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\DOI{10.5802/crchim.314}
\datereceived{2023-12-25}
\daterevised{2024-03-07}
\dateaccepted{2024-04-25}
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\begin{document}

\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{French Network on Solvation (GDR 2035 SolvATE)}
%\def\cdr@specialtitle@french{R\'eseau th\'ematique sur la solvatation (GDR 2035 SolvATE)}
%\makeatother

\CDRsetmeta{articletype}{research-article}

\title{Hydrogen bond interactions of coumarin-153 in molecular
solvents: molecular dynamics and principal component analysis}

\alttitle{Interactions par liaison hydrog\`{e}ne de la coumarine-153
dans des solvants mol\'{e}culaires : dynamique mol\'{e}culaire et
analyse en composantes principales}

\author{\firstname{Kateryna} \lastname{Goloviznina}\CDRorcid{0000-0001-9913-4938}}
\address{Sorbonne Universit\'{e}, CNRS, Physicochimie des
\'{E}lectrolytes et Nanosystemes Interfaciaux, PHENIX, F-75005 Paris, France}

\author{\firstname{Dmytro} \lastname{Dudariev}\CDRorcid{0000-0002-2556-8036}}
\address{Univ. Lille, CNRS, UMR 8516 - LASIRe - Laboratoire Avanc\'{e}
de Spectroscopie pour les Interactions, la R\'{e}activit\'{e} et
l'Environnement, F-59000 Lille, France}
\address{Department of Inorganic Chemistry, V.N. Karazin Kharkiv
National University, Svobody sq. 4, Kharkiv, 61022, Ukarine}

\author{\firstname{Fran\c{c}ois-Alexandre} \lastname{Miannay}\CDRorcid{0000-0003-1131-8287}}
\addressSameAs{2}{Univ. Lille, CNRS, UMR 8516 - LASIRe - Laboratoire Avanc\'{e}
de Spectroscopie pour les Interactions, la R\'{e}activit\'{e} et
l'Environnement, F-59000 Lille, France}

\author{\firstname{Oleg} \lastname{~Kalugin}\CDRorcid{0000-0003-3273-9259}}
\addressSameAs{3}{Department of Inorganic Chemistry, V.N. Karazin Kharkiv
National University, Svobody sq. 4, Kharkiv, 61022, Ukarine}

\author{\firstname{Volodymyr} \lastname{Koverga}}
\address{Department of Chemical Engineering, University of Illinois
Chicago, Chicago, IL, 60608, USA}
\address{Materials Science Division, Argonne National Laboratory,
Lemont, IL, 60439, USA}

\author{\firstname{Toshiyuki} \lastname{Takamuku}\CDRorcid{0000-0002-1975-5476}}
\address{Department of Chemistry and Applied Chemistry, Faculty of
Science and Engineering, Saga University, Honjo-machi, Saga 840-8502, Japan}

\author{\firstname{Raffaele} \lastname{Vitale}\CDRorcid{0000-0002-7497-1673}}
\addressSameAs{1}{Sorbonne Universit\'{e}, CNRS, Physicochimie des
\'{E}lectrolytes et Nanosystemes Interfaciaux, PHENIX, F-75005 Paris, France}

\author{\firstname{Abdenacer} \lastname{Idrissi}\CDRorcid{0000-0002-6924-6434}\IsCorresp}
\addressSameAs{2}{Univ. Lille, CNRS, UMR 8516 - LASIRe - Laboratoire Avanc\'{e}
de Spectroscopie pour les Interactions, la R\'{e}activit\'{e} et
l'Environnement, F-59000 Lille, France}
\email[A. Idrissi]{nacer.idrissi@univ-lille.fr}

\shortrunauthors

\thanks{French National Agency for Research (ANR-19-CE05-0009-01)}

\keywords{\kwd{Coumarin-153}
\kwd{Solvation}
\kwd{Molecular dynamics}
\kwd{Photophysics}
\kwd{Hydrogen bond interactions}
\kwd{Nearest neighbor radial distribution}
\kwd{Principal component analysis (PCA)}}

\altkeywords{\kwd{Coumarine-153}
\kwd{Solvatation}
\kwd{Dynamique mol\'{e}culaire}
\kwd{Photophysique}
\kwd{Interactions par liaisons hydrog\`{e}ne}
\kwd{Fonction de distribution radiale de plus proches voisins}
\kwd{Analyse en composantes principales}}

\begin{abstract}
Hydrogen bond interactions significantly affect the coumarin-153's
(C153) photophysics, including its ability
to act as a donor of weak hydrogen bonds via its 14 C--H
bonds and as an acceptor via its O atoms in the ester and the carbonyl
groups, as well as via its F atom in the trifluoromethyl group. The
distances between the donor atoms and their closest electronegative
neighbor atom served as descriptors of the hydrogen bond interactions.
These descriptors were calculated using the nearest neighbor radial
distribution approach. Principal component analysis (PCA) was then
performed on these distances to compare the unique structures
surrounding donor bond atoms and identify patterns in the interactions
between C153 and various solvent, such as acetonitrile, butyrolactone,
propylene carbonate, methanol, ethanol, propanol, and butanol.

Our findings demonstrate that, when C153 acts as a hydrogen bond donor,
the interaction behavior of the H atoms that are close to the N atom
and that of the H atom close to the trifluoromethyl F atom of C153 is
substantially different. More specifically, the former H atoms interact
preferentially with the hydroxyl oxygen atom of the solvent while the
H$_{10}$ atom interacts preferentially with the ester oxygen
atoms of propylene carbonate. 

