Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Theory, Implementation, and Parameters

Abstract

Semiempirical orthogonalization-corrected methods (OM1, OM2, and OM3) go beyond the standard MNDO model by explicitly including additional interactions into the Fock matrix in an approximate manner (Pauli repulsion, penetration effects, and core–valence interactions), which yields systematic improvements both for ground-state and excited-state properties. In this Article, we describe the underlying theoretical formalism of the OMx methods and their implementation in full detail, and we report all relevant OMx parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine. For a standard set of mostly organic molecules commonly used in semiempirical method development, the OMx results are found to be superior to those from standard MNDO-type methods. Parametrized Grimme-type dispersion corrections can be added to OM2 and OM3 energies to provide a realistic treatment of noncovalent interaction energies, as demonstrated for the complexes in the S22 and S66×8 test sets.

Big data analysis of ab Initio molecular integrals in the neglect of diatomic differential overlap approximation

“…We find a roughly linear correlation for ( r 2 = 0.983), but there are large deviations between the values in the { ϕ i } and representations, with a standard deviation σ of 7.0 eV. Evidently, is severely affected by orthogonalization effects, which should be taken into account explicitly in SQC models (as, e.g., in the OM x methods).…”

“…This Big Data study of ab initio molecular integrals is primarily aimed at providing insights into the approximations underlying NDDO‐based SQC models. The computed molecular integrals are therefore classified into seven and five different types of 2‐e and 1‐e integrals, respectively, according to the NDDO integral convention that is widely adopted in many popular SQC methods, for example, MNDO, AM1, PM x , and the OM x series . In addition, we define two extra types of molecular integrals associated with the interplay between attractive 1‐e and repulsive 2‐e terms in the molecular Hamiltonian.…”

“…The 1‐e core Hamiltonian H core represents the electron kinetic energy and the nuclear‐electron attraction energy. Instead of decomposing H core into individual T μν and V μν ,A contributions for each atom, the 1‐e integrals are classified as diagonal one‐center integrals U μμ , 2‐c NAIs V μν ,B, 2‐c resonance integrals β μλ , off‐diagonal one‐center integrals U μν , and 3‐c NAIs V μλ ,C, in accord with the integral conventions adopted in most NDDO‐based SQC methods . A complete list of these integrals and their mathematical definitions is given in Table .…”

“…The deviations between the values in the { ϕ i } and representations are smaller than those for but not negligible ( σ = 0.77 eV). Hence, it is reasonable to add suitable orthogonalization corrections to the 2‐c NAIs in NDDO‐based SQC methods (as, e.g., in the OM x methods).…”

Towards a barrier height benchmark set for biologically relevant systems

“…Semiempirical electronic structure methods are increasingly parameterized and benchmarked against data obtained by DFT or wavefunction-based calculations rather than experimental data (Stewart, 2007;Dral et al, 2016a;Gaus et al, 2013a). Using calculated data has the advantage that it represents the precise value (usually the electronic energy) that is being parameterized, with little random noise and even coverage of chemical space, including molecules that are difficult to synthesize or perform measurements on.…”