By Brandon Wu & EJ Brannan
Complex Music
By EJ Brannan
The goal of Complex Music is to demonstrate the connection between coordinate metal complexes and their Δo, using music as a tool to show this relationship. I personally created a formula that correlates metal centers and ligands to notes on a music staff based on how they impact the Δo of the complex.
In what follows, I will demonstrate how this formula was derived, show some examples of applications, and provide you with the tools necessary to create your own Complex Music!
What is it?
Crystal Field (Music) Theory
The Chemistry
Orbital Splitting
In accordance with Crystal Field Theory, in the presence of ligands, the d orbitals of transition metals undergo splitting due to electron-electron repulsion. The magnitude of this splitting is dependent on many factors: primarily it depends on the charge of the metal center and the type of ligands attached.
The Music
Musical Chemistry!
To represent the spectrum of change in Δo, I created a formula that interprets the distinguishing features that impact the size of Δo and represents this through consonance or dissonance of a music chord.
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Consonant Chords represent smaller Δo
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Dissonant Chords represent larger Δo
The Objective
Simplicity and Ease
The objective of Complex Music is to give students a fun and intuitive way to learn about complex metals. While it doesn't aim to replace traditional methods, it can help familiarize students with the interactions of metal centers and ligands on the Δo of the metal complex. Furthermore, this can help students understand when complexes will assume a high or low spin electron configuration.
Musical Terminology
Here's some helpful terms to know to best understand this article!
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Interval: the distance between two notes
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Consonant: Beautiful and pleasant in tone
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Dissonant: Harsh and unpleasant in tone
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Octave: The distance between two notes with the same letter name
I will refer to the notes within a single octave, as shown on this piano
How to Make Complex Music
Metal Row
Is the metal center of your complex a 1st row transition metal, or a 2nd/3rd?
Oxidation State
Using techniques established in Chem 165, determine the oxidation state of your metal.
Ligands
Identify each ligand present as π donors, π acceptors, or σ donors.
Translate
Use the formula sheet to easily correlate your observations into your very own Complex Music Chord!
The Formula
Metal Row
The transition metal's row will determine the bass note of the chord
Row:
Note:
1st Row
2nd Row
C
Db
3rd Row
Db
Oxidation State
The metal oxidation state selects a 7th note(s), and under extreme cases stacks a 6ths for higher dissonance
0 or less
B
1+ or 2+
3+ or 4+
Bb
Bb & B
5+ or more
A, Bb, & B
Ligands
The ligands determine the notes in the middle of the chord; as Δo increases, these stack closer and closer together, clashing with the bass note
Examples:
[Ti(Br )]
4
4-
Metal Row: 1 Ox State: 0 Ligands: 6 π donors
W(CO)
6
[CoCl ]
2-
4
[Cu(H 0) ]
2
6
2+
[Fe(CN) ]
6
3-
Metal Row: 3 Ox State: 0 Ligands: 6 π acceptors
Metal Row: 1 Ox State: 2+ Ligands: 4 π donors
Metal Row: 1 Ox State: 2+ Ligands: 6 σ donors
Metal Row: 1 Ox State: 3+ Ligands: 6 π acceptors
Featured Example
[Fe(CN) (I) ]
4
2
3-
Metal Row: 1
Ox State: 3+
Ligands: 2 π donors, 4 π acceptors
So What?
How is Complex Music helpful?
Identify relative Δo
Although it can't identify specific values, Complex Music can be a useful tool to compare two metal complexes and their Δo, as discussed throughout this webpage.
Gain Intuition on Electronic Spin States
The electron spin state of a metal complex is dependent upon its Δo. If a complex has a high Δo, electron pairing energy will be favored, and it will be low spin, but if it has a low Δo, then the electrons will be more stable in a higher energy level, making them high spin. Using Complex Music chords, you can associate that a consonant chord will be more likely to adopt a high spin, and a dissonant chord will be more likely to adopt a low spin.
Have Fun!
The primary goal of Complex Music is to find an enjoyable and creative way to teach a lesson in coordination chemistry. Furthermore, as discussed in Brandon's literature review, creating musical associations in STEM fields such as chemistry can be a very useful tool to help students remember certain concepts.
What Influences Δo?
Metal Center
1. Oxidation State
RULE: Higher Oxidation State = Higher Δo
REASON: As the oxidation state of the metal center increases, the bond length between the metal center and its ligands becomes shorter. This causes a greater electron-electron repulsion between the d-electrons and the ligands, causing a larger Δo.
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2. 1st, 2nd, or 3rd Row Transition Metal
RULE: 4d/5d (2nd/3rd row TM) orbitals have a larger Δo relative to 3d (1st row TM)
REASON: 2nd and 3rd row transition metals have larger radius d orbitals, creating a larger cross section between the metal orbital and ligand orbitals. This causes more electron-electron repulsion and a larger Δo.
Ligands
1. Ligand Field Strength
RULE: Follow the Spectrochemical Series to determine the effect that each ligand has on the Δo
REASON: Although it was originally derived empirically, the spectrochemical series can be explained by the nature of each ligand as a π donor, sigma donor, or π acceptor.
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π donors: by donating an extra set of electrons, the metal-ligand bonds are made longer, decreasing electron-electron repulsion and making a smaller Δo.
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σ donors: standard σ donation doesn't have significant effect one way or another.
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π acceptors: By accepting more electrons from the metal center, π acceptors create smaller metal-ligand bonds and increase the amount of electron-electron repulsion, creating a larger Δo.
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Spectrochemical Series
