Molecular orbitals plots

Fig. 9.13 Molecular orbital plots. The LUMO of compound H (left) is located on the 1,4-dihydropyri-...

The superiority of the molecular orbital approach is clear the activation energy is always positive which is not the case with the CFT, and the molecular orbital plot is quite a faithful reproduction of the observed log (rate) curve. The failure of the CFT is due to the following reason. In the absence of n bonding, Fig. 8 shows that the lowest three d orbitals are equienergetic (b2 + e) for the square-based pyramid, but the nature of the CF method removes this accidental degeneracy considerably. In terms of Dq, the CF energies of the d... 

Figure 20-5. Molecular orbital plots of neural 5 -dTMPH, calculated using the B3LYP/6-31G method. B3LYP/6-31G calculated orbital energies along with scaled values are given in eV. In parentheses the experimental VOEs of thymine (Ref. [94]) are given in eV. (Reprinted with permission from ref. [209], J. Phys. Chem. (2007) American Chemical Society.)...

Tel. 800-424-9737, fax 415-491-8311 (U.S.A.), tel. 41-38-337633 (U.K.) Model building, display, charge density, electrostatic potential, and molecular orbital plots. Stick, sphere, and dot surface display. 2D to 3D conversion. Protein and DNA fragment libraries. MM+, BIO+ (implementations of MM2 and CHARMM, respectively), OPLS, and AMBER molecular mechanics and dynamics. Solvent box. Semiempirical calculations by Extended Hiickel, CNDO, INDO, MINDO/3, MNDO, AMI, and PM3. Originated at Hypercube, Inc. (Dr. N. Ostlund et al.), of Ontario, Canada. Runs under Windows on a 386 or 486 PC and under Motif on a Silicon Graphics workstation. 

Before we move on to the molecular orbital plots, we should consider degenerate MOs briefly. Confusion often arises because we have been taught, for instance, to expect the degenerate HOMOs of benzene to have nodal planes through two opposite carbon atoms and perpendicular thereto (Fig. 5.14). 

Molecular orbitals (plots of tp) derived from combination of two Is atomic orbitals (a) combination by addition and (b) combination by subtraction. Electrons in the bonding MO spend most of their time in the region between the two nuclei and bond the atoms together. Electrons in the antibonding MO lead to repulsion between nuclei and decrease bonding. 

IlyperCl hem can display molecular orbitals and the electron density ol each molecular orbital as contour plots, showing the nodal structure and electron distribution in the molecular orbitals. 

I he electron density distribution of individual molecular orbitals may also be determined and plotted. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are often of particular interest as these are the orbitals most cimimonly involved in chemical reactions. As an illustration, the HOMO and LUMO for Jonnamide are displayed in Figures 2.12 and 2.13 (colour plate section) as surface pictures. 

Wave functions can be visualized as the total electron density, orbital densities, electrostatic potential, atomic densities, or the Laplacian of the electron density. The program computes the data from the basis functions and molecular orbital coefficients. Thus, it does not need a large amount of disk space to store data, but the computation can be time-consuming. Molden can also compute electrostatic charges from the wave function. Several visualization modes are available, including contour plots, three-dimensional isosurfaces, and data slices. 

Once you have calculated an ab initio or a semi-empirical wave function via a single point calculation, geometry optimization, molecular dynamics or vibrations, you can plot the electrostatic potential surrounding the molecule, the total electronic density, the spin density, one or more molecular orbitals /i, and the electron densities of individual orbitals You can examine orbital energies and select orbitals for plotting from an orbital energy level diagram. 

You can use the semi-empirical and ab initio Orbitals dialog box in HyperChem to request a contour plot of any molecular orbital. When requested, the orbital is contoured for a plane that is parallel to the screen and which is specified by a subset selection and a plane offset, as described above. The index of the orbital and its orbital energy (in electron volts, eV) appears in the status line. 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

Many of the figures given in Section II are actually simplified plots of the molecular orbitals. From any MO calculation, these are given by a set of coefficients, c,7, in the linear combination of AOs Xj (LCAO) ... 

Figure 2. Minimum atomic localization energy in benzenoid hydrocarbons plotted against energy of the highest occupied molecular orbital (HOMO).

Fig. 11. Top molecular orbital energies for precursor, structure C (broken lines) and for bridged intermediate, structure D (full lines). Bottom bridging energy (AE) for N =0 (full line) and N = 1 (broken line), where N is the number of electrons transferred from the carbon residue to the platinum. The energies are plotted as functions of the 7rC3-to-platinum overlap integral (S). The energy unit 0 [ is the absolute value of the exchange integral between a pair of p1 orbitals in benzene. For structures C and D, cf. reaction (7). After J. R. Anderson and N. R. Avery, J. Calal. 7, 315 (1967).

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