TABLE 4.

Calculated Properties of the Two Lowest-Lying Excited Singlet States of Fucoxanthin

theoretical method			μg S0 (D)	ΔE $2^1{\mathrm{A}}_{\mathrm{g}}^{*-}$ (eV)	fosc $2^1{\mathrm{A}}_{\mathrm{g}}^{*-}$	ΔE $1^1{\mathrm{B}}_{\mathrm{u}}^{*+}$ (eV)	fosc $1^1{\mathrm{B}}_{\mathrm{u}}^{*+}$	Δμ $2^1{\mathrm{A}}_{\mathrm{g}}^{*-}$ ←S0(D)	Δμ $1^1{\mathrm{B}}_{\mathrm{u}}^{*+}$ ←S0(D)
MNDOCIa	AM1	Slater	8.461	2.628	0.471	2.728	2.532	+ 8.755	−2.365
MNDOCIb	AM1	Slater	8.461	2.541	0.158	2.690	2.697	+ 5.969	+ 0.820
MNDOCI+c	AM1	Slater	8.453	2.432	0.022	2.712	2.910	+ 2.737	+ 4.050
SACCI-CISDd	RHF	D95	10.41	3.796	1.642	3.967	3.263	+ 9.869	−3.502
TD-DFTe	PBE1 PBE	6-31G(d)	8.984	3.107	0.216	2.468	3.594	−1.850	+ 19.55
TD-DFTe	B3LYP	6-31G(d)	9.041	2.941	0.294	2.398	3.447	−3.902	+ 14.60
TD-DFTe	SVWN	6-31G(d)	9.364	1.933	0.004	2.087	2.197	+ 33.10	+ 46.68
expt f				~ 2.4	<0.2	2.737	2.218

^aFull single and double CI for an orbital basis set of the eight highest energy occupied and eight lowest energy unoccupied π orbitals plus single CI involving the three highest energy occupied σ and single lowest energy unoccupied σ orbitals (CISD 8π × 8π + CIS 3 × 1 = 99 singles + 2048 doubles).

^bAs in footnote a but with CISD 9π × 9π + CIS 3 × 1 = 120 singles + 3080 doubles.

^cAs in footnote a but with partial inclusion of quadruples via coupled-cluster perturbation.

^dSACCI-CISD based on the 52 highest energy occupied and 52 lowest energy unoccupied orbitals with full single and partial double CI (2704 singles + 15939 doubles).

^eExcited state dipole moments are calculated by using the one-particle CI density.

^fTransition energies (ΔE ≈ 8062 cm⁻¹) and oscillator strengths (f_osc) based on fucoxanthin in THF assuming molar absorptivity of 109400 L/mol/cm.⁷⁵ The transition energy of the $2^1{\mathrm{A}}_{\mathrm{g}}^{*-}$ -like state is estimated on the basis of fluorescence studies.