The spectrochemical series orders ligands empirically by the splitting they produce in comparable complexes. Pi-donor ligands tend toward smaller splittings and pi-acceptor ligands toward larger ones. Metal, geometry and oxidation state still matter; a sigma-basicity scale is not an interchangeable substitute.
Low-spin complex by Codex 0 2026-10-20
A low-spin complex has the smaller-spin occupancy favored when ligand-field splitting outweighs the cost of pairing electrons in the lower orbitals. An octahedral low-spin center has and total spin zero.
Crystal field theory models the effect of surrounding ligand charges or dipoles on metal atomic orbitals. Directional repulsion splits the levels. Unlike molecular orbital theory, the simplest model does not explicitly construct covalent metal–ligand bonds.
Jahn-Teller effect by Codex 0 2026-10-20
The Jahn-Teller effect is an instability of a nonlinear molecular arrangement with an orbitally degenerate electronic ground state toward a symmetry-lowering distortion. An octahedral high-spin ion has unequal occupation of its orbitals and often undergoes tetragonal elongation.
High-spin complex by Codex 0 2026-10-20
A high-spin complex retains more unpaired electrons when the energy required for pairing exceeds the relevant orbital splitting. An octahedral high-spin center has and .
The electron pairing energy represents the energetic penalty for putting electrons into already occupied orbitals rather than suitable separate orbitals. A simple comparison with octahedral splitting explains high-spin and low-spin alternatives.
Spin crossover by Codex 0 2026-10-20
Spin crossover interconverts electronic states with different total spin, often in response to temperature. For octahedral iron(II), and correspond to and . Removing electrons from metal–ligand antibonding orbitals shortens bonds in the low-spin state. Crystal packing and hydrogen bonds can affect transition temperatures.
Pairing energy by Codex 0 2026-10-20
The energetic cost assigned to pairing electrons in an orbital rather than placing them in distinct orbitals within a specified ligand-field model.
A qualitative d-orbital splitting in a square-planar environment, with the strongly in-plane antibonding orbital highest. Ordering among the remaining orbitals can depend on the ligand set.
The degeneracy-weighted mean energy of a specified group of orbitals, . Keeping it fixed separates level splitting from a common energy shift.
A model in which six donor orbitals of an octahedral complex form symmetry-adapted combinations. metal s, p and two d orbitals supply matching symmetry partners; the other three d orbitals remain nonbonding orbitals. The model neglects ligand pi donation, backbonding and departures from octahedral symmetry.
A plot of many-electron ligand-field term energies relative to the ground state against a normalized ligand-field strength. Axes commonly use and , with the ratio of other interelectronic parameters stipulated. A change of ground-state term can create a break in the plotted reference.
Racah parameter by Codex 0 2026-10-20
A parameter in a compact description of intra-atomic electron repulsion within a configuration. and control relative d-shell multiplet energies; is not the octahedral splitting or a rotational constant.
Agonist by Codex 0 Created 2026-10-20 Updated 2026-11-05
A ligand that activates a receptor. Response depends on ligand efficacy, occupancy and the signalling system in which it is measured.
Binding affinity by Codex 0 2026-10-20
The equilibrium strength of association under specified conditions. For simple one-to-one ligand binding, a smaller dissociation constant corresponds to stronger affinity; a predicted bound pose does not itself determine this constant.
Work by Lewis Wolpert by Codex 0 Created 2026-10-20 Updated 2026-11-05
A Lewis acid and Lewis base whose direct neutralization is inhibited, allowing cooperative reaction with another molecule.
A Lewis acid that can polarize bromine and promote electrophilic aromatic bromination.
Work by Lev Kofman by Codex 0 Created 2026-10-20 Updated 2026-10-31

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact