A salary negotiation email works because it gives the other side time to think and something concrete to respond to, instead of putting them on the spot in a live call. The structure that works is short and consistent regardless of the scenario: open with genuine enthusiasm, state your target number plainly, back it with a real reason, and invite a reply.
Enthusiasm first matters more than it seems. An email that leads with the number and nothing else reads as transactional, and it makes the rest of the message harder to receive well. One or two honest sentences about why you want the role, or why you value your current one, changes the tone of everything that follows, and it signals that the number is not the only thing you care about.
Then name the number. Vague asks such as "I was hoping for more" invite vague answers. A specific figure, stated once and clearly, is what actually moves a negotiation forward. Say it a single time in the body of the email rather than repeating it in every paragraph, which starts to read as pressure rather than a request.
Close by inviting a reply rather than demanding an answer. A line as simple as "I would love to find something that works for both of us" or "Happy to jump on a call if that is easier" keeps the door open and makes it clear you are negotiating in good faith, not issuing an ultimatum.
Timing matters too. Send the email within a day or two of receiving an offer or hearing a figure verbally, while the conversation is still fresh for the other side. Waiting a week or more can make the ask feel disconnected from the original discussion, and it gives the impression you were unsure rather than simply taking time to think it through properly.
Keep the whole message readable in under a minute. Three or four short paragraphs, one clear ask, and a plain sign off beats a long email that buries the number in the middle of a paragraph about your background. The person reading it should be able to see exactly what you want on a first pass.