Investigation of the Change in the Electronic Propertiesof FeF3 by the Introduction of Oxygen Using a MolecularOrbital Method

Yongseon Kim,* Sujin Choi, and Subin Kim

FeF3 has attracted interest as a conversion-reaction-based posi-

tive electrode material in applications to lithium ion batteries.

However, slow reaction kinetics is a major drawback due to its

poor electrical conductivity. The electronic features of FeF3

were examined using the DV-Xa molecular orbital method.

This article reports the effects of oxygen doping on the bond-

ing characteristics and electrical conductivity. An analysis of

the bond overlap population and spatial distribution of elec-

trons showed that the FeAO bond has a more covalent nature

than the FeAF bond. New energy levels were generated in the

original band gap region through an interaction between the

Fe3d and O2p orbitals with the introduction of oxygen. The

electrical conductivity of FeF3 is expected to be increased by

the partial substitution of oxygen for fluorine due to the

higher covalent character and the formation of new energy

levels. VC 2013 Wiley Periodicals, Inc.

DOI: 10.1002/qua.24566

Introduction

Lithium ion batteries (LIBs) are currently the main power

source of mobile electronic devices due to their high density

of energy storage.[1,2] The multifunctionalization of mobile

devices and the expansion of applications of LIBs to electric

vehicles or power storage systems require a persistent increase

in the energy storage capacity of LIBs. For this, the develop-

ment of high-capacity active materials is essential, but difficult.

Moreover, the limit for increasing the capacity of conventional

materials, for which electrochemical performance is based on

intercalation/deintercalation of Li ions, has been reached

because the number of available electrons is determined by

the number of Li sites in the crystal. For example, LiCoO2,

which is the positive electrode material used most widely, can

accommodate only one Li ion; therefore, only one electron per

formula unit is possible by using only two oxidation states of

Co31 and Co41.

As an alternative, new active materials of a conversion reac-

tion have attracted attention.[3–5] Among the various oxide,

nitride, fluoride, and phosphide materials examined thus far,

FeF3 has attracted particular interest because it is expected to

be used as a positive electrode material, due to its relatively

high operating voltage.[5–10] The slow kinetics of the conver-

sion reaction might be the main drawback to the commerciali-

zation of fluorides, including FeF3, causing a decrease in the

discharge voltage and difficulty in achieving a high rate or

room temperature operation. The reaction rate is closely

related to the electrical conductivity and ionic diffusivity.[7–12]

Therefore, improving them may be a key factor for the appli-

cation of these materials to LIBs. Badway et al. reported that

compositing FeF3 with conducting carbon by high energy mill-

ing could increase the electrical conductivity and achieve a

stable electrochemical operation.[6,7] A composite of FeF3 and

carbon nanotube or graphene has been reported.[13–15]

The partial oxidation of fluoride materials has been eval-

uated as a way of improving the intrinsic conductivity.[8,16–18]

Metal oxyfluorides, such as FeOF or Fe2OF4, or partially oxi-

dized FeF3, can show better electrochemical properties than

pure FeF3. Researchers have attributed this improvement to

the increased conductivity by the introduction of covalent

MAO bonds into highly insulating MAF ionic bonds,[8,16,17] but

this interpretation is not based on precise analysis or support-

ing information. In this study, the electronic states of FeF3

were examined by a first principle method, focusing on the

change in the electronic states and the bonding nature with

the partial substitution of F by O in particular. The effect of

the introduction of O on the electrical conductivity of FeF3 is

discussed based on the calculation results.

Methods

The electronic properties, such as the density of states (DOS),

bond overlap population (BOP), and spatial charge distribution

were analyzed using a first-principles discrete variational Xa(DV-Xa) molecular orbital method.[19] This method numerically

solves the Schr€odinger equation for a many-body system

based on a linear combination of atomic orbitals (LCAO)

approximation and the Xa potential using the Har-

tree2Fock2Slater method.[20] The molecular orbitals based on

the LCAO approximation and the exchange interaction term of

the Xa potential are expressed as

Y. Kim, S. Choi, S. Kim

Department of Materials Science and Engineering, Inha University, Incheon

402–751, Korea

Fax: (182) 32 862 5546

E-mail: ys.kim@inha.ac.kr

Contract grant sponsor: Inha University Research Grant;

contract grant number: INHA-46435.

VC 2013 Wiley Periodicals, Inc.

