基组Basis set (chemistry)

斯莱特型轨道（STO，∝ e^(−ζr)）形状接近真实原子轨道，但多中心积分难算；高斯型轨道（GTO，∝ e^(−αr²)）积分容易，但在核处和远处行为不佳，所以常用几个 GTO 组合模拟一个 STO（如 STO-3G）。最小基组每个原子轨道一个基函数；分裂价基（如 6-31G）用多个函数描述价层；极化函数（*、d、p）允许轨道变形，弥散函数（+）用于阴离子和弱相互作用。邓宁的相关一致基组（cc-pVDZ、cc-pVTZ…）可系统外推到完备基组极限。平面波基组常用于周期性固体。

Slater-type orbitals (STO, ∝ e^(−ζr)) resemble real atomic orbitals but make multi-centre integrals hard; Gaussian-type orbitals (GTO, ∝ e^(−αr²)) make integrals easy but behave poorly at the nucleus and far away, so several GTOs are combined to mimic one STO (as in STO-3G). A minimal basis has one function per atomic orbital; split-valence sets such as 6-31G use several for the valence shell; polarisation functions (*, d, p) let orbitals distort, and diffuse functions (+) serve anions and weak interactions. Dunning's correlation-consistent sets (cc-pVDZ, cc-pVTZ…) extrapolate systematically to the complete-basis-set limit. Plane-wave bases are common for periodic solids.

1930 年斯莱特提出斯莱特型轨道。1950 年英国化学家博伊斯提出使用高斯函数，大大简化了分子积分计算，使从头算成为可能。1960–70 年代波普尔团队开发了 STO-3G、6-31G 等基组及 Gaussian 程序。1989 年邓宁提出相关一致基组。

Slater proposed Slater-type orbitals in 1930. In 1950 the British chemist Frank Boys proposed Gaussian functions, which greatly simplified molecular integrals and made ab initio calculations practical. In the 1960s and 1970s Pople's group developed basis sets such as STO-3G and 6-31G and the Gaussian program. Dunning introduced correlation-consistent basis sets in 1989.

基组选择需与方法匹配：DFT 常用 6-31G(d) 或 def2-TZVP；高精度耦合簇计算需 cc-pVTZ 以上并外推。含重元素时常用有效核势（赝势）代替内层电子，并计入相对论效应。有限基组会产生基组重叠误差（BSSE），计算弱相互作用能时需用均衡校正法校正。

The basis must suit the method: DFT commonly uses 6-31G(d) or def2-TZVP, while accurate coupled-cluster work needs cc-pVTZ or larger with extrapolation. For heavy elements effective core potentials (pseudopotentials) replace core electrons and include relativistic effects. Finite bases cause basis-set superposition error (BSSE), which must be corrected by the counterpoise method when computing weak interaction energies.