American Mineralogist, Volume 75, pages 2 56-261, 1990
Molecular orbital (SCF-Xc-SW) theory of Fe2+-Mn3+,Fe3+-Mn2*, and Fe3+-Mn3+charge
transfer and magnetic exchange in oxides and silicates
Dlvro
M. Snnrurl.N
U.S. Geological Survey, M.S. 964, Box 25046, Denver Federal Center, Denver, Colorado 80225, U.S.A.
Ansrnlcr
Metal-metal charge-transferand magnetic exchangeinteractions have irnportant effects
on the optical spectra, crystal chemistry, and physics of minerals. Previous molecular
and Fe2*-Ti4*chargeorbital calculationshave provided insight on the nature ofFe2+-Fe3+
transfer transitions in oxides and silicates.In this work, spin-unrestrictedmolecular orbital
calculationson (FeMnO,o)clustersare used to study the nature of magnetic exchangeand
electron delocalization (chargetransfer) associatedwith Fer*-Mnz+,Fe3+-Mn3+,and Fe2*Mn3+ interactions in oxides and silicates.
The calculated relative energiesof the Fe(3d) and Mn(3d) orbitals indicate that the
formal chargeconfiguration Fe2+-Mn3+
is unstable relative to the configuration Fe3*-Mn2*.
Hence, Mn3* cannot exist in silicatesin which Fe2*occurs in an edge-sharingpolyhedron.
The energy for optically induced Mn2+ - Fe3* charge transfer is estimated to be 14900
cm '. The energy for Mn3* ' Fe3*charge transfer is estimated to be 17800 cm-'. JahnTeller distortion of the Mnr* site will increasethis energy.Becauseof their energies,absorption bands due to Mn-Fe charge transfer will be difficult to resolve from bands due
to the ligand-field transitions of Fe3*,Mn2*, and Mn3*.
Both the Fe3+-Mn2+
and Fe3*-Mn3+interactions are found to be antiferromagnetic.The
calculatedexchangeconstants,however, are probably eFeatlyoverestimated.
INrnooucrroN
paper
This
is the third in a seriesofinvestigations on
metal-metal charge-transfer and magnetic exchange
interactions in minerals (Sherman,1987a, 1987b).Metalmetal charge-transfertransitions are of fundamental interest becausethey provide a mechanism for semiconduction and redox reactions in the solid state. It is also
now realized that metal-metal charge-transferand magnetic-exchange interactions geatly affect the optical (visible to near-infrared)spectraof Fe- and Mn-bearing minerals. In two previous papers (Sherman, 1987a, 1987b)
the nature ofFe2* + Fe3+and Fe2*- Ti4* chargetransfer
was investigated using spin-unrestricted self-consistent
field-Xa-scattered wave (SCF-Xa-SW) molecular orbital
calculationson (FerO,o)'s-and (FeTiO,o)ta-clusters.Those
calculationsshow that weak metal-metal bonding is what
allows the optically and thermally induced charge-transfer transitions. It was also found that the weak metalmetal bonding induces ferromagnetic coupling between
Fe2* and Fe3* cations. This result is in agreementwith
Znner's double-exchangemodel and empirical evidence
on the magnetic structures of mixed-valence minerals (e.g.,
Coey and Ghose, 1988).
In this paper, the possible interactions betweenFe and
Mn cations will be investigated using SCF-Xa-SW calculations on the electronic structures of (FeMnO,o),clusters.Fe-Mn interactions are of particular interest beqluse many iron silicatesand oxides contain substantial
0003-o04x/90/03044256$02.00
amounts of manganese.Within the redox conditions of
the Earth's crust, both metals exist in several oxidation
states(e.g.,Fe2*,Fe3*,Mn2*, Mn3', Mno*). A number of
interesting possibilities arise, therefore, regarding the
crystal chemistry, spectra,and electronic structuresof FeMn solid solutions. It is not clear whether Fe2+and Mn3+
and
cations can coexist in a structure or if only Fe3+-Mn2+
Fe3+-Mn3+pairs are stable. Optically, or perhaps thermally, induced charge-transfertransitions between Fe and
Mn (e.g.,Fe2+- Mn3*, Mn3* - Fe3*,Mn2+ - Fe3*)seem
physically reasonable,yet the eneryiesof such transitions
are unknown. The nature of the magnetic coupling or
exchangeinteractions between Fe and Mn cations is of
interest insofar as Mn may affect the Miissbauer spectra
and magnetochemistryof iron oxides and silicates (e.g.,
Vandenbergheet al., 1986).
