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\begin{document}

\title{Sensing Mechanism Elucidation of a Chemosensor Based on a Metal-Organic
Framework (MOF) Selective to Explosive Aromatic Compounds}



\author[1]{Yoan Hidalgo-Rosa}%
\author[1]{Manuel A. Treto-Suarez}%
\author[2]{Eduardo Schott}%
\author[1]{Ximena Zarate}%
\author[1]{Dayan Paez-Hernandez}%
\affil[1]{Universidad Andres Bello}%
\affil[2]{Pontificia Universidad Catolica de Chile}%


\vspace{-1em}



  
  \date{April 29, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Theoretical elucidation of the turn-off mechanism of the luminescence of
a chemosensor based on a metal-organic framework (MOF)
{[}Zn2(OBA)4(BYP)2{]} (BYP: 4,4'-bipyridine; H2OBA: 4,4'-oxybis(benzoic
acid)), selective to nitrobenzene via quantum chemical computations is
presented. The electronic structure and optical properties of Zn-MOF
were investigated through the combination of density functional theory
(DFT) and time-dependent-DFT methods. Our results indicate that the
fluorescence emission is governed by a linker (BPY) to linker (OBA)
charge transfer (LLCT) involving orbitals \selectlanguage{greek}π-\selectlanguage{english}type. Next, interaction with
the analyte was analyzed, where very interesting results were obtained,
i.e. the LUMO is now composed by orbitals from nitrobenzene, which
changes the emissive state of the Zn-MOF. This fact suggests that the
LLCT process is blocked, inducing then the fluorescence quenching.
Otherwise, the Morokuma-Ziegler energy decomposition and NOCV (Natural
Orbitals for Chemical Valence) on the Zn-MOF-nitrobenzene interactions
were studied in detail, which illustrate the possible channels of charge
transfer between Zn-MOF and nitrobenzene. Finally, we believe that this
proposed methodology can be applied to different chemosensor-analyte
systems to evidence the molecular and electronic factors that govern the
sensing mechanisms.%
\end{abstract}%



\sloppy


\textbf{Keywords}

Luminescence MOFs, TD-DFT, PET, Nitroaromatic compounds

\textbf{Introduction}

The interest on the chemical detection \emph{in situ} of nitroaromatic
compounds (NACs) accurately and reliably, is mainly associated with
security, environment pollution, and human health. This fact has
currently encouraged researches to focus on the design of new chemical
sensors that show selective detection of NACs such as
2,4,6-trinitrophenol (TNP),\textsuperscript{1} nitrobenzene
(NB)\textsuperscript{2}, 2,6-dinitrotoluene (DNT)\textsuperscript{3},
among others.\textsuperscript{4} Furthermore, these compounds are
extensively used in many industrial processes and some of them are
highly toxic or carcinogenic. Moreover, they are potent pollutants of
soils and groundwaters.\textsuperscript{5-6} On the other hand, a
highlighted fact about these chemical compounds is that they represent a
potential risk to security, due to their high explosive power as well as
the easy access to them; being also used in the manufacture of
improvised explosive devices.\textsuperscript{7-8} In this sense, more
research on their effective detection is needed as well as the
implementation and improvement of devices used to this end. The
performance principle of a chemical sensors is based on the change of an
observable response upon interaction with analytes of interest. The
observables are based on physical principles such as absorbance,
transmittance, the polarization of light, luminescence, among others. In
this context, Metal-Organic Frameworks (MOFs) have emerged as a very
interesting alternative for the design of chemosensors due to their
structural and photophysical features; luminescence
specifically.\textsuperscript{9} MOFs are composed of metal centers or
cluster-like arrangements called nodes connected by linkers, which are
organic ligands.\textsuperscript{10}This wide range of possibilities to
get different structures of MOFs, with different nodes and linkers,
confers to these materials different photophysical responses including
luminescent properties.\textsuperscript{11} In this regard, light
emission can arise from either the ligand or the nodes, \emph{i.e.} from
the metal ions or metal clusters. The luminescence mechanism can involve
energy transfer processes, ligand-to-ligand charge transfer (LLCT),
ligand-to-metal charge transfer (LMCT) or metal-to-ligand charge
transfer (MLCT) as well as metal-to-metal charge transfer
(MMCT).\textsuperscript{12} These inorganic and organic species confers
them flexible coordination environment that leads to different secondary
building units (SBUs) and then a variety of topologies of the network
(\emph{i.e.} IRMOF-n series based on the renowned MOF-5, the UiO series
such as UiO-66, UiO-67, UiO-68, etc). \textsuperscript{13-14} The
importance of the porosity and the large surface area of MOFs is
recognized as the system acts as a pre-concentrator of the targeted
analyte, displaying host-guest interactions which can be modulated
because of their synthetic
versatility.\textsuperscript{15}\textsuperscript{-16} When the MOF
encapsulates the analytes, the interactions that occur (host-guest)
might induce changes in the photophysical properties, causing the
activation or deactivation of the luminescent signal of the whole
system.\textsuperscript{17-18} This response to the emission intensity
gives rise to an important classification that groups them as
luminescent turn-off or turn-on chemosensor. In this sense, when the
emission is very weakly or the system does not emit but the resulting
luminescence is enhanced by adding the analyte, it is called a Turn-on
chemosensor. While Turn-off chemosensors are systems whose luminescence
is quenched after interaction with the chemical species of interest
(Scheme 1). \textsuperscript{19-20}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Scheme 1.} Schematic representation of a chemosensor:
(\textbf{a} ) Turn-on of the luminescence, (b) Turn-off of the
luminescence.

