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\begin{document}

\title{Evaluating the properties of ionic liquid at variable temperatures and
pressures by QSPR}



\author[1]{Shuying Zhang}%
\author[1]{Qingzhu  Jia}%
\author[2]{Fangyou Yan}%
\author[3]{Xia Shuqian}%
\author[1]{Qiang Wang}%
\affil[1]{Tianjin University of Science and Technology}%
\affil[2]{Affiliation not available}%
\affil[3]{Tianjin University}%


\vspace{-1em}



  
  \date{May 23, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
ILs thermodynamic properties at variable temperature and pressure, such
as density, viscosity and thermal conductivity, are necessarily basal
parameters of chemical engineering process. In this paper, some norm
descriptors-based QSPR models are established to predict the properties
of ILs at variable temperature and pressure. The f-T-P models are
developed with 9020 data points of 314 ILs for density, 7342 data points
of 351 ILs for viscosity and 608 data points of 87 ILs for thermal
conductivity. These models have satisfactory statistical results for the
calculation of ILs properties. The validation analysis shows that these
QSPR models have good stability and predictability. And the norm
descriptors are universal for predicting the properties of ILs.
Moreover, these QSPR models are applied to predict parameters of f-T-P
models for 16329 ILs generated by combing the cations and anions in the
dataset, which might be valuable and further used handily by other
chemists.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Ionic liquids (ILs) are a kind of common low melting point organic
salts. Recently, ILs have attracted much attention for their unique
physical and chemical properties, such as good thermal stability,
conductivity, wide electrochemical window, incombustibility and
recyclability.\textsuperscript{1,2} Because of these characteristics,
ILs have been successfully applied in the fields of
electrochemistry,\textsuperscript{3-5} separation and extraction
procedures,\textsuperscript{6-8} biological field\textsuperscript{9,10}
and chemical engineering.\textsuperscript{2,11}

The thermodynamic properties of ILs basically determine and affect their
applications. Density (\selectlanguage{greek}\emph{ρ} \selectlanguage{english}) is indispensable in the process design
of material science and chemical engineering. In particular, the density
of ILs can be used to calculate other properties (viscosity, surface
tension, thermal conductivity, etc.). The viscosity (\selectlanguage{greek}\emph{η} \selectlanguage{english}) of ILs
can be used to determine the feasible operation conditions of the actual
chemical process, such as fluids pumping and stirring, liquid-liquid
extraction, distillation process.\textsuperscript{12} Thermal
conductivity (\selectlanguage{greek}\emph{λ} \selectlanguage{english}) is very important for obtaining the heat
transfer coefficient of fluid, which is essential for the design of heat
transfer fluid and equipment.\textsuperscript{13,14} Until now, large
amount of ILs have been synthesized by a variety of cations, anions and
substituents.\textsuperscript{15} However, the existing experimental
properties data of ILs cannot meet the requirements for guiding chemical
industrial applications. Moreover, density, viscosity and thermal
conductivity are significantly affected by the temperature and the
pressure, and it is even impossible for obtaining all these experiment
data under different temperatures and pressures through the
time-consuming and expensive experimental methods. Therefore, it is
urgent to provide a model to calculate these characteristics of ILs
under variable temperature and pressure as an alternative to the
experimental measurement.

To date, different methods have been reported in literatures to
calculate the properties of ILs.\textsuperscript{16-20} These methods
are mainly based on: (i) the group contribution model (GCM), and (ii)
the quantitative structure-property relationship (QSPR). GCM is a very
important method to predict various physical and thermodynamic
properties with satisfy prediction results\textsuperscript{21}. For the
thermal conductivity of ionic liquids, Lazz\selectlanguage{ngerman}ús
\textsuperscript{22}established a GCM with 400 data point of 41 ILs at a
wide range of temperature (253-395 K) and pressure (0.1-20 MPa)
(\emph{R} \textsuperscript{2}=0.9843, \emph{AARD} =2.12 \%). Recently,
Chen et al.\textsuperscript{16} developed a GCM model to calculate
properties at variable temperatures of ILs including the density (7360
data points,143 ILs) and the viscosity (1090 data points, 76 ILs) with
good prediction results. It is undeniable that these models provide
accurate predictions for the physical properties of ILs. However, GCM
depends on the group contribution value, and due to the lack of some
group contribution values, the properties of some ILs cannot be
calculated for some ILs.

In the last decade, QSPR has been profusely employed to study the
properties of ILs, such as heat
capacity,\textsuperscript{23-25}viscosity,\textsuperscript{26-29}
thermal conductivity,\textsuperscript{30,31} surface
tension,\textsuperscript{32,33} and
toxicity.\textsuperscript{34-37}Lazzús\textsuperscript{38} estimated the
density in a wide of temperature (253-473 K) and pressure (0.1-250 MPa)
range with satisfactory results (\emph{AARD} =2.00 \%). Yan et
al.\textsuperscript{39} established a QSPR model to predict the density
of ILs under variable temperature and pressure by using topological
index with \emph{AARD} of 0.42 \%. Recently,
AguirrePaduszyn\selectlanguage{english}ski\textsuperscript{40} established a reference term
model and a modified QSPR model to predict the density (temperature
(217-473 K) and pressure (0.1-250 MPa)) of ILs, and good results could
be obtained with \emph{AARD} of 0.9 \%.
Paduszy\selectlanguage{polish}ń\selectlanguage{english}ski\textsuperscript{41}has proposed a new QSPR method for
calculating ILs density and viscosity with temperature (217-473 K) and
pressure (0.1-250 MPa) by MLR and LSSVM with good results.

Beckner et al\emph{.} \textsuperscript{42} used neural networks to get a
high-precision model to predict the ILs viscosity at variable
temperatures and pressure with satisfactory results (\emph{AARD=} 7.10
\%). Zhao et al.\textsuperscript{43} established a new QSPR model using
multiple linear regression (MLR) and support vector machine (SVM)
algorithm to predict the viscosity of ILs at variable temperature
(253.15-395.32 K) and pressure (0.1-300 MPa) with the overall\emph{AARD}
of 6.58 \%. Yan et al.\textsuperscript{29} predicted the viscosity of
ILs under a wide range of temperature (253.15-573 K) and pressure
(0.06-300 MPa), and obtained satisfactory prediction results with
\emph{AARD} of 4.62 \%.

