# Net electrophilicity as computational route for the choice of favorable
ionic liquids in nanoparticle production

Marta Bon
Electron Microscopy Center
Empa, Swiss Federal Laboratories for Materials Science and Technology CH-8600
Dübendorf, Switzerland
Exscientia
The Schrödinger Building
Oxford Science Park
Oxford OX4 4GE, United Kingdom & Debora Keller
Electron Microscopy Center
Empa, Swiss Federal Laboratories for Materials Science and Technology CH-8600
Dübendorf, Switzerland & Rolf Erni
Electron Microscopy Center
Empa, Swiss Federal Laboratories for Materials Science and Technology CH-8600
Dübendorf, Switzerland
& Daniele Passerone
nanotech@surfaces Laboratory
Empa, Swiss Federal Laboratories for Materials Science and Technology CH-8600
Dübendorf, Switzerland
<EMAIL_ADDRESS>Current addressCorresponding author

###### Abstract

In the last years, the potential of using ionic liquids (IL)s as an
environment for nanoparticle (NP) synthesis has been demonstrated and in
particular, triggering NP formation in ILs by electron irradiation has been
reported as a very simple and clean route for NP production. Starting from the
recent evidence for a correlation between an IL’s capability to support NP
production and the radiochemical instability of the IL’s cation, we used
conceptual Density Functional Theory (DFT) to provide a pre-screening of a set
of different IL cations. The screened quantity is the net electrophilicity
which we suggest as possible measure of this instability. Therefore, our work
not only gives a measure for the likelihood of NP generation in different ILs,
but it also provides a model which can further be extended and applied to
obtain information about any other IL of interest. Moreover, our theoretical
approach outlines a strategy which may reduce a lengthy experimental
investigation for the identification of the most suitable IL for a particular
reaction.

_Keywords_ Conceptual DFT $\cdot$ Global Electrophilicity $\cdot$ Ionic
Liquids $\cdot$ Reactivity $\cdot$ Nanoparticles $\cdot$ Electron Microscopy

Figure 1: Graphical Table of Contents

##  1 Introduction

In the last decades, nanotechnology has been spanning several industrial
sectors, from energy storage to drug delivery.1 The wide range of possible
applications together with their tunable properties make metal nanoparticles
(NP) key materials for further progress in science and technology. Among the
several bottom-up strategies for NP production, liquid phase processes have
recently exploited the use of room-temperature ionic liquids (ILs) that allow
the synthesis of pure NP, not converted with stabilizing agents that can
negatively affect their catalytic activity. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
One possible way to trigger NP formation is to irradiate the IL, which
contains the NP precursor, e.g. with electrons.6 Regarding practical aspects,
this process provides a simple and clean route for NP synthesis. More in
general, this approach opens new possibilities in the field of NPs research.
As ILs have the unique property to withstand high-vacuum conditions in their
liquid state, the early stages of NP formation triggered by an electron beam
can e.g. be studied by in situ transmission electron microscopy (TEM) at very
high spatial and moderate temporal resolution.8 In a simplified way, the NP
production in the IL can be described by a cascade of four subsequent steps:
At first, the metal precursor (usually a salt) dissolves in the IL as metal
cations and other ions (step 1). Second, the electron beam interacts with the
IL, mainly producing solvated electrons and radical IL cations (step 2). Then,
these highly reactive species interact with the metal cations and reduce them
to neutral atoms (step 3). The metal atoms finally undergo a nucleation-and-
growth reaction resulting in the formation of NPs (step 4).
In this respect, it has been recently underlined that while the shape of the
NP is affected by the IL anion,5, 10 the success of metal ion reduction and NP
production mainly depends on the characteristics of the IL’s cation, and in
particular on its radiochemical instability.3, 6, 8 In fact, as the solvated
electrons and the IL’s radicals are expected to be responsible for reducing
the metal precursor, their properties are likely to be critical for the NP
formation mechanism.
Conceptual Density Functional Theory13 qualifies as possible instrument to
identify and rank the different cations on the basis of their reactivity,
estimating the so called net electrophilicity index ($\Delta\omega$).14 This
is a global reactivity indicator (one value is assigned for each system, i.e.
molecule), and is defined as the difference between the electroaccepting
($\omega^{+}$) and the electrodonating ($\omega^{-}$) power, which are
function of the ionization potentials (IP) and the electron affinity (EA):

