Why is Diffie Hellman used alongside public keys?
DH is often used to build session keys, which are used to provide forward secrecy. If you only use the public key in the certificate, then corrupting the private key may reveal all the previous encrypted messages. The attacker can first decrypt the symmetric keys then decrypt previous messages if it keeps records of the previous communications. Using DH can prevent this. Even if you have the private key, you still can not figure out any previous DH results to get the symmetric keys. In this way, the privacy of previous messages is still maintained.