In case of thermal conductivity of ILs, Chen et
al.\textsuperscript{44}and Lazzus et al.\textsuperscript{45} proposed a
QSPR model to predict the thermal conductivity of ILs under the
condition of variable temperature (273.15-390 K) with \emph{AARD} of 2.0
\%-2.3 \%. He et al.\textsuperscript{46} presents a linear QSPR model
based on the norm-indexes for predicting ILs thermal conductivity in a
wide temperature (273.15-355.07 K) and pressure range (0.1-20.0 MPa)
with\emph{AARD} of 1.45 \%.

Indeed, the above QSPR and GCM reference methods have achieved good
results in predicting the properties of ILs. However, in their modelling
process, the descriptors used to build the model were made up of anion
and cation descriptors, and their interactions were often neglected to
some extent. In order to study the interaction between cations and
anions, our previous work regarded the interaction between cations and
anions as a mathematical formula composed of ion
descriptors.\textsuperscript{37,47}Compared with the results in the
above literatures, the accuracy of our previous works on the interaction
between anions and cations have been significantly improved. Recently,
Yan et al.\textsuperscript{25,48}proposed a new method to express the
interaction between anions and cations by calculating descriptors from
ILs molecule, which have been successfully applied for QSPR modelling
for predicting the heat capacity and the eco-toxicity of ILs. The
improved prediction accuracy and stability of the model further suggests
that the interaction between anion and anion has an important impact on
the properties of ILs, which is essential in the construction of the
prediction model.

At present, there are hundreds of common cations and about 100 anions,
and the combination of these anions and anions thus can produce tens of
thousands of ILs. Although many literatures have reported QSPR models to
predict thermodynamic properties, the descriptors used in these models
need to be calculated by complicate software, which will lead to the
inconvenience of model application. Therefore, the convenient and
successful application of QSPR models for predicting the properties of
density, viscosity and thermal conductivity is of great value for the
design, development and application of ILs.

The focus of this work is to establish QSPR models for predicting the
density, viscosity and thermal conductivity properties of ILs under
variable temperature and pressure. There are four main works in this
paper: (1) the \emph{f-T-P} model of ILs under variable temperature and
pressure was established; (2) the cationic, anionic and ILs descriptors
were calculated to build the QSPR model; (3) three QSPR models were
established for three properties of ILs at variable temperatures and
pressures; (4) \emph{f-T-P} model parameters of 16329 ILs were predicted
by the QSPR models.

\textbf{2. Methodology}

\textbf{2.1 Database}

A comprehensive experimental dataset was established by collecting the
experimental data of three properties (density, viscosity, thermal
conductivity) of ILs from the Ionic Liquids database provided by the
National Institute of Standards and Technology (NIST)
(https://ilthermo.boulder.nist.gov/index.html) and papers of Yan et al.
and He et al.\textsuperscript{29,39,46} 9020 density (\selectlanguage{greek}\emph{ρ} \selectlanguage{english}) data
points for 315 ILs, 7342 viscosity (\selectlanguage{greek}\emph{ρ} \selectlanguage{english}) data points for 351 ILs
and 608 thermal conductivity (\selectlanguage{greek}\emph{λ} \selectlanguage{english}) data points for 87 ILs are
covered in the dataset. For density, viscosity and thermal conductivity,
the temperature and pressure ranges are (253.15-473.15 K) and (0.1-250
MPa), (253.15-438.15 K) and (0.06-300 MPa), (273.15-390 K) and (0.1-20.0
MPa), respectively.

The ILs are based on various cations such as imidazoulium (Im),
pyridinium (Py), ammonium (Am), pyrrolidinium (Pyr), phosphonium (Ph),
piperidinium (Pip), morpholinium (Mor), sulphonium (S), pyrrolidonium
(N), diethylthiouronium (Thiur), 1,8-diazabicycloundecenium (Dbu),
N-octylisoquinolinium (Quin), Caprolactam (Cp). And anions included
tetrafluoroborate {[}(BF\textsubscript{4})\textsuperscript{-}{]},
hexafluorophosphate {[}(PF\textsubscript{6})\textsuperscript{-}{]},
dicyanamide {[}(N(CN)\textsubscript{2})\textsuperscript{-}{]},
tetracyanoborate {[}(B(CN)\textsubscript{4})\textsuperscript{-}{]},
trifluoroacetate {[}(C(CN)\textsubscript{3})\textsuperscript{-}{]},
alkyl-phosphate {[}(RPO\textsubscript{4})\textsuperscript{-}{]},
bis{[}(perfluoroethyl)sulfonyl{]}imide
{[}(Pf\textsubscript{2}N)\textsuperscript{-}{]}, alkoxy-alkylsulfates
{[}(RSO\textsubscript{3})\textsuperscript{-}{]},
tris(pentafluoroethyl)trifluorophosphate {[}(FAP)\textsuperscript{-}{]},
alkyl-sulfate
{[}(RSO\textsubscript{4})\textsuperscript{-}{]},thiocyanate
{[}(SCN)\textsuperscript{-}{]}, carboxylicacid
{[}(RCO\textsubscript{2})\textsuperscript{-}{]},
bis{[}(trifluoromethyl)sulfonyl{]}imide
{[}(Tf\textsubscript{2}N)\textsuperscript{-}{]}, halogen
{[}(X)\textsuperscript{-}{]}, 1,2,3-triazolide
{[}(Triz)\textsuperscript{-}{]}, Tetrazolide
{[}(Tetra)\textsuperscript{-}{]},
difluoromono{[}1,2-oxalato(2-)-O,O'{]}borate
{[}(RBF\textsubscript{2})\textsuperscript{-}{]}, 4-nitropyrazolide
{[}(4-NO\textsubscript{2}pyra)\textsuperscript{-}{]}, phenolate
{[}(Phe)\textsuperscript{-}{]}, 2-(cyano)pyrrolide
{[}(2-CNpyr)\textsuperscript{-}{]}. The ILs name together with
corresponding experimental values of density, viscosity and thermal
conductivity were shown in Supporting Information Tables
S1\textasciitilde{}S3.