$\Delta\omega=\omega^{+}-(-\omega^{-})\approx\frac{(IP+3EA)^{2}+(3IP+EA)^{2}}{16(IP-
EA)}.$ (1)

High values of $\Delta\omega$ correspond to highly reactive species, low
values to stable and inert molecules. The quantities in Eq. 1 are computed via
DFT calculation (in this work, hybrid and double hybrid functionals are used,
see Supporting Information (SI) for details) , and the word conceptual in the
method stems from the fact that we extract a measurable quantity and relate it
to a known chemical concept (e.g. chemical potential, chemical hardness,
electrophilicity). Note that different definitions for $\omega^{+}$ and
$\omega^{-}$ are provided in literature,15 and further discussion is reported
in Sections S1.1 and S1.3 of the SI.
In this work, we rank the cationic species on the basis of $\Delta\omega$, and
discuss the results in light of the IL power in NP production as found in
published experimental work (Figures 2 and 3 and Table 1). We further extend
our study to other IL cations that can be used in this field, offering the
first pre-screening predictive study for this purpose (Figure 5).

Figure 2: Cations constituting the ILs used for NP production triggered by irradiation (cfr. Table 1). The corresponding $\Delta\omega$ are reported in Figure 3. Table 1: List of ILs experimentally used for NP production. Structures are reported in the Figure 2. IL Cation | Anion | Precursor | NP
---|---|---|---
IL effective in NP production
$\mathrm{[Al\\_2Im]^{+}}$ | $\mathrm{[Br]^{-}}$ | $\mathrm{NaClO_{3}}$ | Na [9]
$\mathrm{[BuMeIm]^{+}}$ | $\mathrm{[NTf_{2}]^{-}}$ |  $\mathrm{MgCl_{2}}$,$\mathrm{Fe[Tf_{2}N]_{2}}$,$\mathrm{Zn[Tf_{2}N]_{2}}$ | Pd, Pt [7]
$\mathrm{NaAuCl_{4}}$ | Au [3]
$\mathrm{[PF6]^{-}}$ | $\mathrm{Pt_{2}dba)_{3}}$ | Pt[2]
$\mathrm{EtMeIm}^{+}$ | $\mathrm{NTf_{2}^{-}}$ |  $\mathrm{K_{2}PdCl_{4}}$, $\mathrm{K_{2}PtCl_{4}}$ | Pd, Pt [7]
$\mathrm{EtSO_{4}^{-}}$ | $\mathrm{Na_{2}SeO_{3}}$ | Se [12]
$\mathrm{MePyr^{+}}$ | $\mathrm{Ac^{-}}$ | $\mathrm{NO_{3}}$ | Ag [10]
$\mathrm{PrMe_{3}N^{+}}$ | $\mathrm{NTf_{2}^{-}}$ | $\mathrm{Ag_{2}O}$ | Ag [11]
IL ineffective in NP production
$\mathrm{BuMeN^{+}}$ | $\mathrm{NTf_{2}^{-}}$ |  $\mathrm{K_{2}PdCl_{4}}$, $\mathrm{K_{2}PtCl_{4}}$ | Pd, Pt [7]

