgNcRcScFcAAEdAAPE %d
1Tb1–304.76335–0.003560.503130.29125–0.02906–0.057500.42771800.99790.016142924.255.351.17
2nD1–360.25395–0.001460.041370.031890.00050–0.042970.06009720.99060.00263567.230.00270.19
3D1–18–0.44532–0.00320.087090.114890.00235–0.173580.10237710.99020.00847533.810.00410.56
4TC1–165.63571–0.00180.311490.24972–0.03081–0.068590.21747280.99790.01125829.614.770.83
5PC1–161.83078–0.08403–0.06810.26213–0.00361–0.146560.50374280.99320.05285255.110.0953.09
6λ1–12–0.939890.05581–0.464780.54339–0.08985–0.12948–0.04426200.98180.0323457.930.00312.19
7ST1–122.16252–0.035280.523590.85165–0.02943–0.418170.74650230.99610.01853344.130.261.27
8CP1–243.880410.023430.589900.02996–0.00529–0.127630.29125260.99510.05039324.157.893.45
   PLC(n) = a + b(n) + c(SCNE) + d(ΔAOEI) + e(PEI) + f(APEI) + g(GN))      
   abcdefgNRSFAAEAAPE%
9Vc1–1484.6265759.24207–12.7078–0.20054–5.9616736.59312–25.8733270.998312.281002.708.322.16
10Hf1–24–44.731–20.33176.6501998.864746.6209168.09713–39.3626280.99943.992834.762.713.60
11Gf1–14–52.96956.830123.145964.33227.558481.0863–33.6568250.99404.37249.002.643.91
a

Tb, normal boiling point (K); nD, refractive index (293.15 K); D, liquid density (g·cm–3, 293.15 K); Tc, critical temperature (K); Pc, critical pressure (MPa); λ, liquid thermal conductivity (W·m–1·K–1, 298.15 K); ST, surface tension (mN·m–1, 298.15 K); Cp, liquid heat capacity (J·mol–1·K–1, 298.15 K); Vc, critical volume (cm3·mol–1); Hf, gas enthalpy of formation (kJ·mol–1, 298.15 K); Gf, gas Gibbs energy of formation (kJ·mol–1, 298.15 K). These properties data are listed in Table S1 in the Supporting Information.

b

Carbon atom number range.

c

R, S, N, and F are correlation coefficient, standard error, number of data points and Fisher test, respectively.

d

AAE and AAPE % are average absolute error and average absolute percentage error between the experimental value (Pexp.) and calculated value (Pcal.), respectively.

In Table 2, the 10 correlation coefficients (R) (except for λ property) are above 0.99 for the 11 properties of aliphatic amines, indicating that eqs 12 and 13 can be used to express the regularity of nonlinear change and linear change properties of aliphatic amines respectively. The correlation coefficient R is 0.9818 for λ (eq 6 of Table 2), being still good. Since the data distribution ranges of λ (liquid thermal conductivity, W·m–1·K–1, 298.15 K) are narrow, in 0.1140 to 0.1997, in addition, only 20 experimental data are collected for regression, and the data are less so that the correlation coefficient of the equation is less than 0.99. However, its calculation accuracy is good, in which the average absolute percentage error (AAPE) of λ is only 2.19% for 20 compounds used in eq 6 of Table 2. The results of Table 2 show that all AAPEs are less than 4.0%, and nonlinear change and linear change properties of aliphatic amines (including primary, secondary, and tertiary amines) all can be correlated with the six parameters n, SCNE, ΔAOEI, PEI, APEI, and GN. Figures 4 and 5 are plots of experimental versus calculated values of Tb and Hf of aliphatic amines, respectively.

Figure 4

Figure 4. Plot of experimental Tb,exp versus calculated Tb,cal values of aliphatic amines.

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Figure 5

Figure 5. Plot of experimental Hf,exp versus calculated Hf,cal values of aliphatic amines.

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In the model eqs 12 and 13, the parameters n and SCNE express the influence of carbon atoms in molecules on the property of aliphatic amines, ΔAOEI expresses the influence of molecular skeleton differences on the property, PEI and APEI express the influence of intramolecular charge-induced dipole differences on the property, and GN expresses the influence of nitrogen atom in molecules on the property.

