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Unlike these 'normal' calculations, there is a class of calculations where the density-driven error is much larger, so DC-DFT give better a result than self-consistent DFT . We classify these calculations as 'abnormal'. HF-DFT is a simple implementation of DC-DFT and we found that a small HOMO-LUMO gap is an indicator of abnormal calculation, thus, HF-DFT would perform better in such cases. | Unlike these 'normal' calculations, there is a class of calculations where the density-driven error is much larger, so DC-DFT give better a result than self-consistent DFT . We classify these calculations as 'abnormal'. HF-DFT is a simple implementation of DC-DFT and we found that a small HOMO-LUMO gap is an indicator of abnormal calculation, thus, HF-DFT would perform better in such cases. | ||

We are trying to determine which are abnormal cases among well-known problematic cases in DFT, and applying DC-DFT to solve these challenging problems. | We are trying to determine which are abnormal cases among well-known problematic cases in DFT, and applying DC-DFT to solve these challenging problems. | ||

+ | <br> | ||

+ | |||

+ | <br> | ||

+ | == ''How to Perform HF-DFT == | ||

+ | 1. Get converged molecular orbital coefficients with respect to the Hartree-Fock method. | ||

+ | |||

+ | 2. Get 2 electron energy from DFT’s 2 electron operator. | ||

+ | |||

+ | 3. Combine 1 electron energy & Nuclear repulsion energy to get total HF-DFT energy | ||

+ | |||

+ | 4. If one wants to check, compare the energy from 1 electron integral, such as kinetic energy (KE). | ||

+ | <pre>Sample Input | ||

+ | |||

+ | Charge : -1 | ||

+ | Spin Multiplicity : 2 | ||

+ | Geometry Cartesian Coordinates [Angstrom] | ||

+ | O 0.00000000 0.00000000 0.00000000 | ||

+ | H 0.00000000 0.00000000 1.00000000 | ||

+ | Cl 0.00000000 0.00000000 3.10000000 | ||

+ | </pre> | ||

+ | <pre>Sample Output | ||

+ | |||

+ | KE = 534.9476571228 [a.u.] | ||

+ | E(HF-PBE) = -535.796236505 [a.u.] | ||

+ | Compared to E(HF) = -535.018766312 [a.u.] and E(PBE) = -535.819130377 [a.u.] | ||

+ | </pre> | ||

+ | |||

<br> | <br> | ||

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== ''Relevant Publications'' == | == ''Relevant Publications'' == | ||

- | [ | + | [68] S. Song, M.-C. Kim, E. Sim,* A. Benali, O. Heinonen, K. Burke, "Benchmarks and reliable DFT results for spin-crossover complexes," (submitted, 2017) [http://arxiv.org/abs/1708.08425 arXiv]<br> |

- | [ | + | [63] A. Wasserman, J. Nafziger, K. Jiang, M.-C. Kim, E. Sim, and K. Burke, “The Importance of Being Consistent,” Ann. Rev. Phys. Chem., 68, 555-581 (Volume publication date May 2017, '''invited''') [http://www.annualreviews.org/doi/abs/10.1146/annurev-physchem-052516-044957 LINK] [http://arxiv.org/abs/1611.06659 arXiv]<br> |

[55] M.-C. Kim, H. Park, S. Son, E. Sim*, and K. Burke, “Improved DFT Potential Energy Surfaces via Improved Densities,” J. Phys. Chem. Lett., 6, 3802-3807 (accepted on Sept. 8, 2015) [http://dx.doi.org/10.1021/acs.jpclett.5b01724 LINK]<br> | [55] M.-C. Kim, H. Park, S. Son, E. Sim*, and K. Burke, “Improved DFT Potential Energy Surfaces via Improved Densities,” J. Phys. Chem. Lett., 6, 3802-3807 (accepted on Sept. 8, 2015) [http://dx.doi.org/10.1021/acs.jpclett.5b01724 LINK]<br> |

## Latest revision as of 07:40, 14 February 2018

## **Density Corrected-Density Functional Theory (DC-DFT)**

In the early days of DFT, non-self-consistent Kohn-Sham energy was often evaluated upon Hartree-Fock (HF) densities as a way to test new approximations. This method was called HF-DFT. It has been discovered that in some cases, HF-DFT actually gave more accurate answers when compared to self-consistent DFT calculations.
By using a scheme proposed on Ref. 48, we found that DFT calculations can be categorized into two different types of calculations. First we decompose the error of an approximate functional into two parts: error from the functional (functional error), and error from the density (density-driven error). For most calculations, functional error is dominant, and here self-consistent DFT is usually better than non-self consistent DFT on more accurate densities (which we call density corrected DFT (DC-DFT)).
Unlike these 'normal' calculations, there is a class of calculations where the density-driven error is much larger, so DC-DFT give better a result than self-consistent DFT . We classify these calculations as 'abnormal'. HF-DFT is a simple implementation of DC-DFT and we found that a small HOMO-LUMO gap is an indicator of abnormal calculation, thus, HF-DFT would perform better in such cases.
We are trying to determine which are abnormal cases among well-known problematic cases in DFT, and applying DC-DFT to solve these challenging problems.

