semiempirical

Semiempirical refers to a class of electronic structure methods in quantum chemistry that approximate the solution of the Schrödinger equation by replacing many integrals with empirically derived parameters. These methods combine a simplified Hamiltonian and a modest basis set with parameters fitted to experimental data or higher-level calculations, reducing computational cost. The approach enables calculations on larger molecules and broader chemical spaces than conventional ab initio methods.

Typically, semiempirical methods use parameterized forms of the electronic energy, often employing neglect or simplification of certain two-electron integrals (forming families such as CNDO, INDO, MNDO) and then more recent schemes like AM1, PM3, PM6, and PM7. Parameter sets are designed for common elements and bonding types, with emphasis on organic elements such as H, C, N, O, and often S, P, and halogens. The methods are especially geared toward geometry optimization, vibrational properties, heats of formation, and dipole moments, offering faster results at the cost of some accuracy and transferability.

Applications include rapid geometry optimizations and conformational analyses in organic and bio-organic chemistry, high-throughput screening in medicinal chemistry, and preliminary studies of large biomolecules or materials where ab initio methods are impractical. Limitations include variable accuracy across properties, reduced reliability for transition metals, excited states, and barrier heights, and sensitivity to the chosen parameter set. Noncovalent interactions and dispersion are often imperfect unless additional corrections are employed.

Today, semiempirical methods remain useful as fast screening tools and as starting points for higher-level calculations. Ongoing developments aim to broaden chemical space, improve noncovalent and dispersion descriptions, and extend applicability to larger systems.