Jemmis mno rules

Key takeaways

Jemmis mno rules belongs to chemistry; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Jemmis mno rules to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Jemmis mno rules from memory before moving on to harder problems.

Reference excerpt

In chemistry, the Jemmis mno rules represent a unified rule for predicting and systematizing structures of compounds, usually clusters. The rules involve electron counting. They were formulated by E. D. Jemmis to explain the structures of condensed polyhedral boranes such as B20H16, which are obtained by condensing polyhedral boranes by sharing a triangular face, an edge, a single vertex, or four vertices. These rules are additions and extensions to Wade's rules and polyhedral skeletal electron pair theory. The Jemmis mno rule provides the relationship between polyhedral boranes, condensed polyhedral boranes, and β-rhombohedral boron. This is similar to the relationship between benzene, condensed benzenoid aromatics, and graphite, shown by Hückel's 4n + 2 rule, as well as the relationship between tetracoordinate tetrahedral carbon compounds and diamond. The Jemmis mno rules reduce to Hückel's rule when restricted to two dimensions and reduce to Wade's rules when restricted to one polyhedron.

Electron-counting rules Electron-counting rules are used to predict the preferred electron count for molecules. The octet rule, the 18-electron rule, and Hückel's 4n + 2 pi-electron rule are proven to be useful in predicting the molecular stability. Wade's rules were formulated to explain the electronic requirement of monopolyhedral borane clusters. The Jemmis mno rules are an extension of Wade's rules, generalized to include condensed polyhedral boranes as well. The first condensed polyhedral borane, B20H16, is formed by sharing four vertices between two icosahedra. According to Wade's n + 1 rule for n-vertex closo structures, B20H16 should have a charge of +2 (n + 1 = 20 + 1 = 21 pairs required; 16 BH units provide 16 pairs; four shared boron atoms provide 6 pairs; thus 22 pairs are available). To account for the existence of B20H16 as a neutral species, and to understand the electronic requirement of condensed polyhedral clusters, a new variable, m, was introduced and corresponds to the number of polyhedra (sub-clusters). In Wade's n + 1 rule, the 1 corresponds to the core bonding molecular orbital (BMO) and the n corresponds to the number of vertices, which in turn is equal to the number of tangential surface BMOs. If m polyhedra condense to form a macropolyhedron, m core BMOs will be formed. Thus the skeletal electron pair (SEP) requirement of closo-condensed polyhedral clusters is m + n. Single-vertex sharing is a special case where each subcluster needs to satisfy Wade's rule separately. Let a and b be the number of vertices in the subclusters including the shared atom. The first cage requires a + 1 and the second cage requires b + 1 SEPs. Therefore, a total of a + b + 2 or a + b + m SEPs are required; but a + b = n + 1, as the shared atom is counted twice. The rule can be modified to m + n + 1, or generally m + n + o, where o corresponds to the number of single-vertex sharing condensations. The rule can be made more general by introducing a variable, p, corresponding to the number of missing vertices, and q, the number of caps. As such, the generalized Jemmis rule can be stated as follows:

The SEP requirement of condensed polyhedral clusters is m + n + o + p − q, where m is the number of subclusters, n is the number of vertices, o is the number of single-vertex shared condensations, p is the number of missing vertices and q is the number of caps.

Examples

B20H16

m + n + o + p − q = 2 + 20 + 0 + 0 + 0 = 22 SEPs are required; 16 BH units provide 16 pairs; four shared boron atoms provide 6 pairs, which describes why B20H16 is stable as a neutral species.

B21H−18 closo-B21H−18 is formed by the face-sharing condensation of two icosahedra. The m + n + o + p − q rule demands 23 SEPs; 18 BH units provide 18 pairs and 3 shared boron atoms provide 4+1⁄2 pairs; the negative charge provides one half pair.

B12H16 The bis-nido-B12H16 is formed by the edge-sharing condensation of a nido-B8 unit and a nido-B6 unit. The m + n + o + p − q count of 16 SEPs are satisfied by ten BH units which provide 10 pairs, two shared boron atoms which provide 3 pairs, and six bridging H atoms which provide 3 pairs.

Cu(B11H11)3−2 m + n + o + p − q = 26 SEPs. A transition metal with n valence electrons provides n − 6 electrons for skeletal bonding as 6 electrons occupying the metal-like orbitals do not contribute much to the cluster bonding. Therefore Cu provides 2+1⁄2 pairs, 22 BH units provide 22 pairs; three negative charges provide 1+1⁄2 pairs.

Ferrocene

According to the m + n + o + p − q rule, ferrocene requires 2 + 11 + 1 + 2 − 0 = 16 SEPs. 10 CH units provide 15 pairs while Fe provides one pair.

B18H2−20

B18H2−20 is a bis-nido edge-shared polyhedron. Here, m + n + o + p − q = 2 + 18 + 0 + 2 − 0 = 22; 16 BH units provide 16 pairs, 4 bridging hydrogen atoms provide 2 pairs, two shared boron atoms provide 3 pairs, along with the two negative charges which provide 1 pair.

Triple-decker complexes Triple-decker complexes are known to obey a 30-valence electron (VE) rule. Subtracting 6 pairs of nonbonding electrons from the two metal atoms brings the number of SEPs to 9 pairs. For a triple-decker complex with C5H5 as the decks, m + n + o + p − q = 3 + 17 + 2 + 2 − 0 = 24. Subtracting the 15 pairs corresponding to C–C sigma bonds, it becomes 9 pairs. For example, consider (C5(CH3)5)3Ru+2: 15 C–CH3 groups provide 22+1⁄2 pairs. Each ruthenium atom provides one pair. Removing the electron corresponding to the positive charge of the complex leads to a total of 22+1⁄2 + 2 − 1⁄2 = 24 pairs.

β-Rhombohedral boron

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Jemmis mno rules

Start with the simplest possible case. Write down what Jemmis mno rules claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Jemmis mno rules before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Jemmis mno rules ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Jemmis mno rules

In research: Jemmis mno rules appears in chemistry research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Jemmis mno rules in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Jemmis mno rules is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cluster chemistry, Inorganic chemistry, so understanding it makes those chapters shorter.
In everyday life: Look for Jemmis mno rules outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Jemmis mno rules in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Jemmis mno rules means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Jemmis mno rules out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jemmis mno rules in simple terms?

In chemistry, the Jemmis mno rules represent a unified rule for predicting and systematizing structures of compounds, usually clusters. The rules involve electron counting.

Why does Jemmis mno rules matter?

Because it connects several chemistry ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Jemmis mno rules?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Jemmis mno rules.