Tanabe-Sugano Diagrams Overview

A diagram showing energy level changes of metal ions in different crystal fields.

Energy shifts of metal ion states in varying crystal fields, plotted against crystal field strength.

Fixed horizontal axis on T-S diagram representing the energy of the ground state.

Diagram plotted in units of Δ₀/B, showcasing crystal field strength(Δ₀) and energy(B) relationship.

T-S diagrams are commonly used to portray octahedral transition metal complexes, and can be applicable to tetrahedral & related systems (e.g., $d^{10}−n$ (oct) = $d^n$ (tet)).

The second derivative of the wavefunction with respect to position, representing the curvature of the wavefunction.

The second derivative of the wavefunction is proportional to the wavefunction itself, with a negative sign and a constant determined by the momentum squared and Planck's constant.

A mathematical equation that describes the behavior of a quantum system in a stationary state, relating energy, potential energy, and the second derivative of the wavefunction.

Manipulating the Schrödinger equation to isolate the terms related to energy and potential energy on one side and the second derivative term on the other side.

Multiplying the rearranged Schrödinger equation by 2m to simplify the equation and clearly separate the terms.

A fundamental law stating that energy cannot be created or destroyed, only transformed from one form to another. The change in a system's internal energy is equal to the heat added to the system plus the work done on the system.

Another fundamental law stating that the total entropy of an isolated system can never decrease over time. It can only remain constant or increase.

A thermodynamic potential that represents the maximum amount of reversible work that a system can perform at constant temperature and pressure.

A thermodynamic function that measures the maximum useful work obtainable from a closed system at constant temperature and volume.

A process is spontaneous if the change in Helmholtz Free Energy (ΔA) is negative, indicating a decrease in free energy. A positive ΔA implies a non-spontaneous process.

The work function (A) represents the maximum amount of work a system can perform at constant temperature and volume.

The equation relating Gibbs Free Energy (G) to enthalpy (H), temperature (T), and entropy (S): d(ΔG) / dT = (ΔH - ΔG) / T

Derived from the relationship between Gibbs Free Energy and its partial derivatives with respect to temperature and pressure, leading to d(ΔG)/dT = (ΔH - ΔG)/T.

A fundamental equation in quantum mechanics that describes the time evolution of a quantum system. It relates the energy, potential energy, and the wavefunction of a particle.

A mathematical function that describes the state of a quantum system. It contains all the information about the particle, including its probability of being found at a certain location.

An operator in quantum mechanics that represents the total energy of a system. It is the sum of the kinetic and potential energies.

The energy of motion of a particle. It depends on the particle's mass and velocity.

The energy stored within a particle due to its position or configuration. It depends on the forces acting on the particle.

It tells us how the wavefunction of a particle evolves in time, and therefore predicts the probability of finding a particle at a given location. It also helps us understand the energy levels of the particle and how these energy levels change with time.