2.2.2. Relationship between Properties of Aliphatic Amines

Equations 12 and 13 indicate that both nonlinear and linear change properties of aliphatic amines can be correlated with the six parameters n, SCNE, ΔAOEI, PEI, APEI, and GN, which means that, using the parameters n, SCNE, ΔAOEI, PEI, APEI, and GN, we can link the change regularities of different properties of aliphatic amines.
2.2.2.1. Relationship between Nonlinear Change Properties of Aliphatic Amines
Let one property of aliphatic amines be P(n) (e.g., boiling point Tb) and the other be P′(n) (e.g., critical temperature Tc), basing on eq 12, we can theoretically deduce eqs 14 and 15.
[ln(P(n))−ln(P(n)′)]=(a−a′)+(b−b′)n+(c−c′)SCNE+(d−d′)ΔAOEI+(e−e′)PEI+(f−f′)APEI+(g−g′)GN=ar+brn+crSCNE+drΔAOEI+erPEI+frAPEI+grGN
(14)
[ln(P(n))+ln(P(n)′)]=(a+a′)+(b+b′)n+(c+c′)SCNE+(d+d′)ΔAOEI+(e+e′)PEI+(f+f′)APEI+(g+g′)GN=as+bsn+csSCNE+dsΔAOEI+esPEI+fsAPEI+gsGN
(15)
In eq 14, ar = a – a′, br = b – b′, cr = c – c′, dr = d – d′, er = e – e′, fr = f – f′, and gr = g – g′, while in eq 15, as = a + a′, bs = b + b′, cs = c + c′, ds = d + d′, ds = e + e′, fs = f + f′, and gs = g + g′. For the two given physicochemical properties, P(n) and P′(n), of aliphatic amines, coefficients ar, br, cr, dr, er, fr, gr, as, bs, cs, ds, es, fs, and gs can be obtained employing the regression method.
Take critical temperature Tc for example, the relationship between Tc and boiling point Tb of aliphatic amines can be expressed by eq 16.
ln(Tc)=4.1099−0.0025n+0.1755SCNE+0.1636ΔAOEI−0.0200PEI−0.0530APEI+0.1171GN+0.3106ln(Tb)⁣R=0.9980,S=0.0111,N=28,F=728.23
(16)
Taking eq 16 as a model equation and using the experimental Tb values to calculate the critical temperature Tc of aliphatic amines, we obtained the AAE and AAPE % at 4.49 K and 0.78% for the 28 compounds used in eq 16, respectively.
2.2.2.2. Relationship between Nonlinear and Linear Change Properties of Aliphatic Amines
By combining eqs 12 and 13 and using the method described in Section 2.2.2.1, we can obtain eqs 17 and 18.
[PLC(n)−ln(P(n)′)]=(a−a′)+(b−b′)n+(c−c′)SCNE+(d−d′)ΔAOEI+(e−e′)PEI+(f−f′)APEI+(g−g′)GN=ar+brn+crSCNE+drΔAOEI+erPEI+frAPEI+grGN
(17)
[PLC(n)+ln(P(n)′)]=(a+a′)+(b+b′)n+(c+c′)SCNE+(d+d′)ΔAOEI+(e+e′)PEI+(f+f′)APEI+(g+g′)GN=as+bsn+csSCNE+dsΔAOEI+esPEI+fsAPEI+gsGN
(18)
In eqs 17 and 18, for the two given physicochemical properties, PLC(n) and P′(n), of aliphatic amines, coefficients ar, br, cr, dr, er, fr, gr, as, bs, cs, ds, es, and gs can be obtained employing the regression method.
Take critical volume Vc for example, the relationship between Vc and boiling point Tb of aliphatic amines can be expressed by eq 19.
Vc=1365.62+60.6650n+93.1202SCNE+71.5426ΔAOEI−14.534PEI+21.8576APEI+52.0910GN−258.094ln(Tb)⁣R=0.9984,S=12.35,N=27,F=839.94
(19)
Taking eq 19 as a model equation and using the experimental Tb values to calculate the critical volume Vc of aliphatic amines, we obtained the AAE and AAPE % at 8.11 cm3 mol–1 and 2.16% for the 27 compounds used in eq 19, respectively.

2.2.3. Prediction of Properties of Aliphatic Amines

It should be pointed out that due to the lack of experimental data on the properties of aliphatic amines, there is less research on quantitative structure–property relationship (QSPR) via only employing aliphatic amines. Therefore, it is difficult to compare the results of this work with those reported in other works because the data sets and number of variables employed in the various works were different. For example, Cordes and Rarey (17) compared some group contribution methods for predicting the boiling points of acyclic alkanes and observed the average absolute errors ranging from 6.5 to 26.7 K in the mentioned methods. In this work, the average absolute error is 5.53 K for the boiling points of aliphatic amines. We also noticed that, in some reports, the QSPR involves the property of amines. Here, we make a rough comparison. He et al. (18) predicted the critical properties of organic compounds based on group contribution theory. The experimental critical temperatures Tc of 169 compounds as well as experimental critical pressures Pc of 152 compounds were predicted, and AAPE values of 0.54% for Tc and 2.19% for Pc were obtained, in which 44 first-level group contribution parameters and 11 s-level group contribution parameters were employed. In this work, the AAPE values are 0.83% for Tc and 3.09% for Pc, respectively. Zhou et al. (19) applied a support vector machine (SVM) combined with genetic algorithm method to build the models for predicting gas–liquid critical temperatures Tc of organic compounds (including hydrocarbons, aldehydes, alcohols, acids, amines, benzenes, sulfur compounds) and obtained S = 0.027 (log unit, 100.027 = 1.064). In this work, S = 0.01125 (ln unit, e0.01125 = 1.011). Therefore, the model equations in Table 2 are reliable.
Employing the correlation equations in Table 2, we can predict the properties of aliphatic amines. The predicted results are listed in the Supporting Information. These properties involve 107 normal boiling points (105 primary amines,1 secondary amine, and 1 tertiary amine), 10 refractive indexes, 11 liquid densities, 54 critical temperatures, 54 critical pressures, 62 liquid thermal conductivities, 59 surface tensions, 56 heat capacities, 55 critical volumes, 54 gas enthalpies of formation, and 57 gas Gibbs energies of formation for primary, secondary, and tertiary amines (a total of 579 values), which have not been experimentally determined yet.
Take primary amines as an example, their normal boiling points are predicted as follows.
First, the molecular structures of the primary amines are constructed. Lu et al. (20) investigated QSPR of 138 alcohols. Here, we take the alcohols reported by Lu (20) as model molecules and obtain primary amine molecules by replacing group OH with group NH2 (total of 141 samples).
Second, the molecular descriptors, n, SCNE, ΔAOEI, PEI, APEI, and GN, are calculated with the methods described in Section 2.1.1.
And then the boiling points of primary amines are predicted by using eq 1 in Table 2, as shown in eq 20. The predicted results are listed in Table S2 in the Supporting Information.
ln(Tb)=4.76335−0.00356n+0.50313SCNE+0.29125ΔAOEI−0.02906PEI−0.05750APEI+0.42771GN
(20)
For the 141 primary amines, only 36 samples have experimental Tb values, the Tb values of the other 105 samples have not been experimentally determined yet. As for the 36 primary amines with experimental values, the average absolute error between the predicted and experimental values is 3.47 K, indicating that the predicted values are reasonable. To further test the reliability of the predicted Tb values, we compare the Tb values of primary amines to that of alcohols. The molecular structure of primary amines is similar to that of aliphatic alcohols, so their boiling points have a linear relationship theoretically. Figure 6 is the plot of experimental boiling points of 32 primary amines versus that of 32 aliphatic alcohols (carbon atom number range, C4–C20), indicating an excellent linear relationship.

Figure 6

Figure 6. Plot of experimental boiling points Tb of 32 primary amines (RNH2) versus that of 32 aliphatic alcohols (ROH) (carbon atom number range C4–C20).

