We present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been implemented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situin terms of a systematically improvable basis set which is equivalent to plane waves, it is possible to achieve large basis set accuracy in routine calculations. The spatial localisation of the NGWFs allows us to exploit the exponential decay of the density matrix in systems with a band gap in order to compute the exchange energy with a computational effort that increases linearly with the number of atoms. We describe the implementation of this approach in the ONETEPprogram for linear-scaling first principles quantum mechanical calculations. We present extensive numerical validation of all the steps in our method. Furthermore, we find excellent agreement in energies and structures for a wide variety of molecules when comparing with other codes. We use our method to perform calculations with the B3LYP exchange-correlation functional for models of myoglobin systems bound with O2 and CO ligands and confirm that the same qualitative behaviour is obtained as when the same myoglobin models are studied with the DFT+U approach which is also available in ONETEP. Finally, we confirm the linear-scaling capability of our method by performing calculations on polyethylene and polyacetylene chains of increasing length.
Skip Nav Destination
,
,
Article navigation
7 December 2013
Research Article|
December 02 2013
Linear-scaling calculation of Hartree-Fock exchange energy with non-orthogonal generalised Wannier functions
J. Dziedzic;
J. Dziedzic
a)
School of Chemistry,
University of Southampton
, Highfield, Southampton SO17 1BJ, United Kingdom
Search for other works by this author on:
Q. Hill;
Q. Hill
b)
School of Chemistry,
University of Southampton
, Highfield, Southampton SO17 1BJ, United Kingdom
Search for other works by this author on:
C.-K. Skylaris
C.-K. Skylaris
c)
School of Chemistry,
University of Southampton
, Highfield, Southampton SO17 1BJ, United Kingdom
Search for other works by this author on:
J. Dziedzic
a)
Q. Hill
b)
C.-K. Skylaris
c)
School of Chemistry,
University of Southampton
, Highfield, Southampton SO17 1BJ, United Kingdom
a)
Also at Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Gdansk, Poland.
b)
Current address: Arqiva, Crawley Court, Winchester SO21 2QA, United Kingdom.
c)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
J. Chem. Phys. 139, 214103 (2013)
Article history
Received:
April 24 2013
Accepted:
November 06 2013
Citation
J. Dziedzic, Q. Hill, C.-K. Skylaris; Linear-scaling calculation of Hartree-Fock exchange energy with non-orthogonal generalised Wannier functions. J. Chem. Phys. 7 December 2013; 139 (21): 214103. https://doi.org/10.1063/1.4832338
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
DeePMD-kit v2: A software package for deep potential models
Jinzhe Zeng, Duo Zhang, et al.
CREST—A program for the exploration of low-energy molecular chemical space
Philipp Pracht, Stefan Grimme, et al.
Related Content
The ONETEP linear-scaling density functional theory program
J. Chem. Phys. (May 2020)
Massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functionals with plane wave basis set accuracy
J. Chem. Phys. (December 2021)
Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package
J. Chem. Phys. (November 2016)
Exact exchange with non-orthogonal generalized Wannier functions
J. Chem. Phys. (March 2017)
Introducing ONETEP : Linear-scaling density functional simulations on parallel computers
J. Chem. Phys. (February 2005)