American Mineralogist, Volume69, pages 788-799,1984
The electronic structures of manganeseoxide minerals
DevIo M. Snr,nueN
Department of Earth and Planetary Sciences
MassachusettsInstitute of Technology
Cambridge, Massachusetts02I 39
Abstract
Molecular orbital calculations,using the Xa scatteredwave method,were done for the
clusters MnOl,0-, MnO?-, and MnOB- correspondingto Mn2*, Mn3*, and Mna* in
octahedral coordination with O2-. Bond lengths representativeof those observed in
manganeseoxides were chosenand 05 symmetrywas used for each cluster.
The calculated orbital energiesand chargedistributions are usedto describethe nature of
chemicalbonding in manganeseoxides. Spectroscopictransitionenergiesare calculated
and these are compared with experimental optical, X-ray emission and photoelectron
(Esca) spectraof manganeseoxides. The agreementbetweenthe calculatedand experimental spectroscopictransition energiesis fairly good and indicates that isolated clusters
can be used to model the localizedaspectsof the electronicstructureof manganeseoxide
minerals.
The electronicstructureofthese clusterscan also be relatedto the crystal chemistryof
the manganeseoxides. In spite of radius ratio considerations,Mna* is found to be
considerably more stable in octahedral rather than tetrahedral coordination. This is
demonstratedby comparingthe electronicstructureof MnOS- with that of a tetrahedral
MnOX- cluster. A large degreeof covalencyin the MnOS- cluster is consistentwith the
strong Lewis acidity of Mna*. In contrast, the bonding in MnOl,O-is mostly ionic. The
calculated exchangesplittings of the crystal field orbitals show that low-spin Mn2* should
not exist even under high-pressure,but that low spin Mn3* may substitutefor Mna* in
manganese(IV) oxides.
Introduction
In natural environments manganeseoccurs in the
Mn(II), Mn(III) and Mn(IV) oxidation states. All three
valencesform a large number of oxide minerals,ranging
from the simple phases manganosite(MnO), partridgite
(MnzOr) and pyrolusite (MnOJ to complex mixed-valence oxides such as birnessite ((Ca,Na)(Mnt*,
Mna*)zorr' 3H2o) and todorokite ((Na,Ca,K,
Ba,Mn2*)zMnsOrz. 3HzO) (see,for example,Burns and
Burns, 1977,1979).
The classical ionic bonding model of Pauling, although
often useful, cannotrationalizeall of the observedtrends
in the crystal chemistry of these minerals.Many of the
physical properties, crystal-chemicaltrends and consequent geochemicalbehavior of manganeseoxides can
only be understoodin the context ofquantum chemistry.
In this regard,the partially occupiedMn 3d orbitals, the
existence of more than one formal oxidation state of
manganese,and the diverse types of Mn-O and Mn-Mn
interactions give rise to a number of theoretical problems
not associatedwith other minerals. On a more practical
side,a numberofelectronic spectroscopictechniquesare
0003-004x/84/0708-0788$02.00
of direct mineralogicalapplication to the determination of
cation valence statesand coordinationenvironmentsin
manganeseoxides and, in particular, the complex and
poorly crystalline phases in marine manganeseoxide
nodules. Such electronic spectra are difficult to interpret,
however, without a theoreticalunderstandingof the nature and approximate relative energies of the electronic
statesbeing investigated. In short, a greater understanding of the crystal chemistry, physical properties and
electronic spectraof manganeseoxides requires an understandingof their electronic structures.
A complete description of the electronic structure of a
mineralcan only be achievedusing band theory. However, the accuratecalculationofelectronic energybandsin
solids with more than a few atoms per unit cell is often
infeasible.In theory, the electronic states of a mineral
must be invariant under the operations of its crystallographic spacegroup. In practice, one often finds that the
electronicstructureof a systemis only weakly dependent
upon the translational periodicity of the atomic arrangements.This follows becauseelectronsin solidsare generally localized to small atomic regions. This Iocalized
nature of electrons suggestsan alternative, albeit less
78E
SHERMAN: ELECTRONIC
STRI]CTURES OF MANGANESE 1XIDE MINERALS
rigorous, approach to investigating the electronic structure of minerals. Following Tossell and Gibbs (197i), it
shall be referred to as the cluster molecular orbital
method(for a detaileddiscussion,seeSlater, 1974).Here,
the electronic structure of a solid is approximatedby that
of a finite cluster of atoms. For example,the electronic
structure of MnO might be approximated by that of an
octahedral MnOlo- cluster. Ideally, the atomic cluster is
large enough to accommodatemost of the spatial dimensionsover which an electronis delocalizedin the solid. In
general,as the atomic clusterbecomesinfinitely large,its
electronic structure will converge to that of the solid.
However, if the electrons in the solid are fairly localized,
then this convergence limit might be approximately
achieved by the electronic structure of a small cluster of
atoms.
There are a large number of molecular orbital methods
with which one may calculate the approximate electronic
structureof atomic clusters. Of these, the Xa-Scattered
Wave method (described below) is the most useful for
clustersand moleculescontainingtransition metals.The
cluster molecular orbital approach, using the Xa-scatteredwave method,has beenappliedto severaltransition
metal oxides. For example,Tossell et al. (1974)investigatedthe electronicstructureofiron and titanium oxides
using molecular orbital calculationson FeOl,o-, FeOland TiO[-. The close agreementbetweenthe calculated
molecular orbital energies and the experimental spectra
of iron and titanium oxides demonstratethat the cluster
approach can provide a good approximation to the electronic structure of minerals.
In the crystal structures of the manganeseoxides,
manganesecations are octahedrally coordinated by oxygen anions; the resulting MnO6 polyhedraare linked by
either edgeor corner sharingto form infinite chain, sheet,
and three-dimensionalunits. The presence of shared
edgesallows for cation-cation interactions. Goodenough
(1960, l97l), however, has shown that in most of the
manganeseoxides, theseinteractionsare very weak and
that the Mn 3d-electronsare essentiallylocalizedto their
parent cation and its immediate coordination environment. Accordingly, the electronic structures of these
minerals should be fairly well approximated by those of
simpleMnOf,- clusters.
