Semiempirical Methods

New ODMx methods are most consistent among modern NDDO-based semiempirical methods
Four-center two-electron integrals can be safely neglected as they vanish after transformation from the nonorthogonal basis (abscissa) to the Löwdin basis (ordinate) for the valence-only minimal basis sets

We develop the new-generation semiempirical quantum chemical (SQC) methods. Recently, we introduced two new ODM2 and ODM3 (ODMx) methods [7] and suggested tight-binding semiempirical molecular orbital theory scheme [8] . We also performed comprehensive analysis of the NDDO (neglect of diatomic differential overlap) approximation behind most modern SQC methods, where we also discuss how to improve the SQC methods.[6]

Early we published details on OMx methods that include orthogonalization corrections neglected in other MNDO-like semiempirical methods.[4] These corrections make OMx methods the most robust SQC methods as our benchmark of many semiempirical methods shows.[5]

In many cases the accuracy of OMx methods approaches that of the most common DFT methods, but the OMx methods are by three orders of magnitude faster than the DFT techniques, which make semiempirical methods invaluable tool for calculating properties of large systems or performing large number of calculations. [See this excellent review for examples: Walter Thiel, Semiempirical quantum–chemical methods. WIREs Comput. Mol. Sci. 2014, 4, 145-157.]

Electron trap (fullerene in the middle) is clearly seen with the help of the semiempirical unrestricted EAL
Electron trap (fullerene in the middle) is clearly seen with the help of the semiempirical unrestricted EAL

Such local properties as local electron affinity (EAL) and local ionization energy (IEL) have been extensively used for drug design, where closed-shell species are usually modelled. Thus only restricted formulations of EAL and IEL were used for molecular species.

However, now their potential is recognized for application in modeling electronic devices [C. M. Jäger et al. Improving the charge transport in self-assembled monolayer field-effect transistors: from theory to devices. J. Am. Chem. Soc. 2013, 135, 4893-4900]. Since electrons and holes are generated in such devices, I have extended EAL and IEL to unrestricted case.[3]

We have demonstrated on example of carbon peapod that unrestricted EAL and IEL are especially useful for understanding how ambipolar transistors work. We recommend the use of the unrestricted EAL and IEL also for modeling devices built from closed-shell molecular species because of extremely large RHF→UHF instability for such systems. In addition, taking into account known similarity of electrophilic and radical activation of alkanes, we have also demonstrated that the unrestricted EAL can be used to predict radicals reactivity in alkanes activation.

We have also developed semiempirical UNO–CAS and UNO–CI for automatic calculating excited state properties with good accuracy comparable with commonly used TD DFT methods, but by several orders of magnitude faster.[1] This approach allows routine calculations of large molecular systems, for instance, fullerene-porphyrin donor-acceptor conjugates.[2] UNO–CI technique was implemented into serial semiempirical molecular orbital (MO) program VAMP and into massively parallel program EMPIRETM, both on Linux and Windows platforms.


8. Johannes T. Margraf, Pavlo O. Dral, What Is Semiempirical Molecular Orbital Theory Approximating? J. Mol. Model. 2019, 25, 119. DOI: 10.1007/s00894-019-4005-8. (blog post)

7. Pavlo O. Dral, Xin Wu, Walter Thiel, Semiempirical Quantum-Chemical Methods with Orthogonalization and Dispersion Corrections. J. Chem. Theory Comput. 2019, 15, 1743–1760. DOI: 10.1021/acs.jctc.8b01265. (blog post)

6. Xin Wu, Pavlo O. Dral, Axel Koslowski, Walter Thiel, Big Data Analysis of Ab Initio Molecular Integrals in the Neglect of Diatomic Differential Overlap Approximation. J. Comput. Chem. 2019, 40, 638–649. DOI: 10.1002/jcc.25748. (blog post)

5. Pavlo O. Dral, Xin Wu, Lasse Spörkel, Axel Koslowski, Walter Thiel, Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks for Ground-State Properties. J. Chem. Theory Comput. 2016, 12, 1097–1120. DOI: 10.1021/acs.jctc.5b01047. (blog post)

4. Pavlo O. Dral, Xin Wu, Lasse Spörkel, Axel Koslowski, Wolfgang Weber, Rainer Steiger, Mirjam Scholten, Walter Thiel, Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Theory, Implementation, and Parameters. J. Chem. Theory Comput. 2016, 12, 1082–1096. DOI: 10.1021/acs.jctc.5b01046. (blog post)

3. Pavlo O. Dral, The Unrestricted Local Properties: Application in Nanoelectronics and for Predicting Radicals Reactivity. J. Mol. Model. 2014, 20, 2134. DOI: 10.1007/s00894-014-2134-78. (blog post)

2. Pavlo O. Dral, Theoretical study of electronic properties of carbon allotropes. [online] Friedrich-Alexander-Universität Erlangen-Nürnberg, Dissertation (Dr. rer. nat.), 2013, [cited 2 February 2014]

1. Pavlo O. Dral, Timothy Clark, Semiempirical UNO–CAS and UNO–CI: Method and Applications in Nanoelectronics. J. Phys. Chem. A 2011, 115, 11303–11312. DOI: 10.1021/jp204939x.