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When we plotted the predicted boiling point (Tb, pred) values of primary amines against the experimental boiling point values (Tb, exp) of aliphatic alcohols, (20) we still obtained a good linear relationship (as shown in Figure 7). From the slopes and intercepts of Figures 6 and 7, it can be seen that the predicted boiling point values of primary amines in this article are reliable.

Figure 7

Figure 7. Plot of predicted boiling points Tb, pred of primary amines (RNH2) versus experimental boiling points Tb,exp of aliphatic alcohols (ROH) (carbon atom number range C4–C20).

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We noticed that the experimental boiling points of dioctadecanamine (C36H75N) and tridodecylamine (C36H75N) are 541.15 K (2 mmHg) and 493.15 K (0.03 mmHg) in the literature, (12) respectively, which are the boiling point values under reduced pressure. Their normal boiling points, calculated by this work, are 788.42 and 757.44 K, respectively.
Additionally, we also noticed that the liquid densities (g cm–3, 293.15 K) of heptadecanamine (C17H37N) and octadecanamine (C18H39N), reported in the literature, (12) are 0.8510 and 0.8618, respectively. However, the calculated values in this work are 0.8154 and 0.8171, respectively. To verify the rationality of the calculated values, we plotted the experimental and calculated densities of n-alkyl primary amines against the carbon atom numbers respectively, and obtained Figure 8. It is observed, from Figure 8, that the experimental densities of n-alkyl primary amines (C1–C16) steadily increase with the increase of carbon atom number, while the densities of heptadecanamine (C17) and octadecanamine (C18) suddenly increase, which is not reasonable. However, the calculated densities of n-alkyl primary amines steadily increase going from carbon atom C1 to C18, showing a regular change, which is reasonable, that is, the liquid densities of heptadecanamine and octadecanamine should be 0.8154 and 0.8171, respectively. Maybe the values of 0.8510 and 0.8618 were entered incorrectly by the editor of the literature. (12)

Figure 8

Figure 8. Plot of densities versus carbon atom number of n-alkyl primary amines (O represents the experimental value, and Δ represents the calculated value).

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3. Conclusions

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The above research results show that the various nonlinear change properties of aliphatic amines (involving primary, secondary, and tertiary amines) can be expressed by using the general NPAA eq (eq 12), while the various linear change properties of aliphatic amines (involving primary, secondary, and tertiary amines) can be expressed by using the general LPAA eq (eq 13). Both NPAA and LPAA equations all have the same parameters, n, SCNE, ΔAOEI, PEI, APEI, and GN, which can be directly calculated with molecular structures. The parameters n and SCNE express the influence of carbon atoms in molecules on the property of aliphatic amines, ΔAOEI expresses the influence of molecular skeleton differences on their property, PEI and APEI express the influence of intramolecular charge-induced dipole differences on their property, and GN expresses the influence of nitrogen atom in molecules on their property. Furthermore, employing the six parameters n, SCNE, ΔAOEI, PEI, APEI, and GN, a quantitative correlation equation can be established between any two properties of aliphatic amines.
This work established a general equation to express changes in the physicochemical properties of aliphatic amines and provided a simple and convenient prediction method for the properties of aliphatic amines. Maybe this method can provide a reference for the establishment of property estimation for other substituted alkanes.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c06992.

  • Physicochemical properties of aliphatic amines and the predicted values of aliphatic amines (Tables S1 and S2) (PDF)

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Author Information

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  • Corresponding Author
    • Chenzhong Cao - Key Laboratory of Theoretical Organic Chemistry and Function Molecule, Ministry of Education, School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China;  Orcidhttps://orcid.org/0000-0001-5224-7716;  Email: czcao@hnust.edu.cn
  • Authors
    • Chao-Tun Cao - Key Laboratory of Theoretical Organic Chemistry and Function Molecule, Ministry of Education, School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China;  Orcidhttps://orcid.org/0000-0002-3390-7587
    • Shurui Chen - Key Laboratory of Theoretical Organic Chemistry and Function Molecule, Ministry of Education, School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The project was supported by Hunan Natural Science Foundation (2020JJ5155), Research Foundation of Education Bureau of Hunan Province, China (grant no. 20B224), and National Natural Science Foundation of China (21672058).

References

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This article references 20 other publications.