In this paper, the results of molecular orbital calculations (using the Xa scattered wave method) on such
MnO6clustersare presented.Calculationswere done for
MnOl0-, MnOl- and MnOE- correspondingto manganesein the 2+, 3+ and 4+ oxidationstates,respectively.
For all three clusters, octahedral (Oj symmetry was
used. In the structuresof manganeseoxides, however,
the point group symmetries of the MnO6 clusters are
usuallymuch lower (e.g., Czu).Nevertheless,small polyhedral distortions are expectedto have only a small effect
on orbital energiesand chargedistributions and the use of
06 slmmetry should be a good approximation. Still,
calculationson clusters of lower symmetry are desired
789
and will undoubtedly be done as specific examples warrant investigation.For a recentexample,Kai et al. (19E0)
have calculated the electronic structure of MnO!- using
C2, and Da6 symmetry. These results were used to
interpret the optical absorption spectrum of Mn3+ in
andalusite.
In the octahedralclustersinvestigatedhere,the Mn2*-O,
Mn3+-O and Mna*-O bond lengths are2.21A,2.04A and
1.884, respectively.These values are representativeof
those observedin the manganeseoxides.
The calculated molecular orbital energies and charge
distributionswill be usedto describethe natureof chemical bonding in manganeseoxides. The calculated orbital
energieswill then be comparedwith existingspectroscopic data (X-ray emission, Esca and optical spectra).
Finally, the resultswill be appliedto the crystalchemistry
of these minerals.In addition to being of direct application to manganeseoxide mineralogy, the calculationswill
also serve to demonstratethe efect of metal atom oxidation stateon bonding in coordinationsitesin minerals.
Theory and method of calculation
The theory behind the Xa scatteredwave method has been
reviewed in a number of works (Johnsonand Smith, 1973;
Johnson,1973;Slater, 1974)and will only be outlined here.
The MnO$- cluster is partitioned into a set of overlapping
spheres corresponding to the central manganeseatom and six
oxygen atoms. Within each atomic sphere, the one-electron
Schrodingerequation
Ul2V2+ V" + Vxldi : eih
(l)
is solvedfor the orbitalsfr and their energiesei.In (l), V. and V*
are the coulomb and exchangepotentials,respectively.These
areexpressedin termsofthe electronicchargedensitypgiven by
P : I'(i)n;did'
Q)
where n; is the occupancy of orbital i. From the charge density
the coulomb potential is evaluated using electrostatic theory
(solving Poisson's equation) while the exchangepotential is
evaluatedusing Slater'sXa approximation
V^ = -6a l3l4r plt/3
(3)
where o is an adjustable scaling factor chosen so that the Xa
total energyofthe systemequalswhat would be obtainedusing
the conventional Hartree-Fock approach (Schwarz, 1972).
After the individual atomic potentials are calculated to self
consistency,they are superimposedto give an initial molecular
potential. Within eachof the atomic spheres,the new potential is
spherically averaged to give a local radial potential. In the
interatomic region, the superimposed molecular potentiat is
volume averagedto give a simple constant potential. Finally, a
local potential for the extra-molecular region is obtained by
spherically averagingthe potential within the outer sphere. For
each region of the cluster, the Schrodinger equation (using the
appropriate potential) is solved. The solutions are then matched
at the sphere boundaries using multiple scattered wave theory
and the result is then used to derive a new molecular potential.
The processis repeatediteratively until a self-consistentresult is
obtained.
790
SHERMAN: ELECTRONIC STRTJCTURESOF MANGANESE OXIDE MINERALS
Note that the familiar approximation of molecular orbitals as
linear combinationsof atomic orbitals (lcao) is not used. The
conceptualutility of this approach is retained in the multiple
scatteredwave method, however, since the solutionsin each
regionof the clusterare expressedas a summationoffunctions
with definiteangularmomentacenteredat individualatomicsites
(partial waves).
A useful feature of the Xa approximation is that the exchange
potential(equation3) for spin up electronscan be diferent from
that for spin down electrons.This is done simply by settingthe
chargedensityusedin the exchangepotentialto be only that due
to electronswith the samespin. This approachis essentialfor a
realistictreatmentof open shell systems(e.g., transitionmetals
with unpairedelectrons).If unpairedelectronsare present,the
exchangepotentials,and consequentlythe spin-up and spindown orbitalsand orbital energies,will be different.
ln the conventionalHartree-Fock approach,the energyof a
spin-orbital@ is given by
e; = (E(n; - l)) - (E(nr))
(4)
where(E(n)) is the total energyof the systemwhen the occupancy of orbital {; is n;. This is formally known as Koopman's
theorem. Note. however. that its derivation assumesthat the
orbitalsremain unchangedduring the ionization;this may often
be a poor approximationinsofar as one expectsthe orbitals to
"relax" about the new electronicconfigurationof the ionized
state. In the Xa formalism, the orbital eigenvalueshave a
somewhatdifferent meaning: If (E) is the total energy of the
system,then the orbital eigenvaluese; are given by
Calculated molecular orbitals
General
The calculated molecular orbital diagramsof the three
clustersare illustratedin Figure l. Note that the energies
of both the spin-upand spin-downforms of each orbital
are indicated.The energy levels shown are those of the
valence,crystal field, and low energy conduction band
molecular orbitals, which in turn are derived from the
manganese3d,4s,4p and the oxygen 2p atomicorbitals.
Each molecular orbital is labelled according to its associatedirreduciblerepresentationof the Ohpoint group.The
core molecular orbitals (not shown) are essentiallylhe
manganesels, 2s, 2p, 3s, and 3p and the oxygen lr
atomic orbitals.They are at a much lower energy,do not
participatein bonding,and are localizedon either the Mn
or O atoms.The core statesare of interest,however, in
the interpretationof X-ray emissionand EScAspectraof
Mn-oxidesand will be discussedbelow.
Valence band orbitals
The valence orbitals of tru symmetry are nominally
composedof Mn 4p andO 2p character.Both the 511,and
6ttu orbitals, however, have essentiallyno metal atom
character, indicating that the Mn 4p orbitals are not
a(E(nr))
involved in bonding.The /2uand f rsorbitalsare complete(5)
Ai :
dni
ly non-bondingsince they have no symmetry equivalent
Accordingly,the physicalnatureofthe Xa orbital eigenvalues on the metal atom.
