Molecular Modeling and Spectroscopic Studies of Benzothiazole

Table 4

Second-order perturbation theory analysis of Fock matrix in NBO basis for benzothiazole.

Donor (𝑖)	Type	ED/e	Acceptor (𝑗)	Type	ED/e	E(2)	E(𝑗) − E(𝑖)^b (a. u.)	F (𝑖, 𝑗)^c (a. u.)
S1–C2	σ	1.97599	S1–C2	𝜎^∗	0.07093	0.70	0.92	0.023
			C4–C5	𝜎^∗	0.03211	0.78	1.46	0.030
			C4–C6	𝜎^∗	0.02151	1.04	1.50	0.035
			C5–C9	𝜎^∗	0.02268	5.97	1.49	0.084
			C5–C9	𝜋^∗	0.35040	3.63	0.84	0.054
S1–C5	σ	1.97203	C2–N3	𝜋^∗	0.07212	1.82	0.96	0.038
			C2–H10	𝜎^∗	0.02234	2.59	1.46	0.055
			C5–C9	𝜎^∗	0.02268	0.72	1.54	0.030
			C8–C9	𝜎^∗	0.01365	2.97	1.55	0.061
C2–N3	σ	1.99261	C2–H10	𝜎^∗	0.02234	1.26	1.90	0.044
			N3–C4	𝜎^∗	0.02497	0.94	1.77	0.037
			C4–C6	𝜎^∗	0.02151	3.53	1.99	0.075
			C4–C6	𝜋^∗	0.34604	0.80	1.34	0.032
C2–N3	π	1.95466	N3–C4	𝜎^∗	0.02497	1.36	1.07	0.034
			C4–C6	𝜋^∗	0.34604	18.48	0.64	0.106
C2–H10	σ	1.98286	C2–N3	𝜎^∗	0.01757	1.83	1.60	0.048
			N3–C4	𝜎^∗	0.02497	8.01	1.33	0.092
N3–C4	σ	1.97560	S1–C2	𝜎^∗	0.07093	1.12	1.15	0.032
			C2–H10	𝜎^∗	0.02234	7.02	1.64	0.096
			C4–C5	𝜎^∗	0.03211	0.54	1.69	0.027
			C4–C6	𝜎^∗	0.02151	1.23	1.73	0.041
			C5–C9	𝜎^∗	0.02268	2.69	1.73	0.061
			C6–C7	𝜎^∗	0.01185	1.80	1.74	0.050
C4–C5	σ	1.97874	C2–H10	𝜎^∗	0.02234	0.68	1.65	0.030
			C4–C6	𝜎^∗	0.02151	5.03	1.74	0.084
			C5–C9	𝜎^∗	0.02268	5.14	1.74	0.084
			C6–H11	𝜎^∗	0.00915	2.13	1.66	0.053
			C9–H14	𝜎^∗	0.01004	2.37	1.66	0.056
C4–C6	σ	1.97510	S1–C5	𝜎^∗	0.01756	4.16	1.22	0.064
			C2–N3	𝜎^∗	0.01757	1.50	1.76	0.046
			C2–N3	𝜋^∗	0.07212	0.53	1.12	0.022
			N3–C4	𝜎^∗	0.02497	1.34	1.50	0.040
			C4–C5	𝜎^∗	0.03211	5.54	1.68	0.086
			C6–C7	𝜎^∗	0.01185	2.72	1.72	0.061
			C6–H11	𝜎^∗	0.00915	1.69	1.64	0.047
			C7–H12	𝜎^∗	0.00908	2.25	1.64	0.054
C4–C6	π	1.66368	C2–N3	𝜋^∗	0.07212	12.45	0.52	0.077
			N3–C4	𝜎^∗	0.02497	0.94	0.90	0.028
			C5–C9	𝜋^∗	0.35040	39.19	0.46	0.120
			C7–C8	𝜋^∗	0.32093	39.20	0.47	0.122
C5–C9	σ	1.98148	N3–C4	𝜎^∗	0.02497	3.01	1.52	0.060
			C4–C5	𝜎^∗	0.03211	5.38	1.70	0.086
			C8–C9	𝜎^∗	0.01365	3.05	1.74	0.065
			C8–H13	𝜎^∗	0.00886	2.08	1.65	0.052
			C9–H14	𝜎^∗	0.01004	1.87	1.65	0.050
