Nice work on this. I actually like the simplicity of it. Feels light weight and fast.
We live in an era of distrust so without seeing your terms / privacy policy I was not comfortable logging into a site with a password so may be worth adding a blurb about that. On the bottom where you display the URL, I value seeing HTTPS where applicable as well. I don't want to feel like I am losing security by using this. Last thought, it would be nice to customize the homepage away from google. This one is just vanity though. Good work and good luck.