The potential energy curves (Eq. (2) ) of biphenyl (red, solid) and AAC (blue, dashed) vs the torsion angle. The structure of biphenyl is shown on the left, and that of AAC is shown on the right. The biphenyl torsional potential is taken from Ref. 52 , and that of AAC was calculated within density functional theory with the BP86 functional and a TZVP basis set using Q-Chem, 58 and fit to the double cosine form of Eq. (2) . Details of the calculation of the AAC potential energy are given in the supplementary material. 59
Torsional level spectra. (a) The first 26 torsional energy levels of biphenyl superimposed on its potential energy curve. (b) Energy level spacing between adjacent eigenstates for biphenyl (solid red, left ordinate) and AAC (dashed blue, right ordinate). Both molecules exhibit the same level spacing characteristics, differing only in the density of torsional states. Energy levels shown are for the w 1 Whittaker-Hill solution symmetry set.
Maximum alignment achieved as a function of the dimensionless interaction parameter Ω (Eq. (10) ), where Ω = 1 corresponds to 16 TW/cm2 for biphenyl (solid red), and to 3 TW/cm2 for AAC (dashed blue). All simulations correspond to T = 0 K. The Ω = 0 limit corresponds to the field-free equilibrium configuration. ⟨cos 2β⟩ →1 in the limit of coplanarity.
Time evolution of the expectation value ⟨cos 2β⟩ (shown in red) for biphenyl in response to an Ω = 1 laser pulse with a FWHM of 175 fs (shown in black). The left-hand graph shows the dynamics in the presence of the field, whereas the right-hand graph shows the dynamics over 40 ps. The temperature is 0 K.
Roles played by the system and field parameters. The left portion of each panel shows the dynamics in the presence of the laser field (t = 1.5 − 3.0 ps) along with the pulse envelope (black curve), whereas the right portion shows the long time, field-free evolution. (a) Biphenyl at T = 0 K, for a pulse duration of 175 fs FWHM, and interaction strengths of Ω = 1 (16 TW/cm2) (red), Ω = 3 (48 TW/cm2) (blue). (b) Biphenyl for an interaction strength of Ω = 1, pulse duration of 175 fs FWHM, and temperatures T = 0 K (red), T = 300 K (blue). (c) AAC for an interaction strength of Ω = 1 (3 TW/cm2) and temperatures T = 0 K (red), T = 300 K (blue). (d) Both molecules for Ω = 1, pulse duration of 353 fs FWHM and T = 0 K. The biphenyl response is shown in red, and that of AAC in blue.
The probability density associated with a biphenyl torsional wavepacket vs time and the torsion angle for the parameters of Figure 4 . The periodicity of the potential energy curve leads to two equivalent wavepackets, each centered around one of the two minima (only one is shown).
(a) Time evolution of the torsional alignment of AAC for Ω = 7 (corresponding to an intensity of 21 TW/cm2), T = 0 K, and a pulse duration of 615 fs FWHM. Shown is the total expectation value (black, dashed) along with its population ⟨cos 2β⟩ p (red, solid) and coherence ⟨cos 2β⟩ c (blue, dotted) projections along with the pulse profile (green, dashed). (b) The probability densities associated with the torsional eigenfunctions of w 1 symmetry for AAC.
The absolute value of density matrix elements for biphenyl after the pulse turnoff for the WH solutions of the 1st symmetry set at T = 0 K. (a) Ω = 1, (b) Ω = 3, (the conditions of Figure 5(a) ). Although torsional excitation is dominated by single-quantum processes, matrix elements distant from the diagonal (corresponding to high order torsional coherences) have comparable magnitudes to first order coherences.
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