Is it secure to use the hash of key as the IV in AES encryption? I need to store some sensitive data for a program. For each copy of the program, there will be a unique key for encrypting one (and only one) file using AES encryption (OFB). The key will not be changed (probably forever).

Is it secure if the hash value of the key is used as the IV?

Update:
The key is computer generated.
The user of the program have no access to the key since it's obtained by the program via secure Web API.
The user can only edit a portion of data stored in the file via the program.
No, it is not secure.

From NIST 800-38:

The OFB mode requires a unique IV for every message that is ever encrypted
under the given key. If, contrary to this requirement, the same IV is used
for the encryption of more than one message, then the confidentiality of
those messages may be compromised 


Given your description, you are apparently safe, because at any one time you have one file only.

However:


A malicious user may store away an earlier version of the file and do a comparison after a change and learn which bits flipped in the first block where that happened.
In the future, you may add a second file and not remember the rule above.


A unique (not necessarily truly random) IV per message is still recommended.