The orbitals of greatest interest are those with both
is similar to the notion of "orbital electronegativity".
To evaluatethe energy required for a transition from stateA to
metaland ligandcharacter.Theseare the valenceorbitals
stateB, one could calculatethe total energyofthe systemin each
of e", tzg&nd dq* symmetry, the atomic compositionsof
stateand take the diference. Numerically, this would be very
which are given in Table l. The most important bonding
inefficient;electronictransitionenergiesare on the order ofa few
orbitals are the o-bonding 2e" and the n-bonding lr2r.
electron volts while total energiesare on the order of l0a-105
3d and
Both of theseorbitals are composedof manganese
electronvolts. Slater(1974),however, has shown that one may
oxygen 2p atomic orbitals. With increasing oxidation
accuratelyevaluatethe differencebetweenthe Xa total energies
stateof the manganeseatom, theseorbitalsbecomemore
oftwo statesofa systemby usingthe "transition state" concept.
The transition state is defined as having orbital occupancies bondingin characterinsofaras they donatemore electron
density to the Mn atom and become more stable. The
midway betweenthosefound in the initial and final states.Given
spatialnatureof thesetwo orbitalscan be seenin Figures
the transitionstateconfiguration,it can be shownthat the energy
differencebetweenthe initial and final statesof the system is
2 and 3 which show the wave function contours for the
given by
2e, spin up a-bondingand l/2, spin up zr-bondingmolecular orbitals of the MnOl- cluster. The o-bonds(Figs. 2a
(6)
AE = (E)e - (4e - ) {n"(i) - ne(i)}e,.(i)
and 2b) can be pictured as lobes of the Mn d(x2 - y2) and
d(322- l) atomic orbitalspointingdirectly at the oxygen
wheren^(i) and ne(i) are the occupanciesoforbital i in the states p-orbitals while the z'-bonds(Fig. 3) result from overlap
A and B, respectively,and e,,(i) is the energyof orbital i in the
of Mn d(xy), d9d and d(,rz) orbitals with O p-orbitals
transitionstatewith occupancy
directed perpendicularto the metal-ligandinternuclear
(7)
vector. The 2er o-bondsare strongly directionalin charn,.(i) = {ne(i) + ns(i)}/2
acter while the lt2, z-bonds are rather delocalizedover
One importantadvantageofthe transitionstateprocedureis that
the
three metal-ligandplanes.Finally, the o-bonding641,
it allows one to take into account the orbital relaxationwhich
is
importantbondingorbital in the MnOl0- clusterbut
an
occursduring the transition.
is of lesserrelative importancein the MnO?- and MnO[The essentialcomputationalparametersused for the three
clustersare given in the appendix.For all clusters,relativistic clusters.This orbital is composedof the Mn 4s and O 2p
orbitals.
correctionsto the core stateswere employed.
791
SHERMAN: ELECTRONIC STRUCTURES OF MANGANESE OXIDE MINERALS
unofo-
uno!-
un4-
PqP
7.ts
lals
Fig. I . Molecular orbital diagramsof the three clusters. Orbital energieshave beenscaledrelative to the non-bonding I r1", lr2u and
6tru orbital energies.The number ofelectrons in the highestoccupied molecular orbitals are indicated by the arrow symbols. The a
and B symbols indicate spin-up and spin-down orbitals, respectively.
atomic orbitals which have lost their degeneracyby
electrostatic interaction with the surrounding anions: the
2t2Eorbitalstabilized by 4Dq and the 3e* orbital destabilized by 6Dq. In the molecularorbital description,the2t2"
and 3e" crystal field orbitals are the corresponding anti-
Crystal field orbitals
The2t2"and3e*orbitalscorrespondto the one-electron
crystal field states.In the pure ionic binding description
used by crystal field theory these orbitals are the Mn 3d
Table l. Orbital compositionsin the three clusters
Inoul0-
xn069-
tro
itnt
tO
In068-
XInt
%o
XInt
7L
272
4
52
434
I
I
a2
108
73
1E
I
6?
22
10
2
L7
64
L7
26
59
13
3eg{
80
13
6
80
18
I
3egt
73
25
I
56
39
2t2g+
56
2l
23
84
2t2"+
86
E
6
2eg+
7
90
2egr
24
75
I
43
43
13
46
43
10
lt2g*
2
73
24
c
57
36
10
56
33
Lt2"+
7
69
23
2L
46
32
27
43
29
6a1g+
8
76
16
8
57
34
8
62
30
6alg+
10
76
15
10
57
33
s
61
29
792
SHERMAN : ELECTRONIC STRUCTURES OF MANGANESE OXIDE MINERALS
2ee Orbital XY-Plane
As expected,the crystal field splitting(i.e., the energy
separationbetweenthe 3e, and2t2, crystal field orbitals)
increaseswith the formal oxidation state of the mangaoftwo factors:first, an
nesecation.This is a consequence
increased electrostatic interaction between the manganesecation and the oxygenanions,and, more importantly, an increaseddegreeof e, o-relativeto t2ez-bondingin
the clusters.
Conduction band orbitals
2es Orbital XZ-Plane
The energylevels labelledTaluand7t1uin Figure I are
those of the lowest energy conductionband orbitals. In
the molecular orbital description, these are the o-antibondingversionsofthe 6a1,and the 5r1ubondingorbitals.
In an extremely localized or ionic description, these
orbitals correspond to the manganese4s and 4p atomic
orbitals. Their calculatedatomic compositions(not given), however, show that they are delocalizedover the
oxygen, interatomicand extra-molecularregions.
Orbital exchange splittings
As noted previously, when using a spin unrestricted
formalism the presenceof unpaired electronswill give
fise to two different potentials:one for spin up, and one
for spin down electrons. In accordancewith Hund's
rules, electronswith spin up (taken to be the majority
spin)are lower in energythan those with spin down. The
most extremecaseis Mn2* with five unpairedelectrons;
the resultingenergydiference betweenspin up and spin
down statesof the partially filled orbitals (the exchange
splitting) is quite large. Since the unpaired electronsin
each cluster are localized on the metal atom center, the
molecular orbitals with the most metal atom character
exhibit the greatestexchangesplitting.
