187 research outputs found
Selfâconsistent intermediate Hamiltonians : A coupled cluster type formulation of the singles and doubles configuration interaction matrix dressing
This paper presents a new selfâconsistent dressing of a singles and doubles configuration interaction matrix which insures sizeâconsistency, separability into closedâshell subsystems if localized molecular orbitals (MOs) are used, and which includes all fourth order corrections. This method yields, among several schemes, a reformulation of the coupled cluster method, including fully the cluster operators of single and double excitations, and partially those of the triples (Bartlettâs algorithm named CCSDTâ1a). Further improvement can be easily included by adding exclusion principle violating corrections. Since it leads to a matrix diagonalization, the method behaves correctly in case of near degeneracies between the reference determinant and some doubles. Due to its flexibility this formulation offers the possibility of consistent combination with less expensive treatments for the study of very large [email protected] ; [email protected]
A self-consistent perturbative evaluation of ground state energies: application to cohesive energies of spin lattices
The work presents a simple formalism which proposes an estimate of the ground
state energy from a single reference function. It is based on a perturbative
expansion but leads to non linear coupled equations. It can be viewed as well
as a modified coupled cluster formulation. Applied to a series of spin lattices
governed by model Hamiltonians the method leads to simple analytic solutions.
The so-calculated cohesive energies are surprisingly accurate. Two examples
illustrate its applicability to locate phase transition.Comment: Accepted by Phys. Rev.
Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling
Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio
configuration interaction ~CI! calculations using the difference dedicated CI technique. The present
paper shows that the same technique also provides a way to analyze the various physical
contributions to the coupling and performs numerical analysis of their respective roles on four
binuclear complexes of Cu (d9) ions. The bare valence-only description ~including direct and
kinetic exchange! does not result in meaningful values. The spin-polarization phenomenon cannot
be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation
effects have an antiferromagnetic character. The first one goes through the dynamical polarization of
the environment in the ionic valence bond forms ~i.e., the M1ÂŻM2 structures!. The second one is
due to the double excitations involving simultaneously single excitations between the bridging
ligand and the magnetic orbitals and single excitations of the environment. This dispersive effect
results in an increase of the effective hopping integral between the magnetic orbitals. Moreover, it
is demonstrated to be responsible for the previously observed larger metal-ligand delocalization
occurring in natural orbitals with respect to the HartreeâFock one
Local character of magnetic coupling in ionic solids
Magnetic interactions in ionic solids are studied using parameter-free methods designed to provide accurate energy differences associated with quantum states defining the Heisenberg constant J. For a series of ionic solids including KNiF3, K2NiF4, KCuF3, K2CuF4, and high- Tc parent compound La2CuO4, the J experimental value is quantitatively reproduced. This result has fundamental implications because J values have been calculated from a finite cluster model whereas experiments refer to infinite solids. The present study permits us to firmly establish that in these wide-gap insulators, J is determined from strongly local electronic interactions involving two magnetic centers only thus providing an ab initio support to commonly used model Hamiltonians
Direct generation of local orbitals for multireference treatment and subsequent uses for the calculation of the correlation energy
We present a method that uses the one-particle density matrix to generate directly localized orbitals
dedicated to multireference wave functions. On one hand, it is shown that the definition of local
orbitals making possible physically justified truncations of the CAS ~complete active space! is
particularly adequate for the treatment of multireference problems. On the other hand, as it will be
shown in the case of bond breaking, the control of the spatial location of the active orbitals may
permit description of the desired physics with a smaller number of active orbitals than when starting
from canonical molecular orbitals. The subsequent calculation of the dynamical correlation energy
can be achieved with a lower computational effort either due to this reduction of the active space,
or by truncation of the CAS to a shorter set of references. The ground- and excited-state energies are
very close to the current complete active space self-consistent field ones and several examples of
multireference singles and doubles calculations illustrate the interest of the procedur
Ab initio evaluation of local effective interactions in
We will present the numerical evaluation of the hopping and magnetic exchange
integrals for a nearest-neighbor model of the quarter-filled
compound. The effective integrals are obtained from
valence-spectroscopy {\em ab initio} calculations of embedded crystal fragments
(two pyramids in the different geometries corresponding to the desired
parameters). We are using a large configurations interaction (CI) method, where
the CI space is specifically optimized to obtain accurate energy differences.
We show that the system can be seen as a
two-dimensional asymmetric triangular Heisenberg lattice where the effective
sites represent delocalized rung entities supporting the magnetic
electrons.Comment: 24 pages, 5 figure
The McKean-Vlasov Equation in Finite Volume
We study the McKean--Vlasov equation on the finite tori of length scale
in --dimensions. We derive the necessary and sufficient conditions for the
existence of a phase transition, which are based on the criteria first
uncovered in \cite{GP} and \cite{KM}. Therein and in subsequent works, one
finds indications pointing to critical transitions at a particular model
dependent value, of the interaction parameter. We show that
the uniform density (which may be interpreted as the liquid phase) is
dynamically stable for and prove, abstractly, that a
{\it critical} transition must occur at . However for
this system we show that under generic conditions -- large, and
isotropic interactions -- the phase transition is in fact discontinuous and
occurs at some \theta\t < \theta^{\sharp}. Finally, for H--stable, bounded
interactions with discontinuous transitions we show that, with suitable
scaling, the \theta\t(L) tend to a definitive non--trivial limit as
Proposal of an extended t-J Hamiltonian for high-Tc cuprates from ab initio calculations on embedded clusters
A series of accurate ab initio calculations on Cu_pO-q finite clusters,
properly embedded on the Madelung potential of the infinite lattice, have been
performed in order to determine the local effective interactions in the CuO_2
planes of La_{2-x}Sr_xCuO_4 compounds. The values of the first-neighbor
interactions, magnetic coupling (J_{NN}=125 meV) and hopping integral
(t_{NN}=-555 meV), have been confirmed. Important additional effects are
evidenced, concerning essentially the second-neighbor hopping integral
t_{NNN}=+110meV, the displacement of a singlet toward an adjacent colinear
hole, h_{SD}^{abc}=-80 meV, a non-negligible hole-hole repulsion
V_{NN}-V_{NNN}=0.8 eV and a strong anisotropic effect of the presence of an
adjacent hole on the values of the first-neighbor interactions. The dependence
of J_{NN} and t_{NN} on the position of neighbor hole(s) has been rationalized
from the two-band model and checked from a series of additional ab initio
calculations. An extended t-J model Hamiltonian has been proposed on the basis
of these results. It is argued that the here-proposed three-body effects may
play a role in the charge/spin separation observed in these compounds, that is,
in the formation and dynamic of stripes.Comment: 24 pages, 4 figures, submitted to Phys. Rev.
Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation
The connection between many-body theory (MBPT)--in perturbative and
non-perturbative form--and quantum-electrodynamics (QED) is reviewed for
systems of two fermions in an external field. The treatment is mainly based
upon the recently developed covariant-evolution-operator method for QED
calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a
structure quite akin to that of many-body perturbation theory. At the same time
this procedure is closely connected to the S-matrix and the Green's-function
formalisms and can therefore serve as a bridge between various approaches. It
is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to
a Schroedinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A
Bloch equation in commutator form that can be used for an "extended" or
quasi-degenerate model space is derived. It has the same relation to the BS
equation as has the standard Bloch equation to the ordinary Schroedinger
equation and can be used to generate a perturbation expansion compatible with
the BS equation also for a quasi-degenerate model space.Comment: Submitted to Canadian J of Physic
- âŠ