\textbf{2.2 \emph{f-T-P} model}

In this work, the \emph{f-T-P} models are established to describe the
relationship of properties (density, viscosity and thermal conductivity)
with temperature and pressure. The\emph{f-T-P} (\selectlanguage{greek}\emph{ρ-T-P}\selectlanguage{english} ,
\selectlanguage{greek}\emph{η-T-P}\selectlanguage{english} , \selectlanguage{greek}\emph{λ-T-P}\selectlanguage{english} ) model shown as Eq. (1) was used at present
for this study. The fitting parameters\selectlanguage{greek}\emph{α} , \selectlanguage{english}\selectlanguage{greek}\emph{β} , \selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and
\selectlanguage{greek}\emph{χ} , \selectlanguage{english}used to calculate the density, viscosity and thermal
conductivity of ILs are given in Supporting Information Figures
S1\textasciitilde{} S3.

In structure-property relationship, \selectlanguage{greek}\emph{α} \selectlanguage{english}is related to the
structures of ILs and the parameters \selectlanguage{greek}\emph{β} , \selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and \selectlanguage{greek}\emph{χ}
\selectlanguage{english}are obtained by two methods: (1) \selectlanguage{greek}\emph{β} , \selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and \selectlanguage{greek}\emph{χ} \selectlanguage{english}are
set as constants for all ILs; (2) \selectlanguage{greek}\emph{β} , \selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and \selectlanguage{greek}\emph{χ} \selectlanguage{english}are
variables related to the molecular structure. To compare these two
approaches, the density, viscosity and thermal conductivity samples with
multiple data points are fitted using Eq. (1) by the above two methods.
The calculated results are depicted in Figures 1-3. It can be seen that
the second method results in Figure 1 (b), Figure 2 (b) and Figure 3 (b)
are better than the first method results in Figure 1 (a), Figure 2 (a)
and Figure 3 (a). The correlations between the calculated and
experimental values for each sample using the second method are
presented in the supporting information. Compared with the first method,
the average absolute relative deviation (\emph{AARD} ) of the second
method reduced by 76 \%, 79 \% and 70 \% for \selectlanguage{greek}\emph{ρ} , \selectlanguage{english}\selectlanguage{greek}\emph{η} \selectlanguage{english}and
\selectlanguage{greek}\emph{λ} , \selectlanguage{english}respectively. Accordingly, the above calculation results
demonstrated that \selectlanguage{greek}\emph{β} ,\selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and \selectlanguage{greek}\emph{χ} \selectlanguage{english}adjusted by the
molecular structures are necessary and efficient.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\selectlanguage{greek}\textbf{Figure 1. The correlation between observed and
predicted\emph{ρ}: (a) the first method,}\selectlanguage{english}

\textbf{(b) the second method.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\selectlanguage{greek}\textbf{Figure 2. The correlation between observed and
predicted\emph{η}: (a) the first method,}\selectlanguage{english}

\textbf{(b) the second method.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\selectlanguage{greek}\textbf{Figure 3. The correlation between observed and
predicted\emph{λ}: (a) the first method,}\selectlanguage{english}

\textbf{(b) the second method.}

\textbf{2.3 Norm descriptors proposed}

The structure of ILs is the key factor to determine the properties of
ionic liquid. With the \emph{HyperChem} 7.0 software
(http://www.hyper.com/), the \emph{ab} initio method at the ST0-3G level
was used to optimize the structure of cation, anion and IL. In order to
clearly reflect the position relationship of atoms, the step matrix
(\emph{MA, MB, MC MS} ) and Euclidean space distance matrix (\emph{MD} )
are expressed as follows:

In order to reveal the characters of atoms in molecules, the property
matrices based on a series of atomic properties are as Eqs. (7-13):

Where,\emph{aw, mw, e, ip, r, ne, el} and \emph{q} represent atom
weight, molecular weight, electronegativity, ionization potential,
atomic radius, outermost number of electrons, number of electron layers
and atom charge, respectively.

The atomic distribution matrix (\emph{M} ), used for density, viscosity
and thermal conductivity, are shown in Supporting Information Tables
C1-C3. The \emph{M} is composed of the distance matrix or the
combination of step matrix and property matrix, which reflects the
relationship between atoms and the special contribution of each atom.
Then, the norm descriptors (\emph{I} ) were calculated from the
\emph{M}through the following formulas (Eqs. (14-17)).

\textbf{Hosted file}

\verb`image8.wmf`  available at \url{https://authorea.com/users/359155/articles/481358-evaluating-the-properties-of-ionic-liquid-at-variable-temperatures-and-pressures-by-qspr}

Where, \selectlanguage{greek}\emph{λ} \selectlanguage{english}\textsubscript{i} is the matrix eigenvalue, and the is
the Hermite matrix.

\textbf{2.4 Model} \textbf{Validation}

These QSPR models were quantitatively assessed by several statistical
criteria as relative deviation (\emph{RD} ), the Fisher significance
parameter (\emph{F} ) and the average absolute relative deviation
percentage (\emph{AARD} \%). The predictability of the model is
supported by \emph{R\textsuperscript{2}\textsubscript{training}} for the
training set and \emph{R\textsuperscript{2}\textsubscript{testing}} for
the testing set. In addition, Leave-one-out (LOO) validation was
utilized to evaluate the robustness of this QSPR model (\emph{Q}
\textsuperscript{2}). \emph{Y} -randomization test was utilized to avoid
the possibility of chance correlation in the modelling
work.\textsuperscript{32,49}

\textbf{Hosted file}

\verb`image9.wmf`  available at \url{https://authorea.com/users/359155/articles/481358-evaluating-the-properties-of-ionic-liquid-at-variable-temperatures-and-pressures-by-qspr}

\textbf{Hosted file}

\verb`image10.wmf`  available at \url{https://authorea.com/users/359155/articles/481358-evaluating-the-properties-of-ionic-liquid-at-variable-temperatures-and-pressures-by-qspr}

\textbf{Hosted file}

\verb`image11.wmf`  available at \url{https://authorea.com/users/359155/articles/481358-evaluating-the-properties-of-ionic-liquid-at-variable-temperatures-and-pressures-by-qspr}

Herein,

and

are the experimental and calculated values of ILs, respectively.\emph{n}
is the total number of data points.

