Compact expressions for the electron–electron distribution function for the 2S states of three‐electron systems

Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density

We construct improved quantum Monte Carlo estimators for the spherically and system-averaged electron pair density (i.e., the probability density of finding two electrons separated by a relative distance u), also known as the spherically averaged electron position intracule density I(u), using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth nonlocal operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.

Excited states of boron isoelectronic series from explicitly correlated wave functions

The ground state and some low-lying excited states arising from the 1s2 2s2p2 configuration of the boron isoelectronic series are studied starting from explicitly correlated multideterminant wave functions. One- and two-body densities in position space have been calculated and different expectation values such as <delta(r)>, <rn>, <delta(r12)>, <r12 n>, <delta(R)>, and <R(n)>, where r, r12, and R stand for the electron-nucleus, interelectronic, and two electron center of mass coordinates, respectively, have been obtained. The energetic ordering of the excited states and the fulfillment of the Hund's rules is analyzed systematically along the isoelectronic series in terms of the electron-electron and electron-nucleus potential energies. The effects of electronic correlations have been systematically studied by comparing the correlated results with the corresponding noncorrelated ones. All the calculations have been done by using the variational Monte Carlo method.