You need to support Java 8 for security, in package and maybe to force this version.
Significant SSL/TLS improvements in Java 8: http://blog.ivanristic.com/2014/03/ssl-tls-improvements-in-java-8.html
8u66 is current at release time, so can resolve this ticket.
The ubuntu package still needs java-7:
dpkg: regarding /tmp/openfire_4.0.1_all.deb containing openfire, pre-dependency problem:
openfire pre-depends on openjdk-7-jre-headless | openjdk-7-jre | oracle-java7-jre
openjdk-7-jre-headless is not installed.
openjdk-7-jre is not installed.
oracle-java7-jre is not installed.
Java 7 EOL was year ago. Openfire shouldn't support outdated Java. At least 4.0 branch. That said, it should be updated to only require Java 8. I know that Windows version works with Java 8. On Ubuntu tar.gz version (bundled with Java 8) works fine. Deb package should be updated to not require Java 7.