I am only after the company name and website which you can see and then you can see down the side all the staff that work there, then identify the decision makers like CEO's, Business Development Manager etc
You don't contact them through LinkedIn, that looks spammy, you send them an email to the decision maker, its easy to work out the email address by looking at other email addresses from that company, just see what format they use like
[email protected],
[email protected] or
[email protected]
I have in the past sent an invite and been accepted and then broken the ice that way by saying "Thanks for accepting, I notice we have some mutual connections......." I don't offer the domain straight away or it just looks like a sales pitch