Moreover, when C153 behaves as a hydrogen bond acceptor, PCA shows that
the carbonyl O atom of C153 interacts preferentially with the hydroxyl
H atom of the alcohols, while the F atoms mostly interact with the
other ethyl and methyl H atoms of the solvent.
\end{abstract}

\begin{altabstract}
Les interactions par liaison hydrog\`{e}ne affectent significativement
la photophysique de la coumarine-153 (C153), y compris sa capacit\'{e}
\`{a} agir en tant que donneur de liaisons hydrog\`{e}ne faibles via
ses 14 liaisons C--H et en tant qu'accepteur de liaisons
hydrog\`{e}ne via ses atomes O dans les groupes ester et carbonyle,
ainsi que via son atome F dans le groupe trifluorom\'{e}thyle. Les
distances entre les atomes donneurs et leur atome voisin
\'{e}lectron\'{e}gatif le plus proche ont servi de descripteurs des
interactions par liaison hydrog\`{e}ne. Ces descripteurs ont
\'{e}t\'{e} calcul\'{e}s en utilisant l'approche de distribution
radiale des voisins les plus proches. Une analyse en composantes
principales (ACP) a ensuite \'{e}t\'{e} r\'{e}alis\'{e}e sur ces
distances pour comparer les structures uniques entourant les atomes de
liaison donneurs et identifier des motifs dans les interactions entre
C153 et divers solvants, tels que l'ac\'{e}tonitrile, la butyrolactone,
le carbonate de propyl\`{e}ne, le m\'{e}thanol, l'\'{e}thanol, le
propanol et le butanol. Nos r\'{e}sultats d\'{e}montrent que, lorsque
C153 agit en tant que donneur de liaison hydrog\`{e}ne, le comportement
d'interaction des atomes H proches de l'atome N et de l'atome H proche
de l'atome F du groupement trifluorom\'{e}thyle du C153 est
substantiellement diff\'{e}rent entre l'\'{e}tat fondamentale et
l'\'{e}tat excit\'{e}. Plus pr\'{e}cis\'{e}ment, les atomes H proches
de N, interagissent de pr\'{e}f\'{e}rence avec l'atome d'oxyg\`{e}ne du
groupement hydroxyle du solvant tandis que l'atome H proche du
groupement trifluorom\'{e}thyle, interagit de pr\'{e}f\'{e}rence avec
les atomes d'oxyg\`{e}ne ester du carbonate de propyl\`{e}ne. De plus,
lorsque C153 agit en tant qu'accepteur de liaison hydrog\`{e}ne, l'ACP
montre que l'atome O du groupement carbonyle de C153 interagit de
pr\'{e}f\'{e}rence avec l'atome H du groupement hydroxyle des alcools,
tandis que les atomes F interagissent principalement avec les autres
atomes H \'{e}thyle et m\'{e}thyle du solvant.
\end{altabstract}

