As with any professional correspondence, you don't want to seem too stiff or formal, like you're writing a letter from a Victorian template or a bad spam email asking someone to send money to a deposed prince overseas—but you also don't want to be too conversational. You're not in a dialogue yet, so it's important to treat this like a professional first interaction, and not like you're skipping several steps and asking to meet for coffee. The tone you're reaching for is, "You don't know me yet, but I'm interested in your company and want to tell you more about why."
Use a Letter of Intent if: You want to take serious steps towards negotiating the purchase of all or part of a company. You want to secure your interest in a company and request that the sellers exclude negotiating with another buyer.