In this sense, luminescent chemical sensors based on MOFs have emerged
as a successful alternative for sensing of NACs as they show intense
luminescence, low limits of detection (LODs) (up to single-molecule
level), specificity, tunable porosity, chemical functionality and the
ability to use them as powdered materials directly without further
treatments. Specifically, luminescent MOFs (LMOFs), based on
d\textsuperscript{10} metal ions, have been of great interest for
designing and synthesizing chemosensors selective to NACs. Regarding to
this, Allendorf \emph{et al.} in 2007 \textsuperscript{21} pointed out
the importance of the design of LMOFs based on closed-shell metal ions,
and also taking into account that it is possible to tune the
linker-centered emission by modifying the structure of the linker. This
fact is mostly studied since this type of MOFs are unlikely metal light
emisor, as the Zn-based and Cd-based LMOFs reported by W. Liu and
co-workers.\textsuperscript{22} Based on these premises, Lustig \emph{et
al.} (2016)\textsuperscript{23} developed a series of LMOFs with
ligand-centered emission. They performed the modification of the linkers
(tetrakis(4-carboxyphenyl) ethylene) by both fluorination and
elongation. Thus, the quantum yield of luminescence and thermal
stability were improved in these systems, concluding that the adequate
selection of the linker, whose emission can be increased or tuned, is a
versatile strategy to design LMOFs based on closed-shell transition
metal ions. In recent years, vast published literature has been reported
about LMOFs in the area of chemical sensors selective to explosive
aromatic compounds. In most cases, the most efficient reported mechanism
of transduction, is through a luminescence quenching response (turn-off
mechanism). This fact is due to the excellent electron-donating
capability of MOFs, the strong electron-accepting ability of NACs and
probability of photoinduced electron transfer (PET) between both
systems.\textsuperscript{24-25} In this mechanism, the detection pathway
of the analyte involves a PET from the LMOFs to the guest deactivating
the electronic emissive state. Here, the extinction of the luminescence
requires an electron structure where the analyte orbitals have adequate
energy to produce the PET. \textsuperscript{26-27} Regarding this,
several studies of density functional theory (DFT) calculations have
been reported, providing a more detailed description of the proposed
sensing mechanism. From these results, researchers have proposed that
the most probable PET mechanism is due to electron transfer from the
conduction band (CB) of the MOF to lowest unoccupied molecular orbital
(LUMO) of NACs.\textsuperscript{24-28} Nevertheless, since most of the
theoretical reports deal the computations of the MOF and analyte
separately, which have limited the analysis to an orbital energy
comparison between both structures, it becomes imperative to address the
study of host-guest systems to design MOFs as sensors. This last is a
remarkable topic recalled in literature due to their role in changes on
the photophysical properties that govern the recognition mechanisms of
analytes.\textsuperscript{29}\textsuperscript{-30} That is why we
consider that MOF-analyte interaction study is a key to understand the
path of the activation or deactivation of the luminescence in a sensing
process in a more accurately protocol. The current status of
computational methods and theoretical chemistry opens the possibility of
investigating photo-physical processes that modulate the luminescent
properties of LMOFs chemosensors. In this work, we investigated and
assessed the turn-off fluorescence mechanism of the Zn-based LMOF
{[}Zn\textsubscript{2}(OBA)\textsubscript{2}(BYP){]}DMA, where
H\textsubscript{2}OBA: 4,4'-oxybis (benzoic acid); BYP: 4,4'-bipyridine;
DMA = N, N'-dimethylacetamide, through quantum mechanics calculations,
synthesized and reported by Jing Li \emph{et al.} in
2011,\textsuperscript{31} as a selective chemical sensor to high
explosive NACs. A methodology including molecular and electronic
properties of the systems, for evaluating the relationship between the
structure of the LMOF and analyte-induced luminescence change was
successfully established. In terms of MOF-analyte interaction, we are
interested in the contribution of each term to the total interaction
energy, \emph{i.e} , electrostatic interaction, orbital interaction, a
dispersive interaction as well as repulsive Pauli interaction. In this
sense, it was demonstrated that the energy decomposition scheme proposed
by Morokuma-Ziegler provides valuable information to this regard as well
as NOCV (Natural Orbitals for Chemical Valence) calculations to
characterize the charge transfer channels.\textsuperscript{32-33}

