Electrostatic potential maps, also known as electrostatic potential energy maps, or molecular electrical potential surfaces, illustrate the charge distributions of molecules three dimensionally. These maps allow us to visualize variably charged regions of a molecule. Knowledge of the charge distributions can be used to determine how molecules interact with one another.
Introduction
Electrostatic potential maps are very useful three dimensional diagrams of molecules. They enable us to visualize the charge distributions of molecules and
charge related properties of molecules. They also allow us to visualize the size and shape of molecules. In organic chemistry, electrostatic potential maps are invaluable in predicting the behavior of complex molecules.
静电势能图是非常有用的三维分子图示。它们可以形象的表示分子的电荷分布以及和电荷有关的特性。同时也能形象的表示分子的大小和形状。在有机化学中，静电势能图对预测复杂分子的行为意义重大。
The first step involved in creating an electrostatic potential map is collecting a very specific type of data: electrostatic potential energy. An advanced computer program calculates the electrostatic potential energy at a set distance from the nuclei of the molecule. Electrostatic potential energy is fundamentally a measure of the strength of the nearby charges, nuclei and electrons, at a particular position.
To accurately analyze the charge distribution of a molecule, a very large quantity of electrostatic potential energy values must be calculated. The best way to convey this data is to visually represent it, as in an electrostatic potential map. A computer program then imposes the calculated data onto an electron density model of the molecule derived from the Schr?dinger equation. To make the electrostatic potential energy data easy to interpret, a color spectrum, with red as the lowest electrostatic potential energy value and blue as the highest, is employed to convey the varying intensities of the electrostatic potential energy values.
Important Note
For chem 2a, it is not very important to understand the fundamentals behind electrostatic potential maps so this introduction should probably be enough, but an understanding of how to analyze electrostatic potential maps is important. For studying purposes, I suggest you largely focus on the analysis section.
Analogous System
Electrostatic potential maps involve a number of basic concepts. The actual process of mapping the electrostatic potentials of a molecule, however, involves factors that complicate these fundamental concepts. An analogous system will be employed to introduce these basic concepts. Imagine that there is a special type of mine. This mine is simply an explosive with some charged components on top of it. The circles with positive and negative charges in them are the charged components. If the electric field of the electric components are significantly disturbed, the mine triggers and explodes. The disarming device is positively charged. To disarm the mine, the disarming device must take the path of least electric resistance and touch the first charged mine component on this path. Deviating from this minimal energy path will cause a significant disturbance and the mine will explode. The specific charged components within the mine are known.
Q. How do you disarm the following mine?
The mine with positive charge and negative charge.
A. Touch the bottom most portion of negatively charged component, red, with the disarming device.
Introduction to Coulomb's Law and Electrostatic Energy
Coulomb's Law Formula
F=k(qaqb)/r2 F=force
qa =the charge of particle a qb =the charge of particle b
k=Coulomb’s constant (8.99x109 (Nm2/C2)) r= separation between particles
Electrostatic Energy Formula:
Electrostatic Energy= Force X Change in Distance
This answer to the previous question is derived from physics. The charged components in this mine create an electric field. A charged particle, the disarming device, , experiences a force when in an electric field. To touch the charged component, the disarming device must be moved. This involves electrostatic energy. Electrostatic energy is the energy required to move a charged particle through an electric field. Coulomb's Law predicts the force, but the distance is a arbritary. Provided that the disarming device starts from the same distance from the two charges, both indepedently, the energy involved in moving the positively charged disarming device toward the negatively charged component is significantly lower than the energy associated with the alternative pathway. It is important to note that both components affect the particle and that the total energy involved in moving the particle is the sum of the energy required to move the particle along the pathway with respect to each charged component. Consequently the absolute minimum energy pathway is attained when the particle begins and ends as far from the positive component as possible.
Total Energy= Electrostatic Energy
Analogous Introduction to Electrostatic Potential Mapping
But what if the mine looks like this?
Note: the size of the component is directly related to the magnitude of the charge.
There is no equation that would simply provide an answer. A sequence of electrostatic energy equations must be carried out. To solve this problem, measure the energy required to touch the every single point on the surfaces of these component. Then find the minum value calculated to find your answer. But note the variability in distance. Each starting point would result in a different energy value. Scientists found a way to factor out this variability by using Potential Energy.
Introduction to Potential Energy
Potential energy is a measure of the work it takes to move a charged particle from an infinite distance to a particular distance in an electric field, where zero is the origin of the electric field. A particle at an infinite distance experiences zero force from the electric field.
Thus the potential energy is solely the force acting on the particle at the final distance times the distance the particle is from the source of the field.Thus the equation for electrostatic potential energy is Coulomb's law times the radius which, simplified, is the equation shown below. This is equivalent to the definite integral of Coulomb’s Law integrated from infinity to the final position.
Note that one of the charges in the electrostatic potential energy equation is the charged component in the mine, and the other charge must be the positively charged disarming device. the disarming device is a test charge in this scenario.
Additionally, note that the prior total energy is now the total electrostatic potential energy.
Why Use Electrostatic Potential Maps?
The total energy of a pathway is the sum of the energies of the particle interacting with every electric field producing component along the pathway. It requires the sum of nine separate electric potential equations to find the electric potential at one point. Each position on the surface of the components experiences a different total potential energy. To get an accurate indication of the absolute minimum energy, presume it would take ten readings per component. There are nine components, ten readings per component, and ten calculations per reading. To find the total range of potential energies would take 900 calculations.
How do you go about using 900 sets of data? You could graph it, the electrostatic potentials are clear pieces of data, but creating coordinates that correspond to specific locations on specific charged components is a complicated process that convolutes the interpretation of the data.
The best way to represent this data is to map it, imposing the data onto a model that is analogous to the real object to preserve the spatial coordinates of the data. It would then be possible to place the electrostatic potential values with their corresponding positions. But it would be inconvenient to analyze the trends of 900 numerical electrostatic potentials on a map. To resolve this issue, a color spectrum could be incorporated.
Spectral extremes would be associated with extremes in electrostatic potential energy, and the color coded map would be easy to interpret and understand. Color the calculated points on the replica model with the corresponding electrostatic energy potentials color, extrapolate the
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