Multiplet Splitting in Transition Metals

 

Multiplet Splitting of “2p” Orbitals in Transition Metals

due to Unpaired Electrons in Valence Levels

 

Cr (3+), Mn (3+), Fe (3+), Co (3+), Ni (2+), Cu (2+)

 



 

MULTIPLET SPLITTING (split final state) is due to Interaction of Unpaired Electrons in Valence Levels and Unpaired Core Electron
Multiplet Splitting occurs in core level XPS whenever there is one (or more) unpaired electron(s) in the valence levels. Multiplet splitting occurs due to the exchange interaction between the unpaired valence electrons and the unpaired electron left in the core level (after photoionization). This interaction produces “split final states”.

In other words: 
Multiplet splitting arises when an atom contains unpaired electrons in valence orbitals.  

When a core electron vacancy is created by photoionization, there can be coupling between the remaining unpaired electron in the core with the unpaired electrons in the outer shell. This can create a number of final states, which will be seen in the photoelectron spectrum as a multi-peak envelop. The Figure below (Cr 2p spectrum of Cr2O3) shows the multiplet splitting structure that exists for the Cr 2p3/2 peak for a fractured Cr2O3 single crystal.

 

Multiplet Splitting (split final states) occurs for compounds having unpaired valence electrons interacting with unpaired electron in core – after photoionization:

 

  • 2p electrons in transition metal compounds such as:  CuO, CuSO4, MnF2, CuF2, Cr2O3…
  • 3d electrons in rare earth compounds display multiplet splitting:  CeO2…
  • 1s electrons in gases display multiplet splitting for:   O2 gas, CO gas, NO gas, NNO gas,
  • 3s electrons in materials such as: MnO solid, MnF2 solid

 



 

Discussion on Multiplet Splitting from paper by Paul Bagus

P.S. Bagus, E. Ilton and C. Nelin, Surface Science Reports, Vol 68, p273-304, 2013

 

In the present section we expand this earlier treatment to consider a wide variety of many-body effects that can lead to satellites, often with very large intensities. A suitable definition for many-body effects is that they require the use of wavefunctions that cannot be represented by a single configuration or a single CSF. In particular, for closed shell systems, this means that we must go beyond a single determinant description of the wavefunction. Final states that correspond to multiplets are also considered a many-body effect, although the reasoning requires explanation. A multiplet can be regarded as a degenerate set of states that arise from the angular momentum coupling of the open shells in a single configuration and, hence, not a many-body effect. On the other hand, wavefunctions that are eigenfunctions of the orbital and spin angular momentum operators normally are combinations of determinants and, hence, multiplets can be grouped with many body effects. Furthermore, there is a type of angular momentum coupling that is a pure many-body effect.

This occurs when the valence open shell can couple to multiplets other than the ground state multiplet of the initial state configuration. It is often possible to couple the core-hole with the re-coupled valence open shell to give a total multiplet the same as when the core-hole is coupled to the ground state multiplet of the valence open shell. While these angular momentum re-coupled multiplets are XPS forbidden, they are able to mix with the XPS allowed multiplets and thus lead to “satellites” with large intensity. An example of the many-body mixing of XPS forbidden with XPS allowed multiplets in given in Section 6.2. For all these reasons, we chose to group the discussion of XPS multiplets with many body effects. In Section 6.1, we consider the multiplet splitting of the N(1s) and O(1s) XPS of NO. We also examine the Mn 3s XPS, where multiplet theory is not sufficient. In Section 6.2, angular momentum recoupling is introduced as a major correction to the simple angular momentum coupling theory. This recoupling is important because the re-coupled CSFs are nearly degenerate with the XPS allowed multiplets. Other types of near degeneracy are also discussed that provide a more complete description of “atomic” processes than multiplet theory alone. In this section, the effects largely depend on orbitals with dominantly atomic character but which can be modified by ligand field splittings and covalent bonding. In Section 6.3, we consider very recent results for the XPS of the two closed shell oxides, CeO2 and UO3 whose covalent character was discussed in Section 5.

