Orbital plots

For many reasons, including the Woodward-Hoffman rules that describe the likelihood of reaction based on arguments about the shapes of orbitals, it is desirable to be able to visualize molecular orbitals. 

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. 

If a molecule is rotated by changing the position of the viewer (left mouse button rotation) then the molecule s position in the molecular coordinate system has not changed and another contour plot can be requested without recomputing the wave function. That is, many orbitals can be plotted after a single point ab initio or semi-empirical calculation. Any contour map is available without recomputation of the wave function. 

When you request an orbital, you also request a plot of either the orbital itself or of its square. The orbital /j is a signed quantity with 

When you request an orbital, you can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LUMO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

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

Figure 1 illustrates for four molecular waveftinctions that split-localized MOs generate Cl expansions whose configurational convergence is markedly faster than that of the Cl expansions generated by natural orbitals. Plotted are the truncation errors due to Cl truncations versus the number of determinants in the truncated Cl expansions. 

As we have indicated, the fully-variational SC calculations along the 6 in 6 CASSCF IRC curves were performed with CASVB, as implemented in MOLPRO [19]. An older SC code [27] was employed only at the transition structures and at the ends of the calculated IRC segments, mainly in order to assist orbital plotting. 

Figure 2.12. Schematic N 2p and Cu 3d orbital plots. The top figure shows the surface from above with the N sitting in a hollow adsorption site surrounded by four Cu atoms. The bottom picture shows a side-view with a Cu atom from the second layer located directly below the N atom. From Ref. [27].

Figure 2.13. Schematic N 2px, N 2py and Cu 3d orbital plots at the different high symmetry points in the surface Brillouin zone. Note that the degeneracy is lifted at the X point where both N 2px and N 2py orbitals are shown. From Ref. [3].

Let us now turn to the -system. The important adsorbate-orbitals of a-symmetry are depicted in Figure 2.23. From the orbital plots we observe the same polarization as the experimental and theoretical XES spectra indicate, 4a to the inner atom and 5 a to the outer nitrogen atom. The experimental XES spectra do not indicate any intensity in the 4a orbital on the outer nitrogen atom. However, from inspection of the orbital plot we can attribute the component on the outer nitrogen to N 2s character. It is interesting to note that the charge redistribution of the 5 cr orbital into the adsorbate 5cr orbital goes in opposite direction compared with a a donation picture. We also show a da orbital which mainly consists of metal character and can be seen in the XES spectra between the 5a state and the Fermi level. 

Fig. 1. Contour plots of the four unique orbitals in the single-configuration spin-coupled solution for BH3, at / bh=2.24 a . All plots are drawn in the plane of the nuclei. The upper two plots (contours every 0.2 a.u.) depict the two fully-symmetric inner orbitals. The lower two plots (contours every 0.05 a.u.) depict one of the three symmetry-related orbital pairs. The other two pairs can be obtained by rotations through 120° about an axis going through each orbital plot s origin and perpendicular to the plane of the paper (the molecule s C3 axis). All orbitals are normalized.

The orbitals plotted in Figures 11 and 12 are generalized hybrids they are mainly defined on one atom but they show contributions also from neighbouring centres. 

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.)...

Figure 21-23. Unpaired electron orbital plotted with a contour line spacing of 0.03 bohr-3/2 for the two most stable anions of (i) AT pair and (ii) MAMT pair (Figure 2 of [49]. Reprinted with permission. Copyright 2005 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. 

Figure 3 Eg values of 1-D silicon clusters as a function of the size. The calculated Eg values are with ( ) and without (A) silicon 3d orbitals plotted by broken curves. The solid curve shows the Eg values evaluated from Matsumoto s QW model.

Computer-Aided Composition of Atomic Orbitals. Molecular orbital calculations with extended Hiickel method, orbital plots, and Walsh diagrams. Also available via anonymous ftp from cacao.issecc.fi.cnr.it (149.139.10.2). PCs. 

It has been shown that the XES spectra can be simulated using DFT calculations with excellent agreement with experiment. In Fig. 12.7, orbital plots for gas phase... 

Fig. 1.7 Plots of the square of the wave function for the molecular orbitals of H2 (solid lines) and its component atomic orbitals (dashed lines). [The atomic orbital plot is scaled down by a factor of 2 to allow us to compare a2 with the sum of...

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