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\begin{document}

\title{DFT studies of substituted phenols cytotoxicity I. Para-substituted
phenols}



\author[1]{Marek Steklac}%
\author[1]{Martin Breza}%
\affil[1]{Slovak University of Technology in Bratislava}%


\vspace{-1em}



  
  \date{May 19, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
New type of cytotoxicity descriptors based on Cu(II) coordination
ability of p-substituted phenols and subsequent O - Cu electron density
transfer is introduced. Geometries of phenols and of their Cu(II)
complexes are optimized at the DFT level of theory. The amount of
electron density transfer is evaluated using the copper charge or the
electron density Laplacian at the Cu-O bond critical point. The
Cu-phenol interaction energy is a measure of the phenol reactivity.
Statistical parameters for the linear dependence of the published
cytotoxicity data on the above predictors are much better than the
classical ones.%
\end{abstract}%



\sloppy


DFT studies of substituted phenols cytotoxicity I.\emph{Para}
-substituted phenols

Marek \selectlanguage{polish}Š\selectlanguage{english}tekl\selectlanguage{ngerman}á\selectlanguage{polish}č, \selectlanguage{english}Martin Breza*

Department of Physical Chemistry, Faculty of Chemical and Food
Technology, Slovak Technical University, SK-81237, Bratislava, Slovakia

Abstract

New type of cytotoxicity descriptors based on Cu(II) coordination
ability of p-substituted phenols and subsequent O - Cu electron density
transfer is introduced. Geometries of phenols and of their Cu(II)
complexes are optimized at the DFT level of theory. The amount of
electron density transfer is evaluated using the copper charge or the
electron density Laplacian at the Cu-O bond critical point. The
Cu-phenol interaction energy is a measure of the phenol reactivity.
Statistical parameters for the linear dependence of the published
cytotoxicity data on the above predictors are much better than the
classical ones.

Keywords: copper; quantum chemistry; electron density transfer;
cytotoxicity; QSAR

*Corresponding author. Email: martin.breza@stuba.sk (M. Breza)

M. \selectlanguage{polish}Š\selectlanguage{english}tekl\selectlanguage{ngerman}á\selectlanguage{polish}č, \selectlanguage{english}M. Breza

Department of Physical Chemistry, Faculty of Chemical and Food
Technology, Slovak Technical University, SK-81237, Bratislava, Slovakia

Phone: +421259325482

\textbf{1 Introduction}

Phenolic compounds and their derivatives are constituents of numerous
synthetic and natural chemicals such as drugs, cosmetics, dyes,
agricultural products, pesticides, food additives etc. Their properties
have been frequently studied at the molecular and cellular level.
Phenolic-based compounds provide an excellent opportunity to examine
their biological activities and to analyze corresponding mechanistic
details in a comparative fashion using the quantitative structure
activity relationship (QSAR) paradigm. It has been useful in elucidating
the mechanisms of chemical--biological interactions in various
biomolecules, particularly enzymes, membranes, organelles and
cells.\textsuperscript{{[}1{]}}

Selassie \emph{et al} .\textsuperscript{{[}2{]}} studied the
cytotoxicity of a series of 69 simple phenols in a fast growing murine
leukemia L1210 cell line. They developed a Quantitative
Structure--Activity Relationship (QSAR) model where the cytotoxicity of
the substituted phenol was evaluated as log(1/\emph{IC}
\textsubscript{50}), with\emph{IC} \textsubscript{50} being its
concentration that inhibited cell growth by 50\%. These values were
correlated with Brown-Hammett parameters (\selectlanguage{greek}\emph{σ} \selectlanguage{english}\textsuperscript{+}),
the HOMO--LUMO energy difference (\emph{L--H} gap), the logarithmic
n-octanol - water partition coefficients (log \emph{P} ) and homolytic
bond dissociation energies (\emph{BDE} ). Phenols with electron
withdrawing substituents were excluded from the analyses. BDE values
were calculated at B3LYP/6-31G**//AM1 level of theory with effective
core potentials used for bromine- and iodine-substituted molecules. L-H
gap values were obtained by the semiempirical AM1 method only. Despite
these restrictions, the developed QSAR models granted surprisingly good
results with 17 -- 27 outliers depending on the descriptors used. It
seems that the above mentioned cytotoxicity descriptors cannot produce
better results.

