The Vibrational Spectroscopy of the Valence Bonds of Cu-Doped TiO₂ Using Electronegativity Principle Quantitative Calculations

Table 3

The vibration frequency range corresponding to the various bonds of undoped and Cu-doped TiO₂ samples.

Sample	Types of the bonds	The bond length d (Å)	Vibration frequency v (cm^−1)
Undoped TiO2	TiA-O	1.949 Å∼1.980	450 cm^−1∼670
			1100
			1600
	TiR-O	1.930 Å∼1.973	710 cm^−1∼850
			1410 cm^−1∼1550
2.5 mol% Cu-doped TiO2	TiA-O	1.739 Å∼1.976	440 cm^−1∼680
			1100
			1600
	TiR-O	1.627 Å∼1.973	680 cm^−1∼850
			1370 cm^−1∼1650
	Cu^iA-O	1.327 Å∼1.527	450 cm^−1∼480
	Cu^iR-O	1.284 Å∼1.428	550 cm^−1∼720
5 mol% Cu-doped TiO2	TiA-O	1.729 Å∼1.966	435 cm^−1∼675
			1105
			1605
	TiR-O	1.627 Å∼1.973	680 cm^−1∼850
			1370 cm^−1∼1650
	Cu^iA-O	1.327 Å∼1.527	450 cm^−1∼480
	Cu^iR-O	1.284 Å∼1.428	550 cm^−1∼750
	Cu^sA-O	1.276 Å∼1.958	550 cm^−1∼740
	Cu^sR-O	1.364 Å∼1.965	450 cm^−1∼820