Is it ever good for the DM to cause a party split?  I am sending some folks to capture the party but more than likely I will not get them all if I bring in a balanced attack thus causing the party to be split.  

A few things could happen, they try and follow then try a rescue

They just say the hell with them LOL

As I am writing this I think of If you have to ask yourself, then the answer is NO.

This should be fine as long as the captured group is still involved in gameplay. Perhaps allow them to attempt to escape or parley.

You shouldn't force your players into a situation where they have to split the party, splitting the party should be a result of player choice. All you can do is introduce scenarios that might cause them to make that choice. 

For example, in my current game we split the party while going through a dungeon because an npc we were fond of (she was dating one of the PC's) was doing some under-cover work with the campaign baddies, who were after the treasure in the dungeon we were also seeking. We, the players, told the npc to go along with the bad guys and still bring them to the dungeon (so the npc would be close by if they needed to break from the baddies and we could help them), but just to do whatever she could to slow them down so we could still get to the treasure first. 

The Plan was going OK, but then we got a message from the npc that a big bad guy general had shown up to lead the bad guy party and that they were nearly through. The npc asked the party member she was dating how she should proceed. The party member told her to do "anything for the mission... except seducing them" (in response to a previous joke about the npc having a thing for one of the baddies). Silence. We all looked at the player as she said that, who didn't seem to notice anything was wrong. She asked "what's wrong, why are you all staring at me?" We told her "you just essentially told [npc name] to make a sacrifice play. She's gonna try and fight them alone." The player looked back at us in disbelief. "No," she said slowly, "I meant just like, talk her way out, just don't cheat on me." We pointed out to her that the wording the npc used was "*anything* for the mission?" to which the player responded "yes" to. The player's eyes went wide. 

The player runs off back through the dungeon shouting about how she needs to rescue her gf, and since she's a Bard squishier than the Rogue npc she's going to rescue, I tell the Barbarian and the Cleric to go back her up while I go on with the other two npcs we are escorting to get the artifact. Everyone agrees and we spring into action. 

That is an example of a situation arising in which the DM introduces a goal with time pressure (reach the artifact before the baddies), a complication that causes us to re-evaluate the plan (bad guy general showing up), and player choice (choosing to let the baddies get to the dungeon to maintain the npc's cover,  telling the npc to stall them at any cost) resulting in the players deciding to split the party.

You can't necessarily plan for that, but you can introduce the elements that might lead to that. Get the party in a bind, use something they care about to divide their focus, and give them a choice between The Mission and The Thing. See what they do. 

Another thing you could do that I've done before is have the party split as a result of a trap. I once started a dungeon off with a forked tunnel, one entrance marked with a sun and one with a moon. Let the players talk amongst themselves which path to take, and if any players say "ok, while they're looking down the sun path, I'm just going to see what's down the moon path real quick before regrouping" or something like that. I'll confirm with the group; "ok, so it sounds like X and Y are going sun while 1 and 2 are investigating the moon path right?"

Little do the players know that a trap exists that will seal both paths behind the players once they walk through the threshold, and they'll actually find themselves committed to whatever path they choose (until later in the dungeon when they'll have the chance to discover the secret path that connects the two).

That's an example of a party split that's still the result of player choice, even if the players aren't aware of what they're choosing at the time. Because wandering into unknown situations carries with it unknown dangers, and by choosing to spread out and explore more they're engaging in a high-risk/high reward situation. Sure, they might find more treasure, but also they might find themselves cut off from each other. 

That was really long winded so thanks if you read the whole thing, and hopefully the examples helped! 

This was a mistake I made once, long ago. I split the party, thinking it would be entertaining, and my players hated it!

The problem is that there is only one DM, so at any time half the players are sitting around bored, with nothing to do. (Running back and forth does not work. Description takes more time than you anticipate, and players do not need time to consider their next actions when you want them to.)

I think this problem is sometimes missed by DMs, as they are the only ones who get to constantly play in such a scenerio.

Exactly my worries too alex. - I want to keep everyone involved.  I did not want it to feel a railroad.  I allowed them to follow and catch up to the enemy.  

I don't have to split the party. My group does it all on their own. They like to go off and investigate different aspects at the same time which has landed them in hot water more than once. Luckily we have some very creative out of the box thinkers that has saved them more than once. Probably why they keep doing it. Back story we are currently doing a mystery/intrigue game in Neverwinter.