Alagona and Ghio\textsuperscript{{[}3{]}} evaluated the antioxidant
activity of various sites of prenylated pterocarpans according to their
Cu\textsuperscript{2+} coordination ability using the metal ion affinity
(\emph{MIA} ) values determined by B3LYP calculations. Spin density of
the cation upon ligand coordination became negligibly low, whereas the
ligand spin density approached 1. Thus, the ligand was oxidized to a
radical cation (Ligand\textsuperscript{*+}), while Cu(II) was reduced to
Cu(I). In agreement with experimental investigations, the higher
antioxidant activity of individual compounds and their reaction sites
can be assigned to higher \emph{MIA} values and higher reducing
character towards Cu(II). The Cu\textsuperscript{2+} ion serves as a
probe to estimate the extent of the electron density transfer only and
the optimized structures need not correspond to any real complex.
Mammino\textsuperscript{{[}4{]}} analogously tested antioxidant ability
of various sites of hyperjovinol A. Another modification of the
above-mentioned method by including Laplacians at Cu-N bond critical
points (BCP) as the measure of the corresponding electron density
transfer has been used for both N centres of a~series of\emph{para}
-phenylene diamine antioxidants.\textsuperscript{{[}5{]}}

Other 1\textsuperscript{st} row transition metal ions were also used in
the role of similar probes for the compounds with oxygen active sites.
B3LYP, M06-2X, BHandHLYP, MPWLYP1M and G96LYP methods were used to study
antioxidant properties of kanakugiol through its Cu(II) and Co(II)
coordination ability\textsuperscript{{[}6{]}} as well as lucidone,
linderone and methyllinderone through their Fe(II) coordination
ability.\textsuperscript{{[}7{]}} Subsequently the authors continued in
studying antioxidant properties of butein and
homobutein\textsuperscript{{[}8{]}}, chalcone derivatives kanakugiol and
pedicellin\textsuperscript{{[}9{]}} by considering their Fe(II) and
Fe(III) coordination ability using the B3LYP method. A systematic B3LYP
study of a series of para-phenylene diamine antioxidants with the late
1\textsuperscript{st} row transition metals in various spin
states\textsuperscript{{[}10{]}} has shown that using these M(II) probes
yield very similar results of antioxidant effectiveness.

This method was used for the relative cytotoxicity estimation of various
sites of model rutile nanoparticles as well.\textsuperscript{{[}11{]}}It
was shown that the experimentally observed higher cytotoxicity of
rod-like nanoparticles in comparison with the spherical ones might be
explained by the higher electron density transfer to the interacting
cells (as indicated by the extent of the electron density transfer to a
Cu\textsuperscript{2+} probe), whereas \emph{MIA} reflects the
reactivity of individual active sites. The aim of our recent study is
the application of this method to predict the cytotoxicity of\emph{p}
-substituted phenols. Our results will be compared with standard QSAR
correlations used by Selassie \emph{et al} .\textsuperscript{{[}2{]}}

\textbf{2 Method}

Geometries of 24 neutral p-substituted phenol (Ph) molecules (see Table
1) in singlet ground states, as well as of their
the\textsuperscript{2}{[}Ph\textbf{\ldots{}}
Cu{]}\textsuperscript{2+}complexes in doublet ground states (the left
superscript denotes their spin multiplicity) with Cu bonded exclusively
to O atoms, were optimized using B3LYP hybrid
functional\textsuperscript{{[}12{]}} with the DGDZVP pseudopotential and
basis set for iodine\textsuperscript{{[}13{]}} and standard 6-311G*
basis sets from the Gaussian library\textsuperscript{{[}14{]}} for the
remaining atoms. Stability of the obtained geometries was confirmed by
vibrational analysis (no imaginary vibrations). Charges and spin
populations of copper atoms were evaluated using Mulliken
(MPA)\textsuperscript{{[}15{]}} and Natural Bond Orbital
(NBO)\textsuperscript{{[}16{]}} population analyses. Gaussian09 software
was used for all quantum-chemical
calculations.\textsuperscript{{[}14{]}}

