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\begin{document}

\title{Evaluation of noncovalent interactions in L-(S)-lysinium L-(S)-mandelate
dihydrate crystal: Inputs from Hirshfeld surfaces, PIXEL energy and
theoretical charge density}



\author[1]{Venkatachalam Sudarvizhi}%
\author[1]{Thanagavelu Balakrishnan}%
\author[2]{Judith  Percino}%
\author[3]{Helen Stoeckli-Evans}%
\author[4]{Thamotharan Subbiah}%
\affil[1]{Periyar EVR College (Autonomous)}%
\affil[2]{Benemérita Universidad Autónoma de Puebla}%
\affil[3]{University of Neuchâtel}%
\affil[4]{SASTRA University}%


\vspace{-1em}



  
  \date{June 18, 2024}


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\selectlanguage{english}
\begin{abstract}
L-lysine amino acid is cocrystallized with L-mandelic acid by the slow
evaporation method. Single crystal X-ray analysis reveals that
lysine-mandelic acid crystallized as a dihydrate form. In the
crystalline state, the lysine molecule exists in the cationic form in
which the backbone and side chain amino groups are protonated and the
carboxylic acid is deprotonated. The carboxylic acid proton of the
mandelic acid is transferred to the lysine side chain and thus carries a
negatively charged ion. The lattice water molecules are located near the
amino groups of the lysine. Intermolecular interactions formed between
lysinium, mandelate and lattice water molecules are qualitatively
analyzed using Hirshfeld surfaces and 2D-fingerprint plots. The
energetics of different dimeric complexes is quantitatively analyzed
using PIXEL energy analysis. Topological parameters derived from QTAIM
framework are used to delineate the nature of different intermolecular
interactions formed in the title complex.%
\end{abstract}%



\sloppy


\textbf{}\emph{}

\textbf{Introduction}

The basic building blocks of protein and peptides are 20 genetically
encoded amino acids. These amino acids show enormous diversity
concerning solubility, hydrophobicity, acidity and solid-state
aggregation due to variable side chains.\textsuperscript{1} The amino
acids also assume a variety of ionization state and it is well-known
that the zwitterionic form (protonated \selectlanguage{greek}α-\selectlanguage{english}amino group and deprotonated
\selectlanguage{greek}α-\selectlanguage{english}carboxylic acid group) is found to be the most stable form in aqueous
solution. Some of the amino acids display excellent non-linear optical
properties and piezo- or ferroelectricity.\textsuperscript{2-5}Crystal
structures of 20 genetically encoded amino acids have been studied well
to understand the hydrogen bonding, supramolecular self-association and
polymorphism.\textsuperscript{6-9} To understand the molecular
recognition process between protein-inhibitor/drug molecules and
protein-protein molecules, structural studies have been carried out for
different amino acids complexed with other amino acids or with other
coformers.\textsuperscript{10}

Owing to the above, various research groups explored the crystallization
of different amino acids (L, D and DL amino acids) in the presence of
various carboxylic acids such as mono-, di-, tri- or aromatic carboxylic
acids etc. These complexes revealed the most common synthons,
variability in the supramolecular assembly, effect of chirality on the
ionization state and stoichiometry. The crystal structures of L and
DL-lysine complexed with one of the dicarboxylic acids namely adipic
acid have been reported and the structures reveals that the arrangement
of molecular ions in the layer is profoundly
different.\textsuperscript{11} In another study, crystal structures of
L/DL-arginine and L/DL-lysine complexed with L/DL-tartaric acid were
reported. The result suggests that the L-lysine prefers to form a
complex with D-tartrate rather than L-tartrate.\textsuperscript{12} We
also reported the crystal structure of glycine-phthalic acid (an
aromatic dicarboxylic acid) has been studied to delineate hydrogen
bonding interactions.\textsuperscript{13}

In the present study, we obtained a crystalline complex of L-lysine with
L-mandelic acid and the crystal structure has been elucidated. Mandelic
acid is one of a number of the aromatic carboxylic acids and is known to
be an antiseptic used in the treat of urinary tract
infections.\textsuperscript{14} It also acts as a chiral intermediate
for the synthesis of pharmaceutical agents, such as cephalosporins,
vasodilator cyclandelate, hexamine mandelate and antispasmodic mandelic
acid benzyl ester.\textsuperscript{15} Therefore, structural studies on
amino acids with mandelic acid could act as a model system to understand
the molecular recognition of a drug by the protein molecules. A
Cambridge Structural Database (CSD version 5.40, November 2018) search
was conducted for amino acid-mandelic acid complexes. This search
indicated that mandelic acid complexed with four different amino acids,
such as alanine, cysteine, phenylalanine and methionine. In (\emph{R}
)-methionine (\emph{R} )-mandelic acid complex, the methionine exists in
the cationic form (a proton transferred from a carboxylic acid of
mandelic acid), a neutral mandelic acid and an anionic
mandelate.\textsuperscript{16}The mandelic molecules are self-assembled
\emph{via} O--H\selectlanguage{ngerman}···O hydrogen bonding between hydroxy-carboxylate and
hydroxy-hydroxy groups. The crystal structures of phenylalanine-mandelic
acid complexes ((\emph{R} )-phenylalanine (\emph{R} )-mandelic acid,
(\emph{R} )-phenylalanine (\emph{S} )-mandelic acid and (\emph{S}
)-phenylalanine (\emph{S} )-mandelic acid) have been
reported.\textsuperscript{17,18}In all three cases, phenylalanine exists
in the zwitterionic form and mandelic acid is in the neutral form. In
the (\emph{S} )-alanine (\emph{S} )-mandelic acid complex, the amino
acid exists in zwitterionic form and the mandelic acid is in the neutral
form.\textsuperscript{19} The self-assembly of mandelic acid molecules
are mediated by O--H···O hydrogen bonding between hydroxy-carboxylic
groups. The crystal structure of the (\emph{S} )-alanine (\emph{R}
)-mandelic acid hemihydrate complex has also been
reported.\textsuperscript{20} The orientation of the O--H group of the
carboxylic acid is different in the alanine-mandelic acid complexes. In
the cysteine-mandelic acid complexes, the amino acid exists in the
zwitterionic form and mandelic acid is in the neutral
form.\textsuperscript{21}

Herein, the energetics of non-covalent interactions present in the
L-(\emph{S} ) lysinium-L-(\emph{S} )-mandelate complex is investigated
in detail using different theoretical approaches such as Hirshfeld
surface,\textsuperscript{22} 2D fingerprint plots\textsuperscript{23}
and Bader's quantum theory of atoms-in-molecules (QTAIM)
framework.\textsuperscript{24}

\textbf{Methods}

\textbf{Crystallization and Single crystal X-ray diffraction}

Analytical reagent grade L--Lysine (Merck) and L--mandelic acid
(Lobachemie) were taken in a stoichiometric proportion (1:1) and
dissolved in double distilled water. The resultant solution was filtered
and evaporated at room temperature. Transparent needle-shaped single
crystals were obtained after a week and used for X-ray diffraction
analysis.

A good quality single crystal was chosen for X-ray intensity data
collection. The intensity data were collected at room temperature (293
K) on a Bruker Kappa APEX3 CMOS diffractometer equipped with graphite
monochromated Mo \emph{K} \selectlanguage{greek}α \selectlanguage{english}radiation (\selectlanguage{greek}λ \selectlanguage{english}= 0.71073 \selectlanguage{ngerman}Å) using \selectlanguage{greek}ω/\selectlanguage{english}2\selectlanguage{greek}θ \selectlanguage{english}scan
mode. The structure was solved with the SHELXT
program.\textsuperscript{25} All the non-hydrogen atoms were refined
anisotropically using the program SHELXL-2018/3.\textsuperscript{26} The
positions of H atoms of the ammonium groups and the water molecules were
located from a difference Fourier map and the N--H and O--H distances
were restrained to 0.85(2) \selectlanguage{ngerman}Å. The remaining H atoms were positioned by
riding model approach. Since absence of significant anomalous scatterers
in the title complex, the absolute configuration was not established.
However, the absolute configuration of L-lysine and L-mandelic acid from
the starting materials was assumed. The Friedel pairs were merged during
the final cycle of the refinement. The refined coordinates belong to
(\emph{S} )-lysine and (\emph{S} )-mandelate configurations. The crystal
data and refinement parameters of the title complex are presented in
Table 1. The thermal ellipsoidal plot and dimeric motifs were produced
using the program MERCURY.\textsuperscript{27}

