Local diabatization

From Eqs. (30a)-(30c), the singularity in as the conical intersection is approached, is of order 1/p. Only /7, (n= 0, derivative coupling can be used to consfruct a local diabatic representation that removes the singularity [10]. 

It is prerequisite to define localized, diabatic state wave fimctions, representing specific Lewis resonance configurations, in a VB-like method. Although this can in principle be done using an orbital localization technique, the difficulty is that these localization methods not only include orthorgonalization tails, but also include delocalization tails, which make contribution to the electronic delocalization effect and are not appropriate to describe diabatic potential energy surfaces. We have proposed to construct the locahzed diabatic state, or Lewis resonance structure, using a strictly block-localized wave function (BLW) method, which was developed recently for the study of electronic delocalization within a molecule.(28-3 1)... 

Electron transfer (ET) is generally cast in terms of charge-localized diabatic states and charge densities (the initial and final state densities referred to above as pa) [28-30], These states differ from the corresponding eigenstates (the adiabatic states), which may be probed experimentally (spectroscopy) or theoretically (e.g., Cl or TD DFT), and various procedures have been developed for transforming adiabatic to diabatic states [60]. In one... 

There are several fundamental reasons why the GMH and adiabatic formulations are to be preferred over the traditionally employed diabatic formulation. The definition of the diabatic basis set is straightforward for intermolecular ET reactions when the donor and acceptor units are separated before the reaction and form a donor-acceptor complex in the course of diffusion in a liquid solvent. The diabatic states are then defined as those of separate donor and acceptor units. The current trend in experimental design of donor-acceptor systems, however, has focused more attention on intramolecular reactions where the donor and acceptor units are coupled in one molecule by a bridge.The direct donor-acceptor overlap and the mixing to bridge states both lead to electronic delocalization, with the result that the centers of electronic localization and localized diabatic states are ill-defined. It is then more appropriate to use either the GMH or adiabatic formulation. 

The electron transfer distance is defined by the difference between the dipole moments of the localized (diabatic) reactant and product states (Section 1.3.4). 

Thus adiabatic passage in multilevel systems can be considered in general as global adiabatic passage combined with local diabatic evolutions near conical intersections. In multilevel systems, near a conical intersection, where one... 

Equations (23) and (24) presume a knowledge of the relevant electronic states, either the charge-localized diabatic states (pA and b or the adiabatic states Fi and 4 2 (equation 8). Typically, diabatic states are natural for studying electron transfer, whereas the adiabatic states are used for optical transitions. The generalized Mulliken-Hush approximation adopts the definition of diabatic states that are diagonal with respect to the component of the dipole moment operator along... 

This is called the locally diabatic representation, and the set of coupled equations which results when replacing it into the first of (4.1), in matrix form, is ... 

The prescription is not unique, since any p-independent rotation of T is also a solution boundary conditions are imposed on (A7) by requiring V(p) to coincide with e(p) at some p (local diabaticity... 

The BLW method combines the MO and VB theories. In this method, the wavefunction for a localized (diabatic) state is defined by limiting the expansion of each MO (called block-localized MO) to a predefined subspace. Block-localized MOs belonging to different subspaces are generally non-orthogonal. A conceptual advantage of this method is that the BLWs for diabatic states are optimized self-consistently, and the adiabatic state is a combination of a few (usually two or three) diabatic state wavefunctions. 

Several approaches are available in the literature to generate and evaluate Hamiltonian matrix elements with wavefunctions of charge-localized, diabatic states. They differ in the level of theory used in the calculation and in the way localized electronic structures are created [15, 25, 26, 29-31]. When wavefunction-based quantum-chemical methods are employed, the framework of the generalized Mulliken-Hush method (GMH) [29, 32-34], is particularly successful. So far, it has been used in conjunction with accurate electronic structure methods for small and medium sized systems [35-37]. As an alternative to GMH and other derived methods [38, 39], additional methods have been explored for their applicability in larger systems such as constrained density functional method (CDFT) [25, 37, 40, 41], and fragmentation approaches [42-47], which also include the frozen density embedding (FDE) method [48, 49]. 

In the two-state model, the charge localized diabatic states are related with the adiabatic states by the formula ... 

Fig. 4.9 Attachment/detachment plots for the occupiedvirtual separated Boys localized diabatic excited triplet states near the avoided crossing. The molecule here is donor-CH2-acceptor. Taken from Ref. [154], a Detachment density for the first localized diabet. b Attachment density for the first localized diabet. c Detachment density for the second localized diabet. d Attachment density for the second localized diabet...

The CAS/NBO procedure was employed to demonstrate, e.g., that correlation effects in the two aldehyde groups of malonaldehyde (CHOCH2CHO) can be independently treated in a manner similar to isolated formaldehyde. Localized CAS is also useful in describing systems where two or more localized diabatic precursor configurations contribute to the adiabatic potential energy surface, such as the interesting double-well 2 A excited state of formaldehyde. ... 

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