# Semi-local density functional for the exchange-correlation energy of electrons in two dimensions

@article{Rasanen2010SemilocalDF, title={Semi-local density functional for the exchange-correlation energy of electrons in two dimensions}, author={Esa Rasanen and Stefano Pittalis and J. G. Vilhena and Miguel A. L. Marques}, journal={arXiv: Strongly Correlated Electrons}, year={2010} }

We present a practical and accurate density functional for the exchange-correlation energy of electrons in two dimensions. The exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the limits of small and large density gradients. The fully local correlation part is constructed following the Colle-Salvetti scheme and a Gaussian approximation for the pair density. The combination of these expressions is shown to provide an efficient density…

## 12 Citations

### Colle-Salvetti-type local density functional for the exchange-correlation energy in two dimensions

- Physics
- 2010

We derive an approximate local density functional for the exchange-correlation energy to be used in density-functional calculations of two-dimensional systems. In the derivation we employ the…

### Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations.

- PhysicsThe journal of physical chemistry. A
- 2017

The accuracy of results obtained by using the newly constructed functional is quite remarkable as it substantially reduces the errors present in the local and nonempirical exchange functionals proposed so far for two-dimensional quantum systems.

### A Parameter-Free Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems.

- PhysicsThe journal of physical chemistry. A
- 2018

The method of constructing semilocal density functional for exchange in two dimensions using one of the premier approaches, i.e., density matrix expansion, is revisited, and an accurate functional is constructed that satisfies most of the discussed conditions.

### Colle-Salvetti type correlation functionals for two-dimensional quantum dot systems

- PhysicsChemical Physics Letters
- 2019

### Inhomogeneity induced and appropriately parameterized semilocal exchange and correlation energy functionals in two-dimensions.

- PhysicsThe Journal of chemical physics
- 2018

Parameterized semilocal exchange energy functionals based on the density matrix expansion (DME) are proposed and are suitable for two-dimensional quantum systems.

### First-principles quantum corrections for carrier correlations in double-layer two-dimensional heterostructures

- PhysicsPhysical Review B
- 2019

We present systematic ab initio calculations of the puddle correlations between adjacent layers of two-dimensional materials in the presence of both charged impurity and strain disorder potentials…

### Exploration of near the origin and the asymptotic behaviors of the Kohn-Sham kinetic energy density for two-dimensional quantum dot systems with parabolic confinement.

- PhysicsThe Journal of chemical physics
- 2018

It is shown that near the origin of the parabolic quantum dot, the Kohn-Sham kinetic energy differs from its von Weizsäcker counterpart due to the p orbital contributions, whereas in the asymptotic region, the difference between the above two kinetic energy densities goes as ∼ρ(r)r2.

### Semiclassical expansion of a one-body density matrix for noninteracting fermions in d dimensions

- PhysicsJournal of Physics and Chemistry of Solids
- 2019

## References

SHOWING 1-10 OF 69 REFERENCES

### Local correlation functional for electrons in two dimensions

- Physics
- 2008

We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three…

### Density gradients for the exchange energy of electrons in two dimensions

- Computer Science, Physics
- 2009

A generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems with promising results, reducing the error in the exchangeEnergy by a factor of 4 with respect to the simple local density approximation.

### Orbital-free energy functional for electrons in two dimensions

- Physics
- 2009

We derive a nonempirical, orbital-free density functional for the total energy of interacting electrons in two dimensions. The functional consists of a local formula for the interaction energy, where…

### Gaussian approximations for the exchange-energy functional of current-carrying states: Applications to two-dimensional systems

- Physics
- 2009

Electronic structure calculations are routinely carried out within the framework of density-functional theory, often with great success. For electrons in reduced dimensions, however, there is still a…

### Exchange-energy functionals for finite two-dimensional systems

- Physics
- 2007

Implicit and explicit density functionals for the exchange energy in finite two-dimensional systems are developed following the approach of Becke and Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent…

### Exchange-correlation orbital functionals in current-density functional theory: Application to a quantum dot in magnetic fields

- Physics
- 2008

The description of interacting many-electron systems in external magnetic fields is considered in the framework of the optimized effective potential method extended to current-spin-density functional…

### Collapse of the electron gas to two dimensions in density functional theory.

- MathematicsPhysical review letters
- 2008

A fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sjölander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover).

### Density-functional theory for strongly interacting electrons.

- PhysicsPhysical review letters
- 2009

This work presents an alternative to the Kohn-Sham formulation of density-functional theory for the ground-state properties of strongly interacting electronic systems and discusses several schemes for approximating the energy functional, and reports preliminary results for low-density quantum dots.

### Evaluating density functional performance for the quasi-two-dimensional electron gas

- Physics
- 2000

The exchange-correlation energy Exc is a significant part of the total energy of the quasi-two-dimensional electron gas. We investigate the performance of three-dimensional density functionals Exc [n…

### Correlation energy of finite two-dimensional systems: Toward nonempirical and universal modeling

- Physics
- 2008

The capability of density-functional theory to deal with the ground-state of strongly correlated low-dimensional systems, such as semiconductor quantum dots, depends on the accuracy of functionals…