\textbf{\{insert Table 1\}}

\textbf{Details of theoretical calculations}

The crystal structure geometry was taken after normalizing the distances
involving H atoms to their typical neutron values (C--H= 1.083, N--H =
1.009 and O--H = 0.983 Å). The normalized model was used for Hirshfeld
surface analysis\textsuperscript{29} and PIXEL energy
calculation.\textsuperscript{30-32} The Hirshfeld surface analysis was
performed with CrystalExplorer program\textsuperscript{33} to
qualitatively analyze the intermolecular interactions. Further, the
intermolecular interaction energy (\emph{E} \textsubscript{tot}) was
calculated for various dimers using the PIXEL method. The\emph{E}
\textsubscript{tot} value decomposed into the Coulombic (\emph{E}
\textsubscript{coul}), polarization (\emph{E} \textsubscript{pol}),
dispersion (\emph{E} \textsubscript{disp}), and repulsion ((\emph{E}
\textsubscript{rep}) contributions. The PIXEL code handles up to
two-component system, but the title complex is a four-component system
(lysinium, mandalate and two water molecules) which cannot be handled by
PIXEL code. Therefore, the title complex was separated into different
combinations of two-component system which yielded five different pairs.
These pairs were: pair1: L-lysinium-L-mandelate, pair2:
L-lysinium-water1, pair3: L-lysinium-water2, pair4: L-mandelate-water1
and pair5: L-mandelate-water2. We followed this procedure as suggested
for the dihydropyrimidinium hydrochloride derivatives in the
literature.\textsuperscript{34} For each pair, the electron densities
have been obtained using the program GAUSSIAN 09\textsuperscript{35} at
MP2/6-31G** level of theory. The intermolecular interaction energies
(\emph{E} \textsubscript{tot}) of different dimers were computed by the
PIXEL method were further compared with those of dimeric energies
(\selectlanguage{greek}Δ\selectlanguage{english}\emph{E} \textsubscript{cp}) computed using the M06-2X/6-311++G(d,p)
level of theory with Grimme's empirical dispersion
D3.\textsuperscript{36} Further, the value of \selectlanguage{greek}Δ\selectlanguage{english}\emph{E}
\textsubscript{cp} was corrected for basis set superposition error
(BSSE) using the counterpoise method.\textsuperscript{37}

The topological analysis within the framework of Bader's QTAIM approach
was performed for different dimers identified in the title complex to
characterize the nature of bonding. To obtain wave function, single
point energy calculation (with the normalized X-ray structure geometry)
was carried out for these dimers at M06-2X-D3/6-311++G(d,p) level of
theory. From the calculation, we computed topological properties like
electron density \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r), Laplacian of the electron density
[?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r), potential energy density \emph{V} (r),
kinetic energy density \emph{G} (r) and total energy density \emph{H}
(r) for intermolecular interactions at their bond critical points (BCPs)
using the AIMALL package.\textsuperscript{38} Further, the bond
dissociation energies (\emph{D} \textsubscript{e} =\(\frac{-V(r)}{2}\))
for all the intermolecular interactions were calculated using the
relationship of Espinosa \emph{et al} .\textsuperscript{39}

\textbf{Results and Discussion}

The title complex crystallized in the triclinic system with the\emph{P}
1 space group. The unit cell comprises one lysine, one mandelic and two
water molecules (Figure 1). The lysine exists in the cationic form in
which backbone (N1) and side chain (N2) amino groups are protonated and
carboxylic acid group is deprotonated. The mandelic acid carries a
negative charge due to the loss of proton from the carboxylic acid
moiety. This proton is transferred to the lysine side chain amino group
(N2). In the crystal, lysine in the cationic form and mandelic acid in
the anionic form and thus charge neutrality was achieved.