\textbf{2.5 Model} \textbf{Application}

The stable QSPR model could be used to predict the physical and chemical
values of ILs. Based on the ILs studied in this work, 18630 ILs were
obtained by combining 207 anions and 90 cations (Supporting Information
Table S4). 16329 ILs with optimization structures are used to predict
the parameters (\selectlanguage{greek}\emph{α} , \selectlanguage{english}\selectlanguage{greek}\emph{β} , \selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and \selectlanguage{greek}\emph{χ} \selectlanguage{english}) of
the\emph{f-T-P} model by using the three QSPR models for density,
viscosity and thermal conductivity. Based on the experimental values
range of density, viscosity and thermal conductivity, we assume that the
reasonable range of predicted values is 50 \% of the minimum
experimental value and 150 \% of the maximum experimental value. The
coefficients (\selectlanguage{greek}\emph{α} , \selectlanguage{english}\selectlanguage{greek}\emph{β} , \selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and \selectlanguage{greek}\emph{χ} \selectlanguage{english}) of density,
viscosity and thermal conductivity were predicted and provided in
Supporting Information Tables S5-S7.

\textbf{3. Results and discussion}

\selectlanguage{greek}\textbf{3.1 Density (\emph{ρ})}\selectlanguage{english}

\selectlanguage{greek}\textbf{3.1.1 QSPR model proposed for \emph{ρ} (\emph{T, P})}\selectlanguage{english}

A new \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(\emph{T, P} ) model is established to estimate the
temperature and pressure dependent \selectlanguage{greek}\emph{ρ} \selectlanguage{english}of ILs, as shown in Eq.
(20), and its parameter values are shown in Supporting Information Table
C1.

\emph{n} =9020, \emph{R} \textsuperscript{2}=0.9966, \emph{F}
=44685,\emph{Q} \textsuperscript{2}=0.9965, \emph{AARD}
=0.48\%,\emph{RMSE} =0.0097

Where, \emph{I} \textsubscript{ILs}, \emph{I} \textsubscript{Ca}
and\emph{I} \textsubscript{An} represent the norm descriptors of ILs,
cation and anion, respectively.

The experimental and calculated\selectlanguage{greek}\emph{ρ} \selectlanguage{english}values by the model (Eq. (20))
were shown in Supporting Information Table S1. The comparison between
the observed value and the calculated value, as well as the residual
distribution of the model and Leave-one-out cross-validation (LOO-CV)
are shown in Figure 4. Figure 4 (a) indicated that that the model is
accurate for most points distributed nearby, with \emph{R}
\textsuperscript{2} of 0.9966,\emph{AARD} of 0.48 \% and \emph{RMSE} of
0.0097. Figure 4 (b) suggested that about 96 \% \selectlanguage{greek}\emph{ρ} \selectlanguage{english}data points
residuals range from -0.005 to 0.005. Thus, it suggests that the model
based on the norm index to calculate the density is stable and reliable.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

\textbf{Figure 4. Observed\emph{vs}. calculated values (a) and
distribution of the residual (b) of density}

314 ionic liquids can be divided into 13 types cations and 25 types
anions. Figure 5 analyzes \emph{AARD} and the \selectlanguage{greek}\emph{ρ} \selectlanguage{english}data points of
each type of ILs. It can be seen that the predicted \emph{AARD} values
of {[}Am{]}{[}RSO\textsubscript{4}{]} and
{[}Dbu{]}{[}RSO\textsubscript{3}{]} are relatively large, which may lead
to inaccurate prediction results for this two types ILs. However, most
of the data point errors are within the acceptable range. Therefore,
this model can be used to predict the density of ILs with different
structures under different temperatures and pressures.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}

\end{center}
\end{figure}

\textbf{Figure 5. The numbers (a) and \emph{AARD} \% (b) for each kind
of ILs for density.}

\textbf{3.1.2 Internal-validation and External-validation}

The robustness and predictability of the model were evaluated using the
internal and external procedure.\textsuperscript{50}The validation
parameters such as \emph{R} \textsuperscript{2},\emph{Q}
\textsuperscript{2}, \emph{AARD} and \emph{RMSE} are listed in Table 1.
As shown in Figure 6 (a), the good results of LOO-CV with high\emph{Q}
\textsuperscript{2} of 0.9965 suggested the model's stability. For the
external validation, the data set was randomly divided into the training
set (7216 data points) and the testing set (1804 data points). The
calculated and experimental \selectlanguage{greek}\emph{ρ} \selectlanguage{english}values of the training set and the
testing set were plotted in Figure 6 (b). The\emph{R}
\textsuperscript{2} of the training set and testing set were 0.9954 and
0.9964, respectively. The \emph{AARD} value were 0.56 \% and 0.54 \%,
respectively. Results showed that the \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(\emph{T, P} ) model was
stable and has good predictability.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image16/image16}

\end{center}
\end{figure}

\textbf{Figure 6. Scatter plots of the internal-validation (a) and
external-validation (b).}

\textbf{Table 1. The results of internal-validation and
external-validation for density}\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
Status & Data points &
\emph{R}\textsuperscript{2}(\emph{Q}\textsuperscript{2}) & \emph{AARD}
\% & \emph{RMSE}\tabularnewline
\midrule
\endhead
Model & 9020 & 0.9966 & 0.4764 & 0.0097\tabularnewline
LOO-CV & 9020 & 0.9965 & 0.4815 & 0.0110\tabularnewline
Training set & 7216 & 0.9954 & 0.5654 & 0.0101\tabularnewline
Testing set & 1804 & 0.9964 & 0.5464 & 0.0111\tabularnewline
\bottomrule
\end{longtable}