##  2 Results

###  2.1 Benchmarking

At first, we performed the calculation of $\Delta\omega$ on the ILs cations
already tested in NP production (Figures 2-3 and Table 1).
As shown in Figure 3, cations exhibiting higher values of $\Delta\omega$ are
the ones that have experimentally shown to be more effective in the NP
production and thus radiochemically less stable (Table 1). Vice versa,
$\mathrm{[Bu_{3}MeN]^{+}}$, the species testified in literature not producing
NP, has by far the lowest value of $\Delta\omega$ in this series.
Unfortunately, it is cumbersome to find reference to studies of negative
cases, namely ILs ineffective in NP production through electron irradiation.
Nevertheless, we can comment some of the available (or predicted) trends in
literature. Based on the work by Lu et al.,16 Tsuda and coworkers7 predicted
that ILs constituted by cations having short alkyl chain, like ethyl groups,
enhance crystal growth. We therefore examined the effect of alkyl chain length
(Figure 4) on the reactivity of alkylmethylimidazolium
($\mathrm{[R_{1}MeIm]^{+}}$), and on alkyltrimethylammonium
($\mathrm{[R_{1}Me_{3}N]^{+}}$). We find the expected inverse relation between
$\Delta\omega$ and chain length for both types of cations, although more
pronounced for $\mathrm{[R_{1}Me_{3}N]^{+}}$ than for
$\mathrm{[R_{1}MeIm]^{+}}$, because of the resonance effects. Interestingly,
we found that in general $\mathrm{[R_{1}MeIm]^{+}}$ is more reactive than
$\mathrm{[R_{1}Me_{3}N]^{+}}$ with few exceptions corresponding to alkyl
chains of only one or two carbons. In particular, we propose the cation
$\mathrm{[Me_{4}N]^{+}}$ (chain length equal to 1) as good candidate for NP
production, because it shows higher $\Delta\omega$ compared to
$\mathrm{[MePyr]^{+}}$ (dashed black line in Figure 4), the latter being the
most reactive among the cations currently experimentally tested for electron
irradiation (Figure 2). To the best of our knowledge, $\mathrm{[Me_{4}N]^{+}}$
has not been used to produce NPs upon electron irradiation so far, but only
e.g. to peptize $\mathrm{Fe_{3}O_{4}}$ magnetic NPs through chemical
interaction of the cations with the NP surface.16, 17, 18

Figure 3: Relative ($\Delta$) net electrophilicity index ($\Delta\omega$) for
cations reported in Table 1. The lowest value for $\Delta\omega$ is taken as
reference and corresponds to the least reactive cation
($\mathrm{[Bu_{3}MeN]^{+}}$). The red dashed line indicates a hand-made
threshold defined as lowest $\Delta\omega$ amongst the working ILs of Table 1.
Figure 4: Relative ($\Delta$) net electrophilicity index ($\Delta\omega$) as
function of alkyl chain length. The reference is the same of Figure 3 and
corresponds to $\mathrm{[Bu_{3}MeN]^{+}}$. In blue
$\mathrm{[R_{1}Me_{3}N]^{+}}$ while in green $\mathrm{[R_{1}MeIm]^{+}}$
cations. On the $x-$axis, the number of carbon atoms constituting the
$\mathrm{R_{1}}$ chain. The three members of this series
($\mathrm{[BuMeIm]^{+}}$, $\mathrm{[EtMeIm]^{+}}$, and
$\mathrm{[PrMe_{3}N]^{+}}$), already considered in Figure 3 are marked by
yellow, while the empirical effective/non-effective threshold drawn in Figure
3 is marked with a red-dashed line. The gray-dashed line corresponds to the
highest value of $\Delta\omega$ in Figure 3.

###  2.2 Prescreening

The majority of ILs synthesized is based on alkylated amines and imidazolium
(N-ILs), and only a few on sulfur (S-ILs) and phosphor (P-ILs) cations. For
this reason, there is no indication in literature regarding S-ILs’ and P-ILs’
performances in NP production with electron irradiation techniques. The
computational pre-screening in Figure 5 considers for the first time their
possible role in this field by assessing ten possible candidates per category
(Figure S2-S3 in SI). Twenty N-ILs cations in addition to the ones presented
in Figures 3 are instead considered from N-ILs (S1 in SI), yielding a global
pre-screening of forty cations. As shown in Figure 3, all the cations are
characterized by a similar range of $\Delta\omega$ (from about -0.1 to 4.0
eV), and the ones constituting S-ILs and P-ILs seem to be the more stable than
the N-based, in line with experimental expectations.19

##  3 Conclusions

To conclude, we used the net electrophilicity as a criteria to classify the
reactivity of forty cations, constituents of ILs. After successfully
benchmarking the protocol against the existing experimental evidence, for each
cation category (N-ILs, P-ILs, and S-ILs) we found several good candidates for
NP production. Our prediction should be tested experimentally relatively
straightforwardly. The computational protocol can be easily extended to
thousands of species, opening new horizons e.g. for NP synthesis observation
by in situ TEM in ILs, and in general for NP synthesis in ILs including all
their possible applications, from catalysis to electrochemistry.

