Start with the electrons
Before we talk about spin dynamics, we need to know what the electrons are doing. Electronic-structure theory is the layer that gives us energies, densities, excited states and ultimately the magnetic parameters that enter a spin Hamiltonian.
Distinguish the many-electron wavefunction, molecular orbitals and electron density.
Explain what HF, DFT, correlation methods and basis sets approximate differently.
Identify which electronic-structure outputs become parameters of a spin Hamiltonian.
The electronic problem
Freeze the nuclei for a moment
Wavefunction and electron density describe the same electrons at different levels of information
What it is: A complex quantum amplitude defined over the coordinates and spins of all electrons simultaneously.
What it changes: Its antisymmetry enforces fermionic exchange and, in principle, contains all electronic observables and correlations.
What you observe: The wavefunction itself is not directly measured; probabilities, densities, energies and response properties are derived from it.
What it is: The probability density for finding electronic charge around position \(\mathbf r\), obtained after integrating the many-electron information over all other coordinates.
What it changes: It determines electrostatics, bonding patterns and—within ground-state DFT—the total energy in principle.
What you observe: Charge distributions, electrostatic potentials and density-derived quantities; experimentally it is related to X-ray/electron scattering rather than to an orbital picture.
What it is: The approximation that electrons adjust much faster than nuclei because nuclei are far heavier.
What it changes: It lets us solve an electronic problem at each fixed nuclear geometry and interpret the resulting energy as a potential-energy surface for nuclear motion.
What you observe: Molecular geometries, vibrational surfaces and reaction paths; breakdown appears in strongly nonadiabatic regions such as conical intersections.
Within the Born–Oppenheimer picture we first treat the nuclei as fixed. For that molecular geometry, the electronic Hamiltonian is
The difficult term is the electron–electron repulsion. It couples the motion of all electrons, which is why the exact many-electron problem grows so quickly with system size.
Orbitals & basis sets
An orbital is a representation tool, not an electron trajectory
A molecular orbital \(\phi_p(\mathbf r)\) is a one-electron function. In most quantum-chemistry codes it is expanded in atom-centred basis functions \(\chi_\mu\):
The basis controls how flexibly the electronic wavefunction or density can respond. A minimal basis is cheap but restrictive; polarized and diffuse functions give the electrons more freedom. The important point is that a basis-set name is not just a technical label—it defines the variational space in which the electronic problem is solved.
What do polarization and diffuse functions actually do?
Polarization functions add angular flexibility, allowing the density to distort away from isolated-atom shapes. Diffuse functions add slowly decaying radial functions and are important for anions, Rydberg states and spatially extended charge-transfer states.
Approximations
HF, DFT and correlation answer the same question differently
Exchange and correlation are distinct consequences of having many electrons
What it is: A purely quantum effect arising from antisymmetry of the many-electron wavefunction for identical fermions. Same-spin electrons avoid one another even without invoking classical electrostatic repulsion.
What it changes: It changes orbital energies, spin-state energetics and magnetic coupling, and is treated exactly within a Hartree–Fock determinant.
What you observe: Spin-state splittings, bond energetics and the strong dependence of many magnetic properties on the exchange treatment.
What it is: The additional correlated motion of electrons beyond the average-field picture, including dynamical avoidance from Coulomb repulsion and, in multireference cases, near-degenerate configurations.
What it changes: It corrects energies, charge distributions, bond breaking and magnetic couplings that a single determinant can misrepresent.
What you observe: Improved reaction energies, excitation energies and spin-state orderings; failures can be dramatic when static correlation is strong.
What it is: In Kohn–Sham DFT, the approximate energy functional that contains the many-body physics not represented by the non-interacting kinetic energy and classical Coulomb term.
What it changes: Its form controls self-interaction error, delocalization, spin densities and response properties.
What you observe: Functional dependence of geometries, charge-transfer energies, hyperfine couplings and magnetic tensors.
