Topic

# Ground state

About: Ground state is a research topic. Over the lifetime, 70014 publications have been published within this topic receiving 1538032 citations. The topic is also known as: vacuum state & vacuum.

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TL;DR: A way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects as well as significant interconfigurational and interterm errors remain.

Abstract: Generalized gradient approximations (GGA's) seek to improve upon the accuracy of the local-spin-density (LSD) approximation in electronic-structure calculations. Perdew and Wang have developed a GGA based on real-space cutoff of the spurious long-range components of the second-order gradient expansion for the exchange-correlation hole. We have found that this density functional performs well in numerical tests for a variety of systems: (1) Total energies of 30 atoms are highly accurate. (2) Ionization energies and electron affinities are improved in a statistical sense, although significant interconfigurational and interterm errors remain. (3) Accurate atomization energies are found for seven hydrocarbon molecules, with a rms error per bond of 0.1 eV, compared with 0.7 eV for the LSD approximation and 2.4 eV for the Hartree-Fock approximation. (4) For atoms and molecules, there is a cancellation of error between density functionals for exchange and correlation, which is most striking whenever the Hartree-Fock result is furthest from experiment. (5) The surprising LSD underestimation of the lattice constants of Li and Na by 3--4 % is corrected, and the magnetic ground state of solid Fe is restored. (6) The work function, surface energy (neglecting the long-range contribution), and curvature energy of a metallic surface are all slightly reduced in comparison with LSD. Taking account of the positive long-range contribution, we find surface and curvature energies in good agreement with experimental or exact values. Finally, a way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects.

17,848 citations

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TL;DR: An exact stochastic simulation of the Schroedinger equation for charged Bosons and Fermions was used to calculate the correlation energies, to locate the transitions to their respective crystal phases at zero temperature within 10%, and to establish the stability at intermediate densities of a ferromagnetic fluid of electrons.

Abstract: An exact stochastic simulation of the Schroedinger equation for charged Bosons and Fermions was used to calculate the correlation energies, to locate the transitions to their respective crystal phases at zero temperature within 10%, and to establish the stability at intermediate densities of a ferromagnetic fluid of electrons.

10,743 citations

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TL;DR: In this article, a theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, and it is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction.

Abstract: A theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, $\ensuremath{\hbar}\ensuremath{\omega}$. It is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction. The normal phase is described by the Bloch individual-particle model. The ground state of a superconductor, formed from a linear combination of normal state configurations in which electrons are virtually excited in pairs of opposite spin and momentum, is lower in energy than the normal state by amount proportional to an average ${(\ensuremath{\hbar}\ensuremath{\omega})}^{2}$, consistent with the isotope effect. A mutually orthogonal set of excited states in one-to-one correspondence with those of the normal phase is obtained by specifying occupation of certain Bloch states and by using the rest to form a linear combination of virtual pair configurations. The theory yields a second-order phase transition and a Meissner effect in the form suggested by Pippard. Calculated values of specific heats and penetration depths and their temperature variation are in good agreement with experiment. There is an energy gap for individual-particle excitations which decreases from about $3.5k{T}_{c}$ at $T=0\ifmmode^\circ\else\textdegree\fi{}$K to zero at ${T}_{c}$. Tables of matrix elements of single-particle operators between the excited-state superconducting wave functions, useful for perturbation expansions and calculations of transition probabilities, are given.

9,619 citations

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TL;DR: In this article, an extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first row atoms carbon to fluorine, where each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively.

Abstract: An extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first‐row atoms carbon to fluorine. In this set, described as 4–31 G, each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively. The expansion coefficients and Gaussian exponents are determined by minimizing the total calculated energy of the atomic ground state. This basis set is then used in single‐determinant molecular‐orbital studies of a group of small polyatomic molecules. Optimization of valence‐shell scaling factors shows that considerable rescaling of atomic functions occurs in molecules, the largest effects being observed for hydrogen and carbon. However, the range of optimum scale factors for each atom is small enough to allow the selection of a standard molecular set. The use of this standard basis gives theoretical equilibrium geometries in reasonable agreement with experiment.

8,551 citations

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TL;DR: In this article, various contracted Gaussian basis sets for atoms up to Kr are presented which have been determined by optimizing atomic self-consistent field ground state energies with respect to all basis set parameters, i.e., orbital exponents and contraction coefficients.

Abstract: Various contracted Gaussian basis sets for atoms up to Kr are presented which have been determined by optimizing atomic self‐consistent field ground state energies with respect to all basis set parameters, i.e., orbital exponents and contraction coefficients.

8,258 citations