Polyhedral skeletal electron pair theory
Encyclopedia
In chemistry
the polyhedral skeletal electron pair theory provides electron counting
rules useful for predicting the structures of clusters such as borane
and carborane
clusters. The electron counting rules were originally formulated by Kenneth Wade
and were further developed by D. M. P. Mingos
and others; they are sometimes known as Wade's rules or the Wade/Mingos rules. The rules are based on a molecular orbital
treatment of the bonding.. Recently these rules are extended and unified for macropolyhedral boranes, metallocenes and borides. The unified electron counting rules are called Jemmis mno rules.
The 4n rules are reasonably accurate in predicting the structures of clusters having about 4 electrons per vertex, as is the case for many borane
s and carborane
s. For such clusters, the structures are based on deltahedra, which are polyhedra in which every face is triangular. The 4n clusters are classified as closo-, nido-, arachno- or hypho-, based on whether they represent a complete (closo-) deltahedron
, or a deltahedron that is missing one (nido-), two (arachno-) or three (hypho) vertices.
However, hypho clusters are relatively uncommon due to the fact that the electron count is high enough to start to fill antibonding orbitals and destabilize the 4n structure. If the electron count is close to 5 electrons per vertex, the structure often changes to one governed by the 5n rules, which are based on 3-connected polyhedra.
As the electron count increases further, the structures of clusters with 5n electron counts become unstable, so the 6n rules can be implemented. The 6n clusters have structures that are based on rings.
A molecular orbital treatment can be used to rationalize the bonding of cluster compounds of the 4n, 5n, and 6n types.
Using the electron count, the predicted structure can be found. n is the number of vertices in the cluster. The 4n rules are enumerated in the following table.
When counting electrons for each cluster, the number of valence electrons is enumerated. For each transition metal
present, 10 electrons are subtracted from the total electron count. For example, in Rh6(CO)16 the total number of electrons would be 6(9) + 16(2) - 6(10) = 86 – 6(10) = 26. Therefore, the cluster is a closo polyhedron because n = 6, with 4n + 2 = 26.
Other rules may be considered when predicting the structure of clusters:
In general, closo structures with n vertices are n-vertex polyhedra.
To predict the structure of a nido cluster, the closo cluster with n + 1 vertices is used as a starting point; if the cluster is composed of small atoms a high connectivity vertex is removed, while if the cluster is composed of large atoms a low connectivity vertex is removed.
To predict the structure of an arachno cluster, the closo polyhedron with n + 2 vertices is used as the starting point, and the n+1 vertex nido complex is generated by following the rule above; a second vertex adjacent to the first is removed if the cluster is composed of mostly small atoms, a second vertex not adjacent to the first is removed if the cluster is composed mostly of large atoms.
Example: Pb102–
Example: S42+
Example: Os6(CO)18
Example: B5H54–
The rules are useful in also predicting the structure of carboranes.
Example: C2B7H13
The bookkeeping for deltahedral clusters is sometimes carried out by counting skeletal electrons instead of the total number of electrons. The skeletal orbital (electron pair) and skeletal electron counts for the four types of deltahedral
clusters are:
The skeletal electron counts are determined by summing the total of the following number of electrons:
The 5n rules are as follows.
Example: P4
Example: P4S3
Example: P4O6
Example: S8
Hexane (C6H14)
with BH then it can, in principle at least, be substituted for a BH unit, even though that BH and CH are not isoelectronic. The CH+ unit is isolobal, hence the reason why the rules are applicable to carboranes.
This can be explained due to a frontier orbital treatment.
Additionally there are isolobal transition metal units. For example Fe(CO)3 provides 2 electrons. The derivation of this is briefly as follows:
The bonding in diborane is best described by treating each B as sp3 hybridized
. Two sp3 hybrid orbitals on each boron form the bonds to the terminal hydrogens. The remaining sp3 orbitals create the bonds with the bridging hydrogens. Because the angles in the diborane structure are not tetrahedral the orbitals also likely contain some sp2 character.
