The Electrostatic Potential

One of the fundamental objectives of chemistry is the prediction and rationalization of molecular reactivity. In principle, this involves the construction of an 

We can distinguish between static theories, which in essence give a description of the electron density, and dynamic theories, where an attempt is marie to measure the response of a molecule to (e.g.) an approaching N02 ion. In recent years, the electrostatic potential has been used to give a simple representation of the more important features of molecular reactivity. It can be calculated quite easily at points in space  

Finally we computed the exact atomic electrostatic potential and its value obtained via multipole expansion for molecules including molecular nitro- 

We then tried to understand the cause of this excellent convergence behaviour. How can it be compatible with the admittedly highly non-spherical shape of the topological atoms The answer [142] lies in the exponentially decaying electron density. The convergence behaviour of the electron density inside an atomic basin is due to its decay rather than to the atom s shape. Indeed when the atom is filled with a uniform density the convergence worsens. 

The PPD and shell models are nearly equivalent in this sense, because they model the electrostatic potential via static point charges and polarizable dipoles (of either zero or very small extent). Accuracy can be improved by extending the expansion to include polarizable quadrupoles or higher order terms.The added computational expense and difficulty in parameterizing these higher order methods has prevented them from being used widely. The accuracy of the ESP for dipole-based methods can also be improved by adding off-atom dipolar sites. 

Despite the many differences between the various polarizable models, it is encouraging to note that the most recent models seem to be converging on the same set of necessary features. A variety of successful models based on different formalisms all share many of the same characteristics.Regardless of the direction from which the models evolved, there is a growing consensus that accurate treatment of polarization requires (1) either diffuse charge distributions or some other type of electrostatic screening (2) a mixture of both monopoles and dipoles to represent the electrostatic charge distribution, and (3) only linear polarizability. 

Although much work remains to be done before there is a truly accurate, transferable model for a wide range of conditions and systems, it is fair to say that polarizable models have matured considerably since their earliest implementations. Future developments will almost certainly include continued development and parameterization of the more mainstream models, along with their incorporation into commercial and academic simulation software 

Future directions in the development of polarizable models and simulation algorithms are sure to include the combination of classical or semiempir-ical polarizable models with fully quantum mechanical simulations, and with empirical reactive potentials. The increasingly frequent application of Car-Parrinello ab initio simulations methods may also influence the development of potential models by providing additional data for the validation of models, perhaps most importantly in terms of the importance of various interactions (e.g., polarizability, charge transfer, partially covalent hydrogen bonds, lone-pair-type interactions). It is also likely that we will see continued work toward better coupling of charge-transfer models (i.e., EE and semiem-pirical models) with purely local models of polarization (polarizable dipole and shell models). 

McCammon and S. C. Harvey, Dynamics of Proteins and Nucleic Acids, Cambridge 

Wakeham, and G. C. Maitland, The Forces Between Molecules, 

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The electrostatic potential within a phase, that is, l/e times the electrical work of bringing unit charge from vacuum at infinity into the phase, is called the Galvani, or inner, potential Similarly, the electrostatic potential difference... 

The electrostatic potential generated by a molecule A at a distant point B can be expanded m inverse powers of the distance r between B and the centre of mass (CM) of A. This series is called the multipole expansion because the coefficients can be expressed in temis of the multipole moments of the molecule. With this expansion in hand, it is... 

In these equations the electrostatic potential i might be thought to be the potential at the actual electrodes, the platinum on the left and the silver on the right. However, electrons are not the hypothetical test particles of physics, and the electrostatic potential difference at a junction between two metals is nnmeasurable. Wliat is measurable is the difference in the electrochemical potential p of the electron, which at equilibrium must be the same in any two wires that are in electrical contact. One assumes that the electrochemical potential can be written as the combination of two tenns, a chemical potential minus the electrical potential (- / because of the negative charge on the electron). Wlien two copper wires are connected to the two electrodes, the... 

