(a) Geometrical structure of (P)-2,2′-biphenol and transition moment vectors. (b) Three electronic excited states and optical transitions to create the coherent electronic states.
Occupied and unoccupied MOs relevant to the coherent electronic states. a, b 1, and b 2 electronic states have electronic configurations of 46 → 52, 46 → 53, and 46 →51, respectively. A (B) denotes the totally symmetric (antisymmetric) irreducible representation of the C2 point group.
Time evolution of coherent angular momentum (left-hand side) created by π pulse excitation (right-hand side): (a) for (b 1 + b 2) electronic coherence created by pulse with the amplitude of 0.19 TW/cm2, (b) for (a + b 1) electronic coherence created by pulse with the amplitude of 0.83 TW/cm2, and (c) for (a + b 2) electronic coherence created by pulse with the amplitude of 3.32 TW/cm2. Dephasing constants were set as γb1b2 = γab1 = γab2 = 0.01 eV (1/50 fs−1).
Bond currents J ij for the three types of electronic coherence at t = t* when the maximum coherence is created, i.e., , , or . denotes the averaged ring current given by Eq. (14) . The blue arrows above C–C bonds denote the initial direction of the currents. Dephasing effects were omitted. Note that the bridge current J 1,7 = 0 for (b 1 + b 2) electronic coherence, while J 1,7 ≠ 0 for the other two (a + b 1) and (a + b 2) electronic coherences. The same magnitudes of pulses as those in Fig. 3 were used.
Inter-atomic bond current as a function of θ. The values are normalized by . θ, (0 ⩽ θ ⩽ π/3) is defined in the inserted figure. Here, r i and r j are the positions of two atomic sites of the bond. s is the position of the half plane S. . The red broken line refers to the first term of and the blue dotted line refers to the second term. The black line indicates the total value of .
Time evolution of coherent ring currents created by a π pulse excitation. J R and J L denote the ring currents created on R and L rings, respectively. The same pulse excitation conditions as those shown in Fig. 3 are used. J B denotes the ring current created on the bridging bond: (a) for (b 1 + b 2) electronic coherence, (b) for (a + b 1) electronic coherence, and (c) for (a + b 2) electronic coherence. Dephasing constants were set as γb1b2 = 0.01 eV (1/50 fs−1) and 0.05 eV (1/10 fs−1) for (a); γab1 = γab2 = 0.01 eV for (b) and (c). The same magnitudes of pulses as those in Fig. 3 were used.
Induced magnetic fields for the (b 1 + b 2) electronic coherence as a function of height h from the center of aromatic ring K at the time of maximum coherence t = t*. and B K (t*, h) are the induced magnetic field calculated by a SRL model and that calculated by a distribution of the current density, respectively.
Contour plot of the bridge bond current density [μA/ Å2] on the perpendicular plane at the bond center, which is calculated at the maximum value for the (a + b 1) electronic coherence at t = t*. The region in which the current density flows from the back (L ring) to the front (R ring) is denoted by positive values, while the region in which the current density flows from the front to the back is denoted by negative values.
(a) Relation between the molecular frame denoted by xy and that of the new frame XY for evaluation of angular momentum at O, the direction of which is perpendicular to the molecular plane, xOy. is the angular momentum operator. (b) Coordinates on the new frame.
Coordinates for the inter-atomic bond current from atom j to the nearest neighbor atom i, in a hexagonal ring, which determines the current passing through a half-plane S perpendicular to the bond at the center R c .
Coordinates for the inter-atomic bond current, , which is perpendicular to a half-plane S (x = 0) at carbon nuclei C j of bond C i –C j .
Coordinates for the inter-atomic bond current in a general case. The half plane S is set at a position between carbon atomic sites, C i and C j . N is the number of carbon atoms. Angle θ is defined in the range 0 ⩽ θ ⩽ θ N in which θ N is the angle between C i and C j from the center of the ring.
Coordinates for the induced magnetic field created at the center of ring K at height h by a ring current density ⟨J(t)⟩ K f(x, z)dxdz. The bond between i and j lies on the y-axis.
Angular momenta of the two phenol rings, l L and l R , and the resultant angular momenta l X an l Z at the maximum coherence. a
Article metrics loading...
Full text loading...