340 International Journal of Quantum Chemistry 2014, 114, 340–344 WWW.CHEMISTRYVIEWS.ORG

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uj rð Þ5X

icijvi rð Þ;VXC rð Þ523a 3q rð Þ=4pð Þ1=3

where uj is the molecular orbital wave function, cij is a weight-

ing coefficient, vi is the atomic orbital wave function, and q is

the electron density. The a parameter varies in value depend-

ing on the atomic species and approaches 2/3 with increasing

the atomic number.[21]

The DV-Xa molecular orbital method requires no restrictions

imposed in the form of the basis functions because the calcu-

lation is conducted numerically. Consequently, LCAO can be

used without modification. This method does not use the

pseudopotential approximation. All the atomic orbitals of the

model cluster are included in the calculation, which can pro-

vide reliable information on the molecular orbitals and elec-

tron distributions.[22–24]

[Fe19F84] and [Fe19F83O1] cluster models were prepared for

the calculation of this study. A Fe atom was centered in both

clusters, and one of the six neighboring F atoms was substi-

tuted by O in the [Fe19F83O1] cluster. Substitution of only one

F atom with an O atom may seem too small, but the introduc-

tion of many O atoms affects the Madelung field. The consid-

eration of many configurations to locate O atoms in the

cluster would be necessary, making the calculation far more

complicated. Decreasing the cluster size could be an alterna-

tive way to increase the relative amount of O, but a smaller

cluster results in poor accuracy. Although only one O atom is

introduced in this study, the analysis provides insight by focus-

ing on the local change near the O site.

To prepare the cluster models, a large FeF3 crystal model

composed of more than 1000 atoms was constructed. Atoms

beyond a certain distance from the central Fe atom were

removed, and the clusters were modified so that the surface

would be terminated with F atoms. Although the Fe/F ratio of

the clusters deviated from the stoichiometric value used for

the preparation method, this caused neither any significant

calculation error nor inaccuracy of the oxidation number of Fe,

because an analysis of the electronic properties was per-

formed only for atoms of the inner position in the cluster, and

the oxidation number was programmed to be input independ-

ently. This technique appears reasonable because the surface

F atoms provide a bulk-like environment for the target atoms

inside by ensuring that they contain no broken bonds.[22]

Any changes in the lattice structure with the substitution of

O for F was not reflected, which might be justified considering

that the introduction of O made only a slight change to the

lattice parameter for FeF3 due to the similar ionic radii of O

and F.[16] A distortion of the structure is expected to be negli-

gible because only one F atom out of 84 was substituted. The

calculation results of the DV-Xa method were compared with

and without prior crystal structure relaxation using the density

functional theory (DFT) method, which did not show any sig-

nificant difference. Figure 1 shows a diagram of the clusters,

and Table 1 provides the structural information, in which

opposite magnetic moments were applied to Fe1, Fe2, and

Fe3, considering that FeF3 is an antiferromagnetic material.[25]

The electronic states and bonding characteristics were calcu-

lated using the SCAT program of the DV-Xa software package.

The distribution of charge was calculated by Mulliken popula-

tion analysis. All DOS diagrams were constructed assuming

that each energy level shows a Gaussian distribution, of which

the full width half maximum is 0.1 eV. The clusters were

located in a uniform Madelung potential field to reflect the

electrostatic interaction with the surrounding atoms because

the DV-Xa method does not use periodic boundary conditions.

The Madelung potential field was determined by positioning

point charges at the atomic sites and translating three unit

cells for each direction.

Results and Discussion

Figures 2 and 3 show the DOS diagrams calculated using the

DV-Xa molecular orbital method. The energy level of the high-

est occupied molecular orbital (HOMO) was positioned at 0 eV

in the figures. Figure 2a shows the total DOS of pure FeF3, for

which the band gap was calculated to be �2.5 eV. Li et al. cal-

culated the band gap with a ferromagnetic or antiferromag-

netic configuration by DFT, applying the generalized gradient

approximation (GGA) or GGA 1 U, and reported a band gap of

0.267 eV (ferromagnetic/GGA) �4.138 eV (antiferromagnetic/

GGA 1 U).[25] Although the band gap energy of this study is

slightly underestimated, the value of 2.5 eV, which can be

interpreted as the band gap of a semiconductor or insulator

depending on the viewpoint, may be acceptable for a discus-

sion of the change in electronic states upon the introduction

of O.

