The commercial certificated pilot was conducting agricultural spraying under Title 14, CFR Part 137, in a turbine-powered airplane, and had been refueling throughout the day at a local airport. The pilot reported that he and his ground crew kept a log of spray loads, flight time, and the quantity of fuel that was added upon each return to the airport. The pilot indicated that each refueling usually required about 70 gallons, and the airplane's fuel capacity was 104 gallons. He said that while spraying over an area of pine trees about 800 feet above ground level (agl), the engine lost power. He made a forced landing in an area of cut trees, and the airplane received structural damage to the landing gear, fuselage, and wings. The pilot said that after the accident, he inspected the fuel tanks and found them dry. The operator reported that their examination of the airplane after the accident did not reveal any mechanical malfunction.