Hi, 

Pachysandra is probably more shade-loving than the spot is allowing for. You can check out the plant lists on our groundcover page for more sun loving plants. They are broken up into native plants and non-native but not invasive or harmful groundcovers with varying degrees of how aggressive they can be. 

Perhaps a plant like Moss Phlox would be better suited to that area, and you may want to consider mixing a few different species. That way, if some of the plants die, it won't be so obvious that there is a "hole" in the planting bed. Maybe doing a type of pattern of 3 different plants would be nice? Moss phlox, a sun-loving Carex (sedge) species, and maybe a sedum groundcover for a mix of textures? 

To keep it from creeping into the grass, you may want to add a border. There are various options depending on your budget and the look you want to achieve. You could invest in a type of stone or cement block that would be more decorative, or you could sink a plastic or metal border along the edge. Otherwise, as the plants grow, you could just edge the bed with a shovel or spade to keep a neat line between the ground cover planting area and the lawn. 

If it is pooling after heavy rains, you could also consider raising the bed slightly by mounding it. It depends on where the water is coming from, though, as you don't want to create a dam that would block the water from flowing all today. 

Let us know if you have further questions. 

Emily