Figure 1. The [Fe19F84] cluster model used for the calculation. One of the

six neighboring F atoms of the central Fe was substituted by O for the cal-

culation of the [Fe19F83O1] cluster. [Color figure can be viewed in the online

issue, which is available at wileyonlinelibrary.com.]

Table 1. Structural information of the cluster used for the calculation.

Distance from

the center (A)

Number

of atoms Spin

Fe 0 (centered atom) 1 High (up)

F (O) 1.9191 6 –

Fe 3.7327 6 High (down)

F 3.8551�–5.1030 30 –

Fe 5.1963�–5.3600 12 High (up)

F 5.6168�–7.0071 48 –

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International Journal of Quantum Chemistry 2014, 114, 340–344 341

Figure 2b shows the DOS diagram of FeF3, for which F ions

are partially substituted by O (O-doped FeF3). The overall

shape of the DOS was similar to that of pure FeF3, as shown

in Figure 2a, except for the newly formed levels marked in the

square with a broken line. The position of the DOS curve

shifted because the HOMO level energy changed with the for-

mation of new levels. The DOS curve of O-doped FeF3 became

more continuous than that of pure FeF3 because new levels

were formed in the region, which was a band gap region

before the introduction of O.

For a close examination of the energy levels formed with the

introduction of O, Figure 3 presents the projected DOS (p-DOS)

of each atom. Figures 3a–3c show Fe3d, F2p, and Fe4s 1 4p

p-DOS of pure FeF3, respectively. The DOS around the band gap

was constructed mainly by Fe3d and F2p orbitals and their inter-

actions. The contribution of the Fe4s and Fe4p orbitals was neg-

ligible in the region (Fig. 3c). One of the spin directions was fully

filled with electrons (i.e., the levels were all below the HOMO

level which was positioned at 0 eV) and the others were almost

empty (Fig. 3a), indicating that Fe was in a high spin state. The

magnetic moment of Fe was calculated to be 4.4 lB. Figures

3d–3f show the p-DOS of Fe3d, F2p, and O2p of O-doped FeF3,

respectively. The diagrams show that the new levels were

formed mainly by an interaction of the Fe3d and O2p orbitals.

The change in the bonding nature of FeF3 was investigated

by examining the effective charge of the atoms and the BOP

of the bonds among them. Table 2 lists the effective charge of

Figure 3. DOS diagrams calculated using the DV-Xa molecular orbital method: a)–c) Fe3d, F2p, and Fe4s 1 Fe4p p-DOS of pure FeF3, d)–f ) Fe3d, F2p, and

O2p p-DOS of oxygen-doped FeF3, respectively. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 2. DOS diagrams calculated using the DV-Xa molecular orbital

method: a) total DOS of pure FeF3 and b) that of oxygen-doped FeF3.

[Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com.]

Table 2. Effective charge of the ions calculated using the DV-Xaa molecu-

lar orbital method.

FeF3 O-doped FeF3 Change of charge

Fe 11.773 11.727 2.6%#F 20.599 20.598 0.2%#O – 20.775 –

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342 International Journal of Quantum Chemistry 2014, 114, 340–344 WWW.CHEMISTRYVIEWS.ORG

each atom obtained from a calculation of the molecular orbi-

tals. The introduction of O slightly decreased the effective

charge of Fe and F. The change in the effective charge of Fe

with the introduction of O was examined as a function of the

distance between Fe and O. The effective charge of the three

types of Fe in Table 1 decreased by 2.6, 1.1, and 0.4%, respec-

tively, indicating that the effective charge of Fe differs accord-

ing to the distance from O, or the introduction of O induces a

deviation of the effective charge of the Fe ions.

Figure 4 presents overlap population (OP) diagrams. The left

and right parts of each diagram in Figure 4 denote the OP of

antibonding and bonding orbitals, respectively. The integrated

value of the OP below the HOMO level, that is, the BOP, is a

measure of the covalent nature of the bonds.[20] Figures 4a–4c

show OP diagrams of FeAF, FeAFe, and FAF bonds of pure

FeF3, and Figures 4d–4f present the OP diagrams of FeAF,

FeAO, and FAO in O-doped FeF3, respectively. The formation of

FeAFe, FAF, and FAO molecular orbitals are negligible com-

pared to the cases of FeAF and FeAO. A comparison of Figures

4d and 4e reveal the FeAO bond to be more covalent than the

FeAF bond. This indicates that the substitution of F with O

increases the covalent nature of the FeF3 crystal.

