Charge transfer variables

By applying this relation, the energy function of the QEq-type fluctuating-charge model (3) can be rewritten in terms of charge-transfer variables as... 

The key insight is that the bond-space hardness matrix J in (19) is rank deficient and that its nullspace is spanned by vectors describing cyclic charge transport [43]. In order to show this, we note that relationship between charges and charge-transfer variables (16) is linear. Therefore, the mapping from solutions in bond space to those in atom space can be expressed by a rectangular matrix T such that... 

While the atom-space hardness matrix J is of full rank, J has dimension N (N -V) jl but only rank N -1. This is because combinations of charge-transfer variables that correspond to cyclic charge transport belong to the nullspace of J. For illustrative purposes, consider a four-charge system that is described by the variables... 

To overcome the over-polarization problem a number of approaches based on the concepts of atom-atom charge transfer (AACT) or other charge transfer variables were developed. In the AACT method [96], the energy is Taylor expanded in terms of... 

Irradiation of coordination compounds in the charge-transfer spectral region can often enhance redox reactions. The quantum yields are variable. 

Fig. 1.20 Cell consisting of two reversible Ag /Ag electrodes (Ag in AgN03 solution). The rate and direction of charge transfer is indicated by the length and arrow-head as follows gain of electrons by Ag -he- Ag—> loss of electrons by Ag - Ag + e- —. (o) Both electrodes at equilibrium and (f>) electrodes polarised by an external source of e.m.f. the position of the electrodes in the vertical direction indicates the potential change. (K, high-impedance voltmeter A, ammeter R, variable resistance)...

Consider now the transfer of electrons from electrode II to electrode I by means of an external source of e.m.f. and a variable resistance (Fig.. 20b). Prior to this transfer the electrodes are both at equilibrium, and the equilibrium potentials of the metal/solution interfaces will therefore be the same, i.e. Ey — Ell = E, where E, is the reversible or equilibrium potential. When transfer of electrons at a slow rate is made to take place by means of the external e.m.f., the equilibrium is disturbed and Uie rat of the charge transfer processes become unequal. At electrode I, /ai.i > - ai.i. 3nd there is... 

Keffer DJ, Mintmire JW (2000) Efficient parallel algorithms for molecular dynamics simulations using variable charge transfer electrostatic potentials. Int J Quant Chem 80(4-5) 733-742... 

Callis PR, Vivian JT (2003) Understanding the variable fluorescence quantum yield of tryptophan in proteins using QM-MM simulations. Quenching by charge transfer to the peptide backbone. Chem Phys Lett 369 409-414... 

Variable charge-transfer structures of nitrosonium-EDA complexes leading to thermal and photo-induced electron transfer 224... 

There are two approaches to map crystal charge density from the measured structure factors by inverse Fourier transform or by the multipole method [32]. Direct Fourier transform of experimental structure factors was not useful due to the missing reflections in the collected data set, so a multipole refinement is a better approach to map charge density from the measured structure factors. In the multipole method, the crystal charge density is expanded as a sum of non-spherical pseudo-atomic densities. These consist of a spherical-atom (or ion) charge density obtained from multi-configuration Dirac-Fock (MCDF) calculations [33] with variable orbital occupation factors to allow for charge transfer, and a small non-spherical part in which local symmetry-adapted spherical harmonic functions were used. 

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