Using the APEX sub-millimeter telescope we have investigated the ^ { 12 } CO ( 3 - 2 ) emission in five face-on nearby barred spiral galaxies , where three of them are high surface brightness galaxies ( HSBs ) lying at the Freeman limit , and two are low surface brightness galaxies ( LSBs ) . We have positive detections for two of three HSB spirals and non-detections for the LSBs . For the galaxies with positive detection ( NGC0521 and PGC070519 ) , the emission is confined to their bulges , with velocity dispersions of \sim 90 and \sim 73 km s ^ { -1 } and integrated intensities of 1.20 and 0.76 K km s ^ { -1 } , respectively . For the non-detections , the estimated upper limit for the integrated intensity is \sim 0.54 K km s ^ { -1 } . With these figures we estimate the H _ { 2 } masses as well as the atomic-to-molecular mass ratios . Although all the galaxies are barred , we observe ^ { 12 } CO ( 3 - 2 ) emission only for galaxies with prominent bars . We speculate that bars could dynamically favor the ^ { 12 } CO ( 3 - 2 ) emission , as a second parameter after surface brightness . Therefore , secular evolution could play a major role in boosting collisional transitions of molecular gas , such as ^ { 12 } CO ( 3 - 2 ) , especially in LSBs .