Accurate nonrelativistic ground-state energies of 3d transition metal atoms

Abstract

We present accurate nonrelativistic ground-state energies of the transition metal atoms of the 3d series calculated with Fixed-Node Diffusion Monte Carlo (FN-DMC). Selected multi-determinantal expansions obtained with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) method and including the most prominent determinants of the full configuration interaction expansion are used as trial wavefunctions. Using a maximum of a few tens of thousands determinants, fixed-node errors on total DMC energies are found to be greatly reduced for some atoms with respect to those obtained with Hartree-Fock nodes. To the best of our knowledge, the FN-DMC/(CIPSI nodes) ground-state energies presented here are the lowest variational total energies reported so far. They differ from the recently recommended non-variational values of McCarthy and Thakkar [J. Chem. Phys. 136, 054107 (2012)] only by a few percents of the correlation energy. Thanks to the variational property of FN-DMC total energies, our results provide exact lower bounds for the absolute value of all-electron correlation energies, |Ec|.

Using CIPSI Nodes in Diffusion Monte Carlo

“…A remarkable property systematically observed so far in our DMC applications using large CIPSI expansions [1,3,4] is that, except for a possible transient regime at small number of determinants, [83] the fixed-node error resulting from the use of CIPSI nodes is found to decrease monotonically, both as a function of the number of selected determinants, N dets , and of the basis set size, M . This result is illustrated here in the case of the water molecule at equilibrium geometry.…”

“…The price to pay for not re-optimizing the determinantal part in the presence of a Jastrow is that for small basis sets larger fixed-node errors are usually obtained. However, when increasing sufficiently the quality of basis set, it is no longer true as illustrated for example in the case of the oxygen atom, [1] the water molecule, [5] and the 3d-transition metal atoms [3] for which benchmark total energies have been obtained.…”

“…In each case, the huge size of the FCI space forbids exact FCI calculations. CIPSI has been applied to larger systems, for example for calculating accurate total energies for the atoms of the 3d series, [3] and for obtaining near-FCI quality results for the CuCl 2 molecule (calculations including 63 electrons and 25 active valence electrons). [94] Note that by using Effective Core Potentials as described in section V even larger systems can be treated.…”

“…[1][2][3][4][5] The purpose of this paper is to review the present situation, to clarify some important aspects of DMC-CIPSI, and to present some new illustrative results.…”

The Total Ground State Energies and First Ionization Energies of the Incomplete 3d-Transition Metal-Elements Atoms

“…Moreover, our calculations is better than those obtained by them, since our results for these atoms is lower than their results [14,15]. On the other hand, for the sake of comparison, the results we got with basis set VTZ ANO are the best in comparison to those with other two basis sets (i.e.…”