A study of the chemical origin of the broad IR absorption band of the O-H stretching vibration (v(OH)) of liquid water is mentioned. The study is performed by measuring the local v(OH) mode of the half-deuterated water (HDO) dissolved in deuterated water (D2O) with an aid of quantum chemical calculation. The band position of a local v(ON) mode is analyzed as a function of hydrogen (H)-bond coordination pattern, which is taken into account by using a useful index of MOH based on the DA(3) pattern method. The DA(3) method focuses on a HDO-D2O (donor-accepter: DA) molecular pair, and the hydration about the DA pair is categorized into 36 patterns with respect to the H-bond coordination pattern. The M-OH index summarizes the patterns by considering the positive and negative contributions of the hydration to the H-bond in the DA pair. The calculated band position of the H-bonded v(OH) in the pair is readily grouped by using the M-OH index, which can also be used as an index for evaluating H-bonding energy. This paper demonstrates the potential of the DA(3) method to analyze the v(OH) band and H-bonding energy of liquid water and ice by referring to QC calculation results for relatively small water clusters. (C) 2012 Elsevier B.V. All rights reserved.