Energetics electronic states and magnetism of iron phthalocyanine on pristine and defected graphene layers Aleksei Koshevarnikovand Jacek A. Majewskiy

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Energetics, electronic states, and magnetism of iron phthalocyanine on pristine and

defected graphene layers

Aleksei Koshevarnikov∗and Jacek A. Majewski†

Institute of Theoretical Physics, Faculty of Physics,

University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

Transition metal phthalocyanines (TMPc’s) are under intense scrutiny in the ﬁeld of spintronics,

as they may be promising storage devices. The simplicity and cheapness of such molecules increase

their commercial potential. There is an active study of how the magnetic moment of the metal

centre of such molecules can be changed. Here, we particularly consider the iron phthalocyanine

molecule (FePc) on a graphene layer as a substrate. We study how graphene defects (the Stone-Wales

defect, B-doping, N-doping, S-doping, and combined B (N, S)-doped Stone-Wales defects) change

the FePc electronic structure. We present ab initio study of the systems, which is done using several

approaches: based on periodic plane wave density functional theory (DFT), a linear combination of

atomic orbitals (LCAO) DFT with a cluster representation of graphene, and multiconﬁgurational

methods with the pyrene molecule presented as a miniaturised graphene cluster. The treatment of

the FePc/Graphene hybrid system using multiconﬁgurational methods was done for the ﬁrst time.

It was found that the hybrid systems with B- and N- dopings have quasi-degenerate ground states

and it is necessary to go beyond the approximation of one Slater determinant.

I. INTRODUCTION

The development of spintronics is inextricably linked

with the commercial component. The commercial sphere

is always interested in miniaturising devices and reduc-

ing the cost of production. Recently, for such purposes,

magnetic tetrapyrrole molecules (such as porphyrin and

phthalocyanine) with a metalic atom in the centre have

been studied. Such molecules have been known for a

long time,[1] are easy to manufacture, and were originally

used as a colour pigment. Nowadays, they have an im-

plementation in spintronics and optoelectronics,[2–4] or-

ganic photodetector,[5] and as a ﬁeld-eﬀect transistor.[6]

Tetrapyrrole molecules with a 3d-transition metal in the

centre have a stable ﬂat structure that allows to layer

molecules on the substrate as an additional thin layer or

tightly pack them vertically.[7] A substrate for planting

such organometallic molecules is important, since upon

contact the magnetic properties of molecules can change

for better or worse. The nature of the adhesion and the

change of molecules morphology also depend on the prop-

erties of the substrate.

Graphene is a layer of one carbon atom thick, consist-

ing of condensed six-membered rings, constituting a hon-

eycomb lattice. Carbon atoms in graphene are linked by

sp2-bonds in a hexagonal two-dimensional (2D) lattice.

The ﬁrst description of the production of graphene was

published in 2004.[8] A separate layer of graphene was

obtained by mechanical peeling a graphite rod on a sili-

con dioxide surface. Recent studies have shown the pos-

sibility of changing the magnetisation of a single metal-

organic molecule. The control of the magnetic moment

of the manganese phthalocyanine (MnPc) molecule lying

∗aleksei.koshevarnikov@fuw.edu.pl

†jacek.majewski@fuw.edu.pl

on the BiAg2nanostructure using an external electric

ﬁeld was demonstrated.[9] It was theoretically predicted

that control of the spin state of a structurally similar

iron porphyrin molecule by stretching and compressing

a graphene substrate would be also possible.[10] In both

studies, the central metal atom has two adaptive states

with diﬀerent magnetic moments. Computational predic-

tions [11] also indicate that ZrPc or HfPc deposited on

the graphene/Ni(111) substrate have two diﬀerent struc-

tural conformations, for which the molecules attain dif-

ferent magnetic states depending on the position of the

centre metallic ion, either above the Pc or between the

Pc and the substrate. Such bistability lets us represent

these molecules as elementary keepers of a bit of infor-

mation. Creating a controlled array of such molecules

will bring us closer to creating a storage device based on

single-molecular excitations, which in turn will lead to a

signiﬁcant increase in the density of information.

