Notification when a shopping cart is abandoned
I'd start by trying the existing Commerce Abandoned Cart Notification module. This module was specifically designed to send abandoned cart notifications.

This module allows you to notify your customers by email about their abandoned their cart.
Abandoned Shopping Cart mailings generate more than 55% more conversion compared to regular email campaigns. –SeeWhy research (2011)
Features

List your customers abandoned carts
100% integration with Commerce VBO
Edit the notification email directly from the Rule component