Figure 5: Relative ($\Delta$) net electrophilicity index ($\Delta\omega$)
N-based, P-based and S-based cations. The reference (black dashed line) is the
same of Figure 3 and corresponds to $\mathrm{[Bu_{3}MeN]^{+}}$. The red dashed
line indicates the threshold defined in Figure 3. Structures are reported in
Figures S1-S3 of SI.

##  4 Supporting Information

###  S1.1 Theory: Conceptual DFT

####  S1.1.1 Net Electrophilicity

In the following, we report the different definitions14 for $\Delta\omega$,
$\omega^{+}$ and $\omega^{-}$.

$\Delta\omega=\omega^{+}+-(-\omega^{-})=\omega^{+}+\omega^{-},$ (S1)
$\Delta\omega=\omega^{+}+\left(\frac{1}{\omega^{-}}\right).$ (S2)

Def 1 for $\omega^{+}$ and $\omega^{-}$ :

$\omega^{-}=\frac{(3IP+EA)^{2}}{16(IP-EA)},$ (S3)
$\omega^{+}=\frac{(IP+3EA)^{2}}{16(IP-EA)}.$ (S4)

Def 2 for $\omega^{+}$ and $\omega^{-}$ :

$\omega^{-}=\frac{(IP)^{2}}{2(IP-EA)},$ (S5) $\omega^{-}=\frac{(EA)^{2}}{2(IP-
EA)}.$ (S6)

IP, and EA are the ionization potential and electron affinity, whose
calculation is discussed in S1.1.2.

####  S1.1.2 Ionization Potentials and Electron Affinities

The accuracy of the calculation of IP and EA is expected to vary depending
both on the level of theory and on the basis set. For Hartree Fock
calculations, IP and EA can be calculated as the negative of the energies of
the HOMO and LUMO respectively, using Koopmans’ theorem.20 For Density
Functional Theory (DFT) methods, the HOMO and LUMO orbitals are well known not
to accurately reproduce IPs without corrections.21 This limitation can be
overcome calculating the IP and EA from the absolute energies between the N,
N+1, and N-1 electrons system:

$IP=E(N-1)-E(N),$ (S7) $EA=E(N)-E(N+1).$ (S8)

###  S1.2 Methods

Calculations were performed with GAMESS code.22 At first, geometry
optimizations are carried out at B3LYP/6-311+G(d,p).23 Although DFT B3LYP
functional has been successfully used in a wide range of applications, after
the geometry optimizations, we chose to carry out more accurate energy
calculations at the B2PLYPD level,24 proven to outperform the other DFT and
some beyond-DFT methods (MP2) especially in the estimation of EA.21

####  S1.2.1 Simulated Systems

Table S1: Abbreviations used for the cations Abbreviation |  | Abbreviation |
---|---|---|---
Al | ally | Phol | pholanium
Bu | buthyl | Pr | propyl
Et | ethyl | Pyr | pyrrolidinium
Im | imidazolium | S | sulfonium
Me | methyl | ThPyr | thiopyrylium
N | ammonium | Tl | thiolanium
P | phosphonium |  |
Figure S1: Schematic of the N-ILs cations considered. Gray-highlighted
structures are reported in the benchmark cal-culation of Figure 1. Orange-
highlighted cation is the reference ($\Delta\omega=0$) for Figures 3-5 of the
manuscript. Green and blue-highlighted cations are reported in Figure 2 of the
manuscript. Figure S2: Schematic of the P-ILs cations considered. The
corresponding $\Delta\omega$ is reported in Figure 5. Figure S3: Schematic of
the S-ILs cations considered. The corresponding $\Delta\omega$ is reported in
Figure 5.

###  S1.3 Preliminary Tests

####  S1.3.1 On the Different Definitions of Net Electrophilicy

On the six cations reported in the main paper, we tested the validity of the
definitions reported in Eqs. S1-S6. As shown in Figure S4, although Eqs. S1
and S2 give rise to different values of $\Delta\Delta\omega$, a similar trend
is recognized. The use of Eqs. S5,S6 in place of Eqs. S3,S4 does not affect
the results.

