Author Correction: From a quantum-electrodynamical light–matter description to novel spectroscopies

Nature Reviews Chemistry (2018) https://doi.org/10.1038/s41570-018-0118 Published online 07 March 2018

Equation 1 in the original version of the article (pdf and online) should read:

$$\begin{array}{l}{\hat{H}}_{{\rm{PF}}}\left(t\right)=\sum _{l=1}^{{N}_{e}}\frac{1}{2m}{\left[{{\boldsymbol{\sigma }}}_{l}\cdot \left(-i\hslash {\nabla }_{{{\bf{r}}}_{l}}+\frac{\left|e\right|}{c}{\widehat{{\bf{A}}}}_{\perp }^{{\rm{tot}}}({{\bf{r}}}_{l},t)\right)\right]}^{2}\,\,\,\,+\sum _{l=1}^{{N}_{n}}\left\{\frac{1}{2{M}_{l}}{\left(-i\hslash {\nabla }_{{{\bf{R}}}_{l}}-\frac{{Z}_{l}\left|e\right|}{c}{\widehat{{\bf{A}}}}_{\perp }^{{\rm{tot}}}({{\bf{R}}}_{l},t)\right)}^{2}\right.\\ \left.\,\,\,\,-\frac{{Z}_{l}\left|e\right|\hslash }{2{M}_{l}c}{{\bf{S}}}_{l}^{({n}_{l}/2)}\cdot \left({\nabla }_{{{\bf{R}}}_{l}}\times {\widehat{{\bf{A}}}}_{\perp }^{{\rm{tot}}}({{\bf{R}}}_{l},t)\right)\right\}\\ \,\,\,\,+\frac{1}{2}\sum _{l\ne m}^{{N}_{e}}w\left(\left|{{\bf{r}}}_{l}-{{\bf{r}}}_{m}\right|\right)+\frac{1}{2}\sum _{l\ne m}^{{N}_{n}}{Z}_{l}{Z}_{m}w\left(\left|{{\bf{R}}}_{l}-{{\bf{R}}}_{m}\right|\right)\\ \,\,\,\,-\sum _{l}^{{N}_{e}}\sum _{m}^{{N}_{n}}{Z}_{m}w\left(\left|{{\bf{r}}}_{l}-{{\bf{R}}}_{m}\right|\right)+\sum _{{\bf{k}},{\rm{\lambda }}}\hslash {\omega }_{{\bf{k}}}{\hat{a}}_{{\bf{k}},{\rm{\lambda }}}^{\dagger }{\hat{a}}_{{\bf{k}},{\rm{\lambda }}}\end{array}$$

Pauli Hamiltonian for Ne electrons and Np nuclei in Box 1 (pdf and online) should read:

$$\begin{array}{l}{\hat{H}}_{{\rm{P}}}\left(t\right)=\sum _{l=1}^{{N}_{e}}\frac{1}{2m}{\left[{{\boldsymbol{\sigma }}}_{l}\cdot \left(-i\hslash {\nabla }_{{{\bf{r}}}_{l}}+\frac{\left|e\right|}{c}{{\bf{A}}}_{\perp }^{{\rm{tot}}}({{\bf{r}}}_{l},t)\right)\right]}^{2}\\ \,\,\,\,+\sum _{l=1}^{{N}_{n}}\left\{\frac{1}{2{M}_{l}}{\left(-i\hslash {\nabla }_{{{\bf{R}}}_{l}}-\frac{{Z}_{l}\left|e\right|}{c}{{\bf{A}}}_{\perp }^{{\rm{tot}}}({{\bf{R}}}_{l},t)\right)}^{2}\right.\\ \,\,\,\,\left.-\frac{{Z}_{l}\left|e\right|\hslash }{2{M}_{l}c}{{\bf{S}}}_{l}^{({n}_{l}/2)}\cdot \left({\nabla }_{{{\bf{R}}}_{l}}\times {{\bf{A}}}_{\perp }^{{\rm{tot}}}({{\bf{R}}}_{l},t)\right)\right\}\\ \,\,\,\,+\frac{1}{2}\sum _{l\ne m}^{{N}_{e}}w\left(\left|{{\bf{r}}}_{l}-{{\bf{r}}}_{m}\right|\right)+\frac{1}{2}\sum _{l\ne m}^{{N}_{n}}{Z}_{l}{Z}_{m}w\left(\left|{{\bf{R}}}_{l}-{{\bf{R}}}_{m}\right|\right)\\ \,\,\,\,-\sum _{l}^{{N}_{e}}\sum _{m}^{{N}_{n}}{Z}_{m}w\left(\left|{{\bf{r}}}_{l}-{{\bf{R}}}_{m}\right|\right)\end{array}$$