C5–C9	π	1.70971	C2–N3	𝜋^∗	0.07212	1.23	0.54	0.024
			N3–C4	𝜎^∗	0.02497	0.92	0.92	0.028
			C4–C6	𝜋^∗	0.34604	36.07	0.48	0.120
			C7–C8	𝜋^∗	0.32093	35.76	0.49	0.120
C6–C7	σ	1.98054	N3–C4	𝜎^∗	0.02497	4.51	1.49	0.07
			C4–C6	𝜎^∗	0.02151	3.29	1.71	0.067
			C6–H11	𝜎^∗	0.00915	1.53	1.63	0.045
			C7–C8	𝜎^∗	0.01359	2.85	1.71	0.062
			C7–H12	𝜎^∗	0.00908	1.44	1.63	0.043
			C8–H13	𝜎^∗	0.00886	2.56	1.62	0.058
C6–H11	σ	1.98222	N3–C4	𝜎^∗	0.02497	0.55	1.28	0.024
			C4–C5	𝜎^∗	0.03211	5.08	1.46	0.077
			C4–C6	𝜎^∗	0.02151	1.42	1.50	0.041
			C6–C7	𝜎^∗	0.01185	1.33	1.50	0.040
			C7–C8	𝜎^∗	0.01359	4.20	1.50	0.071
C7–C8	σ	1.98272	C6–C7	𝜎^∗	0.01185	2.83	1.71	0.062
			C6–H11	𝜎^∗	0.00915	2.48	1.63	0.057
			C7–H12	𝜎^∗	0.00908	1.55	1.63	0.045
			C8–C9	𝜎^∗	0.01365	2.90	1.71	0.063
			C8–H13	𝜎^∗	0.00886	1.56	1.62	0.045
			C9–H14	𝜎^∗	0.01004	2.59	1.62	0.058
C7–C8	π	1.67584	C4–C6	𝜋^∗	0.34604	42.89	0.46	0.126
			C5–C9	𝜋^∗	0.35040	42.80	0.45	0.125
C7–H12	σ	1.98449	C4–C6	𝜎^∗	0.02151	4.40	1.50	0.073
			C6–C7	𝜎^∗	0.01185	1.28	1.50	0.039
			C7–C8	𝜎^∗	0.01359	1.29	1.50	0.039
			C8–C9	𝜎^∗	0.01365	4.20	1.50	0.071
C8–C9	σ	1.97778	S1–C5	𝜎^∗	0.01756	5.69	1.21	0.074
			C5–C9	𝜎^∗	0.02268	3.97	1.70	0.073
			C7–C8	𝜎^∗	0.01359	2.83	1.71	0.062
			C7–H12	𝜎^∗	0.00908	2.51	1.63	0.057
			C8–H13	𝜎^∗	0.00886	1.43	1.63	0.043
			C9–H14	𝜎^∗	0.01004	1.53	1.62	0.045
C8–H13	σ	1.98412	C5–C9	𝜎^∗	0.02268	4.70	1.49	0.075
			C6–C7	𝜎^∗	0.01185	4.16	1.50	0.071
			C7–C8	𝜎^∗	0.01359	1.29	1.50	0.039
			C8–C9	𝜎^∗	0.01365	1.26	1.50	0.039
C9–H14	σ	1.98424	C4–C5	𝜎^∗	0.03211	4.44	1.46	0.072
			C5–C9	𝜎^∗	0.02268	1.54	1.49	0.043
			C7–C8	𝜎^∗	0.01359	4.07	1.50	0.070
			C8–C9	𝜎^∗	0.01365	1.33	1.50	0.040
C4–C6	𝜋^∗	0.34604	C2–N3	𝜋^∗	0.07212	18.62	0.05	0.062
			N3–C4	𝜎^∗	0.02497	2.79	0.43	0.072
C5–C9	𝜋^∗	0.35040	C2–N3	𝜋^∗	0.07212	3.79	0.06	0.030
			C7–C8	𝜋^∗	0.32093	371.30	0.02	0.122

aE(2) means energy of hyperconjugative interaction (stabilization energy).
bEnergy difference between donor and acceptor 𝑖 and 𝑗 NBO orbitals.
cF(𝑖, 𝑗) is the Fock matrix element between 𝑖 and 𝑗 NBO orbitals.