Struct IntegralEngine 

pub struct IntegralEngine;

Evaluator engine for molecular integrals

Implementations

impl IntegralEngine

pub fn evaluate_overlap<const N: usize, const M: usize>( basis_a: &[GtoPrimitive; N], basis_b: &[GtoPrimitive; M], ) -> ZeroHeapMatrix<f64, N, M>

Evaluates the overlap matrix S between two sets of GTO primitives. Returns a ZeroHeapMatrix containing the overlap elements.

pub fn overlap_s(a: &GtoPrimitive, b: &GtoPrimitive) -> f64

Bare s-type overlap (a|b) between two primitive Gaussians, INCLUDING the primitives’ coefficient factors. Exact closed form (Szabo & Ostlund, appendix A): S_ab = (π/p)^{3/2} · exp(−μ·|A−B|²) · c_a · c_b, with p = α+β and μ = αβ/p. Valid for s-type (l = 0); the STO-3G H/He validation set contains only s primitives.

pub fn kinetic_s(a: &GtoPrimitive, b: &GtoPrimitive) -> f64

Kinetic-energy integral (a|−½∇²|b) for two s-type primitives, INCLUDING the coefficient factors. Exact closed form: T_ab = μ·(3 − 2μ·|A−B|²) · S_ab, μ = αβ/(α+β), where S_ab is the bare s overlap above (Szabo & Ostlund, appendix A).

pub fn nuclear_s( a: &GtoPrimitive, b: &GtoPrimitive, center: [f64; 3], z: f64, ) -> f64

Nuclear-attraction integral (a|−Z/|r−C||b) for two s-type primitives and one nucleus of charge z at center, INCLUDING the coefficient factors. Exact closed form via the Boys function F₀: V_ab^C = −Z · (2π/p) · exp(−μ·|A−B|²) · F₀(p·|P−C|²), with p = α+β, μ = αβ/p and P the Gaussian-product center (Szabo & Ostlund, appendix A). The total one-electron nuclear attraction is the sum over all nuclei.

pub fn dipole_s(a: &GtoPrimitive, b: &GtoPrimitive) -> [f64; 3]

Cartesian dipole-moment integrals (a|x|b), (a|y|b), (a|z|b) for two s-type primitives, INCLUDING the coefficient factors, measured about the global coordinate origin. Exact closed form: the first moment of the product Gaussian is its center P, so (a|w|b) = P_w · S_ab.

pub fn evaluate_eri( a: &GtoPrimitive, b: &GtoPrimitive, c: &GtoPrimitive, d: &GtoPrimitive, ) -> f64

Evaluates the Two-Electron Repulsion Integrals (ERI). Since ERIs are 4-center (N x N x N x N), we return a specific slice or compute on demand. For this engine, we evaluate a single (ab|cd) primitive set.

pub fn boys_function(n: u8, t: f64) -> f64

Evaluates the Boys function F_n(t) using a zero-heap segmented method:

• Small T: Taylor series expansion
• Intermediate T: Minimax polynomial interpolation (lookup table)
• Large T: Asymptotic expansion