Molecular Structure, NMR, HOMO, LUMO, and Vibrational Analysis of O-Anisic Acid and Anisic Acid Based on DFT Calculations

Table 4

Definition of natural internal coordinates of O-Anisic acid (OAA).

No. (i)	Symbol^a	Definition^b
1–4	C–H stretch	𝑟1,𝑟2,𝑟3,𝑟4
5–11	C–C stretch	𝑟5,𝑟6,𝑟7,𝑟8,𝑟9,𝑟10,𝑟11
12–14	C–O stretch	𝑟12,𝑟13,𝑟14
15	O–C stretch	𝑟15
16	O–H stretch	𝑟16
17	CH3 ss	𝑟17+𝑟18+𝑟19/√3
18	CH3 ips	2𝑟17−𝑟18−𝑟19/√6
19	CH3 ops	𝑟18−𝑟19/√2
20	bC–C–C	𝛽20−𝛽21/√2
21–24	bC–C–H	𝛽22−𝛽23/√2,𝛽24−𝛽25/√2,𝛽26−𝛽27/√2,𝛽28−𝛽29/√2
25	CH3 sb	−𝛽30−𝛽31−𝛽32+𝛽33+𝛽34+𝛽35/√6
26	CH3 ipb	(−𝛽33−𝛽34−2𝛽35)/√6
27	CH3 opb	𝛽33−𝛽34/√2
28	CH3 ipr	(2𝛽30−𝛽31−𝛽32)/√6
29	CH3 opr	(𝛽31−𝛽32)/√2
30	bC–C–O	𝛽36−𝛽37/√2
31	bC–O–H	𝛽38
32-33	bC–C–O	𝛽39,𝛽40
34	bC–O–C	𝛽41
35	Rtrigd	𝛽42−𝛽43+𝛽44−𝛽45+𝛽46−𝛽47/√6
36	Rsymd	(−𝛽42−𝛽43+𝛽44−𝛽45−𝛽46+2𝛽47)/√12
37	Rasymd	𝛽42−𝛽43+𝛽45−𝛽46/2
38–41	𝜔C–H	𝜔48,𝜔49,𝜔50,𝜔51
42	𝜔C–C	𝜔52
43	𝜔C–O	𝜔53
44-45	tC–O	𝜏54,𝜏55
46	tC–O–C	1/2𝜏56+𝜏57
47	tCH3	1/3𝜏58+𝜏59+𝜏60
48	tO–H	𝜏61
49	Ttrigd	𝜏62−𝜏63+𝜏64−𝜏65+𝜏66−𝜏67/√6
50	Tsymd	𝜏62−𝜏63+𝜏65+𝜏66/2
51	Tasymd	−𝜏62+2𝜏63−𝜏64−𝜏65+𝜏66−𝜏67/√12

aThese symbols are used for description of the normal modes by PED in Table 7.
bThe internal coordinates used here are defined in Table 2.