Fig. 2. Wave function contoursfor the 2e* sigmabonding
orbitalin theMna*centered
MnOS-cluster.Solidlinesindicate
thewavefunctionis negativewhiledashedlinesindicatepositive
values.Contourintervalsare givenat 0.005,0.01,0.02,0.04,
0.08,and0.16.
1t2sOrbital
bonding versions of the lt2s and 2eEbonding orbitals.
Note that as the metal atom character of the bonding lt2n
and2esorbitalsincreases,the ligandcharacterofthe antibonding 2t2, and 3e, orbitals increases accordingly.
Hence, as the lt2s and zeeorbitalsbecomemore bonding
in character,the 2t2" and3e" crystal field orbitalsbecome
more antibonding.In spite of their antibondingnature,
the averageenergyofthe crystal field orbitals,relative to
the O 2p valenceband orbitals,decreaseswith increasing
oxidation state of the manganeseatom. Since these
orbitalsare mostly manganesein character,their increasing stabilityis a cbnsequence
ofthe increasingelectronegativity of the manganeseatom. This has importantconsequenceson the ligandto metal charge-transferspectraof
Fig. 3. Wave function contoursfor the zr-bondingspin-uplr2"
manganeseoxides and will be discussedbelow.
orbital in MnOS-. Contour intervalsare as in Fig. 2.
SHERMAN: ELECTRONIC STR{JCTI]RES OF MANGANESE OXIDE MINERALS
Electronic spectra of manganese oxides
General
The calculated results can be verified by comparingthe
theoreticalorbital energieswith existingX-ray emission,
tsca and optical spectra of manganeseoxides. The
calculated orbital energies can also be used to interpret
electronic spectra when band assignmentsare uncertain.
It is important to recognize, however, that the Xa
scattered wave calculations, like all molecular orbital
methods,are done using a one-electronformalism.Spectroscopic transitions, however, are between multielectronic wave functions(spectroscopicstates).As a consequence of interelectronic repulsion, a given electronic
configuration over several one electron orbitals can generate several multielectronic states (see, for example,
Lever, 1968).For example, the ground state electronic
configurationof Mna* in MnO[- is (2t2,1)3.This configuration gives the multielectronicstateaA2r.However, the
excited state configuration(r2,1)' @rt)t yields the two
states 4T2, and aTl*. Hence, the energy of the oneelectrontransition 2t2"-->3e, correspondsto a weighted
averageof the energiesof the spectroscopictransitions
4Aze- aT2"and,4Aze- aTlr. As a secondexample,the
excited state configuration (2t2r1)2(2tzel)tof MnOEgives the states2E, I 272"+ 221u.Hence, the energy of
the one-electrontransition 2t2"1 --->2t2sJcorrespondsto
an average energy for the spin-forbidden spectroscopic
transitions+Aze- 2E", oAzr-- 2Tzs,and aA2,- 2Tte.ln
some cases, an electronic transition between two oneelectron orbitals correspondsto a unique transition between two multielectronicspectroscopicstates.An example is the 2t2"1 to 3e, 1 transitio-nin MnO?-; this
correspondsexactly to the '8, - )T2* spectroscopic
transition. Such casesprovide an opportunity for direct
comparisonbetweencalculatedand experimentalresults.
Optical spectra
Transitionsbetween the crystal field orbitals occur in
the near-ultraviolet, visible and near-infrared spectral
regions.Apart from transitionsto higher energy crystal
field states,two additional types of transitionsoccur in
the near-ultraviolet: ligand to metal charge transfer and
metal to conduction band transitions. Ligand to metal
charge-transfertransitionsare betweenthe non-bonding
ligand orbitals and the metal crystal field orbitals. With
reference to the molecular orbitals in Figure I these are
the 6tru-- 2tzeand /2u-- 2tzctransitions.The 1r1,--- 2tze
transitionis Laporte forbidden.Metal to conductionband
transitions, however, are from the 2t2" and 3e* crystal
field orbitals(localizedon the metal atom) to the 7a1uand
7/1uconduction band states. Becausethese transitions
may be Laporte allowed, absorptionbands are of much
greater intensity than those due to crystal field transitions, and often result in an absorptionedgein the visible
region spectraof transitionmetal-bearingminerals.
793
Severalinvestigationshavebeenmadeofthe spectraof
Mn2* in oxides and silicates. Pratt and Coelho (1959)
obtained the optical spectrum of MnO and estimated
valuesfor the ligandfield parameters,but thesewere later
revisedby the high resolutionspectrumof MnO obtained
by Huffman et al. (1969). Keester and White (1968)
present spectraof Mn2* in a number of minerals. The
ground state d5 electronicconfigurationgives rise to the
65 Russel-Saunders
term which in turn, gives rise to the
641 spectroscopicstate in the crystal field. The excited
state d-electron configurationswhich result from promoting a d-electron to one of the spin down d-orbitals,
however, give rise to several quartet Russel-Saunders
terms. Each of these is split into several states in the
crystal field. Hence, a one-electronorbital schemecan
provide only the crudest descriptionof the crystal field
spectraarising from a high-spind5 system. The visible
and near-infraredspectrum of Mn2* in octahedralcoordiag,
nationconsistsof the uAr- oTt,uAr --t nT, and6Ar'-aA transitions. The first two transitions are of the set
which arise from the 3er( t ) --> Ztze(J ) one-electron
transition. The 641 --t oE, oAr and higher energy transitions arise from the 2tze(I) -- 2tze(J) and 3er(f ) -3er(J ) one-electrontransitions.ln particular, these two
"spin-flip" transitions give rise to the quartet states
whoseenergiesare independantof 10Dq in the TunabeSuganoor Orgel diagramfor a high-spind5 system.One
approach to relating the one-electron orbital energiesof
the Mnd60- calculation with experimental spectra is to
calculate the ligand field parameter l0Do. Ligand field
theory, however, is cast in a spin-restrictedformalism.
Hence, a spin-restrictedXa calculationmust be done to
evaluate ligand field parameters (the correct relation
between ligand field theory and the Xa approach is
presentedby Sambe and Felton, 1976).From such a
calculation,the crystal field splittingis found to be 10,9fi)
cm-l; this is in good agreementwith the best experimental value of 10,100cm-r for MnO (Hutrmanet al., 1969).
Messicket al. /l97D have obtainedthe near-ultraviolet
spectrum of MnO. Transition state calculations were
done for the lowest energy absorption features and are
compared with the experimental results in Table 2. The
calculatedresultsare in good agreementwith experimental absorptionband energies,yet the band assignments
given here are somewhatdiferent. Messick et al. (1972)
assignedmost of the featuresbetween4.5 and 7.0 eV to
transitionsfrom the valenceand crystal field bandsto the
conductionband. Other transitions,basedon their temperature dependance, were assigned as metal-metal
charge-transfer(i.e., 2Mn2+---rMn* Mn3*). No features
were assigned as ligand to metal charge-transfer. The
calculatedresults, however, indicatethat the first ligand
to metal charge-transfertransition is at a very high energy
(7.0eV). At lower energies,but still well into the ultraviolet, are the O 2p to conduction band and the metal to
conductionband transitions.
Optical absorption spectra are useful for the identifica-
794
SHERMAN: ELECTRONIC STRUCTURES OF MANGANESE OXIDE MINERALS
Table 2. Calculated (and observed)optical spectral band energiesin manganeseoxides
One-E lectron
Trans i t ion
E(catc. )'
Corresponding
Transitions'"
Spectral
References
( M n O 6) E -
92- + M C T
rt2q( +)
2t,2g( t )
5. L7
6t1a( * )
2 1 2 9 (+ )
4.32
62- '
4tz '
M C{ (ca.
1
4.3)
2 t 2 s (+)
3 e g (r )
3. 33
2 r 2 s (+)
2 t 2 g ( +)
2.95
4 r 2 1 z . a n >, 4 ' t t
4tz , 2 8 , 2 T r , 2 T 2
6.27
02-+MCT
I
( Mno6)91t2a(+) + 2t,2g(+)
6 t 1 u ( +) + 2 t 2 s ( + ' )
02-+MCT
6t1y(r ) | 3es(r)
4.65
02-
2t2s( r ) + 3 e g ( r )
2.42
5B r 51,
2t29(+) ' 2t2E(+')
3.42
r
M Cl
(4.O9,4.2,4.5\
e.2S-2.79)
2
3,4,5
( MnO6
) l0+ M C-I (7.2,
6
6t1u( * )
2 t 2 9 (+ )
7. O0
02-
1 t 1 g (r )
Tttu( t)
5.80
vB + CB (5.7)
6
2 t 2 g ( +)
T t l u ( +)
5.t7
cF '
6
+Energies
6.9)
cB (5.4?)
rtobserved
spectral
in ev (1 ev = 8.066 ' 1g3 q6-1;.
given in pa.rentheses.
References:
1. Geschwind et 41.(1962);
Abu-Eid (1979); 3. Burns end Strens (1967); 4. Burns (1970);
5. Halenius (1978);6.
Messlck et eI. (19?2).
tion of Mn3+cationsin oxidesand silicates(Burns, 1970).
The calculated energy for the tE" - 5T2, crystal field
transitionin the MnOl- cluster is 19,520cm-r. This also
correspondsto the l0Do parameterof ligandfield theory.
In most Mn3*-bearingminerals the local coordination
environmentis distortedto tetragonal(Do,) synrmetryby
the Jahn-Teller effect. There has been some confusion as
to the definition of l0Do in non-cubic symmetriesand
hence the l0Do values reported for Mn3* in epidote
(Burns and Strens, 1967),manganophyllite(Burns, 1970)
and andalusite(Halenius, 1978;Kai et al., 1980)do not
colTespondto the cubic crystal field value of l0Do. In Da6
symmetry, the cubic crystal field parameter 10Dqcorrespondsto the sB1,--+582sspectroscopictransitionenergy
(see, for example, Konig and Kremer, 1977).From the
spectra of Mn3+ in epidote (Burns and Strens, 1967),
manganophyllite(Burns, 1970)and andalusite(Halenius,
1978)the cubic l0Do values are therefore found to be
lE,l70 cm-r, 19,050cm-rand 22,000cm-r, respectively.
Hence, the value calculated for the MnO?- cluster is
reasonable.McClure (1962), however, has obtained a
l0Dq value of 19,470cm-l for Mn3* in corundum; since
the Mn3+-0 bond length in -thisphaseis expectedto be
much shorter than the 2.(XA used in this calculation,it
appearsthat the value of 10Doobtained here may be too
high. On the other hand, the l0Do value of the Mnr*
aquocomplexis 21,000cm-r (Orgel, 1966).
The only near-ultravioletspectral data for Mn3* in
features
2. Langer
and
minerals, from which one may obtain ligand-to-metal
charge-transferenergies,is the spectrum of piemontite
obtained by Langer and Abu-Eid (1977). Strong bands
were observedat 33,000and 34,000cm-r. Thesemay be
assignedto the 6t1u--+3e, transitionwhich is calculatedto
be at 4.6 eV (37,000cm-r) in the MnOB- cluster. Calculated values for other spectral band energiesare given in
Table 2.
The spectrumof Mn4+ in corundumhas beenobtained
by Geschwindet al. (1962).As noted previously,the oneelectronorbital transition 2tz, (I ) --+3e" ( t ) in MnOSaA2--->
corresponds to the two spectroscopic transitions
aT2andoAr--oTr.Inthe spectrumof Mn4+in corundum,
however,only the oAr'- oTrtransitionwas observedand
its energy'was 2l ,300cm- r. The energy calculatedfor the
3enis 26,860cm-l'
one-electronorbital transition 2t2n--->
Sincethis correspondsto an averageof the two spectroscopic transition energies, it is in qualitative agreement
with experiment. Finally, the energy of the first ligand to
metal charge-transfer transition was estimated to be
about 35,0fi)cm-r. This agreeswith the calculatedvalue
of 34,850cm-r for the 6tru --;Ztzsligand to metal charge
transfer transition. The calculated energies for the remaining ligand to metal charge-transferand crystal field
orbital transitionsof MnO[- are given in Table 2.
