The most important quantitative aspects of computational structural crystallography can be introduced in a satisfactory way using 1D truncated and periodic Gaussian functions to represent the atoms in a crystal lattice. This paper describes in detail and demonstrates 1D structural crystallography starting with the definition of such truncated Gaussians. The availability of the computer programme CRONE makes possible the repetition of the examples provided in the paper as well as the creation of new ones.

A simple and easy to implement method for improving the convergence of a power series is presented. We observe that the most obvious or analytically convenient point about which to make a series expansion is not always the most computationally efficient. Series convergence can be dramatically improved by choosing the center of the series expansion to be at or near the average value at which the series is to be evaluated. For illustration, we apply this method to the well-known simple pendulum and to the Mexican hat type of potential. Large performance gains are demonstrated. While the method is not always the most computationally efficient on its own, it is effective, straightforward, quite general, and can be used in combination with other methods.

Extreme ultraviolet spectra of highly charged tungsten ions were produced with an electron beam ion trap at the National Institute of Standards and Technology and recorded with a flat-field grazing-incidence spectrometer. The spectra were measured in the wavelength range 2.7-17.3 nm while the beam energy varied between 1.65 and 2.00 keV. At these energies, the ionization stages from Zr-like W to Se-like W ions were observed. Large-scale collisional-radiative modelling was used to identify the strong lines, including 15 new ones, which represent electric dipole = 4-4 transitions in these ions. While a good quantitative agreement between theoretical and experimental data was found for almost all ions, some of the tentatively identified wavelengths in W significantly disagree from all available calculations.