\maketitle

\twocolumngrid

\end{noXML}

\section{Introduction}\label{sec1}

Solvent environment and, particularly, the presence of hydrogen
bonds-donating or -accepting interactions as well as the occurrence
of stacking and dipole--dipole interactions are expected to have a
significant impact on the photophysics of fluorophores like coumarin
153 (C153)~\cite{1,2,4,5}. For this reason, the effect of the solvent
on the photophysics of C153 has been explored in a range of solvents,
including alcohols~\cite{6,7,8},  acetonitrile~\cite{2,9,10,11},
propylene carbonate~\cite{7}, dimethyl sulfoxide, formamide,
nitromethane, acetone~\cite{2}, methanol, ethanol and fluorinated
ethanol solvents~\cite{12}, in mixtures such as
dioxane--water~\cite{13}, acetonitrile--benzene~\cite{14},
hexane--propionitrile~\cite{13}, tert-butyl alcohol--water and
trimethylamine N-oxide--water~\cite{15}, acetonitrile--propylene
carbonate~\cite{16} dimethyl sulfoxide--glycerol~\cite{17,18},
toluene--acetonitrile~\cite{19}, and cyclohexane--phenol
solvent~\cite{20}. These studies were extended to aqueous and
non-aqueous reverse micelles~\cite{21}, Triton X-100-cyclohexane
microemulsions~\cite{22}, and also to various ionic liquids, such as
1-butyl-3-methylimidazolium hexafluorophosphate~\cite{23},
1-hexyl-3-methylimidazolium hexafluorophosphate~\cite{9},
1-butyl-3-methylimidazolium tetrafluoroborate~\cite{11},
hydroxylfunctionalized ionic liquids~\cite{24}, ionic liquids
containing fluoroalkylphosphate~\cite{25} and tetraalkylammonium
bromide~\cite{26}, 1-dodecyl-3-methylimidazolium
bis(trifluoromethylsulfonyl)amide with benzene, chloroform, propylene
carbonate solvents~\cite{35}, and deep eutectic solvents such as
choline chloride~\cite{27} and acetamide--urea~\cite{28}. One should
notice that the properties of the mixtures are modulated through the
change of the mixture composition. The aforementioned works showed that
the strength and nature of the hydrogen bonds can influence the
electronic transitions of C153, resulting in either fluorescence
quenching or enhancement. Indeed, the efficiency of fluorescence,
expressed in terms of quantum yield, can be affected by hydrogen bond
interactions as they may promote non-radiative decay processes and
reduce the quantum yield. It is therefore \mbox{essential} to take into
account the specific molecular structure of C153 (namely, the donor or
acceptor nature of its atoms) and the characteristics of the solvent in
experimental studies to understand how hydrogen bond interactions
influence C153 photophysics in a given environment. This can be
illustrated through the following examples. First, Maronceli
et~al.\ showed that the presence of hydrogen bonds between C153 and
alcohols results (beyond the effects of solvent polarity) in a small
additional shift in both the absorption and emission spectra of C153.
However, when examining the solvation dynamics of C153 in
N-methylpropionamide, a solvent with hydrogen bond donor ability,
distinct differences in dynamics were observed compared to the case
when alcohol solvents were considered~\cite{7}. On the other hand, in
propylene carbonate, a non-associated solvent lacking hydrogen bond
donor capability, the behavior of the solvation function closely
resembles that observed in alcohols. Other studies, instead, showed
that coumarin 102 and C153 have different photophysical behaviors in
the same solvent and that these different behaviors are due to their
methyl CH$_{3}$ and trifluoryl CF$_{3}$ substituents,
respectively~\cite{29,31}. Computer molecular modeling could
corroborate these experimental results, since simulation approaches can
provide deep atomistic insights into the local structure of the solvent
around the donor and acceptor regions of C153, insights that cannot be
obtained by any kind of experimental strategy. As a matter of fact, the
microscopic environment surrounding the C153 molecule was also
investigated through quantum-chemical calculations and molecular
dynamics (MD) simulations~\cite{12,33}, which permitted to analyze
interatomic and intermolecular radial distribution functions
(RDF)---considering either the center-of-masses or specific atoms like
O, F, N, and C---without explicitly accounting for the hydrogen atoms
of C153 and the solvent molecules. Notably, these investigations were
conducted for both the ground state (GS) and excited state (ES) of
C153. Based on molecular dynamics simulations of C153 in 1,4-dioxane,
Cinacchi et~al.\ \cite{34} suggested that changes in the solvation shell
around the GS and ES of C153 are primarily due to alterations in the
orientation of the solvent molecules. In other MD \mbox{studies,} the local
structure around the hydrogen atoms of C153 has been 
explored~\cite{35,33}. It has been observed that C153 is solvated by
alcohols or water through hydrogen bonds, specifically between the
hydroxyl OH group of the solvents and the carbonyl oxygen atom of C153.
Furthermore, MD simulations of C153 in dimethyl sulfoxide (DMSO)--water
mixtures have shown that the hydration structures in GS and ES differ
from those in pure water due to the significant influence of DMSO
molecules~\cite{27}. This was attributed to the formation of a hydrogen
bond network between DMSO and water molecules upon mixing. In the case
of imidazolium ionic liquids (ILs), MD studies of C153 in
1-ethyl-3-methylimidazolium tetrafluoroborate (EmimBF$_4$)~\cite{23}
demonstrated a preferential solvation of C153 by the Emim$^{+}$ cation.
In a study by  Barman~\cite{61}, MD simulations, quantum-chemical
calculations and infrared (IR) spectroscopy were combined to
investigate the formation of hydrogen bonds between aniline and C153.
It was concluded that the carbonyl group of C153 serves as a primary
hydrogen bond-accepting site and shows a higher bond strength in the
ES. Furthermore, the formation of a C${=}$O$\cdots$H--N hydrogen bond was
confirmed by the observation of the IR absorption band at
1736~cm$^{-1}$ in the IR spectrum of C153 in the aniline--cyclohexane
mixture, shifted compared to the stretching band of the C${=}$O group
(1748~cm$^{-1}$) which is commonly measured in pure cyclohexane.
Similar experiments were conducted for the coumarin C102--aniline
system~\cite{36}, and the formation of the stronger hydrogen bond for
C153 in the ES was also observed in methanol solutions~\cite{37}.
Furthermore, the solvation of C153 in ionic 1-butyl-3-methylimidazolium
tetrafluoroborate--propylene carbonate mixtures was investigated by
coupling MD simulations, time-correlated photon counting and
fluorescence upconversion techniques. It was established that the
solvation of C153 is determined by its interaction with the ions at
high IL content, and with the solvent molecules at a IL molar fraction
lower than 0.2~\cite{38}. Xu et~al.\ \cite{39} conducted B3LYP/TZVP
calculations to thoroughly explore the formation of hydrogen bonds
between C153 and ethanol in both GS and ES. They observed that the
hydrogen bond C${=}$O$\cdots$H--O is strengthened in the electronic ES,
i.e., the bond length decreases from 1.867~\AA{}~in GS to
1.813~\AA{}~in ES, as also shown by Han and coworkers \cite{40}, This
observation suggests that the hydrogen bond O$\cdots$H--O in the
C153--EtOH complex in the ES must be strengthened. This suggestion was
also substantiated by IR experiments conducted in this 
study~\cite{40}.\looseness=-1



In order to retrieve essential information about hydrogen bond
interactions, geometric data~\cite{41,42},\break spectroscopic
data~\cite{43,44,45,46,47,48,49}, physical chemical data~\cite{50}, and
MD simulation data~\cite{51,52,53,54,55} have been usually analyzed by
means of principal components analysis (PCA). PCA can provide a
comprehensive overview of hydrogen bond interactions offering insights
into dominant spectral features, their variations, global trends, and
correlations, and aiding in the identification and understanding of
hydrogen bond-related patterns in the collected data.

