NO-MNDO:  Reintroduction of the Overlap Matrix into MNDO

Abstract

The effect of reintroducing the overlap matrix into the secular equations for an NDDO (neglect of diatomic differential overlap)-based semiempirical molecular orbital method has been investigated. The modification is expected to improve the description of interactions between electron pairs. The idea has been tested by implementation and evaluation of a nonorthogonal version of the MNDO method (NO-MNDO) with parametrization for hydrogen, carbon, nitrogen, and oxygen. Overall, the accuracy of NO-MNDO for heats of formation is nearly identical to that for the more highly parametrized AM1 method. The mean absolute error (MAE) for heats of formation of a comprehensive set of 622 neutral, closed-shell molecules is reduced from 8.4 kcal/mol with MNDO to 6.8 kcal/mol with NO-MNDO. In addition, the performance for conformational equilibria and torsional barriers is significantly improved with NO-MNDO, presumably owing to the improved description of closed-shell interactions. For molecular geometries, the usual training and test sets have been expanded through use of MP2/6-31G(d) results for consistent comparisons. The performance of NO-MNDO for bond lengths, bond angles, and dihedral angles remains good with MAEs of 0.017 Å, 2.5°, and 4.5°. Additionally, NO-MNDO corrects severe errors by MNDO for R(•) + H-R' hydrogen-atom transfers, while testing for activation barriers for nine pericyclic reactions reveals only modest improvement.

Advances in Quantum and Molecular Mechanical (QM/MM) Simulations for Organic and Enzymatic Reactions

“…Subsequent attempts to re-optimize the parameter sets using modern optimizers provided little improvement 25,26. However, SQM methods suffer from several well-known problems 22,23.…”

“…For the SQM methods, blame could be attributable to both the valence-only sp basis sets and neglect of differential overlap (NDO). Ameliorating efforts included reintroduction of the overlap matrix into the secular equations in MNDO yielding NO-MNDO, and the addition of d-orbitals on the first row with MNDO and AM1 26. The mean unsigned error (mue) for heats of formation was reduced from 8.4 kcal/mol using MNDO to 6.8 kcal/mol with NO-MNDO for a diverse set of 622 neutral, closed-shell molecules containing C, H, N, and O atoms, and it also gave modest improvements for the activation barriers of nine pericyclic reactions 26.…”

“…Ameliorating efforts included reintroduction of the overlap matrix into the secular equations in MNDO yielding NO-MNDO, and the addition of d-orbitals on the first row with MNDO and AM1 26. The mean unsigned error (mue) for heats of formation was reduced from 8.4 kcal/mol using MNDO to 6.8 kcal/mol with NO-MNDO for a diverse set of 622 neutral, closed-shell molecules containing C, H, N, and O atoms, and it also gave modest improvements for the activation barriers of nine pericyclic reactions 26. The addition of d-orbitals for 217 hydrocarbons excluding alkynes, reduced the mue for Δ H f with MNDO from 9.3 to 6.8 and for AM1 from 5.3 to 3.8 with ring compounds improving from 7.1 to 4.5 kcal/mol.…”

Specific Reaction Parametrization of the AM1/d Hamiltonian for Phosphoryl Transfer Reactions: H, O, and P Atoms

“…45,46,65 Other recently developed semiempirical methods that show promise include the OMx models, 66,67 the PDDG/PM3 model, [68][69][70] the PM3-MAIS and PM3-PIF models, 71,72 the SCC-DFTB method, [73][74][75][76] and the very recent NO-MNDO model. 77 One problem that is prevalent in almost all semiempirical models that utilize a minimal valence basis methods is that they typically underpredict molecular polarizabilities as a function of charge. Recently a method has been proposed that greatly improves the modeling of charge-dependent response properties without increasing the atomic orbital basis and with minimal computational overhead.…”

Implementation and benchmark tests of the DFTB method and its application in the ONIOM method

“…With a careful parameterization, errors in semiempirical calculations are often within a qualitatively acceptable range. Consequently, efforts in the development and applications of semiempirical methods still continue more than three decades after their inception 2–29. Semiempirical methods are also considered to be the low‐level QM method in hybrid ONIOM (QM:QM′) or ONIOM (QM:QM′:MM) methods 30–34.…”