Localized wavefunction

The proposed scenario is mainly based on the molecular approach, which considers conjugated polymer films as an ensemble of short (molecular) segments. The main point in the model is that the nature of the electronic state is molecular, i.e. described by localized wavefunctions and discrete energy levels. In spite of the success of this model, in which disorder plays a fundamental role, the description of the basic intrachain properties remains unsatisfactory. The nature of the lowest excited state in m-LPPP is still elusive. Extrinsic dissociation mechanisms (such as charge transfer at accepting impurities) are not clearly distinguished from intrinsic ones, and the question of intrachain versus interchain charge separation is not yet answered. 

The localized wavefunction EL formed from N/2 doubly occupied Lewis-type NBOs,... 

An increasing disorder potential causes first strong electron scattering and eventually electron localization, in which the wave-function is confined to a smaU volume of material rather than being extended. The form of the localized wavefunction is illustrated in Fig. 

Fig. 8.2. Illustration of the dependence of the recombination rate on the separation of localized wavefunctions (a) complete overlap, (b) weak overlap.

To illustrate these considerations, we choose a specific example of the localized wavefunction - that of the ground state in the isotropic parabolic potential ... 

Alternatively, the height of the crossing point can be calculated with any MO-based method, by determining the energy of the reactant wave function at zero iteration (see Appendix 23A), by constrained optimization of block-localized wavefunctions [44], or by an energy decomposition scheme of the Morokuma-analysis type [45]. Lastly, the height of the crossing point can be computed by means of molecular mechanical methods [46], or related empirical VB calculations [47,48]. 

The activated state X = 0 then corresponds to resonance of the donor and acceptor electronic levels at which electron tunneling may occur. The energy of the reacting system as a function of this coordinate is shown in Figure 2. The two intersecting curves (a) correspond to the fully localized wavefunctions < a. mixed wavefunctions, with different... 

The assumption of the preparation of the localized wavefunction ho at f = 0 is of paramount importance to the theoretical-mathematical description of decaying (resonance) states. It is only then that notions and observations such as irreversible fragmentation of unstable states or interference effects in transition processes involving the continuous spectrum can be understood conceptually and quantitatively. 

The state-specific, correlated, localized wavefunctions of the n = 2 DES, 2s, 2p S, 2s2p P° and 2p D were included. The theory and justification of the computation of the localized component of resonance states is discussed in Ref. [1]. Since it takes 12 photons of k = 248 nm to reach these DES, which lie around 60 eV above the ground state, and since the expansion included the scattering states for the one-electron continuum up to 110 eV, it is unnecessary to consider the infinity of DES between 60 and 79 eV (which is the two-electron IT). 

NBO)-based approaches (iv) aromatic fluctuation index (FLU) by M. Sola and coworkers (v) block-localized wavefunction (BLW) method by P. v. R. Schleyer and Y. Mo and (vi) energy decomposition analysis (EDA) by F. M. Bickelhaupt and coworkers. 

Block localized wavefunction (BLW) method s The electron delocalization to the cationic carbon and neutral boron center can be estimated by removing the vacant p-orbitals from the expansion space of molecular orbitals. Although this simple orbital deletion procedure (ODP) technique is limited to the analysis of positive hyperconjugation in carbocations and boranes, it has been generalized and extended to the block localized wavefunction (BLW) method. ... 

Figure 6.40 B3LYP geometries and block localized wavefunction (BLW) estimates of delocalization energies in...

FIGURE 15.9 (a) The Anderson transition and (b) the form of the localized wavefunction in an Anderson metal-... 

Mo Y, Song L, Lin Y (2007) Block-localized wavefunction (blw) method at the density functional theory (dft) level. J Phys Chem A 111(34) 8291-8301. dol 10.1021/jp0724065... 

Substantial advantage of FEM is the flexibility of choosing irregular meshes, treatment of special boundary conditions and optimizing the local wavefunctions inside each element [11-13]. 

Figure 12.7. Schematic representation of Anderson localization in a one-dimensional periodic system of atoms. The left panels show the atomic positions (indicated by the filled circles) and electronic wavefunctions (x). The right panels show the distribution of electronic energies e associated with the different sites labeled by the index i. Top delocalized wavefunctions, which arise from identical energies at each atomic site and a band structure of width B. Center delocalized wavefunctions, which arise from random on-site energies distributed over a range W < B. Bottom localized wavefunctions, which arise from random on-site energies distributed over a range W B.

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