Zero-temperature equation-of-motion of electron pair in the BCS theory of superconductivity

1996 ◽  
Vol 74 (6) ◽  
pp. 1106-1115
Author(s):  
Akitomo Tachibana
Keyword(s):  
Hilbert Space ◽  
Density Functional ◽  
Electron Pair ◽  
Equation Of Motion ◽  
Real Space ◽  
Bcs Theory ◽  
Zero Temperature ◽  
Functional Theory ◽  
Theory Of Superconductivity ◽  
Pair Function

By projecting the BCS ground state of superconducting electron condensate on the N-electron Hilbert space, a real-space equation-of-motion is obtained for the electron pair function [Formula: see text] at absolute zero temperature (T = 0):[Formula: see text]where ρN−2 denotes electron density of the (N – 2)-electron condensate given as[Formula: see text]Since the exchange-correlation potential is given as an explicit functional of electron density, this equation represents the fundamental working equation for the new density functional theory of superconductivity. The 2nd-order density matrix ΓN(1, 2|1′, 2′) projected on the N-electron Hilbert space satisfies[Formula: see text]so that asymptotically[Formula: see text]where [Formula: see text] denotes the center-of-mass coordinate of electrons e1and e2; this is considered the ODLRO (off-diagonal long-range order) at T = 0 projected on the N-electron Hilbert space. A new attractive potential analysis for the two-electron scattering problem (A. Tachibana, Bull. Chem. Soc. Jpn. 66, 3319 (1993); Int. J. Quantum Chem. 49, 625 (1994)) is straightforwardly applicable to the present equation-of-motion, and we can also plug in the vibronic interaction for the enhancement of the attractive force. Our approach is purely mathematical and basic, restricted merely at T = 0, but proves to serve as a real-space analysis of the pair function itself. Key words: equation-of-motion of electron pair, BCS theory, superconductivity, electron pair function, density functional theory.

scholarly journals Tensor-structured algorithm for reduced-order scaling large-scale Kohn–Sham density functional theory calculations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Chih-Chuen Lin ◽  
Phani Motamarri ◽  
Vikram Gavini
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Large Scale ◽  
Density Functional Theory Calculations ◽  
System Size ◽  
Real Space ◽  
Functional Theory ◽  
Reduced Order ◽  
Separable Approximation ◽  
Tensor Basis

AbstractWe present a tensor-structured algorithm for efficient large-scale density functional theory (DFT) calculations by constructing a Tucker tensor basis that is adapted to the Kohn–Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn–Sham Hamiltonian and an L1 localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system-size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2000 electrons.

scholarly journals ATLAS: A real-space finite-difference implementation of orbital-free density functional theory

2016 ◽  
Vol 200 ◽  
pp. 87-95 ◽  
Author(s):  
Wenhui Mi ◽  
Xuecheng Shao ◽  
Chuanxun Su ◽  
Yuanyuan Zhou ◽  
Shoutao Zhang ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Finite Difference ◽  
Density Functional ◽  
Real Space ◽  
Functional Theory ◽  
Orbital Free

scholarly journals Metal-Rich Metallaboranes: Synthesis, Structures and Bonding of Bi- and Trimetallic Open-Faced Cobaltaboranes

Inorganics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 28
Author(s):  
Kriti Pathak ◽  
Chandan Nandi ◽  
Jean-François Halet ◽  
Sundargopal Ghosh
Keyword(s):  
Electronic Structures ◽  
Density Functional ◽  
Room Temperature ◽  
Electron Pair ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
X Ray ◽  
Cluster 2 ◽  
Cobalt Center

