# Shape of Multinuclear Low-Nuclearity Carbonyl Clusters using PEC and TEC

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Complex cluster compounds having 3 and more metal atoms with the metal in low oxidation states. Many compounds contain M—M bonds and fall into the category of metal carbonyl clusters- low nuclearity carbonyl clusters (LNCC) and high nuclearity carbonyl clusters (HNCC).

## Low-Nuclearity Carbonyl Clusters

### Calculations of M—M Bonds

Tentative structure to the given molecular formula, requires total number of metal—metal bonds in the complex and number of bonds. Metal core is written first. Carbonyl groups and other ligands are arranged so that each metal follows the 18-electron rule. The CO group can occupy cither the terminal or bridged position since it contributes 2e in each case.

Molecule | TEC | Total M-M Bonds | Bonds Per Metal | Basic Geometry of metal atoms |

Mo- Mo | ||||

Co-Co |

### TEC: Total Valence Electron Count

and clusters are electronically saturated- these have

sufficient number of electrons to provide each metal atom with an 18 electrons in closed shell configuration. Thus there must be a total of 48 and electrons respectively.

cluster can be derived from and has only 46e. This unsaturated molecule has a different structure where one edge of the

triangle is shorter and bridged by two hydrogen atoms. By having one Os=Os double bond, each osmium atom attains the 18 electron configuration.

Four-atom clusters have tetrahedral geometry also butterfly and planar are found.

### High Nuclearity Carbonyl Clusters (HNCC)

High nuclearity carbonyl clusters have five or more metal atoms, each at least one M—M bond. The first HNCC whose structure was discovered is (1963).

### Electron Counting Schemes in High Nuclearity Clusters

The rules that apply to LNCC do not follow for IINCC clusters- bonding

skeleton cannot be described in terms of localised 2e-2e M—M bonds With each metal attaining 18e. For example of with total valence electron count (TEC) , in terms of the rule. Each Rh acquires four electrons from two terminal carbonyls. With a share of four electrons in four Rh—Rh bonds it has nine electrons. Therefore, a total of electrons and so the cluster is short by electron. Four triply bridged carbonyls contribute a total of electron. Thus the entire molecule has electron too many based on rule.

Clusters like and also do not follow 18 electron rule and are are isoclectronic with a TEC of .

These HNCCs are large, structurally complex and contain heavier (2^{nd} and 3^{rd} series) transition metals. These are not amenable to conventional interpretation of their electronic structures.

All of these large clusters are electron deficient since there are insufficient electrons to permit the assignment of an electron pair bond between each adjacent pair of metal atoms.

To resolve the problems associated with the electron counting in HNCC, Wade proposed a qualitative model which is an extension of his earlier model originally proposed for boron hydrides, .

He correlated the structure of a borane or its derivatives with number of electrons involved in the bonding in the framework of the deltahedron. **The number of vertices in the deltahedron is one less than the number of bonding pairs in the framework. This approach is sometimes called the polyhedral skeletal electron pair theory or more often Wade’s rules**. Prediction of structures of the transition metal carbonyl clusters using Wade’s rules not always, correct.

In . One B—H unit uses one boron orbital and two electrons. This leaves three orbitals and two electrons on boron to be used in forming the cage. One of the orbitals is an or hybrid orbital that points towards the centre of the polyhedron. Other two orbitals, , and , lie near the surface of the polyhedron. For polyhedra, the surface orbitals will overlap to generate n bonding and n antibonding orbitals. The set of n orbitals point at centre of polyhedron. They overlap at the centre of the polyhedron to generate one strongly bonding orbital and weakly bonding/nonbonding/antibonding orbitals. .in a cage, thus has bonding orbitals. As there are n electron pairs contributed by units, an additional electron pair is required for .This is the reason why the ions are more stable thanitself.

unit is analogous to the B—H unit (for instance M is Ru). Ru has nine valence orbitals (s, p and d) compared to four (s and p) in the case of boron. Six orbitals and three electron pairs form , unit. Ru atom is left with three orbitals and two electrons similar to the unit. A total of electron pairs are now needed to completely fill the cluster bonding orbitals in an structure. has stable This is the anion of the corresponding .

The TEC comes from

The number of valence electrons of each metal

2e for each CO group irrespective of its bonding, terminal or bridged

1e for each negative charge

Number of valence electrons for each heteroatom and/or interstitial atom- 1 for H, 4 for C, 5 for N and so on.

The **polyhedral electron count (PEC)** is thus, per skeletal metal atom.

For non-transition element present on the vertex, subtract 2e per element instead of 12e. From TEC and PEC, based on that n + 1 pairs of electrons required for a polyhedron with n vertices we can find the number of vertices.

### Correlation of PEC with Structure

Boranes | Metal Cluster | PEC | Structure |

Closo | |||

Nido | |||

Arachno | |||

Hypho |

Parent Polyhedron is one less than the PEC, the most likely structure may be selected based on table below which shows TEC, PEC and predicated structure of some high nuclarity carbonyl clusters.

Compound | TEC | n# | PEC | Predicated Structure |

86 | 6 | Closo (Oct) | ||

86 | 6 | Closo(Oct) | ||

C | 74 | 5 | Nido-Oct (Sq Py) | |

62 62 | 4 5 | Arachno (Oct) (Butterfly) Closo(TBP)** | ||

72 | 5 | Closo(TBP) | ||

72 | 5 | Closo(TBP) | ||

72 | 5 | Closo(TBP) | ||

72 | 5 | Closo(TBP) | ||

72 | 5 | Arachno (Pentagonal bipyramid) |

#Number of Vertices in Parent Polyhedron, * Wades rule cannot predict the position of H, ** Carbon is on the vertex.