Which role best describes the presidents duties as head of the executive branch of government

The president is the chief executive officer of the United States.

Article II of the Constitution outlines the powers of the Executive Branch headed by the President.

The United States Constitution begins Article II (in Section 1), saying:  "The Executive Power shall be vested in a President of the United States of America."

Then, in Section 2, Article II of the Constitution goes on to lay out powers  of the Executive Branch, with statements like these:

"The President shall be Commander in Chief of the Army and Navy of the United States""He may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any Subject relating to the Duties of their respective Offices""He shall have Power to grant Reprieves and Pardons for Offenses against the United States""He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur""He shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law"