Closo-B6H62–
The boron atoms lie on each vertex of the octahedron and are sp hybridized. One sp hybrid radiates away from the structure forming the bond with the hydrogen atom. The other sp hybrid radiates into the center of the structure forming a large bonding molecular orbital at the center of the cluster. The remaining two unhybridized orbitals lie along the tangent of the sphere like structure creating more bonding and antibonding orbitals between the boron vertices.
The orbital diagram breaks down as follows
The 18 framework molecular orbitals, (MOs), derived from the 18 boron atomic orbitals are:
The total skeletal bonding orbitals is therefore 7, i.e. (n+1).
Main group atom clusters
The bonding in other main group cluster compounds follow similar rules as those described for the boron cluster bonding. The atoms at the vertex hybridize
in a way which allows the lowest energy structure to form.
The 18 framework molecular orbitals, (MOs), derived from the 18 boron atomic orbitals are:
The total skeletal bonding orbitals is therefore 7, i.e. (n+1).
so have up to nine bonding orbitals, instead of only the four present in boron and main group clusters. There is also more bonding flexibility in transition metal clusters depending on whether vertex metal electron pairs are involved in cluster bonding or appear as lone pairs.
The cluster chlorides and carbonyls of transition metals will be briefly discussed here as they represent opposite ends of the spectrochemical series
and show important features of the differences between transition metal clusters with different ligands. In chloride clusters the energy splitting of the valence d orbitals increases upon formation of the cluster
. The number and symmetry of these orbitals are dependent upon the type and structure of each individual cluster complex. Conversely in the carbonyl clusters the energy splitting of the valence d orbitals is greater before the formation of the cluster.
of organic compounds including olefins, ketones and aldehydes. Heteronuclear cluster H4Pt3Ru6(CO)21 catalyses various alkyne transformations. There has been general debate about whether the cluster remains intact during the catalysis or they fragment to from mononuclear species or aggregate to form nanoparticles. It is now known that examples involving all three possibilities exist and in the same reaction more than one catalyst can operate simultaneously.
, because such cluster complexes display photoluminescence in the spectral region where the photodynamic therapy is effective.
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
the polyhedral skeletal electron pair theory provides electron counting
Electron counting
Electron counting is a formalism used for classifying compounds and for explaining or predicting electronic structure and bonding. Many rules in chemistry rely on electron-counting:...
rules useful for predicting the structures of clusters such as borane
Borane
In chemistry, a borane is a chemical compound of boron and hydrogen. The boranes comprise a large group of compounds with the generic formulae of BxHy. These compounds do not occur in nature. Many of the boranes readily oxidise on contact with air, some violently. The parent member BH3 is called...
and carborane
Carborane
A carborane is a cluster composed of boron and carbon atoms. Like many of the related boranes, these clusters are polyhedra and are similarly classified as closo-, nido-, arachno-, hypho-, etc...
clusters. The electron counting rules were originally formulated by Kenneth Wade
Kenneth Wade
Kenneth Wade, FRS is a British chemist, and professor emeritus at Durham University.He graduated from Nottingham University, and Cornell University....
and were further developed by D. M. P. Mingos
Michael Mingos
David Michael Patrick Mingos FRS was Principal of St Edmund Hall, Oxford from 1999 to 2009, and Professor of Inorganic Chemistry in the University of Oxford...
and others; they are sometimes known as Wade's rules or the Wade/Mingos rules. The rules are based on a molecular orbital
Molecular orbital
In chemistry, a molecular orbital is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The term "orbital" was first...
treatment of the bonding.. Recently these rules are extended and unified for macropolyhedral boranes, metallocenes and borides. The unified electron counting rules are called Jemmis mno rules.