This article provides a thorough study of the hydrogen bond
interactions between C153 and various solvents, including methanol,
ethanol, 1-propanol, 1-butanol, acetonitrile,
${\upgamma}$-butyrolactone, and propylene carbonate. These solvents
exhibit distinct properties such as dipole moment, viscosity,
dielectric constant, density, and the capacity to form hydrogen bonds,
as well as stacking interactions and dipole--dipole interactions. In
this study, we combine MD simulations with PCA. Atomistic simulations
provide the coordinates of atoms that are involved in the hydrogen bond
interactions. The generic hydrogen bond between a donor D--H and
acceptor atom A is described by the configuration given in
Figure~\ref{fig1}. 

\begin{figure}
\vspace*{-2pt}
\includegraphics{fig01}
\vspace*{-2pt}
\caption{\fontsize{9.8}{12}\selectfont\label{fig1}Definition
of the distances describing the
hydrogen bond interactions between a generic donor D--H and a generic
electronegative acceptor A. The distances
$d_{\mathrm{H}\ldots\mathrm{A}}$ and  $d_{\mathrm{D}\ldots \mathrm{A}}$
are calculated using molecular dynamic simulations relying on the
nearest neighbor \mbox{approach}.}
\vspace*{-2pt}
\end{figure}

\begin{figure*}
\includegraphics{fig02}
\vspace*{-1pt}
\caption{\label{fig2}Atomic labels for Coumarin-153 (a) and the
investigated solvents ((b)~methanol, (c)~ethanol, (d)~1-propanol, 
(e)~1-butanol, (f)~${\upgamma}$-butyrolactone, (g)~propylene
carbonate, (h)~acetonitrile).}
\vspace*{-1pt}
\end{figure*}

The D--H and A moieties may belong to any of the mixture's
constituents. The intramolecular distance $d_{\mathrm{D}\ndash\mathrm{H}}$
is assumed to remain constant in our simulations, while
$d_{\mathrm{H}\ldots \mathrm{A}}$ and $d_{\mathrm{D}\ldots \mathrm{A}}$
are determined as the average distances of the nearest neighbor {radial}
{distributions} of the first neighbor \mbox{electronegative} atom A with respect
to the H and D, respectively. It is worth noting that once 
$d_{\mathrm{D}\ndash\mathrm{H}}$,
$d_{\mathrm{H}\ldots \mathrm{A}}$ and $d_{\mathrm{D}\ldots \mathrm{A}}$
are determined, the angle ${\alpha}$ can be calculated using the law
of cosines (see Figure~\ref{fig1}).

The average values of distances $d_{\mathrm{H}\ldots \mathrm{A}}$ and
$d_{\mathrm{D}\ldots \mathrm{A}}$ were calculated for both GS and ES of
C153 and serve as indicators of the strength of the hydrogen bond
interactions between C153 and the solvent molecules. Importantly, the
GS and ES of C153 were simulated by considering their corresponding
charge distributions, which were determined through quantum\break
{calculations} (see Figure~\ref{fig3}).\ These distances 
were calculated for cases where C153
acted as either a hydrogen bond donor or acceptor. In the former
scenario, the 14~C--H bonds of C153 were considered, and these
distances were calculated from electronegative atoms such as the
N$_{1}$ atom of acetonitrile, the O$_{1}$  atoms of the alcohol
solvents, and the O$_{1}$, O$_2$, and O$_{3}$ of the other solvents. In
the latter case, these distances were calculated between each of the 39
C--H bonds of the solvent molecules and the 6 electronegative atoms of
C153, i.e., the N$_{1}$, O$_{1\ndash2}$ and F$_{1\ndash3}$ {atoms (see
Figure~\ref{fig2} for more details on the numbering of the atoms).
\looseness=-1

\begin{figure}
\includegraphics{fig03}
\vspace*{-2pt}
\caption{\label{fig3}Charge values associated to the atoms of C153 in
the ground state and excited state as determined from quantum-chemical
calculations performed with B3LYP/6-311+G(d).}
\end{figure}

PCA was then applied to analyze the two distance matrices obtained in
the two aforementioned cases. The first matrix contained 10 rows
corresponding to the 10 electronegative atoms of the different solvents
under study and 28 columns corresponding to the 14~C--H bonds of C153
in both GS and ES. The second matrix contained 43 rows corresponding to
the 39~C--H and the 4 O--H bonds of the different solvents under study
and 12 columns corresponding to the 6 electronegative atoms of C153 in
both GS and ES. PCA helps in understanding the structural patterns
encoded by the investigated data and extracting essential information
regarding the nature of the hydrogen bond interactions as captured by
the calculated distance values. The questions we would like to answer
in this paper are: When C153 is acting as a hydrogen bond donor, are
all its H atoms equivalent or do some of them exhibit a particular
behavior? Is there any difference among the acceptor atoms of the
solvents? What happens to the hydrogen atoms that are close to the
electronegative atoms of C153? Is there a difference in the behavior of
the H atoms of the solvents depending on their respective location
(e.g., close to or far from the solvent electronegative atoms)? \looseness=-1

The paper is organized as follows: the second section details the MD
simulation procedure and the calculation of the distance matrices which
were used to investigate the hydrogen bond interactions of C153 in the
selected solvents. In the third section, the results of this study are
discussed. The fourth section provides conclusions and future
perspectives.

