We have theoretically examined the relative binding affinities (RBA) of typical ligands, 17beta-estradiol (EST), 17alpha-estradiol (ESTA), genistein (GEN), raloxifene (RAL), 4-hydroxytamoxifen (OHT), tamoxifen (TAM), clomifene (CLO), 4-hydroxyclomifene (OHC), diethylstilbestrol (DES), bisphenol A (BISA), and bisphenol F (BISF), to the alpha-subtype of the human estrogen receptor ligand-binding domain (hERalpha LBD), by calculating their binding energies. The ab initio fragment molecular orbital (FMO) method, which we have recently proposed for the calculations of macromolecules such as proteins, was applied at the HF/STO-3G level. The receptor protein was primarily modeled by 50 amino acid residues surrounding the ligand. The number of atoms in these model complexes is about 850, including hydrogen atoms. For the complexes with EST, RAL, OHT, and DES, the binding energies were calculated again with the entire ERalphaLBD consisting of 241 residues or about 4000 atoms. No significant difference was found in the calculated binding energies between the model and the real protein complexes. This indicates that the binding between the protein and its ligands is well characterized by the model protein with the 50 residues. The calculated binding energies relative to EST were very well correlated with the experimental RBA (the correlation coefficient r=0.837) for the ligands studied in this work. We also found that the charge transfer between ER and ligands is significant on ER-ligand binding. To our knowledge, this is the first achievement of ab initio quantum mechanical calculations of large molecules such as the entire ERalphaLBD protein.