Predicting structures of cluster compounds
Different rules (4n, 5n, or 6n) are invoked depending on the number of electrons per vertex.The 4n rules are reasonably accurate in predicting the structures of clusters having about 4 electrons per vertex, as is the case for many borane
Borane
In chemistry, a borane is a chemical compound of boron and hydrogen. The boranes comprise a large group of compounds with the generic formulae of BxHy. These compounds do not occur in nature. Many of the boranes readily oxidise on contact with air, some violently. The parent member BH3 is called...
s and carborane
Carborane
A carborane is a cluster composed of boron and carbon atoms. Like many of the related boranes, these clusters are polyhedra and are similarly classified as closo-, nido-, arachno-, hypho-, etc...
s. For such clusters, the structures are based on deltahedra, which are polyhedra in which every face is triangular. The 4n clusters are classified as closo-, nido-, arachno- or hypho-, based on whether they represent a complete (closo-) deltahedron
Deltahedron
A deltahedron is a polyhedron whose faces are all equilateral triangles. The name is taken from the Greek majuscule delta , which has the shape of an equilateral triangle. There are infinitely many deltahedra, but of these only eight are convex, having 4, 6, 8, 10, 12, 14, 16 and 20 faces...
, or a deltahedron that is missing one (nido-), two (arachno-) or three (hypho) vertices.
However, hypho clusters are relatively uncommon due to the fact that the electron count is high enough to start to fill antibonding orbitals and destabilize the 4n structure. If the electron count is close to 5 electrons per vertex, the structure often changes to one governed by the 5n rules, which are based on 3-connected polyhedra.
As the electron count increases further, the structures of clusters with 5n electron counts become unstable, so the 6n rules can be implemented. The 6n clusters have structures that are based on rings.
A molecular orbital treatment can be used to rationalize the bonding of cluster compounds of the 4n, 5n, and 6n types.
4n rules
The following polyhedra are the basis for the 4n rules; each of these have triangular faces. The number of vertices in the cluster determines what polyhedron the structure is based on.| Number of vertices | Polyhedron |
|---|---|
| 4 | Tetrahedron |
| 5 | Trigonal bipyramid |
| 6 | Octahedron |
| 7 | Pentagonal bipyramid |
| 8 | D2d (trigonal) dodecahedron |
| 9 | Tricapped trigonal prism |
| 10 | Bicapped square antiprism |
| 11 | Octadecahedron |
| 12 | Icosahedron (bicapped pentagonal antiprism) |
Using the electron count, the predicted structure can be found. n is the number of vertices in the cluster. The 4n rules are enumerated in the following table.
| Electron count | Name | Predicted structure |
|---|---|---|
| 4n – 2 | Bicapped closo | n–2 vertex closo polyhedron with 2 capped faces |
| 4n | Capped closo | n–1 vertex closo polyhedron with 1 face capped |
| 4n + 2 | Closo | Closo polyhedron with n vertices |
| 4n + 4 | Nido | n + 1 vertex closo polyhedron with 1 missing vertex |
| 4n + 6 | Arachno | n + 2 vertex closo polyhedron with 2 missing vertices |
| 4n + 8 | Hypho | n + 3 vertex closo polyhderon with 3 missing vertices |
When counting electrons for each cluster, the number of valence electrons is enumerated. For each transition metal
Transition metal
The term transition metal has two possible meanings:*The IUPAC definition states that a transition metal is "an element whose atom has an incomplete d sub-shell, or which can give rise to cations with an incomplete d sub-shell." Group 12 elements are not transition metals in this definition.*Some...
present, 10 electrons are subtracted from the total electron count. For example, in Rh6(CO)16 the total number of electrons would be 6(9) + 16(2) - 6(10) = 86 – 6(10) = 26. Therefore, the cluster is a closo polyhedron because n = 6, with 4n + 2 = 26.
Other rules may be considered when predicting the structure of clusters:
- For clusters consisting mostly of transition metals, any main group elements present are often best counted as ligands or interstitial atoms, rather than vertices.
- Larger and more electropositive atoms tend to occupy vertices of high connectivity and smaller more electronegative atoms tend to occupy vertices of low connectivity.
- In the special case of boron hydride clusters, each boron connected to 3 or more vertices has one terminal hydride, while a boron connected to 2 other vertices has 2 terminal hydrogens. If more hydrogens are present, they are placed in open face positions to even out the coordination number of the vertices.
- For the special case of transition metal clusters, ligands are added to the metal centers to give the metals reasonable coordination numbers, and if any hydrogenHydrogenHydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
atoms are present they are placed in bridging positions to even out the coordination numbers of the vertices.
In general, closo structures with n vertices are n-vertex polyhedra.
