Electron Correlation Effects on the Longitudinal Polarizabilities and Second Hyperpolarizabilities of Polyenes: A Finite Field Study

Table 2

Longitudinal second hyperpolarizabilities per unit cell 𝛾_𝐿/𝑁 of polyenes obtained by various chemical models (in 10⁴ a.u., N is the number of unit cells or double bonds in the system).

N	2	3	4	5	6	7	8	9	10
6-31G
HF	−0.12	1.93	5.85	12.9	23. 6	37.6	54.5	67.8
MP2	0.84	4.33	11. 8	24. 9	44.4	70.2	101	131
CCSD	0.80	3.11	7.44	15.3	26.5	34.5	46.7	52.3
SVWN	0.15	2.80	9.91	26.9	61.8	126	232	403	659
BLYP	0.15	2.09	9.30	26.1	61.4	125	229	398	650
B3LYP	0.14	2.29	9.25	24.5	54.2	104	190	301	458
6-31G(d)
HF	−0.11	1.79	5.38	11.9	21.4	33.9	49.3
MP2	0.67	3.83	10.8	23.4	42.2	67.4	98.8
CCSD	0.60	4.04	8.71	16.6	27.2	40.3	56.3
SVWN	0.14	2.59	9.26	22.6	63.9	116	232	392	644
BLYP	0.13	2.57	9.25	23.1	60.0	121	231	384	637
B3LYP	0.12	2.63	9.07	23.5	51.6	99.2	173	278	422
6-31+G
HF	0.42	3.56	8.78	17.4	30.0	45.5	62.3	85.2
MP2	1.92	7.08	16.9	33.0	56.1	85.6	125	161
CCSD	1.59	5.39	11.7	21.0	31.8	45.5	63.2	70.8
SVWN	1.07	5.45	15.4	37.2	79.3	158	285	433	711
BLYP	1.18	5.71	16.9	40.0	83.2	159	357	468	728
B3LYP	0.98	5.30	15.2	35.1	69.0	148	216	335	497
6-31+G(d)
HF	0.75	5.80	14.1	26.4	46.7	71.5
MP2	2.88	11.1	26.8	51.5	91.5	141
CCSD	2.70	9.01	19.5	35.3	59.3	89.0
SVWN	1.08	5.26	14.76	35.5	76.0	148	269	450	709
BLYP	1.19	5.76	15.2	36.1	78.8	154	280	468	782
B3LYP	0.99	5.27	13.9	31.0	66.6	117	209	342	485