You can't catch Mespirit if you killed it, it will mysteriously disappear in the game.
It's the same thing as if you defeat a Legendary Pokemon, you won't have another chance to catch it.
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by searching in the grass
Well you would think on Dialga but no, you should use it on Mespirit because when you try to catch Mespirit it keeps running away from you so you mite as well get it on your first try.
Yes, it does it causes cresselia and mespirit to not run away for a few turns.
Dialga, Giratina, Heatran, Mespirit, Uxie, Azelf, Regigigas, Rotom, Cresselia,
After you defeat/catch Dialga(Palkia)go to any of the 3 lakes (Snowpoint, Twinleaf or place with hotels) use surf, travel into middle, one is Mespirit (runs off, Rowan comes) another is Uxie (intelligent so really hard to catch) and Azelf (what i think as the easiest one to catch)also, when and if you find cresselia, it'll run off like mespirit.