Recently, the TMPc/2D-material hybrid structures

have also been actively investigated as catalysts for re-

dox reactions. The emerging ﬁeld of hydrogen energetics

needs cheaper catalysts for fuel cells to reduce the cost of

commercial production. Currently, the most popular cat-

alysts are based on platinum group metals,[12] and the

cost of producing such cells is quite high. Recent labo-

ratory studies already show that the use of the FePc/2D

materials structures shows a higher speciﬁc activity of re-

dox reactions. In such catalysts, the iron atom is used as

a centre for trapping oxygen. Then, this atomic oxygen

attaches to itself two protons (the result of the splitting

of a hydrogen molecule) and forms water. Among 2D

materials, the best results were obtained using Ti3C2X2

MXene layer,[13] but there are also many studies with

graphene as a substrate for FePc molecules.[14, 15]

Also, FePc/Graphene structures can be tuned in var-

ious ways. The use of substituents on the periphery of

the phthalocyanine isoindole rings helps to change the

electron density around the central iron atom.[16] Si-

arXiv:2210.01025v1 [cond-mat.mtrl-sci] 3 Oct 2022

FePc-Graphene sandwich structures [17] can also serve

as catalysts, with the outer graphene layer protecting

the device from external poisons. Axial Fe-O coordina-

tion improves oxygen adsorption and thus increases redox

productivity.[18] The use of defects in the graphene layer

increases the catalytic eﬃciency of the elements. For ex-

ample, FePc/Graphene systems with nitrogen impurities

on the surface demonstrated [19] better speciﬁc activity

than platinum catalysts, while such systems were char-

acterised by a higher current density.

The interaction between graphene and transition metal

phthalocyanine (TMPc) molecules is well understood.

The results show that phthalocyanine molecules are at-

tracted to the surface by van der Waals forces, and the

electronic conﬁguration of metal atoms in the centre does

not change signiﬁcantly. The presence of the TMPc

molecule does not open the graphene band gap.[20] FePc

and CoPc molecules on the top of MoS2and graphene

2D layers were studied theoretically [21] and it was found

that while the adsorption energy of a molecule to a sur-

face in the MoS2cases is about 2.5 eV higher than in the

graphene cases, both layers do not signiﬁcantly change

magnetic anisotropy parameters and metallic d-orbitals

distributions. When using graphene as a layer between

the FePc molecule and a metal surface, graphene weak-

ens their ferromagnetic interaction.[22] The perpendicu-

lar stuck of FePc on graphene is also possible.[7] It was

found that such a combination is stable and graphene

barely inﬂuences on FePc magnetic properties.

In experiments, FePc molecules found on pure

graphene tend to form self-connecting structures based

on the attraction of molecules to each other by van

der Waals forces.[23] For artiﬁcial isolation of a single

molecule from the ﬁlm, injection of defects on graphene

can be used. Theoretical calculations of the FePc

molecule adsorped to the defected graphene were car-

ried out for single vacancy, double vacancy,[24] and (B,

N, S)-dopings,[25] whereas the N-doping was also exper-

imentally studied.[23] The above studies show a little bit

higher adsorption energy of FePc to defected graphene

compared to pristine graphene. Scanning tunnelling mi-

croscopy images clearly show the FePc molecule adsor-

ped on top of the N-doping. Moreover, it turns out that

the magnetic moment of the system depends on the type

of defect. In particular, B-dopants induce the increase of

the magnetic moment, N-doping leads to a decrease of the

magnetic moment, whereas introducing of S-impurities

causes the quenching of the magnetic moment.

In the literature, a similar interaction of TMPc

molecules with a Stone-Wales defect [26] in graphene was

considered. This defect, which consists of two pairs of

ﬁve and seven carbon polygons, occurs due to the rota-

tion of two adjacent carbon atoms relative to their centre

by 90 degrees. Thus, when a defect is formed, there is

no change in the chemical composition of the material.

This fact may lead to the idea of maintaining the mag-

netic moment of the TMPc - defected graphene system.

The adsorption energy of TMPc to graphene with the

Stone-Wales defect was calculated [27] to be 6% higher

for Zn as TM in TMPc and 10% higher for Cu. Studies of

the iron porphyrin/graphene/Ni(111) revealed [28] that

when the Stone-Wales defect is formed the graphene layer

is not ﬂat anymore, just exhibiting a wavelike shape.