Synthesis, isolation, and structural characterization of unique metal rich diamagnetic cobaltaborane clusters are reported. They were obtained from reactions of monoborane as well as modified borohydride reagents with cobalt sources. For example, the reaction of [Cp*CoCl]2 with [LiBH4·THF] and subsequent photolysis with excess [BH3·THF] (THF = tetrahydrofuran) at room temperature afforded the 11-vertex tricobaltaborane nido-[(Cp*Co)3B8H10] (1, Cp* = η5-C5Me5). The reaction of Li[BH2S3] with the dicobaltaoctaborane(12) [(Cp*Co)2B6H10] yielded the 10-vertex nido-2,4-[(Cp*Co)2B8H12] cluster (2), extending the library of dicobaltadecaborane(14) analogues. Although cluster 1 adopts a classical 11-vertex-nido-geometry with one cobalt center and four boron atoms forming the open pentagonal face, it disobeys the Polyhedral Skeletal Electron Pair Theory (PSEPT). Compound 2 adopts a perfectly symmetrical 10-vertex-nido framework with a plane of symmetry bisecting the basal boron plane resulting in two {CoB3} units bridged at the base by two boron atoms and possesses the expected electron count. Both compounds were characterized in solution by multinuclear NMR and IR spectroscopies and by mass spectrometry. Single-crystal X-ray diffraction analyses confirmed the structures of the compounds. Additionally, density functional theory (DFT) calculations were performed in order to study and interpret the nature of bonding and electronic structures of these complexes.

First-principle investigations on structural, elastic, electronic and thermodynamic properties of ScX3(X = Ir,Pd,Pt and Rh) under high pressure

2015 ◽  
Vol 29 (32) ◽  
pp. 1550201 ◽  
Author(s):  
Bao Chen ◽  
Santao Qi ◽  
Hongquan Song ◽  
Chuanhui Zhang ◽  
Jiang Shen
Keyword(s):  
Density Functional Theory ◽  
Thermodynamic Properties ◽  
Bulk Modulus ◽  
Density Functional ◽  
External Pressure ◽  
First Principle ◽  
Zero Temperature ◽  
Functional Theory ◽  
Change Trend ◽  
Experimental Values

In this paper, the structural, elastic, electronic and thermodynamic properties of [Formula: see text] and [Formula: see text] intermetallic compound are investigated using pseudopotential method based on density functional theory (DFT) under pressure. In this work, the calculated lattice constant and bulk modulus are in accordance with experimental values at zero temperature and zero pressure. The bulk modulus [Formula: see text], shear modulus [Formula: see text] and Young’s modulus [Formula: see text] for [Formula: see text] and [Formula: see text] increase with the increasing external pressure. It is noted that [Formula: see text] of investigated compound has the largest [Formula: see text], [Formula: see text] and [Formula: see text]. The results of [Formula: see text] and [Formula: see text] have the same change trend, but [Formula: see text] presents an irregular change for [Formula: see text] and [Formula: see text]. The density of states for [Formula: see text] and [Formula: see text] are investigated at 0, 30 and 50 GPa. In addition, the thermodynamic properties as a function of temperature at different pressure are also studied.

Visible-light Photoresponse of Nitrogen-doped TiO2: Excited State Studies Using Time-dependent Density Functional Theory and Equation-of-Motion Coupled Cluster Methods

2010 ◽  
Vol 1263 ◽  
Author(s):  
Niranjan Govind ◽  
Roger Rousseau ◽  
Amity Andersen ◽  
Karol Kowalski
Keyword(s):  
Excited State ◽  
Density Functional ◽  
Equation Of Motion ◽  
Coupled Cluster ◽  
Functional Theory ◽  
Experimental Findings ◽  
High Level ◽  
Cluster Methods ◽  
Compare And Contrast

AbstractTo shed light on the nature of the electronic states at play in N-doped TiO2 nanoparticles, we have performed detailed ground and excited state calculations on pure and N-doped TiO2 rutile using an embedding model. We have validated our model by comparing ground-state embedded results with those obtained from periodic DFT calculations. Our results are consistent with periodic calculations. Using this embedding model we have performed B3LYP based TDDFT calculations of the excited state spectrum. We have also studied the lowest excitations using high-level equation-of-motion coupled cluster (EOMCC) approaches involving all single and inter-band double excitations. We compare and contrast the nature of the excitations in detail for the pure and doped systems using these calculations. Our calculations indicate a lowering of the bandgap and confirm the role of the N3- states on the UV/Vis spectrum of N-doped TiO2 rutile supported by experimental findings.

