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Tom Pitts

Bio: Tom Pitts is an academic researcher from Durham University. The author has contributed to research in topics: Physics & Effective nuclear charge. The author has an hindex of 3, co-authored 4 publications receiving 19 citations.

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TL;DR: In this paper, the Hartree exchange and correlation Kohn-Sham potential of a finite N-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of N − 1 electrons.
Abstract: In the constrained minimization method of Gidopoulos and Lathiotakis [N.I. Gidopoulos, N.N. Lathiotakis, J. Chem. Phys. 136, 224109 (2012)], the Hartree exchange and correlation Kohn-Sham potential of a finite N-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of N − 1 electrons. The optimal effective charge density (electron repulsion density, ρrep) and the corresponding optimal effective potential (electron repulsion potential vrep) are obtained by minimizing the electronic total energy in any density functional approximation. The two constraints are sufficient to remove the self-interaction errors from vrep, correcting its asymptotic behavior at large distances from the system. In the present work, we describe, in complete detail, the constrained minimization method, including recent refinements. We also assess its performance in removing the self-interaction errors for three popular density functional approximations, namely LDA, PBE and B3LYP, by comparing the obtained ionization energies to their experimental values for an extended set of molecules. We show that the results of the constrained minimizations are almost independent of the specific approximation with average percentage errors 15%, 14%, 13% for the above DFAs respectively. These errors are substantially smaller than the corresponding errors of the plain (unconstrained) Kohn-Sham calculations at 38%, 39% and 27% respectively. Finally, we showed that this method correctly predicts negative values for the HOMO energies of several anions.

12 citations

Journal ArticleDOI
TL;DR: It is demonstrated that appropriately constraining the 'screening charge' which corresponds to the Hartree, exchange and correlation potential not only corrects its asymptotic behaviour but also allows the exchange and correlated potential to exhibit a non-zero derivative discontinuity, a feature of the exact KS potential that is necessary for the accurate prediction of band-gaps in solids but very hard to capture with semi-local density-functional approximations.
Abstract: We review and expand on our work to impose constraints on the effective Kohn-Sham (KS) potential of local and semi-local density-functional approximations. Constraining the minimisation of the approximate total energy density-functional invariably leads to an optimised effective potential (OEP) equation, the solution of which yields the KS potential. We review briefly our previous work on this and demonstrate with numerous examples that despite the well-known mathematical issues of the OEP with finite basis sets, our OEP equations are numerically robust. We demonstrate that appropriately constraining the 'screening charge' which corresponds to the Hartree, exchange and correlation potential not only corrects its asymptotic behaviour but also allows the exchange and correlation potential to exhibit a non-zero derivative discontinuity, a feature of the exact KS potential that is necessary for the accurate prediction of band-gaps in solids but very hard to capture with semi-local approximations.

10 citations

Journal ArticleDOI
TL;DR: In this paper, the Hartree exchange and correlation Kohn-Sham potential of a finite $N$-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of $N-1$ electrons.
Abstract: In the constrained minimization method of Gidopoulos and Lathiotakis (J. Chem. Phys. 136, 224109), the Hartree exchange and correlation Kohn-Sham potential of a finite $N$-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of $N-1$ electrons. The optimal effective charge density (electron repulsion density, $\rho_{\rm rep}$) and the corresponding optimal effective potential (electron repulsion potential $v_{\rm rep}$) are obtained by minimizing the electronic total energy in any density functional approximation. The two constraints are sufficient to remove the self-interaction errors from $v_{\rm rep}$, correcting its asymptotic behavior at large distances from the system. In the present work, we describe, in complete detail, the constrained minimization method, including recent refinements. We also assess its performance in removing the self-interaction errors for three popular density functional approximations, namely LDA, PBE, and B3LYP, by comparing the obtained ionization energies to their experimental values for an extended set of molecules. We show that the results of the constrained minimizations are almost independent of the specific approximation with average percentage errors 15%, 14%, 13% for the above DFAs respectively. These errors are substantially smaller than the corresponding errors of the plain (unconstrained) Kohn-Sham calculations at 38%, 39%, and 27% respectively. Finally, we showed that this method correctly predicts negative values for the HOMO energies of several anions.

4 citations

Journal ArticleDOI
TL;DR: In this article , the high-pressure II-III phase transition in solid hydrogen is investigated using the random phase approximation and diffusion Monte Carlo, and it is shown that an accurate treatment of exchange and correlation increases the transition pressure by more than 100 GPa with respect to semilocal density functional approximations.
Abstract: The high-pressure II-III phase transition in solid hydrogen is investigated using the random phase approximation and diffusion Monte Carlo. Good agreement between the methods is found confirming that an accurate treatment of exchange and correlation increases the transition pressure by more than 100 GPa with respect to semilocal density functional approximations. Using an optimized hybrid functional, we then reveal a low-symmetry structure for phase II generated by an out-of-plane librational instability of the C2/c phase III structure. This instability weakens the in-plane polarization of C2/c leading to the well-known experimental signatures of the II-III phase transition such as a sharp shift in vibron frequency, infrared activity and c/a lattice parameter ratio. Finally, we discuss the zero-point vibrational energy that plays an important role in stabilizing phase III at lower pressures.

1 citations

Journal ArticleDOI
TL;DR: In this article, the authors relax a previously imposed positivity constraint, which increased the computational cost and find that it is safe to do so, except in systems with very few electrons.
Abstract: We review and expand on our work to impose constraints on the effective Kohn Sham (KS) potential of local and semi-local density functional approximations. In this work, we relax a previously imposed positivity constraint, which increased the computational cost and we find that it is safe to do so, except in systems with very few electrons. The constrained minimisation leads invariably to the solution of an optimised effective potential (OEP) equation in order to determine the KS potential. We review briefly our previous work on this problem and demonstrate with numerous examples that despite well-known mathematical issues of the OEP with finite basis sets, our OEP equations are well behaved. We demonstrate that constraining the screening charge of the Hartree, exchange and correlation potential not only corrects its asymptotic behaviour but also allows the exchange and correlation potential to exhibit nonzero derivative discontinuity, a feature of the exact KS potential that is necessary for the accurate prediction of band-gaps in solids but very hard to capture with semi-local approximations.

1 citations


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TL;DR: A simple and computationally undemanding atomic self-interaction correction (SIC) opens conduction gaps in I-V characteristics that otherwise are predicted metallic, as in the case of the prototype Au/ditholated-benzene/Au junction.
Abstract: All density-functional calculations of single-molecule transport to date have used continuous exchange-correlation approximations. The lack of derivative discontinuity in such calculations leads to the erroneous prediction of metallic transport for insulating molecules. A simple and computationally undemanding atomic self-interaction correction (SIC) opens conduction gaps in I-V characteristics that otherwise are predicted metallic, as in the case of the prototype Au/ditholated-benzene/Au junction.

220 citations

Journal ArticleDOI
TL;DR: The history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners as discussed by the authors .
Abstract: In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

38 citations