18 U.S. Code S 2423(c): Engaging in Illicit Sexual Conduct in Foreign Places.
Any United States citizen or alien admitted for permanent residence who travels in foreign commerce or resides, either temporarily or permanently, in a foreign country, and engages in any illicit sexual conduct with another person shall be fined under this title or imprisoned not more than 30 years, or both.
Torture under 18 USC Sec. 2340A: "(a) Whoever outside the United States commits or attempts to commit torture shall be fined under this title or imprisoned not more than 20 years, or both, and if death results to any person from conduct prohibited by this subsection, shall be punished by death or imprisoned for any term of years or for life."
Terrorism offenses involving homicide or attempted homicide under 18 USC Sec. 2332:
"(a) Homicide.--Whoever kills a national of the United States, while such national is outside the United States, shall [...]"
"(b)Attempt or Conspiracy With Respect to Homicide.--Whoever outside the United States attempts to kill, or engages in a conspiracy to kill, a national of the United States shall [...]"
"(c) Other Conduct.--Whoever outside the United States engages in physical violence (1) with intent to cause serious bodily injury to a national of the United States; or (2) with the result that serious bodily injury is caused to a national of the United States [...]"
