How do I transfer all my iPhoto library to an external drive without losing the organising

My iMac's internal drive is almost full - mainly with 25,000 photos accumulated over the last 10 years. These are carefully sorted into Events, Smart Albums, etc., and given titles, ratings, etc.

As my iMac is becoming rather 'clunky' with little space left, I want to transfer most or all of my iPhoto library onto a newly purchased 1TB external hard drive to be used just for photos / movies.

I already have another external hard drive linked to Time Machine backing up everything on the iMac.

I followed Apple's support team's instruction to create iPhoto on the new external hard drive (My Passport) - and then drag and drop the existing iPhoto library onto it from the Master file.

It's successfully copied all 25,000 photos into the new iPhoto library on My Passport, but I'm dismayed to find that all the original events, titles, etc. are now all shuffled up and haphazard, with all titles, grading, etc. apparently gone.

Fortunately I haven't yet started to delete the photos on the original Iphoto library on my internal hard drive .................. but surely there's a way to 'back up' my iPhoto library without losing all the hard work I've put into the organising & editing ............isn't there ???

What am I doing wrong?