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Ground-state wave function model

It may be concluded thus that the Half-Projected Hartree-Fock model proposed more than two decades ago for introducing some correlation effects in the ground state wave-function [1,2], could be employed advantageously for the direct determination of the lowest triplet and singlet excited states, in which Ms = 0. This procedure could be especially suitable for the singlet excited states of medium size molecules for which no other efficient procedure exists. [Pg.187]

In the ground state of helium, according to this model, the two electrons are in the Is orbital with opposing spins. The ground-state wave function is... [Pg.225]

Since this Hamilton operator does not contain any electron-electron interactions it indeed describes a non-interacting system. Accordingly, its ground state wave function is represented by a Slater determinant (switching to 0S and (p rather than Osd and % for the determinant and the spin orbitals, respectively, in order to underline that these new quantities are not related to the HF model)... [Pg.60]

Experimental mobility values, 1.2 X 10-2 cm2/v.s. for eam and 1.9 x 10-3 cm2/v.s. for eh, indicate a localized electron with a low-density first solvation layer. This, together with the temperature coefficient, is consistent with the semicontinuum models. Considering an effective radius given by the ground state wave-function, the absolute mobility calculated in a brownian motion model comes close to the experimental value. The activation energy for mobility, attributed to that of viscosity in this model, also is in fair agreement with experiment, although a little lower. [Pg.175]

Overlapping Ion Model. The ground-state wave function for an individual electron in an ionic crystal has been discussed by Lowdin (24). To explain the macroscopic properties of the alkali halides, Lowdin has introduced the symmetrical orthogonaliz tion technique. He has shown that an atomic orbital, x//, in an alkali halide can be given by... [Pg.135]

An electronic transition involves excitation of an electron from the ground state wave function to one of the excited state wave functions. An adiabatic excitation is one that involves adjustment of the nuclear geometry to minimize the energy of the excited molecular system. A vertical excitation is one that occurs so rapidly that the ground state geometry does not have time to change. This latter type of excitation is usually adequate for modeling UV-Vis spectra. [Pg.395]

In this paper we present a set of ID and 2D spin-1/2 models with competing F and AF interactions for which the singlet ground-state wave function can be found exactly. This function has a special form expressed in terms of auxiliary Bose operators. This form of the wave function is similar to the MP one but with infinite matrices. For special values of model parameters it can be reduced to the standard MP form. [Pg.770]

The paper is organized as follows. In See.2 we consider the frustrated spin chain at F-AF transition point and describe the exact singlet ground-state wave function as well as details of the spin correlation function calculations. We discuss the phase diagram of this model and its magnetic properties in the AF phase. In Sec.3 the special spin ladder will be considered. A two-dimensional frustrated spin model with the exact ground state is considered in Sec.4. Sec. 5 is devoted to the construction of the electronic models with the SB type of wave function. The results of this paper are summarized in Sec.6. [Pg.771]

We studied previously a one-parameter ladder model (46-48) with non-degenerate singlet ground state. The exact ground state wave function of the cyclic ladder was written in the MP form (39). Now we write the wave function I>o in a form more suitable for subsequent generalization to other types of lattices [31]. [Pg.789]

Thus, the singlet ground-state wave function of the model (46) can be also written in a spinor form (55). [Pg.791]

To calculate the above-indicated expected values, we carry out Monte Carlo calculations on 20 x 20-site lattices. As mentioned, the ground-state wave function of the model depends on 14 parameters and, of course, cannot possibly be analyzed completely. We confine the numerical calculations to the case in which the spinor 4>A/" P depends on one parameter a ... [Pg.796]

As the first example we consider the ID electronic model with the two-fold degenerate ground state in the form of the simple product of SB dimers, similarly to the ground state of the well-known spin-5 Majumdar-Ghosh model [6]. For the half-filling case the proposed ground state wave functions are ... [Pg.801]

One of these models is the spin- ladder with competing interactions of the ferro- and antiferromagnetic types at the F-AF transition line. The exact singlet ground-state wave function on this line is found in the special form expressed in terms of auxiliary Bose-operators. The spin correlators in the singlet state show double-spiral ordering with the period of spirals equal to the system size. [Pg.807]

