### Abstract

The results of a theoretical investigation of coherent π-electron dynamics for nonplanar (*P*)-2,2′-biphenol induced by ultrashort linearly polarized UV pulses are presented. Expressions for the time-dependent coherent angular momentum and ring current are derived by using the density matrix method. The time dependence of these coherences is determined by the off-diagonal density matrix element, which can be obtained by solving the coupled equations of motion of the electronic-state density matrix. Dephasing effects on coherent angular momentum and ring current are taken into account within the Markov approximation. The magnitudes of the electronic angular momentum and current are expressed as the sum of expectation values of the corresponding operators in the two phenol rings (*L* and *R* rings). Here, *L* (*R*) denotes the phenol ring in the left (right)-hand side of (*P*)-2,2′-biphenol. We define the bond current between the nearest neighbor carbon atoms C_{ i } and C_{ j } as an electric current through a half plane perpendicular to the C_{ i }–C_{ j } bond. The bond current can be expressed in terms of the inter-atomic bond current. The inter-atomic bond current (bond current) depends on the position of the half plane on the bond and has the maximum value at the center. The coherent ring current in each ring is defined by averaging over the bond currents. Since (*P*)-2,2′-biphenol is nonplanar, the resultant angular momentum is not one-dimensional. Simulations of the time-dependent coherent angular momentum and ring current of (*P*)-2,2′-biphenol excited by ultrashort linearly polarized UV pulses are carried out using the molecular parameters obtained by the time-dependent density functional theory (TD-DFT) method. Oscillatory behaviors in the time-dependent angular momentum (ring current), which can be called angular momentum (ring current) quantum beats, are classified by the symmetry of the coherent state, symmetric or antisymmetric. The bond current of the bridge bond linking the *L* and *R* rings is zero for the symmetric coherent state, while it is nonzero for the antisymmetric coherent state. The magnitudes of ring current and ring current-induced magnetic field are also evaluated, and their possibility as a control parameter in ultrafast switching devices is discussed. The present results give a detailed description of the theoretical treatment reported in our previous paper [H. Mineo, M. Yamaki, Y. Teranish, M. Hayashi, S. H. Lin, and Y. Fujimura, J. Am. Chem. Soc.134, 14279 (Year: 2012)10.1021/ja3047848].

Received 08 November 2012
Accepted 22 January 2013
Published online 15 February 2013

Acknowledgments:
We are grateful to Professor M. Hayashi for his useful comments on the electronic structure theory of molecules. This work was supported by a JSPS Research Grant (No. 23550003) and the National Science Council of Taiwan. H.M. would like to thank Professor J.-L. Kuo for his critical comments and supports.

Article outline:

I. INTRODUCTION
II. COHERENT π-ELECTRON ANGULAR MOMENTUM AND CURRENT
A. Equations of motion for π electrons in a pulsed laser field
B. Coherent electric angular momentum
C. Coherent ring current
III. RESULTS AND DISCUSSION
A. Generation of two-state electronic coherence by linearly polarized UV pulses
B. Angular momentum quantum beats
C. Bondcurrents and time evolution of coherent ring current
D. Coherent ring current-induced magnetic field
E. Bridge bondcurrent density
IV. SUMMARY AND CONCLUSION

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