Clusters

Question 1

What is the definition of a electron precise cluster?

Answer 1

Clusters consisting of only 2c2e bonds. That is, clusters with electron numbers that account for exactly one electron pair per polyhedron edge.

Question 2

What is a cluster?

Answer 2

The accumulation of three or more atoms of the same element or of similar elements that are directly linked with each other.

Question 3

How can you count total electrons (g) for clusters?

Answer 3

g = Σ (8-i)*ni = 7n1 + 6n2 + 5n3 + 4n2 (for sp-compounds)
g = Σ (18-i)*ni = 17n1 + 16n2 + 15n3 + 14n4

Where n1 is number of 1-connected atoms, n2 is number of 2-connected atoms etc. Clusters with 5 or more edges per vertex are generally not electron precise.

Question 4

What is the expected valence electron number for a triangular cluster?

Answer 4

Triangle has three two-connected centres.

Main group elements:
g = 3*6 = 15

Transition group elements:
g = 3*16 = 48

Question 5

What is the expected valence electron number for a tetrahedron?

Answer 5

Tetrahedron has four three-connected centres.

Main group elements:
g = 4*5 = 20

Transition group elements:
g = 4*15 = 60

Question 6

What is the expected valence electron number for a trigonal bipyramid?

Answer 6

A trigonal bipyramid has 2 3-connected centres and 3 4-connected centres.

Main group elements:
g = 25 + 34 = 22

Transition group elements:
g = 215 + 314 = 72

Question 7

What is the expected valence electron number for an octahedron?

Answer 7

An octahedron has 6 4-connected centres.

Main group elements:
Does not fit into the scheme of electron precise clusters (se Tl6^6- for example)

Transition group elements:
g = 6 * 14 = 84 (+2 according to Pavel’s slides)

Question 8

What is the expected valence electron number for a trigonal prism?

Answer 8

A trigonal prism has 6 3-connected centres.

Main group elements:
g = 6*5 = 30

Transition group elements:
g = 6*15 = 90

Question 9

What is the expected valence electron number for a cube?

Answer 9

A cube has 8 3-connected centres.

Main group elements:
g = 8*5 = 40

Transition group elements:
g = 8*15 = 120

Question 10

How do transition element clusters attain enough electrons to make electron precise clusters?

Answer 10

Each cluster atom obtains electrons from coordinated ligans, and tends to attain a total of 18 valence electron per atom.

Question 11

What is the number of M-M bonds in an electron precise cluster?

Answer 11

The number of M-M bonds (also the number of polyhedron edges) is:

Main group: b = 1/2 * (8n - g)
Transition group: b = 1/2 * (18n - g)

Question 12

How would one go about predicting the polyhedron of an electron precise cluster?

Answer 12

Calculate the number of bonds expected for an electron precise cluster:

Main group: b = 1/2 * (8n - g)
Transition group: b = 1/2 * (18n - g)

Compare this value with the number of edges of polyhedra using Euler’s polyhedron rule (we know edges (= bonds) and vertices (= atoms)):

edges = faces + vertices - 2

Question 13

When using the Effective Atomic Number rule to calculate electrons supplied by ligands, how does one go about doing it?

Answer 13

Assume that we start with neutral central atoms and ligands. Then count the electrons contributed from bonds.

Examples: 
Uncharged O (6 valence electrons) takes 2 electrons to fulfill octet, and donates 2 electrons to create a 2c2e-bond. It contributed 2 - 2 = 0 electrons.

Uncharged Cl (7 valence electrons) takes 1 electon to fulfill octet, and donates 2 electrons to create a 2c2e-bond. It contributed 2 - 1 = 1 electron.

Question 14

What is the number of electrons that H can contribute in TM clusters?

Answer 14

H only has one electron, and will be able to contribute 1 electron as terminal ligand, as a ligand bridging two atoms or as a ligand briding three atoms. In this latter two cases the bond order is distributed over the bonds.

Question 15

What is the number of electrons that CO can contribute in TM clusters?

Answer 15

2 as a terminal ligand, as a ligand briding two atoms or as a ligand bridging three atoms.

Question 16

What is the number of electrons that NH3 cna contribute in TM clusters?

Answer 16

2 as a terminal ligand, as a ligand briding two atoms or as a ligand bridging three atoms.

Question 17

What is the number of electrons that NO cna contribute in TM clusters?

Answer 17

3 as a terminal ligand.

Question 18

What is the number of electrons that a halgon can contribute in TM clusters?

Answer 18

1 as a terminal ligand, 3 as a ligand bridging two atoms or 5 as a ligand bridging three atoms.

Question 19

What is the number of electrons that a chalgocen can contribute in TM clusters?

Answer 19

0 as a terminal ligand, 2 as a ligand bridging two atoms or 4 as a ligand bridging three atoms.

Question 20

Calculate the number of bonds for triosmium dodecamonoxide (Os3(CO)12) and determine the type of cluster.

Answer 20

3 Os = 3 * 8 (5d6 6s2) = 24
12 CO = 12 * 2 = 24
g = 48

Which is the number for an electron precise triangle.