\textbf{Computational Details}

According to Zhong-Min (2014)\textsuperscript{34} and Lu
(2019)\textsuperscript{22} from the point of view of the molecular
orbitals, MOFs can be treated as discrete molecular systems. This fact
is especially applicable in LMOFs based on d\textsuperscript{10} metal,
due that they present narrow band gaps energies and highly localized
electronic states.\textsuperscript{35} The LMOF understudy is formed by
molecular units of {[}Zn\textsubscript{2}(OBA)\textsubscript{4}{]}
(OBA=4,4'-oxybis (benzoic acid)) linked together forming two-dimensional
(2D) networks where the ligand 4,4'-bipyridine (BYP) acts as linker
between the {[}Zn\textsubscript{2}(OBA)\textsubscript{4}{]} units of two
adjacent layers, to get a highly porous three-dimensional (3D) network.
Therefore, in our system model, the structure was truncated to one node
and six linkers
{[}Zn\textsubscript{2}(OBA)\textsubscript{4}(BYP)\textsubscript{2}{]},
which we will refer to as Zn-MOF (see Figure 1). The truncated
structural proposal has been previously used to describe the electronic
structure, photophysical and catalytic properties in MOFs, where
theoretical results have shown excellent agreement with the experimental
data.\textsuperscript{36} \textsuperscript{37} \textsuperscript{3839}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 1.} Optimized geometry of the truncated Zn-MOF
(BP86/def2-TZVPP).

The first step consisted in optimizing the Zn-MOF as well as the
interacting system Zn-MOF-analyte with the ORCA
package.\textsuperscript{40} All structures were optimized via the
gradient-corrected Becke--Perdew
(BP86)\textsuperscript{41}exchange-correlation functional using the
triple-zeta valence with two sets of polarization functions (def2-TZVPP)
\textsuperscript{42} basis set. In the second stage of this work, we
performed a study of the optical properties of the Zn-MOF and
Zn-MOF-analyte systems by means of the Time-dependent Density Functional
Theory (TD-DFT) approach. To simulate the vertical transitions, 50
excitations were computed at the hybrid exchange-correlation functional
(B3LYP) \textsuperscript{43} as well as the Coulomb Attenuated Method
(functional, CAM-B3LYP)\textsuperscript{44} and def2-TZVPP basis set.
Finally, we analyzed the nature of the interaction Zn-MOF-analyte based
on the energy decomposition analysis (EDA) proposed by
Morokuma--Ziegler.\textsuperscript{45} The interaction energy
(\selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{int}) between two defined fragments according to the
EDA scheme can be divided into four components:

\selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{int} = \selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{Elec} +
\selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{Pauli}+ \selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{Orb} + \selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{Disp}
(1)

Where \selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{Elec} accounts for the classical electrostatic
interaction between the fragments as they are brought to their positions
in the final structure. The second term \selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{Pauli} is
related to the repulsive interaction of Pauli, between occupied orbitals
of both molecular fragments. The third term
\selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{Orb}expresses the possible interactions between
molecular orbitals related to the charge transfer, polarization, etc.
This term can be analyzed by the natural orbital of chemical valence
method proposed by Mitoraj.\textsuperscript{46-47} The term
\selectlanguage{greek}Δ\selectlanguage{english}E\textsubscript{Disp}describes the dispersion forces acting between the
fragments. We consider the long-range interactions, using Grimme's D3
dispersion correction for EDA calculations.\textsuperscript{48}

\textbf{Results and discussion}

The geometrical parameters upon geometry optimization of the Zn-MOF are
in good agreement with experimental X-ray data.\textsuperscript{31} The
results showed that the computed {[}Zn(28)--Zn(93){]},
{[}Zn(28)--N(34){]} and {[}Zn(28)--O(29){]} bond lengths are \selectlanguage{ngerman}Å 2.84 Å,
2.08 Å, and 2.07 Å, while the experimental values for Zn-MOF are 2.89 Å
2.02 Å, and 2.04, respectively.\textsuperscript{31} These are also
consistent with theoretical reported 2.23 Å, 2.25 Å and 2.06 Å
respectively values, computed at the PBE-D3/ Triple-zeta (TZP)
theoretical level and used a truncated structural model, for this MOF by
Ce Hao \emph{et. al.} \textsuperscript{24} in 2016.

Besides, the calculations reveal similar results regarding the
{[}N(34)--Zn(28)--O(4){]}, and {[}O(29)--C(35)--O(30){]} bond angles
which are 97.8\selectlanguage{english}@and 123.5@, \selectlanguage{english}see the structure on Figure 1. These values
agree with the experimental X-ray data which are 97.9@ \selectlanguage{english}and 124.2@
\selectlanguage{english}respectively\textsuperscript{31} and reported 96.9@\selectlanguage{english}and 124.2@
\selectlanguage{english}theoretical values.\textsuperscript{24}.

These results suggest that the proposed structural truncated model is
consistent with models previously reported and based on a fragmentation
scheme. Based on this fact, the optical properties of the Zn-MOF were
explored on the minimum optimized structure of the ground state
(S\textsubscript{0}) by means of TDDFT approaches. The simulated UV-vis
spectrum using both CAM-B3LYP and B3LYP functional (with maxima of 248
and 281 nm respectively) showed an excellent agreement with the
experimental absorption wavelength value\textsuperscript{31}, 280 nm.
The TDDFT(B3LYP) computed values are closer to the experimental one,
presumably due to the absence of the charge transfer between the metals
and ligands. Table 1 reports the maximum absorption wavelength (in
nanometer, nm), oscillator strengths (\emph{f} ) as well as the
assignments to the electronic transitions with the largest \emph{f} .
The molecular orbitals involved in the excitations are localized along
with the OBA linker as can be seen from Figure 2.

\textbf{Table 1.} Singlet - Singlet electronic transitions for Zn-MOF.\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Zn-MOF & Funtional & \selectlanguage{greek}λ\selectlanguage{english}max (nm) & \emph{f} & Assignment & Active MO & Cts
(\%)\tabularnewline
\midrule
\endhead
Absorption & B3LYP & 281 & 1.31 &
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})
& H-2-L+2 & 43\tabularnewline
& & & &
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})
& H-3-L+3 & 34\tabularnewline
& & & &
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})
& H-L+3 & 14\tabularnewline
& CAM-B3LYP & 248 & 1.04 &
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})
& H-3-L+3 & 31\tabularnewline
& & & &
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})
& H-2-L+2 & 28\tabularnewline
& & & &
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})
& H-L+3 & 7\tabularnewline
\bottomrule
\end{longtable}

Where: H: is HOMO, L is LUMO, Cts (\%) is contributions corresponding of
electronic transitions.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 2.} Molecular orbital energy diagram for Zn-MOF showing
the vertical electronic transitions for the maxima absorption band at
B3LYP/def2-TZVPP theoretical level.