This small deviation from the statistical is relevant for the Mn 3s XPS multiplet splitting, discussed next. Other examples of multiplet splitting in molecules can be found. The dominantly ionic character of MnO, Section 5, where the 5 open shell electrons are ∼90% Mn 3d, even for a deep 2p core-hole, suggests that an isolated Mn2+ cation with a 3d5 open shell coupled to the high spin, 6S, multiplet would be a suitable model for the Mn XPS. A direct comparison of the measured 3s XPS in Mn atoms and in MnF2 and MnO crystals shows that the spectra are very similar for all these systems, which justifies the belief that Mn2+ is a good model for the XPS of MnO. It should be noted that the atomic XPS data in Ref. [169] was for Mn atoms and not the Mn2+ cations appropriate for ionic crystals and that the energy separation of the first two peaks is slightly larger for Mn0 than for MnF2 and MnO. This slightly larger separation is reproduced in the calculated separation of the first two peaks between Mn0 and Mn2+

One expects that the energy separations and the relative intensities of the 3s XPS peaks should be similar for Mn2+ and Mn0 since the 4s electrons, present in Mn0, are spectators for the core-level ionization, However, there will be some differences, which arise because a portion of the 4s charge density penetrates toward the core of the Mn atom. It is important that the differences between the theoretical results for Mn0 and for Mn2+ are mirrored in the differences between the XPS for the MnO or MnF2 crystals and the Mn atom. Following the logic for NO, discussed above, the 3s XPS should have two peaks. 7S and 5S split by 6K(3s,3d). HF theory predicts a splitting of ∼14 eV and an intensity ratio of 1.4:1 while the XPS measurements for several ionic crystals give a splitting of ∼6 eV with an intensity ratio of ∼2:1. This ratio is larger, by over 40%, than the statistical ratio of the two multiplets and is outside the range of deviation suggested from the results for NO; see above. The ∼8 eV error in the multiplet splitting is also much greater than would be expected from the errors of BEs calculated from atomic HF calculations. Clearly, many-body effects other than multiplets must make important contributions as discussed in the following sub-section.

 



Table 1. First row transition metal species show multiplet splitting in their “2p” XPS spectra.

 

Beisinger Summary Table

 

 

 



 

Peak-fitted spectra from Mark Beisinger at U. Western Ontario, Surface Science Western
Calculated Peak-shapes from Gupta and Sen, Physical Review, Vol 12, p15-18, 1975

 

2p Multiplet Splitting – Cr (3+), Mn (3+), Fe (3+), Co (3+), Ni (2+), Cu (2+)

MULTIPLET SPLITTING (split final state) is due to Interaction of Unpaired Electrons in Valence Levels with Unpaired Core Electron(s)

 

Element
Spin-Orbit
Oxidation State

Experimental Spectra
Multiplet Splitting
Peak-fits / Peakshapes
by M. Beisinger, http://www.xpsfitting.com / UWO, SSW
Calculated Spectra
Multiplet Splitting 
Calculated Peakshapes  (1eV FWHM)
by Gupta and Sen, Physical Review, vol 12, p15-18, 1975

Ab Initio Calculated Spectra – Multiplet Splitting

Paul Bagus 




Chromium (Cr)

Cr (2p3)

 (3+) oxidation state

Cr2O– Cr(3+)

Experimental – Multiplet Splitting – Beisinger
Cr2O3 – Cr (3+) oxidation state

Cr(3+) oxidation state

Calculated – Multiplet Splitting – 1975
Gupta & Sen

Theoretical Calculation

 

 

Cr(3+) for Cr2O3

Calculated – Multiplet Splitting
Paul Bagus

 

 

 

 




Chromium (Cr)

Cr (2p)

Cr (3+) oxidation state

NiCr2O4 – Cr(3+)

Experimental – Multiplet Splitting – Beisinger
Cr2O3 – Cr (3+) oxidation state


Cr(3+) oxidation state

Calculated – Multiplet Splitting – 1975 –
Gupta & Sen
Theoretical Calculation

 

 

Cr(3+) for Cr2O3
Calculated – Multiplet Splitting
Paul Bagus

Chromium (Cr)

Cr (2p)

Cr (3+) oxidation state

CrCl3 (anhydrous)  – Cr(3+)