To predict the structure of a nido cluster, the closo cluster with n + 1 vertices is used as a starting point; if the cluster is composed of small atoms a high connectivity vertex is removed, while if the cluster is composed of large atoms a low connectivity vertex is removed.
To predict the structure of an arachno cluster, the closo polyhedron with n + 2 vertices is used as the starting point, and the n+1 vertex nido complex is generated by following the rule above; a second vertex adjacent to the first is removed if the cluster is composed of mostly small atoms, a second vertex not adjacent to the first is removed if the cluster is composed mostly of large atoms.
Example: Pb102–
- Electron count: 10(Pb) + 2 (for the negative charge) = 10(4) + 2 = 42 electrons.
- Since n = 10, 4n + 2 = 42, so the cluster is a closo bicapped square antiprism.
Example: S42+
- Electron count: 4(S) – 2 (for the positive charge) = 4(6) – 2 = 22 electrons.
- Since n = 4, 4n + 6 = 22, so the cluster is arachno.
- Starting from an octahedron, a vertex of high connectivity is removed, and then a non-adjacent vertex is removed.
Example: Os6(CO)18
- Electron count: 6(Os) + 18(CO) – 60 (for 6 osmium atoms) = 6(8) + 18(2) – 60 = 24
- Since n = 6, 4n = 24, so the cluster is capped closo.
- Starting from a trigonal bipyramid, a face is capped. The carbonyls have been omitted for clarity.
Example: B5H54–
- Electron count: 5(B) + 5(H) + 4 (for the negative charge) = 5(3) + 5(1) + 4 = 24
- Since n = 5, 4n + 4 = 24, so the cluster is nido.
- Starting from an octahedron, one of the vertices is removed.
The rules are useful in also predicting the structure of carboranes.
Example: C2B7H13
- Electron count = (2×4) + (3×7) + (13×1) = 42
- Since n in this case is 9, 4n + 6 = 42, the cluster is arachno
The bookkeeping for deltahedral clusters is sometimes carried out by counting skeletal electrons instead of the total number of electrons. The skeletal orbital (electron pair) and skeletal electron counts for the four types of deltahedral
Deltahedron
A deltahedron is a polyhedron whose faces are all equilateral triangles. The name is taken from the Greek majuscule delta , which has the shape of an equilateral triangle. There are infinitely many deltahedra, but of these only eight are convex, having 4, 6, 8, 10, 12, 14, 16 and 20 faces...
clusters are:
- n-vertex closo: (n+1) skeletal orbitals, (2n+2) skeletal electrons
- n-vertex nido: (n+2) skeletal orbitals, (2n+4) skeletal electrons
- n-vertex arachno: (n+3) skeletal orbitals, (2n+6) skeletal electrons
- n-vertex hypho: (n+4) skeletal orbitals, (2n+8) skeletal electrons
The skeletal electron counts are determined by summing the total of the following number of electrons:
- 2 from each BH unit
- 3 from each CH unit
- 1 from each additional hydrogen atom (over and above the ones on the BH and CH units)
- the anionic charge electrons
5n rules
As discussed previously, the 4n rule mainly deals with clusters with electron counts of 4n+k, in which approximately 4 electrons are on each vertex. As more electrons are added per vertex, the number of the electrons per vertex approaches 5. Rather than adopting structures based on deltahedra, the 5n-type clusters have structures based on a different series of polyhedra known as the 3-connected polyhedra, in which each vertex is connected to 3 other vertices. The common types of 3-connected polyhedra are listed below.| Number of vertices | Type of 3-connected polyhedron |
|---|---|
| 4 | Tetrahedron |
| 6 | Trigonal prism |
| 8 | Cube |
| 10 | Pentagonal prism |
| 12 | D2d Pseudo-octahedron |
The 5n rules are as follows.