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    Cao, C.-T.; Zhang, L.; Cao, C. Modified NPOH Equation Showing Terminal Effect: Boiling point of homologs monosubstituted alkanes (RX). J. Phys. Org. Chem. 2023, 36 (5), e4482  DOI: 10.1002/poc.4482
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    Changes in various physicochem. properties (P(n)) of noncyclic alkanes can be roughly classified as linear and nonlinear changes. In our previous study, the NPOH equation was proposed to express nonlinear changes in the properties of org. homologues. Until now, there has been no general equation to express nonlinear changes in the properties of noncyclic alkanes involving linear and branched alkane isomers. This work, on the basis of NPOH equation, proposes a general equation to express nonlinear changes in the physicochem. properties of noncyclic alkanes, including a total of 12 properties, b.p., crit. temp., crit. pressure, acentric factor, heat capacity, liq. viscosity, and flash point, named as the "NPNA equation", as follows: ln(P(n)) = a + b(n - 1) + c(SCNE) + d (ΔAOEI) + f(ΔAIMPI), where a, b, c, and f are coeffs., and P(n) represents the property of the alkane with n carbon atom no. n, SCNE, ΔAOEI, and ΔAIMPI are no. of carbon atoms, sum of carbon no. effects, av. odd-even index difference, and av. inner mol. polarizability index difference, resp. The obtained results show that various nonlinear changes in the properties of noncyclic alkanes can be expressed by the NPNA equation. Nonlinear and linear change properties of noncyclic alkanes can be correlated with four parameters, n, SCNE, ΔAOEI, and ΔAIMPI. The NPNA equation has the advantages of uniform expression, usage of fewer parameters, and high estn. accuracy. Furthermore, using the above four parameters, a quant. correlation equation can be established between any two properties of noncyclic alkanes. Employing the obtained equations as model equations, the property data of noncyclic alkanes, involving 142 crit. temps., 142 crit. pressures, 115 acentric factors, 116 flash points, 174 heat capacities, 142 crit. vols., and 155 gas enthalpies of formation, a total of 986 values, were predicted, which have not been exptl. measured. NPNA equation not only can provide a simple and convenient estn. or prediction method for the properties of noncyclic alkanes but also can provide new perspectives for studying quant. structure-property relationships of branched org. compds.
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    Tran, K. V. B.; Sato, M.; Yanase, K.; Yamaguchi, T.; Machida, H.; Norinaga, K. Density and Viscosity Calculation of a Quaternary System of Amine Absorbents before and after Carbon Dioxide Absorption. J. Chem. Eng. Data 2021, 66 (8), 3057– 3071,  DOI: 10.1021/acs.jced.1c00195
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    Density and Viscosity Calculation of a Quaternary System of Amine Absorbents before and after Carbon Dioxide Absorption
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    Journal of Chemical & Engineering Data (2021), 66 (8), 3057-3071CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
    Viscosity and d. of amine absorbents affect directly their flow, which is involved in the process design and simulation of carbon dioxide capture. A mixt. of 2-(Etamino)ethanol (EAE), diethylene glycol di-Et ether (DEGDEE), and water changes its phase from homogeneous to two-liq. ones on CO2 absorption. It is difficult to calc. the viscosity and d. of this phase sepn. soln., esp. those of quaternary-component phases. In this research, models to calc. the d. and viscosity of the quaternary-component system of EAE/DEGDEE/water/carbamate were suggested based on nonrandom two-liq. (NRTL)-DVOL and NRTL-DVIS models. Given the component concns., these models can replicate well the viscosity and d. of the solns. A good calcn. result with a few nos. of parameters makes the models simple and easy to use.
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    Recently, we developed a method using FT-IR spectroscopy coupled with partial least squares (PLS) regression to measure the four most abundant org. functional groups, aliph. C-H, alc. OH, carboxylic acid OH and carbonyl C=O, in atm. particulate matter. These functional groups are summed to est. org. matter (OM) while the carbon from the functional groups is summed to est. org. carbon (OC). With this method, OM and OM/OC can be estd. for each sample rather than relying on one assumed value to convert OC measurements to OM. This study continues the development of the FT-IR and PLS method for estg. OM and OM/OC by including the amine functional group. Amines are ubiquitous in the atm. and come from motor vehicle exhaust, animal husbandry, biomass burning, and vegetation among other sources. In this study, calibration stds. for amines are produced by aerosolizing individual amine compds. and collecting them on PTFE filters using an IMPROVE sampler, thereby mimicking the filter media and collection geometry of ambient stds. The moles of amine functional group on each std. and a narrow range of amine-specific wavenumbers in the FT-IR spectra (wavenumber range 1 550-1 500 cm-1) are used to develop a PLS calibration model. The PLS model is validated using three methods: prediction of a set of lab. stds. not included in the model, a peak height anal. and a PLS model with a broader wavenumber range. The model is then applied to the ambient samples collected throughout 2013 from 16 IMPROVE sites in the USA. Urban sites have higher amine concns. than most rural sites, but amine functional groups account for a lower fraction of OM at urban sites. Amine concns., contributions to OM and seasonality vary by site and sample. Amine has a small impact on the annual av. OM/OC for urban sites, but for some rural sites including amine in the OM/OC calcns. increased OM/OC by 0.1 or more.
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    Zhou, L.; Wang, B.; Jiang, J.; Pan, Y.; Wang, Q. Quantitative Structure-Property Relationship (QSPR) Study for Predicting Gas-Liquid Critical Temperatures of Organic Compounds. Thermochim. Acta 2017, 655, 112– 116,  DOI: 10.1016/j.tca.2017.06.021
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  1. Yunzhi Ling, Chao-Tun Cao, Chenzhong Cao. Using a Hierarchical Molecular Structure-Based Method to Estimate the Physicochemical Properties of Halogen/Cyano-Substituted Alkanes. ACS Omega 2026, 11 (4) , 5339-5351. https://doi.org/10.1021/acsomega.5c08380
  2. Qing Deng, Chao-Tun Cao, Chenzhong Cao. General Equation for Expressing the Physicochemical Properties of Aliphatic Alcohols. ACS Omega 2025, 10 (1) , 1571-1580. https://doi.org/10.1021/acsomega.4c09457
  3. Luca D'Angelo, Florian Ungeheuer, Jialiang Ma, Luca Ferrero, Cristina Colombi, Eleonora Cuccia, Umberto Dal Santo, Beatrice Biffi, Alexander L. Vogel. Contrasting organic aerosol molecular composition between the urban and agricultural environment of the Po Valley. Atmospheric Chemistry and Physics 2026, 26 (10) , 6799-6823. https://doi.org/10.5194/acp-26-6799-2026
  4. Jincan Long, Chao‐Tun Cao, Chenzhong Cao. Hierarchical Molecular Structure–Based Method to Estimate the Normal Boiling Point of Aliphatic Oxygen‐Containing Organic Compounds. Journal of Physical Organic Chemistry 2025, 38 (7) https://doi.org/10.1002/poc.70020
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  • Abstract

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    Figure 1

    Figure 1. Ideal QSPR model

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    Figure 2

    Figure 2. Comparison of the molecular structure of C3H8 versus C3H9N: (a) propane, (b) propylamine, (c) 2-propylamine, (d) N-methyl-ethylamine, and (e) trimethylamine.

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    Figure 3

    Figure 3. Molecular skeleton diagram of (a) butylamine, (b) 2-methyl-1-propylamine, and (c) trimethylamine (numbers indicate the numbering of atoms). Molecular graphs of (d) butylamine, (e) 2-methyl-1-propylamine, and (f) trimethylamine (numbers indicate the numbering of vertexes).

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    Figure 4

    Figure 4. Plot of experimental Tb,exp versus calculated Tb,cal values of aliphatic amines.

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    Figure 5

    Figure 5. Plot of experimental Hf,exp versus calculated Hf,cal values of aliphatic amines.

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    Figure 6

    Figure 6. Plot of experimental boiling points Tb of 32 primary amines (RNH2) versus that of 32 aliphatic alcohols (ROH) (carbon atom number range C4–C20).