\textbf{3. 1.3 Y-randomization test}

\emph{Y} -randomized trials were conducted and Figure 7 shows the
results of 1000 random validations. The\emph{R}
\textsubscript{r}\textsuperscript{2} and\emph{Q}
\textsubscript{r}\textsuperscript{2} of \emph{Y} -type randomized test
results were lower than 0.011. Therefore, it can be considered that the
\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(\emph{T, P} ) model is robust and is not developed by the
chance correlation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image17/image17}

\end{center}
\end{figure}

\textbf{Figure 7. Results of the 1000 times \emph{Y}-randomization test
for density.}

\textbf{3.1.4 Comparison with References}

\textbf{Table 2. The comparisons of this work with references for the
density}\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
References & Method & D.P & ILs & T/K & P/MPa &
\emph{R}\textsuperscript{2} & \emph{AARD} (\%)\tabularnewline
\midrule
\endhead
Barati-Harooni et al. 2016\textsuperscript{51} & GCM & 602 & 146 &
278-358 & 0.1 & 0.9808 & 0.89\tabularnewline
Lazz\selectlanguage{ngerman}ús 2010\textsuperscript{52} & GCM & 3530 & 76 & 258-393 & 0.1-207 &
0.9989 & 0.73\tabularnewline
Chen et al. 2019\textsuperscript{16} & GCM & 7360 & 143 & 273.15-473.15
& 0.1--250 & & 0.49\tabularnewline
Lazz\selectlanguage{ngerman}ús 2009\textsuperscript{53} & QSPR & 3020 & 163 & 258-473 & 0.1-207
& 0.9307 & 2.00\tabularnewline
Yan et al. 2015\textsuperscript{54} & QSPR & 5948 & 188 & 253.15-473.15
& 0.1--250 & 0.9980 & 0.42\tabularnewline
This work & QSPR & 9020 & 314 & 253.15-473.15 & 0.1-250 & 0.9966 &
0.48\tabularnewline
\bottomrule
\end{longtable}

D.P is data points. T and P were temperature and pressure, respectively.

This model was compared with some other corresponding methods from
literatures and the results were listed in Table 2. Based on GCM,
Barati-Harooni et al.\textsuperscript{51} constructed a model to predict
the density of ILs at variable temperature with \emph{AARD} of 0.98 \%.
Lazz\selectlanguage{ngerman}ús\textsuperscript{52} and Chen et al.\textsuperscript{16} have made
a good prediction for the density of ILs, in which the \emph{AARD} value
is about 0.73 \% and 0.49 \%. For the QSPR model of
Lazzús\textsuperscript{53}, a moderate prediction result is obtained
(\emph{AARD} =2 \%). Obviously, the statistical results of these models
are good. Although the \emph{AARD} (0.48 \%) and\emph{R}
\textsuperscript{2} (0.9966) of this work are slightly worse than those
of prior studies,\textsuperscript{54} the amount of ILs datasets in this
paper is the larger. At the same time, a large number of ILs datasets
with different structures are used for modeling in our work, and the
satisfactory prediction results further confirm the robustness and
reliability of the \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(\emph{T, P} ) model.

\textbf{3.1.5 The application of QSPR model}

The parameters of ILs \selectlanguage{greek}\emph{ρ} \selectlanguage{english}model are located in Supporting
Information Table S5. Figure 8 shows prediction results of the density
of 16329 ILs at variable temperature (273-573 K) and pressure (0.1-10
MPa). Most of the predicted values for density are acceptable and
reasonable, except those of {[}bmim{]}{[}FS{]}, {[}Hprthiur{]}{[}I{]},
{[}mC\textsubscript{10}im{]}{[}Pf2N{]}, {[}N113(eOH){]}{[}FAP{]} and
{[}odbu{]}{[}C\textsubscript{8}SO\textsubscript{3}{]}.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image18/image18}

\end{center}
\end{figure}

\textbf{Figure 8. Prediction results of density: green-reasonable,
blue-unreasonable.}

\selectlanguage{greek}\textbf{3.2. Viscosity (\emph{η})}\selectlanguage{english}

\selectlanguage{greek}\textbf{3.2.1 QSPR model proposed for log \emph{η} (\emph{T, P})}\selectlanguage{english}

ILs \selectlanguage{greek}\emph{η} \selectlanguage{english}model is expressed as Eq. (21). The coefficients of the
model are shown in Supporting Information Table C2. The predicted and
experimental log \selectlanguage{greek}\emph{η} \selectlanguage{english}values of ILs are listed in Supporting
Information Table S2.

\emph{n} =7342, \emph{R} \textsuperscript{2}=0.9676, \emph{F}
=4540,\emph{Q} \textsuperscript{2}=0.9668, \emph{AARD}
=3.91\%,\emph{RMSE} =0.1069

Where, \emph{I} \textsubscript{ILs}, \emph{I} \textsubscript{Ca}
and\emph{I} \textsubscript{An} represent the norm descriptors of ILs,
cation and anion, respectively.

Additionally, the comparison between the observed and calculated
log\selectlanguage{greek}\emph{η} \selectlanguage{english}values is shown in Figure 9 (a). The distribution of the
residuals is shown in Figure 9 (b).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image20/image20}

\end{center}
\end{figure}

\textbf{Figure 9. Observed \emph{vs}. calculated values (a) and
distribution of the residual (b) of viscosity}

It can be seen that most of points are distributed near the diagonal,
which means that the calculated value is close to the experimental
value. The good prediction results are also denoted
with\emph{R\textsuperscript{2}} of 0.9676 and the \emph{AARD} of 3.91
\%. Figure 9 (b) showed that the residual distribution of most ILs
(about 80 \%) log \selectlanguage{greek}\emph{η} \selectlanguage{english}data in the model are between
-0.5\textasciitilde{}0.5, which further proves the reliability and
stability of the model.

