Electrostatic deformation potential

When the electrostatic properties are evaluated by AF summation, the effect of the spherical-atom molecule must be evaluated separately. According to electrostatic theory, on the surface of any spherical charge distribution, the distribution acts as if concentrated at its center. Thus, outside the spherical-atom molecule s density, the potential due to this density is zero. At a point inside the distribution the nuclei are incompletely screened, and the potential will be repulsive, that is, positive. Since the spherical atom potential converges rapidly, it can be evaluated in real space, while the deformation potential A(r) is evaluated in reciprocal space. When the promolecule density, rather than the superposition of rc-modified non-neutral spherical-atom densities advocated by Hansen (1993), is evaluated in direct space, the pertinent expressions are given by (Destro et al. 1989)... 

A promising lead in the estimation of electrostatic interactions is the use of electrostatic molecular potentials [24]. This method simulates the coulombic contribution to the intermolecular interaction by substituting appropriately chosen point charges, which may be fractional, to replace actual neighbouring molecules. The potential is a function of the electronic distribution and the position of the nuclei in the molecule and is computed from molecular wave functions. It is the basic premise of the use of electrostatic potentials that - pol> - Ct and fi disp much less important than electrostatic effects in determining structural features of complex formation. The deformations of the special charge distribution of a set of atoms bound together to form a molecule are quite complex and the electrostatic potential, like all other... 

Grahame introdnced the idea that electrostatic and chemical adsorption of ions are different in character. In the former, the adsorption forces are weak, and the ions are not deformed dnring adsorption and continne to participate in thermal motion. Their distance of closest approach to the electrode surface is called the outer Helmholtz plane (coordinate x, potential /2, charge of the diffuse EDL part When the more intense (and localized) chemical forces are operative, the ions are deformed, undergo partial dehydration, and lose mobility. The centers of the specifically adsorbed ions constituting the charge are at the inner Helmholtz plane with the potential /i and coordinate JCj < Xj. 

A better alternative is to use the difference structure factor AF in the summations. The electrostatic properties of the procrystal are rapidly convergent and can therefore be easily evaluated in direct space. Stewart (1991) describes a series of model calculations on the diatomic molecules N2, CO, and SiO, placed in cubic crystal lattices and assigned realistic mean-square amplitudes of vibration. He reports that for an error tolerance level of 1%, (sin 0/2)max = 1-1.1 A-1 is adequate for the deformation electrostatic potential, 1.5 A-1 for the electric field, and 2.0 A 1 for the deformation density and the deformation electric field gradient (which both have Fourier coefficients proportional to H°). 

Stewart s conclusion underscores the need for short-wavelength, low-temperature studies, if very high accuracy electrostatic properties are to be evaluated by Fourier summation. But, as pointed out by Hansen (1993), the convergence can be improved if the spherical atoms subtracted out are modified by the k values obtained with the multipole model. Failure to do this causes pronounced oscillations in the deformation density near the nuclei. For the binuclear manganese complex ( -dioxo)Mn(III)Mn(IV)(2,2 -bipyridyl)4, convergence of the electrostatic potential at the Mn nucleus is reached at 0.7 A" as checked by the inclusion of higher-order data (Frost-Jensen et al. 1995). 

Once the multipole analysis of the X-ray data is done, it provides an analytical description of the electron density that can be used to calculate electrostatic properties (static model density, topology of the density, dipole moments, electrostatic potential, net charges, d orbital populations, etc.). It also allows the calculation of accurate structure factors phases which enables the calculation of experimental dynamic deformation density maps [16] ... 

The electrostatic potential Ve is the inverse Fourier transform of FT2 F(H). However, there is a singularity for H = 0 [42], In order to avoid this problem, one calculates the deformation electrostatic potential at r ... 

Deformation density and electrostatic potential measurements are used to study the electronic structure associated with hydrogen bonding. These methods seek to... 

The distinction between hydrogen-bond donors, i.e., N-H, and nondonors, i.e., C-H, is often not apparent in deformation density maps. This distinction appears much more clearly on the electrostatic potential maps, such as illustrated in Fig. 3.4 [218]. Such maps may therefore provide a more effective means of quantitatively analyzing the electronic differences between the different donor-acceptor hydrogen-bond combinations which is manifested by the different mean bond lengths described in Part IB, Chapter 7 [222- 226]. It has been suggested that hydrogen-bond strengths can be at least qualitatively compared from the values of the electrostatic potentials at fixed distances from the donor and acceptor atoms, i.e., 2.0 A [227]. 

Deformation density maps have been used to examine the effects of hydrogen bonding on the electron distribution in molecules. In this method, the deformation density (or electrostatic potential) measured experimentally for the hydrogen-bonded molecule in the crystal is compared with that calculated theoretically for the isolated molecule. Since both the experiment and theory are concerned with small differences between large quantities, very high precision is necessary in both. In the case of the experiment, this requires very accurate diffraction intensity measurements at low temperature with good thermal motion corrections. In the case of theory, it requires a high level of ab-initio molecular orbital approximation, as discussed in Chapter 4. 

A similar situation prevails for a charge q subjected to an electrostatic potential thermodynamic deformation coordinates. However, if an element of charge dq is taken from infinity and placed in a location at the electrostatic potential 0, then dW = 0dq. Here the thermodynamic coordinates as well as the potential energies are altered. 

M. Eisenstein, Int. J. Quantum Chem., 33, 127 (1988). SCF Deformation Densities and Electrostatic Potentials of Purines and Pyrimidines. 

Deformation density maps of crystal structures were described in Chapter 9 (see Figures 9.16 and 9.17). Methods for refining data to obtain charge information was also described. From the experimental charge parameters so derived it is possible to map the electrostatic potential in the crystal,or for a molecule or group of atoms removed from the crystal. These electrostatic potential maps show which areas around a molecule are electronegative and which are electropositive. 

The radial deformation of the valence density is accounted for by the expansion-contraction variables (k and k ). The ED parameters P, Pim , k, and k are optimized, along with conventional crystallographic variables (Ra and Ua for each atom), in an LS refinement against a set of measured structure factor amplitudes. The use of individual atomic coordinate systems provides a convenient way to constrain multipole populations according to chemical and local symmetries. Superposition of pseudoatoms (15) yields an efficient and relatively simple analytic representation of the molecular and crystalline ED. Density-related properties, such as electric moments electrostatic potential and energy, can readily be obtained from the pseudoatomic properties [53]. 

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