Calculation Of Exchange Energy Research Articles

How the Exchange Energy Can Affect the Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit.

Finite size error is commonly removed from coupled cluster theory calculations by N-1 extrapolations over correlation energy calculations of different system sizes (N), where the N-1 scaling comes from the total energy rather than the correlation energy. However, previous studies in the quantum Monte Carlo community suggest an exchange-energy-like power law of N-2/3 should also be present in the correlation energy when using the conventional Coulomb interaction. The rationale for this is that the total energy goes as N-1 and the exchange energy goes as N-2/3; thus, the correlation energy should be a combination of these two power laws. Further, in coupled cluster theory, these power laws are related to the low G scaling of the transition structure factor, S(G), which is a property of the coupled cluster wave function calculated from the amplitudes. We show here that data from coupled cluster doubles calculations on the uniform electron gas fit a function with a low G behavior of S(G) ∼ G. The prefactor for this linear term is derived from the exchange energy to be consistent with an N-2/3 power law at large N. Incorporating the exchange structure factor into the transition structure factor results in a combined structure factor of S(G) ∼ G2, consistent with an N-1 scaling of the exchange-correlation energy. We then look for the presence of an N-2/3 power law in the energy. To do so, we first develop a plane-wave cutoff scheme with less noise than the traditional basis set used for the uniform electron gas. Then, we collect data from a wide range of electron numbers and densities to systematically test five methods using N-1 scaling, N-2/3 scaling, or combinations of both scaling behaviors. We find that power laws that incorporate both N-1 and N-2/3 scaling perform better than either alone, especially when the prefactor for N-2/3 scaling can be found from exchange energy calculations.

Highly tunable exchange in donor qubits in silicon

AbstractIn this article we have investigated the electrical control of the exchange coupling (J) between donor-bound electrons in silicon with a detuning gate bias, crucial for the implementation of the two-qubit gate in a silicon quantum computer. We found that the asymmetric 2P–1P system provides a highly tunable exchange curve with mitigated J-oscillation, in which 5 orders of magnitude change in the exchange coupling can be achieved using a modest range of electric field (3 MV/m) for ~15-nm qubit separation. Compared with the barrier gate control of exchange in the Kane qubit, the detuning gate design reduces the gate density by a factor of ~2. By combining large-scale atomistic tight-binding method with a full configuration interaction technique, we captured the full two-electron spectrum of gated donors, providing state-of-the-art calculations of exchange energy in 1P–1P and 2P–1P qubits.

Compressed Representation of Kohn–Sham Orbitals via Selected Columns of the Density Matrix

Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient, and highly parallelizable method to construct a set of optionally orthogonal, localized basis functions for the associated subspace. Our method explicitly uses the fact that density matrices associated with insulating systems decay exponentially along the off-diagonal direction in the real space representation. We avoid the usage of an optimization procedure, and the localized basis functions are constructed directly from a set of selected columns of the density matrix (SCDM). Consequently, the core portion of our localization procedure is not dependent on any adjustable parameters. The only adjustable parameters present pertain to the use of the SCDM after their computation (for example, at what value should the SCDM be truncated). Our method can be used in any electronic structure software package with an arbitrary basis set. We demonstrate the numerical accuracy and parallel scalability of the SCDM procedure using orbitals generated by the Quantum ESPRESSO software package. We also demonstrate a procedure for combining the orthogonalized SCDM with Hockney's algorithm to efficiently perform Hartree-Fock exchange energy calculations with near-linear scaling.

Communication: Monte Carlo calculation of the exchange energy

In recent generalized Kohn-Sham (GKS) schemes for density functional theory (DFT) Hartree-Fock type exchange is important. In plane waves and grid approaches the high cost of exchange energy calculations makes these GKS considerably more expensive than Kohn-Sham DFT calculations. We develop a stochastic approach for speeding up the calculation of exchange for large systems. We show that stochastic error per particle does not grow and can even decrease with system size (at a given number of iterations). We discuss several alternative approaches and explain how these ideas can be included in the GKS framework.

A variational approach to exchange energy calculations in micromagnetics

This article presents a magnetization interpolation method for micromagnetic exchange energy calculations using a variational procedure to relax spins on a supplemental (refined) lattice. The approximations implicit in standard micromagnetic discretization schemes fail when angles between neighboring spins in the model become large, but the proposed approach effectively reduces the angle between neighboring spins, alleviating many of the associated problems. Moreover, this method does not introduce excessive discretization-induced vortex pinning observed with some large angle exchange energy formulations. This article includes details on proper post-interpolation exchange torque calculation, bounds on nearest-neighbor angles for interpolated lattices, a simple model predicting discretization-induced Néel wall collapse, and an example of a collapsed (1 cell wide) domain wall that can be restored by the proposed technique.

Calculation of exchange energy in quantum dots : application to porous silicon

We present a variational calculation of the envelope wave function of an exciton inside a cube, in the effective mass approximation, with one parameter which plays the part of a Bohr radius. This geometry allows one to reduce the sixfold integrals to threefold integrals which shortens tremendously computer calculations. This wave function is used to obtain the exchange energy and the oscillator strength. The limiting cases (large or small cubes) are recovered. We show that recent experimental results in porous silicon can be explained without further hypothesis

Superluminal Sound and Ferromagnetic Transition in the Zeldovich Model

The implications of the Zeldovich model (baryons interacting through a massive vector field) for the problem of superluminal sound propagation and ferromagnetic transition are examined. In a classical baryon gas at high densities correlation effects lead to the pressure increasing faster than the energy, ultimately resulting in superluminal sound; crystallization phase transition appears however at comparable densities, thus competing with the onset of superluminal sound. For a high density fermi gas the domains of ferromagnetic transition are delineated, indicating a minimal and maximal density below and above which no ferromagnetic transition can be expected. The latter is further affected by relativistic effects requiring a different approach to the calculation of exchange energy and of the ferromagnetic phase.

On the exchange energy in a SCF method using non-orthogonal basis functions

A method is developed for the calculation of exchange energy in a simple SCF method or atomic one-electron eigenfunctions using non-orthogonal basis functions.

Mirror Nuclei Radii Utilizing Self-Energy Term and Nonuniform Charge Distributions

The nature of the self-energy term in the mirror nucleus energy-difference formula is investigated. Two approaches are used. In the first this self-energy term is assumed to be a constant equal to the Coulomb self-energy of a single proton, and in the second a more refined quantum mechanical approach based on the Swamy and Green Coulomb exchange energy calculations is used. Both approaches yield ${r}_{0}$ values which possess the correct general trend with increasing $A$, but which disagree with theoretical values for very low $A$. The effect of nonuniform charge distributions on the values of nuclear radii obtained from mirror nuclei is investigated, and expressions for the Coulomb energy for various charge distributions are given. A direct comparison between the mirror nucleus radii and those obtained from electron scattering is made in the few cases where this is possible. Finally, the possible validity of a suggested value of 0.58 Mev for the Coulomb self-energy of the proton is discussed briefly.