Maps of the molecular electrostatic potential

Chemical reaction dynamics is possible only for very simple systems. Chemists, however, have most often to do with medium-size or large molecules. Would it be 

We may use an electrostatic probe (e.g., a unit positive charge) to detect, which parts of the molecule like the approaching charge (energy lowering), and which do not (energy increasing). 

The electrostatic interaction energy of the point-like probe in position r with molecule A is described by the formula (the definition of the electrostatic potential produced by molecule A, see Fig. 14.13.a)  

In the Hartree-Fock or Kohn-Sham approximation (Chapter 11, p. 570 we assume the n -tuple occupation of the molecular orbital (pA.i Hi = 0,1,2) 

In order to obtain Va (r) at point r it is sufficient to calculate the distances of the point from any of the nuclei (trivial) as well as the one-electron integrals, which appear after inserting into (14.34) p (/) =2J2i WA,i(j ) - Within the LCAO MO approximation the electron density distribution pA represents the sum of products of two atomic orbitals (in general centred at two different points). As a result the task reduces to calculating typical one-electron three-centre integrals of the nuclear attraction type (cf. Chapter 8 and Appendix P), because the third centre corresponds to the point r (Fig. 14.13). There is no computational problem with this for contemporary quantum chemistry. 

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The methods applied in recent years by various groups to construct QSAR models for ART and analogues include docking calculations to heme [104, 105], CoMFA [106-109] and hologram QSAR [108] as well as the hypothetical active-site lattice (HASL) approach [107], self-organizing maps of the molecular electrostatic potential [110], quantum-similarity measures [111] and topological molecular connectivity descriptors [112]. 

Fig. 2. Equipotential contour map of the molecular electrostatic potential (MEP) of H2O at intervals of 15.94 X 10 fc(SCF/4 — 31G ). Full lines, MEP < 0 dotted lines, MEP > 0 dashed line, MEP = 0. Left section in the molecular plane a ) right perpendicular section in the symmetry plane ((t )...

Figure 1 Contour map of the negative of the molecular electrostatic potential for acetamide at the HF/3-21G( ) level calculated from the full molecular wavefunction. Shading indicates approximate value of the potential in the region. Thus, the MEP near the oxygen is negative, and the MEP near the amide hydrogens (not shown) is positive. The basis set has polarization functions only on second-row atoms.

Figure 2 Contour map of the negative of the molecular electrostatic potential for acetamide at the HF/S-ZIGI ) level calculated using the monopole approximation and the CHELP charges. Scale same as in Figure 1.

Whereas Eq.(5.58) serves for the determination of local interactions between cluster models of a zeolite and interacting molecules, analytical expressions are needed for the interaction potential if one wishes to compute vibrational frequencies for purpose of comparison with experiment or if the potentials are to be used in Monte Carlo or molecular-dynamics simulation calculations. Sauer and co-workers developed such analytical potentials for the water-silica interaction system. The method makes use of the molecular electrostatic potential (MEP) maps and the functional form of EPEN/2 (Empirical Potential based on interactions of Electrons and Nuclei). EPEN/2 potential functions consist of a point-charge interaction term and... 

Kohonen map of this molecular electrostatic potential. The Kohonen projection is made onto the surface of a torus to produce a map without beginning and without end just as the surface of a molecule. The positive electrostatic potential (dark blue) cannot be seen in three-dimensional model because it is hidden on the opposite side... 

A more sophisticated way to look at charge distribution is the molecular electrostatic potential energy map of the reactant(s). Programs like SPARTAN can compute and display the MEP of a molecule as part of its quantum mechanical repertoire. In an alternate visualization of the MEP, it is common for such graphics programs to display the electron... 

Figure 3-6. A diagram of mapping of the molecular system onto a grid in the PB model. The molecule represented with a fixed point charges is depicted in gray. The exterior is described by parameter k dependent on the ionic strength. The electrostatic potential is solved in the nodes of the 3D grid...

Mascal et al. [17] performed ab initio orbital calculations at the MP2 level of theory with the 6-31-fG basis set, including counterpoise corrections for the basis set superposition error (BSSE), for the interaction of both 1,3,5-triazine and trifluoro-1,3,5-triazine with chloride and fluoride. The molecular electrostatic potential (MEP) maps of 1,3,5-triazine and trifluoro-1,3,5-triazine clearly indicate an area of positive density concentrated on the C3 rotational axis passing through the center of the hexagonal ring and being perpendicular to the plane of the aromatic ring, similar to that observed for CeHe on the Ce rotational axis. 

