Contour plots hydrogen atom

Let us now turn to the influence of vibrations on exchange chemical reactions, like transfer of hydrogen between two O atoms in fig. 2. The potential is symmetric and, depending on the coupling symmetry, there are two possible types of contour plot, schematically drawn in fig. 17a, b. The O atoms participate in different intra- and intermolecular vibrations. Those normal skeleton... 

Figure 14. Contour plot of the electron density of B2H6 in the plane of the bridging hydrogen. Each hydrogen is connected to the two boron atoms by a bond path to each. In contrast, the boron atoms do not share a bond path linking them to one another. (See legend to Fig. 2 for contour values.)...

Fig. 5. Contour plot of the adiabatic potential-energy surface of an H atom in the (110) plane for the neutral H—B pair from a local-density pseudopotential calculation. The boron atom is at the center. For every hydrogen position, the B and Si atoms are allowed to relax, but only unrelaxed positions are indicated in the figure (Reprinted with permission from the American Physical Society, Denteneer, P.J.H., Van de Walle, C.G., and Pantelides, S.T. (1989). Phys. Rev. B 39, 10809.)...

Fig. 15.12 Calculated contour diagrams for the isoiobal u orbitals of [MnHj]"- (left) and (CH,) (right). The contours are plotted in a plane passing through manganese and three hydrogen atoms and through carbon and one hydrogen. (From Hoffmann, R. Angew. Chem. Itil. Ed. Engl. 1982, 21, 711-724. Reproduced with permission.]...

FIGURE 5.4 Four representations of hydrogen s orbitals, (a) A contour plot of the wave function amplitude for a hydrogen atom in its Is, 2s, and 3s states. The contours identify points at which i//takes on 0.05, 0.1, 0.3, 0.5, 0.7, and 0.9 of its maximum value. Contours with positive phase are shown in red those with negative phase are shown in blue. Nodal contours, where the amplitude of the wave function is zero, are shown in black. They are connected to the nodes in the lower plots by the vertical green lines, (b) The radial wave functions plotted against distance from the nucleus, r. (c) The radial probability density, equal to the square of the radial wave function multiplied by 1. (d) The "size" of the orbitals, as represented by spheres whose radius is the distance at which the probability falls to 0.05 of its maximum value. 

FIGURE 5.7 Contour plot for the amplitude in the orbital for the hydrogen atom. This plot lies in the x-z plane. The z-axis (not shown) would be vertical In this figure, and the x-axIs (not shown) would be horizontal. The lobe with positive phase Is shown In red, and the lobe with negative phase In blue. The x-y nodal plane Is shown as a dashed black line. Compare with Figure 5.5a. 

Figure 5 shows a contour plot of the time-dependent electron density for a hydrogen atom disturbed by a positively (displayed on left) and negatively (displayed on right) charged particle at 10 keV with an impact parameter of 1 a.u. These electronic densities correspond to a cut in the collision plane and were obtained directly from the calculated transition amplitudes u,(0 according to... 

Fig. 5. Contour plot of the time-dependent electronic density of a hydrogen atom disturbed by a 10 keV proton (on left) and antiproton (on right) at b = 1. The plot corresponds to a cut of the density across the collision plane.

Fig. 8. A SNOOPI diagram (E. K. Davies, plotting routine, 1984, Chemical Crystallography Laboratory, 9 Parks Road, Oxford, England) of the hemin chloride of 202a (50% probability contours for all atoms hydrogen atoms have been omitted for clarity the dashed bonds are used to distinguish between the strap and the porphyrin skeleton)...

The heteronuclear variant of NOESY is HOESY (Heteronuclear Overhauser Effect SpectroscopY). Figure 4.60 shows a HOESY spectmm for the tetramethylethylenediamine (tmeda) adduct of 2-lithio-l-phenylpyrrole, whose dimeric structure is also shown in the figure. The normal H and Li NMR spectra are shown along the axes of the 2D contour plot, which contains just three peaks. The lithium atom is therefore close (i.e. less than about 3.5 A) to three different sets of three protons, which can be readily identified as H(7) and H(ll), equivalent by virtue of fast rotation about the N(l)-C(6) bond in solution, H(3), and the methyl protons of the tmeda ligand. Note that the hydrogen atoms are numbered according to the numbers of the carbon atoms to which they are attached. The close contact between Li and H(11) seen in the crystal structure is thus maintained in solution, and it is of chemical significance, as it leads to... 

Figure 10.53 shows plots of L for our example diimine, HN=NH, in relief and contour modes. The nitrogen atoms show a shell structure but the hydrogen atoms do not. This is the usual appearance of atoms from different rows of the periodic table. More interesting are the valence-shell charge concentrations (CCs). 

Fig. 2.4 The hydrogen-atom and 2s orbitals. (A, B) Contour plots (lines of constant amplitude) of the wavefunctions in the plane of the nucleus, with so/id lines for positive amplitudes and dashed lines for negative amplitudes. The Cartesian coordinates x and y are expressed as dimensionless multiples of the Bohr radius (Aq = 0.529 A). The contour intervals for the amplitude are in (A) and 0.05a<, in (B). (C, D) The amplitudes of the wavefunctions as functions of the X coordinate. (E, F) The radial distribution functions...

Fig. 2.6 (A) A contour plot of the amplitude of the hydrogen-atom 2py wavefunction in the xy plane, with solid lines for positive amplitudes, dashed lines for negative amplitudes and a dot-dashed line for zero. Distances are given as dimensionless multiples of the Bohr radius. The contour intervals for the amplitude are (B) The amplitude of the 2py wavefunction in the xy plane as a function of position along the y-axis...

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...

FIG U RE 7.12 Contour plot of the potential energy surface with respect to 7th and 19th normal coordinates (Q and Q19) of malonaldehyde calculated at the level of MP2/cc-pVDZ. Q and Qi9 represent the out-of-plane vibration of the tunneling hydrogen atom and the OH stretching vibration, respectively. The contour increment is set to 800 cm . See also Figure 3 of Reference [168] and discussion therein. (Taken from Reference [183] with permission.)... 

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. 

Figure 2.1 Hydrogen atom Is orbital in (a) IDprofile, (b) 2D contour, and (c) 3D surface plot. (Seethe color version of this figure in Color Plates section.)...

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