Table 1.

a) Orientational coefficients for Feynman paths for an oblate symmetric diffuser having two vibrational transition dipole moments in a plane perpendicular to the symmetry axis and b) The orientational factors for ±2π/3 flips.

a)
Tensor *e2D(t+τ)	Feynman path (α β γ δ)
	(iiii)	(ijij)	(iijj)	(ijji)
<XαXβYγYδ>	$\frac{1}{45}[5-2e^{-6DT}]$	$-\frac{1}{30}{e}^{-6DT}$	$\frac{1}{45}[5+2e^{-6DT}]$	<X1X2Y1Y2>
<XαXβXγXδ>	$\frac{1}{45}[5+4e^{-6DT}]$	$\frac{1}{15}{e}^{-6DT}$	$\frac{1}{45}[5-2e^{-6DT}]$	<X1X2Y1Y2>

b)
$\langle X_{\alpha }^{A1}{X}_{\beta }^{A1}{Y}_{\gamma }^{A1}{Y}_{\delta }^{A1}\rangle$	1/15	−1/30	2/15	−1/30
$\langle X_{\alpha }^{A1}{X}_{\beta }^{A1}{Y}_{\gamma }^{A2}{Y}_{\delta }^{A2}\rangle =\langle X_{\alpha }^{A1}{X}_{\beta }^{A1}{Y}_{\gamma }^{A3}{Y}_{\delta }^{A3}\rangle$	7/60	1/60	1/12	1/60
$\langle X_{\alpha }^{A1}{X}_{\beta }^{A1}{X}_{\gamma }^{A1}{X}_{\delta }^{A1}\rangle$	1/5	1/15	1/15	1/15
$\langle X_{\alpha }^{A1}{X}_{\beta }^{A1}{X}_{\gamma }^{A2}{X}_{\delta }^{A2}\rangle =\langle X_{\alpha }^{A1}{X}_{\beta }^{A1}{X}_{\gamma }^{A3}{X}_{\delta }^{A3}\rangle$	1/10	−1/30	1/6	−1/30