If you do a search here, you'll find quite a few posts regarding this diet. The theory
is, that if you eat stuff that's really low in calories, like celery and grapefruit and that sort of thing, they take more calories to burn off than what is contained in them - thus the 'negative' calorie theory.
A couple threads from the past:
Negative Calorie Diet
negative calorie diets?
And if Suzanne doesn't mind me quoting her...she pretty much summed it up:
Originally Posted by Suzanne 3FC
If weight is lost, it's because the foods are very low in calories, so you're just on another low calorie diet. There really isn't such a thing as negative calories, it's all a myth. It is true that there are some foods, such as celery, that contain so few calories that between chewing and digestion, you may burn an extra calorie or two more than they contain. But seriously, the amount is so SMALL that you would have to binge on celery nonstop all day long, and it would still take a long time to see any result from that. You have to burn 3500 calories more than you consume to lose one pound of fat. At least that's all that the so-called negative calorie effect can do. Many of the foods on those lists don't even qualify in the same way.
However, they are all low calorie, and the foods are usually healthy enough, but not on their own. Any weight lost will be because you are on a low calorie diet, and NOT because you burned more than you consumed just by eating special foods. You still need to eat grains, dairy, and other foods to make sure that you consume enough calories and balance the diet nutritionally.
The whole "negative calorie" issue is a bad idea, it's just another fad diet. Not surprisingly enough, there are a lot of websites out there that want to sell those lists of miracle foods for $19.95. It's a gimmick.