Question 21

Calculate the number of bonds for Os4(CO)14 and determine the type of cluster.

Answer 21

4 Os = 4 * 8 = 32
14 CO = 14 * 2 = 28
g = 60

Which is the number for an electron precise tetrahedron.

Question 22

What is a deltahedron?

Answer 22

A deltahedron is a polyhedron with triangular faces.

Question 23

What is the deltahedron with 5 vertices?

Answer 23

Trigonal bipyramid (3 in pyramid base, 2 at the tops)

Fake name: hexa-hedron

Question 24

What is the deltahedron with 6 vertices?

Answer 24

Octahedron.

Question 25

What is the deltahedron with 7 vertices?

Answer 25

Pentagonal bipyramid (5 in base, 2 at the tops)

Fake name: deka-hedron

Question 26

What is the deltahedron with 8 vertices?

Answer 26

Dodecahedron (two pentagons that share four vertices, and have one “free” vertex each. And one vertex off each pentagon)

Question 27

What is the deltahedron with 9 vertices?

Answer 27

Tricapped trigonal prism (6 as in a regular trigonal prism, and then 3 off each face)

Question 28

What is the deltahedron with 10 vertices?

Answer 28

Twocapped square antiprism (8 as in a regular square antiprism, and then 2 off each square face)

Question 29

What is the deltahedron with 11 vertices?

Answer 29

Octadecahedron

Question 30

What is the deltahedron with 12 vertices?

Answer 30

Icosahedron (like a twocapped pentagonal antiprism).

Question 31

How many skeletal electrons does a stable closo cluster need?

Answer 31

2n + 2 = n + 1 electron pairs

n = number of atoms in cluster.

Question 32

Explain why a stable closo cluster needs 2n + 2 skeletal electrons.

Answer 32

Consider an octahedron. Each of the atoms will have an sp-hybridised orbital pointing towards the centre forming one bonding orbital and n - 1 non-bonding or antibonding orbitals. Each nonhybridised p-orbital will form a bonding and a anti-bonding orbital with the other p-orbitals, in total n bonding and n anti-bonding.

This yields n + 1 bonding oribtals with each 2 electrons in it.

Question 33

For how many atoms does the Wade rules hold?

Answer 33

For n ≥ 5 (trigonal bipyramid and up)

Question 34

How are open clusters interpreted?

Answer 34

As deltahedra with missing vertices.

Question 35

One kind of Wade clusers can we have?

Answer 35

closo cluster - no missing vertices
nido cluster - 1 missing vertex, n + 2 bonding skeleton orbitals
arachno cluster 2 missing vertices, n + 3 bonding skeleton orbitals
hypho cluster, 3 missing vertices, n + 4 bonding skeleton orbitals.

Question 36

How can we apply the Wade rules to ligand-free clusters?

Answer 36

We postulate that each atom has one lone pair pointing outwards. Then we count the number of electrons, subtract 2n. We can then see what kind of cluster type it will form by comparing the electrons left to form the skeleton matches 2n + 2, 2n + 4 etc.

Question 37

Calculate the type of cluster that B6H6^2- forms.

Answer 37

Number of electrons is: 3 * 6 (B) + 1 * 6 (H) + 2 (charge) = 26

12 will go to B-H bonds.

14 left to form skeletal pairs -> 0Of these, 2n + 2 will be skeletal pairs = 14.

Question 38

Calculate type of cluster that B5H11 forms.

Answer 38

Number of electrons:
5 * 3 (B) + 11 * 1 (H) = 26

5 B-H-pairs = 10

Remaining electrons to form skeleton is 16 -> 2n + 6

Arachno cluster.

Question 39

Calculate type of cluster that B10H14 forms.

Answer 39

Number of electrons:
10 * 3 (B) + 14 * 1 (H) = 44

Of these, 10 B-H pairs = 20 electrons

24 electrons left to form cluster. 2n + 2 = 22 electrons,. 2n + 4 = 24 electrons.

Alternatively:
24 = 12 skeletal pairs left. Defines a 11-vertex geometry for 10 atoms.

Nido cluster.

Question 40

Calculate type of cluster that Na2B10H10 forms.

Answer 40

Number of electrons:
10 * 3 (B) + 10 * 1 (H) + 2 * 1 (Na) = 42 = 21 pairs

Of these, 10 B-H pairs = 11 pairs left. Defines a 10-vertex geometry => Closo cluster.

Alternatively:
22 electrons left. 2n + 2 = 22, so closo cluster.

Question 41

Comment on the nature of B12 clusters.

Answer 41

Number of electrons:
12 * 3 = 36 electrons = 18 pairs

12 vertices means that 13 pairs are skeletal pairs.

5 pairs = 10 electrons remain. 6 B will have single bonds and 6 B will have 3c2e bonds yielding a total of 10 electrons.

Question 42

Comment on the nature of CaB6 clusters.

Answer 42

Number of electrons:
6 * 3 (B) + 2 = 20 electrons = 10 pairs

7 pairs are skeletal pairs = 3 pairs left to be distributed.

6 B will have single bonds.