Did God Die On The Cross?

I'm going to have to think more on this. I always thought the cross did change God and the relationship between the Father and Son: Did God Die On The Cross? by R.C. Sproul | Ligonier Ministries Blog:

We should shrink in horror from the idea that God actually died on the cross. The atonement was made by the human nature of Christ. Somehow people tend to think that this lessens the dignity or the value of the substitutionary act, as if we were somehow implicitly denying the deity of Christ. God forbid. It’s the God-man Who dies, but death is something that is experienced only by the human nature, because the divine nature isn’t capable of experiencing death.