In order to carry out a strong analysis of host-guest interactions, the
Zn-MOF ground state was optimized with the incorporation of the
analytes. The analytes were selected considering the reported largest
and the lowest quenching efficiency of the Zn-MOF
fluorescence;\emph{i.e.} nitrobenzene (quenching, 84\%) and toluene
(non-quenching).\textsuperscript{31} All Zn-MOF-analyte systems were
optimized at the same theoretical level as the free Zn-MOF. The proposed
input geometries consisted on the pi-staking/aromatic interaction
between the linkers and target molecules. Two interaction models were
considered for each analyte, one where the interaction occurs with the
aromatic ring of the OBA linker while the other displays the interaction
with the BPY fragment. Both initial structures converged to the
host-guest interaction between the analyte and BPY, with a distance
between them within the range of 3.15--3.34 \selectlanguage{ngerman}Å. Zn-MOF-nitrobenzene and
Zn-MOF-toluene minima structures were selected for the calculations and
the analyzes described below. The geometrical parameters computed for
the Zn-MOF interacting with the analytes did not show significant
differences in relation to the ground state of the free Zn-MOF, see
Table S1, Supporting Information.

\textbf{Fluorescence Quenching Pathway}

Frontier molecular orbital (FMO) analysis of host-guest systems showed
that of electron density distribution changes upon the incorporation of
an analyte with electron\selectlanguage{english}-acceptor (-NO\textsubscript{2}) groups or
electron\selectlanguage{english}-donor (-CH\textsubscript{3}) groups, see Figure 3. The FMOs of
Zn-MOF-toluene and Zn-MOF indicate that both systems exhibit similar
features, as the HOMO in both systems exhibits that electron density is
distributed on the OBA linkers while the LUMO is located on BPY linkers.
In case of Zn-MOF-toluene, the molecular orbitals located on the guest
molecule appear in a set of inner occupied molecular orbitals, as well
as more external molecular orbital into the virtual space, see Figure S1
Supporting Information. However, when the guest is the NACs such as
nitrobenzene, the HOMO is totally distributed on the OBA linkers whereas
the LUMO is extended on the nitrobenzene framework, see Figure 3. These
results are consistent with the reported by Ce Chao et
al.\textsuperscript{24} in regarding the analysis of the FMOs
considering the interaction between Zn-MOF and analyte.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 3.} Frontier molecular orbitals of Zn-MOF and
Zn-MOF-analyte systems.

Furthermore, TD-DFT calculations allowed us to confirm that the
absorption spectra only implies electronic transitions involving active
orbitals of the OBA linkers. This result was observed regardless of
whether the systems do or do not have an analyte, see Table 2.

The absorption spectrum of the Zn-MOF-nitrobenzene showed that the
molecular orbitals involved in the absorption bands are localized on the
OBA linker. These molecular orbitals are presented in Figure 4, which
evidences the excitations of intra-ligand charge-transfer (ILCT)
character. Similar results were obtained for Zn-MOF-toluene computed at
the same level of theory, see Figure S2 in the Supporting Information.

\textbf{Table 2.} Singlet - Singlet electronic transitions, absorption
data, for Zn-MOF-analyte at B3LYP/ def2-TZVPP theoretical level.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
\begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
Zn-MOF-analyte\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
\selectlanguage{greek}λ\selectlanguage{english}max (nm)\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
\emph{f}\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
Assignment\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
Active MO\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
Cts (\%)\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Zn-MOF-nitrobenzene\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
281\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1.16\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
H-2-L+4\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
38\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
H-L+6\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
18\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
H-L+5\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
11\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Zn-MOF-toluene\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
281\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1.33\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
H-L+4\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
16\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
H-L+5\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
12\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\selectlanguage{greek}\emph{π(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})-\selectlanguage{greek}\emph{π*(L\textsuperscript{\textbf{OBA}}}\selectlanguage{english})\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
H-1-L+5\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
14\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Where: H: is HOMO, L is LUMO, Cts (\%) is contributions corresponding of
electronic transitions\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 4.} Molecular orbital energy diagram for
Zn-MOF-nitrobenzene showing the vertical electronic transitions for the
maxima absorption band at B3LYP/def2-TZVPP theoretical level.

