Practical approaches of Quantum Chemistry [part 4] : Semi-empirical Quantum Chemistry

Anant　Babu Marahatta
Ph.D. student in Chemistry
Tohoku University
Japan

(This article is intended to introduce the semi-empirical techniques of Quantum chemistry) I am a part of it and currently mastering on “Density Functional Tight Binding (DFTB) approximation with and without Gaussian” by implementing them to investigate the rotational dynamics of the crystalline “Molecular Gyroscope”.

(Interested fellows are suggested to read Part 1 to part 3 of this article before proceeding it. And if necessary, you are reminded to consult the article “Computational Chemistry” archived herewith.)

Unlike the ab initio techniques [part 3] which are based entirely on the solution of the Schrödinger equations, semi-empirical techniques employ experimental results. In order to simplify the approximation, such techniques use parameters derived from the experimental data to the Schrödinger equation.

Basically, semiempirical techniques attempt to address the limitations like slow speed and low accuracy by omitting or parameterizing certain integrals based on experimental data, such as ionization energies of atoms, or dipole moments of molecules. As a result, semi-empirical methods are very fast, computationally inexpensive and applicable to very, very large molecules, and may give accurate results. However, accuracy of such methods lacks consistency on many systems.

Following animation explains about the action of the Quantum Molecular Dynamics Simulations of Molecules on a Metal Surface.



In computational chemistry, consideration of the more accurate methods (ab initio techniques) to study the molecular systems consisting thousands of atoms is impossible. The same is valid well to the case of crystalline solid even bearing medium sized molecules due to the inclusion of periodic boundary condition (PBC). In such cases, semi-empirical techniques are the good option. Similarly, in order to obtain the starting structure for an ab initio calculations (eg. Hartree-Fock, Density functional theory etc.), one might run semi-empirical calculations. However, the limitations of them must be considered before selecting the proper one and the level of accuracy depends on the system to be studied.

Semi-empirical methods may only be used for systems where parameters have been developed for all of their component atoms.　In addition to this, types of problems on which they do not perform well include hydrogen bonding, transition structures, van der Waals type interactions and so on. AM1 (Austin Model 1), AM1* (extended AM1), PM3 (Parameterized Model number 3) and MNDO (Modified Neglect of Differential Overlap) are the best known semi-empirical methods which can be run using Gaussian scheme.

The very recent approach “DFTB technique” especially focused to the solid state science has become a very popular for exploring the solid state dynamics computationally. I am also a part of it and mastering on “DFTB with and without Gaussian” by implementing them to investigate the rotational dynamics of the crystalline “Molecular Gyroscope”.

References:
http://www.chm.bris.ac.uk/motm/pentacene/pentacene.htm