gtensor

G-tensor, or g-tensor, is a term used in physics and chemistry to describe the anisotropic coupling between an electron’s magnetic moment and an external magnetic field. In systems with unpaired electrons, the interaction is described by a second-rank tensor g, which generalizes the scalar g-factor of the free electron.

In the spin Hamiltonian that governs electron paramagnetic resonance (EPR) or electron spin resonance, the energy is given by H = μ_B B · g · S, where μ_B is the Bohr magneton, B is the magnetic field, and S is the electron spin operator. Diagonalizing g yields principal values g_x, g_y, g_z and corresponding principal axes, which define the g-tensor’s orientation relative to the molecular frame. The anisotropy is often expressed as principal values, with deviations from the free-electron g ≈ 2.0023 indicating spin–orbit and crystal-field effects.

Applications: G-tensors are used to interpret EPR spectra of transition-metal ions, defects in solids, and organic radicals; they provide information about electronic structure, geometry, and symmetry. The tensor can be measured experimentally by rotating the sample or by comparing spectra at different orientations, and it is often computed theoretically using quantum chemistry methods.

In mathematics and differential geometry, g denotes the metric tensor on a manifold; occasionally the combined term “g-tensor” may appear in older literature when discussing metric properties, but the standard term is simply metric tensor.

Note: There exist software implementations and studies that compute or utilize g-tensors in spectroscopy and modeling, but GTensor as a standalone project refers to domain-specific tools and should be consulted directly for details.