Should I ask for more details about the second interview round or just wait?

Question

Exactly 1 week ago (Thursday morning) I did an interview with a potential new employer.
The director was leading the interview, and apparently the interview went pretty well as the afternoon of the same day he sent me an e-mail inviting me for a second round (during the interview he told me he would get back to me only the week after).
In the e-mail the director wrote something like: "we would like to invite you to a second interview round. If you accept I'll come back next week with more details".
Of course I accepted.

Now 1 week passed by and I still didn't receive any details about it. I'm very interested in the job, so I'm eager to proceed further.
Should I send him an e-mail and ask? If so, what's the most appropriate way of doing this?

Answer 1

"Next week" doesn't mean exactly one week after, it could be anytime during the next week. I would wait until the week is up before sending an email and then reply to his previous email with something like:

Hello Director, just following up on the details for the next interview. Look forward to hearing from you.

You need to keep in mind that the director has other priorities besides your candidacy and may be busy with them. Give him the benefit of the doubt.

Answer 2

Tricky.

I believe it's time to send an email.

I would go ahead and email Director and ideally cc others involved:

Ideally simply "quote" Director's email where he offered a second meeting, if you still have that, you're golden.

"Dear Director, again thanks for the interview last Thursday. Again I'm certainly ready and standing by for any further questions or interviews! Thanks again! Johnnie Keen
{ quoted email ... }

I think you're good to go - you should do it right now.

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One further thought. I always suggest in negotiation/communications advice, a little enthusiasm never hurts.

I, personally, would write more like this:

"Dear Director, again thanks for the interview last Thursday. As you know I'm incredibly excited about the company and everything I learned talking to the team. I am standing for any next steps! Thanks again! Johnnie Verykeen

The way you phrase this depends deeply on your personality and previous language, but go for it!

In all events YES, time to email for sure.