351 ionic liquids were divided into 11 categories of cations and 27
kinds of anions. A summary of \selectlanguage{greek}\emph{η} \selectlanguage{english}estimation of ILs using QSPR
method is given in Figure 10, in which the number of fitted data points
and the \emph{AARD} \% of each type based ILs are provided.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image21/image21}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image22/image22}

\end{center}
\end{figure}

\textbf{Figure 10. The numbers (a) and \emph{AARD} \% (b) for each kind
of ILs for viscosity}

As shown in Figure 10 (b), all the \emph{AARD} locates in acceptable
range except for {[}Dbu{]}{[}NTf\textsubscript{2}{]} and
{[}Dbu{]}{[}RCO\textsubscript{2}{]}, but this two types ILs only account
for a small proportion in the whole data set. Accordingly, it could be
concluded that the model is appropriate for predicting \selectlanguage{greek}\emph{η} \selectlanguage{english}at
variable temperature and pressure of ILs with various structures.

\textbf{3.2.2 Internal-validation and External-validation}

The Cross-validation calculated values versus experimental values of log
\selectlanguage{greek}\emph{η} \selectlanguage{english}data were showed in Figure 11 (a). The statistical parameters
for validation are listed in Table 3. The Figure 11 (a) shows that the
experimental value is close to the log \selectlanguage{greek}\emph{η} \selectlanguage{english}value calculated by
Cross-validation. Table 3 shows that the \emph{Q\textsuperscript{2}}
(0.9668), \emph{AARD} (3.95\%) and\emph{RMSE} (0.1276) are acceptable,
which suggests the good stability and robustness of this \selectlanguage{greek}\emph{η} \selectlanguage{english}model.

7432 data points were randomly divided into the training set (5874 data
points) and the testing set (1468 data points). The calculated values
for the training set and the testing set with the experimental values
were showed in Figure 11 (b). The performance parameters for external
validation results are listed in Table 3. External validation results
showed that the \emph{R} \textsuperscript{2} of training set and testing
set were 0.9535 and 0.9607, and the \emph{AARD} were 5.051 \% and 4.743
\%, respectively. These result showed that the QSPR model based on norm
descriptor was stable and has good predictive ability for
\selectlanguage{greek}\emph{η}\selectlanguage{english}prediction of ILs with diverse structures.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image23/image23}

\end{center}
\end{figure}

\textbf{Figure 11. Scatter plots of the internal-validation (a) and
external-validation (b)}

\textbf{Table 3. The results of internal-validation and
external-validation for viscosity}\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
Status & Data points &
\emph{R}\textsuperscript{2}(\emph{Q}\textsuperscript{2}) & \emph{AARD}
\% & \emph{RMSE}\tabularnewline
\midrule
\endhead
Model & 7342 & 0.9676 & 3.914 & 0.1069\tabularnewline
LOO-CV & 7342 & 0.9668 & 3.951 & 0.1276\tabularnewline
Training set & 5874 & 0.9535 & 5.051 & 0.1285\tabularnewline
Testing set & 1468 & 0.9607 & 4.743 & 0.1166\tabularnewline
\bottomrule
\end{longtable}

\textbf{3.2.3 Y-randomization test}

1000 \emph{Y} -random verifications were repeated in this study and the
results were showed in Figure 12. Figure 12 denoted that all\emph{R}
\textsubscript{i}\textsuperscript{2} and\emph{Q}
\textsubscript{i}\textsuperscript{2} values were lower than 0.012, which
indicated that this model was not established by accident.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image24/image24}

\end{center}
\end{figure}

\textbf{Figure 12. Results of the 1000 times Y-randomization test for
viscosity.}

\textbf{3.2.4 Comparison with References}

\textbf{Table 4. The comparisons of this work with references for the
viscosity}\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
References & Model & D.P & ILs & T/K & P/MPa &
\emph{R}\textsuperscript{2} & \emph{AARD} (\%)\tabularnewline
\midrule
\endhead
Chen et al. 2019\textsuperscript{16} & GCM & 1090 & 76 & 278.0-408.15 &
& & 3.58\tabularnewline
Beckner et al. 2018\textsuperscript{42} & FF-ANN & 723 & 33 &
273.15-373.15 & 0.06-0.16 & & 7.10\tabularnewline
Zhao et al. 2015\textsuperscript{55} & QSPR & 1502 & 89 & 253.15-395.32
& 0.1-300 & 0.9440 & 6.58\tabularnewline
Yan et al. 2018\textsuperscript{29} & QSPR & 3228 & 349 & 253.15-573 &
0.06-300 & 0.9640 & 4.62\tabularnewline
This work & QSPR & 7342 & 351 & 253.15-438.15 & 0.06-300 & 0.9676 &
3.91\tabularnewline
\bottomrule
\end{longtable}

Table 4 listed the comparison results between literatures and this work.
Compared with the results of Chen et al.\textsuperscript{16} and Beckner
et al.\textsuperscript{42}, our model obtained good statistical results
under a wider range of temperature and pressure. Compared with Zhao et
al.\textsuperscript{55} and Yan et al.\textsuperscript{29}, it was clear
that our model has a larger amount of data and a wider variety of ILs
with higher \emph{R} \textsuperscript{2} and lower \emph{AARD} , which
further demonstrated that our model for predicting \selectlanguage{greek}\emph{η} \selectlanguage{english}values was
more precise.

\textbf{3.2.5 The application of QSPR model}

The parameters of viscosity model are located in Supporting Information
Table S6. As shown in Figure 13, 16329 ILs are utilized for predicting
the viscosity under variable temperature (273-573 K) and pressure
(0.1-10 MPa) and the results are shown in Figure 13. As shown in Figure
13, most of the viscosity predictions of ILs are reasonable, except the
viscosity prediction of {[}N113(eOH){]}{[}FAP{]}, {[}bmim{]}{[}FS{]},
{[}mC\textsubscript{10}im{]}{[}Pf2N{]} and
{[}odbu{]}{[}C\textsubscript{8}SO\textsubscript{3}{]} with the four blue
spots.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image25/image25}

\end{center}
\end{figure}

\textbf{Figure 13. Prediction results of viscosity: green-reasonable,
blue-unreasonable.}

\selectlanguage{greek}\textbf{3.3. Thermal conductivity (\emph{λ})}\selectlanguage{english}

\selectlanguage{greek}\textbf{3.3.1 QSPR model proposed for \emph{λ} (\emph{T, P})}\selectlanguage{english}

A QSPR model is proposed to predict the thermal conductivity of ILs and
expressed as Eq. (22). The parameter values are shown in Supporting
Information Table C3.