\textbf{\{insert Figure 1\}}

\textbf{Molecular dimers in the complex}

We performed PIXEL energy calculation to obtain intermolecular
interactions energies for different molecular dimers formed in the
crystal structure (Table 2). These dimers are held together by various
intermolecular interactions. It should be noted that both stabilizing
and destabilizing molecular pairs are existed in the dihydrated complex.

The stabilizing molecular dimers are formed between different
charged-charged and charged-uncharged species such as cation\selectlanguage{ngerman}···anion
{[}+1···-1{]}, cation···H\textsubscript{2}O {[}+1···0{]} and
anion···H\textsubscript{2}O {[}-1···0{]} pairs. Among stabilizing
dimers, the dimers (motifs D1-D4, Table 2) formed by
lysinium···mandelate ions are strong. The other stabilizing pairs
(motifs D5-D9) formed by cation-water and anion-water components are
relatively weaker dimers.

\textbf{\{insert Table 2\}}

The destabilizing molecular pairs (motifs D10-D11) are formed through
the same charged ions (lysinium···lysinium and mandelate···mandelate).
The intermolecular interactions present in the stabilizing and
destabilizing molecular pairs are discussed below.

\textbf{Stabilizing molecular pairs}

The intermolecular interaction energies for the stabilizing molecular
pairs formed by cation and anion species of the type {[}+1···-1{]}
ranging from -462.8 to -250.4 kJ mol\textsuperscript{-1}. These
molecular pairs are depicted in Fig. 2. The molecular dimer D1 is
stabilized by three intermolecular interactions (N--H···O, C--H···O and
C--H···C(\selectlanguage{greek}π\selectlanguage{english})). The lysinium acts as donors for N--H\selectlanguage{ngerman}···O and C--H···C(\selectlanguage{greek}π\selectlanguage{english})
interactions, whereas mandelate anion is involved as a donor for the
C--H\selectlanguage{ngerman}···O interaction and one of the oxygens (O4) of the carboxylate
group of lysinium cation acts as an acceptor for this interaction. The
D2 dimer is formed by N--H···O (involving side chain N2 of the cation
and hydroxy group of the anion) and C--H···C(\selectlanguage{greek}π\selectlanguage{english}) interactions. The D1
dimer is flanked on the both sides molecules formed by the motif D2.
Motifs D1 and D2 are combined to form a layer which runs parallel to the
crystallographic \emph{b} axis. In this layer, lysinium and mandelate
ions are alternately arranged and forming the --D2-D1-D2-D1- sequence as
shown in Fig. 2. Dimer D3 is generated by three-centered intermolecular
interactions (C--H\selectlanguage{ngerman}···O and a short C\emph{sp}
\textsuperscript{3}--H···H--C\emph{sp} \textsuperscript{2}contact formed
formed between cation and anion with a distance of 1.98 Å). The least
stabilizing dimer D4 which belongs to {[}+1···-1{]} type is formed by
intermolecular N--H···O (involving backbone amino group of the lysinium
and carboxylate group of the anion), O--H···O (involving hydroxy of the
anion and carboxylate of the cation). It should be noted that there is a
short contact formed between C1···O3 which provides additional stability
to the dimer D4. Further, the adjacent layers of --D2-D1-D2-D1-
supramolecular motifs are interconnected by the motif D4 as shown in
Fig. 2.

\textbf{\{Insert Figure 2\}}

As mentioned earlier, relatively weak stabilizing molecular dimers are
formed between cation-water and anion-water dimeric complexes in the
solid state. Both water molecules (O1W and O2W) interact with lysinium
and mandelate ions forming {[}0···-1{]} and {[}0···+1{]} molecular
species with stabilizing in nature. There are five such molecular types
observed in which cation-water complex makes four molecular dimers
(motifs D5, D7-9 and {[}0···+1{]} type) and anion-water complex forms
only one dimer (motif D6 and {[}0···-1{]} type).

