Wave functions nodal properties

The diffusion and Greens function Monte Carlo methods use numerical wave functions. In this case, care must be taken to ensure that the wave function has the nodal properties of an antisymmetric function. Often, nodal sur-... 

HyperChem can plot orbital wave functions resulting from semi-empirical and ab initio quantum mechanical calculations. It is interesting to view both the nodal properties and the relative sizes of the wave functions. Orbital wave functions can provide chemical insights. 

Figure 11.4 also shows the orbital overlaps and nodal properties of the benzene MOs. Recall that a wave function changes sign on passing through a nodal plane and is... 

If we imagine the nuclei to be forced together to = 0, the wave function Is A + Iss will approach, as a limit, a charge distribution around the united atom that has neither radial nor angular nodal planes. This limiting charge distribution has the same symmetry as the Is orbital on the united atom, Helium. On the other hand, the combination Isa Iss has a nodal plane perpendicular to the molecular axis at all intemuclear separations. Hence its limit in the united atom has the symmetry properties of a 2p orbital. A simple correlation diagram for this case is ... 

The structure and properties of the nodal hypersurfaces of the wavefunc-tions for atomic and molecular systems have received little attention. In analytic variational calculations, the wavefunctions obtained are seldom examined, and, although electron densities are often examined, these reveal little or nothing about the node structure. Examination of the basis set of a determinantal wave-function also reveals little or nothing because the many operations of the determinant scramble the properties of the basis functions. Only recently, with knowledge of node structure required for developing Monte Carlo methods, have the structure and properties of nodal hypersurfaces been examined in detail. 

Firstly it provides a rather convenient mental picture of delocalized jr-electrons and the nodal properties of their wave functions. Secondly, it is a convenient way of remembering the number and position of the nodes in the 7r-orbitals of linear polyenes. The wave functions obtained by the HMO and FEM methods are shown in Fig. 1.31. 

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