The introduction to Carter Burwell's theme for Bella's Lullaby from the film Twilight is in D major, but uses a G minor instead of the usual G major.
The G minor is often with an extra E to make G minor 6:
Bella's Lullaby (from Twilight) for String Orchestra ((Solo Piano Feature with opt. winds)). By Carter Burwell. Arranged by Paul Lavender. For solo piano with string orchestra and optional winds (Score & Parts). Pop Specials for Strings. Movies. Grade 3-4. Published by Hal Leonard