Initial observations by Samson of the far-uv photoabsorption by molecules suggest that the spectrum of photoelectrons emerging from a multicenter molecular field is modulated by interferences. This effect is discussed in terms of Huygens' approach and of a partial-wave analysis with a Born-approximation calculation. It is compared with processes of diffraction by molecules. It appears related to the onset of photoionizing transitions to states of increasing orbital momenta which occurs at increasing photon energies.

A method for the calculation of the dipole polarizabilities of closed-shell atomic systems is presented. This method involves the direct calculation of the Hartree—Fock wavefunction of the atom in the presence of the perturbing field. The orbitals are expressed as linear combinations of Slater-type functions. A large number of carefully chosen and optimized basis functions are used so as to assure a good fit to the true Hartree—Fock wavefunction. The polarizability is then calculated from the limiting value of α=p/F for F=0, where F is the electric field strength, and p is the induced dipole moment.

Results are presented for the electronic-dipole polarizabilities of the isoelectronic series of helium and beryllium in the presence of a finite electric field. These calculations were done analytically, but large numbers of carefully chosen and optimized basis functions were used in order to assure a good fit to the exact solution for the perturbed Hartree—Fock wavefunction. It was found that the polarizabilities of the helium series increase, and those of the beryllium series decrease, as the field increases.

SUMMARYAn algorithm is given to discretize a polygon or curved surface into triangular arrays. The method first involves the manual division of the array into quadrilaterals with specified numbers on rows and columns. The individual points are then filled in automatically and elements are automatically generated. A point of particular importance is that the number of columns or rows may be made to change. A subroutine is given to perform this task.Edgeberg' and Zienkiewicz and Phillips' proposed a method for generating two-dimensional grid structures by first manually partitioning the domain into quadrilaterals (the 'piece and side' method). In each of these quadrilaterals the number of points on each side was restricted to the same number as those on the opposite side. While the method has proved quite useful in partitioning many types of structure, it often requires complex and inconvenient structures involving triangles (a special case of the generalized quadrilateral) in order to change the number of points in one direction. THE METHODOur method of discretizing a quadrilateral region is based on a method of storing its elemental corner points. They are arranged in rows and columns with no more columns at the top than at the bottom. Such a set of consecutively numbered points is shown in Figure 1.Note that there are two types of regions in this structure: one in which the number of columns is constant, and the other in which the columns decrease with descending rows. The top array may be treated by the method of Zienkiewicz and Phillips, while the bottom array must be treated differently. The elements are connected as shown in Figure 2. The method of connecting the points in the bottom rows is unique. The actual location of the points can be specified by a procedure similar to a transfinite i n t e r p~l a t i o n~.~ or a Coons patch.5 The location (x, y) of each point is given bywhere s = -1 + 2 ( i -l)/(n, -l), and t = -1 + 2 ( j -l)/(nc -1). The number of the row from the top is i, and n, is the total number of rows. The number of the column from the left is j, and n, is the total number of columns for that particular point. The vector location of the kth corner of the quadrilateral piece has been given as (x, y), and the number of these corners starts in the lower left corner and increases counterclockwise. Examples of the row and column blending functions, f and g, are given in Table I.

Self-consistent-field calculations have been performed by the Hartree-Fock-Roothaan method for a number of excited states of Cu and Cu + . A large number of carefully chosen and optimized Slater-type basis functions are used in order to assure a good fit to the true self-consistent-field function.