Niu Y.L.Lin C.K.Zhu C.Y.Mineo H.Chao S.D.Fujimura Y.Hayashi M.Lin S.H.2022-10-122022-10-122012https://www.scopus.com/inward/record.uri?eid=2-s2.0-85047003029&doi=10.1007%2f978-94-007-5297-9_4&partnerID=40&md5=14fad959861c85a73a9c0b2460fd2869https://scholars.lib.ntu.edu.tw/handle/123456789/623488The density matrix method is a powerful theoretical technique to describe the ultrafast processes and to analyze the femtosecond time-resolved spectra in the pump-probe experiment. The dynamics of population and coherence of the system can be described by the evolution of density matrix elements. In this chapter, the applications of density matrix method on internal conversion and vibrational relaxation processes will be presented. As an example, the ultrafast internal conversion process of ??* ??n?* transition of pyrazine will be presented, in which case the conical intersection is commonly believed to play an important role. A treatment with Q-dependent nonadiabatic coupling will be applied to deal with the internal conversion rate. Another important ultrafast process, vibrational relaxation, which usually takes place in sub-ps and ps range, will be treated using adiabatic approximation. Then the vibrational relaxation in water dimer and aniline will be chosen to demonstrate the calculation. ? 2012, Springer Science+Business Media Dordrecht.Adiabatic Approximation; Conical Intersection; Internal Conversion; Vibrational Relaxation; Water Dimerjournal article10.1007/978-94-007-5297-9_42-s2.0-85047003029