Table 1. Experimental toxicity data of Selassie \emph{et al.}
\textsuperscript{{[}2{]}} for 4-R-phenols.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Data set & R & log(1/\emph{IC}\textsubscript{50})\tabularnewline
\midrule
\endhead
A & -H & 3.27\tabularnewline
& -CH\textsubscript{3} & 3.85\tabularnewline
& -C\textsubscript{2}H\textsubscript{5} & 3.86\tabularnewline
& -C\textsubscript{3}H\textsubscript{7} & 4.04\tabularnewline
& -C\textsubscript{4}H\textsubscript{9} & 4.33\tabularnewline
& -C\textsubscript{5}H\textsubscript{11} & 4.47\tabularnewline
& -C\textsubscript{7}H\textsubscript{15} & 4.49\tabularnewline
& -C\textsubscript{8}H\textsubscript{17} & 4.62\tabularnewline
& -C\textsubscript{9}H\textsubscript{19} & 4.75\tabularnewline
& -C(CH\textsubscript{3})\textsubscript{3} & 4.09\tabularnewline
& -OC\textsubscript{6}H\textsubscript{5} & 4.97\tabularnewline
& -I & 3.86\tabularnewline
B & -OCH\textsubscript{3} & 4.48\tabularnewline
& -OC\textsubscript{2}H\textsubscript{5} & 4.64\tabularnewline
& -OC\textsubscript{3}H\textsubscript{7} & 4.85\tabularnewline
& -OC\textsubscript{4}H\textsubscript{9} & 5.20\tabularnewline
& -OC\textsubscript{6}H\textsubscript{13} & 5.50\tabularnewline
& -NO\textsubscript{2} & 3.45\tabularnewline
& -F & 3.83\tabularnewline
& -NH\textsubscript{2} & 5.09\tabularnewline
& -OH & 4.59\tabularnewline
& -Cl & 4.29\tabularnewline
& -Br & 4.20\tabularnewline
& -CN & 3.44\tabularnewline
C & -CONH\textsubscript{2} & 2.48\tabularnewline
& -SO\textsubscript{2}NH\textsubscript{2} & 2.50\tabularnewline
& -CHO & 3.08\tabularnewline
& -NHCOCH\textsubscript{3} & 3.73\tabularnewline
\bottomrule
\end{longtable}

Alternatively, the charge and spin population of Cu was evaluated in
terms of Quantum Theory of Atoms-in-Molecules
(QTAIM)\textsuperscript{{[}17{]}} (see Supplementary Information for
details). The O - Cu electron density transfer was alternatively
estimated as the Laplacian of the electron density
([?]\textsuperscript{2}\selectlanguage{greek}ρ\selectlanguage{english}) at Cu -- O bond critical points (BCP) using
AIMAll software.\textsuperscript{{[}18{]}} The MOLDRAW
software\textsuperscript{{[}19{]}} was used for geometry manipulation
and visualisation purposes.

MIA is evaluated as the interaction energy

\emph{E}\textsubscript{int} = \emph{E}\textsubscript{complex}
--\emph{E}\textsubscript{Cu(II)} - \emph{E}\textsubscript{Ph} (1)

where \emph{E} \textsubscript{complex} is the DFT energy of
the\textsuperscript{2}{[}Ph\textbf{\ldots{}}
Cu{]}\textsuperscript{2+}complex, \emph{E} \textsubscript{Cu(II)} is the
DFT energy of the Cu\textsuperscript{2+} ion and \emph{E}
\textsubscript{Ph} is the DFT energy of the p-substituted phenol
molecule.