The radiative deactivation of the excited state can occur by two
mechanisms, fluorescence or phosphorescence, after photoexcitation. It
is well-known since 1950, from Michael Kasha's works that ``the emitting
electronic level of a given multiplicity is the lowest excited level of
that multiplicity'' \textsuperscript{49}, which is known as the kasha's
rule. In this sense, fluorescence is the emission processes, due to
radiative deactivation from first excited singlet states to the ground
state. In the particular case of phosphorescence, it is necessary to
populate an excited triplet (T\textsubscript{1}) with less energy than
the first singlet excited S\textsubscript{1} state, this mechanism is
known as an intersystem cross (ISC), for relaxes to its ground
state.\textsuperscript{50-51} The importance of the precise description
of these states, the S\textsubscript{1} state or
T\textsubscript{1}state, to understand the mechanisms by which activate
or deactivate the luminescence in chemosensors optical has been
emphasized by Briggs and Besley in 2015.\textsuperscript{52} In recent
studies, our group proposed and verified a theoretical protocol, based
on this statement, from the elucidation of the sensing mechanism in
chemosensor selective to metal ions.

A precise description, both of the S\textsubscript{0} state and of the
S\textsubscript{1} state, in terms of energy and structure, allowed us
to explain in detail the turn-on fluorescent mechanism of the two
chemosensor luminescent based in Schiff basis selective to metal
ions.\textsuperscript{53-54}

Considering the importance of knowing the emissive state of chemosensor
is optimized S\textsubscript{1} state of the Zn-MOF to understand the
origin of fluorescence in this system. Thus, the optimized geometry of
the S\textsubscript{1} state was taken as input data to calculate the
electronic transitions that constitute emission spectrum of Zn-MOF by
means of TD-DFT methods. These calculations confirmed that the molecular
orbitals involved in the emission band are linkers-localized. This
result indicates that fluorescence is originated by a transition \selectlanguage{greek}π-π\selectlanguage{english}*
linker-centered from the LUMO to HOMO, whit 97\% of contributions
corresponding to this electronic transition. It also shows that the
electron density of LUMO is located on the BYP linker, while the HOMO is
localized on the OBA linkers see Figure 5. This result is consistent
with those observed in other LMOFs based on metals ions
d\textsuperscript{10} recently reported, which origin of emission is
assigned to ligand-to-ligand charge transfer. \textsuperscript{2212}
This emission pathway is observed mainly in LMOFs based
Zn\textsuperscript{2+} and Cd\textsuperscript{2+} since these ions with
oxidation state \textsuperscript{2+}, tend to retain the
d\textsuperscript{10} configuration.\textsuperscript{5556}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Figure 5.} Molecular orbital energy diagram for
Zn-MOF-nitrobenzene showing the vertical electronic transitions for the
maxima absorption band at B3LYP/def2-TZVPP theoretical level

Guang-Yue and Ke-Li in 2018 highlight that the host-guest interaction
can be generated and that some molecular orbitals of guests appear
located between the molecular orbitals involved in the emissive state,
for that reason, radiative deactivation is blocked, resulting in the
Turn-off .\textsuperscript{57} In this sense, our results indicated that
when nitrobenzene is confined into the Zn-MOF is generates a mixture of
states of Zn-MOF and nitrobenzene. In the Zn-MOF-nitrobenzene is
observed that the analyte-centered molecular orbital corresponds to the
LUMO, while the orbitals just above the LUMO are orbitals located on the
BYP linker, which represent the molecular orbitals that correspond to
the emissive states in analyte-free Zn-MOF, see Figure 6.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Figure 6.} Frontier molecular orbitals of Zn-MOF-nitrobenzene.