An Electrostatic Preludium-The Maps of the Molecular Potential A Simple Model of Nucleophilic Substitution-MO, AD, and VB Formalisms MO Picture—> AD Picture Reaction Stages... 

Musumeci and coworkers used the molecular electrostatic potential (MEP) of drug and coformer derived from a DFT calculation to identify potential cocrystals by a hierarchical mapping of complementary donor and acceptor sites [50]. 

The description above has assumed that the property that is stored at the vertices of the tessellated icosahedron describing a molecule is either the minimal or the radial distance to the molecular surface. However, it is equally possible to store at each vertex any sort of property that can be calculated for that point in 3D space, such as the molecular electrostatic potential. Thus SPERM, like atom-mapping, allows local, property-based 3D similarity searching. 

The PCM method is one of the best known of such models. In essence, it involves the generation of a solvent cavity from spheres centered at each atom in the solute the polarization of the solvent is represented by means of virtual point charges mapped onto the cavity surface and proportional to the derivative of the solute electrostatic potential at each point, calculated from the molecular wavefunction. The point charges are then included into the one-electron Hamiltonian, and therefore they induce a polarization of the solute. An iterative procedure is performed until the wavefunction and the point charges are self-consistent. 

The results of electrostatic potential calculations can be used to predict initial attack positions of protons (or other ions) during a reaction. You can use the Contour Plot dialog box to request a plot of the contour map of the electrostatic potential of a molecular system after you done a semi-empirical or ab initio calculation. By definition, the electrostatic potential is calculated using the following expression ... 

Electron densities, bond densities, and spin densities, as well as particular molecular orbitals may be displayed as graphical surfaces. In addition, the value of the electrostatic potential or the absolute value of a particular molecular orbital may be mapped onto an electron density surface. These maps provide information about the environment around the accessible surface of a molecule. Electrostatic potential maps show overall charge distribution, while orbital maps reveal likely sites for electrophilic and/or nucleophilic attack. Surface displays may be combined with any type of model display. 

Although the most important, the electrostatic potential is not only the quantity which when mapped onto an electron density surface may provide useful chemical information. Maps of certain key molecular orbitals, in particular, the HOMO and LUMO, may also lead to informative models. Consider, for example, a map of the (absolute) value of the lowest-unoccupied molecular orbital (LUMO) in cyclohexanone, two views of which are shown below. 

The molecule below has four stereoisomeric forms exoO exoCH2Br, exoO endoCH2Br, and so on. Examine electrostatic potential maps of the four ions and identify the most nucleophilic (electron-rich) atom in each. Examine the electron-acceptor orbital (the lowest-unoccuped molecular orbital or LUMO) in each and identify electrophilic sites that are in close proximity to the nucleophilic. Which isomers can undergo an intramolecular E2 reaction Draw the expected 8 2 and E2 products. Which isomers should not readily undergo intramolecular reactions Why are these inert ... 

Repeat your analysis for tautomeric equilibria between 4-hydroxypyridine and 4-pyridone, 2-hydroxypyrimidine and 2-pyrimidone and 4-hydroxypyrimidine and 4-pyrimidone. For each, identify the favored (lower-energy) tautomer, and then use equation (1) to calculate the ratio of tautomers present at equilibrium. Point out any major differences among the four systems and rationalize what you observe. (Hint Compare dipole moments and electrostatic potential maps of the two pyridones and the two pyrimidones. How are these related to molecular stability )... 

Physicochemical properties rather than reactivities were also explored. Molecular electrostatic potential (MEP) was calculated for the [l,2,4]triazolo[4,3- ]pyridine fragment 23, according to the CHELPG algorithm. This afforded a prediction of its H-bond acceptor ability in view of the synthesis of p38 MAP kinase inhibitors <2005JME5728>. Tautomerism was also examined for compound 24, also postulated as two possible acyclic structures. The ab initio self-consistent field (SCF)-calculated energies support 24a as the most stable tautomer <1999MRC493>. 

This chapter introduces and illustrates isosurface displays of molecular orbitals, electron and spin densities, electrostatic potentials and local ionization potentials, as well as maps of the lowest-unoccupied molecular orbital, the electrostatic and local ionization potentials and the spin density (on top of electron density surfaces). Applications of these models to the description of molecular properties and chemical reactivity and selectivity are provided in Chapter 19 of this guide. 

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