Photoelectron circular dichroism of chiral molecules studied with a continuum-state-corrected strong-field approximation

Motivated by recent experiments on circular dichroism in the photoelectron momentum distributions from strong-field ionization of chiral molecules [C. Lux et al., Angew. Chem. Int. Ed. 51, 5001 (2012); C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013)], we investigate the origin of this effect theoretically. We show that it is not possible to describe photoelectron circular dichroism with the commonly used strong-field approximation due to its plane-wave nature. We therefore apply the Born approximation to the scattering state and use this as a continuum-state correction in the strong-field approximation. We obtain electron distributions for the molecules camphor and fenchone. In order to gain physical insight into the process, we study the contributions of individual molecular orientations.

Figure 1

HOMO orbitals of the molecules camphor (a) and fenchone (b) as obtained from gaussian [32]. The CO bond points upwards.

Figure 2

Illustration of the PECD effect in camphor. On the left, a cut ($k_y=0$) through a momentum distribution at an arbitrary orientation of camphor is shown. In the middle, the corresponding orientation-averaged distribution is shown, and on the right the difference between forward and backward emission is shown in units relative to the average amplitude on the inner (three-photon) ring. The LCP [as defined in Eq. (9)] laser pulse propagates from left to right, as indicated by the arrow.

Figure 3

Legendre coefficients $b_{2n+1}$ for the molecules (a) camphor and (b) fenchone according to Eq. (12). Shown are the values for three-photon ionization (red, solid), four-photon ionization (green, crossed), and five-photon ionization (blue, striped), which are normalized such that the coefficient $b_0$ (the total ionization yield) is one for each case. A LCP cw field of 398 nm wavelength and an intensity of $2.5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ have been used.

Figure 4

Legendre coefficients $b_0$ (a), $b_1$ (b), $b_2$ (c), and $b_3$ (d) for camphor in dependence of the molecular orientation $(\eta ,\xi )$. All values are given relative to the average yield $b_{0,\mathrm{avg}}$ and correspond to three-photon ionization. Note the different color scales in the plots.

Figure 5

Dichroism of each molecular orientation $(\eta ,\xi )$ of camphor, decomposed into the Legendre coefficients (a) $b_0$, (b) $b_1$, (c) $b_2$, and (d) $b_3$. All values are given in relation to the average yield $b_{0,\mathrm{avg}}$ and correspond to three-photon ionization. Note the different color scales in the plots.

Figure 6

Same as Fig. 5, but for fenchone.