God the eternal Father could not accomplish the atonement of himself because he is an exalted man. He has a body of flesh and bones that is immortal that cannot be separated from his spirit. Thus he is in a state where he cannot die. The atonement required the suffering and death of one to fulfill the requirement of the atonement. For this reason, God chose his Only Begotten Son to be the redeemer who had not yet gained a body. So when he came to this earth, Jesus was born of an immortal Father and a mortal mother. Without sinning, he could chose to not die or he could choose to die.
John 10:17-18
17 Therefore doth my Father love me, because I lay down my life, that I might take it again.
18 No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again. This commandment have I received of my Father.
As a perfect and sinless being, Jesus was worthy as an infinite and eternal sacrifice. He layed down his life of his own free will. He did not die because the Jews and Rome forced it upon him but he died because he chose to lay his life down for our sake.
He was not worthy of death and thus he was able to take his life up again in the resurrection. And it is a gift he gives to us as part of his mercy. All mankind will resurrect and live an immortal existence, thanks to Jesus and his atonement.
Doctrine and Covenants 76:17
17 And shall come forth; they who have done good, in the resurrection of the just; and they who have done evil, in the resurrection of the unjust.
Acts 24:15
15 And have hope toward God, which they themselves also allow, that there shall be a resurrection of the dead, both of the just and unjust.
The atonement of Christ has brought a refreshing of the soul to those who repent of their sins. It has also brought the resurrection of all men, women and children who have died. Christ brings eternal hope for all of us who must face death at one time or another.
His great mercy covers all of us in the resurrection to immortality but also covers the repentant soul for gaining Eternal life. Eternal life is to have a life like God. Those who repent and follow after the true teachings of Jesus can become his sons and daughters. And if they remain faithful, they will become like God.
1 John 3:2
2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.
John 17:9-22
9 I pray for them: I pray not for the world, but for them which thou hast given me; for they are thine.
10 And all mine are thine, and thine are mine; and I am glorified in them.
11 And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are.
12 While I was with them in the world, I kept them in thy name: those that thou gavest me I have kept, and none of them is lost, but the son of perdition; that the scripture might be fulfilled.
13 And now come I to thee; and these things I speak in the world, that they might have my joy fulfilled in themselves.
14 I have given them thy word; and the world hath hated them, because they are not of the world, even as I am not of the world.
15 I pray not that thou shouldest take them out of the world, but that thou shouldest keep them from the evil.
16 They are not of the world, even as I am not of the world.
17 Sanctify them through thy truth: thy word is truth.
18 As thou hast sent me into the world, even so have I also sent them into the world.
19 And for their sakes I sanctify myself, that they also might be sanctified through the truth.
20 Neither pray I for these alone, but for them also which shall believe on me through their word;
21 That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me.
22 And the glory which thou gavest me I have given them; that they may be one, even as we are one:
Now that Christ has resurrected, He, like the Father, is immortal and can never die again.
Alma 11:45
45 Now, behold, I have spoken unto you concerning the death of the mortal body, and also concerning the resurrection of the mortal body. I say unto you that this mortal body is raised to an immortal body, that is from death, even from the first death unto life, that they can die no more; their spirits uniting with their bodies, never to be divided; thus the whole becoming spiritual and immortal, that they can no more see corruption.
Revelation 1:18
18 I am he that liveth, and was dead; and, behold, I am alive for evermore, Amen; and have the keys of hell and of death.