The standard linear regression analysis was used to obtain the
regression parameters a and b of the relation

log (1/\emph{IC} \textsubscript{50}) = a X + b (2)

where log(1/\emph{IC} \textsubscript{\textbf{50}}\textbf{)} are the
experimental toxicity data of Selassie \emph{et al}
.\textsuperscript{{[}2{]}} and X stands for predictor variables under
study. The goodness of fit is evaluated by standard statistical
parameters such as the coefficient of determination R\textsuperscript{2}
or the critical value \selectlanguage{greek}α \selectlanguage{english}of the F-test.

\textbf{3 Results and discussion}

Our study deals with 28 p-substituted phenols of the set of
Selassie\emph{et al.} \textsuperscript{{[}2{]}} despite five to seven of
them with electron withdrawing substituents (-NO\textsubscript{2},
-NH\textsubscript{2}, -CN, -Cl, -Br, -CONH\textsubscript{2}, -CHO,
-NHCOCH\textsubscript{3} -SO\textsubscript{2}NH\textsubscript{2}) were
omitted from their analyses. We suppose that the phenols cannot be
investigated as a whole. Therefore we have classified the whole group
into three datasets as follows (Table 1):

\begin{enumerate}
\tightlist
\item
  Dataset A contains electron donating substituents such as R = H or
  alkyl. The iodine atom can be assigned to this dataset due to its low
  electronegativity as well. Surprisingly, also the phenoxyl substituent
  behaves as the remaining ones of this dataset probably due to
  neutralization of opposite electron withdrawing properties by its
  bonded aromatic ring (resonance effect). Therefore this dataset
  contains 12 molecules.
\item
  Dataset B contains electron withdrawing substituents such as R =
  alkoxyls and hydroxyl, halogens (except I), cyano- , nitro- and amino-
  groups, altogether 12 molecules (some of them were omitted by
  Selassie\emph{et al} .\textsuperscript{{[}2{]}})
\item
  Dataset C contains four molecules (omitted by Selassie \emph{et al.}
  \textsuperscript{{[}2{]}}) with substituents containing C=O or S=O
  bonds which might affect the toxicity by different mechanisms than
  phenols. This dataset is too small to be treated by regression
  analyses.
\end{enumerate}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1. Plot of the relation between p-phenols toxicity,
log(1/\emph{IC} \textsubscript{50}), and Cu-O bond lengths,\emph{d}
\textsubscript{Cu-O}, of data sets A (black squares), B (red circles)
and C (blue triangles). Dashed lines correspond to linear parameters in
Table 2.

