Distributed Gaussian orbitals for the description of electrons in an external potential
TL;DR: This work demonstrates the viability of using distributed Gaussian orbitals as a basis set for the calculation of the properties of electrons subjected to an external potential, and shows how this approach can be applied to many-electron problems.
Abstract: In this work, we demonstrate the viability of using distributed Gaussian orbitals as a basis set for the calculation of the properties of electrons subjected to an external potential We validate our method by studying one-electron systems for which we can compare to exact analytical results We highlight numerical aspects that require particular care when using a distributedGaussian basis set In particular, we discuss the optimal choice for the distance between two neighboring Gaussian orbitals Finally, we show how our approach can be applied to many-electron problems
Citations
More filters
11 Nov 2019
TL;DR: In this article, a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter was studied, and the Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian was investigated.
Abstract: In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state and it can be applied to systems of all sizes.
11 citations
TL;DR: In this paper, the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian was investigated.
Abstract: In this work, we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function, we use a regular distribution in space of Gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach, we are able to observe the Wigner localization without ambiguity.
5 citations
TL;DR: In this article, the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian was investigated.
Abstract: In this work we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function we use a regular distribution in space of gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach we are able to observe the Wigner localization without ambiguity.
3 citations
TL;DR: In this paper, it was shown that the localization spread evaluated on a finite ring system of radius R with open boundary conditions leads, in the large R limit, to the same formula derived by Resta and co-workers [C. Sgiarovello, M. Peressi, and R. Resta, Phys. Rev. B 64, 115202 (2001)] for 1D systems with periodic Born-von Karman boundary conditions.
Abstract: The localization spread gives a criterion to decide between metallic and insulating behavior of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different operators are used for systems treated with open or periodic boundary conditions. In particular, in the case of periodic systems, we use the complex position definition, which was already used in similar contexts for the treatment of both classical and quantum situations. In this study, we show that the localization spread evaluated on a finite ring system of radius R with open boundary conditions leads, in the large R limit, to the same formula derived by Resta and co-workers [C. Sgiarovello, M. Peressi, and R. Resta, Phys. Rev. B 64, 115202 (2001)] for 1D systems with periodic Born–von Karman boundary conditions. A second formula, alternative to Resta’s, is also given based on the sum-over-state formalism, allowing for an interesting generalization to polarizability and other similar quantities.
2 citations
TL;DR: In this article, the possible use of sets of basis functions alternative with respect to the usual atom-centred orbitals sets is considered, and the orbitals describing the inner part of the basis function are considered.
Abstract: In this article, the possible use of sets of basis functions alternative with respect to the usual atom-centred orbitals sets is considered. The orbitals describing the inner part of the wa...
2 citations
References
More filters
Book•
01 May 2010
TL;DR: This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.
Abstract: Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full color, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Included with every copy of the book is a CD with a searchable PDF of each chapter.
3,646 citations
TL;DR: In this article, the energy of interaction between free electrons in an electron gas is considered and the correlation energy is calculated by an approximation method which is, essentially, a development of the energy by means of the Rayleigh-Schrodinger perturbation theory in a power series of e2.
Abstract: The energy of interaction between free electrons in an electron gas is considered. The interaction energy of electrons with parallel spin is known to be that of the space charges plus the exchange integrals, and these terms modify the shape of the wave functions but slightly. The interaction of the electrons with antiparallel spin, contains, in addition to the interaction of uniformly distributed space charges, another term. This term is due to the fact that the electrons repell each other and try to keep as far apart as possible. The total energy of the system will be decreased through the corresponding modification of the wave function. In the present paper it is attempted to calculate this “correlation energy” by an approximation method which is, essentially, a development of the energy by means of the Rayleigh-Schrodinger perturbation theory in a power series of e2.
1,815 citations
TL;DR: In this paper, it was shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation, and that all necessary integrals can be explicitly evaluated.
Abstract: This communication deals with the general theory of obtaining numerical electronic wave functions for the stationary states of atoms and molecules. It is shown that by taking Gaussian functions, and functions derived from these by differentiation with respect to the parameters, complete systems of functions can be constructed appropriate to any molecular problem, and that all the necessary integrals can be explicitly evaluated. These can be used in connexion with the molecular orbital method, or localized bond method, or the general method of treating linear combinations of many Slater determinants by the variational procedure. This general method of obtaining a sequence of solutions converging to the accurate solution is examined. It is shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation. A modification of the general method applicable to atoms is discussed and considered to be extremely practicable.
1,036 citations
TL;DR: In this article, the Kimball-Neumark spherical Gaussian orbital model is extended to apply to the singlet ground states of the general molecule with localized orbitals and the results are discussed in detail.
Abstract: The Kimball—Neumark spherical Gaussian orbital model is extended to apply to the singlet ground states of the general molecule with localized orbitals Formulas are presented for energy, electron density, dipole moment, and the forces on nuclei and the computational procedure is described The model is applied to LiH and the results are discussed in detail
312 citations