Click is a book about such instant connections. It's a really short book: I got started on it this morning and it took no more than a couple of hours to read. The authors claim that instant connections are made more easily possible by five factors:
Some of these are within your control. For instance, choosing to be vulnerable to someone else by revealing something about yourself is entirely your decision. To some extent having the environment be something conducive to a connection is also something of a choice: I deliberately chose to stay in youth hostels, for instance, because it put everyone staying in one into the same frame of mind. Other factors seem to be something nearly everyone does: we try to find similarities to one another, and obviously, it's hard to make a connection with someone who's not near you (Google understood this by always shuffling teams to be in close proximity to one another).
What's fascinating to me is the chapter on people who seem to be able to click with everyone all the time. The authors refer to these people as having "high self monitors." In other words, they are social chameleons, able to adapt themselves to any situation and person by expressing sympathy and empathy with them in ways that are appropriate to the social context. High end politicians and fashion models have these, and my PCP is also someone who is like this. Unfortunately, whether you can train yourself to be "high self monitoring" is not covered in the book. I think it would be very exciting to see if such abilities can be trained, given the evidence in the book about how well high self monitors do in their careers in terms of success and flexibility. For instance, high self monitors apparently also change jobs more frequently because their skills are more portable.
All in all, this short book is a quick read the packs a ton of information in a short space. The problem with this book is the lack of depth. In particular, one of the examples is a comparison survey between married couples who met with an "instant connection" and those who didn't. What's missing in that case is to see how many of these "instant connection" marriages failed versus the less dramatic connections. The authors apparently did not realize that there's a significant survivorship bias in the survey they studied.
Nevertheless, despite the flaws, this book is highly recommended. The chapter about how to get teams to gel so they can achieve high performance makes this book a must-have on any manager's bookshelf.