Based on these results, the Franck-Condon principle and selection rules,
we support the hypothesis that upon photoexcitation the electron relaxes
until reaching the first excited electronic state, presumably located in
de nitrobenzene, from which the dissipates of energy through the
non-radiative transition. For that reason, the electron relaxation from
PBY linker of the OBA linker is blocked resulting in the turn-off of the
fluorescence. Besides, this electronic configuration of the coupled
system Zn-MOF-nitrobenzene would explain the experimental interpretation
of the quenching fluorescence is due to the LUMO of nitrobenzene appear
below the emissive state of the MOF.\textsuperscript{31}

Considering these results, this theoretical insight was carried out from
another perspective based on a theoretical approach most commonly
reported in the literature. This method consists of separately treating
the electro-donor species, MOF, and electro-acceptor species, NACs, at
the same level of theory. \textsuperscript{58-59} The FMO analysis
showed that the LUMO of the nitrobenzene is located lower energy level
than the LUMO of Zn-MOF, see Figure 7, thus the photoinduced
charge-transfer (PET) between Zn-MOF and nitrobenzene is possible.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

\textbf{Figure 7.} Calculated frontier molecular orbital energies (eV)
of the nitrobenzene, toluene, and Zn-MOF.

These results are consistent with the quenching mechanism that has been
widely accepted for this type of luminescence chemosensor for
nitroaromatics compounds. According to literature, deactivation of the
luminescent is produced by the transfer of electrons, after a
photoinduced excitation, between the conduction band of MOF and lowest
unoccupied molecular orbital of the analyte.
\textsuperscript{60-61}Finally, the calculations of Zn-MOF-toluene
system showed that the active molecular orbitals are similar to the
Zn-MOF without a guest. It should also be noted that according to
observed experimentally, in the presence of toluene, it is not observed
fluorescence attenuation. The result also suggests that the mixture of
the Zn-MOF orbitals and the analyte orbitals in the active space has an
important role in the quenching of fluorescence.

\textbf{Host-guest interaction based on Morokuma-Ziegler analysis}

The analysis of host-guest interactions based on the Morokuma-Ziegler
decomposition scheme has proven successful procedure for interpretation
of the nature of the interaction between the two structures. In the case
of MOFs, analysis of the interaction has recently been reported,
considering the MOF and the guest as the two molecular fragments that
constitute the whole system.\textsuperscript{33-35}

From this perspective, the energy decomposition analyses (EDA) was
carried out, where each system studied was divided into two fragments:
Zn-MOF and the analyte (\emph{i.e} . nitrobenzene and toluene). Due to
our interest in the dispersive forces (van der Waals force) acting
between the fragments {[}Zn-MOF{]} and {[}analyte{]}, were incorporating
Grimme's (D3) dispersion correction this analysis. According to the
results, interaction energies for all systems does not exceed -6
kcal/mol, which indicates the predominant the long-range interactions.
The Zn-MOF-analyte interactions are more intense in the case of analytes
more electron-deficient (i.e. nitrobenzene), for which electrostatic
interaction represents 51\% of interaction energy. While the toluene,
containing the electron-donating group, shows that weaker interaction
energy with Zn-MOF, in which the dispersive contribution represents 67
\%, see Table 3. These results evidence that in the case of the
Zn-MOF-nitrobenzene is possible a charge transfer between the Zn-MOF and
nitrobenzene.

\textbf{Table 3.} Morokuma--Ziegler's scheme energy decomposition
analysis (EDA kcal/mol) of denoting the Zn-MOF-analyte interaction.\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
\textbf{System} & \selectlanguage{greek}\textbf{ΔE\textsubscript{Pauli}}\selectlanguage{english} &
\selectlanguage{greek}\textbf{ΔE\textsubscript{Elestat}}\selectlanguage{english} & \selectlanguage{greek}\textbf{ΔE\textsubscript{Orb}}\selectlanguage{english} &
\selectlanguage{greek}\textbf{ΔE\textsubscript{Disp}}\selectlanguage{english} & \selectlanguage{greek}\textbf{ΔE\textsubscript{Disp}}\selectlanguage{english} &
\selectlanguage{greek}\textbf{ΔE\textsubscript{Int}}\selectlanguage{english}\tabularnewline
\textbf{Zn-MOF-nitrobenzene} & 2.35 & -3.76 (51\%) & -1.13(15\%) &
-2.53(34\%) & -2.53(34\%) & -5.60\tabularnewline
\textbf{Zn-MOF-toluene} & 0.89 & -0.86 (23\%) & -0.36 (10\%) & -2.52
(67\%) & -1.07 & -1.07\tabularnewline
\bottomrule
\end{longtable}

