Can the President of the United States be impeached for endangering the security of the state? "Endangering the security of the state" defined as leaking or telling sensitive information to other countries or third parties, abuse of power in a way harmful or destructive to the Judicial or Legislative branches of the government and/or beneficial to other countries, or degradation of the defensive military in a way directly or indirectly harmful to the security of the United States.
Under Art I Sect 4 of the Constitution, the President "shall be removed from Office on Impeachment for, and conviction of, Treason, Bribery, or other High Crimes and Misdemeanors". There is no existing crime or misdemeanor "Endangering the security of the state". However, in the case of Clinton's impeachment, the articles did not refer to a specific statutory crime, rather the charge was that "The president provided perjurious, false and misleading testimony to the grand jury regarding the Paula Jones case and his relationship with Monica Lewinsky" and that "The president obstructed justice in an effort to delay, impede, cover up and conceal the existence of evidence related to the Jones case". It is true that in these cases, there exist corresponding crimes of obstruction of justice and perjury: still, an impeachment need not be based on a specific statutory crime. Likewise, the articles of impeachment against Andrew Johnson specify a number of acts which are not statutory crimes / misdemeanors.
Since the Constitution speaks in general terms about the grounds for impeachment, such an impeachment would not be clearly unconstitutional. It is likewise not clearly constitutional. There is no legal precedent that tells us how the Supreme Court would interpret the power of the House to impeach, in particular whether it would be unconstitutional to impeach a president for "abuse of power in a way harmful or destructive to the Judicial or Legislative branches of the government and/or beneficial to other countries, or degradation of the defensive military in a way directly or indirectly harmful to the security of the United States".
Since the Constitution does not clearly prohibit such an impeachment, it is unlikely that SCOTUS would rule that such an impeachment is unconstitutional, although it has the theoretical power to so rule. In light of the fact that Article 1, Section 2, Clause 5 states "The House of Representatives shall chuse their Speaker and other Officers; and shall have the sole Power of Impeachment", and the fact that in Nixon v. US it was held that the Senate's decision to convict and remove that judge based on the analogous "sole power" clause for trials, there is no realistic chance that the courts would review any aspect of the impeachment process.