In the general case the proposed form of the wave function corresponds to the MP form but with matrices of infinite size. However, for special values of parameters of the model it can be reduced to the standard MP form. In particular, we consider a spin-1 ladder with nondegenerate antiferromagnetic ground state for which the ground state wave function is the MP one with 2x2 matrices. This model has some properties of ID AKLT model and reduces to it in definite limiting case. [Pg.807]

The ground state wave function of the spin ladders can be represented in an alternative form as a product of second-rank spinors associated with the lattice sites and the metric spinors corresponding to bonds between nearest neighbor sites. Two-dimensional spin-1 model is constructed with exact ground state wave function of this type. The ground state of this model is a nondegenerate singlet... [Pg.807]

In conclusion we note that the construction of considered models is based on the following property. Their Hamiltonians are the sums of the cell Hamiltonians that are local and non-commuting with each other. At the same time the ground-state wave function of the total Hamiltonian is the ground state for each cell Hamiltonian. It is clear that these models are rather special. Nevertheless, the study of them is useful for understanding properties of the real frustrated spin systems and strongly correlated electronic models. [Pg.808]

An important qualitative description of the spectral behavior of class II compounds was presented by Robin and Day. This simple model has found apphcabihty to the discussion of the spectra of numerous mixed valence compounds in which some delocalization occurs. In this model, it is assumed that the ground-state wave function contains the function, a, which describes mixing of the wave function for site A with the wave function of site B. [Pg.2717]

A discussion is given of electron correlations in d- and f-electron systems. In the former case we concentrate on transition metals for which the correlated ground-state wave function can be calculated when a model Hamiltonian is used, i.e. a five-band Hubbard Hamiltonian. Various correlation effects are discussed. In f-electron systems a singlet ground-state forms due to the strong correlations. It is pointed out how quasiparticle excitations can be computed for Ce systems. [Pg.279]

Several requirements have been put forward in order to model chemisorption processes in infinite surfaces with metal clusters. The ground state wave function should have a conduction band near the Fermi level with significant amplitude near the chemisorption site. The cluster should exhibit a high density of states and should be highly polarizable. It should also possess an ionization potential similar to that of the bulk. Finally, the orbital structure of the cluster employed in the model must be in a suitable bonding state, which is often not the ground state. However, this rule implies that it is not important to describe the density of states, the ionization potential, or, the polarizability of the bulk with the cluster system in order to obtain stable chemisorption energies. [Pg.204]

Qian and Sahni [111] have used the Holas-March route to the exchange-correlation potential Vxc r) to construct this quantity in an exactly solvable model. This is the so-called Hooke s atom, in which two electrons, mutually repelling Coulombically, move in an external harmonic potential. For a particular choice of spring constant, the ground-state wave function is analytically known. In the study of Qian and Sahni (see their Fig. 12), the exchange-correlation potential Vxc is calculated exactly from the Holas-March [52] approach. In particular, Qian and Sahni make a full study of the contribution to VXc from the correlation kinetic energy. [Pg.227]

A model of the spectral dependence of the photoionization spectrum of group-III acceptors in silicon has been presented by Edwards and Fowler [52]. This model uses hydrogenic continuum states and hydrogenic ground-state wave functions scaled to account for central-cell corrections, and it provides a good description of the energy dependence of the cross-sections, as can be seen from Fig. 7.8. [Pg.295]


See other pages where Ground-state wave function model is mentioned: [Pg.264]    [Pg.369]    [Pg.381]    [Pg.91]    [Pg.36]    [Pg.159]    [Pg.17]    [Pg.462]    [Pg.549]    [Pg.551]    [Pg.769]    [Pg.770]    [Pg.782]    [Pg.800]    [Pg.801]    [Pg.803]    [Pg.266]    [Pg.5824]    [Pg.280]    [Pg.196]    [Pg.91]    [Pg.323]    [Pg.154]    [Pg.35]   
See also in sourсe #XX -- [ Pg.389 , Pg.390 , Pg.391 , Pg.392 ]

See also in sourсe #XX -- [ Pg.389 , Pg.390 , Pg.391 , Pg.392 ]




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Functional grounding

Functional modeling

Functional models

Functional state

Functions state function

Ground state functional

Ground state functions

Ground-state modeling

Ground-state wave function

Model function

Model wave function

State functions

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