Anisotropic intracule densities and electron correlation in H2: a quantum Monte Carlo study.

We derive efficient quantum Monte Carlo estimators for the anisotropic intracule and extracule densities. These estimators are used in conjunction with an accurate explicitly correlated wave function to investigate the bond-length dependence of electron correlation effects in the ground-state H(2) molecule. It is shown that the localized increase in the magnitude of the correlation energy as the bond is stretched is accompanied by highly anisotropic correlation effects. In addition, we find a small long-range part of the Coulomb hole, which is present even at the equilibrium bond length.

[1]  M. Caffarel,et al.  Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces , 2003, physics/0310035.

[2]  V. H. Smith,et al.  Anisotropic electronic intracule densities for diatomics , 1984 .

[3]  R. Needs,et al.  Quantum Monte Carlo simulations of solids , 2001 .

[4]  R. J. Boyd,et al.  Intracule densities and electron correlation in the hydrogen molecule , 1988 .

[5]  A. Scemama,et al.  Improved Monte Carlo estimators for the one-body density. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  C. Coulson,et al.  Electron Correlation in the Ground State of Helium , 1961 .

[7]  A. J. Coleman,et al.  Density matrices and density functionals : proceedings of the A. John Coleman symposium , 1987 .

[8]  H. Monkhorst,et al.  New Born–Oppenheimer potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule , 1986 .

[9]  Wang,et al.  Pair-correlation function and single-particle occupation numbers in diamond and silicon. , 1990, Physical review letters.

[10]  R. Coldwell,et al.  A ground state potential energy surface for H2 using Monte Carlo methods. , 2004, The Journal of chemical physics.

[11]  R. Needs,et al.  Monte Carlo Investigation of Exchange and Correlation in Silicon , 1996 .

[12]  F. Jensen.  The basis set convergence of the Hartree–Fock energy for H2 , 1999 .

[13]  Jesus M. Ugalde,et al.  Can correlation bring electrons closer together? , 2009 .

[14]  M. Ratner,et al.  Electron correlation in chemical bonds , 2000 .

[15]  K. E. Banyard,et al.  Coulomb correlation in the H2 molecule: A two‐particle density analysis , 1992 .

[16]  Wilson,et al.  Optimized trial wave functions for quantum Monte Carlo calculations. , 1988, Physical review letters.

[17]  V. H. Smith,et al.  The influence of electron correlation on anisotropic electron intracule and extracule densities , 1992 .

[18]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[19]  Wim Vanroose,et al.  Complete Photo-Induced Breakup of the H2 Molecule as a Probe of Molecular Electron Correlation , 2005, Science.

[20]  R. Needs,et al.  Jastrow correlation factor for atoms, molecules, and solids , 2004, 0801.0378.

[21]  C J Umrigar,et al.  Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density. , 2007, The Journal of chemical physics.

[22]  Manolo C Per,et al.  Electron-nucleus cusp correction and forces in quantum Monte Carlo. , 2008, The Journal of chemical physics.

[23]  E. Rotenberg,et al.  Complete photo-fragmentation of the deuterium molecule , 2004, Nature.

[24]  A. Thakkar,et al.  Anisotropy of the Coulomb hole in H2 , 1984 .