Large-D limit

Here, we report on high-field ESR properties of the 5=1 Heisenberg chain system Ni(C2H8N2)2Ni(CN)4 (NENC) [16,31], This material is characterized by strong in-plane anisotropy D/k= 6 K, and so far can be considered as the best known candidate for a quantum 5=1 chain in the large-D limit (D/J=1.5) [32],... 

Figure 1. The asymmetry parameter r] as a function of the nuclear charge Z for the Hartree-Fock two-electron atom at the large D limit.

In the Z — 1 limit, the kinetic terms involving derivatives remain, the centrifugal terms drop out, and the scaled Coulombic potentials metamorphize into delta functions. This hyperquantum limit is tantamount to — oo in the unsealed wave equation. For electronic structure, the low-D limit is generally less useful than the large-D limit, because only the ground state of a delta-function potential [2,5,9] is bound and that can accommodate only two electrons. However, for... 

In order to finitize the large-D limit, we scale according to Eq. (9). The virial theorem then reads... 

The subhamiltonian approach is especially appealing because it allows one to use simple classical models based on those of the large-D limit, but corrected quantitatively for the effects of finite D. The structures obtained by minimizing the subhamiltonians might be considered as optimal localized representations of real electronic structures. 

Z. Zhen and J. G. Loeser, Large-D limit for N-electron atoms, this book. 

The instanton method is particularly congenial for the large-D limit, in that the zero-energy trajectory in imaginary time corresponds precisely to tunneling between minima in the effective potential with D oo. Despite the infinite effective mass, timneling still occurs because quantum fiuctuations persist in this limit. As usual with semiclassical methods, the dynamical aspects are evaluated by classical mechanics. However, the unusual and striking aspect of our... 

Another feature of general interest is the Jacobian correction to AE, which proves to be inversely proportional to R and thus is a significant factor. It is extremely easy to evaluate this factor in the large-D limit. Many treatments of tunneling assume or approximate... 

The poor convergence of the partial sums of the 1/D expansion for atomic and molecular energies is due to the fact that the energy function E 6), = l/ >, is not a polynomial. The large-D limit appears to he an excellent qualitative model, but in order to accurately continue the solution from 8 = Q to 8 = 1/Z it is necessary to take into account the functional form ofE 8) in that general region of the complex plane. The most important feature in this functional form is a second-order... 

Inequalities for oscillator strengths, previously used for estimating dipole polarizabilities in three dimensions, are generalized to D dimensions, and expressions for the dipole polarizability in the large D limit are obtained. The exact results, the dimensional scaling calculations, and the expressions obtained from inequalities are compared and evaluated. It is shown that the exact first order correction to the unperturbed wave function reduces to one term in the sum over states expression. The asymptotic result for the dipole polarizabilities is, in atomic units, 2 = (64Z ) D . 

Using the large-d limit and defining the flatness order parameter C for the flat phase = where < > means the thermal average, one can derive a set of saddle point equations [9]. We only present the most important one about the full inverse propagator K(k) =... 

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