There has never been a better time for you to move their desks back together. You might need to make a couple more adjustments to your classroom though to make it truly effective.
Let's state the obvious, students want to sit next to each other. Stated even more generally, humans are social creatures. We as educators love to meet in the lounge or department meetings and catch up and talk even if it isn't always about education. I believe that if the students already have motivation and energy to do something we should not fight it but harness it.
When students are sitting next to each other they are going to talk, the question is what will they talk about? Well if your assignment is compelling and worthy of their time then they will talk about that. Maybe not the entire time but we ask our students to work for 8-10 hours straight. This flies in the face of all wisdom about productivity. Those of us who are great at getting things done know that it can't be all work and no play.
You might say, well some topics are boring and simply must be learned and there is no way to make it otherwise. I say you are not being creative enough. Can the topic be placed into a social context like a game or involve peer review? Yesterday my students played the game battleship on graph paper to review/learn coordinate graphing, and I heard so many of the coveted "Ohhh now I get it" and there wasn't a student not playing/learning (and no I do not teach a magical class of students who love any and all things math).
So if you have a compelling assignment and are willing to accept that they will not be 100% efficient (no one truly is), then lets consider the benefits of putting them in a collaborative setup:
Peer Feedback and Instruction: If you have instituted a culture of collaboration and team success, then your students will look at each others work and give them ideas on how to refine their work. Most useful is when they start to help each other to understand their work. Students can speak to each other and explain things much more efficiently and effectively than those outside their circle can. If you constantly are encouraging your students to help each other to understand (and not cheat them by giving them the answer) then you will quite simply be blown away by how much students will want to help each other.
This also allows you to help more people because when you have explained something to someone else, you can ask them to help the other person with the same question. Every educator knows that teaching a concept to someone else helps them understand the concept even more. Give that gift to your students as well. As they struggle to coherently explain it to someone else they create deeper understanding. I tell both students that if either of them still have questions they can come back and ask me. You will find overtime that even those who are not typically well versed in math will eventually come around and become better at asking for help and giving help at what they do understand.
Initially students can be reticent to ask or give help to each other. This is due to years of training the students to be solely reliant upon the teacher. When I have given instructions to the students, placed them on my website for later reference, and/or placed them on the whiteboard. I ask the students for 2-3 questions as a class(and then wait until they ask them, sometimes they need some time to think about it). Then we begin group work.
When the students want to ask me questions, I will redirect them to students. "Have you asked everyone around you?" If they answer yes, then I have 3 or 4 students to work with, otherwise I move onto another student and only answer the questions that the students can't answer. This can be painful for students and teachers to do initially but it pays off greatly and will allow you to spend more time with struggling students or with those who need an additional challenge.
Social Innovation: When you are in the presence of thoughtful colleagues great ideas emerge. When students are working on projects or assignments and are in a creative mindset, it is an exciting environment to be in. This culture that is so willing to explore and try new things can take your curriculum to new heights. This is especially useful when my students are programming in Python. Some great side collaboration projects in the class and outside have emerged out of this.
21st Century Skills: Report after report from business leaders says that the two skills they wish their incoming employees had were the ability to think creatively (outside-the-box) and collaborate well with others. Collaboration is also listed as one of the 7 survival skills in Tony Wagner's The Global Achievement Gap. Please do not deny your students the opportunity to grow in this critical area. Using effective social skills to communicate ideas and learn is just as important if not more than any one thing you will teach them.
Digital Natives: A term coined by Marc Prensky, it describes those who have grown up in a world with YouTube, Google, Smartphones, and everything else that provides instant information. Just as teachers in the past needed to adapt their teaching style to incorporate other innovations (e.g. television, radio, chalkboards, books) we would do well to observe their natural learning state and utilize the power inherent in it.
Students from this generation and those of us who have migrated to this type of thinking, use the vast information of the Internet to learn skills and understand. What brought about "Web 2.0" was the increase in video content but also the ability to share information with others. Where the Internet used to be a digital repository, it has now become a living breathing community, truly a World Wide Web.
My students are often sharing ideas on others blogs and finding people from all over the world to collaborate with. Through free communication tools, they have found experts willing to work with them and bounce ideas back and forth. This was simply not a feasible option for them a few years ago. Bring in an author, expert, community member through video conference for free and see how it will change all that you do. Make sure that you have coaching sessions about how to professionally meet and speak with others as this tends to be a skill that students need improvement.
If you can find and encourage opportunities for your students to use this to learn traditional content (e.g. Personal Learning Networks - PLNs, Instructables, YouTube Tutorials, Khan Academy) your students might be more willing to "buy-in".
My experimenting with Social Learning began a couple of years ago when I asked students to work together on an SAT Math study packet. After they finished, I asked them to honestly share. Their responses included that they felt like they had understood it better than when they had heard it in a lecture (and their scores reflected this), they also admitted that the chances of them "cheating" and simply getting the answer was likely.
When we discussed this, I explained to them that the goal of these group activities is not simply to get the "A" but to learn and understand. I remind them that while they might have good short term results, "no one cheats their way through medical school". A statement that may not be true, but it drives home the point that at some point they will be asked to demonstrate their knowledge on their own and it is in their best interests to not take the shortcut.
I am not saying that students should only learn via the Internet or games, these are just some ideas for encouraging social exchange of information, and yes I do assess individually via tests, so while individual learning is the goal, you will find that the learning occurs will just as much and creates an environment electric with discovery and ideas.
If you need further convincing of how powerfully this can transform your classroom, I suggest you watch this TED Talk. Sugata Mitra is showing the world the power of each of your students. Below that is the Dean of Pixar Univerity (yes that Pixar) about the need for students and adults to collaborate.