Table 3 lists BOP data. The introduction of O slightly

increases the antibonding BOP, but decreases the bonding

BOP of the FeAF bond. This may be caused by some change

in the relative position of the bonding and antibonding energy

levels and the HOMO level with O-doping. Despite the change,

covalent characteristics were relatively constant. The covalent

nature of the FeAFe and FAF bonds was basically small and

relatively constant. Figure 4 confirms that the covalent feature

of the FeAO bond is larger than the FeAF bond, based on the

quantitative data of Table 3.

Figure 5 shows a contour map of the electron density on the

plane, which includes one Fe at the center and four negative ions

out of six neighbors of the Fe, before (Fig. 5a) and after (Fig. 5b)

the substitution of one of the four F ions with O. The electron

density of O was smaller than that of F because the atomic num-

ber of O is smaller than F by one, and the effective charge of O

was not large enough to compensate for this. An examination of

the contour lines between Fe and F or O indicates that the elec-

tron density between Fe and O is larger than that between Fe

and F. Therefore, the density of delocalized electrons for the

Figure 4. OP diagrams: a)–c) OP diagrams of FeAF, FeAFe, and FAF of pure FeF3, d)–f ) OP diagrams of FeAF, FeAO, and FAO of oxygen-doped FeF3. [Color

figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Table 3. BOP of the bonds calculated using the DV-Xaa molecular orbital

method.

FeF3 O-doped FeF3

Antibonding Bonding Antibonding Bonding

FeAF 0.105 0.264 0.115 0.251

FeAO – 0.090 0.377

FeAFe 0.002 0.002 0.002 0.002

FAF 0.004 0.004 0.004 0.004

FAO – 0.003 0.002

Figure 5. Contour map of electron density: a) pure FeF3 and b) oxygen-

doped FeF3. [Color figure can be viewed in the online issue, which is avail-

able at wileyonlinelibrary.com.]

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International Journal of Quantum Chemistry 2014, 114, 340–344 343

FeAO bond is larger than that for the FeAF bond, indicating that

the FeAO bond has more covalent features than the FeAF bond.

The increase in the covalent characteristics could improve

the electrical conductivity of FeF3, resulting in faster kinetics of

the conversion reaction, 3Li 1 FeF3 $ 3LiF 1 Fe.[16,17] FeF3 was

reported to be a Mott–Hubbard type insulator, not a charge

transfer insulator.[25] The p-DOS diagram of Fe3d obtained in

this study, presented in Figure 3a, agrees with the features of

a Mott–Hubbard type insulator. In a Mott–Hubbard type insu-

lator, electrical conduction is known to occur through charge

transfer among metal ions.[26]

The change in the electronic states with O-doping is expected

to provide a favorable environment for the electrical conduction

of FeF3, which is a Mott–Hubbard type insulator, considering the

results: with the introduction of O, the Fe3d and O2p orbitals

interact and form rather continuous new energy levels in the

original band gap region. This could facilitate charge transfer

among the Fe ions. The difference in the effective charge among

Fe ions caused by the introduction of O might have an effect

on conduction, but this point requires further investigation. The

effect of Li insertion into the FeF3 crystal would also need to be

considered because the conversion reaction is a complicated,

mixed process of Li insertion and ion diffusion.

Conclusions

The electronic states of FeF3, which has attracted interest as a

conversion-reaction-based positive electrode material in LIBs,

was investigated by a molecular orbital method using the DV-

Xa simulation package. The effect of oxygen doping on the

bonding characteristics and electrical conductivity was dis-

cussed. An analysis of the BOP and distribution of electrons

showed that the FeAO bond has more covalent features than

the FeAF bond. The DOS calculated using this method

showed the characteristics of a Mott–Hubbard type insulator.

New energy levels, which were composed mainly of an inter-

action of Fe3d and O2p orbitals, formed in the band gap

region after the substitution of oxygen for some of the fluo-

rine ions. The changes with the introduction of oxygen are

expected to increase the electrical conduction of FeF3.

Keywords: FeF3 � molecular orbital method � conductivity �lithium ion battery

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Received: 15 August 2013Revised: 3 September 2013Accepted: 9 September 2013Published online 10 October 2013

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