Impeaching a President and ratifying a treaty are in many respects twin siblings. The calculation of the 2/3 conviction threshold is done the same way a treaty is ratified. The reasons for the need to have impeachment power and ratification of treaty power are the same. The enclosed essay is intended to inform the average citizen of the relatively straight forward reasons both systems were put into place in the constitution.
Alexander Hamilton describing the need for Senate ratification of a treaty wrote in Federalist No. 75:
"An avaricious man might be tempted to betray the interests of the state to the acquisition of wealth. An ambitious man might make his own aggrandizement, by the aid of a foreign power, the price of his treachery to his constituents. The history of human conduct does not warrant that exalted opinion of human virtue which would make it wise in a nation to commit interests of so delicate and momentous a kind, as those which concern its intercourse with the rest of the world to the sole disposal of a President of the United States."
The same can be said to a President's conduct that warrants impeachment.
As to the nature of the impeachment trial, Hamilton in Federalist No. 65 wrote:
"A well-constituted court for the trial of impeachments is an object not more to be desired than difficult to be obtained in a government wholly elective. The subjects of its jurisdiction are those offenses which proceed from the misconduct of public men, or, in other words, from the abuse or violation of some public trust."
During the debate over the impeachment clause at the Constitutional Convention a short but very revealing debate occurred. First Colonel Mason asked, "Why is the provision restrained to, treason and bribery only? Attempts to subvert the Constitution may not be treason". He proposed to add "maladministration" to the impeachment clause. Mr. Madison objected because the phrase was too vague and by implication could be used for political purposes. It was withdrawn and substituted with "other high crimes and misdemeanours against the state." Subsequently, "against the state" was deleted from the final text.
Gouverneur Morris summed up the debate which was in retrospect remarkably short, "An election of every four years, will prevent maladministration."
The central question of President Trump's conduct, is whether the alleged strong arming of a foreign leader to dig up dirt on a political rival and subsequently taking steps to subvert the investigation into this conduct merely "maladministration" or is it an "abuse or violation of some public trust" that subverts the Constitution?