LCAO近似Linear combination of atomic orbitals

n 个原子轨道组合成 n 个分子轨道，其中同号重叠（相位相同）形成能量低于原子轨道的成键轨道，异号重叠形成能量更高的反键轨道。有效组合需满足三原则：对称性匹配（只有对称性相同的轨道才能组合）、能量相近、最大重叠。以 H₂ 为例，两个 1s 轨道组合成 σ₁ₛ（成键）和 σ*₁ₛ（反键），两个电子占据成键轨道，键级 1。

n atomic orbitals combine into n molecular orbitals; in-phase overlap gives bonding orbitals below the atomic orbitals and out-of-phase overlap antibonding orbitals above them. Effective combination requires matching symmetry, similar energies and maximum overlap. For H₂ the two 1s orbitals give σ₁ₛ (bonding) and σ*₁ₛ (antibonding); two electrons fill the bonding orbital, a bond order of 1.

1929 年英国物理学家伦纳德-琼斯在研究双原子分子时提出用原子轨道线性组合构造分子轨道。洪德和密立根同期发展了分子轨道理论，密立根因此获 1966 年诺贝尔化学奖。1951 年罗特汉把 LCAO 与哈特里-福克方法结合，奠定了现代量子化学计算的基础，基组概念由此而来。

In 1929 the British physicist John Lennard-Jones, studying diatomic molecules, proposed building molecular orbitals from linear combinations of atomic orbitals. Hund and Mulliken developed molecular orbital theory in the same period, and Mulliken received the 1966 Nobel Prize in Chemistry. In 1951 Roothaan combined LCAO with Hartree–Fock, founding modern computational quantum chemistry and giving rise to the idea of basis sets.

LCAO 用于画出 O₂、N₂ 等双原子分子的分子轨道能级图，解释 O₂ 的顺磁性和 N₂ 的三键；用于休克尔法处理共轭体系；在固体物理中称为紧束缚近似，用于计算能带结构；也是所有基于高斯基组的从头算和 DFT 程序的基础。

LCAO is used to draw MO diagrams for diatomics such as O₂ and N₂, explaining O₂'s paramagnetism and N₂'s triple bond; to treat conjugated systems in the Hückel method; in solid-state physics as the tight-binding approximation for band structures; and as the foundation of every ab initio and DFT program using Gaussian basis sets.