DENSITY FUNCTIONALS

• B3LYP

1. D. Becke, Density‐functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98 (1993) 5648–5652. https://doi.org/10.1063/1.464913.
2. Lee, W. Yang, R.G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B. 37 (1988) 785. https://doi.org/10.1103/PhysRevB.37.785.
3. H. Vosko, L. Wilk, M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis, Can. J. Phys. 58 (1980) 1200–1211. https://doi.org/10.1139/p80-159.
4. J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields, J. Phys. Chem. 98 (1994) 11623–11627. https://doi.org/10.1021/j100096a001.

Information is taken from an extremely useful link: http://www.ccl.net/chemistry/resources/messages/2002/05/22.008-dir/

These citations are available in the following .ris file (right click – save link as)

• PBE

1. P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys Rev Lett. 77 (1996) 3865–3868. https://doi.org/10.1103/PhysRevLett.77.3865.
2. P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)], Phys. Rev. Lett. 78 (1997) 1396–1396. https://doi.org/10.1103/PhysRevLett.78.1396.

These citations are available in the following .ris file (right click – save link as)

• M06 family; M06-2X, M06, etc

The main paper where M06 family of functionals is introduced is:

1. Zhao, D.G. Truhlar, The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals, Theor. Chem. Acc. 120 (2008) 215–241. https://doi.org/10.1007/s00214-007-0310-x

Aside from developing these fantastic functionals, Prof. Truhlar and coworkers made amazing efforts to test functionals and present the results of benchmarks in several amazing works. Therefore, it is warmly recommended to cite and check the following papers as they will certainly help you decide which functional to apply for your molecules:

2. Zhao, D.G. Truhlar, Density Functionals with Broad Applicability in Chemistry, Acc. Chem. Res. 41 (2008) 157–167. https://doi.org/10.1021/ar700111a
3. Jacquemin, E.A. Perpète, I. Ciofini, C. Adamo, R. Valero, Y. Zhao, D.G. Truhlar, On the Performances of the M06 Family of Density Functionals for Electronic Excitation Energies, J. Chem. Theory Comput. 6 (2010) 2071–2085. https://doi.org/10.1021/ct100119e
4. Valero, R. Costa, I. de P. R. Moreira, D.G. Truhlar, F. Illas, Performance of the M06 family of exchange-correlation functionals for predicting magnetic coupling in organic and inorganic molecules, J. Chem. Phys. 128 (2008) 114103. https://doi.org/10.1063/1.2838987

All these references are available in the following .ris file (right click – save link as)

• revM06

1. Wang, P. Verma, X. Jin, D.G. Truhlar, X. He, Revised M06 density functional for main-group and transition-metal chemistry, Proc. Natl. Acad. Sci. 115 (2018) 10257–10262. https://doi.org/10.1073/pnas.1810421115 .

This citation is available in the following .ris file (right click – save link as)

Wang, Verma, Jin, Truhlar and He have developed a revM06 functional and compared its performance against M06-L and M06-2X. As they mentioned in their work revM06 has “broader accuracy than either M06 or M06-2X” and “the revM06 functional is well suited for a broad range of applications on main-group chemistry, transition-metal chemistry, and molecular structure prediction”

• CAM-B3LYP

1. Yanai, D.P. Tew, N.C. Handy, A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP), Chem. Phys. Lett. 393 (2004) 51–57. https://doi.org/10.1016/j.cplett.2004.06.011

This is a long-range corrected version of the famous B3LYP functional. B3LYP does not provide adequate results when studying excitations. Instead, it is advised to use some long-range corrected, such as CAM-B3LYP, or other specially designed functionals.

This citation is available in the following .ris file (right click – save link as)

• ωB97X-D

1. -D. Chai, M. Head-Gordon, Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections, Phys. Chem. Chem. Phys. 10 (2008) 6615–6620. https://doi.org/10.1039/B810189B

Aside from long-range corrections, ωB97X-D also includes “empirical atom-atom dispersion corrections”. Since the ωB97X-D was obtained by re-parametrization of ωB97X to include mentioned dispersion corrections, we believe it is fair also to cite the paper where ωB97X was introduced as well, which is:

2. -D. Chai, M. Head-Gordon, Systematic optimization of long-range corrected hybrid density functionals, J. Chem. Phys. 128 (2008) 084106. https://doi.org/10.1063/1.2834918

These citations are available in the following .ris file (right click – save link as)

Important notice: in input and output files of modeling packages, it is impossible to use rich text and other special characters, so Greek and other symbols are unavailable. For that reason, “ω” is written as “w”. I.e. “ωB97X-D” will be written as “wB97X-D” in input and output files.

• Empirically-corrected functionals: DFT-D3 and DFT-D4

One of the ways to adequately treat dispersion interactions is to empirically correct density functionals. This means that an additional empirically derived term is added to the energy, while the values of added terms are determined through parametrization. In brief, parametrization implies the adjustment of some parameters to produce good values.

Concerning parametrization of density functionals, it means the following: Calculations are first performed using highly accurate methods. Then, lower-level methods are corrected by adding term(s) to reproduce the results obtained with more accurate methods. This is time-consuming since it is necessary to consider many structures to perform quality parametrization. But, the result is that you obtain corrected lower-level methods much faster than highly accurate ones.

The best-known empirical corrections for density functionals are the ones coming from the group of Prof. Stefan Grimme. This group has built an amazing number of computational tools for molecular modeling, and their website is regularly updated with information about how to properly cite their works. Therefore, for D3 and D4 corrections, we are directing you to the website of Prof. Grimme’s group, where you will find all the necessary information on how to cite D3 and D4 corrections.

https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3

https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dftd4

Here, we are providing .ris files containing citations for D3 and D4 corrections (right click – save link as), mentioned on the aforementioned pages of Prof. Grimme’s group.

Needless to say, the warmest recommendation is to check the whole website of Prof. Grimme’s group. You will find so many useful computational tools, all free to use. Most probably one of the most, if not the most, precious web site for the molecular modeling community.