The word 'corruption' was in early drafts of the Constitution (Article II, section 4), accompanying treason and bribery as explicit grounds for impeachment of a President, Vice President, and civil officers of the United States.
Concerns were expressed in committee (perhaps, quite reasonable ones) during the Convention that, although 'treason' and 'bribery' were pretty specific, 'corruption' was much less so, and could be used in bad faith to remove political opponents from office through impeachment. Additionally, it was discussed that 'corruption' was included in 'bribery,' as political corruption involves acting on behalf of a party that is providing you with material benefit to do so, which is basically the same thing as bribery. So, corruption was dropped. (And a suggestion to include 'maladministration' never got into a draft.)
This ought to be very, very informative on the concept of Bribery at the time the Constitution was ratified. According to the standards of the 1780s, actual bribery is practiced on a massive scale as everyday business in today's politics, and just about every President and Vice President at least as far back as Reagan/Bush should have been impeached and removed after their first week in office.
Fascinating that someone like Clarence Thomas, (OK, he's a lunatic, but...) who claims to be a strict 'originalist,' (and Scalia, when he was on the Bench), would completely ignore the Constitution's clear proscription against bribery when ruling that parties can use wealth to engage in it on a completely routine basis. There is, by far, a clearer Constitutional proscription against it than, say, a grant of a 'personal right' to bear firearms by way of the Second Amendment, which seems to indicate that the right to bear arms is tied to the maintenance of well-regulated militias. These guys have always been quite OK with bribery, but have completely ignored the 'well-regulated militia' statement of the Second Amendment.
A constitutional Amendment explicitly defining bribery, extending the impeachment power to include Senators and Representatives, and enabling impeachment by State initiative (like the Amendment process), would get things moving in the right direction.