For white papers, I usually charge $1.25 USD per word via the creative agencies I work with. But that is pretty high and its based on the client size and the agency's reputation. This involves a 1 hour kickoff call with an SME, an outline, and two revisions. Three in a pinch. Other clients don't want the kickoff call.
I just negotiated a white paper rate with a new startup client for $1,500 for 1500-2000 words which is about $0.80 per word.
White papers require significant research and background knowledge in many sectors. Clients can be really picky about them. But I find I make a higher hourly rate writing them than other content. I have one client where I can make up to $750 an hour writing white papers that are accepted with zero revisions because I know the space so well.
Clients can range in their ability to pay that and my niche is IT strategy stuff for B2B tech/consultancies and dev tools where there aren't a ton of folks that are able to write at the right level -- so my agencies or I am able to charge at a premium. I will adjust rates depending on what clients can afford.