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 5200 Å 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 \pm 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 \sim - 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 .