The Delta a photometric system provides an efficient observational method to identify and distinguish magnetic and several other types of chemically peculiar (CP) stars of spectral types B to F from other classes of stars in the same range of effective temperatures. We have developed a synthetic photometric system which can be used to explore the capability of model atmospheres with individual element abundances to predict photometric Delta a magnitudes which measure the extent of the flux depression around 5200A found in different types of CP stars. In this first paper, we confirm the observed dependency of the a-index as a function of various colour indices sensitive to the effective temperature of stars as well as its average scatter expected from surface gravity variations within the main sequence band. The behaviour of the so-called normality line of Delta a systems used in photometric observations of CP stars is well reproduced. The metallicity dependence of the normality line of the Delta a system was computed for several grids of model atmospheres where the abundances of elements heavier than He had been scaled +-0.5 dex with respect to the solar value. We estimate a lowering of Delta a magnitudes for CP stars within the Magellanic Clouds by approximately -3 mmag relative to those in the solar neighbourhood assuming an average metallicity of [Fe/H]= -0.5 dex. Using these results on the metallicity bias of the Delta a system we find the observational systems in use suitable to identify CP stars in other galaxies or distant regions of our own galaxy and capable to provide data samples on a statistically meaningful basis. In turn, the synthetic system is suitable to test the performance of model atmospheres for CP stars. This work will be presented in follow-up papers of this series.