\emph{n} =608, \emph{R} \textsuperscript{2}=0.9847, \emph{F}
=961,\emph{Q} \textsuperscript{2}=0.9825, \emph{AARD}
=1.02\%,\emph{RMSE} =0.0026

Where, \emph{I} \textsubscript{ILs}, \emph{I} \textsubscript{Ca}
and\emph{I} \textsubscript{An} represent the norm descriptors of ILs,
cation and anion, respectively.

The calculated \selectlanguage{greek}\emph{λ} \selectlanguage{english}data of ILs by Eq. (22) are listed in Supporting
Information Table S3 together with the observed \selectlanguage{greek}\emph{λ} \selectlanguage{english}data. Figure 14
(a) presented the comparison between experimental and predicted
\selectlanguage{greek}\emph{λ}\selectlanguage{english}of ILs. Distribution of the residual by the model and LOO-CV is
shown in Figure 14 (b).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image27/image27}

\end{center}
\end{figure}

\textbf{Figure 14. Observed \emph{vs}. predicted values (a) and
distribution of the residual (b) of thermal conductivity}

Figure 14 (a) indicated that the calculated values agreed very well with
observed data for \selectlanguage{greek}\emph{λ} \selectlanguage{english}values. Also, the good performance of this
model could be demonstrated by the high \emph{R} \textsuperscript{2} of
0.9847 and the low \emph{AARD} of 1.02\%. As seen from Figure 14 (b),
most of the points fell between -0.0025 and 0.0025 W
m\textsuperscript{-1} K\textsuperscript{-1}, and only a small number of
predicted residual errors were greater than 0.0075 W
m\textsuperscript{-1} K\textsuperscript{-1}. Therefore, it might be
possible to successfully calculate the \selectlanguage{greek}\emph{λ} \selectlanguage{english}of ILs at variable
temperatures and pressures by this model.

Experimental data on the \selectlanguage{greek}\emph{λ} \selectlanguage{english}of 87 ILs were collected in this
paper, including 5 classes of cations and 12 classes of anions. It can
be easily noted from Figure 15 (a) that, despite the great diversity of
the cations and anions of ILs, only a few types of ions have been widely
studied. Figure 15 (b) shows that the \emph{AARD} calculated from all
reported data of a given cation / anion group is small and all types of
ILs residuals are acceptable range except for
{[}Im{]}{[}N(CN)\textsubscript{2}{]}. Therefore, the model is suitable
for accessing the \selectlanguage{greek}\emph{λ} \selectlanguage{english}data of these kinds of ILs with reasonable
results.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image28/image28}

\end{center}
\end{figure}

\textbf{Figure 15. The numbers (a) and \emph{AARD} \% (b) for each kind
of ILs for thermal conductivity}

\textbf{3.3.2 Internal-validation and External-validation}

Figure 16 (a) was plotted with the predicted values by LOO-CV and the
experimental \selectlanguage{greek}\emph{λ} \selectlanguage{english}values. The large \emph{Q}
\textsuperscript{2}(0.9825) and the good agreement between the predicted
and experimental\selectlanguage{greek}\emph{λ} \selectlanguage{english}further indicated the good stability of this
model.

The \selectlanguage{greek}\emph{λ} \selectlanguage{english}data set is divided into the training set (487) and the
testing set (121). Results in Figure 16 (b) indicated that the
predicted\selectlanguage{greek}\emph{λ} \selectlanguage{english}were in good agreement with the experimental \selectlanguage{greek}\emph{λ}
\selectlanguage{english}values of ILs. The statistical parameters listed in Table 5 showed that
the\emph{R} \textsuperscript{2} of training set and testing set were
0.9806 and 0.9834, and the \emph{AARD} were 1.292 \% and 1.146 \%,
respectively, which further proved the predictability of this
\selectlanguage{greek}\emph{λ}\selectlanguage{english}model.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image29/image29}

\end{center}
\end{figure}

\textbf{Figure 16. Scatter plots of the internal-validation (a) and
external-validation (b)}

\textbf{Table 5. The results of internal-validation and
external-validation for thermal conductivity.}\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
Status & Data points &
\emph{R}\textsuperscript{2}(\emph{Q}\textsuperscript{2}) & \emph{AARD}
\% & \emph{RMSE}\tabularnewline
\midrule
\endhead
Model & 608 & 0.9847 & 1.0176 & 0.0026\tabularnewline
LOO-CV & 608 & 0.9825 & 1.0192 & 0.0031\tabularnewline
Training set & 487 & 0.9806 & 1.2923 & 0.0030\tabularnewline
Testing set & 121 & 0.9837 & 1.1457 & 0.0025\tabularnewline
\bottomrule
\end{longtable}

\textbf{3.2.3 Y -randomization test}

Figure 17 shows the results of 10,000 \emph{Y} -random validations.
The\emph{R} \textsubscript{r}\textsuperscript{2} and\emph{Q}
\textsubscript{r}\textsuperscript{2} of \emph{Y} -type randomized test
were lower than 0.08, which was significantly smaller than those of the
original \selectlanguage{greek}\emph{λ} \selectlanguage{english}model. Therefore, it can be considered that the QSPR
model were not affected by the chance correlation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image30/image30}

\end{center}
\end{figure}

\textbf{Figure 17. Results of the 10000 times Y-randomization test for
thermal conductivity.}

\textbf{3.3.4 Comparison with References}

\textbf{Table 6. The comparisons of this work with references for
thermal conductivity}\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
\begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
References\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
Model\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
D.P\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
ILs\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
T/K\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
P/MPa\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\emph{R}\textsuperscript{2}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\emph{AARD} (\%)\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Lazz\selectlanguage{ngerman}ús 2015\textsuperscript{22}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
GCM\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
400\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
41\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
273--390\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.1-20\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.9843\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2.12\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Chen et al. 2014\textsuperscript{44}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
QSPR\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
359\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
45\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
273.15-353.15\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1.01\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2.30\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Lazzus 2015\textsuperscript{45}\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
QSPR\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
195\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
273.15-390\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1.01\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.9919\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2.00\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
He et al. 2017\textsuperscript{56}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
QSPR\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
475\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
50\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
273.15-355.07\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1-20\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.9840 840\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
1.45\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
This work\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
QSPR\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
608\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
87\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
273.15-390\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.1-20\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.9847\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1.02\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

