NOVELTY - Synthesis of 1,3-di-(2-ethoxyphenyl)-(1R,3H)-pyrimidine-2,4-dione involves Chapman rearrangement of 2,4-di-(2-ethoxyphenoxy)-pyrimidine at 160 degrees C.    USE - The methods are useful for synthesizing 1,3-di-(2-ethoxyphenyl)-(1R,3H)-pyrimidine-2,4-dione; 1,3-di-(4-ethoxyphenyl)-(1H,3H)-pyrimidine-2,4-dione; 1,3-diphenyl-(1H,3H)-pyrimidine-2,4-dione; 1,3-di-(2-carbethoxyphenyl)-(1H,3H)-pyrimidine-2,4-dione; 1,3-di-(4-carbethoxy-2,6-dimethoxyphenyl)-(1H,3H)-pyrimidine-2,4-dione; 1,3-di-(4-carbmethoxyphenyl)-(1H,3H)-pyrimidine-2,4-dione; 1,3-di-(4-chloro-3,5-dimethylphenyl)-(1H,3H)-pyrimidine-2,4-dione; and 1,3-di-(2-methylphenyl)-(1H,3H)-pyrimidine-2,4-dione (all claimed). The pyrimidinedione derivatives are used for treating or preventing metabolic disorders, dyslipidemia, neurological disorders, hematological diseases, cancer, inflammation, respiratory diseases, gastroenterological diseases, diabetic complications, obesity-related disorders and non-alcoholic fatty liver diseases.    ADVANTAGE - Chapman rearrangement of imidates of formulae (3a-3h) has afforded 1,3-diarylpyrimidine-2,4-diones of formulae (4a-4h), providing an environmental friendly procedure (claimed). The methods can synthesize 1,3-diarylpyrimidine-2,4-diones having: (1) few steps of reactions, (2) minimum use of solvents, (3) clean work up, and (4) better reaction yield.    DETAILED DESCRIPTION - Synthesis of 1,3-di-(2-ethoxyphenyl)-(1R,3H)-pyrimidine-2,4-dione of formula (4a) involves Chapman rearrangement of 2,4-di-(2-ethoxyphenoxy)-pyrimidine of formula (3a) at 160 degrees C. INDEPENDENT CLAIMS are included for:    (1) a method for synthesizing 1,3-di-(4-ethoxyphenyl)-(1H,3H)-pyrimidine-2,4-dione of formula (4b) which involves Chapman rearrangement of 2,4-di-(4-ethoxyphenoxy)-pyrimidine of formula (3b) at 175 degrees C;    (2) a method for synthesizing 1,3-diphenyl-(1H,3H)-pyrimidine-2,4-dione of formula (4c) which involves Chapman rearrangement of 2,4-diphenoxypyrimidine of formula (3c) at 180 degrees C;    (3) a method for synthesizing 1,3-di-(2-carbethoxyphenyl)-(1H,3H)-pyrimidine-2,4-dione of formula (4d) which involves Chapman rearrangement of 2,4-di-(2-carbethoxyphenoxy)-pyrimidine of formula (3d) at 175 degrees C;    (4) a method for synthesizing 1,3-di-(4-carbethoxy-2,6-dimethoxyphenyl)-(1H,3H)-pyrimidine-2,4-dione of formula (4e) which involves Chapman rearrangement of 2,4-di-(4-carbethoxy-2,6-dimethoxyphenoxy)-pyrimidine of formula (3e) at 178 degrees C;    (5) a method for synthesizing 1,3-di-(4-carbmethoxyphenyl)-(1H,3H)-pyrimidine-2,4-dione of formula (4f) which involves Chapman rearrangement of 2,4-di-(4-carbmethoxyphenoxy)-pyrimidine of formula (3f) at 182 degrees C;    (6) a method for synthesizing 1,3-di-(4-chloro-3,5-dimethylphenyl)-(1H,3H)-pyrimidine-2,4-dione of formula (4g) which involves Chapman rearrangement of 2,4-di-(4-chloro-3,5-dimethylphenoxy)-pyrimidine of formula (3g) at 165 degrees C; and    (7) a method for synthesizing 1,3-di-(2-methylphenyl)-(1H,3H)-pyrimidine-2,4-dione of formula (4h) which involves Chapman rearrangement of 2,4-di-(2-methylphenoxy)-pyrimidine of formula (3h)at 175 degrees C.