Ground-State Properties of Crystalline Ice from Periodic Hartree-Fock Calculations and a Coupled-Cluster-Based Many-Body Decomposition of the Correlation Energy

2008 ◽  
Vol 101 (18) ◽  
Author(s):  
Andreas Hermann ◽  
Peter Schwerdtfeger
Keyword(s):  
Ground State ◽  
Correlation Energy ◽  
Coupled Cluster ◽  
Many Body ◽  
Hartree Fock ◽  
Ground State Properties

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

EFFECTS OF CORE POLARIZATION AND PAIRING CORRELATIONS ON SOME GROUND-STATE PROPERTIES OF DEFORMED ODD-MASS NUCLEI WITHIN THE HIGHER TAMM–DANCOFF APPROACH

2011 ◽  
Vol 20 (02) ◽  
pp. 252-258 ◽  
Author(s):  
LUDOVIC BONNEAU ◽  
JULIEN LE BLOAS ◽  
PHILIPPE QUENTIN ◽  
NIKOLAY MINKOV
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Energy Difference ◽  
Pair Type ◽  
Many Body ◽  
Hartree Fock ◽  
Ground State Properties ◽  
Pairing Correlations ◽  
The Many ◽  
The Impact

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24 Mg and 48 Cr , namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

scholarly journals Ground state properties of graphene in Hartree-Fock theory

2012 ◽  
Vol 53 (9) ◽  
pp. 095220 ◽  
Author(s):  
Christian Hainzl ◽  
Mathieu Lewin ◽  
Christof Sparber
Keyword(s):  
Ground State ◽  
Hartree Fock ◽  
Ground State Properties

scholarly journals Study of Zero Temperature Ground State Properties of the Repulsive Bose-Einstein Condensate in an Anharmonic Trap

2021 ◽  
Vol 13 (3) ◽  
pp. 733-744
Author(s):  
P. K. DEBNATH
Keyword(s):  
Ground State ◽  
Expansion Method ◽  
Einstein Condensate ◽  
Zero Temperature ◽  
Many Body ◽  
Ground State Properties ◽  
Potential Harmonic ◽  
The Stability ◽  
Average Size ◽  
Body Potential

The zero-temperature ground state properties of experimental 87Rb condensate are studied in a harmonic plus quartic trap [ V(r) =  ½mω2r2 + λr4 ]. The anharmonic parameter (λ) is slowly tuned from harmonic to anharmonic. For each choice of λ, the many-particle Schrödinger equation is solved using the potential harmonic expansion method and determines the lowest effective many-body potential. We utilize the correlated two-body basis function, which keeps all possible two-body correlations. The use of van der Waals interaction gives realistic pictures. We calculate kinetic energy, trapping potential energy, interaction energy, and total ground state energy of the condensate in this confining potential, modelled experimentally. The motivation of the present study is to investigate the crucial dependency of the properties of an interacting quantum many-body system on λ. The average size of the condensate has also been calculated to observe how the stability of repulsive condensate depends on anharmonicity. In particular, our calculation presents a clear physical picture of the repulsive condensate in an anharmonic trap.

Some Properties of Coupled RPA Equations with Separable Interactions

1997 ◽  
Vol 06 (02) ◽  
pp. 251-258 ◽  
Author(s):  
Hideo Sakamoto
Keyword(s):  
Ground State ◽  
Random Phase Approximation ◽  
Strength Function ◽  
Random Phase ◽  
Transition Strength ◽  
Body System ◽  
Many Body ◽  
Hartree Fock ◽  
Secular Equations ◽  
The Stability

We investigate some properties of coupled eigenvalue equations in the random phase approximation for fundamental modes of motion in a nuclear many-body system undergoing several separable two-body interactions. Based on the Sturm's method, a new algorithm is proposed for solving such coupled secular equations and for testing the stability condition of the Hartree-Fock ground state. A transition strength in general is expressed in a compact form and, in a restricted case, a continuous strength function is constructed by averaging with a Lorentzian distribution function.

Dynamical Electron Correlation Within Hartree-Fock Limitation

2017 ◽  
Author(s):  
Arijit Bag
Keyword(s):  
Small Molecules ◽  
Electron Correlation ◽  
Present Method ◽  
Correlation Energy ◽  
Electronic Structure Theory ◽  
Structure Theory ◽  
Coupled Cluster ◽  
Energy Correlation ◽  
Good Tool ◽  
Hartree Fock

<b>Aim:</b> Calculation of dynamical electron<br>correlation energy within Hartree Fock formalism<br>to achieve post Hartree Fock accuracy.<br><br><b>Achievement: </b>Using intermediate Hamiltonian<br>technique and perturbation methodology we can<br>construct a weave equation which on projection<br>gives very simple equation for correlation<br>energy. Correlation energy only depends on the<br>amount of perturbation. This method is applied<br>for few small molecules. It is found that this<br>method produces very accurate results which is<br>comparable to CCSD method.<br><br><b>Conclusion:</b> The present method which is<br>termed as Extended Hartree Fock (EHF)<br>method is proved to be a very good tool for<br>electronic structure theory as its computational<br>requirement is equivalent to HF method but its<br>accuracy is comparable to Coupled Cluster<br>based methods.<br><br>

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