The QSPR model for predicting \selectlanguage{greek}\emph{λ} \selectlanguage{english}is established and compared with
other models as shown in Table 6. Lazz\selectlanguage{ngerman}ús\textsuperscript{22} using GCM
to predict the \selectlanguage{greek}\emph{λ} \selectlanguage{english}at variable temperature and pressure and got
good results (\emph{R} \textsuperscript{2}=0.9843,\emph{AARD} =2.12\%).
Compared with Chen et al.\textsuperscript{44},
Lazzus\textsuperscript{45} and He et al.\textsuperscript{56}, our work
has a larger amount of data points, and obtained a higher\emph{R}
\textsuperscript{2} of 0.9847, a lower \emph{AARD} of 1.02 \%.
Therefore, our QSPR model for \selectlanguage{greek}\emph{λ} \selectlanguage{english}prediction has the higher
precision.

\textbf{3.3.5 The application of QSPR model}

The parameters of thermal conductivity model are located in Supporting
Information Table S7. For 16329 ILs, the prediction of ILs thermal
conductivity at variable temperature (273-573 K) and pressure (0.1-10
MPa) is shown in Figure 18. It can be seen from Figure 18 that this
model is suitable for the thermal conductivity calculation of most ILs
at variable temperature and atmospheric pressure; the prediction of
thermal conductivity of ILs corresponding to these seven anions
({[}BF4{]}, {[}ClO4{]}, {[}Cl{]}, {[}For{]}, {[}NO3{]}, {[}PF6{]},
{[}SCN{]}) at other temperatures and pressures is in a reasonable range;
however, the thermal conductivity of ILs corresponding to four cations
({[}(prOH)py{]}, {[}C11mim{]}, {[}P1444{]}, {[}P2228{]}) and six anions
({[}BF2Ox{]}, {[}Br{]}, {[}C2H5BF3{]}, {[}C3F7BF3{]}, {[}C3H7BF3{]},
{[}I{]}) is not within the reasonable range.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image31/image31}

\end{center}
\end{figure}

\textbf{Figure 18. Prediction results of thermal conductivity:
purple-reasonable at variable temperature and 0.1 MPa;}

\textbf{red-reasonable at variable temperature and pressure, pale
blue-unreasonable.}

\textbf{4. Conclusions}

In this paper, three groups of norm descriptors were established by the
structure of ILs, anion and anion. Based on 9020 \selectlanguage{greek}\emph{ρ} \selectlanguage{english}data points,
7324 \selectlanguage{greek}\emph{η} \selectlanguage{english}data points and 608 \selectlanguage{greek}\emph{λ} \selectlanguage{english}data points, three QSPR
models were established to calculate the properties of ILs (density,
viscosity and thermal conductivity) at variable temperatures and
pressures. The performance of the \emph{f} -\emph{T} -\emph{P} QSPR
models was improved by introducing norm descriptors into temperature and
pressure terms. The statistical results indicate that these models have
good prediction accuracy and credibility with the high
\emph{R}\textsuperscript{2} of 0.9966, 0.9676 and 0.9847, the low
\emph{AARD} of 0.48 \%, 3.91 \% and 1.02 \% for predicting the density,
viscosity and thermal conductivity, respectively. Validation analysis
shows that these QSPR models have good prediction ability and
robustness. Moreover, parameters (\selectlanguage{greek}\emph{α} , \selectlanguage{english}\selectlanguage{greek}\emph{β} , \selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and
\selectlanguage{greek}\emph{χ} \selectlanguage{english}) of the\emph{f-T-P} model for 16329 ILs are predicted by QSPR
models and most of the predictions of density and viscosity values of
ILs at variable temperature and pressure are within a reasonable range,
except for {[}bmim{]}{[}FS{]}, {[}Hprthiur{]}{[}I{]},
{[}mC\textsubscript{10}im{]}{[}Pf\textsubscript{2}N{]},
{[}N113(eOH){]}{[}FAP{]} and
{[}odbu{]}{[}C\textsubscript{8}SO\textsubscript{3}{]}. At variable
temperature and atmospheric pressure, the predicted thermal
conductivities of most ILs are in a reasonable range. At variable
temperature and pressure, the predicted thermal conductivity of these
ILs corresponding to seven anions are within the reasonable range, and
the predictions of these ILs corresponding to four cations and six
anions are not in the reasonable range. The prediction results show that
the model is stable and widely used.

\textbf{Supplementary Material}

The fitting parameters \selectlanguage{greek}\emph{α} , \selectlanguage{english}\selectlanguage{greek}\emph{β} , \selectlanguage{english}\selectlanguage{greek}\emph{γ} \selectlanguage{english}and \selectlanguage{greek}\emph{χ}
\selectlanguage{english}of\emph{f-T-P} model, used to calculate the density, viscosity and
thermal conductivity of ILs are given in Supporting Information Figures
S1\textasciitilde{} S3. The experimental and calculated values of
density, viscosity and thermal conductivity were listed in Tables
S1\textasciitilde{}S3. The atomic distribution matrix (\emph{M} ), used
for density, viscosity and thermal conductivity, are shown in Supporting
Information Tables C1-C3. The coefficients (\selectlanguage{greek}\emph{α} , \selectlanguage{english}\selectlanguage{greek}\emph{β} ,
\selectlanguage{english}\selectlanguage{greek}\emph{γ}\selectlanguage{english}and \selectlanguage{greek}\emph{χ} \selectlanguage{english}) of density, viscosity and thermal conductivity
were predicted and provided in Supporting Information Tables S5-S7.
Also, an example for calculating the thermal conductivity with the
established model was given.

\textbf{Conflict interest statement}

The authors confirm that this article has no conflicts of interest.

\textbf{Acknowledgements}

This work was supported by the National Natural Science Foundation of
China {[}NO: 21808167 and 21676203{]}.

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\selectlanguage{english}
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