PARAMETERS
CoprpuranroNAl
The geometry of the (FeMnO,o)'- clusters is shown in
Figure l. The symmetry of each cluster is Cr" (2 mm).
The theory of the SCF-Xa-SW method is describedby Johnson (1973) but will be outlined here:The @eMnO'o)'- cluster
is partitioned into a set of overlapping spheres corresponding to the Fe, Mn, and O atoms. The cluster is
surrounded by an outer sphere,and to stabilize the charged
cluster, a Watson sphere (with charge n+) is used. An
initial potential for the cluster is obtained by superpositioning the charge densities of free Feo,Mno, and O-'5
256
SHERMAN: CHARGE TRANSFER AND MAGNETIC EXCHANGE
ions. Within the atomic and outer spheres,the potential
is spherically averaged;in the intersphereregion, the potential is volume-averagedto give a constant value. The
Schrddinger equation [with the exchange term given by
the Xa approximation (Slater, 1974)l is solved within
each region, and the solutions are matched at the sphere
boundaries. From the new one-electronwave functions,
a new potential is generated,and the procedure is repeated. About 20-30 iterations are needed to obtain a
self-consistentcalculation. The most important adjustable parametersin the method are the atomic sphereradii.
These were chosen using the overlapping sphere approach of Norman (1976). The atomic a valueswere taken from Schwarz (1972). The Fe-O and Mn-O bond
Iengths used were obtained from the Shannon and Prewitt
(1969)ionic radii.
257
(Fd*Mn3eo)1s-
)to{Fe3*Mn3*o1s
Rrsur,rs
AND DrscussroN
Fe3+-Mn2+
and Fe2t-Mn3*interactions
The electronic structure of the (FeMnO,o)'a- cluster with
Fe-O and Mn-O bond lengthsof 2.00 and 2.16 A, respectively, is shown in Figures 2a and,2b. The orbitals
within lhe O(2p) band are Mn-O and Fe-O bonding and
O(2p) nonbonding. In the molecular orbital diagrams,the
O(2p) orbitals are not shown explicitly, but their energy
ranges are indicated by the shaded regions. The nature of
the Fe-O and Mn-O bonds and the electronic structures
of simple FeOu and MnOu coordination polyhedra are
given in Sherman(1984) and Sherman(1985). What is
of primary interest here is the relative eneryies of the
Mn(3d)- and Fe(3d)Jike molecular orbitals. These are
Mn-O or Fe-O antibonding. Octahedral coordination
causesthe five 3d orbitals of a transition-metal cation to
be split into a threefold degenerate lr" set and a twofold
degenerate e" set. The energy difference between the tzs
and e" set is the crystal-field splitting. Each d-orbital set
is split, in turn, into its spin-up and spin-down counterparts. Hence, in the (FeMnO,o),- clusters,there are eight
sets ofd orbitals correspondingto the spin-up and spindown Mn e, and tr" sets together with the spin-up and
spin-down Fe e" and Fe /r" sets.In the FeMnO,o cluster,
the orbitals within each e, or /2s set are nondegenerate
becauseof weak Fe-Mn bonding or antibonding interactions. Becauseof these weak metal-metal bonding interactions, the d orbitals of transition-metal cations may
give rise to narrow bands in a solid instead of discrete
levels as in a simple complex.
