An efficient dye sensitized solar cell (DSSC) is one possible solution to meet the world's rapidly increasing energy demands and associated climate challenges. This requires inexpensive and stable dyes with well-positioned frontier energy levels for maximal solar absorption, efficient charge separation, and high output voltage. Here we demonstrate an extensive computational screening of zinc porphyrins functionalized with electron donating side groups and electron accepting anchoring groups. The trends in frontier energy levels versus side groups are analyzed and a no-loss DSSC level alignment quality is estimated. Out of the initial 1029 molecules, we find around 50 candidates with level alignment qualities within 5% of the optimal limit. We show that the level alignment of five zinc porphyrin dyes which were recently used in DSSCs with high efficiencies can be further improved by simple side group substitutions. All frontier energy levels, gaps and level alignment quality values are stored in a database publicly available.