Name a tort for which there must be an intent to harm?

There is no "Intent to Harm" embodied in civil law. If there was an intent, the charge would be being made under the criminal statutes.

Negligent acts (i.e.: unthinking or unintended) are prosecutable under civil law.

Yes there are. For example, there is the intentional tort of embezzlement. Which can be a crime AND a tort. Knowledge ahead of time of libel; knowing what the outcome will be before you commit the libel etc....