Figure S4: Differences in Net Electrophilicity (eV). The lowest $\Delta\omega$
calculated using Eqs. S1, S3-S4 has been taken as reference. IP and EA have
been calculated using Koopmans’ theorem using HOMO-LUMO energies calculated at
B2PLYPD level.

####  S1.3.2 Net Electrophilicy at Different Levels of Theory

For the six cations reported in Table 1 of the manuscript, we tested the
estimation of the net electrophilicity at different levels of theory, namely
HF, DFT/B3LYP,23 and DFT/B2PLYPD.24 The geometries were optimized with
DFT/B3LYP functional. The calculation of $\Delta\omega$ was performed
estimating IP and EA using Koopmans’ theorem and through the differences of
absolute energies (B3LYP and B2LYP). The results are reported in Figure S5. In
our opinion, the use of Koopmans’ theorem is not recommended if approximating
DFT exchange-correlation functional with B3LYP, because it predicts
$\Delta\Delta\omega$ values in a range that significantly differs from the
ones of the values resulting from HF and DFT/B2PLYPD calculations. The
calculation of IP and EA using Koopmans’ theorem at DFT/B2PLYPD level gives
similar results to the dif-ferences in absolute energies (cfr. the dashed
green and the solid red lines), hence it has been used for the calcula-tion of
the net electrophilicity of the radical species. HF and DFT/ B2PLYPD show
similar trends, with the exception of one cation, $\mathrm{[Bu3MeN]^{+}}$ and
$\mathrm{[Al2Im]^{+}}$. We analyzed this result comparing HOMO and LUMO
orbitals.

Figure S5: Differences in Net Electrophilicity (eV). The lowest $\Delta\omega$
value for each level of theory has been taken as reference. Legend: (K)
indicates that IP and EA have been calculated using Koopmans’ theorem.
($\Delta E$) indicates that they have been evaluated accordingly to Eqs.
S6-S7.

####  S1.3.3 The Effect of the Implicit Solvent

In the following, we comment the effect of the SMD-GIL implicit solvent
developed by Bernales and coworkers25 on the estimation of $\Delta\omega$. We
modified the parameters for the aromaticity ($\Phi$) and halogenicity
($\Psi$), accordingly to the IL, keeping all the other parameters unchanged.
For the calculation of $\Phi$ and $\Psi$, we considered two different anions,
to test if the trend for $\Delta\omega$ is maintained, taking as reference the
gas phase case. We conducted this test on the six cations reported in Table
S2, performing energy calculations at B2PLYPD level on the geometries
optimized with the B3LYP functional in presence of the SMD-GIL solvent. As
shown in Figure S6, no significant differences from the calculation in gas
phase are observed. EA and IP were calculated again using Koopmans’ theorem.

Table S2: Parameters cation/anion dependent for the SMD-GIL implicit solvent.
Additional parameters: $\sum\alpha_{2}^{H}=0.229$, $\sum\beta_{2}^{H}=0.265$, $\varepsilon=11.50$, $n=1.43$, $\gamma=61.24$ Anion represented by the SMD-GIL $\rightarrow$ | $\mathrm{[NTf2]^{-}}$ | $\mathrm{Cl^{-}}$
---|---|---
Cation $\downarrow$ |  |  |  |
$\mathrm{[Al2Im^{]}+}$ | 0.12 | 0.23 | 0.25 | 0.08
$\mathrm{[Bu3MeN]^{+}}$ | 0 | 0.21 | 0 | 0.07
$\mathrm{[BuMeIm]^{+}}$ | 0.12 | 0.24 | 0.27 | 0.09
$\mathrm{[EtMeIm]^{+}}$ | 0.13 | 0.26 | 0.33 | 0.11
$\mathrm{[MePyr]^{+}}$ | 0.19 | 0.29 | 0.57 | 0.14
$\mathrm{[PrMe3N]^{+}}$ | 0 | 0.27 | 0 | 0.13
Figure S6: The lowest $\Delta\omega$ value in gas phase (corresponding to
$\mathrm{[Bu3MeN]^{+}}$) was taken as reference. Parameters describing the
SMD-GIL are reported in Table S2.

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