Contour maps, wavefunction

Fig. 1.8. Dalton s atoms and the electronic states in an atom. A, a chart in Dalton s A New System of Chemical Philosophy, published in 1808. In modern symbols, these atoms are 1, H 2, N 3, C 4, O 5, P 6, S 7, Mg 8, Ca 9, Na 10, K 11, Sr 12, Ba 13, Fe 14, Zn 15, Cu 16, Pb 17, Ag 18, Pt 19, Au 20, Hg. The major modem modification to Dalton s theory is that the atoms are divisible. The contour maps in B represent typical electronic states in atoms. The outermost contour on each map represents a density of 10 A The successive contours rcpre.sent an increase of a factor of 2. The regions with dashed-curve contours have opposite phases in the wavefunction from those with solid-curve contours.

Figure 11. Contour map of hybrids 4>i-5 used for the VB structure Iq obtained by analyzing the CASSCF wavefunction at the transition state geometry for the electrophilic attachment of chlorine to ethylene in aqueous solution.

Fig. 4. The anatomy of a p-like state . Two isodensity contour maps (+ 0.01 and + 0.03 a.u." ) of the same LUMO orbital are shown side by side. Unlike the p-Uke orbitals in one-electron models, LUMO states in MQC MD-DFT and CIS models have the lobes pushed outwards between the first and the second solvation shells, with < 20% of the spin density residing inside the cavity. This results in considerable firagmentation of the diffuse part of the wavefunction. The O 2p orbitals are strongly polarized, with opposite signs of the orbitals attained by water molecules on the opposite sides of the cavity in the direction of transition dipole moment.

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.

The Wigner function for the ground state of the D-dimensional hydrogen atom cannot be evaluated in an analytically closed form. It may, however, be evaluated analytically in a representation in which the wavefunction is written as a linear combination of gaussians. Using such a representation, we have determined the Wigner function for a number of D-values. The results are displayed through a series of contour maps. 

The analysis of this wavefunction in terms of contour maps of a weighted scattering wavefunction probability density defined by... 

Fig, 5. Contour maps of the scattering-wavefunction probability density at four values of s, in constant-s planes. The vertical axis is m, while the horizontal axis is n, the distance in the col-linear plane to the or Zp axis. The "clock in the upper right corner shows the intersection of the constant-s plane with the col-linear plane. The black dot on the n axis is the collinear reaction path. Cross-hatched regions are local density maxima. The contour... 

In this chapter, we have presented an analysis of the scattering wavefunction for the three-dimensional F + H2 reaction, for total angular momentum J = 0, at the resonance energy, 0.36 eV. The results were mainly presented in terms of a series of contour maps of the weighted the weighted scattering wavefunction density. 

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...

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