The theory behind this diet is that some foods need more calories to digest them that they contain.

The Negative Calorie diet supposedly works because some 'negative calorie' foods contain lots of vitamins and minerals which improve your enzyme production enough to break down not only calories in that food, but also other calories present in your digestive system. Here are some 'negative calorie' foods:
apple
cranberries
grapefruit
lemon
mango
orange
papaya
pineapple
raspberries
strawberries
tangerine
asparagus
beet
broccoli
cabbage
carrot
cauliflower
celeriac
celery
chicory
chile peppers
cucumber
dandelion
endive
garden cress
garlic
green beans
lamb's lettuce
lettuce
onion
radishes
spinach
turnip
zucchini

The idea is to eat as much of these foods as you like. Starvation makes your body save body fat. Hopefully these foods will increase your metabolism and your extra fat will burn itself off.

My personal take is to eat those foods raw. Then you get all their enzymes as well. Cooking kills all the enzymes naturally present in foods.