Contour plots hydrogen molecule

Fig. 1. Molecular electrostatic potential contour plot (values in au) for a portion of the benzene molecule in the molecular plane. Carbon nuclei are located at C and D with the hydrogen nuclei at C and >. Saddlepoint-like structures are seen at the points P and F. (Reproduced from [9] copyright-American Institute of Physics)...

To illustrate the effect of mass-weighting or mass-scaling the coordinates, consider two noninteracting hydrogen molecules. The potential energy is a function of the two internuclear separations, r and r2- For small displacements from the equilibrium positions, a contour plot of the potential energy surface looks like a series of concentric circles. If the hydrogen molecules are each... 

Fig. 2.8 Contour plots of the wavefunction amplitudes for the highest occupied molecular orbital HOMO) and lowest unoccupied molecular orbital (LUMO) of 3-methylindole. Positive amplitudes are indicated by solid lines, negative amplitudes by dotted lines, and zero by dot-dashed lines. The plane of the map is parallel to the plane of the indole ring and is above the ring by o as in Fig. 2.7, panels D and E. The contour intervals for the amplitude are 0.05ao. Small contributions from the carbon and hydrogen atoms of the methyl group are neglected. The straight black lines indicate the carbon and nitrogen skeleton of the molecule. The atomic coefficients for the molecular orbitals were obtained as described by Callis [37-39]. Slater-type atomic orbitals (Eq. 2.40) with with f = 3.071/A (1.625/ao) and 3.685/A (1.949/ o) were used to represent C and N, respectively...

The most elementary example of course is just the H2 molecule. As described by equations (4) or (17), there are two orbitals, 0a and 0b which overlap. These are displayed in Figure 3. On the right of the figure, contour plots of the two orbitals are shown, while on the left, orbital 0a is shown as a three-dimensional shape with the intemuclear axis superimposed. As the intemuclear distance R increases, the deformation of each orbital 0a and 0b decreases to 0, leaving just a pure hydrogen Is orbital on each atom. 

Fig. 5.4. The one- and twc-electron density functions of the bonding. o ) (upper plots) and antibonding 11ct > (lower plots) configurations of the hydrogen molecule on the molecular axis (atomic units). The two-electron densities are represented by surface and contour plots. In the contour plot for the antibonding configuration, the two-electron nodes are represented by dashed lines. The density functions have been calculated in a minimal basis of hydrogenic Is functions with unit exponents.

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