Table 3.

IR and Raman vibrational modes (in cm⁻¹) of the phosphate group of hexagonal hydroxylapatite (space group P6₃) calculated at the DFT level of theory, compared with experimental results.

Normal Mode	IRREP	IR Active	Raman Active	Theoretical		Experimental
				B3LYP-D* [90]	B3LYP [89]	IR [74]	Raman [91]
ν2 (PO4)	A	✓	✓	465	459		432
	A	✓	✓	494	489		454
	E 1	✓	✓	441	437
	E 1	✓	✓	478	475		432
	E 2	x	✓	442	440	462	449
	E 2	x	✓	460	457
ν4 (PO4)	A	✓	✓	568	566	566
	A	✓	✓	600	599	660–520	593
	A	✓	✓	623	621		609
	E 1	✓	✓	575	573
	E 1	✓	✓	601	600	632
	E 1	✓	✓	611	609	602
	E 2	x	✓	567	566		581
	E 2	x	✓	590	588		609
	E 2	x	✓	635	633		617
ν1 (PO4)	A	✓	✓	975	972		962
	E 1	✓	✓	976	972	962
	E 2	x	✓	978	974		962
ν3 (PO4)	A	✓	✓	1057	1054	1190–976	1034
	A	✓	✓	1069	1064		1048
	A	✓	✓	1102	1096		1077
	E 1	✓	✓	1050	1045		1043
	E 1	✓	✓	1072	1068	1042
	E 1	✓	✓	1114	1110	1091
	E 2	x	✓	1046	1041		1028
	E 2	x	✓	1081	1077		1055
	E 2	x	✓	1086	1081		1077