As shown in Fig. 3, water molecules bridge the adjacent cations and
adjacent anion in the solid state. We note that the lysinium side chain
amino group (\emph{via} H2A) interacts with water molecule (O2W) through
N--H···O interaction and found to be stronger dimer (motif D5,\emph{E}
\textsubscript{tot}: -86.4 kJ mol\textsuperscript{-1}) among four
{[}0···+1{]} type molecular dimers. The backbone amino group (\emph{via}
H1B) also interacts with the water molecule (O1W) through intermolecular
N--H···O interaction (motif D9,\emph{E} \textsubscript{tot}: -21.4 kJ
mol\textsuperscript{-1}). This dimer is relatively weaker than that of
the dimers formed by water molecules and oxygens of the carboxylate
group of the lysinium (motif D7, \emph{E} \textsubscript{tot}: -32.8 kJ
mol\textsuperscript{-1} and motif D8, \emph{E} \textsubscript{tot}:
-22.4 kJ mol\textsuperscript{-1}). The water molecule (O2W) interacts
with carboxylate group of the anion forming a molecular dimer D6. The
strength of this dimer (\emph{E} \textsubscript{tot}: -51.4 kJ
mol\textsuperscript{-1}) is found to be stronger than the dimer formed
by intermolecular N--H···O interaction involving backbone nitrogen and
water molecule (motif D9). From the energetic point of view, one can see
that water molecules in the complex make stronger interactions with side
chain N of the cation and carboxylate group of the anion.

\textbf{\{Insert Figure 3\}}

\textbf{Destabilizing molecular pairs}

There are three pairs identified as destabilizing molecular dimers
(motifs D10-D12) in the title complex. These dimers exist between
cation-cation, anion-anion and water-anion pairs. Among them, the
anion-water complex has a weak nature of destabilization with
the\emph{E} \textsubscript{tot} value being 3.4 kJ
mol\textsuperscript{-1}. We note that the destabilization nature is
remarkably higher (almost 2-fold) in the case of anion-anion complex as
compared to the cation-cation complex. As depicted in Fig. 4, the
adjacent anions are self-assembled \emph{via} intermolecular C--H···O
interaction (motif D12, Table 2) which produces 1D chain that has a
graph-set motif of\emph{C} (6).\textsuperscript{40} It should be
emphasized that the hydroxy is not participated in the self-assembly of
mandelate anions as observed in other amino acids-mandelic acid
complexes.

\textbf{\{insert Figure 4\}}

\textbf{Qualitative analysis of intermolecular interactions: Hirshfeld
surface and 2D fingerprint plots}

Hirshfeld surface (HS) has widely been used as a qualitative tool to
analyze the intermolecular contacts present in the title complex. The
2D-fingerprint plots (2D-FP) were obtained for the individual component
of the complex from the HS analysis (Fig. 5). For the lysinium cation,
the intermolecular H···H interactions (with the contribution of 45.9\%)
are appeared as a single spike (\emph{d} \textsubscript{i}+\emph{d}
\textsubscript{e} = 2.0 Å;\emph{d} \textsubscript{i} and \emph{d}
\textsubscript{e} are the distances from the surface to the nearest
nucleus internal and external to the surface, respectively) which
confirms the existence of C6--H6B···H14--C14 contact (motif D3). The
next contribution comes from the intermolecular H···O interactions and
shown as double spikes with the shortest \emph{d}
\textsubscript{i}+\emph{d} \textsubscript{e}distance of 1.8 Å. It should
be noted that the intermolecular H···C contacts (sum of \emph{d}
\textsubscript{i} and \emph{d} \textsubscript{e}distance is being 2.8 Å)
are contributing 11\% to the total HS area of the cation. The entire
contribution emanated from the donor molecules (\emph{d}
\textsubscript{e} \textgreater{} \emph{d} \textsubscript{i}) for these
interactions. The C=O\textsubscript{lp}···C\selectlanguage{greek}\textsubscript{π}\selectlanguage{english}contacts
contribute about 0.8\% to the total HS area.