The atomic scattering factor for electrons is somewhat more complicated. It is again a Fourier transfonn of a density of scattering matter, but, because the electron is a charged particle, it interacts with the nucleus as well as with the electron cloud. Thus p(r) in equation (B1.8.2h) is replaced by (p(r), the electrostatic potential of an electron situated at radius r from the nucleus. Under a range of conditions the electron scattering factor, y (0, can be represented in temis... 

Task 1 Calculate the first non-vanishing multipole moment of the electrostatic potential of composed objects (i.e., structural units and clusters). 

Gilson, M. K., Sharp, K. A., Honig, B. H. Calculating the electrostatic potential of molecules in solution Method and error assessment. J. Comp. Chem. 9 (1988) 327-335. 

If there are ions in the solution, they will try to change their location according to the electrostatic potential in the system. Their distribution can be described according to Boltzmarm. Including these effects and applying some mathematics leads to the final linearized Poisson-Boltzmann equation (Eq. (43)). 

The calculation of autocorrelation vectors of surface properties [25] is similar (Eq. (21), with the distance d XiXj) between two points and Xj on the molecular surface within the interval between d[ and d a certain property p, e.g., the electrostatic potential (ESP) at a point on the molecular surface and the number of distance intervals 1). 

The representation of molecules by molecular surface properties was introduced in Section 2.10. Different properties such as the electrostatic potential, hydrogen bonding potential, or hydrophobicity potential can be mapped to this surface and seiwe for shape analysis [44] or the calculation of surface autocorrelation vectors (refer to Section 8.4.2). 

The possibilities for the application for neural networks in chemistry arc huge [10. They can be used for various tasks for the classification of structures or reactions, for establishing spcctra-strncturc correlations, for modeling and predicting biological activities, or to map the electrostatic potential on molecular surfaces. 

If you calculate the electrostatic potential for cyclopropane, three minima occur in regions that bisect the carbon-carbon bonds. This result IS consistent with protonalion of cyclopropane occurring along Ih e bond bisector. 

IlyperChetn displays the electrostatic potential as a contour plot when you select th e appropriate option in th e Con tour Plot dialog box. Choose the values for the starting contour and the contour increment so that you can observe the minimum (typically about 0.5 for polar organ ic molecules) and so that the zero potential line appears. 

The second summation is over all the orbitals of the system. This equation is used in IlyperChem ah imiio calculations to generate contour plots of electrostatic potential, [fwe choose the approximation whereby we n eglect the effects of the diatomic differen tial overlap (NDDO). then the electrostatic potential can be rewritten... 

The electrostatic potential at a point r, 0(r), is defined as the work done to bring unit positive charge from infinity to the point. The electrostatic interaction energy between a point charge q located at r and the molecule equals The electrostatic potential has contributions from both the nuclei and from the electrons, unlike the electron density, which only reflects the electronic distribution. The electrostatic potential due to the M nuclei is ... 

Non-covalent interactions between molecules often occur at separations where the van der Waals radii of the atoms are just touching and so it is often most useful to examine the electrostatic potential in this region. For this reason, the electrostatic potential is often calculated at the molecular surface (defined in Section 1.5) or the equivalent isodensity surface as shown in Figure 2.18 (colour plate section). Such pictorial representations... 

I is the bond length. The experimental quadrupole moment is consistent with a charge, q, of approximately 0.5e. In fact, a better representation of the electrostatic potential around the nitrogen molecule is obtained using the five-charge model shown in Figure 4.20. 

Two charge models for N2 with the electrostatic potentials that they generate. Also shown is the... 

The electrostatic potential at a point is the force acting on a unit positive charge placed at that point. The nuclei give rise to a positive (i.e. repulsive) force, whereas the electrons give rise to a negative potential. The electrostatic potential is an observable quantity that can be determined from a wavefunction using Equations (2.222) and (2.223) ... 

Price S L, R J Harrison and M F Guest 1989. An Ab Initio Distributed Multipole Study of the Electrostatic Potential Around an Undecapeptide Cyclosporin Derivative and a Comparison with Point Charge Electrostatic Models. Journal of Computational Chemistry 10 552-567. 

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