Correction to Implementation of Constrained DFT for Computing

Erratum Cite This: J. Chem. Theory Comput. 2018, 14, 1170−1170

pubs.acs.org/JCTC

Correction to Implementation of Constrained DFT for Computing Charge Transfer Rates within the Projector Augmented Wave Method Marko Melander,* Elvar Ö . Jónsson, Jens J. Mortensen, Tejs Vegge, and Juan Maria García Lastra* J. Chem. Theory Comput. 2016, 12 (11), 5367−5378. DOI: 10.1021/acs.jctc.6b00815

I

n the original article k-point integration of eq 51 is incorrect. The corrected version is SAB = ⟨ψA|ψB⟩ = ≈

∫ dk ⟨ψAk|ψBk⟩

∑ wk⟨ψAk|ψBk⟩ = ∑ wk SAB(k) k

k

⎡ = ∑ wk det⎣⎢ k

∫ dr nAα1,αB,1k(r), ∫ dr nAβ1,βB,2k(r), ...⎤⎦⎥ k,α,β

(1)

⟨ψAnk,α|ψBmk,β⟩,

The pair density is defined as nnm = and the determinants are written using the convention of presenting the diagonal values. Similarly, the incorrect k-point integration is presented in eq 52 of the original article. The same equation was also misspelled and the correct version is ̂ |ψ ⟩ = WAB = ⟨ψA|Wab B ≈

∫ dk ⟨ψAk|Wab̂ |ψBk⟩

∑ wk⟨ψAk|Wab̂ |ψBk⟩ k

=

∑ wk Wab(k) (2)

k

with Wab(k) =

, k −1 ∑ (SAB(k)σAiBj ) det[SAB(k)] ij

∑ ⟨ψAik,σ|VcBwcB|ψBjk,σ ⟩ c

(3)

We want to emphasize that the form of the weight matrix presented here (except the corrected k-point summation) was used in all the calculations of the original article, and therefore the results remain unchanged. Also, the error in the k-point integration does not affect the results of the original article as only nonperiodic systems with just one k-point were studied (wk= 1). The error was corrected in the development version of GPAW before any periodic systems were studied, and thus, all work citing the original paper have used the correct k-point integration.

Published: January 29, 2018 © 2018 American Chemical Society

1170

DOI: 10.1021/acs.jctc.8b00053 J. Chem. Theory Comput. 2018, 14, 1170−1170