While the Constitution does give the House broad discretion in impeachments, there are limits. The most explicit of these is that impeachment can only be for, “Treason, Bribery, or other high Crimes and Misdemeanors.” (Art. II, Sec. 4, U.S. Constitution) However, the articles for impeachment voted on by this entirely partisan Democratic Congress, which are currently being unconstitutionally withheld from the Senate, charge no such offenses. In fact, abuse of power and obstruction of Congress are not crimes of any kind, high or low.
However you feel about Democrats not directly accusing Trump of a crime in the articles of impeachment — and I’ve suggested it might not be optimal from a strategic standpoint — there is basically no dispute among constitutional scholars that the Constitution doesn’t require them to. “High crimes” doesn’t refer to very bad crimes; it means misdeeds related to high office. And “misdemeanors” doesn’t mean a crime that isn’t a felony, as it does in the American criminal code; it refers broadly to offenses. Even Jonathan Turley, the constitutional scholar Republicans called as an expert on impeachment, said a crime was not required to impeach a president.