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    Figure 7

    Figure 7. Plot of predicted boiling points Tb, pred of primary amines (RNH2) versus experimental boiling points Tb,exp of aliphatic alcohols (ROH) (carbon atom number range C4–C20).

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    Figure 8

    Figure 8. Plot of densities versus carbon atom number of n-alkyl primary amines (O represents the experimental value, and Δ represents the calculated value).

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  • References

    This article references 20 other publications.

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      The present review summarizes recent QSPR research methods and applications. The main focus is placed on QSPR based upon structural descriptors derived solely from chem. structure for the correlation and prediction of various phys., chem., and physicochem. properties of compds.
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      Kontogeorgis, G. M.; Dohrn, R.; Economou, I. G.; Hemptinne, J.-C.; Kate, A.; Kuitunen, S.; Mooijer, M.; Žilnik, L. F.; Vesovic, V. Industrial Requirements for Thermodynamic and Transport Properties: 2020. Ind. Eng. Chem. Res. 2021, 60, 4987– 5013,  DOI: 10.1021/acs.iecr.0c05356
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      Kontogeorgis, Georgios M.; Dohrn, Ralf; Economou, Ioannis G.; de Hemptinne, Jean-Charles; ten Kate, Antoon; Kuitunen, Susanna; Mooijer, Miranda; Zilnik, Ljudmila Fele; Vesovic, Velisa
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      A review. This paper reports the results of an investigation of industrial requirements for thermodn. and transport properties carried out during the years 2019-2020. It is a follow-up of a similar investigation performed and published 10 years ago by the Working Party (WP) of Thermodn. and Transport Properties of European Federation of Chem. Engineering (EFCE). The main goal was to investigate the advances in this area over the past 10 years, to identify the limitations that still exist, and to propose future R&D directions that will address the industrial needs. An updated questionnaire, with two new categories, digitalization and comparison to previous survey/changes over the past 10 years, was sent to a broad no. of experts in companies with a diverse activity spectrum, in oil and gas, chems., pharmaceuticals/biotechnol., food, chem./mech. engineering, consultancy, and power generation, among others, and in software suppliers and contract research labs. Very comprehensive answers were received by 37 companies, mostly from Europe (operating globally), but answers were also provided by companies in the USA and Japan. The response rate was ∼ 60%, compared to 47% in the year 2010. The paper is written in such a way that both the majority and minority points of view are presented, and although the discussion is focused on needs and challenges, the benefits of thermodn. and success stories are also reported. The results of the survey are thematically structured and cover changes, challenges, and further needs for a no. of areas of interest such as data, models, systems, properties, and computational aspects (mol. simulation, algorithms and stds., and digitalization). Education and collaboration are discussed and recommendations on the future research activities are also outlined. In addn., a few initiatives, books, and reviews published in the past decade are briefly discussed. It is a long paper and, to provide the reader with a more complete understanding of the survey, many (anonymous) quotations (indicated with "..." and italics) from the industrial colleagues who have participated in the survey are provided. To help disseminate the specific information of interest only to particular industrial sectors, the paper has been written in such a way that the individual sections can also be read independently of each other.
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      Cao, C.-T.; Cao, C. General Equation to Express Changes in the Physicochemical Properties of Organic Homologues. ACS Omega 2022, 7 (30), 26670– 26679,  DOI: 10.1021/acsomega.2c02828
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      General Equation to Express Changes in the Physicochemical Properties of Organic Homologues
      Cao, Chao-Tun; Cao, Chenzhong
      ACS Omega (2022), 7 (30), 26670-26679CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)
      Changes in various physicochem. properties (P(n)) of org. compds. with the no. of carbon atoms (n) can be roughly divided into linear and nonlinear changes. To date, there has been no general equation to express nonlinear changes in the properties of org. homologues. This study proposes a general equation expressing nonlinear changes in the physicochem. properties of org. homologues, including b.p., viscosity, ionization potential, and vapor pressure, named the "NPOH equation", as follows: P(n) = P(1)αn - 1e.sum.i=2n(β/(i - 1)) where α and β are adjustable parameters, and P(1) represents the property of the starting compd. (pseudo-value at n = 1) of each homolog. The results show that various nonlinear changes in the properties of homologues can be expressed by the NPOH equation. Linear and nonlinear changes in the properties of homologues can all be correlated with n and the "sum of carbon no. effects", .sum.i=2n(1/i - 1). Using these two parameters, a quant. correlation equation can be established between any two properties of each homolog, providing convenient mutual estn. of the properties of a homolog series. The NPOH equation can also be used in property correlation for structures with functionality located elsewhere along a linear alkyl chain as well as for branched org. compds. This work can provide new perspectives for studying quant. structure-property relationships.
    5. 5
      Cao, C.-T.; Zhang, L.; Cao, C. Modified NPOH Equation Showing Terminal Effect: Boiling point of homologs monosubstituted alkanes (RX). J. Phys. Org. Chem. 2023, 36 (5), e4482  DOI: 10.1002/poc.4482
      5
      Modified NPOH Equation Showing Terminal Effect: Boiling point of homologs monosubstituted alkanes (RX)
      Cao, Chao-Tun; Zhang, Lanyu; Cao, Chenzhong
      Journal of Physical Organic Chemistry (2023), 36 (5), e4482CODEN: JPOCEE; ISSN:0894-3230. (John Wiley & Sons Ltd.)
