Perturbation theory donor-acceptor interactions

Perturbation theory can also be used to estimate the quantity of charge transferred in a donor-acceptor interaction. From first-order perturbation theory,... 

Figure 2.17 Leading 2pF (spx)M donor-acceptor interactions in SrF2, showing the sp1 acceptor hybrid interacting with the two incoming fluoride lone pairs. Each interaction is estimated as 8.18 kcal moL1 by second-order perturbation theory.

For Li—F, the quantal ionic interaction can be qualitatively pictured in terms of the donor-acceptor interaction between a filled 2pf. orbital of the anion and the vacant 2su orbital of the cation. However, ionic-bond formation is accompanied by continuous changes in orbital hybridization and atomic charges whose magnitude can be estimated by the perturbation theory of donor-acceptor interactions. These changes affect not only the attractive interactions between filled and unfilled orbitals, but also the opposing filled—filled orbital interactions (steric repulsions) as the ionic valence shells begin to overlap. 

Although the (3-nc orbital is formally vacant in the cation, Table 3.7 shows that a small residual population (0.0346c) survives in this orbital. This occupancy can be attributed to a strong donor-acceptor interaction with the filled no orbital as depicted in Fig. 3.14. This n0 nc interaction is estimated by second-order perturbation theory (Eq. (1.24)) to stabilize the ion by 19.5 kcal mol-1, a significant delocalization that is primarily responsible for the slightly lower %p(L) value in this ion. 

Radiationless excitation transfer occurs only when (D + A) initial state is in or near resonance with (D +A ) final state and there is a suitable donor-acceptor interaction between them. The rate of transfer, kt> a. is given by the time-dependent perturbation theory,... 

The perturbation theory of NBO donor-acceptor interactions can be expressed quite simply in graphical or equation form for the leading (second-order) correction for each donor-acceptor pair. The schematic perturbation diagram... 

Further studies were carried out on the Pd/Mo(l 1 0), Pd/Ru(0001), and Cu/Mo(l 10) systems. The shifts in core-level binding energies indicate that adatoms in a monolayer of Cu or Pd are electronically perturbed with respect to surface atoms of Cu(lOO) or Pd(lOO). By comparing these results with those previously presented in the literature for adlayers of Pd or Cu, a simple theory is developed that explains the nature of electron donor-electron acceptor interactions in metal overlayer formation of surface metal-metal bonds leads to a gain in electrons by the element initially having the larger fraction of empty states in its valence band. This behavior indicates that the electro-negativities of the surface atoms are substantially different from those of the bulk [65]. 

As for Erep, Ect is derived from an early simplified perturbation theory due to Murrel [46], Its formulation [47,48] also takes into account the Lrj lone pairs of the electron donor molecule (denoted molecule A). Indeed, they are the most exposed in this case of interaction (see Section 6.2.3) and have, with the n orbital, the lowest ionization potentials. The acceptor molecule is represented by bond involving an hydrogen (denoted BH) mimicking the set, denoted < > bh, of virtual bond orbitals involved in the interaction. 

As a further illustration of the dependence of n i 7t pi-backbonding interactions on metal and ligand character, we may compare simple NiL complexes of nickel with carbonyl (CO), cyanide (CN-), and isocyanide (NC-) ligands, as shown in Fig. 4.41. This figure shows that the nNi 7rL pi-backbonding interaction decreases appreciably (from 28.5 kcal mol-1 in NiCO to 6.3 kcalmol-1 in NiNC-, estimated by second-order perturbation theory) as the polarity of the 7Tl acceptor shifts unfavorably away from the metal donor orbital. The interaction in NiCO is stronger than that in NiCN- partially due to the shorter Ni—C distance in the... 

Simple second-order perturbation theory is well adapted to describe the energy lowering and occupancy shifts associated with delocalizing interactions between specific Lewis and non-Lewis NBOs. The unperturbed wave function /l corresponds to the perfectly localized Lewis structure limit, with all Lewis-type (electron donor) NBOs fully occupied and all non-Lewis-type (electron acceptor) NBOs completely vacant. The perturbative interaction of donor NBO a B with acceptor NBO CD leads to the approximate second-order energy lowering... 

However, the strength of Lewis acid-base interaction can be expressed in energy terms, such as the exothermic molar heat, —for the equilibrium (III) of adduct formation. The enthalpy term is preferred because entropy effects accompanying the formation of coordinative bonds are difficult to determine. Various models have been proposed for the theoretical estimation of the enthalpy term based on molecular properties of reactants and are reviewed in Ref 5. The most significant developments have been the hard and soft acid-base principle of Pearson [6], the E C equation of Drago and Wayland [7], the donor and acceptor numbers of Gutmann [8], and the perturbation theory of Hudson and Klopman [9]. 

A quantitative theoretical treatment was developed by Forster [39], who applied time-dependent perturbation theory to dipole-dipole interactions. The following is a simplified account. The probability of resonance energy-transfer from D to A at a distance R may be represented by a first-order rate parameter et (often, but inaccurately, called a rate constant), which is proportional to R and to the integral J representing the spectral overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor. Forster s expression is ... 

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