The energiesofthe ligand to metal charge-transferand
metal to conductionband transitionsin the three clusters
correlate with the relative oxidation and reduction poten-
795
SHERMAN: ELECTRONIC STRUCTURES OF MANGANESE OXIDE MINERALS
tials of the three valencesof manganese(e.g., Huheey,
197E).In the Mnd60- cluster,the first metalto conduction
band transition is much lower in energy than the first
ligand to metal charge-transfer transition; likewise the
oxidation of Mn2* to Mn3+ requiresless energythan the
reductionof Mn2+ to Mn+. In the MnO[- cluster however, the first ligand to metal charge transfer transitions are
much lower in energy than the first metal to conduction
band transitions;Iikewisethe reductionof Mna* to Mn3+
is more energetically favorable than the oxidation of
Mna+ to Mn5+. An intermediatesituationis provided by
MnO!- where the two types of transitionsare of similar
energies.
et al., 1976; Wood and Urch, 1976). The agreement
between theory and experiment is good for the case of
MnO although the KB energiesmay be overestimatedfor
the case of MnO2. The results can also be used to
interpret the Kp spectra of MnO, Mn2O3 and MnO2
phases. The assignmentof KB" (Koster and Mendel,
1970)or "peak A" (Tsutsumiet al., 1976)to the O 2s --->
Mn ls crossovertransitionseemsto be correct.Similarly,
the assignment of Kp" to a transition of an excited
electron in the Mn 4p (7t1) orbital to the Mn ls orbital
(Koster and Mendel, 1970)seemsreasonable.An additional satellite peak, labeled KB', was attributed by
Koster and Mendel (1970) to a discrete energy loss
processwhereby a Kp1 photon excitesa Mn 3d electron
X-ray emission spectra
into the Tttuconductionband. Basedon the ground state
When an electron from a ls core orbital has been energies,this does not appearto be correct. Tsutsumiet
photoejected,transitionsfrom the higherenergyoccupied al. (1976)attribute this feature to exchangesplitting of the
orbitals to the ls orbital occur. The emitted photons KB1peak.
accompanyingthe relaxation give rise to the K spectrum.
For first row transitionmetals,the transitionsof greatest X-ray photoelectron spectra (esce)
interest are those that originate from the n : 3 atomic
Valence region photoelectronspectraof MnO, Mn2O3
orbitals (M-shell) since these are strongly influencedby and Mn3Oa have been investigated.A low resolution
the oxidation stateand local coordinationenvironmentof spectral profile encompassingthe Mn 3d, O 2p and O 2s
the metal atom. The transitionsof the type 3p312,3p1p,3d valence bands of MnO (Wertheim and Hufner, 1972;
etc. ---) ls define the KB spectrum. The main peak in the Hufner and Wertheim, 1973)showed that the O 2p and O
Kp spectrum results from the Mn 3p -.> Mn ls transition 2s bandsare separatedby their free ion value of -16 eV;
and is designatedKp1. In addition to the KB1 transirion, this is in agreementwith the results obtainedhere (i.e.,
severaladditionpeaksare observed.The KB5peak is due the ltlr, 6tn(2p) - leg, ttu,ag(2s) energyseparations).
to transitions which are nominally of the type Mn 3d, O Rao et aI. (1979) have obtained fairly high resolution
2p -, Mn ls. The satellite lines KB" and K$" are spectra profiling the O 2p and Mn 3d bands in MnO,
attributed to O 2s --+ Mn ls and Mn 4p (conduction band) Mn2O3 and MnrOa. In the spectra of both MnO and
--+Mn ls transitions,respectively.By analogywith the K Mn2O3,four peaks were observedand were assignedto
spectrum,the I, spectrumresultsfrom transitionsto the n be the Mn 3d (er), Mn 3d (tz"), O 2p (o) and O 2p (tr)
= 2 atomic levels (i.e., 2s and 2p levels).The2p level is bands. The peaks were separatedby about 1.5-2.0 eV
split by spin-orbitcouplinginto the Zplpand 2p372
states. and, accordingly,are in fairly nice agreementwith the
Hence, in first-row transitionmetals,two allowedtransi- groundstateenergylevel diagramspresentedin Figure l.
tions are present:3d --->
2prn(LB) and3d--+2g12(Lar.z). In the spectrumof the mixed-valencephasehausmannite
The KB and La, Zp spectra of MnO and MnO2 were (MnlOe), they were able to easily resolve the Mn2+ and
calculated using the transition state formalism. These Mn3* 3d-bands.These states were found to have the
results are presented in Table 3 and compared with energeticorder Mn2* (e*) > Mn3* (er) > Mn2* (tz) >
experimentalvalues(Koster and Mendel, 1970;Tsutsumi Mn3* (12). This orderingis in agreementwith the ground
Table 3. Calculated and experimentalK and L spectra of MnO and MnO2
fn()2
fn()
Band
Tra.nsltlon
E (erp)
E (ca1c)
Ksl
lln 3p + l s
6 4 9 1. 8
6495.1
6490.0
6495. 1
L,2
^6521.0
6 5 2 0 .0
6 5 2 1. 0
6528.5
I
6 5 4 1. 0
L, 2 , 3
KPtr
O2s+
KB5
5 t 1 u + 1s
6 5 3 3 .2
Kgttt
7t1o * 1a
^ 6 5 4 9. 8
Lq
2 t 2 " + 2p
1s
1. Koster and llendel (1970);
643.
E (exp)
6532.4
6534.7
6549.5
6549.8
643. 1
643.
2. Tsutsuml et al.
(19?6);
E (calc
1
643. 3
3. lood and Urch (1976).
3
796
SHERMAN: ELECTRONIC STRUCTURES OF MANGANESE OXIDE MINERALS
ganese(IV)oxides is mostly covalent. The strong covalency of the Mn4+-O bond is also in agreementwith the
strong Lewis acidity of Mna* in aqueousenvironments.
In contrast, the bonding in the Mn2+ cluster is mostly
Applications to the crystal chemistry of manganese
ionic; this is in agreementwith the tendencyfor Mn2* to
oxides
act as a weak Lewis acid and as an exchangablecation in
sedimentaryenvironments.