## *How to Perform HF-DFT *

1. Get converged molecular orbital coefficients with respect to the Hartree-Fock method.

2. Get 2 electron energy from DFT’s 2 electron operator.

3. Combine 1 electron energy & Nuclear repulsion energy to get total HF-DFT energy

4. If one wants to check, compare the energy from 1 electron integral, such as kinetic energy (KE).

Sample Input Charge : -1 Spin Multiplicity : 2 Geometry Cartesian Coordinates [Angstrom] O 0.00000000 0.00000000 0.00000000 H 0.00000000 0.00000000 1.00000000 Cl 0.00000000 0.00000000 3.10000000

Sample Output KE = 534.9476571228 [a.u.] E(HF-PBE) = -535.796236505 [a.u.] Compared to E(HF) = -535.018766312 [a.u.] and E(PBE) = -535.819130377 [a.u.]

## *How to Perform HF-DFT on Gaussian09*

You may use the **link1** command to perform HF-DFT as a continous job of orbital calculation with HF, and energy evaluation of DFT.

For the HF part, just add 'guess=save' to the HF part. In case of the DFT part, you need to set the maximum scf cycle to -1 with 'scf(maxcycle=-1)' and add 'guess=read geom=check'.

Following is a sample input for HF-DFT.

%chk=hocl-_hfpbe_avtz.chk %mem=12MW %nproc=1 #p hf nosymm aug-cc-pVTZ guess=save HOCl- HF/AVTZ -1 2 O 0.00000000 0.00000000 0.00000000 H 0.00000000 0.00000000 1.00000000 Cl 0.00000000 0.00000000 3.10000000 1 2 1.0 2 3 --Link1-- %chk=hocl-_hfpbe_avtz.chk %mem=12MW %nproc=1 #p pbepbe aug-cc-pVTZ scf(maxcycle=-1) geom=check guess=read HOCl- HF-PBE/AVTZ -1 2

*Special thanks to Prof. Dongwook Kim.*

*Scf(maxcycles=-1) is not supported for Gaussian03.*

## *How to Perform HF-DFT on Turbomole*

1. Run a dscf calculation with HF.

2. From the directory where you did the HF calculation, use 'define' (or manually fix the control file) to turn on DFT.

3. After that, you edit the 'control' file changing '$scfiterlimit 30' to '$scfiterlimit 1'

4. Run a dscf calculation on the folder. Then it is done.

## *How to Perform HF-DFT on NWChem*

NWChem has an internal keyword for DC-DFT in a form of non self-consistent DFT. For example, to perform HF-PBE, the input needs to contain below sections to first calculate KS orbitals from exact exchange functional (EXX), and then evaluate non self-consistent DFT energy on the orbital with the **noscf** keyword.

dft xc hfexch vectors output hf.movecs end task dft energy dft xc xpbe96 cpbe96 vectors input hf.movecs noscf end

## *How to Perform HF-DFT on Jaguar 7.X*

Jaguar has an internal keyword **jdft** for DC-DFT in a form of post-SCF DFT evaluation. For a HF-PBE/aug-cc-pVTZ calculation, the &gen section looks like:

&gen jdft=9490 basis=cc-pvtz++ &

The jdft keyword follows the format of **idft** keyword. Consult the Jaguar manual for more detailed explanation of idft formatting.

## *How to Perform HF-DFT on Jaguar 8.X*

*We have not tested it out for this version yet. This is only a guideline based on the manual.*

The jdft keyword in Jaguar 7.X has changed to **pdftname** keyword. Instead of using idft format, you can just use the **dftname** formatting. So the &gen section of a HF-PBE/aug-cc-pVTZ calculation would look like:

&gen pdftname=pbe basis=cc-pvtz++ &

## *How to Perform HF-DFT on Other Packages*

To Be Added...

If you are willing to share a manual of performing HF-DFT in any available quantum-chemical simulation program, please contact us We'll update this page in courtesy of your help.

## *Relevant Publications*

[68] S. Song, M.-C. Kim, E. Sim,* A. Benali, O. Heinonen, K. Burke, "Benchmarks and reliable DFT results for spin-crossover complexes," (submitted, 2017) arXiv

[63] A. Wasserman, J. Nafziger, K. Jiang, M.-C. Kim, E. Sim, and K. Burke, “The Importance of Being Consistent,” Ann. Rev. Phys. Chem., 68, 555-581 (Volume publication date May 2017, **invited**) LINK arXiv

[55] M.-C. Kim, H. Park, S. Son, E. Sim*, and K. Burke, “Improved DFT Potential Energy Surfaces via Improved Densities,” J. Phys. Chem. Lett., 6, 3802-3807 (accepted on Sept. 8, 2015) LINK

[50] M.-C. Kim, E. Sim*, and K. Burke "Ions in solution: Density Corrected Density Functional Theory," J. Chem. Phys., 140, 18A528 (printed on May 14, 2014) **Featured article of a special issue of the Journal of Chemical Physics celebrating 50 years of DFT, Cover** LINK

[49] M.-C. Kim, E. Sim*, and K. Burke, " Understanding and Reducing Errors in Density Functional Calculations," Phys. Rev. Lett., 111, 073003 (2013) LINK

[42] M.-C. Kim, E. Sim*, and K. Burke, "Avoiding Unbound Anions in Density Functional Calculations," J. Chem. Phys., 134(17), 171103 (2011) **Most Accessed Communications of J. Chem. Phys. in 2013** LINK

[Collaborator] D. Lee, K. Burke, "Finding electron affinities with approximate density functionals," Mol. Phys., 108, 2687-2701 (2010). LINK

[Collaborator] D. Lee, F. Furche, K. Burke, "Accuracy of Electron Affinities of Atoms in Approximate Density Functional Theory," J. Phys. Chem. Lett., 1, 2124-2129 (2010). LINK