\section{Methodology}\label{sec2}


A single C153 molecule was immersed into pure solvents-acetonitrile
(AN), ${\upgamma}$-butyrolactone (GBL), propylene carbonate (PC),
methanol (MeOH), ethanol (EtOH), 1-propanol (PrOH), and 1-butanol
(BuOH). Both solvent and solute molecules were modeled as
non-polarizable, rigid bodies containing a collection of interaction
sites. All-atom models were used for the solvents and the solute.
Initial configuration and force field files were prepared using 
PACKMOL~[86] and DL\_FIELD (version 3.3), respectively~\cite{56}, and the
simulations were carried out in DL\_POLY (version 4.07)~\cite{57}.
These simulations were performed at constant values of the number of
molecules, $N$, the pressure $P$, and the \mbox{temperature} $T$ on systems
containing 1 molecule of solute and 863 molecules of solvents, placed
in a cubic box with periodic boundary conditions at an average
temperature of 298 K and pressure 1 atm. The NPT ensemble was
maintained using a Berendsen thermobarostat, with a relaxation time of
0.1 and 0.2~ps for the thermostat and the barostat, respectively. The
Lennard-Jones forces were cut off at 15~\AA{}~and long-range Coulomb
interactions were treated using the Ewald sum method. The equations of
motion were solved using combined SHAKE and velocity algorithms. The
equilibration of the systems as well as the production of the HISTORY
file for further analysis were performed with a time step of 0.0005 ps
and a total number of steps equal to 1,000,000. The configurations of
the system were recorded in the HISTORY file every 10 steps, which
produced 100,000 configurations that were treated by TRAVIS (version
17/08/12)~\cite{58}. This permitted better statistics and a noise
level decrease for the radial distribution \mbox{functions}
calculated between
a single C153 molecule and the solvents.

\begin{figure*}
{\vspace*{-3pt}}
\includegraphics{fig04}
\caption{\label{fig4}Raw $d$ values obtained through molecular dynamics
simulations when considering C153 as a hydrogen bond donor (left) or
acceptor (right). The numbering of atoms is given in
Figure~\ref{fig2}.}
{\vspace*{-3pt}}
\end{figure*}

All the calculations were performed in both GS and ES of C153. The
charges of the equilibrated system in GS were switched to that of the
ES (without changes in the C153 geometry) and the system was left to
evolve under the new solute-solvent interactions for 1,000,000 steps
with a time step of 0.0005 ps. The geometry of the molecule did not
undergo any change. 

We used the force field developed by Cinacchi for C153. The atoms'
numbering is given in Figure~\ref{fig2}~\cite{34}.

Quantum-chemical calculations were performed with the B3LYP/6-311+G(d)
level of theory using Gaussian09W [91] to obtain the atom positions as
well as the Mulliken atomic charges for GS and ES of C153~\cite{43}.
The values of these charges are displayed in Figure~\ref{fig1}. The
OPLS2005 force field was used for alcohols~\cite{59}, while the force
field proposed by Koverga was used for propylene carbonate (PC),
${\upgamma}$-butyrolactone (GBL), and acetonitrile (AN)~\cite{60}.

PCA [96] was then used to get insights into the solvation structure of
C153 in GS and ES. Indeed, for each possible hydrogen bond
D--H}$\cdots$A, the \mbox{nearest} neighbor radial distribution of the
electronegative atom of a given compound around either the H or D atoms
of the donor compound was calculated. Based on this distribution, the
average interatomic distances 
$d_{\mathrm{H}\ldots \mathrm{A}}$ and $d_{\mathrm{D}\ldots \mathrm{A}}$
were computed and merged for the sake of simplicity in a unique
distance metric $d$ as follows: 
{\begin{equation*}
d_{\mathrm{D}\ldots \mathrm{A}}=\sqrt{{d}_{\mathrm{D}-\mathrm{A}}^{2}+
{d}_{\mathrm{H}\ldots \mathrm{A}}^{2}} 
\end{equation*}}\unskip

The resulting distance values were finally gathered into two different
data matrices, one containing the $d$ values estimated when C153 was
assumed to act as a donor of hydrogen bonds and the other when C153 was
assumed to act as a hydrogen bond acceptor. The first matrix contains
10 rows corresponding to the 10 electronegative atoms of the different
solvents under study and 28 columns corresponding to the 14 C--H bonds
of C153 in both GS and ES. Each one of its elements represents the
distance between a given electronegative atom and one of the 28 C--H
bonds of C153. The second matrix contained 43 rows corresponding to the
39 C--H and the 4 O--H bonds of the different solvents under study and
12 columns corresponding to the 6 electronegative atoms of C153 in both
GS and ES. Each one of its elements represents the distance between one
of the 43 solvent bonds and a given electronegative atom of C153. Both
distance matrices were double-centered and finally subjected to PCA by
means of in-house-developed Matlab routines. Raw data are displayed in
Figure~\ref{fig4}.

\begin{figure*}
\includegraphics{fig05}
\caption{\label{fig5}First/second (left) and third/fourth (right)
principal component biplots resulting from the PCA decomposition of the
distance matrix obtained when considering C153 as a hydrogen bond donor
in both its ground and excited states. Blue squares refer to the
solvent's electronegative atoms (acceptors), while red diamonds refer
to C153's hydrogen atoms (donors).}
\end{figure*}

