Search results for "Hartree"
showing 10 items of 85 documents
Towards the Hartree-Fock and coupled-cluster singles and doubles basis set limit: A study of various models that employ single excitations into a com…
2010
In explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] calculations, the basis set incompleteness error in the double excitations is reduced to such an extent that the error in the Hartree–Fock energy and the error in the single excitations become important. Using arguments from perturbation theory to systematically truncate the coupled-cluster singles and CCSD(F12) Lagrangians, a series of coupled-cluster models are proposed and studied that reduce these basis set incompleteness errors through additional single excitations into a complementary auxiliary basis. Convergence with model and size of complementary basis is rapid and there appears to be no need to go beyond seco…
Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation
2005
As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential mu) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that the ch…
Multicomponent density-functional theory for time-dependent systems
2007
We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried out in order to achieve an electron density that reflects the internal symmetry of the system. We discuss the implications of this body-fixed frame transformation and establish a Runge-Gross-type theorem and derive Kohn-Sham equations for the electrons and nuclei. We illustrate the formalism by performing calculations on a one-dimensional diatomic molecule for which the many-body Schrodinger equati…
Experimental and theoretical study of thenf-level lifetimes of potassium
2008
The theoretical and experimental values of the 5f ,6 f ,7 f, and 8f radiative lifetimes of neutral potassium are reported. The reduced matrix elements for all allowed electric-dipole nf5/2-nd5/2, nf5/2-nd3/2, and nf7/2-nd5/2 transitions with n =5–8 in K arecalculated using the relativistic linearized coupled-cluster method with single and double excitations of Dirac-Fock wave functions included to all orders in many-body perturbation theory. The resulting electric-dipole matrix elements are used to evaluate the lifetimes of the 5f ,6 f ,7 f, and 8f states in neutral K and their uncertainties. The contributions from the nf5/2-ng7/2, nf7/2-ng7/2, and nf7/2-ng9/2 transitions to the lifetimes o…
Direct perturbation theory in terms of energy derivatives: Fourth-order relativistic corrections at the Hartree–Fock level
2011
In this work, the quantum-chemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ(rel) = c(2) and c as the speed of light. To facilitate the implementation in standard quantum-chemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ(rel). The corresponding expressions, which incorp…
Empirical determination of Einstein A-coefficient ratios of bright [Fe II] lines
2014
The Einstein spontaneous rates (A-coefficients) of Fe+ lines have been computed by several authors with results that differ from each other by up to 40%. Consequently, models for line emissivities suffer from uncertainties that in turn affect the determination of the physical conditions at the base of line excitation. We provide an empirical determination of the A-coefficient ratios of bright [Fe II] lines that would represent both a valid benchmark for theoretical computations and a reference for the physical interpretation of the observed lines. With the ESO-Very Large Telescope X-shooter instrument between 3000 Å and 24700 Å, we obtained a spectrum of the bright Herbig-Haro object HH 1. …
Spin projected unrestricted Hartree-Fock ground states for harmonic quantum dots
2008
We report results for the ground state energies and wave functions obtained by projecting spatially unrestricted Hartree Fock states to eigenstates of the total spin and the angular momentum for harmonic quantum dots with $N\leq 12$ interacting electrons including a magnetic field states with the correct spatial and spin symmetries have lower energies than those obtained by the unrestricted method. The chemical potential as a function of a perpendicular magnetic field is obtained. Signature of an intrinsic spin blockade effect is found.
Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry
2017
International audience; We present the development of the extended Skyrme N2LO pseudopotential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behavior of the solutions at the origin. Finally, a fitting procedure for such an N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.
Angular momentum projection of cranked Hartree-Fock states: Application to terminating bands inA~44nuclei
2007
We present the first systematic calculations based on the angular-momentum projection of cranked Slater determinants. We propose the Iy --> I scheme, by which one projects the angular momentum I from the 1D cranked state constrained to the average spin projection of =I. Calculations performed for the rotational band in 46Ti show that the AMP Iy --> I scheme offers a natural mechanism for correcting the cranking moment of inertia at low-spins and shifting the terminating state up by ~2 MeV, in accordance with data. We also apply this scheme to high-spin states near the band termination in A~44 nuclei, and compare results thereof with experimental data, shell-model calculations, and res…
Additivity of effective quadrupole moments and angular momentum alignments in the A~130 nuclei
2007
The additivity principle of the extreme shell model stipulates that an average value of a one-body operator be equal to the sum of the core contribution and effective contributions of valence (particle or hole) nucleons. For quadrupole moment and angular momentum operators, we test this principle for highly and superdeformed rotational bands in the A~130 nuclei. Calculations are done in the self-consistent cranked non-relativistic Hartree-Fock and relativistic Hartree mean-field approaches. Results indicate that the additivity principle is a valid concept that justifies the use of an extreme single-particle model in an unpaired regime typical of high angular momenta.