Molecular orbital calculations on finite clusters can be
It can be seenthat in the Mn3+ and Mna* clustersmost
usedto assessthe stability of a given cation valencestate
and electronicconfiguration(e.9., high-spinvs. low-spin) of the metal-ligand interaction is through the e, o-type
in a given coordinationenvironment.Ideally, this infor- bonds(Mn 3d4 2p overlap).There is also an appreciable
mation can then be applied to understandingmineral degree of zr-type bonding interaction as well. Since the
stabilities,cation site occupancies,and the speciationand former bond type is quite directional in character, it is
transport of transition metals in geochemicalenviron- expectedthat the stabilities of these cations in oxides
should have a strong dependence on coordination site
ments.
geometry.Molecular orbital calculationson MnO?- and
Chemical bonding in manganese oxides
MnOS-clustersusingdifferentsitegeometriesmightthereOf fundamentalimportanceis the relative ionic versus fore be of interest. In contrast, most of the metal-ligand
covalentnatureof the manganese-oxygen
bond. Of addi- interactionin the MnOl0- clusterresultsfrom the spheritional interestis the exact nature of the covalentinterac- cally symmetric a4 o-type interaction and the spatially
tion. In eachof the clusters,electronicchargeis donated diffuse tlu interaction. This situation, together with the
from the 02- anionsto the Mn2+, Mn3* or Mna+ cations. fairly ionic natureof the Mn2+-O bond, suggeststhat the
One way to describethe natureofthe manganese-oxygen stability of a Mn2+ cations should exhibit a weaker
dependenceon its coordinationgeometry.
bond in each cluster is to calculatethe net amount of
electronic charge donated to the manganesecenter by
eachof the differenttypes of metal-ligandbondinginter- Octahedral versus tetrahedral coordination
actions.For eachorbital, however,the relativeamountof
In the crystal structuresof the manganese(IV)oxides,
electronicchargein the atomic versusinteratomicregions the Mua+ cations are only in octahedral coordination
is a function of the atomic sphere radii used in the (Burns and Burns. 1977 1979D.
The ionic radiusof Mna*
calculation.To eliminatethe dependanceof the bonding (Shannonand Prewitt, 1969),however, is less than or
descriptionon the sphereradii, it is necessaryto partition equal to that of several cations which often occur in
the intersphereelectronic charge among the manganese tetrahedral coordination (e.g., Al3*, Fe3*, and even
and oxygen atomic regions. A reasonableway of doing Mnt*). Crystal field theory explainsthe greater stability
this is according to the ratio of manganeseto oxygen of octahedrallycoordinatedMna* since a d3 transition
atomicspherecharges.This was donefor eachorbital and metal cation will have an octahedral site preference
the calculatednet amountofelectronic chargedonatedto energyof 38/45Ao".(where A is the crystal field splitting
the manganesecenter by the different types of orbital and it is assumedthat A,"1= 4/9Ao"t).Given the calculated
interactionsis presentedin Table 4.
crystal field splitting of the d-orbitals in the MnOSBy summingthe amount of electronicchargedonated cluster, the octahedralsite preferenceenergyis found to
by each type of orbital interaction,one may calculatea be 2.79 eV. This is an extremely large value and it
relative degree of covalancy of the bonding in each accounts well for the absenceof tetrahedrally coordinatcluster. The calculationsshow that the bondine in man- ed Mna* in minerals.
Although crystal field theory has beenquite successful
when applied to the crystal chemistry of the transition
Table4. Net electronicchargedonatedto themanganese
cations metals(Burns, 1970),its physical basis is unfounded.A
by eachtypeof orbital.
more physically correct approach is molecular orbital
theory. To apply molecularorbital theory to understanding the stability of octahedrally coordinated Mn4* in
xtr068xnO6loxn069oxide minerals, a calculation was done for a tetrahedral
-t.624
-o, L24
-0.986
eg(o)
MnOl- cluster.The bond lengthis taken to be the sum of
-0.831
-0.096
-o .549
tzs(, )
the Shannon and Prewitt (1969) ionic radii for fourfoldo
.
2
7
-o.224
o
.
coordinated Mna* and twofold-coordinatedO2-. The
|
alg( o )
2 13
resulting molecular orbital diagram is compared with that
o
.
2
7
2
-o.261
-0. 156
tlu( o )
of the octahedral MnOS- cluster in Figure 4. In the
molecular orbital formalism, the notion of octahedral site
-0.589
-2.078
-2.945
I q preferenceenergyis somewhatcomplicated;still, several
69. 3
73.6
n.5
f Covaleqcy
differencesbetweenthe two clustersare apparent.Relative to the top of the oxygen 2p valence band (the tr
state electronic structures of the isolated MnOl0- and
MnO?- clusters if their orbital energiesare related by
settingthe interspherepotentialsto be equal(asin Fig. l).
SHERMAN: ELECTRONIC STRTJCTURESOF MANGANESE OXIDE MINERALS
unoXt-9
>4
g)
o
c
u2
o
go
ltr
3ar
o
G
=
ii;
Fig. 4. Molecularorbitaldiagramfor tetrahedralMnOl-G :
t.744).
797
unlikely, and that Mn2* in the Earth's mantle is in the
high-spinstate.
In contrast, the smaller exchangesplitting of the 2t2"
orbital and the larger crystal field splitting in the MnO!cluster suggestthat a high-spinto low-spin transition of
Mn3* can occur. When the Mn-O distancein the MnO?cluster is decreasedfrom 2.04 to 1.88A, the low-spin
configurationis found to be the most stable;this suggests
that low-spin Mn3* may substitute for Mna* in the
manganese(IV)oxides, the ionic radii of Mna+ and lowspin Mn3+ being fairly similar (Shannon-and Prewitt,
1969).It shouldbe noted, however,that Mnr* distortsits
coordination environment via the Jahn-Teller effect and
that the resulting tetragonal distortion will stabilize the
high-spinconfiguration.Spin-unrestrictedcalculationson
fvtnO?- clusters with Da6 symmetry should therefore be
done to investigatethis problem.