Experimental – Multiplet Splitting – Beisinger
CrCl– Cr (3+) oxidation state

Cr(3+) oxidation state

Calculated – Multiplet Splitting – 1975 –
Gupta & Sen
Theoretical Calculation

 

 

Cr(3+) for Cr2O3
Calculated – Multiplet Splitting
Paul Bagus

Chromium (Cr)

Cr (2p)

Cr (3+) oxidation state

CrBr3-6H2O  –  Cr(3+)

Experimental Multiplet Splitting – Beisinger
CrBr
– Cr (3+) oxidation state

 

Cr(3+) oxidation state

Calculated – Multiplet Splitting – 1975 – Gupta & Sen
Theoretical Calculation

 

Cr(3+) for Cr2O3
Calculated – Multiplet Splitting
Paul Bagus

Chromium (Cr)

Cr (2p)

Cr (3+) oxidation state

 

CrF3 –  Cr(3+)

Experimental – Multiplet Splitting – Beisinger
CrF– Cr (3+) oxidation state


Cr(3+) oxidation state

Calculated – Multiplet Splitting – 1975 – Gupta & Sen
Theoretical Calculation

 

Cr(3+) for Cr2O3
Calculated – Multiplet Splitting
Paul Bagus

Chromium (Cr)

Cr (2p)

Cr (3+) oxidation state

 

Cr(OH)3  –  Cr(3+)

Experimental – Multiplet Splitting – Beisinger Cr(OH)3 – Cr(3+) oxidation state

Cr(3+) oxidation state

Calculated – Multiplet Splitting – 1975 – Gupta & Sen
Theoretical Calculation

Cr(3+) for Cr2O3
Calculated – Multiplet Splitting
Paul Bagus






Manganese (Mn)

Mn (2p)

Mn (4+) oxidation state

MnO2  –  Mn (4+)

Experimental – Multiplet Splitting – Beisinger
Mn (4+) oxidation state

Mn(4+) Oxidation State
Calculated – Multiplet Splitting – 1975 – Gupta & Sen
Theoretical Calculation

Manganese (Mn)

Mn (2p)

Mn (2+) oxidation state

MnO  –  Mn (2+)
Mn (2+) oxidation state
Mn(2+) Oxidation State
Calculated – Multiplet Splitting – 1975 – Gupta & Sen
Theoretical Calculation

Manganese (Mn)

Mn (2p)

Mn (3+) oxidation state

Mn2O3
Mn (3+) oxidation state

Manganese (Mn)

Mn (2p)

Mn (7+) oxidation state

Iron (Fe)   

Iron (Fe) Fe2O3   
Fe (3+) oxidation state
   

Iron (Fe)

Fe3O4    (FeO-Fe2O3)  
Fe (3+) oxidation states
 Iron (Fe)  FeCO3

Iron (Fe)

FeF3

Iron (Fe)

FeCl3 
Fe (3+) oxidation state

Iron (Fe)

FeBr
Iron (Fe) K4Fe(CN)6   
Fe (2+) oxidation stat

Iron (Fe) Fe (3+) vs Fe (2+)

 

 

Cobalt (Co) CoO
Cobalt (Co) Co3O4
Cobalt (Co) Co(OH)2
 
Cobalt (Co)






Nickel (Ni) NiO 
Ni (2+)
Nickel (Ni) NiOOH
Ni (3+)
Nickel (Ni) Ni(OH)2
Nickel (Ni) NiSO4
Nickel (Ni) NiCr2O4
Nickel (Ni) NiFe2O4
Copper (Cu)
Copper (Cu)
Copper (Cu)
Copper (Cu)
Copper (Cu)
Copper (Cu)
 

 

Crist Spectra from The XPS Library

Copper (Cu)

                   Cu, Cu2O and CuO
Experimental Spectra

                     Cu (2+) Oxidation state
Calculated Spectrum – Gupta & Sen

Copper (Cu)

Initial State:
Final State:  xxx

Copper (Cu)

Initial State:
Final State:  xxx

Copper (Cu)

CuSO4 (Cu2+)

Initial State:
Final State:  xxx