1209.5140 (Hua Zhao)

Density matrix theory in real space of exchange and correlation energies
for organic $π$ electronic systems    [PDF]

Hua Zhao

A density matrix theory in real space for exchange-correlation energy $E_{xc}$, long-range electronic correlation energy $E_c$, exchange energy $E_x$ that contain long-range electron-electron interactions $V_{i,j}$($i\neq j$), off-diagonal electron-electron interactions $W_{ij,ij}$ ($i\neq j$) and $X_{ii,ij}$ ($i\neq j$) for one-, two-, and three-dimensional organic $\pi$ electron systems is proposed for the first time by use of local density approximation (LDA) relation: $E_{xc}=E_x+E_c$. In this theory, analytical formulae of calculating $E_{xc}$, $E_c$, and $E_x$ are developed in detail, without approximations for electron-electron interactions referred. Unlike the density functional theory, in this theory the formulae for $E_{xc}$, $E_x$ and $E_c$ are expressed as functions of diagonal density matrix elements $\rho^{\sigma}_{ii}$ and off-diagonal density matrix elements $\rho^{\sigma}_{ij}$ ($i\neq j$), and a complete long-range electronic correlation Hamiltonian $\hat{H}_c$ containing both $W_{ij,ij}$ and $X_{ii,ij}$ and $V_{i,j}$ is given, which enables us to explicitly discuss correction of band gap from the correlation energy and excited states of the systems at which point this theory is beyond LDA. The influences of the off-diagonal interactions on $E_{xc}$, $E_c$, and $E_x$ under different electronic interactions and different screening strengths are discussed. The contribution of the long-range electronic correlation to the band gap with the off-diagonal interactions and without the off-diagonal interactions are discussed also. It is found that influence of the nearest-neighbor off-diagonal interaction $W$ is to increase $E_x$ and that of the nearest-neighbor off-diagonal interaction $X$ is to decrease $E_x$.

View original: http://arxiv.org/abs/1209.5140