Pseudo state

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

O.I. Tolstikhin, V.N. Ostrovsky, H. Nakamura, Siegert pseudo-states as a universal tool Resonances, S matrix, Green function, Phys. Rev. Lett. 79 (1997) 2026. 

The different results for the 4 d2 4 f energy levels are summarized in Table 3. The level given by the zeroth-order basis (Eq. (55)) corresponds to case (e), and if the level is made self-consistent it becomes pushed up by JEff to the vicinity of the 4ji2 threshold. Obviously, a single configuration treatment then breaks down, and case (f) therefore represents a pseudo-state describing an average over the actual levels. 

The pseudo-state method of Margoliash et al. and the very simple Dalgamo refractivity scheme " for calculating molecular dispersion coeflicients can be considered as empirical versions of this approach. 

The method has been applied to the Ne-HF interaction, in which the H-F distance was kept fixed at 1.7328ao The pseudo-states were determined by a method described below. The maximum well depth is 41.6 cm and occurs... 

The equations divide into two sets because of the parity of the operator fi functions which contribute to the ground-state wavefunction give a zero contribution to the pseudo-state and vice versa. The pseudo-states d>p are thus given by... 

A very similar procedure was also used to determine the relevant pseudo-states for the He-HF interaction. It can be shown reasonably directly that this procedure is the same (to order F ) as minimizing the functional... 

However, as discussed briefly above, in order to produce highly accurate results, both the SCF functions and the pseudo-states require additional correlation. Thus both <1>a and for example, must be augmented by double replacements. This generates such a large number of configurations that the... 

Common models are mixed algebraic-differential systems, i.e., pseudo-state kinetic models ... 

Server state-machine diagram is depicted in Figure 8. Initial pseudo-state indicates nDevices servers ready in the system. Each available server can concurrently attend up to nThreads started up through event attendCustomer (), which indeed initiates a sub-state machine specified in Figure 9. The server has been supplied with interfaces (recovery() and recoveredO) to interact with the PRR component via events (note that here is where we incorporate the recovery techniques into the system). Consequently, the actual functional behaviour of a server is specified in the sub-state machine, which inherits the interfaces then allowing to abort normal behaviours. Besides, we have wanted to show how other kinds of faults, e.g. hardware faults, can also be expressed within this... 

Such formal properties are certainly satisfied by the exact wfs of each molecule, which unfortunately are not available. Henceforth we make the more realistic assumption that only approximate free-molecule functions are available and that these pseudo-states have been obtained by separate diagonalization of the matrix representatives of (H — E ) and (Hf — E over a finite set of suitable basis functions, individually antisymmetrized, A for A and 5 for B [31, 36]. The final conclusions are then... 

One practical way to implement the calculation of all the coherent amplitudes needed in the IPM is the FHBS method. We form many-electron states from suitably antisymmetrised single particle pseudo-states, we shall call these states Xn-... 

Some mixed modes do not have the properly to be completely pseudo-state modes. We will show how to deal with such a problem, which is the possibly the simplest among the non-pseudo-steady state modes. 

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