For mandelate anion, the H\selectlanguage{ngerman}···H contacts are also shown as a single spike
on the FP with the shortest contact at 2.0 Å. In the case of H···O
contacts, there is a remarkable difference noticed on the FP as compared
to the lysinium ion. The contribution from donor molecules (\emph{d}
\textsubscript{e} \textgreater{} \emph{d} \textsubscript{i}) is reduced
by \emph{ca} . 2.5\% that of the acceptor molecules (\emph{d}
\textsubscript{e} \textless{} \emph{d} \textsubscript{i}) of the anion.
Similarly, the acceptor molecules contributing more to the H···C
contacts from the anion as compared to the cation in which the
contribution of donor molecules is more towards crystal packing.
Furthermore, the contributions of H···H and H···O also varied between
water molecules.

\textbf{\{insert Figure 5\}}

\textbf{Topological analysis of intermolecular interactions}

The intermolecular interactions present in the title complex were
quantitatively analyzed using topological parameters. These parameters
for the intermolecular interactions at the BCPs are summarized in Table
3 and the molecular graphs of various dimeric motifs are depicted in the
supporting information (Fig. S1). The molecular graphs In the title
complex, six intermolecular N--H···O hydrogen bonding interactions are
observed in which three of them are
N--H\textsuperscript{+}···O\textsuperscript{-} type HB (involving
protonated side chain/backbone N atoms and deprotonated carboxylate
groups of lysine and mandelate) and the remaining three of them are
N--H\textsuperscript{+}···O type HB (involving oxygens of water and
hydroxy groups).

\textbf{\{insert Table 3\}}

The electron densities (\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r)) and Laplacian of the electron
densities ([?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r)) of the
H\textsuperscript{+}\selectlanguage{ngerman}···O\textsuperscript{-} interactions (involving
ammonium and carboxylate groups) are 0.215 to 0.277 e
Å\textsuperscript{-3} and 2.610 to 3.041 e Å\textsuperscript{-5}. The
corresponding values for H\textsuperscript{+}···O interactions are
ranging from 0.114 to 0.227 e Å\textsuperscript{-3} and 1.79 to 2.796 e
Å\textsuperscript{-5}. The \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) and [?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ}
\selectlanguage{english}(r) values are slightly lower for
N--H\textsuperscript{+}\selectlanguage{ngerman}···O\textsubscript{water} interactions as
compared to other
N--H\textsuperscript{+}···O/O\textsuperscript{-}interactions. The
theoretical \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) and [?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) values for
these interactions are comparable to those of values obtained from
experimental charge densities studies.\textsuperscript{41}Moreover, both
\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) and [?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) values for the
intermolecular N--H\textsuperscript{+}\selectlanguage{ngerman}···O/O\textsuperscript{-}hydrogen
bonding interactions show exponential decay trend with the magnitude of
bond path (\emph{R} \textsubscript{ij}) values (\emph{R}
\textsuperscript{2}=0.993 for \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) and\emph{R}
\textsuperscript{2}=0.938 for [?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r)).
However, there is a linear correlation between\emph{R}
\textsubscript{ij} values and the bond dissociation energies (\emph{D}
\textsubscript{e}) with the \emph{R} \textsuperscript{2} value of 0.975.
For different HBs, these types of correlations have been found in
previous work.\textsuperscript{42,43}Among the above six interactions,
four interactions (N2--H2C\selectlanguage{ngerman}···O1, N1--H1C···O3, N2--H2A···O2W and
N1--H1B···O1W) satisfy the conditions i.e. \(|\frac{V(r)}{G(r)}\)\textbar{}
\textless{} 1; \emph{H} (r) \textgreater{} 0 and
\selectlanguage{english}[?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) \textgreater{} 0) and these
interactions are categorized as closed shell interactions and the
remaining two interactions (N2--H2B \selectlanguage{ngerman}···O2 and N1--H1A···O5) have
intermediate (\(|\frac{V(r)}{G(r)}\)\textbar{} \textgreater{} 1;\emph{H} (r)
\textless{} 0 and \selectlanguage{english}[?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) \textgreater{} 0)
values between closed and shared shell interactions.\textsuperscript{44}
The Laplacian of the electron density and the total electronic energy
density for these two interactions are shown in Fig. 6.