A single Slater determinant. Exchange is exact within that determinant, but dynamical electron correlation is absent.
Uses the density and a Kohn–Sham reference system. The practical approximation is the exchange–correlation functional.
MP2, coupled cluster and related methods recover correlation beyond a single determinant, at increasing computational cost.
Necessary when several electronic configurations are genuinely important and a single determinant is qualitatively insufficient.
There is no universal “best” method. The right level depends on the observable. Ground-state geometries, charge-transfer states, bond breaking and magnetic response can have very different sensitivities.
Interactive
State mixing and avoided crossings
Two states can have very different physical character and still mix strongly if they come close in energy. This tiny two-state model is a useful prototype:
Two coupled electronic states
Away from the crossing, the lower state is mostly localized on one diabatic state.
Excited & magnetic states
Electronic structure supplies the spin Hamiltonian
The magnetic parameters are response properties of the electronic state
What it is: The factor that converts an applied magnetic field into electron-spin Zeeman splitting. A free electron has \(g\approx2.0023\); a molecule deviates from this because orbital motion and excited electronic states admix through spin–orbit coupling.
What it changes: It sets the spin precession frequency and, when anisotropic, makes that frequency depend on molecular orientation.
What you observe: EPR resonance positions and their orientation dependence.
What it is: The magnetic interaction between an electron spin and a nuclear spin. Its contact part probes spin density at the nucleus; its anisotropic part reflects the spatial distribution of the unpaired electron.
What it changes: It splits spin energy levels and creates different local magnetic fields for different nuclear-spin states.
What you observe: Hyperfine multiplets in EPR/ENDOR and nuclear-dependent singlet–triplet mixing in radical pairs.
What it is: A relativistic interaction linking the electron's spin angular momentum to its orbital motion in the molecular electrostatic field.
What it changes: It mixes states of different spin character, shifts the \(g\)-tensor away from the free-electron value and can enable intersystem crossing.
What you observe: \(g\)-anisotropy, zero-field splitting, spin-forbidden intensity and singlet↔triplet population transfer.
What it is: A splitting of sublevels within an \(S>\tfrac12\) spin multiplet even when no external magnetic field is applied.
What it changes: It sets an intrinsic anisotropic energy scale through spin–spin and spin–orbit contributions.
What you observe: Field-independent level splittings and characteristic EPR transitions of triplets and higher-spin centres.
For photochemistry, ground-state DFT is only the start. We also need excited-state energies, oscillator strengths, charge-transfer character and sometimes spin–orbit coupling between states. TD-DFT is often the practical workhorse, while multireference methods become important when several configurations matter simultaneously.
For spin dynamics, the key output is often a set of effective magnetic parameters:
Selected reading
Examples from my work
Importance of Polarizable Embedding for Absorption Spectrum Calculations of Arabidopsis thaliana Cryptochrome 1
How the protein environment changes flavin excitation energies.
J. Phys. Chem. B (2024) →Peculiar Differences between Two Copper Complexes Containing Similar Redox-Active Ligands
DFT and multiconfigurational descriptions of electronically non-trivial transition-metal complexes.
Inorg. Chem. (2024) →Revealing the Impact of g-Tensor Anisotropy on the Charge Recombination in Donor–Acceptor Dyads Under High Magnetic Fields
An electronic-structure-derived magnetic interaction controlling spin-dependent kinetics.
JACS (2025) →Key external literature
Where to read next
These are deliberately selected from outside my own work: foundational papers or reviews that are especially useful for this topic.
Inhomogeneous Electron Gas
P. Hohenberg and W. Kohn · Physical Review (1964). The first Hohenberg–Kohn theorem establishes the density as a sufficient ground-state variable.
Open DOI →Self-Consistent Equations Including Exchange and Correlation Effects
W. Kohn and L. J. Sham · Physical Review (1965). The practical construction underlying most modern density-functional calculations.
Open DOI →