\section{Results}\label{sec3} 

\subsection{Coumarin-153 as hydrogen bond donor}\label{sec31} 

Figure~\ref{fig5} displays the first/second and the third/{\ubreak}fourth
principal component biplots resulting from the PCA decomposition of the
distance matrix obtained in the case C153 acts as hydrogen bond
donor\footnote{In this case, the first four principal components
account for approximately 90\% of the total data variation.}. PC1
highlights a difference in the interacting trend of the H$_{1}$  and
H$_2$ atoms located near the nitrogen atom of the quinolizidine
heterobicyclic group of C153 with respect to the H$_{10}$ atom that is
close to the trifluoromethyl group of C153. The former seems to
interact preferentially with the hydroxyl O$_{1}$  atom of BuOH, EtOH,
and PrOH and be located relatively far from the O atoms (O$_{1}$  and
O$_2$) of the PC. The latter exhibits the opposite behavior. This is
corroborated by the nearest neighbor distributions represented in
Figure~\ref{fig6} and calculated using the following configurations:
C$_{14}$--H$_{10}\cdots$A and C$_{8}$--H$_2\cdots$A (A $=$ O$_{1}$  or
O$_2$ of PC or O$_{1}$  of BuOH), respectively.

\begin{figure*}
\includegraphics{fig06}
\caption{\label{fig6}Radial distribution of the nearest neighbor for
the atomic couples (i) O$_{1}$ of BuOH/H$_{10}$ of C153 (left black),
(ii) O$_{1}$ of PC/H$_{10}$ of C153 (left red), (iii) O$_{1}$ of
BuOH/H$_{2}$  of C153 (right black) and (iv) O$_{1}$ of PC/H$_{2}$ of C153.}
{\vspace*{2pt}}
\end{figure*}

\begin{figure*}
\includegraphics{fig07}
\caption{\label{fig7}Radial distribution of the nearest neighbor for
the atomic couples (i) O$_{1}$ of PC/H$_{3}$ of C153 in its ground
state (GS) (left black), (ii) O$_{1}$ of PC/H$_4$ of C153 in GS (left
red), (iii) O$_{1}$ of PC/H$_{3}$ of C153 in its excited state (ES)
(left green), (iv) O$_{1}$ of PC/H$_4$ of C153 in ES (left blue), (v)
O$_{2}$ of PC/H$_{3}$ of C153 in GS (right black), (vi) O$_{2}$ of 
PC/H$_4$ of C153 in GS (right red), (vii) O$_{2}$ of PC/H$_{3}$ of C153
in ES (right green) and (viii) O$_{2}$ of PC/H$_4$ of C153 in ES
(right blue).}
\end{figure*}

Interestingly, PC2 suggests that the distances between the H$_{3}$ and
H$_4$ atoms of C153 to the O$_{1}$ atom of PC are shortened when C153
goes from GS to ES. The opposite occurs when considering the distances
of these H atoms to the O$_{2}$ atom of PC. This is in good agreement
with the changes observed for the nearest neighbor radial distributions
concerning these H atoms and the O$_{1}$ and O$_{2}$ of PC (see
Figure~\ref{fig7}). Figure~\ref{fig7} left highlights, in fact, the
\mbox{emergence} of a \mbox{short-distance} contribution that reduces the average
distance between H$_{3}$ and H$_{4}$ to the O$_{1}$ of PC. Conversely,
from Figure~\ref{fig7} right, it is evident that a long-distance
contribution makes the average distance between H$_{3}$ and H$_{4}$ to
the O$_{2}$ of PC increase. It is interesting to notice that the same
conclusion cannot be drawn for the H$_{1}$ and H$_{2}$ atoms of C153
(their projection coordinates remain positive along PC2 when C153 goes
from GS to ES). This suggests that the distance
H$_{1}{\cdots}$O$_{1}$, H$_{1}{\cdots}$O$_{2}$, 
H$_{2}{\cdots}$O$_{1}$ and H$_{2}{\cdots}$O$_{2}$  do not vary as
much as for H$_{3}$ and H$_4$ when C153 goes from GS to ES (see also
Figure~\ref{fig8}).


Finally, PC3 highlights a difference in the interacting behavior of the
H$_{5}$ atom of C153 in ES and the H$_{14}$ atom of C153 in GS. It
seems that H$_{5}$ interacts \mbox{preferentially} with the O atom of BuOH and
the O$_{2}$ atom of PC and is located relatively far from the O atom of
PrOH and the O$_{1}$ atom of PC. An opposite interaction trend is
instead observed for H$_{14}$. 

It is also interesting to notice that PC4 points out a difference in
the interacting behavior of the H$_{7}$ atom when C153 goes from GS to
ES. When C153 is in GS, H$_{7}$ seems to be located quite far from the
O of PrOH. In contrast, this distance seems to significantly decrease
when C153 is in ES. Additionally, the PC3--PC4 biplot suggests that the
interacting behavior of the atoms O$_{3}$ in PC and O$_{2}$ in GBL
might exhibit similarities.



\begin{figure*}
\includegraphics{fig08}
\caption{\label{fig8}Radial distribution of the nearest neighbor for
the atomic couples (i) O$_{1}$ of PC/H$_{1}$ of C153 in its ground
state (GS) (left black), (ii) O$_{1}$ of PC/H$_{2}$ of C153 in GS (left
red), (iii) O$_{1}$ of PC/H$_{1}$ of C153 in its excited state (ES)
(left green), (iv) O$_{1}$ of PC/H$_{2}$ of C153 in ES (left blue), (v)
O$_{2}$ of PC/H$_{1}$ of C153 in GS (right black), (vi) O$_{2}$ of
PC/H$_{2}$ of C153 in GS (right red), (vii) O$_{2}$ of PC/H$_{1}$ of
C153 in ES (right green) and (viii) O$_{2}$ of PC/H$_{2}$ of C153 in ES
(right blue).}
\end{figure*}

\begin{figure}
\includegraphics{fig09}
\caption{\label{fig9}First/second component biplot resulting from the
PCA decomposition of the distance matrix obtained when considering C153
as a hydrogen bond acceptor in both its ground and excited states. Blue
squares refer to the solvent's hydrogen atoms (donors), while red
diamonds refer to C153's electronegative atoms (acceptors).}
\end{figure}

\subsection{Coumarin-153 as hydrogen bond acceptor}\label{sec32} 

Figure~\ref{fig9} displays the first/second principal component biplot
resulting from the PCA decomposition of the distance matrix obtained in
the case C153 acts as a hydrogen bond acceptor\footnote{In this case,
the first two principal components account for approximately 86\% of
the total data variation.}. PC1 highlights a difference in the
interacting trend of the carboxyl O$_2$ atom of C153 with respect to
the F atoms of the trifluoromethyl group of C153 in both GS and ES. The
O$_2$ atom, in fact, seems to interact preferentially with the H$_{1}$
atoms of the hydroxyl groups of the alcohol solvents from which the
F$_{1-3}$ atoms appear relatively far. The latter, on the other hand,
were found to generate preferential interactions with the terminal
methyl or ethyl groups of some of the investigated solvents.
Furthermore, PC1 also suggests that, overall, the distance between the
N$_{1}$  atom of C153 and the terminal H atoms of some of the
investigated solvents (e.g., PrOH and BuOH) increases when C153 goes
from GS to ES. This is clearly corroborated by the nearest neighbor
distributions displayed in Figure~\ref{fig10}.

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig10}
\caption{\label{fig10}Radial distribution of the nearest neighbor for
the atomic couples (i) O$_{2}$ of C153 in its ground state (GS) and
excited state (ES)/H$_{1}$ of EtOH (left black), (ii) F$_{1}$ of C153 in
GS/ES/H$_{1}$ of EtOH (left red), (iii) O$_{2}$ of C153 in GS/ES/H$_{5}$
of EtOH (left green), (iv) F$_{1}$ of C153 in GS/ES/H$_{5}$ of EtOH
(left blue), (v) N$_{1}$ of C153 in GS/H$_{6}$ of BuOH (right
black), (vi) N$_{1}$ of C153 in GS/H$_{8}$ of BuOH (right
red), (vii) N$_{1}$ of C153 in ES/H$_{6}$ of BuOH (right
green) and (viii) N$_{1}$ of C153 in ES/H$_{8}$ of BuOH
(right blue).}
{\vspace*{4pt}}
\end{figure*}

\begin{figure*}
\includegraphics{fig11}
\caption{\label{fig11}Graphical representation of the two distance
values characteristics of the hydrogen-bonding interaction between the
carbonyl O$_2$ atom of C153 and the hydroxyl H$_{1}$  atom of alcohols
for the five nearest neighbors in the ground (a) and excited state (b)
of C153. The line corresponding to
${\alpha}=180$\textdegree\ reflects a  linear
O$_{1}$--H$_{1}\cdots$O$_{2}$ configuration (i.e.,
$d_{\mathrm{O}_{2}\ldots\mathrm{O}_{1}}=
d_{\mathrm{O}_{2}\ldots \mathrm{H}_{1}}+
d_{\mathrm{O}_{1}}$--${\mathrm{H}_{1}}$), while the line
corresponding to ${\alpha}= 90$\textdegree\ reflects a bent
O$_{1}$--H$_{1}\cdots$O$_2$ configuration (i.e.,
$d_{\mathrm{O}_{2}\ldots \mathrm{O}_{1}}=
\sqrt{d_{\mathrm{O}_{2}\ldots \mathrm{H}_{1}}^{2}+
{d}_{\mathrm{O}_{1}-\mathrm{H}_{1}}^{2}}$).}
{\vspace*{2pt}}
\end{figure*}

The following paragraphs will focus on the hydrogen-bonding
interactions involving O$_2$ of C153 and H$_{1}$  of the hydroxyl
group of the alcohol solvent on the one hand and H$_{1}$  of the PC and
GBL solvents on the other hand. We then calculated the values of the
distances $d_{\mathrm{H}\ldots \mathrm{A}}$ and 
$d_{\mathrm{D}\ldots \mathrm{A}}$ describing their
interactions. More precisely, we calculated these distances for the
fifth neighbors. These distances were compared to those representative
of two extreme configurations of D--H corresponding to linear and bent
geometries. In the former, angle $\alpha$ is equal to
180\textdegree, which implies 
$d_{\mathrm{D}\ldots \mathrm{A}}=
d_{\mathrm{D}-\mathrm{H}}+d_{\mathrm{H}\ldots \mathrm{A}}$.
This corresponds to a strong interaction. In the latter, $\alpha $
is equal to 90\textdegree\ implying $d_{\mathrm{D}\ldots
\mathrm{A}}=\sqrt{{d}_{\mathrm{D}-\mathrm{A}}^{2}+{d}_{\mathrm{H}\ldots
\mathrm{A}}^{2}}$. This corresponds to a weak interaction.
Figure~\ref{fig11} shows that for all the alcohol solvents, the values
of the first two neighbor distances are similar to those typical of a
linear geometry of the O$_{1}$--H$_{1}\cdots$O$_2$. In the ES, this
similarity is even more pronounced, which indicates a general
reinforcement of the interactions between the solvents and C153. This
is in accordance with the findings of Cerezo et~al.\ \cite{61}.