      Effect of terminal group on the changes in physicochem. properties (P(n)) of homologs monosubstituted alkanes (RX) is still unclear topic. In this work, take the b.ps. (Tb) of 15 homologs RX as examples; the effects of terminal X on the Tb were investigated, in which the X involves F, Cl, Br, I, OH, CN, NH2, CO2H, CHO, SH, C6H5, CH=CH2, CCH, c-C5H9, and c-C6H11. A general equation expressing the Tb of the homologs RX was proposed, named the NPOH Equation Showing Terminal Effect, as follows: ln (Tb(n)) = a + b(n-1) + cSCNE + dItg, where Itg is the terminal effect and its attenuation coeff. is 1/n. The results show that this equation is more accurate to express the Tb change of homologs RX than the NPOH equation in our previous paper. The parameter Itg has important influence on the Tb of RX, while it has less influence on the Tb of homologs α,ω-disubstituted alkanes XRX and can be ignored. The Tb changes of 15 homologs RX and homolog alkane can be expressed using a general equation (Equation 11 in text). The effect of intramol. charge-induced dipole μind on the b.p. of homologs RX cannot be ignored.
    6. 6
      Wu, Y.-x.; Cao, C.; Yuan, H. Equalized Electronegativity Based on the Valence Electrons and Its Application. Chin. J. Chem. Phys. 2011, 24 (1), 31– 39,  DOI: 10.1088/1674-0068/24/01/31-39
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      Equalized electronegativity based on the valence electrons and its application
      Wu, Ya-xin; Cao, Chen-zhong; Yuan, Hua
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      We take the contribution of all valence electrons into consideration and propose a new valence electrons equilibration method to calc. the equalized electronegativity including mol. electronegativity, group electronegativity, and at. charge. The ionization potential of alkanes and mono-substituted alkanes, the chem. shift of 1H NMR, and the gas phase proton affinity of aliph. amines, alcs., and ethers were estd. All the expressions have good correlations. Moreover, the Sanderson method and Bratsch method were modified on the basis of the valence electrons equilibration theory. The modified Sanderson method and modified Bratsch method are more effective than their original methods to est. these properties.
    7. 7
      Cao, C.-T.; Chen, M.; Fang, Z.; Au, C.; Cao, C. Relationship Investigation between C(sp2)-X and C(sp3)-X Bond Energies Based on Substituted Benzene and Methane. ACS Omega 2020, 5 (30), 19304– 19311,  DOI: 10.1021/acsomega.0c02964
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      Relationship Investigation between C(sp2)-X and C(sp3)-X Bond Energies Based on Substituted Benzene and Methane
      Cao, Chao-Tun; Chen, Miaomiao; Fang, Zhengjun; Au, Chaktong; Cao, Chenzhong
      ACS Omega (2020), 5 (30), 19304-19311CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)
      The C-X bonds of org. compds. between group X and a satd. or unsatd. carbon atom differ in bond energy. To identify the causes of variation is of great significance in terms of bond nature understanding and bond energy estn. In this paper, the electronegativity χ[X] of group X was calcd. by the "valence electron equalized electronegativity" method. Then, χ[X] and the electronic effect const. of the substituent were taken as variables to establish equations for quant. correlation between C(sp3)-X and C(sp2)-X for the calcn. of C-X bond energies. The aim is make comparison between substituted methane, Me-X, and substituted benzene, Ph-X, as well as that between Me-X and substituted ethylene, C2H3-X. We conducted calcn. over 40 compds. that contain different X groups, and the results reveal that the C(sp3)-X and C(sp2)-X bond energies are under the influence of a no. of factors. In addn. to the covalent properties of C and X atoms and χ[X], the bond energies of C(sp2)-X (i.e., D[C(sp2)-X]) are under the influence of the field/inductive effect (σF[X]) and conjugated effect (σR[X]) of group X, with the former causing a decrease while the latter an increase of D[C(sp2)-X]. Using the acquired quant. correlation equations and on the basis of a relatively rich set of measured D[Me-X] data, we estd. D[Ph-X] of Ph-X and D[C2H3-X] of C2H3-X, and the estn. accuracy is within exptl. uncertainty. Employing the above method, the D[C(sp2)-X] of 33 substituted benzenes, 53 substituted ethenes, and 82 α-substituted naphthalenes was estd. with satisfactory outcomes.
    8. 8
      Cao, C.; Li, Z. Molecular Polarizability I: Relationship to Water Solubility of Alkanes and Alcohols. J. Chem. Inf. Comput. Sci. 1998, 38, 1– 7,  DOI: 10.1021/ci9601729
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      Molecular Polarizability. 1. Relationship to Water Solubility of Alkanes and Alcohols
      Cao, Chenzhong; Li, Zhiliang
      Journal of Chemical Information and Computer Sciences (1998), 38 (1), 1-7CODEN: JCISD8; ISSN:0095-2338. (American Chemical Society)
      The polarizability effect index (PEI) of groups and the mol. polarizability effect index (MPEI) are proposed on the basis of the principle that mols. are polarized by elec. fields. Furthermore, by taking the sum of bond lengths (SBL) in a mol. and the difference in mol. polarizability effect index values (ΔMPEI) between branching chain and normal chain isomers as parameters, we studied the correlations of cavity surface area (CSA), water soly. (-log S), and partition coeffs. in n-octanol/water (log P) with the SBL and ΔMPEI parameters for the alkanes and alcs. and got excellent linear correlations.
    9. 9
      Cao, C.-T.; Cao, C. New Method of NPOH Equation-Based to Estimate the Physicochemical Properties of Noncyclic Alkanes. ACS Omega 2023, 8 (7), 6492– 6506,  DOI: 10.1021/acsomega.2c06856
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      New Method of NPOH Equation-Based to Estimate the Physicochemical Properties of Noncyclic Alkanes
      Cao, Chao-Tun; Cao, Chenzhong
      ACS Omega (2023), 8 (7), 6492-6506CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)
