Table 4.

Comparison of the calculated lifetimes of the all-trans and central-cis C₁₈ polyene with the observed lifetimes of the corresponding configurations of neurosporene.

#	Assumptions(a)	τ(all-trans) (ps)	τ(cis) (ps)	$\frac{\tau (\mathit{\text{trans}})}{\tau (\mathit{\text{cis}})}$
0	Neurosporene (Experimental)	34.8	22.0	1.58
1	N=20,000; Γ=400 cm-1	70.0	36.8	1.90
2	N=15,000; Γ=400 cm-1	74.0	37.3	1.98
3	N=10,000; Γ=400 cm-1	84.7	42.5	1.99
4	N=10,000; Γ=800 cm-1	108	55.0	1.97
5	N=10,000; Γ=200 cm-1	86.1	40.1	2.15
6	N=10,000; Γ=50 cm-1	66.7	29.6	2.26
7	N=20,000; Γ=400 cm-1; $E_{\mathit{\text{trans}}}^{00}=E_{\mathit{\text{cis}}}^{00}$	84.5	25.9	3.26
8	N=10,000; Γ=400 cm-1; $E_{\mathit{\text{trans}}}^{00}=E_{\mathit{\text{cis}}}^{00}$	111	34.9	3.20

^(a)N is the number of unique ground state vibrational combinations evaluated in the calculation. Γ is the inhomogeneous linewidth used in Eq. 5. Other assumptions for calculations 1-6 include: system origin of all-trans C₁₈ =14,400 cm^-1, system origin of central-cis C₁₈ =14,950 cm^-1. Calculations 7 and 8 were carried out by arbitrarily setting the system origin energies of the initial states equal: $E_{\mathit{\text{trans}}}^{00}=E_{\mathit{\text{cis}}}^{00}=\mathrm{14,675}$ cm^-1.