Table 2. Regression parameters of Eq. (2) with standard deviations,
coefficients of determination R\textsuperscript{2}, root-mean-squares
(RMS) errors and critical values \selectlanguage{greek}α \selectlanguage{english}of the F-test for various predictor
variables X as well as A and B datasets (see Table 1).\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
X & Data set & a \textsuperscript{a} & b & R\textsuperscript{2} & RMS
error & \selectlanguage{greek}α\selectlanguage{english}\tabularnewline
\midrule
\endhead
\emph{d}\textsubscript{Cu-O} {[}10\textsuperscript{-10} m{]} & A &
-22.2\selectlanguage{ngerman}±2.6 & 47.2\selectlanguage{ngerman}±5.1 & 0.86653 & 0.030 &
6.8\selectlanguage{ngerman}×10\textsuperscript{-6}\tabularnewline
& B & -46.2\selectlanguage{ngerman}±8.8 & 95. \selectlanguage{ngerman}±17. & 0.70541 & 0.13 &
3.8\selectlanguage{ngerman}×10\textsuperscript{-4}\tabularnewline
\emph{Q}\textsubscript{MPA} & A & -20.3\selectlanguage{ngerman}±2.3 & 23.7\selectlanguage{ngerman}±2.2 & 0.87635 & 0.028
& 4.6\selectlanguage{ngerman}×10\textsuperscript{-6}\tabularnewline
& B & -40.7\selectlanguage{ngerman}±6.9 & 44.0\selectlanguage{ngerman}±6.7 & 0.75246 & 0.11 &
1.6\selectlanguage{ngerman}×10\textsuperscript{-4}\tabularnewline
\emph{Q}\textsubscript{NBO} & A & -24.2\selectlanguage{ngerman}±2.4 & 27.6\selectlanguage{ngerman}±2.3 & 0.90003 & 0.023
& 1.6\selectlanguage{ngerman}×10\textsuperscript{-4}\tabularnewline
& B & -38.1\selectlanguage{ngerman}±7.4 & 41.8\selectlanguage{ngerman}±7.3 & 0.69754 & 0.13 &
4.6\selectlanguage{ngerman}×10\textsuperscript{-4}\tabularnewline
Q\textsubscript{QTAIM} & A & -23.1\selectlanguage{ngerman}±2.2 & 25.2\selectlanguage{ngerman}±2.0 & 0.91125 & 0.020 &
8.7\selectlanguage{ngerman}×10\textsuperscript{-7}\tabularnewline
& B & -43.2\selectlanguage{ngerman}±5.0 & 44.2\selectlanguage{ngerman}±4.6 & 0.86900 & 0.057 &
6.2\selectlanguage{ngerman}×10\textsuperscript{-7}\tabularnewline
\selectlanguage{english}[?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ}\selectlanguage{english}\textsubscript{BCP}
{[}e/bohr\textsuperscript{5}{]} & A & 14.3\selectlanguage{ngerman}±1.7 & -3.24\selectlanguage{ngerman}±0.88 & 0.86661 &
0.030 & 6.8\selectlanguage{ngerman}×10\textsuperscript{-6}\tabularnewline
& B & 29.6\selectlanguage{ngerman}±6.0 & -10.2\selectlanguage{ngerman}±3.0 & 0.68103 & 0.14 &
5.8\selectlanguage{ngerman}×10\textsuperscript{-4}\tabularnewline
\emph{E}\textsubscript{int} {[}kJ/mol{]} & A & (-8.86\selectlanguage{ngerman}±0.70)
×10\textsuperscript{-3} & -4.36\selectlanguage{ngerman}±0.68 & 0.93598 & 0.015 &
1.7\selectlanguage{ngerman}×10\textsuperscript{-7}\tabularnewline
& B & (-6.85\selectlanguage{ngerman}±0.81) ×10\textsuperscript{-3} & -2.05\selectlanguage{ngerman}±0.77 & 0.86562 &
0.058 & 7.1\selectlanguage{ngerman}×10\textsuperscript{-6}\tabularnewline
\selectlanguage{greek}\emph{σ}\selectlanguage{english}\textsuperscript{+} & A & -1.98\selectlanguage{ngerman}±0.68 & 3.73\selectlanguage{ngerman}±0.20 & 0.40400 &
0.14 & 1.5\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& B & -0.85\selectlanguage{ngerman}±0.15 & 4.14\selectlanguage{ngerman}±0.11 & 0.74386 & 0.11 &
8.8\selectlanguage{ngerman}×10\textsuperscript{-4}\tabularnewline
log \emph{P} & A & 0.258\selectlanguage{ngerman}±0.064 & 3.29\selectlanguage{ngerman}±0.25 & 0.58097 & 0.095 &
2.4\selectlanguage{ngerman}×10\textsuperscript{-3}\tabularnewline
& B & 0.16\selectlanguage{ngerman}±0.19 & 4.15\selectlanguage{ngerman}±0.41 & 0.02374 & 0.45 &
4.1\selectlanguage{ngerman}×10\textsuperscript{-1}\tabularnewline
\emph{L-H} gap {[}eV{]} & A & 2.11\selectlanguage{ngerman}±0.87 & 23.9\selectlanguage{ngerman}±8.1 & 0.30805 & 0.16 &
3.6\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& B & 2.12\selectlanguage{ngerman}±0.60 & 23.7\selectlanguage{ngerman}±5.5 & 0.50888 & 0.21 &
5.5\selectlanguage{ngerman}×10\textsuperscript{-3}\tabularnewline
\emph{BDE} {[}kcal/mol{]} & A & -0.359\selectlanguage{ngerman}±0.082 & 3.51\selectlanguage{ngerman}±0.18 & 0.61973 &
0.086 & 1.4\selectlanguage{ngerman}×10\textsuperscript{-3}\tabularnewline
& B & -0.138\selectlanguage{ngerman}±0.023 & 3.97\selectlanguage{ngerman}±0.13 & 0.75527 & 0.10 &
1.5\selectlanguage{ngerman}×10\textsuperscript{-4}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{ngerman}