From the orbital occupancies and charge distributions,
the Fe and Mn atoms are unambiguouslyin the Fe3*and
Mn2* oxidation states.In both the ferromagneticand antiferromagnetic configurations, there is some weak d-electron delocalization over the two metal atoms through
Fe(/r")-Mn(e) and Fe(e")-Mn(l) overlap acrossthe shared
edge(the Fe-Mn bonding and antibonding interactions).
The highest-energy occupied orbital is shown in Figure
3. This is a Mn(e") orbital that is Fe-Mn antibonding.
Becauseboth the Fe-Mn bonding and antibonding orbit-
tFe3.Mn2Qo)1s-
in the
Fig. l. Structwesand bondlengths(in A x 10'?used
FeMnO,oclusters.The bondlengthswereobtainedfrom the sum
ofthe Shannonand Prewitt(1969)ionic radii.
als are filled, there is no net Fe-Mn bond. That is to be
contrasted with the situation found for rh. p"z+-ps:+ pair
in the (FerO,o)rs-clusters(Sherman, 1987a).There, a net
Fe-Fe bonding interaction results from the d-orbital overlap provided that the Fe2*and Fe3*cations are ferromagnetically coupled (this is the "double-exchange" mechanism described by Znner). The absence of Fer+-Mn2t
bonding precludes ferromagnetic coupling by double ex-
258
SHERMAN: CHARGE TRANSFER AND MAGNETIC EXCHANGE
(a) Ferromagnetic
Spin Up
(b) Antiterromagnetic
Spin Down
Spin Dotryn
Spin Up
M n ( e s)
Mn(es)
M n ( t , ^)
rr..rr
------
F e ( e ^)
r====-
F e ( t , -)
o
Io
c
U
o
o
o
G
======
Mn(t2g)
F e ( e g)
I
Mn(es )
Fe(es )
o
o
U
o
Mn(es)
F"(t'g)
Fe(es )
d
M n ( t 2 9)
.-....
:
Mn(t2s) -
o
E
-10
Fe(t2s )
6
.o
N
Fig.2. Molecular orbital diagram for the Fe3*Mn2*O,ocluster in the (a) ferromagnetic and (b) antiferromagnetic configurations. Orbitals indicated with a dashed line are unoccupied.
Note that the orbital energiescorrespond to "orbital electronegativities" (Slater, 1974). The energy differences between orbitals
in a given configuration do not necessarily correspond to electronic transition energies. For example, the spin-up Mn(e.) and
-o
(D
-N
spin-down Fe(/r") orbitals are nearly degeneratein the MO diagram; however, the energy for the Mn(e) - Fe(/r") transition is
found to be 14900 cm r. As an electron is transferredfrom one
orbital to another, the orbital energieswill "relax" about the new
electronic configuration. To account for the orbital relaxation,
electronic transition eneryies must be calculated using the transition-state formalism of Slater (1974).
change.In fact, the energyJeveldiagrams in Figure 2 immate J. This gives J : - 1093 cm-', implying that the
ply that the antiferromagnetic configuration is the ground coupling is strongly antiferromagnetic.
state according to Fermi statistics (in the ferromagretic
The lowest-energy optically induced Mn2+ + Fe3+
configuration, unoccupiedorbitals lie below occupiedor- charge-transfertransition is from the Mn(er) to the Fe(/rs)
bitals). Antiferromagnetic coupling is found for Fe3+-Fe3+ orbitals. Using the transition state formalism, this is calpairs, which are isoelectronic with Fe3+-Mn2+.The anti- culated to be 14900 cm '. No evidence for such an abferromagneticcoupling can be modeled by using the Hei- sorption band in the spectra of minerals has been found.
senbergHamiltonian:
However, a band with this energy would be difficult to
resolve from the bands due to ligand-field transitions of
11 : -"I.15.56
Mn2* and Fe3".Even though such ligand-freld transitions
where "I.o is the exchange integral and S" and Sb are the are nominally spin-forbidden, they are greatly intensified
spins of atoms a and b. The Hamiltonian yields states in solids becauseof the magnetic coupling betweennextwith energies
nearest-neighborcations (e.g.,Fergusonet al., 1966;Iohr,
1972;Rossman,1975;Rossman,1976).
