Quantum molecular subunits

The initial intent of this chapter was to provide a broad overview and a critical assessment of various trends in the theory of effectively unpaired electrons. In the process of preparing the manuscripts some accents were shifted, and we would unavoidably restrict ourselves to a narrow set of issues and examples for discussion. For instance, we only slightly touched on the electron unpairing analysis in stmctures with a spatial separation of molecular subunits. These are bichromophore systems, molecular dimers and complexes, radical and ion-radical pairs, etc. The recent papers [77, 78, 125] are dedicated just to these problems. Besides, many interesting systems, e.g., semiconductor quantum dots, fell beyond the scope of this review. Indeed, many-electron aspects of the multiple exciton generation (MEG) in quantum dots are closely related to the EUE theory, but only circumstantial evidence about EUE effects in MEG can be found in the current literature [127, 128]. 

It may be useful to devise a word for complementary partners. One may propose pleromers (from the greek 7tA,f p(op.a complement p poa part) i.e., parts that complement each other. Complementary interaction sites, binding subunits, molecular fragments or species could be described by the bra-ket notation < and I > used in quantum mechanics to describe elements (vectors) belonging to conjugate spaces. Thus < A B > would mean that A and B are either complementary entities, (pleromers) or complementary fragments or just complementary interaction sites [1.20],... 

The absorption spectmm of the monomer is essentially equal to the sum of absorptions of its components. On the other hand, the fluorescence quantum yield ofthe ap monomer is much higher than that of any ofthe separate components. These results suggest that association ofthe a- and P-subunits to form an ap monomer results in a reduction ofthe flexibility ofthe molecular skeletons of the bilins without altering their environment in any other spectroscopically significant way, as it is well known that a less flexible chromophore conformation inhibits the excited state from following alternative de-excitation pathways such as internal conversion. In the case of a denatured phycobiliprotein, the absorption is sharply decreased in the visible and it is non-fluorescent. 

The excitation localization indices are the main quantities in ESSA, and we describe them more completely. Before giving some specific relations, we briefly notice that the structural-chemistry interpretation of excited states is in conformity with the rich chemical and spectrochemical experience. Really, the latter conclusively shows that molecular systems can possess separated fragments (subunits) even in excited states (see e.g. [52-54]). Therefore, it was practically important to estimate a measure of excitation localization in one or another way. The technique of excitation localization indices [22] and charge transfer numbers [23, 55] opened a possibility for an internally consistent quantum description of localization phenomena in spectrochemistry. Initially this was applied to the CIS 7r-electron model. Notice that more elementary, but not invariant, scheme was earlier proposed in [56]. 

Models have also been developed which predict periodic structures by using lattice energy minimization and vibrational spectra using lattice dynamics. In this case the proper determination of potential functions used to describe the interactions between atoms is critical for canying out adequate predictions. Very recently a very powerful shell model ion-pair potential for aluminosilicates has been derived by fitting its parameters to data obtained from quantum-chemical calculations on molecular models that represent typical subunits of zeolites [8j. The correct use of such potential describes accurately the long-range... 

The possibility of consideration of atoms as elementary subunits of the molecular systems is a consequence of Born-Oppenheimer or adiabatic approximation ( separation of electron and nuclear movements) aU quantum chemistry approaches start from this assumption. Additivity (or linear combination) is a common approach to construction of complex functions for physical description of the systems of various levels of complexity (cf orbital approximation, MO LCAO approximation, basis sets of wave functions, and some other approximations in quantum mechanics). The final justification of the method is good correlation of the results of its applications with the available experimental data and the potential to predict the characteristics of molecular systems before experimental data become available. It can be achieved after careful parameter adjustment and proper use of the force field in the area of its validity. The contributions not considered explicitly in the force field formulae are included implicitly into parameter values of the energy terms considered. 

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