Time-Dependent Nuclear Quantum Dynamics Simulations

4 Time-Dependent Nuclear Quantum Dynamics Simulations 

Quantum dynamics simulations of the UV absorption spectrum and of the electronic state population dynamics of the molecule excited by a short laser pulse resonant with the transition to the bright B2u t t ) state, based on the models described in Sect. 5.3 were performed using the MCTDH method in the multi-set formalism (see Sect. 4.2.5 in Chap. 4). For the representation of the Hamiltonian and the wave function, a Hermite polynomial DVR scheme [60] was used for all the degrees of freedom. The number of SPF and primitive basis functions used in the calculations are listed in Table 5.4. Test calculations with both larger primitive and SPF bases have been 

Model Combinations of modes Numbers of SPFs Numbers of grid points 

---

For the dynamics simulation, we again used our approach [80] for the coupled electron and nuclear quantum dynamics. We followed the time-dependent expectation value of the induced electric dipole moment nit) = which is related to the time-dependent electron density ptot r,t R t)) of Eq. (8.12) through n(t)) = (ptotir,l R(l)) fi (ptot(r,t, R(t )r) with the dipole operator. 

The standard translation of the full quantum formula of the absorbance, Eq. (31), to a mixed quantum classical description (see, e.g., [16-18]) is similar to what is the essence of the (electronic ground-state) classical path approximation introduced in the foregoing section. One assumes that all involved nuclear coordinates behave classically and their time-dependence is obtained by carrying out MD simulations in the systems electronic ground state. This approach when applied to the absorbance is known as the dynamical classical limit (DCL, see, for example, Res. [17]). 

Modem first principles computational methodologies, such as those based on Density Functional Theory (DFT) and its Time Dependent extension (TDDFT), provide the theoretical/computational framework to describe most of the desired properties of the individual dye/semiconductor/electrolyte systems and of their relevant interfaces. The information extracted from these calculations constitutes the basis for the explicit simulation of photo-induced electron transfer by means of quantum or non-adiabatic dynamics. The dynamics introduces a further degree of complexity in the simulation, due to the simultaneous description of the coupled nuclear/electronic problem. Various combinations of electronic stmcture/ excited states and nuclear dynamics descriptions have been applied to dye-sensitized interfaces [54—57]. In most cases these approaches rely either on semi-empirical Hamiltonians [58, 59] or on the time-dependent propagation of single particle DFT orbitals [60, 61], with the nuclear dynamics being described within mixed quantum-classical [54, 55, 59, 60] or fuUy quantum mechanical approaches [61]. Real time propagation of the TDDFT excited states [62] has... 

---