-,r"b[,S(,S
E:
+ l) - ^t.(.t, + l) - ^Sb(Sb
+ D]/2.
Figure 4 shows the electronic structure of a
Here,,S": I S" I and So: I So| . The spin quantum number (Fe2*Mn3*O,o)rs-cluster with Fe-O and Mn-O bond
for the a-b pair can take the values
lengths of 2.21 and 2.01 A, respectively.The electronic
correspondingto Fe2*and Mn3* cations is
configuration
S : l S " + S b l ,l S . * S o 1 1 , . . . , l S " - S o l .
not that of the ground state, since the unoccupied spinpair, ,S": Sr: 5/2.The antiferromag- up Mn(e") orbital lies below the occupied spin-down Fe(lr)
For the Mn2+-Fe3+
netic state has S: 0, whereasthe ferromagneticstate has orbital. It follows that the Fe2+-Mn3+
chargeconfiguration
S: 5. Using the transition-stateformalism (Slater, 1974; is unstable. This is in accord with the rur for the redox
Ginsberg, 1980; Gubanov et al., 1983), it is possible to reaction
calculate the energy difference between the antiferroMn3**Fe2*:Mn2++Fe3+.
magnetic and ferromagnetic configurations and then esti-
259
SHERMAN: CHARGE TRANSFER AND MAGNETIC EXCHANGE
18a1 Mn 3d(en) Spin up
Spin Up
Spin Down
Mn(es)
------
llllll
-
Fe(e^)
Mn(t'n)
Fe{trn)
Mn(es )
o
g'
Fs(es)
U
o
6
o
E
Mn(t2s)
Fs(t,-)
-10
Fig. 3. Wave function contoursfor the highestoccupiedorbital in the antiferromagrretic
(FeMnoro)r5cluster.This orbital
O(2p) Band
is a Mn(e") d orbital (looking down the z axis), but there is a
significantdegreeof electrondelocalizationvia interactionwiih
the Fe3+(lr")
d orbital.Note,however,that the contourlinesare
notequally
spaced
butareat 0.025,0.05,0.1,
0.2,0.4,0.8,
and
1.6(dashedcontoursarenegative).
Hence,only about97oofthe
Mn 3d(e) electronis delocalizedonto the Fe3+cation. The FeFig. 4. Molecularorbital diagramfor the chargeconfiguraMn interactionthroughthis orbital is antibondingand cancels
This is not a stableelectronicconfiguration,
out the effectof lower-energy
Fe-Mn bondingorbitals.In the tion Fe2*Mn3*O,0.
(FeMnO,o)rscluster,therefore,thereis no net Fe-Mn bonding sincean occupiedspin-downFe(tr")orbital lies abovean unoccupiedspin-upMn(e")orbital.
interaction.
which, in acidic aqueoussolutionhas.Eo:0.77 V (Milazzo and Caroli, 1978). If the Mn site underyoesa strong
tetragonaldistortion, the occupied Mn(e) orbital may be
sufficiently stabilized to allow the Mn3t-Fe2* configuration in the ground state.There does not appearto be any
pairs in minerals.
crystallographicevidencelbr Fe2+-Mn3+
Such pairs might be indicated by optical absorption spectra, although the spectra of silicates containing both Fe
and Mn are difficult to interpret. An important example
is that of manganophyllite. Burns (1970) atrributed absorption bands in manganophyllite to Mn3* cations. This
would imply the coexistenceof Mn3+ and Fe2+.Smith et
al. (1983), however, assignedabsorption bands in Mnbearing phlogopites to octahedrally coordinated Mn2* and
octahedral or tetrahedrally coordinated Fe3*. The calculations presented here support the assignmentof bands
in manganophyllite to the ligand-field transitions of Mn2*,
Fe2*,and Fe3*.Further study of the optical spectrum of
manganophyllite may resolve absorption bands due to
Mn2* - Fe3+chargetransfer.
