Part 1.    Quantum-mechanical methods

Summary:

1. Use DFT methods for obtaining accurate geometries of molecules
2. Use DFT methods with careful density functional choice for accurate energetic properties with highly affordable computational cost.
3. Use DFT methods with careful choice of density functional and basis set for studying excitations with highly affordable computational cost.
4. Use wavefunction methods (such as (L)MP2 or CCSD(T)) for improved accuracy on energetic properties and spectroscopic properties, at a high computational cost.
5. Consider combining DFT methods: Use lower-level functionals for geometrical optimizations, then use higher-level functionals for calculating properties
   • Taking into account the accuracy-cost ratio, functionals such as B3LYP (for molecules) and PBE (for periodical structures) are good choices for geometrical optimizations. Use them with smaller basis sets (for example, 6-31G(d,p) for initial geometrical optimizations.
   • Use improved functionals for thermochemical properties (for example, M06-2X from the M06 family of functionals) or excitations (for example CAM-B3LYP or wB97X-D). 
6. Consider combining DFT and wavefunction methods: use DFT with low-cost functionals (such as B3LYP) for geometrical optimizations, then use wavefunction methods for thermochemical properties (for example, (L)MP2 or CCSD(T) methods) and excitation properties (for example, CCSD(T) or ADC(2)). This is expensive in terms of computational cost, but offers improved accuracy.
7. For optimizing systems consisting of noncovalently interacting molecules (for example, physical adsorption of some molecule on the surface of some nanostructure, interaction between two molecules, etc), or for studying noncovalent interactions between molecules, never use B3LYP functional as it cannot correctly consider London dispersion interactions. In this case, you can use:
   • Functionals that are empirically corrected for dispersion interactions (for example, B3LYP-D3 or PBE-D3). Famous Prof. Stefan Grimme has developed dispersion correction, so the readers are directed to Prof. Grimme’s website for further details on dispersion corrections.
   • Functionals that have been adjusted/parametrized to produce the correct electron density in case of noncovalent interactions (for example, the M06-2X)
8. Empirically corrected functionals such as B3LYP-D3 are just slightly more computationally expensive than the regular B3LYP. This is because empirically corrected functionals don’t change electron density; they actually contain the empirical term in the energy equation. On the other side, heavily parametrized functionals specially adjusted for noncovalent interactions, such as M06-2X, are much more computationally expensive than empirically corrected ones (comparison benchmarks comming soon). Keep in mind that empirical correction can also be applied to adjusted functionals, so you also have a choice to use, for example, M06-2X-D3 functional.
9. For studying excitations (for simulating the UV/Vis spectra), the TD-DFT approach is seen as a compromise between accuracy and cost. For improved accuracy, wavefunction methods are advised, such as CCSD(T) or ADC(2). If your choice is the TD-DFT method, don’t use B3LYP. Instead, use some long-range corrected, such as CAM-B3LYP or wB97X‑D functionals. Keep in mind that a sufficiently large basis set should be used for accurate results – in the case of the Pople basis sets, be sure to use diffuse functions on at least heavy atoms (6-31+G(d,p)). Of course, it is advised to use 6-311++G(d,p) basis set. More information about basis sets is coming soon.

Part 2.    Semiempirical methods

When to use:

1. For large molecular structures
2. For pre-optimization

Background

If your molecule is far from equilibrium geometry, it would be a waste of computational resources to run geometrical optimizations straight at quantum mechanical levels of theory (such as DFT or MP2). In these cases, it is highly beneficial first to perform a pre-optimization of your molecule using some of the semi-empiric levels of theory.

Semi-empiric levels of theory are derived from quantum-mechanical levels of theory, and they contain additional approximations. These additional approximations make them less accurate but orders of magnitude faster. In other words, the optimization of medium sized simple organic molecules (such as some common pharmaceutical molecules) might last between 10 and 60 minutes using the DFT method, depending on the speed of your computer. However, optimizing that molecule using some semiempirical method would take just a few seconds. Yes, just a few seconds. It is very important to mention that in the case of organic molecules, modern semiempirical methods will provide molecular geometries that are very close to ones obtained at higher levels of theory, such as DFT or MP2.

What are the best semiempirical methods?

The two best known semi-empirical methods are PM7 and DFTB. Both of these methods have several variants and provide great results.

PM7 method is a method based on a wavefunction. To obtain accurate results, this method is parametrized over a large number of molecules. PM7 has several modifications to consider noncovalent interactions and other properties properly. It is warmly recommended to read the paper by James Stewart (2013) https://doi.org/10.1007%2Fs00894-012-1667-x to obtain a deeper understanding of this method and its capabilities. You might also find useful the following paper https://pubs.acs.org/doi/10.1021/acs.jpca.9b11474

PM7 (parametrization method 7) method is available in MOPAC2016 modeling program, developed by Dr. James Stewart which is a free-for-academic tool. MOPAC is also available as a part of some commercial modeling packages, such as Schrodinger Materials Science Suite and SCM ADF. We have also built a web application for running MOPAC2016 program from your browser – online MOPAC calculator.

DFTB (Density-functional tight-binding) method is a method based on electron density. To use this method, it is required to provide parameters, or the so called Slater-Koster files, for each element of the molecule. It is a more accurate method than PM7, but it lacks parameters for each element of the periodic system. Recently, Prof. Stefan Grimme developed a DFTB method called extended tight binding (xTB), with several variants available: for example GFN2-xTB and GFB1-xTB. Aside from the amazing accuracy, this method is characterized by the fantastic coverage of the periodic system of elements (all elements up to radon are supported), making the DFTB method available for different systems. You can perform these calculations for free, thanks to the fact that the binaries are available at the website of Prof. Grimme’s group at https://www.chemie.uni-bonn.de/pctc/mulliken-center/software/xtb/xtb . We have also built a web application for running xtb program in your browser – online xtb calculator.