%0 Journal Article
%T Electron-Pair Densities with Time-Dependent Quantum Monte Carlo
%A Ivan P. Christov
%J Journal of Atomic and Molecular Physics
%D 2013
%R 10.1155/2013/424570
%X We use sets of de Broglie-Bohm trajectories to describe the quantum correlation effects which take place between the electrons in helium atom due to exchange and Coulomb interactions. A short-range screening of the Coulomb potential is used to modify the repulsion between the same spin electrons in physical space in order to comply with Pauli's exclusion principle. By calculating the electron-pair density for orthohelium, we found that the shape of the exchange hole can be controlled uniquely by a simple screening parameter. For parahelium the interelectronic distance, hence the Coulomb hole, results from the combined action of the Coulomb repulsion and the nonlocal quantum correlations. In this way, a robust and self-interaction-free approach is presented to find both the ground state and the time evolution of nonrelativistic quantum systems. 1. Introduction The electronic many-body problem is of key importance for the theoretical treatments of physics and chemistry. A typical manifestation of the quantum many-body effects is the electron correlation which results from the Coulomb and exchange interactions between the electrons combined with the underlying quantum nonlocality. Since in general the electron correlation reshapes the probability density in configuration space, it is difficult to elucidate this effect for higher dimensions. Therefore, to better understand the effects of electron correlation in atoms and molecules, one needs, besides one-particle quantities such as the electron density function, to consider also extensions which explicitly incorporate many-body effects. Such an appropriate quantity is the electronic pair-density function which represents the probability density of finding two electrons at distance from each other [1, 2]: where is the position of the th electron and the many-body wave function resides in configuration space with arguments being the instantaneous coordinates of all electrons . The importance of the electron-pair density, also known as electron position intracule, comes from the fact that it can be associated with experimental data obtained from X-ray scattering, and it can also be used to visualize the notion of exchange and correlation holes which surround the quantum particles. However, the calculation of the many-body wave function in (1) is hampered by the computational cost which scales exponentially with system dimensionality. Therefore, different approximations have been employed in order to calculate the electronic pair densities. These include Hartree-Fock (HF) approximation as well as Hylleraas type
%U http://www.hindawi.com/journals/jamp/2013/424570/