ODMx: New Consistent Semiempirical Methods

We have introduced two new NDDO-based semiempirical quantum-chemical methods ODM2 and ODM3, which are more consistent and accurate than other existing methods of this type.

Semiempirical quantum chemical (SQC) methods based on the NDDO (neglect of diatomic differential overlap) are currently enjoying a resurgence of interest due to their low computational cost and reasonable accuracy. There is still a room and need for their improvement to widen their applicability domain.

Thus, in our latest publication [1], we introduce two new SQC methods with orthogonalization and dispersion corrections ODM2 and ODM3 (ODMx). You can access this article for free as it is an open access article published under a Creative Commons Attribution (CC-BY) License.

Electronic structure model employed by the ODMx methods is the same as the model employed in the corresponding Thiel’s OMx methods (OM2 and OM3), which is the most accurate among the NDDO-based models as follows from both our theoretical analysis and validation study. There are however differences between the ODMx and OMx methods that make the ODMx methods more consistent and accurate.

Abstract Image
The make-up of the ODMx methods

The ODMx methods include Grimme’s D3 dispersion corrections with three-body corrections EABC for the Axilrod–Teller–Muto dispersion interaction as their integral part. These corrections are necessary for proper description of the noncovalent interactions. Unfortunately, simple augmentation of the OMx methods with D3T (D3T = D3 + EABC) corrections deteriorates such properties as heats of formation, because these ad-hoc corrections were not present during the parametrization of the OMx methods.

The previous general-purpose methods were parametrized exclusively on ground-state properties, although they are often used for excited-state simulations. To address this apparent inconsistency, the training set of the new ODMx methods also included excited-state properties.

Another important distinction between other modern SQC methods and the ODMx methods is that the total energy obtained with the new methods is treated consistently with ab initio approaches. Older SQC methods used the total energy to calculate heats of formation directly without ever calculating zero-point vibrational energies (ZPVE) and thermal corrections explicitly. This convention was useful in early days of SQC method development, but it is no longer justified. Heats of formation are therefore calculated with the ODMx methods by evaluating ZPVEs within the harmonic-oscillator and rigid-rotor approximations in full analogy with ab initio conventions. This new re-definition of the total energy eliminates ambiguities in what relative energies calculated with the SQC methods actually represent (relative enthalpies at 298 K or relative ZPVE-exclusive energies at 0 K?), which has to be resolved in some cases (e.g. atomization energies at 0 K) by explicitly correcting SQC energies.

In the older SQC methods, atomization energy evaluated at the SCF level was set equal to atomization enthalpy at 298 K without calculating zero-point vibrational energies and thermal corrections explicitly. This historical convention is abandoned in the new ODMx methods.

The ODMx methods were parametrized on a broad selection of the training data reflecting our objectives: good and balanced description of ground-state and excited-state properties and noncovalent interactions. This is a highly nontrivial task due to the diversity of the objectives and it required specially designed parametrization procedure.

The performance of the ODMx methods was evaluated on very large collection of accurate data sets, overwhelming majority of which were not in the training set. This benchmarking revealed that the new methods reached above objectives and generally outperform other NDDO-based SQC methods. The ODMx methods are also consistent, i.e. you can use them as is, without explicitly switching on or off dispersion corrections or converting from enthalpies to ZPVE-exclusive energies. Thus, we recommend the new methods as standard tools for fast electronic-structure explorations.

1. Pavlo O. Dral, Xin Wu, Walter Thiel, Semiempirical Quantum-Chemical Methods with Orthogonalization and Dispersion Corrections. J. Chem. Theory Comput. 2019, Article ASAP. DOI: 10.1021/acs.jctc.8b01265.

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