Structure of DPM in the principal axis frame. The three soft degrees of freedom associated with the lowest frequency modes are shown and include the two torsional coordinates and defined as the dihedral angle between the planes formed by and the three ring carbon atoms nearest to the methylene group and the coordinate defined as the bend (butterfly).
Ground state torsional potential energy surface for DPM calculated at the level of theory. The axes represent the torsion angles of the phenyl rings, and . The phenyl torsional normal mode displacement directions (symmetric) and (antisymmetric) are shown by double-headed arrows. The structures associated with the two enantiomeric minima, the gable transition state, and the perpendicular transition state are all shown.
Rotationally resolved spectrum of the origin band of DPM-. The full spectrum is shown in the top panel with residuals (Res). The residuals with and without 5% -type character over an expanded portion blue of the central -type branch in the lower panel illustrates the complete absence of -type character.
Rotationally resolved spectrum of the origin band in DPM-. The full spectrum is shown in the top panel with residuals (Res). The residuals with and without 5% -type character over an expanded portion blue of the central -type branch in the lower panel illustrates the complete absence of -type character.
Rotationally resolved spectrum of the origin band in DPM (upper panel) and an expanded region near the center of this band (lower panel). The top spectrum in each panel was obtained under warmer expansion conditions and compared with the lower spectrum obtained under similar conditions used for the origin of DPM-. The two sets of tie lines in the lower panel designate progressions that closely resemble -type -branch series in the quantum number .
Rotationally resolved spectrum of the origin band in DPM-. The spectrum was obtained under similar conditions used for the origin of DPM-.
Theoretical rotational constants of DPM shown as a function of the ring torsional angle for the optimized symmetric structures. The equilibrium structure is designated with a vertical line and near the axis interchange angle of .
The delocalized TDM vectors of the and states of DPM that agree with observed relative intensity ratio. Also shown are the vectors of the state that were fitted to the dipole model for . The corresponding directions of for the state (not shown) are the in-phase components. Projections are shown along the axis in (a), along the axis in (b), and along an axis from in the plane in (c) to illustrate the out-of-ring-plane component (left ring) and in-plane rotation (right ring) of . To reduce clutter and preserve phase, only one direction of all TDM vectors (which are double-headed arrows) is shown. The experimentally fitted MP2/cc-pVTZ geometry is shown in each panel ( and ).
Energies of the exciton levels for symmetric structures from (a) the dipole-dipole coupling model and (b) TD-B3LYP//MP2 and CIS levels of theory ( basis sets) as a function of the ring torsion angle . The splitting are shown in (a) for (dotted lines), and from CIS (solid lines), and and from TD-DFT (dashed lines).
(a) The TDM components (in Debye) of DPM predicted by (solid lines) and the in-plane dipole model (dashed lines). (b) In-plane angles and out-of-plane angles of the dipole model that describe the TDM components from CIS (solid lines) and TD-DFT (dashed lines) in (a). The optimized values of the inter-ring angle are included in the dipole model as a function of the ring torsion angle and range between and for both calculations.
The relative band strengths as a function of the ring torsion angle in the principal axis frame of DPM at the (a) CIS and (b) TD-B3LYP//MP2 levels of theory ( basis sets). The best correspondence with the observed components occurs near from CIS and from TD-DFT.
Rotational constants and distortion parameters from least-squares fits of the ground state and origin spectra of DPM- and DPM-. The parameters of DPM- were determined from fits of the MW spectrum. Other parameters were determined from the UV spectra using a combination of techniques that made use of GA and nonlinear least-squares fitting routines (see text for details).
Experimental and calculated ground state rotational constants of DPM. The rotational parameters are also given for fitted structures where the two parameters and defined in Fig. 1 were least-squares fitted to the observed moments of inertia.
Results of excited state calculations on DPM.
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