Stability of Mnt+ cations in oxides
The Mn3* ion is often unstableand frequently disproportionatesto Mn2+ and Mn3* ions (Stummand Morgan,
orbital in Td symmetry and the rlg orbital in 06 slmme1970;Huheey, 1978:,Cotton and Wilkinson, 1980).The
try), the occupied Mna* crystal field orbitals are less
molecular orbital diagrams in Figure I suggestthat the
stablein the tetrahedralcluster. Moreover, in T6 slmmestability of the MnO?- cluster is approximatelymidway
try one electron must occupy the least stable5t2 orbital
betweenthat of the MnOl0- and MnO[- clusters.Hence,
which is o-antibonding.Finally, the bonding molecular
in oxides, the energy requiredfor the disproportionation
orbitalsin the MnOS- clusterare more stable(by about I
of two Mn3* ions shouldbe quite low. Following Tossell
eV) than the analogousorbitals in the MnOf- cluster.
(1973),one may perform a transitionstatecalculationfor
This is probably due to an increaseddelocalizationofthe
the disproportionationof two MnOl- clustersto a MnO[,valenceorbital electronsin the largerMnO[ cluster.The
and a MnOA0- cluster as follows: 0.5 electrons are
molecular orbital approach shows that Mna* is more
removedfrom the 3e, orbital of the MnOl,0- cluster and
stablein octahedralcoordinationalthoughit is somewhat
addedto the 3e, orbital of the MnO[ cluster.The orbital
ambiguousas to how one may define an octahedralsite
energiesofthe two isolatedclusterscan be placedon the
preferenceenergy.
samescaleby equatingtheir constantinterspherepotentials. The resultingenergydifferencebetweenthe MnOB
High- versus Low-spin Mnz* and Mn3*
and MnOl0- 3enorbitals would correspondto the energy
Transition metals with more than three electronscan required for the disproportionation.This is found to be
exist in both high spin and low spin statesin octahedral less than 0.25 eV. This approach,however, neglectsthe
coordination.The two spin statesof a transition metal electrostaticcomponent of the cluster energies.Morecation have different ionic radii (Shannonand Prewitt, over, the Mn3* cation will stabilizeitself by inducing a
1969)and, hence, different crystal-chemicalbehavior. tetragonal distortion of its coordination environment.
The spin-unrestrictedcalculations can provide insight Still, the calculationsseemto be qualitativelyconsistent
into the stability of the high-spinrelative to the low-spin with the known chemicalbehavior of Mn3* and suggest
configurationin a given coordination environment. As
that one may relate trends in redox chemistry with
noted previously, the calculationsshow that both Mn2+ theoreticalvalenceorbital energies.
and Mn3* are in high-spin configurations at the metalligand bond distanceused for the MnOAO-and MnO!Conclusions
clusters.The exchangesplitting of the Mn2* crystal field
orbitals (Fig. l) is quite large (4.5 eV); this indicates that
The agreement between the calculated results and
the high-spinconfigurationt2" (l)3e"(t)2 of Mn2* is
experimentalspectraof manganeseoxides demonstrates
much more stable than the low-sprn configuration r2*(t )
that isolated clusters can be used to model chemical
trrr(
I )t . It is known that with increasingpressuretransi- bondingin theseminerals.
tion metals may undergo a high spin to low-spin transiAs the formal oxidation state of the manganeseatom
tion. Such a transitionof Fe2* is inferred to occur in the
increases,the Mn-O bond becomesmore covalent, the
Earth's mantle (Fyfe, 1960;Strens, 1969;Burns, 1970). crystal field splittingincreasesand the exchangesplitting
The electronicstructureof the MnOlo- cluster,however, of the d-orbitals decreases.The covalent nature of the
implies that a high-spinto low-spin transitionof Mn2* is
bondingin the MnO[- clusterexplainsthe low solubilities
798
SHERMAN: ELECTRONIC STRUCTURES OF MANGANESE OXIDE MINERALS
of manganese (IV) oxides in solutions where strong
complexing agents are absent. In contrast, the ionic
nature of the bonding in the MnO[o- cluster is in agreement with the higher solubility of Mn2+ in aqueous
solutionsand the ability of Mn2* to act as an exchangeable cation in complex oxides.
In terms of crystal field theory, the large crystal field
splitting in the MnOS- cluster explains the absenceof
tetrahedrallycoordinatedMna* in minerals.In terms of
molecular orbital theory, a comparison of the calculated
electronic structures of octahedral MnOE- and tetrahedral MnOf- clusters indicates that Mna+ is much less
stablein tetrahedralcoordination.
Becausethe bonding in the MnOl0- cluster is mostly
ionic, the Mn2+ 3d-orbitalelectronsare stronglylocalized
on the metal atom. Since there are five unpaired electrons, this gives rise to a large exchangesplitting of the
crystal field orbitals. This, in turn, indicatesthat a highspin to low-spintransitionof Mn2* in oxidesand silicates
at high pressureis unlikely.
Finally, the calculationsare in qualitative agreement
with the tendencyfor Mn3* cations to disproportionate.
In addition, it is found that at the Mn-O bond distances
found in the manganese(IV) oxides, Mn3* would be in a
low-spinconfiguration.This suggeststhat low-spin Mn3*
may substitutefor Mna* in manganeseoxides.
Acknowledgments
grateful
I am especially
to JackTossell,Dept.of Chemistry,
Universityof Maryland,for initialguidance
andencouragement.
I wouldalsoliketo thankRogerBurns,KeithJohnson
andPaco
Leonfor manyhelpfuldiscussions.
Thisworkwassupported
by
NASA grantNSG-7604
and NSF grantNo. EAR E0-16163
to
RogerBurns.
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Appendix
For the MnOAGcalculation, sphere radii were chosen
usingthe procedureof Norman (1977).Mn, O, and outer
sphereradii used were 2,4266,2.5919,and 6.7681bohrs,
respectively.This choice of radii gave a virial theorem
coefrcient of 1.006.
For the MnO?- and MnOS- calculations sphere radii
were chosen using the above procedure but without
taking into account the Watson spheressurroundingthe
oxygenatoms.The Mn, O and outer sphereradii usedin
the MnO?- calculation were 2.2580, 1.7099and 5.5656
bohrs, respectively.This choice gave a virial theorem
coemcientof 1.008.The Mn, O and outer sphere radii
and 5.2610
usedin the MnOS- cluster were2.0790,1.7080
bohrs, respectively.The resulting virial theorem coefficient was 1.fi)8.
In each cluster, partial waves up to / = 2 were used for
manganese,/ = I were used for oxygen, and / : 4 were
usedfor the Outer sphere.