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Hohenberg-Kohn theorem for time-dependent ensembles

Tiecheng Li, Peiqing Tong

It is proven that the Runge-Gross version of the Hohenberg-Kohn theorem is valid for arbitrary time-dependent ensembles.Received 20 August 1984DOI:https://doi.org/10.1103/PhysRevA.31.1950©1985 American Physical Society

Physical Review AMar 1, 198540 citations

Time-dependent density-functional theory for multicomponent systems

Tiecheng Li, Peiqing Tong

The Runge-Gross version of the Hohenberg-Kohn-Sham density-functional theory is generalized to multicomponent systems.Received 9 December 1985DOI:https://doi.org/10.1103/PhysRevA.34.529©1986 American Physical Society

Physical Review AJul 1, 198657 citations

Exact solutions to the time-dependent Schrödinger equation

John R. Ray

New exact solutions to the time-dependent Schrödinger equation are presented and the equivalence of two methods of arriving at these solutions shown.Received 12 February 1982DOI:https://doi.org/10.1103/PhysRevA.26.729©1982 American Physical Society

Physical Review AAug 1, 198285 citations

Time-dependent adiabatic approximation

Saul T. Epstein

A time-dependent adiabatic formalism is introduced and some of its properties discussed. It is similar but not identical to one proposed earlier by Schulman and Detrano.Received 1 June 1976DOI:https://doi.org/10.1103/PhysRevA.14.1929©1976 American Physical Society

Physical Review ANov 1, 19761 citation

Time-dependent Kohn-Sham density-functional theory

Libero J. Bartolotti

A time-dependent Kohn-Sham theory is presented for obtaining the time-dependent density which has a periodic dependence on time. A set of coupled single-particle equations $\ensuremath{-}\frac{1}{2}{\ensuremath{\nabla}}^{2}{\ensuremath{\chi}}_{i}+{v}_{\mathrm{eff}}{\ensuremath{\chi}}_{i}={\ensuremath{\epsilon}}_{i}{\ensuremath{\chi}}_{i}$ and $\frac{\ensuremath{\partial}{\ensuremath{\chi}}_{i}^{2}}{\ensuremath{\partial}t}+\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}\ifmmode\cdot\else\textperiodcentered\fi{}({\ensuremath{\chi}}_{i}^{2}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}{S}_{i})=0$ are obtained. The ${\ensuremath{\chi}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ and ${S}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ are the phase and amplitude, respectively, of the time-dependent Kohn-Sham orbitals, ${v}_{\mathrm{eff}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ is the time-dependent Kohn-Sham effective potential, and ${\ensuremath{\epsilon}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)=\ensuremath{-}\frac{\ensuremath{\partial}{S}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)}{\ensuremath{\partial}t}$. The density $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ is equal to the sum of the squares of the ${\ensuremath{\chi}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$.A time-dependent Kohn-Sham theory is presented for obtaining the time-dependent density which has a periodic dependence on time. A set of coupled single-particle equations $\ensuremath{-}\frac{1}{2}{\ensuremath{\nabla}}^{2}{\ensuremath{\chi}}_{i}+{v}_{\mathrm{eff}}{\ensuremath{\chi}}_{i}={\ensuremath{\epsilon}}_{i}{\ensuremath{\chi}}_{i}$ and $\frac{\ensuremath{\partial}{\ensuremath{\chi}}_{i}^{2}}{\ensuremath{\partial}t}+\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}\ifmmode\cdot\else\textperiodcentered\fi{}({\ensuremath{\chi}}_{i}^{2}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}{S}_{i})=0$ are obtained. The ${\ensuremath{\chi}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ and ${S}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ are the phase and amplitude, respectively, of the time-dependent Kohn-Sham orbitals, ${v}_{\mathrm{eff}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ is the time-dependent Kohn-Sham effective potential, and ${\ensuremath{\epsilon}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)=\ensuremath{-}\frac{\ensuremath{\partial}{S}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)}{\ensuremath{\partial}t}$. The density $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ is equal to the sum of the squares of the ${\ensuremath{\chi}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$.

Physical Review AOct 1, 1982105 citations

Zero-thickness membrane interface and Schrödinger equation

M. Q. Zhang

The inverse profile equation for the zero-thickness membrane interface model is derived from the Schrödinger equation with an arbitrary external time-dependent potential.Received 16 July 1990DOI:https://doi.org/10.1103/PhysRevA.42.4588©1990 American Physical Society

Physical Review AOct 1, 19900 citations

Kohn-Sham equation for time-dependent ensembles

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Kohn-Sham equation for time-dependent ensembles

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