The description of collective motions in terms of many-body perturbation theory III. The extension of the theory to the non-uniform gas

1958 ◽  
Vol 244 (1237) ◽  
pp. 199-211 ◽  
Keyword(s):  
Correlation Energy ◽  
Electron Gas ◽  
Approximate Expression ◽  
Many Body ◽  
Local Field Correction ◽  
Consistent Field ◽  
Homogeneous Integral Equation ◽  
Collective Motions ◽  
Self Consistent Field ◽  
Many Body Perturbation Theory

The theory previously developed and applied to calculate the correlation energy of a free-electron gas is extended in this paper to calculate the energy of an electron gas in a potential field. Two new features arise: (i) the introduction of a self-consistent field which is a generalization of the ordinary Hartree field; (ii) the occurrence of ‘local field correction’ effects. It is shown that the energy of the gas can be expressed in terms of the eigenvalues of a certain homogeneous integral equation and a stationary principle for these eigenvalues is given. The theory is applied to crystals and an approximate expression for the correlation energy of a metal is derived neglecting Lorentz-Lorenz corrections effects.

THE SCREENING FUNCTION OF AN INTERACTING ELECTRON GAS

1966 ◽  
Vol 44 (9) ◽  
pp. 2137-2171 ◽  
Author(s):  
D. J. W. Geldart ◽  
S. H. Vosko
Keyword(s):  
Electron Gas ◽  
Substantial Contribution ◽  
Fundamental Relation ◽  
Many Body ◽  
Screening Constant ◽  
Self Energy ◽  
Self Consistent ◽  
Small Wave ◽  
Many Body Perturbation Theory ◽  
Zero Frequency

The screening function of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. The analysis is guided by a fundamental relation between the compressibility of the system and the zero-frequency small wave-vector screening function (i.e. screening constant). It is shown that the contribution from a graph not included in previous work is essential to obtain the lowest-order correlation correction to the screening constant at high density. Also, this graph gives a substantial contribution to the screening constant at metallic densities. The general problem of choosing a self-consistent set of graphs for calculating the screening function is discussed in terms of a coupled set of integral equations for the propagator, the self-energy, the vertex function, and the screening function. A modification of Hubbard's (1957) form of the screening function is put forward on the basis of these results.

Calculation and measurement of electron ionization cross sections for L and M shells

1992 ◽  
Vol 50 (2) ◽  
pp. 1642-1643
Author(s):  
Suichu Luo ◽  
David C. Joy ◽  
John R. Dunlap ◽  
Xinlei Wang
Keyword(s):  
Cross Sections ◽  
Correlation Energy ◽  
Calculation Algorithm ◽  
Ionization Cross ◽  
X Ray ◽  
Primary Mechanism ◽  
Consistent Field ◽  
Self Consistent Field ◽  
Ionization Cross Sections ◽  
Shell Ionization

The ionization of atoms by electrons is a process of great importance in physics, because it is the primary mechanism for energy loss of electron in matter and for X-ray microanalysis. Powell has critically compared various theoretical, semi- or empirical formulations with experiments and it is clear that although calculations and measurements have been carried out previously for K and to a lesser extent for L shells, very little data, both experimental and theoretical, exist for M shells.We have calculated K ,L (L1 and L23 ) and M( M1 ,M23 M45 )shell ionization cross section covering the entire periodic table and spanning the energy range from the critical ionization energy for a particular element up to 100 keV using Hartree-Slater central self- consistent field model. The calculation algorithm is essentially that described in Ref.3 but both exchange and correlation energy effects have been included in the computations to ensure that the computed cross-sections are valid at low overvoltage ratios, and relativistic corrections have also been included for accuracy at high incident energies.

Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development

2018 ◽  
Author(s):  
Daniel Smith ◽  
Lori A Burns ◽  
Dominic A. Sirianni ◽  
Daniel R. Nascimento ◽  
Ashutosh Kumar ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Quantum Chemistry ◽  
Rapid Development ◽  
Computer Code ◽  
Programming Approach ◽  
Many Body ◽  
Imple Mentation ◽  
Self Consistent Field ◽  
Many Body Perturbation Theory ◽  
Python Programming

<div> <div> <div> <p><i>Psi4NumPy</i> demonstrates the use of efficient computational kernels from the open- source <i>Psi4</i> program through the popular <i>NumPy</i> library for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Further, several reference codes have been integrated into Jupyter notebooks, allowing background and explanatory information to be associated with the imple- mentation. <i>Psi4NumPy</i> tools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementa- tions also demonstrate the power of the hybrid C++/Python programming approach employed by the <i>Psi4</i> program. </p> </div> </div> </div>

Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development

2018 ◽  
Author(s):  
Daniel Smith ◽  
Lori A Burns ◽  
Dominic A. Sirianni ◽  
Daniel R. Nascimento ◽  
Ashutosh Kumar ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Quantum Chemistry ◽  
Rapid Development ◽  
Computer Code ◽  
Programming Approach ◽  
Many Body ◽  
Imple Mentation ◽  
Self Consistent Field ◽  
Many Body Perturbation Theory ◽  
Python Programming

<div> <div> <div> <p><i>Psi4NumPy</i> demonstrates the use of efficient computational kernels from the open- source <i>Psi4</i> program through the popular <i>NumPy</i> library for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Further, several reference codes have been integrated into Jupyter notebooks, allowing background and explanatory information to be associated with the imple- mentation. <i>Psi4NumPy</i> tools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementations also demonstrate the power of the hybrid C++/Python programming approach employed by the <i>Psi4</i> program. </p> </div> </div> </div>

THE PAIR DISTRIBUTION FUNCTION OF AN INTERACTING ELECTRON GAS

1967 ◽  
Vol 45 (9) ◽  
pp. 3139-3161 ◽  
Author(s):  
D. J. W. Geldart
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Electron Gas ◽  
Pauli Principle ◽  
Distribution Functions ◽  
Upper And Lower Bounds ◽  
Wave Number ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Simple Class

The pair distribution function, in the limit of zero separation, of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. It is shown that the usual methods for maintaining self-consistency in approximate calculations violate, in general, the nonnegativity of the pair distribution function. In particular, the Pauli principle yields a rigorous sum rule for the parallel spin density fluctuation propagator which is not satisfied. Upper and lower bounds on one-loop and multiloop contributions to the pair distribution functions are given. These bounds are used to discuss correlation corrections. An improved wave-number dependence is given for Hubbard's (1957) approximation to the screening function and numerical results are given for a simple class of exchange corrections.

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