Most of the studies of systems consisting of a two-

dimensional surface and a metal-organic molecule were

carried out using the Kohn-Sham realisation of the den-

sity functional theory (DFT) employing plane-waves as

the basis set. This method reproduces well the geometry

of a two-dimensional surface due to the fact that periodic

conditions are used but does not allow one to study the

d,f- orbitals of metal atoms, which are of direct interest

for such structures.

Nowadays, the computational capabilities allow us to

carry out studies of 2D-surface - metal-organic molecule

complexes using multireference methods. For example,

the iron porphyrin molecule and a graphene ribbon were

treated separately with very high-level accuracy.[29] Por-

phyrin without a central metal on the graphene oxide was

studied using multireference methods with 8 orbitals as

active ones.[30] To employ multireference methods, the

problem has to be reformulated in terms of ﬁnite, non-

periodic systems, commonly used in quantum molecular

chemistry. This problem can be easily solved in the case

of graphene. A limited piece of the graphene layer, here-

inafter referred to as a cluster, can be limited by function-

alising the extreme carbon atoms with hydrogen. With

a suﬃciently large graphene layer in the area, it is pos-

sible to create a structure very similar in physical and

chemical properties to pure graphene.

Here, we use both DFT and multireference approaches

to investigate the FePc/Graphene hybrid system. In ad-

dition to the interaction of FePc with the pure sheet

of graphene, the interaction of FePc with defects in

graphene is also of interest. One of the main defect selec-

tion factors was the compliance of geometric parameters

between the system with boundary conditions and the

cluster. For example, it was found that graphene clus-

ters, in the centre of which one (single valence) or two

(double valence) atoms are missing, do not repeat the ﬂat

structure of analogous periodic systems; stable states ob-

tained after optimization have strong curvatures. There-

fore, further comparison of periodic and cluster systems

with these defects is not possible.

Stone-Wales defects and doping of atoms are of partic-

ular interest for studying. The interaction of the Stone-

Wales graphene defect with the FePc molecule has not

been studied thoroughly enough, limiting itself to de-

scribing similar structures.[27, 28] Doping of atoms in

the case of a graphene cluster requires special considera-

tion, because, in contrast to a doped periodic structure,

in which there may be no magnetic moment, the cluster

must have an initial multiplicity in the case of adding an

atom with an odd number of electrons. When a molecule

with an intrinsic spin moment is added to a doped cluster,

several options for choosing the spin moment arise. To

study this situation, boron, nitrogen, and sulfur atoms

were considered. Systems with the same doped atoms

were studied previously [25] using density functional the-

ory and these results could be compared with obtained re-

sults from cluster representation and multireference anal-

ysis.

The combined eﬀects formed by replacing one of the

atoms in the Stone-Wales defect were also studied. A

theoretical study of such a multilevel defect using density

functional theory predicts a slight broadening of the band

gap, as well as an improvement in the accumulation of

surface charge.[31] Also boron, nitrogen and sulfur were

considered as dopants.

The multireference analysis was done by replacing the

graphene cluster with a smaller pyrene molecule. This

change barely inﬂuences on geometrical and energetical

properties of the hybrid system but allows us to perform

the multireference analysis on a much higher level of the-

ory. The FePc/Pyrene hybrid systems with the defects

were also studied and discussed.

II. THEORETICAL METHODS

The periodic DFT calculations were performed em-

ploying the Quantum Espresso 6.5 package[32] on the

level of the generalized gradient approximation (GGA)

[33] using the Perdew-Burke-Ernzerhof (PBE) exchange-

correlation functional.[34] The Van der Waals interac-

tion between a molecule and a layer was included us-

ing the Grimme DFT-D3 methodology.[35] To treat the

strong on-site Coulomb interaction of TM d-electrons, we

used DFT+U approach within the Hubbard model.[36]

The U parameter value for the iron atom was taken

from the results of linear response calculations for TMPc

molecules.[37] The kinetic energy cutoﬀ for wavefunc-

tions was taken to be 45 Ry, and a corresponding parame-

ter for charge density and potential was 450 Ry. Prelimi-

nary estimations, optimization, and calculation of energy

parameters were performed at the Γ point. Calculations

of densities of states were performed using the 2 ×2×1

Monkhorst–Pack k-point mesh. Optimisation was carried

out until a force value of less than 0.001 Ry/a.u on every

atom and in each cartesian direction was achieved, and

simultaneously stress tensor components reached values

smaller than 0.5 kbar.