scholarly journals Linear scaling algorithm of real-space density functional theory of electrons with correlated overlapping domains

2012 ◽  
Vol 183 (8) ◽  
pp. 1664-1673 ◽  
Author(s):  
Nobuko Ohba ◽  
Shuji Ogata ◽  
Takahisa Kouno ◽  
Tomoyuki Tamura ◽  
Ryo Kobayashi
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Real Space ◽  
Linear Scaling ◽  
Functional Theory ◽  
Space Density ◽  
Overlapping Domains

REAL-TIME APPROACH TO TIME-DEPENDENT DENSITY-FUNCTIONAL THEORY IN THE LINEAR AND NONLINEAR REGIME

2009 ◽  
Vol 08 (04) ◽  
pp. 561-574 ◽  
Author(s):  
MICHAEL MUNDT
Keyword(s):  
Density Functional Theory ◽  
Real Time ◽  
Density Functional ◽  
High Harmonic ◽  
External Perturbation ◽  
Real Space ◽  
Time Dependent ◽  
Functional Theory ◽  
Linear And Nonlinear ◽  
Dependent Density

The linear and nonlinear response of Si 4 and Na 4 to an external perturbation is investigated in the framework of time-dependent density-functional theory. The time-dependent Kohn–Sham equations, which are the central equations in this approach, are solved in real space and real time. A parallelized implementation to solve these nonlinear, one-particle Schrödinger equations is presented. In contrast to Na 4, Si 4 shows high-harmonic generation far beyond the cut-off predicted by the quasiclassical model and predictions for extended systems.

scholarly journals Persistence of the stereochemical activity of the Bi3+ lone electron pair in Bi2Ga4O9 up to 50 GPa and crystal structure of the high-pressure phase

2010 ◽  
Vol 66 (3) ◽  
pp. 323-337 ◽  
Author(s):  
Alexandra Friedrich ◽  
Erick A. Juarez-Arellano ◽  
Eiken Haussühl ◽  
Reinhard Boehler ◽  
Björn Winkler ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Phase Transition ◽  
High Pressure ◽  
Density Functional ◽  
Lone Electron Pair ◽  
Electron Pair ◽  
High Pressure Phase ◽  
Functional Theory ◽  
Pressure Phase ◽  
Stereochemical Activity

The crystal structure of the high-pressure phase of bismuth gallium oxide, Bi2Ga4O9, was determined up to 30.5 (5) GPa from in situ single-crystal in-house and synchrotron X-ray diffraction. Structures were refined at ambient conditions and at pressures of 3.3 (2), 6.2 (3), 8.9 (1) and 14.9 (3) GPa for the low-pressure phase, and at 21.4 (5) and 30.5 (5) GPa for the high-pressure phase. The mode-Grüneisen parameters for the Raman modes of the low-pressure structure and the changes of the modes induced by the phase transition were obtained from Raman spectroscopic measurements. Complementary quantum-mechanical calculations based on density-functional theory were performed between 0 and 50 GPa. The phase transition is driven by a large spontaneous displacement of one O atom from a fully constrained position. The density-functional theory (DFT) model confirmed the persistence of the stereochemical activity of the lone electron pair up to at least 50 GPa in accordance with the crystal structure of the high-pressure phase. While the stereochemcial activity of the lone electron pair of Bi^{3+} is reduced at increasing pressure, a symmetrization of the bismuth coordination was not observed in this pressure range. This shows an unexpected stability of the localization of the lone electron pair and of its stereochemical activity at high pressure.

Sign in / Sign up

Export Citation Format

Share Document