| Total electron count | Predicted structure |
|---|---|
| 5n | n-vertex 3-connected polyhedron |
| 5n+1 | n–1 vertex 3-connected polyhedron with one vertex inserted into an edge |
| 5n+2 | n–2 vertex 3-connected polyhedron with two vertexes inserted into edges |
| 5n+k | n-k vertex 3-connected polyhedron with k vertexes inserted into edges |
Example: P4
- Electron count: 4(P)= 4(5)= 20
- It is 5n structure with n=4, so it is tetrahedral
Example: P4S3
- Electron count 4(P)+ 3(S)= 4(5)+3(6)= 38
- It is 5n+3 structure with n=7. Three vertices are inserted into edges
Example: P4O6
- Electron count 4(P)+ 6(O)= 4(5)+ 6(6)= 56
- It is 5n+6 structure with n=10. Six vertices are inserted into edges
6n rules
As more electrons are added to a 5n cluster, the number of electrons per vertex approaches 6. Instead of adopting structures based on 4n or 5n rules, the clusters tend to have structures goverened by the 6n rules, which are based on rings. The rules for the 6n structures are as follows.| Total electron count | Predicted structure |
|---|---|
| 6n–k | n-membered ring with k/2 trans-annular bonds |
| 6n–4 | n-membered ring with 2 trans-annular bonds |
| 6n–2 | n-membered ring with 1 trans-annular bond |
| 6n | n-membered ring |
| 6n+2 | n-membered chain (n-membered ring with 1 broken bond) |
Example: S8
- Electron count = S(8) = 6(8) = 48 electrons.
- Since n = 8, 6n = 48, so the cluster is an 8 membered ring.
Hexane (C6H14)
- Electron count = C(6)+H(14) = 6(6) + 1(14)=38
- Since n=6, 6n=36 and 6n+2=38 so the cluster is a 6 membered chain.
Isolobal vertex units
Provided a vertex unit is isolobalIsolobal principle
The isolobal principle is a strategy used in organometallic chemistry to relate the structure of organic and inorganic molecular fragments in order to predict bonding properties of organometallic compounds...
with BH then it can, in principle at least, be substituted for a BH unit, even though that BH and CH are not isoelectronic. The CH+ unit is isolobal, hence the reason why the rules are applicable to carboranes.
This can be explained due to a frontier orbital treatment.
Additionally there are isolobal transition metal units. For example Fe(CO)3 provides 2 electrons. The derivation of this is briefly as follows:
- Fe has 8 valence electrons.
- Each carbonyl group is a net 2 electron donor after the internal σSigma bondIn chemistry, sigma bonds are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most clearly defined for diatomic molecules using the language and tools of symmetry groups. In this formal approach, a σ-bond is...
and π bondingPi bondIn chemistry, pi bonds are covalent chemical bonds where two lobes of one involved atomic orbital overlap two lobes of the other involved atomic orbital...
are taken into account making 14 electrons. - 3 pairs are considered to be involved in Fe – CO σ-bondingSigma bondIn chemistry, sigma bonds are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most clearly defined for diatomic molecules using the language and tools of symmetry groups. In this formal approach, a σ-bond is...
and 3 pairs are involved in πPi bondIn chemistry, pi bonds are covalent chemical bonds where two lobes of one involved atomic orbital overlap two lobes of the other involved atomic orbital...
back bonding from Fe to CO reducing the 14 to 2.
Polyhedron
B2H6The bonding in diborane is best described by treating each B as sp3 hybridized
Orbital hybridisation
In chemistry, hybridisation is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. Hybridised orbitals are very useful in the explanation of the shape of molecular orbitals for molecules. It is an integral part...
. Two sp3 hybrid orbitals on each boron form the bonds to the terminal hydrogens. The remaining sp3 orbitals create the bonds with the bridging hydrogens. Because the angles in the diborane structure are not tetrahedral the orbitals also likely contain some sp2 character.
Closo-B6H62–
The boron atoms lie on each vertex of the octahedron and are sp hybridized. One sp hybrid radiates away from the structure forming the bond with the hydrogen atom. The other sp hybrid radiates into the center of the structure forming a large bonding molecular orbital at the center of the cluster. The remaining two unhybridized orbitals lie along the tangent of the sphere like structure creating more bonding and antibonding orbitals between the boron vertices.
The orbital diagram breaks down as follows
The 18 framework molecular orbitals, (MOs), derived from the 18 boron atomic orbitals are:
- 1 bonding MO at the center of the cluster and 5 antibonding MOs from the 6 sp radial hybrid orbitals
- 6 bonding MOs and 6 antibonding MOs from the 12 tangential p orbitals.