In this context, an analysis via the NOCV approach can provide useful
information on the channels of charge transfer between the fragments.
While it is true that both systems the interaction energy have weak the
covalent character, the NOCV analysis revealed that the interaction
host-guest involves a charge transfer or donor-acceptor interactions. As
observed in Figure 8, the plots of NOCV deformation density (\selectlanguage{greek}ρ\selectlanguage{english}) for
Zn-MOF-analyte systems are can be identified of the deformation density
channel between the host and guest. These charge density accumulations
describe intermolecular interaction, between the BPY linker of Zn-MOF
and analyte. Taking into account that the coupled Zn-MOF-nitrobenzene
system, generates that the orbitals localized on the BPY linkers appear
just above the LUMO orbital (totally located on the of nitrobenzene), it
may be possible to occur intermolecular PET from Zn-MOF to nitrobenzene.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\textbf{Figure 8} . NOCV-based deformation densities (\selectlanguage{greek}Δρ\selectlanguage{english}) for the
host-guest interactions for Zn-MOF-analytes.

\par\null

\textbf{Conclusions}

Quantum chemical approaches were successfully employed to assess the
relationship between the structure of the LMOF and analyte-induced
luminescence change.

First, we found that the molecular orbitals involved in the absorption
bands of the spectrum profile of the Zn-MOF, are localized on the
4,4'-oxybis (benzoic acid) (OBA) linker. Besides, the emission
phenomenon was characterized as fluorescence emission \emph{via} LLCT
processes, which takes place from 4,4'-bipyridine (BYP) to the
4,4'-oxybis (benzoic acid) (OBA) linker. As second part of the work,
analyte (nitrobenzene) confinement was studied into the Zn-MOF, which
gave rise to a mixture of the molecular orbitals from both systems.
Interesting, the LUMO corresponds to orbitals of the nitrobenzene and
appears energetically close to the molecular orbital localized at the
BYP, which is involved in the emissive state of the free Zn-MOF. These
results suggest that the LUMO, located on nitrobenzene, blocked the LLCT
process between BPY and OBA, leading to the fluorescence quenching.
Therefore, it is demonstrated that the simulation of the host-guest
system is imperative to understand the luminescence changes that govern
the sensing mechanism in a chemosensor. Otherwise, the study of the
interaction via the Morokuma-Ziegler decomposition scheme and Natural
Orbital of Chemical Valence (NOCV) analysis, proposed by the Mitoraj,
were useful to propose possible channels of charge transfer between
Zn-MOF and nitrobenzene.

In summary, the intention of this study was to get theoretical insights
into the sensing mechanism MOF chemosensor selective to nitrobenzene
through analysis of host-guest interactions. Due to the large size of
this system, it was applied a fragmentation scheme of experimental X-ray
single-crystal data of the Zn-MOF, reaching a finite structural model
{[}Zn\textsubscript{2}(OBA)\textsubscript{4}(BYP)\textsubscript{2}{]} to
optimize time and computational resources. This structural model has
satisfactorily reproduced geometry parameters and photophysical
properties of the Zn-MOF with and without the analyte.

\textbf{Funding Information}

The authors thank to Ph.D. Program in Molecular Physical Chemistry from
University Andr\selectlanguage{ngerman}és Bello, subsidy of the DAD-UNAB, FONDECYT 1180017,
FONDECYT 1180565, FONDECYT 1161416, Millennium Science Initiative of the
Ministry of Economy, Development and Tourism-Chile grant Nuclei on
Catalytic Processes towards Sustainable Chemistry (CSC).

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