      Changes in various physicochem. properties (P(n)) of noncyclic alkanes can be roughly classified as linear and nonlinear changes. In our previous study, the NPOH equation was proposed to express nonlinear changes in the properties of org. homologues. Until now, there has been no general equation to express nonlinear changes in the properties of noncyclic alkanes involving linear and branched alkane isomers. This work, on the basis of NPOH equation, proposes a general equation to express nonlinear changes in the physicochem. properties of noncyclic alkanes, including a total of 12 properties, b.p., crit. temp., crit. pressure, acentric factor, heat capacity, liq. viscosity, and flash point, named as the "NPNA equation", as follows: ln(P(n)) = a + b(n - 1) + c(SCNE) + d (ΔAOEI) + f(ΔAIMPI), where a, b, c, and f are coeffs., and P(n) represents the property of the alkane with n carbon atom no. n, SCNE, ΔAOEI, and ΔAIMPI are no. of carbon atoms, sum of carbon no. effects, av. odd-even index difference, and av. inner mol. polarizability index difference, resp. The obtained results show that various nonlinear changes in the properties of noncyclic alkanes can be expressed by the NPNA equation. Nonlinear and linear change properties of noncyclic alkanes can be correlated with four parameters, n, SCNE, ΔAOEI, and ΔAIMPI. The NPNA equation has the advantages of uniform expression, usage of fewer parameters, and high estn. accuracy. Furthermore, using the above four parameters, a quant. correlation equation can be established between any two properties of noncyclic alkanes. Employing the obtained equations as model equations, the property data of noncyclic alkanes, involving 142 crit. temps., 142 crit. pressures, 115 acentric factors, 116 flash points, 174 heat capacities, 142 crit. vols., and 155 gas enthalpies of formation, a total of 986 values, were predicted, which have not been exptl. measured. NPNA equation not only can provide a simple and convenient estn. or prediction method for the properties of noncyclic alkanes but also can provide new perspectives for studying quant. structure-property relationships of branched org. compds.
    10. 10
      Tran, K. V. B.; Sato, M.; Yanase, K.; Yamaguchi, T.; Machida, H.; Norinaga, K. Density and Viscosity Calculation of a Quaternary System of Amine Absorbents before and after Carbon Dioxide Absorption. J. Chem. Eng. Data 2021, 66 (8), 3057– 3071,  DOI: 10.1021/acs.jced.1c00195
      10
      Density and Viscosity Calculation of a Quaternary System of Amine Absorbents before and after Carbon Dioxide Absorption
      Tran, Khuyen Viet Bao; Sato, Miho; Yanase, Keiichi; Yamaguchi, Tsuyoshi; Machida, Hiroshi; Norinaga, Koyo
      Journal of Chemical & Engineering Data (2021), 66 (8), 3057-3071CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
      Viscosity and d. of amine absorbents affect directly their flow, which is involved in the process design and simulation of carbon dioxide capture. A mixt. of 2-(Etamino)ethanol (EAE), diethylene glycol di-Et ether (DEGDEE), and water changes its phase from homogeneous to two-liq. ones on CO2 absorption. It is difficult to calc. the viscosity and d. of this phase sepn. soln., esp. those of quaternary-component phases. In this research, models to calc. the d. and viscosity of the quaternary-component system of EAE/DEGDEE/water/carbamate were suggested based on nonrandom two-liq. (NRTL)-DVOL and NRTL-DVIS models. Given the component concns., these models can replicate well the viscosity and d. of the solns. A good calcn. result with a few nos. of parameters makes the models simple and easy to use.
    11. 11
      Kamruzzaman, M.; Takahama, S.; Dillner, A. M. Quantification of Amine Functional Groups and Their Influence on OM/OC in the IMPROVE Network. Atmos. Environ. 2018, 172, 124– 132,  DOI: 10.1016/j.atmosenv.2017.10.053
      11
      Quantification of amine functional groups and their influence on OM/OC in the IMPROVE network
      Kamruzzaman, Mohammed; Takahama, Satoshi; Dillner, Ann M.
      Atmospheric Environment (2018), 172 (), 124-132CODEN: AENVEQ; ISSN:1352-2310. (Elsevier Ltd.)
      Recently, we developed a method using FT-IR spectroscopy coupled with partial least squares (PLS) regression to measure the four most abundant org. functional groups, aliph. C-H, alc. OH, carboxylic acid OH and carbonyl C=O, in atm. particulate matter. These functional groups are summed to est. org. matter (OM) while the carbon from the functional groups is summed to est. org. carbon (OC). With this method, OM and OM/OC can be estd. for each sample rather than relying on one assumed value to convert OC measurements to OM. This study continues the development of the FT-IR and PLS method for estg. OM and OM/OC by including the amine functional group. Amines are ubiquitous in the atm. and come from motor vehicle exhaust, animal husbandry, biomass burning, and vegetation among other sources. In this study, calibration stds. for amines are produced by aerosolizing individual amine compds. and collecting them on PTFE filters using an IMPROVE sampler, thereby mimicking the filter media and collection geometry of ambient stds. The moles of amine functional group on each std. and a narrow range of amine-specific wavenumbers in the FT-IR spectra (wavenumber range 1 550-1 500 cm-1) are used to develop a PLS calibration model. The PLS model is validated using three methods: prediction of a set of lab. stds. not included in the model, a peak height anal. and a PLS model with a broader wavenumber range. The model is then applied to the ambient samples collected throughout 2013 from 16 IMPROVE sites in the USA. Urban sites have higher amine concns. than most rural sites, but amine functional groups account for a lower fraction of OM at urban sites. Amine concns., contributions to OM and seasonality vary by site and sample. Amine has a small impact on the annual av. OM/OC for urban sites, but for some rural sites including amine in the OM/OC calcns. increased OM/OC by 0.1 or more.
    12. 12
      CRC Handbook of Chemistry and Physics, 91st ed.; Haynes, W. M., Ed.; CRC Press, 2011; pp 6– 58, 6–73, 10–199, 10–216, 5–68.
      There is no corresponding record for this reference.
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      Yaws, C. L. Chemical Properties Handbook, McGraw-Hill Book Co., Beijing 1999; pp 185– 531.
      There is no corresponding record for this reference.
    14. 14
      Yuan, H.; Cao, C. Topological Indices Based on Vertex, Edge, Ring, and Distance: Application to Various Physicochemical Properties of Diverse Hydrocarbons. J. Chem. Inf. Comput. Sci. 2003, 43, 501– 512,  DOI: 10.1021/ci0202988
      14
      Topological Indices Based on Vertex, Edge, Ring, and Distance: Application to Various Physicochemical Properties of Diverse Hydrocarbons
      Yuan, Hua; Cao, Chenzhong