\textbf{\{Insert Figure 6\}}

The magnitude of the \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) and [?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r)
values for the five intermolecular O--H\selectlanguage{ngerman}···O interactions fall in the
range (0.013 \textless{} \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) e \selectlanguage{ngerman}Å\textsuperscript{-3}
\textless{} 0.236; 0.580 \textless{} \selectlanguage{english}[?]\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) e
\selectlanguage{ngerman}Å\textsuperscript{-5} \textless{} 3.355) proposed by Koch-Popelier for
hydrogen bonds.\textsuperscript{45}Further, these interactions are found
to be closed shell in nature. It is of interest to note that \emph{R}
\textsubscript{ij} and\emph{D} \textsubscript{e} values for the O--H···O
interactions follow the exponential decay trend (\emph{R}
\textsuperscript{2}=0.972) rather than linear correlation (\emph{R}
\textsuperscript{2}=0.844). The title complex also stabilized by three
intermolecular C--H···O interactions. As can be seen from the table 3,
the \selectlanguage{greek}\emph{ρ} \selectlanguage{english}(r) values for these interactions lie within the suggested
limit of Koch-Popelier. However, only one interaction (C10--H10\selectlanguage{ngerman}···O2)
which is involving in the self-assembly of mandelate anions satisfying
the suggested limit of the Laplacian.

In addition to N--H\textsuperscript{+}···O/O\textsuperscript{-},
O--H···O and C--H···O interactions, some of the motifs are additionally
stabilized by intermolecular C--H···C(\selectlanguage{greek}π\selectlanguage{english}), C\emph{sp}
\textsuperscript{3}--H\selectlanguage{ngerman}···H--C\emph{sp} \textsuperscript{2} type
dihydrogen bonding and
C\selectlanguage{greek}\textsubscript{π}\selectlanguage{ngerman}···O\textsubscript{lp}interactions. These three
interactions are of closed shell in nature as revealed by the
topological parameters. It should be noted that the C\emph{sp}
\textsuperscript{3}--H···H--C\emph{sp} \textsuperscript{2} type
dihydrogen bonding interaction is found be to strongest based on the
values of \emph{D} \textsubscript{e} and \emph{H} (r) as compared to
C--H···C(\selectlanguage{greek}π\selectlanguage{english}) interactions.

\textbf{Conclusions}

The lysine amino acid was cocrystallized with an important antiseptic
agent mandelic acid. Single crystal X-ray analysis revealed that there
was a proton transfer from the carboxylic acid group of mandelic acid to
the lysine side chain and lysine also exhibits a zwitterionic form due
to the proton transfer from the carboxylic acid of lysine to the
backbone amino group. The inclusion of water molecules in the crystal
lattice facilitates the formation of intermolecular N--H\selectlanguage{ngerman}···O and
O--H···O interactions. The strength and stabilizing/destabilizing nature
of different dimeric complexes were evaluated by the PIXEL energy
analysis. The relative contribution of different inter-contacts was
qualitatively analyzed using Hirshfeld surface analysis and 2D
fingerprint plots. Topological analysis suggested that
N--H\textsuperscript{+}···O\textsuperscript{-} interactions which
emanated from proton transfer between the side chain N2 of lysine and
the carboxylate of the mandelate and between atom backbone N1 and the
carboxylate group of lysine showed intermediate bonding character
between closed and shared shell interactions. Other interactions that
exist in the title complex are closed shell in nature.

\textbf{Acknowledgments}

The authors TB and VS would like to acknowledge the CSIR, New Delhi,
India for providing financial support {[}Project ref. No.
03(1314)/14/EMR II dt.16-04-14{]}. The authors gratefully acknowledge
the scientific supports extended by Sophisticated Analytical Instrument
Facility (SAIF), Indian Institute of Technology Madras, India. ST and
MJP would like to thank Laboratorio Nacional de Supercomputo del Sureste
(LNS-BUAP, Mexico) for computational resources.

\textbf{Keywords:} lysine . mandelic acid . QTAIM . PIXEL . Hirshfeld
surface

\textbf{Conflict of interests}

The authors declare no potential conflict of interest.

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\textbf{Hosted file}

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