Remarks

\textsuperscript{a}In units reciprocal to X units

Molecular graphs of the the\textsuperscript{2}{[}Ph\textbf{\ldots{}}
Cu{]}\textsuperscript{2+}complexes (see Fig. S1 of Supplementary
information) suggest the Cu-O distance, \emph{d} \textsubscript{Cu-O},
as the most simple predictor variable (Fig. 1, Table S1 of Supplementary
information) which might reflect the strength of the phenolic oxygen
bonding with the interacting cell. The corresponding statistical
parameters of Eq. (2) are fairly good, especially for the dataset A
(Table 2).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2. Plot of the relation between p-phenols toxicity,
log(1/\emph{IC} \textsubscript{50}), and QTAIM charges of Cu atoms of
data sets A (black squares), B (red circles) and C (blue triangles).
Dashed lines correspond to linear parameters in Table 2.

Copper charges in the\textsuperscript{2}{[}Ph\textbf{\ldots{}}
Cu{]}\textsuperscript{2+}complexes (as compared with
original\textsuperscript{2}Cu\textsuperscript{2+} ion charges) are a
measure of the O - Cu electron density transfer (Table S1 in
Supplementary information) and reflect the phenol toxicity (Table 2,
Figs. 2, S2 and S3 in Supplementary information). The QTAIM charges
exhibit better statistical parameters for Eq. (2) than the NBO and MPA
ones, especially for the dataset A (Table 2). Nevertheless, in all cases
their fit is better than for the Cu-O distances above.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3. Plot of the relation between p-phenols toxicity,
log(1/\emph{IC} \textsubscript{50}), and BCP electron density Laplacians
of Cu-O bonds, [?]\textsuperscript{2}\selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{BCP}, of data sets A
(black squares), B (red circles) and C (blue triangles). Dashed lines
correspond to linear parameters in Table 2.

Alternatively, the extent of the O - Cu electron density transfer can be
evaluated in terms of the BCP electron density Laplacian,
[?]\textsuperscript{2}\selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{BCP}, of the Cu -- O bond (Fig. 3,
Tables 2 and S1 in Supplementary information). Their correlation with
the cytotoxicity according to Eq. (2) exhibits a little bit worse
statistical characteristics than in the case of QTAIM charges for both A
and B datasets.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4. Plot of the relation between p-phenols toxicity,
log(1/\emph{IC} \textsubscript{50}), and interaction energies,\emph{E}
\textsubscript{int}, of data sets A (black squares), B (red circles) and
C (blue triangles). Dashed lines correspond to linear parameters in
Table 2.

Finally, the cytotoxicity correlation with the interaction energy data,
E\textsubscript{int}, (Table S1 in Supplementary information) as a
measure of the phenol reactivity\textsuperscript{{[}11{]}} according to
Eq. (2) exhibit the best statistical parameters (Table 2, Fig. 4) for
the dataset A.

There are significant differences between the regression parameters of
the Eq. (2) for both A and B datasets. Except for E\textsubscript{int},
the B dataset ones are nearly doubled. In agreement with worse
statistical parameters for the B dataset, a similar relation holds for
their standard deviations as well. With few exceptions, the B dataset
cytotoxicity values are higher than the A ones for similar predictor
values whereas the C ones are even lower. The rightness of inclusion of
the iodine substituent into the A dataset is confirmed by comparing the
corresponding data evaluated by the Eq. (2) by using its regression
parameters both for A and B datasets (Table S3 of Supplementary
information).

