Development of NOTCH, an all-electron, beyond-NDDO semiempirical method: Application to diatomic molecules

In this work, we develop a new semiempirical method, dubbed NOTCH (Natural Orbital Tied Constructed Hamiltonian). Compared to existing semiempirical methods, NOTCH is less empirical in its functional form as well as parameterization. Specifically, in NOTCH, (1) the core electrons are treated explicitly; (2) the nuclear–nuclear repulsion term is calculated analytically, without any empirical parameterization; (3) the contraction coefficients of the atomic orbital (AO) basis depend on the coordinates of the neighboring atoms, which allows the size of AOs to depend on the molecular environment, despite the fact that a minimal basis set is used; (4) the one-center integrals of free atoms are derived from scalar relativistic multireference equation-of-motion coupled cluster calculations instead of empirical fitting, drastically reducing the number of necessary empirical parameters; (5) the (AA|AB) and (AB|AB)-type two-center integrals are explicitly included, going beyond the neglect of differential diatomic overlap approximation; and (6) the integrals depend on the atomic charges, effectively mimicking the “breathing” of AOs when the atomic charge varies. For this preliminary report, the model has been parameterized for the elements H–Ne, giving only 8 empirical global parameters. Preliminary results on the ionization potentials, electron affinities, and excitation energies of atoms and diatomic molecules, as well as the equilibrium geometries, vibrational frequencies dipole moments, and bond dissociation energies of diatomic molecules, show that the accuracy of NOTCH rivals or exceeds those of popular semiempirical methods (including PM3, PM7, OM2, OM3, GFN-xTB, and GFN2-xTB) as well as the cost-effective ab initio method Hartree–Fock-3c.