      Journal of Chemical Information and Computer Sciences (2003), 43 (2), 501-512CODEN: JCISD8; ISSN:0095-2338. (American Chemical Society)
      This paper developed the Edge degree-Distance Index (EDI) and Sum of edges (Se) based on the edge and distance of mol. graph. This set of topol. indexes, EDI, Se combined with VDI, OEI, and RDI proposed in our previous paper can characterize the mol. structures of diverse hydrocarbons well. The regression analyses against nine physicochem. properties, such as b.ps. (Bp), crit. properties (Tc, Pc, Vc), heat capacities (Cp), and so on, of 1038 diverse hydrocarbons were investigated, and good correlations were obtained.
    15. 15
      Dean, J. A. Lange’s Handbook of Chemistry, 15st ed.; McGraw-Hill Book Co., Beijing 1999; pp 5.90– 5.154, 6.1–6.143.
      There is no corresponding record for this reference.
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      Lu, H. Handbook of Basic Data for Petrochemical Industry; Chemical Industry Press: Beijing, 1982; pp 135– 189.
      There is no corresponding record for this reference.
    17. 17
      Cordes, W.; Rarey, J. A New Method for the Estimation of the Normal Boiling Point of Nonelectrolyte Organic Compounds. Fluid Phase Equilib. 2002, 201, 409– 433,  DOI: 10.1016/S0378-3812(02)00050-X
      17
      A new method for the estimation of the normal boiling point of non-electrolyte organic compounds
      Cordes, Wilfried; Rarey, Jurgen
      Fluid Phase Equilibria (2002), 201 (2), 409-433CODEN: FPEQDT; ISSN:0378-3812. (Elsevier Science B.V.)
      A group contribution method for the estn. of the normal b.p. of non-electrolyte org. compds. was developed using exptl. data for approx. 2500 components stored in the Dortmund Data Bank (DDB). Predictions are based exclusively on the mol. structure of the compd. The results of the new method are compared to currently-used methods and are shown to be far more accurate. Structural groups were defined in a standardized form and the fragmentation of the mol. structures was performed by an automatic procedure to eliminate any arbitrary assumptions.
    18. 18
      He, M.; Wang, C.; Chen, J.; Liu, X. Prediction of the Critical Properties of Mixtures Based on Group Contribution Theory. J. Mol. Liq. 2018, 271, 313– 318,  DOI: 10.1016/j.molliq.2018.08.048
      18
      Prediction of the critical properties of mixtures based on group contribution theory
      He, Maogang; Wang, Chengjie; Chen, Junshuai; Liu, Xiangyang
      Journal of Molecular Liquids (2018), 271 (), 313-318CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
      A new simple model was proposed to predict the crit. temp. (Tc) and crit. pressure (pc) of mixts. based on group contribution (GC) theory. In this model, the crit. properties of mixts. can be predicted without crit. parameters of each component. The exptl. crit. temps. of 169 compds. and 379 binary mixts. as well as exptl. crit. pressures of 152 compds. and 188 binary mixts. were used to det. the group contribution parameters and model parameters. The av. abs. relative deviations (AARDs) of correlation for compds. are 0.54% for Tc and 2.19% for pc. AARDs of correlation for binary mixts. are 1.22% and 4.54% for Tc and pc, resp. The predictive ability of presented model was evaluated with Tc of 42 binary mixts. and 12 ternary mixts. as well as pc of 8 binary mixts. and 12 ternary mixts.; predicted results agree well with exptl. crit. properties.
    19. 19
      Zhou, L.; Wang, B.; Jiang, J.; Pan, Y.; Wang, Q. Quantitative Structure-Property Relationship (QSPR) Study for Predicting Gas-Liquid Critical Temperatures of Organic Compounds. Thermochim. Acta 2017, 655, 112– 116,  DOI: 10.1016/j.tca.2017.06.021
      19
      Quantitative structure-property relationship (QSPR) study for predicting gas-liquid critical temperatures of organic compounds
      Zhou, Lulu; Wang, Beibei; Jiang, Juncheng; Pan, Yong; Wang, Qingsheng
      Thermochimica Acta (2017), 655 (), 112-116CODEN: THACAS; ISSN:0040-6031. (Elsevier B.V.)
      Gas-liq. crit. temp. is an important parameter of crit. state. Org. compds. are under rapid phase changes leading to explosions when conditions are changed at their crit. states. Therefore, for safety purposes it is important to study the gas-liq. crit. properties for different org. compds., esp. their crit. temps. In this work, crit. temps. of 692 org. compds. were collected and applied to build quant. structure-property relationship (QSPR) models. Dragon software was used to obtain their mol. structure information. Methods of multiple linear regression (MLR) and support vector machine (SVM) were applied to build the models, combined with genetic algorithm method. Between these two models, the MLR model has better internal robustness and the SVM model has better goodness-of-fit predictive ability. The results show the developed models have great performance in predicting the gas-liq. crit. temps. With these models, crit. temps. of org. compds. can be predicted solely based on their mol. structures.
    20. 20
      Lu, C.; Guo, W.; Wang, Y.; Yin, C. Novel Distance-Based Atom-Type Topological Indices DAI for QSPR/QSAR Studies of Alcohols. J. Mol. Model. 2006, 12, 749– 756,  DOI: 10.1007/s00894-005-0089-4
      20
      Novel distance-based atom-type topological indices DAI for QSPR/QSAR studies of alcohols
      Lu, Chunhui; Guo, Weimin; Wang, Yang; Yin, Chunsheng
      Journal of Molecular Modeling (2006), 12 (6), 749-756CODEN: JMMOFK; ISSN:0948-5023. (Springer GmbH)
      The authors propose a distance-based atom-type topol. index (DAI) for quant. structure-property/activity relation (QSPR/QSAR) studies. The newly constructed index, which codes the structural environment of each atom type in a mol., can be calcd. simply. These atom-type topol. indexes, along with recently proposed Lu index, were used to construct QSPR/QSAR models for several representative phys. properties and biol. activities of several data sets of alcs. with a range of nonhydrogen atoms by using multiple linear regression (MLR) anal. The efficiency of these indexes is verified by high quality QSPR models. The combined use of Lu and DAI indexes promises to be a useful method for QSPR/QSAR anal. of complex compds.

  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c06992.

    • Physicochemical properties of aliphatic amines and the predicted values of aliphatic amines (Tables S1 and S2) (PDF)


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