Beer-Lambert Law (Lambert-Beer law), also known as Beer's law, the Beer-Lambert-Bouguer law, describes the relationship between the strength of a substance's absorption of light at a certain wavelength and the concentration of the absorbing substance and the thickness of its liquid layer.

Molecular Orbital Theory (MO):

Discusses molecular structure from the perspective of the molecule as a whole, holding that after atoms form molecules, electrons no longer belong to individual atomic orbitals but to molecular orbitals of the entire molecule; molecular orbitals are multi-centered.

Molecular orbitals are formed by combining atomic orbitals, following the principles of energy proximity, symmetry matching, and maximum overlap, commonly known as the “three bonding principles.”

The principles for electrons filling molecular orbitals in a molecule also follow the Aufbau principle (lowest energy), the Pauli exclusion principle, and Hund's rule.

Crystal-Field Theory (CFT):

Crystal Field Theory is a theory studying the chemical bonds of transition elements (complexes). Based on electrostatic theory and combined with quantum mechanics and group theory (the study of substance symmetry), it explains the physical and chemical properties of transition and lanthanide elements, focusing on the influence of ligands on the d and f orbitals of the central ion.

1. The interaction between the central ion and the ligand is viewed as purely electrostatic. The central atom is a positively charged point charge, and the ligands (or coordinating atoms) are negatively charged point charges. Their interaction is like ionic bonds between positive and negative ions in an ionic crystal—pure electrostatic attraction and repulsion, forming no covalent bonds.

2. Under the influence of the negative electric field formed by surrounding ligands, the five d orbitals of the central atom with the same energy undergo energy level splitting. Some d orbital energies increase, while others decrease.

3. Due to the splitting of d orbital energy levels, electrons on the d orbitals of the central atom will rearrange, preferentially occupying lower energy orbitals, reducing the system's total energy and making the complex more stable.

Ligand Field Theory (LFT):

Ligand Field Theory explains the structure and properties of coordination compounds. It is a development of Crystal Field Theory; its essence is the molecular orbital theory of coordination compounds. When dealing with the change in energy levels of central metal atom orbitals under the electric field produced by ligands, it primarily uses molecular orbital theory methods, adopting mathematical methods like the linear combination of atomic orbitals (LCAO), simplifying based on the symmetry of the ligand field, and absorbing the results of Crystal Field Theory to clarify the structure and properties of coordination compounds.

In some complexes, the central ion (usually called the central atom) is surrounded by ligands distributed according to a certain symmetry to form a structural unit. The coordination field is the electrostatic potential field of the ligands acting on the central ion (mostly referring to transition metal complexes here). Due to various symmetrical arrangements of ligands, there are various types of coordination fields, such as the tetrahedral field formed by tetrahedral coordination compounds and the octahedral field formed by octahedral coordination compounds.