# Correlation energies of the high-density spin-polarized electron gas to meV accuracy

@article{Ruggeri2018CorrelationEO, title={Correlation energies of the high-density spin-polarized electron gas to meV accuracy}, author={Michele Ruggeri and Pablo L'opez R'ios and Ali Alavi}, journal={Physical Review B}, year={2018} }

We present a novel combination of quantum Monte Carlo methods and a finite size extrapolation framework with which we calculate the thermodynamic limit of the exact correlation energy of the polarized electron gas at high densities to meV accuracy, $-40.44(5)$ and $-31.70(4)$ mHa at $r_{\rm s}=0.5$ and $1$, respectively. The fixed-node error is characterized and found to exceed $1$ mHa, and we show that the magnitude of the correlation energy of the polarized electron gas is underestimated by…

## 9 Citations

### Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit.

- PhysicsJournal of chemical theory and computation
- 2021

An analysis of the transition structure factor showing that N-1 still applies to large system sizes and that the apparent N- 1/3 power law occurs only at low N is provided.

### Electronic band gaps from quantum Monte Carlo methods

- PhysicsPhysical Review B
- 2020

We develop a method for calculating the fundamental electronic gap of semiconductors and insulators using grand canonical Quantum Monte Carlo simulations. We discuss the origin of the bias introduced…

### A comparative study using state-of-the-art electronic structure theories on solid hydrogen phases under high pressures

- Materials Science, Physicsnpj Computational Materials
- 2019

Identifying the atomic structure and properties of solid hydrogen under high pressures is a long-standing problem of high-pressure physics with far-reaching significance in planetary and materials…

### Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian

- PhysicsPhysical Review A
- 2022

Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to…

### The HANDE-QMC Project: Open-Source Stochastic Quantum Chemistry from the Ground State Up.

- PhysicsJournal of chemical theory and computation
- 2019

The HANDE-QMC code is described, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations, allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively.

### Accurate correlation energy functional for uniform electron gas from an interpolation ansatz without fitting parameters

- Materials Science
- 2021

We report an analytical representation of the correlation energy ${e}_{\mathrm{c}}({r}_{s},\ensuremath{\zeta})$ for a uniform electron gas (UEG), where ${r}_{s}$ is the Seitz radius or density…

### Variational and diffusion quantum Monte Carlo calculations with the CASINO code.

- Physics, EconomicsThe Journal of chemical physics
- 2020

An overview of the variational and diffusion quantum Monte Carlo methods as implemented in the casino program is presented, describing state-of-the-art quantum Monte Monte Carlo algorithms and software and discussing their strengths and weaknesses.

### Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas

- Physics
- 2022

Max Wilson, ∗ Saverio Moroni, Markus Holzmann, Nicholas Gao, Filip Wudarski, 6 Tejs Vegge, and Arghya Bhowmik Technical University of Denmark, Department of Applied Mathematics and Computer Science,…

### Itinerant-Electron Magnetism: The Importance of Many-Body Correlations.

- PhysicsPhysical review letters
- 2020

Calculations on the three-dimensional electron gas imply that itinerant ferromagnetism of delocalized electrons without lattice and band structure is suppressed due to many-body correlations, and a possible ferromagnetic transition lowering the density is precluded by the formation of the Wigner crystal.

## References

SHOWING 1-10 OF 55 REFERENCES

### Benchmark quantum Monte Carlo calculations of the ground-state kinetic, interaction and total energy of the three-dimensional electron gas

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2010

We report variational and diffusion quantum Monte Carlo ground-state energies of the three-dimensional electron gas using a model periodic Coulomb interaction and backflow corrections for N = 54,…

### Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas

- Physics
- 2013

We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations…

### Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis

- Physics
- 1980

We assess various approximate forms for the correlation energy per particle of the spin-polarized homogeneous electron gas that have frequently been used in applications of the local spin density…

### A study of the dense uniform electron gas with high orders of coupled cluster.

- Physics, ChemistryThe Journal of chemical physics
- 2017

The accuracies of different coupled cluster levels in a finite model solid, the 14 electron spin-non-polarised uniform electron gas, are investigated and ground state correlation energies with stochastic coupled cluster ranging from coupled cluster singles and doubles to coupled cluster including all excitations up to quintuples are calculated.

### Correlation energy of a spin-polarized electron gas at high density.

- PhysicsPhysical review. B, Condensed matter
- 1992

The contributions to the correlation energy of a spin-polarized electron gas that do not vanish in the high-density limit are evaluated exactly and a closed-form expression is given for the generalization of an integral that has previously been evaluated numerically.

### Quantum Monte Carlo study of the first-row atoms and ions.

- PhysicsThe Journal of chemical physics
- 2011

The first ionization potentials to chemical accuracy are obtained and scalar relativistic corrections to the energies, mass-polarization terms, and one- and two-electron expectation values are reported.

### Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study

- Physics
- 1998

The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that…

### Correlation Energy of an Electron Gas at High Density

- Physics
- 1957

The quantity ec is defined as the correlation energy per particle of an electron gas expressed in rydbergs. It is a function of the conventional dimensionless parameter rs, where rs-3 is proportional…

### Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models.

- PhysicsThe Journal of chemical physics
- 2012

The fixed-shift phase of the i-FCIQMC can be used to effectively assess stochastic and initiator error, and the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds.

### Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids

- Physics
- 2016

Concentrating on zero temperature quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic…