When does the non-variational nature of second-order Møller-Plesset energies manifest itself? All-electron correlation energies for open-shell atoms from K to Br

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|.

Section: Resultsmentioning

confidence: 90%

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

Scemama

Applencourt

Giner

et al. 2014

“…Nevertheless recent work has determined an accurate estimate of B C , 32 based on coupled-cluster calculations for closed-shell atoms up through Z = 86, 44 and all atoms up through Z = 54. 45 These, along with the earlier benchmark set 58 have made possible a reasonably accurate extrapolation of B C .…”

Section: Correlation: Determining Bcmentioning

confidence: 98%

Fitting a round peg into a round hole: Asymptotically correcting the generalized gradient approximation for correlation

Cancio

Chen

Krull

et al. 2018

We consider the implications of the Lieb-Simon limit for correlation in density functional theory. In this limit, exemplified by the scaling of neutral atoms to large atomic number, local density approximation (LDA) becomes relatively exact, and the leading correction to this limit for correlation has recently been determined for neutral atoms. We use the leading correction to the LDA and the properties of the real-space cutoff of the exchange-correlation hole to design, based upon Perdew-Burke-Ernzerhof (PBE) correlation, an asymptotically corrected generalized gradient approximation (acGGA) correlation which becomes more accurate per electron for atoms with increasing atomic number. When paired with a similar correction for exchange, this acGGA satisfies more exact conditions than PBE. Combined with the known -dependence of the gradient expansion for correlation, this correction accurately reproduces correlation energies of closed-shell atoms down to Be. We test this acGGA for atoms and molecules, finding consistent improvement over PBE but also showing that optimal global hybrids of acGGA do not improve upon PBE0 and are similar to meta-GGA values. We discuss the relevance of these results to Jacob's ladder of non-empirical density functional construction.

“…4s 1 3d 10 for Cu and 5s 1 4d 4 for Nb), which allow ready comparison with the results of McCarthy and Thakkar. 69 For the atoms in Row 6 we simply fill the orbitals according to Hund's rules to avoid issues of (near-)degeneracy.…”

Section: Rpa Calculationsmentioning

confidence: 99%

“…All our data will come from non-relativistic atomic calculations. Our starting point is the relatively recent publication of total correlation energies of spherical atoms 28 up to Z = 86 and non-spherical ones 69 up to Z = 36. These add to the well-known benchmark set 70 up to Z = 18, although they are not quite as accurate.…”

Section: Quantum Chemical Datamentioning

confidence: 99%

Locality of correlation in density functional theory

Burke

Cancio

Gould

et al. 2016

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e, the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms supports the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E C → −A C Z ln Z + B C Z as Z → ∞, where Z is the atomic number, A C is known, and we estimate B C to be about 37 millihartrees. The local density approximation yields A C exactly, but a very incorrect value for B C , showing that the local approximation is less relevant for correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B C a functional of the TF density for the system. The implications for construction of approximate density functionals are discussed.