Time-dependent electronic population

Figure 33. Time-dependent electronic population probability of Model IVa. Compared...

Fig. 6. Time-dependent electronic population of the E2B2u state of Bz+ for a vertical transition. The wave-packet is located initially at the E state surface and seen to undergo an efficient radiationless transition at a time scale of 10-20 fs. The results of the full calculation (solid line) and of the propensity rule (dashed line) are compared.

In this review, we shall present and discuss spectra at various resolutions, time-dependent electronic populations and reduced densities. 

Pig. 7. Comparison of time-dependent electronic populations of upper (P+) lower (P ) adiabatic states for the Chappuis band of ozone, (a) Reference data from Ref. 81. (b) Results from the concept of regularized diabatic states, from Ref. 40. 

Fig. 13. Time-dependent electronic populations of the X, B and C states of Bz+ obtained from wavepacket dynamical calculations. The ab initio parameters of Ref. 148 and the MGTDH wavepacket propagation method have been employed in the study. The initial wavepacket is defined by a FC transition to the C state potential energy surface it is seen to undergo a stepwise transition to the B and then to the X state of the cation. The respective time constants are approximately 20fs and 200fs. (a) Calculation with degenerate vibrational modes and electronic states, (b) Analogous calculation, but suppressing these degeneracies. Apparently, this simpler calculation reproduces the full result of panel (a) quite well. For more details see text.

Figure 6.21 presents the time dependent electronic population for the excited state. It is defined as... 

Fig. 6.1 S Time-dependent electronic populations of the C ( A2u) — B( E2g) — X CE g) manifold of Bz+ following a vertical transition to the C CA2u) state of the system. The full calculation, with all degeneracies retained (upper panel) is compared with an approximate one where the electronic and vibrational degeneracies are suppressed (lowerpanel)...

Fig. 6.17 Time-dependent electronic populations of the lowest five electronic states of the mono-and 1,2,3-tiifluorobenzene radical cations (lower and upper panel, respectively). The initial...

Fig. 6.19 Time-dependent electronic populations (upper panel) and reactive flux (lower panel) for the relevant states of pyrrole after excitation to the B2 state of Fig. 6.18...

Mechanism. Finally, the build-up dynamics and the time dependence of the induced electronic population dynamics are investigated. Subsequently we consider whether, in addition to the vibrational dynamics, the time-resolved electronic population dynamics are detectable in the ion-signal. 

Collision-induced vibrational relaxation was studied on vibrationally excited NH(X produced by pulsed electron impact on N2-H2 or N2-H2-Ar gaseous mixtures time-resolved IR Fourier transform spectroscopy was used to observe the v = 3 2, 2 1, and 1 0 fundamental band emission (2500 to 3400 cm ) which allowed the time-dependent vibrational populations to be determined. The following rate constants for v v-1 transitions, were derived at room temperature for the collision partners N2, Ar, and H2 [1] ... 

Hydrogen transfer in excited electronic states is being intensively studied with time-resolved spectroscopy. A typical scheme of electronic terms is shown in fig. 46. A vertical optical transition, induced by a picosecond laser pulse, populates the initial well of the excited Si state. The reverse optical transition, observed as the fluorescence band Fj, is accompanied by proton transfer to the second well with lower energy. This transfer is registered as the appearance of another fluorescence band, F2, with a large anti-Stokes shift. The rate constant is inferred from the time dependence of the relative intensities of these bands in dual fluorescence. The experimental data obtained by this method have been reviewed by Barbara et al. [1989]. We only quote the example of hydrogen transfer in the excited state of... 

Molecular rearrangement resulting from molecular collisions or excitation by light can be described with time-dependent many-electron density operators. The initial density operator can be constructed from the collection of initially (or asymptotically) accessible electronic states, with populations wj. In many cases these states can be chosen as single Slater determinants formed from a set of orthonormal molecular spin orbitals (MSOs) im as / =... 

To describe the electronic relaxation dynamics of a photoexcited molecular system, it is instructive to consider the time-dependent population of an electronic state, which can be defined in a diabatic or the adiabatic representation [163]. The population probability of the diabatic electronic state /jt) is defined as the expectation value of the diabatic projector... 

Figure 1. Quantum-mechanical (thick lines) and mean-field-trajectory (thin lines) calculations obtained for Model 1 describing the S2 — Si internal-conversion process in pyrazine. Shown are the time-dependent population probabilities Pf t) and Pf (t) of the initially prepared adiabatic and diabatic electronic state, respectively, as well as the mean momenta pi (t) and P2 t) of the two totally symmetric modes Vi and V( of the model.

Figure 3. Time-dependent simulations of the nonadiabatic photoisomerization dynamics exhibited by Model III, comparing results of the mean-field-trajectory method (dashed lines), the surface-hopping approach (thin lines), and exact quanmm calculations (full lines). Shown are the population probabilities of the initially prepared (a) adiabatic and (b) diabatic electronic state, respectively, as well as (c) the probability Pdsit) that the sytem remains in the initially prepared cis conformation.

Figure 7. Comparison of SH (thin solid line), MFT (dashed line), and quantum path-integral (solid line with dots) calculations (Ref. 198) obtained for Model Va describing electron transfer in solution. Shown is the time-dependent population probability Pf t) of the initially prepared diabatic electronic state.

That is, the classical DoF propagate according to a mean-field potential, the value of which is weighted by the instantaneous populations of the different quantum states. A MFT calculation thus consists of the self-consistent solution of the time-dependent Schrodinger equation (28) for the quantum DoF and Newton s equation (32) for the classical DoF. To represent the initial state (15) of the molecular system, the electronic DoF dk Q) as well as the nuclear DoF xj Q) and Pj 0) are sampled from a quasi-classical phase-space distribution [23, 24, 26]. 

Figure 11. Time-dependent population probability of the upper (a) adiabatic and (b) diabatic electronic state of Model 1. The quantum-mechanical results (thick lines) are compared to SH results obtained directly from the electronic coefficients (dashed lines) and to SH results obtained from binned coefficients (thin solid lines), reflecting the percentage N2(t) of trajectories propagating on the upper adiabatic surface. Panel (c) shows the absolute number of successful (thick hue) and rejected (thin line) surface hops occurring in the SH calculation.

Figure 19. Time-dependent (a) diabatic and (b) adiabatic electronic excited-state populations and (c) vibrational mean positions as obtained for Model 1. Shown are results of the mean-field trajectory method (dotted lines), the quasi-classical mapping approach (thin full lines), and exact quantum calculations (thick full lines).

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