\begin{figure*}
\includegraphics{fig12}
\caption{\label{fig12}Graphical representation of the two distance
values characteristics of the hydrogen-bonding interaction between the
carbonyl O$_2$ atom of C153 and the H$_{1}$  atom of propylene
carbonate, ${\upgamma}$-butyrolactone, and acetonitrile for the five
nearest neighbors in the ground (a) and excited state (b) of C153. The
line corresponding to ${\alpha}= 180$\textdegree\ reflects a linear
C--H$_{1}\cdots$O$_2$ configuration (i.e., $d_{{\mathrm{O}_{2}}\ldots
{\mathrm{O}_{1}}}=d_{{\mathrm{O}_{2}}\ldots
{\mathrm{H}_{1}}}+d_{{\mathrm{O}_{1}}-{\mathrm{H}_{1}}}$), while the
line corresponding to ${\alpha}= 90$\textdegree\ reflects a bent
C--H$_{1}\cdots$O$_{2}$ configuration (i.e., $d_{{\mathrm{O}_{2}}\ldots
{\mathrm{O}_{1}}}=\sqrt{{d}_{\mathrm{O}_{2}\ldots
\mathrm{H}_{1}}^{2}+{d}_{\mathrm{O}_{1}-\mathrm{H}_{1}}^{2}}$).}
\end{figure*}

Conversely, regarding AN, GBL, and PC (see Figure~\ref{fig12}), the
calculated distances are very close to those characteristic of a bent
geometry which emphasizes the occurrence of weak interactions between
C153 and these solvents. Notice that when C153 is in ES, these
distances do not vary and remain similar to those typical of a bent
geometry.

\section{Conclusions}\label{sec4}

The aim of this work was to study the hydrogen bond interactions of
C153 in various solvents, including alcohols, acetonitrile,
${\upgamma}$-butyrolactone, and propylene carbonate. To do this and
highlight the existence of similarity patterns in the interacting
behavior of donor and acceptor moieties, we combined MD simulations and
PCA. Hydrogen bonds were here described by the distances between donor
and acceptor atoms. These distance values were calculated using the
nearest neighbor radial distribution approach in both GS and ES of
C153. These two states were modeled with different charge distributions
but retained the geometrical structure of C153. PCA highlighted that,
when C153 acts as a hydrogen bond donor: 

\begin{itemize}
\item the H$_{1}$ and H$_{2}$ atoms of C153 interact preferentially
with the hydroxyl O$_{1}$ atom of BuOH, EtOH, and PrOH;
\item the H$_{10}$ atom of C153 is instead located at a short distance
to the O$_{1}$ and O$_{2}$ of the PC;
\item the distances between the H$_{3}$ and H$_4$ atoms of C153 to the
O$_{1}$ atom of PC are shortened when C153 goes from GS to ES. The
opposite occurs when considering the distances of these H atoms to the
O$_{2}$ atom of PC;
\item the H$_{5}$  atom of C153 interacts preferentially with the
O$_{1}$ atom of BuOH and the O$_{2}$ atom of PC and is located
relatively far from the O$_{1}$ atom of PrOH and the O$_{1}$ atom of
PC. An opposite interaction trend is instead observed for H$_{14}$;
\item when C153 is in GS, its H$_{7}$ atom seems to be located quite
far from the O$_{1}$ of PrOH. In contrast, this distance seems to
significantly decrease when C153 is in ES.
\end{itemize}
In addition, it was observed that when C153 acts as a hydrogen bond acceptor:
\begin{itemize}
\item the carboxyl O$_{2}$ atom of C153 interacts preferentially with
the H$_{1}$ atoms of the hydroxyl groups of the alcohol solvents;
\item the F$_{1-3}$ atoms of C153 were found to generate preferential
interactions with the terminal methyl or ethyl groups of some of the
investigated solvents; 
\item the distance between the N$_{1}$ atom of C153 and the terminal H
atoms of several of the solvents under study (e.g., PrOH and BuOH)
increases when C153 goes from GS to ES.
\end{itemize}
The hydrogen bond interactions of C153 were also assessed via the
behavior of the fifth first neighbors. Our results show that the
distance values involving the hydroxyl H atoms of the alcohols are
close to those associated with strong hydrogen bond interactions
(linear configuration of O$_{2}{\cdots}$H$_{1}$--O$_{2}$). These
distances are even shortened in the ES of C153 which indicates a
further reinforcement of the hydrogen bonds. On the other hand, the
distance values involving the H atoms of PC and GBL are closer to those
associated with weak hydrogen bond interactions (bent configuration of
O$_{2}{\cdots}$H$_{1}$--C). Moreover, they do not vary when C153 goes
from GS to ES.

\section*{Declaration of interests} 
The authors do not work for advise, own shares in, or receive funds
from any organization that could \mbox{benefit} from this article, and have
declared no affiliations other than their research organizations.


\section*{Funding}
\vspace*{-5pt}
The authors acknowledge financial support from the French~National
Agency for Research (ANR-19-CE05-0009-01 Ultrafast photoinduced
processes of organic dyes in ionic liquid/molecular solvent mixtures
\mbox{designed} for dye solar cells).
\vspace*{-5pt}

\section*{Acknowledgments}
\vspace*{-2pt}

This work was performed using computational facilities of the Centre de
Resources Informatiques (CRI) de l'Universit\'{e} de Lille and Centre
R\'{e}gional \mbox{Informatique} et d'Applications Num\'{e}riques de 
\mbox{Normandie} (CRIANN) which are thankfully acknowledged for the CPU
time allocation.

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