The total transversal vector potential in Box 1 (pdf and online) needs to be expressed as:

$${{\bf{A}}}_{\perp }^{{\rm{tot}}}\left({\bf{r}},t\right)={{\bf{A}}}_{\perp }({\bf{r}},t)+{{\bf{A}}}^{{\rm{ext}}}({\bf{r}},t)$$

Maxwell–Kohn–Sham Hamiltonian in Box 2 (pdf and online) should read:

$$\begin{array}{l}{\hat{H}}_{{\rm{MKS}}}\left(t\right)=\sum _{l=1}^{{N}_{e}}\frac{1}{2m}{\left[{{\boldsymbol{\sigma }}}_{l}\cdot \left(-i\hslash {\nabla }_{{{\bf{r}}}_{l}}+\frac{\left|e\right|}{c}({{\bf{A}}}_{\perp }^{{\rm{tot}}}({{\bf{r}}}_{l},t)+{{\bf{A}}}^{{\rm{xc}}}({{\bf{r}}}_{l},t))\right)\right]}^{2}\\ \,\,\,\,+\sum _{l=1}^{{N}_{n}}\left\{\frac{1}{2{M}_{l}}{\left[-i\hslash {\nabla }_{{{\bf{R}}}_{l}}-\frac{{Z}_{l}\left|e\right|}{c}({{\bf{A}}}_{\perp }^{{\rm{tot}}}({{\bf{R}}}_{l},t)+{{\bf{A}}}^{{\rm{xc}}}({{\bf{R}}}_{l},t))\right]}^{2}\right.\\ \,\,\,\,\left.-\frac{{Z}_{l}\left|e\right|\hslash }{2{M}_{l}c}{{\bf{S}}}_{l}^{({n}_{l}/2)}\cdot \left[{\nabla }_{{{\bf{R}}}_{l}}\times ({{\bf{A}}}_{\perp }^{{\rm{tot}}}({{\bf{R}}}_{l},t)+{{\bf{A}}}^{{\rm{xc}}}({{\bf{R}}}_{l},t))\right]\right\}\end{array}$$

Density–current response function in Box 3 (online only) should read as:

$${\chi }_{n,{\bf{J}}}^{\left(1\right)}\left({\bf{r}},t;{{\bf{r}}}^{^{\prime} },{t}^{^{\prime} }\right)=-i\theta (t-{t}^{^{\prime} })\langle \left[{\widehat{n}}_{I}\left({\bf{r}},t\right);{\widehat{{\bf{J}}}}_{I}({{\bf{r}}}^{^{\prime} },{t}^{^{\prime} })\right]\rangle $$

In Box 4 (pdf only), the splitting of the excited electronic states observed in recent molecular experiment has been found proportional to:

$${{\rm{\Omega }}}_{{\bf{R}}}/{\omega }_{k}\approx 0.25$$

The induced density response function in Box 5 (online only) should read:

$${\chi }_{n,{\bf{A}}}\left({\bf{r}},t;{{\bf{r}}}^{^{\prime} },{t}^{^{\prime} }\right)=-i\theta (t-{t}^{^{\prime} })\langle \left[{\widehat{n}}_{I}\left({\bf{r}},t\right);\,{\widehat{{\bf{A}}}}_{I}({{\bf{r}}}^{^{\prime} },{t}^{^{\prime} })\right]\rangle $$

and in Box 5 (online only) the above mode-resolved response function leads to:

$${\chi }_{n,q}\left({\bf{r}},t;\alpha ,{t}^{^{\prime} }\right)=-i\theta (t-{t}^{^{\prime} })\langle [{\widehat{n}}_{I}\left({\bf{r}},t\right);\,{\widehat{q}}_{\alpha I}({t}^{^{\prime} })]\rangle $$

Author information

Affiliations

Authors

Corresponding authors

Correspondence to Michael Ruggenthaler or Nicolas Tancogne-Dejean or Johannes Flick or Heiko Appel or Angel Rubio.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ruggenthaler, M., Tancogne-Dejean, N., Flick, J. et al. Author Correction: From a quantum-electrodynamical light–matter description to novel spectroscopies. Nat Rev Chem 2, 390–391 (2018). https://doi.org/10.1038/s41570-018-0035-5

Download citation

Further reading