We performed regression analysis for the predictor data of the
Brown-Hammett parameters (\selectlanguage{greek}\emph{σ} \selectlanguage{english}\textsuperscript{+}), the HOMO--LUMO
energy difference (\emph{L--H} gap), the logarithmic n-octanol - water
partition coefficients (log \emph{P} ) and homolytic bond dissociation
energies (\emph{BDE} ) used by Selassie \emph{et al.}
\textsuperscript{{[}2{]}} as well. The obtained results for the
regression parameters of Eq. (2) and related statistical data are
presented in Table 2 and Figs. S4 -- S7 of Supplementary information. In
all cases these variables offer much worse statistical parameters than
our predictors related to a Cu(II) probe. The distribution of A and B
dataset data is more chaotic despite the b parameter of the Eq. (2) for
both datasets is nearly identical.

Finally it can be concluded that the QSAR model based on
quantum-chemical calculations of the Cu(II) coordination ability of
p-substituted phenols offers much better results than classical
treatments.\textsuperscript{{[}2{]}} The predictors based on the O - Cu
electron density transfer, such as copper charges and BCP electron
density Laplacian of the Cu-O bond in
the\textsuperscript{2}{[}Ph\textbf{\ldots{}}
Cu{]}\textsuperscript{2+}complexes, as well as the corresponding
interaction energy are able of a very good toxicity prediction. The
p-substituted phenols with electron withdrawing and electron donating
substituents must be treated separately due to different linear
dependencies of both groups. Nevertheless, there may be more than one
mechanism for various types of toxicity as indicated by the phenols of
the C dataset. Further experimental as well as theoretical studies in
this field are desirable.

\textbf{Declarations of interest}

None.

\textbf{Funding information}

This work was supported by the Slovak Grant Agency VEGA (contracts no.
1/0139/20 and 1/0482/20) and by the Slovak Science and Technology
Assistance Agency (contract no. APVV-19-0087). We thank the HPC center
at the Slovak University of Technology in Bratislava, which is a part of
the Slovak Infrastructure of High Performance Computing (SIVVP Project
No. 26230120002, funded by the European Region Development Funds), for
computing facilities. M.B. thanks the Ministry of Education, Science,
Research and Sport of the Slovak Republic for funding within the scheme
`Excellent research teams'.

\textbf{Appendix. Supplementary data}

\section*{Supplementary data to this article can be found online at
https://}

{\label{supplementary-data-to-this-article-can-be-found-online-at-https}}

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Published online:

Figure captions:

Figure 1. Plot of the relation between p-phenols toxicity,
log(1/\emph{IC} \textsubscript{50}), and Cu-O bond lengths,\emph{d}
\textsubscript{Cu-O}, of data sets A (black squares), B (red circles)
and C (blue triangles). Dashed lines correspond to linear parameters in
Table 2.

Figure 2. Plot of the relation between p-phenols toxicity,
log(1/\emph{IC} \textsubscript{50}), and QTAIM charges of Cu atoms of
data sets A (black squares), B (red circles) and C (blue triangles).
Dashed lines correspond to linear parameters in Table 2.

Figure 3. Plot of the relation between p-phenols toxicity,
log(1/\emph{IC} \textsubscript{50}), and BCP electron density Laplacians
of Cu-O bonds, [?]\textsuperscript{2}\selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{BCP}, of data sets A
(black squares), B (red circles) and C (blue triangles). Dashed lines
correspond to linear parameters in Table 2.

Figure 4. Plot of the relation between p-phenols toxicity,
log(1/\emph{IC} \textsubscript{50}), and interaction energies,\emph{E}
\textsubscript{int}, of data sets A (black squares), B (red circles) and
C (blue triangles). Dashed lines correspond to linear parameters in
Table 2.\selectlanguage{english}
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\textbf{Hosted file}

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\verb`Table2.docx`  available at \url{https://authorea.com/users/468262/articles/561973-dft-studies-of-substituted-phenols-cytotoxicity-i-para-substituted-phenols}

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