The calculations of cluster systems were performed

using the ORCA package,[38, 39] where the GGA-PBE

functional and the D3 correction were used as in compu-

tations with periodic boundary conditions. The triple-

ζpolarized def2-TZVP basis set [40] was implemented

and a semi-empirical counterpoise-type correction [41]

was used to decrease the basis set superposition error

(BSSE).

The following equation was used to estimate the ad-

sorption energy Ea:

Ea=EF eP c+Gr −EF eP c −EGr,(1)

where EF eP c+Gr denotes the total energy of the

FePc/graphene hybrid system, whereas EF eP c, and EGr

are energies of the free molecule, and the surface, respec-

tively.

Cohesive energies for defected graphene clusters and

pyrene were calculated using the formula

Ecoh =Edoped gr −PN

iEi

N,(2)

where Edoped gr is the total energy of the doped system,

Eiis the total energy of the individual elements i (i =

C, B, N, S, H), and N is the total number of atoms in

the cluster. Cohesive energy shows the energy diﬀerence

between the energy of atoms in the molecular state and

in the gas state. This parameter allows for comparing

the stability of defected structures. Similar calculations

have also been done before.[42]

The multireference calculations of cluster systems were

performed using the ORCA package.[38, 39] Optimisa-

tion of systems geometry was performed using DFT

methods. Multireference calculations were done using

diﬀerent basis sets for diﬀerent types of atoms: polarized

valence double-zeta basis set def2-SVP for hydrogen and

carbon atoms, diﬀuse polarized triple-zeta basis set def2-

TZVPD for nitrogen, boron and sulfur atoms and diﬀuse

doubly polarised triple-zeta basis set def2-TZVPPD for

the iron atom. Also, the RIJCOSX [43] algorithm that

treats the Coulomb term via RI (repulsion integrals) and

the exchange term via seminumerical integration was im-

plemented. Corrected energetic states of the hybrid sys-

tems were found using strongly contracted NEVPT2 [44]

perturbation theory.

One of the most important aspects at the beginning

of CASSCF calculations is the choice of the orbitals for

the active space. The method of constructing initial or-

bitals for further analysis that works quite well is the

fragment derived guess which is implemented in ORCA.

This method assumes the fragmentation of the molecular

complex into ligand, and metal centre parts. Molecular

orbitals are obtained for each fragment, where ligand and

metal orbitals are found using DFT and CASSCF meth-

ods, respectively. Then the resulting orbitals are merged

for further calculations. This method allows for the use

of orbitals based on pure metal once in the analysis.

The fragment derived guess works well for systems

where a multiplicity of a ligand is odd. In this case,

a ﬁrst CASSCF calculation can be performed using only

metal d-orbitals as active CAS(6,5), where 6 is the num-

ber of electrons and 5 is the number of orbitals. Then

the active space can be expanded using the ligand or-

bitals to CAS(10,9). The diﬃculty is that the CASSCF

method requires full occupation of core orbitals. It means

that FePc/Pyrene systems with an odd number of elec-

trons in defects (B- and N-dopings) can not be treated

using the CASSCF method with only metal d-orbitals

in the active space. The solution to this problem was

the gradual inclusion of orbitals in space. After the frag-

ment derived guess analysis, such systems were studied

using CASSCF(5,5), where one electron was removed

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Energetics,electronicstates,andmagnetismofironphthalocyanineonpristineanddefectedgraphenelayersAlekseiKoshevarnikovandJacekA.MajewskiyInstituteofTheoreticalPhysics,FacultyofPhysics,UniversityofWarsaw,Pasteura5,02-093Warsaw,PolandTransitionmetalphthalocyanines(TMPc's)areunderintensescrutinyintheeld...

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Energetics electronic states and magnetism of iron phthalocyanine on pristine and defected graphene layers Aleksei Koshevarnikovand Jacek A. Majewskiy

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