Geometry-dependent charges

One of the deficiencies of the force fields in use today is that they commonly use the fixed charge approximation, whereas in reality the atomic charges vary in response to changes of both the molecular conformation and the environment. Obviously, a scheme with geometry-dependent charges would extend capabilities of the force field methods. 

One of the force fields with geometry-dependent charges was mentioned above. A model with such charges (Eq. [24]) was employed by Hill and Sauer ° within the ab initio parameterized MM force field model for protonated aluminosilicates. Deficiencies of the scheme originate from the absence of a solid theoretical background for the model it is just a first-order Taylor expansion of atomic charges with respect to distances between bonded atoms, and it neglects the influence of the environment. In addition, its parameterization is hampered by the use of bond rather than atomic parameters. 

In 1996 a force field model was proposed in which geometry-dependent charges are calculated by EEM. This model, called consistent implementation of the electronegativity equalization method (CIEEM), combines a force field representation for the PES (e.g., Eq. [19]) with the EEM equation for the electronic energy (Eq. [7]) in such a way that the atomic terms of Eq. [7] explicitly enter the expression for the potential energy. Thus, within the CIEEM, the expression for the steric energy in the MM force field model will read... 

The use of a force field model with geometry-dependent charges implies that dqlda, where a = x,y, z, must be evaluated in both energy minimization and MD calculations. Calculation of these charge derivatives can be avoided, however, in the CIEEM approach, which also simplifies the calculations when using a second derivative minimizer. 

A. C. T. van Duin, J. M. A. Baas, and B. van de Graaf, /. Chem. Soc., Faraday Trans., 90, 2881 (1994). Delft Molecular Mechanics A New Approach to Hydrocarbon Force Fields. Inclusion of a Geometry-Dependent Charge Calculation. 

Burnham, C. J., Xantheas, S. S. (2002b). Development of transferable interaction models for water. IV. A flexible, all-atom polarizable potential (TTM2-F) based on geometry dependent charges derived from an ab initio monomer dipole moment surface. Journal of Chemical Physics, 116,1479-1492. 

C. J. Burnham and S. S. Xantheas,/. Chem. Phys., 116(12), 5115-5124 (2002). Development of Transferable Interaction Models for Water. III. A Flexible, All-Atom Polarizable Potential (TTM2-F) Based on Geometry Dependent Charges Derived from an Ab Initio Monomer Dipole Moment Surface. 

In contrast to the point charge model, which needs atom-centered charges from an external source (because of the geometry dependence of the charge distribution they cannot be parameterized and are often pre-calculated by quantum mechanics), the relatively few different bond dipoles are parameterized. An elegant way to calculate charges is by the use of so-called bond increments (Eq. (26)), which are defined as the charge contribution of each atom j bound to atom i. 

Dinur U and A T Hagler 1995. Geometry-Dependent Atomic Charges Methodology and Application to Alkcmes, Aldehydes, Ketones and Amides. Journal of Computational Chemistry 16 154-170. 

Obviously, the charges are geometry dependent because of the last term in Eq. [8]. The EEM scheme derived for a molecule can be extended to macromolecu-lar systems where equilibration of electronegativities occurs within parts of the system rather than in the system as a whole. Such an extension leads to an (N + M) X (N + M) matrix equation, where N is the total number of atoms and M the number of separate parts in the system. Equation [8] can also be adapted to include the long-range character of the electrostatic interactions and the periodicity of zeolite structures. 

There are numerous attempts to channel the different empirical observations and geometry dependences chemical shifts into predictive schemes, and some of them have been successfully used in structure elucidation. One of these models is CHARGE(X) where X reached 5 in recent publications. The central point is that for protons and certain other resonances a correlation of atomic charges with chemical shifts was observed. Within the framework of the bond polarization theory we arrive in the case of a proton at a linear dependence with just one parameter for its chemical shift and for the atomic charge. Therefore, one dependence can be easily calculated from the other. 

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