The total skeletal bonding orbitals is therefore 7, i.e. (n+1).
Main group atom clusters
The bonding in other main group cluster compounds follow similar rules as those described for the boron cluster bonding. The atoms at the vertex hybridize
Orbital hybridisation
In chemistry, hybridisation is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. Hybridised orbitals are very useful in the explanation of the shape of molecular orbitals for molecules. It is an integral part...
in a way which allows the lowest energy structure to form.
The 18 framework molecular orbitals, (MOs), derived from the 18 boron atomic orbitals are:
- 1 bonding MO at the center of the cluster and 5 antibonding MOs from the 6 sp radial hybrid orbitals
- 6 bonding MOs and 6 antibonding MOs from the 12 tangential p orbitals.
The total skeletal bonding orbitals is therefore 7, i.e. (n+1).
Transition metal clusters
Transition metal clusters use the d orbitals for bondingChemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...
so have up to nine bonding orbitals, instead of only the four present in boron and main group clusters. There is also more bonding flexibility in transition metal clusters depending on whether vertex metal electron pairs are involved in cluster bonding or appear as lone pairs.
The cluster chlorides and carbonyls of transition metals will be briefly discussed here as they represent opposite ends of the spectrochemical series
Spectrochemical series
A spectrochemical series is a list of ligands ordered on ligand strength and a list of metal ions based on oxidation number, group and its identity...
and show important features of the differences between transition metal clusters with different ligands. In chloride clusters the energy splitting of the valence d orbitals increases upon formation of the cluster
Cluster
-In science:* Cluster , a small group of atoms or molecules* Cluster chemistry, an array of bound atoms intermediate in character between a molecule and a solid...
. The number and symmetry of these orbitals are dependent upon the type and structure of each individual cluster complex. Conversely in the carbonyl clusters the energy splitting of the valence d orbitals is greater before the formation of the cluster.
Catalysis
Due to the wide variety of cluster material discovered, the applications of cluster materials lie in many fields. One major application of the metal based cluster is in catalysis. It is believed that the cluster material can serve as the model material to study heterogeneous catalyst, since it is easier to characterize the surface species and study the mechanism of the reactions that take place in the solution than those on the metal surface. Apart from the application in model study, the cluster its own can be used as effective catalyst. For instance, Pt cluster, [Pt15(CO)30]2– has been reported to catalyze the selective hydrogenationHydrogenation
Hydrogenation, to treat with hydrogen, also a form of chemical reduction, is a chemical reaction between molecular hydrogen and another compound or element, usually in the presence of a catalyst. The process is commonly employed to reduce or saturate organic compounds. Hydrogenation typically...
of organic compounds including olefins, ketones and aldehydes. Heteronuclear cluster H4Pt3Ru6(CO)21 catalyses various alkyne transformations. There has been general debate about whether the cluster remains intact during the catalysis or they fragment to from mononuclear species or aggregate to form nanoparticles. It is now known that examples involving all three possibilities exist and in the same reaction more than one catalyst can operate simultaneously.
Medical treatment
Metal clusters with radioactive isotopes are considered as potential candidates for medical treatment of cancer. Compared with mononuclear rhenium complexes, the polynuclear rhenium cluster has higher density of the metal isotopes, which is beneficial to the radiotherapy, since the active materials in the treatment are the metal elements. One typical sample is the octahedral rhenium metal cluster based on the radioactive isotopes 186Re and 188Re, such as K4[{Re6-Se8}(OH)6]∙8H2O and K4[{Re6-S8}(OH)6]∙8H2O. The former does not show acute cytotoxic effect up to 50 micromoles, which is the practical concentration level of biological applications. Meanwhile, the octahedral rhenium cluster complexes can be potentially applied for photodynamic therapyPhotodynamic therapy
Photodynamic therapy is used clinically to treat a wide range of medical conditions, including malignant cancers, and is recognised as a treatment strategy which is both minimally invasive and minimally toxic...
, because such cluster complexes display photoluminescence in the spectral region where the photodynamic therapy is effective.