Fe3t-Mn3+interactions
The electronic structure of an (FeMnO,o)ta cluster with
Fe-O and Mn-O bond lengths of 2.01 A is shown in Figures 5a and 5b. Both the ferromagneticand antiferromagnetic spin configurationscorrespondto Fe3+-Mn3+
charge
configurations. In both the ferromagnetic and antiferromagnetic configurations, there is a net Fe-Mn bonding interaction that is presumablyquite weak. A magnetictransition-state calculation was done to evaluate the sign and
magnitude of the Fe3*-Mn3+magnetic coupling. The calculation predicts that the coupling will be antiferromagnetic with J : -2104 cm-'. This is probably much greater than the actual value: coupling across edge-sharing
polyhedra (90" superexchange)typically results in "I values of l0-100 cm ' (e.g.,Goodenou$r, 1972).
The lowest energy charge-transfer transition is
Mn3*(e") - Fe3*(t') and is calculated to be 17800 cm-'.
This energy would be a lower limit, however, since it
assumesthat the Mn3t cation is in a nondistorted site. A
tetragonal distortion via the Jahn-Teller effect of the Mn3*
site would destabilize the unoccupied Mn3*(e") orbital by
as much as 4000 cm-r, and this energywould have to be
added to the charge-transfer energy. Mn3+ - Fe3" charge
transfer might, therefore, contribute to the visible region
absorption edgein the spectraof Fe-Mn minerals. However, interference from the strong exchange-enhancedligand-field bands of Fe3* and the spin-allowed bands of
Mn3* would make resolution of Mn3+ - Fe3* charge
transfer difficult.
CoNcLusroNs
SomeelectrondelocalizationbetweenFe andMn atoms
is found in the Fe3*-Mn3* and Fe3+-Mn2+clusters and
occursthrough Mn(l)-Fe(e") and Mn(e")-Fe(t) d-orbital
pairs, however,the Fe-Mn bonding
overlap. In Fe3+-Mn2+
and antibonding interactions cancelout. The electron delocalization in the Fe-Mn clusters apparently does not
induce ferromagnetic coupling via Zener's double-exchangemechanism. Both Fe3*-Mn3*and Fe3+-Mn2*cou-
260
SHERMAN: CHARGE TRANSFER AND MAGNETIC EXCHANGE
(b) Antitsrromagnatic
(a) Ferromagnstic
S p i nU p
Spin Oo$rn
======
Spin Up
-5
======
M n ( O g)
Fe(eg )
______
M n ( t 2 s)
o
u
Mn(es) -
::::
=:
F e ( t 2 s)
@
F e ( e s)
6
tvtnttrnt
Fe(t2s )
,5 -ro
-10
"
Mn(es)
P
o
M n ( e )n
F e ( e s)
!i-Iii
g
o
@
Spin Down
E
M n ( t 2 s)
Fe(t2n)
Fe(ee )
o
o
E.
o
Mn(t2s)
E
o
co
o
-15
G
m
N
-t5
Fig. 5. Molecular orbital diagam for the Fe3tMn3*O,ocluster in the (a) ferromagnetic and (b) antiferromagtetic configurations.
pling acrosssharedoctahedraledgesis antiferromagnetic
via superexchange.
Absorption bands due to optically induced Mn2* + Fe3+and Mn3+ - Fe3*chargetransfer should
occur in the visible region spectraof minerals. However,
neither Mn2+-Fe3+nor Mn3+-Fe3*charge-transferbands
may be easily resolv€d from the Fe and Mn ligand-field
bands.
AcrNowr.nocMENTS
Helpful comments were provided by D. Williamson (Colorado School
of Mines), A. Zunger (Solar Energy Research Institute), and an anonymous reviewer. Research on the quanturn chemistry and spectroscopy of
minerals is supported by the U.S. Geological Survey Development of
Assessment Techniques program.
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M*uscrupt
Meruscrurr
RrcErvEDAucusr 12, 1989
AccEprrD DeervrsER 2, 1989