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Hierarchical transformation of Hamiltonians with linear and quadratic couplings for nonadiabatic quantum dynamics: Application to the ππ*/nπ* internal conversion in thymine
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10.1063/1.4729049
/content/aip/journal/jcp/136/24/10.1063/1.4729049
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/24/10.1063/1.4729049

Figures

Image of FIG. 1.
FIG. 1.

Schematic picture of the thymine molecule, and representation of the orbitals involved in the definition of the first two excited states. The “dark” nπ* state originates mainly from the HOMO−1 → LUMO transition, while the ππ* state is essentially the HOMO → LUMO transition.

Image of FIG. 2.
FIG. 2.

Diabatic populations as a function of time for the LVC (left panel) and the QVC (right panel) models. For the LVC model, the results are reported for the first (3 modes, dotted line), second (6 modes, dashed line), and third (9 modes, continuous line) effective Hamiltonians of the hierarchy. For the QVC case, the results are shown for the first (3 modes, dashed line) and the second (9 modes, continuous line) effective Hamiltonians.

Image of FIG. 3.
FIG. 3.

Curves representing the quantities ΔE ± σΔE , as a function of propagation time for the 3-, 6-, and 9-modes LVC models. ΔE is the energy difference between the LVC diabatic PESs and σΔE is its standard deviation. The mean values are computed relatively to the S π wave packet.

Image of FIG. 4.
FIG. 4.

Standard deviation of the coupling dimensionless coordinate (see text), as a function of time, for the LVC and QVC 9-modes models. The initial value is exactly in both cases since it is the width of the initial Gaussian exp (− Q 2/2) .

Image of FIG. 5.
FIG. 5.

Value, in eV, of the diabatic potentials W π and W n for the LVC (left panel) and QVC (right panel) 9-modes models, at the average position of the wave packet located on the S π state. The horizontal axes of times are set in correspondence of the value of the W π potential at its minimum.

Image of FIG. 6.
FIG. 6.

Comparison between the population transfer predicted by the LVC (dashed line) and QVC (continuous line) models, for computations which involve the same number of effective modes (9).

Image of FIG. 7.
FIG. 7.

Amplitudes of the autocorrelation function for the LVC (top panel) and QVC (middle panel) models and their direct comparison (bottom panel), for the first 130 fs of dynamics.

Image of FIG. 8.
FIG. 8.

Nonadiabatic absorption spectra computed for the two models, LVC (left panel) and QVC (right panel), using different numbers of effective modes.

Tables

Generic image for table
Table I.

Parameters, in eV, for the 9-modes LVC Hamiltonian. For the matrix, since it is symmetric, only the upper diagonal part has been reported.

Generic image for table
Table II.

Parameters, in eV, for the 9-modes QVC Hamiltonian. For the matrices, since they are symmetric, only the upper diagonal part has been reported.

Generic image for table
Table III.

Energies (in eV) at relevant points of the potential energy surfaces for the Hamiltonian models discussed in the text. For each model the energies of the two electronic states S π and S n and their difference are reported at the Franck-Condon point (first row) and at the minima of the two PESs (second and third row).

Generic image for table
Table IV.

First, second, and third order cumulants computed for thymine according to the LVC and QVC models. In the LVC case, the cumulants are recovered exactly for any truncation of the Hamiltonian. In the QVC case only the first order cumulant is reproduced exactly in any truncation. In the last two columns, the cumulants relative to the first two effective Hamiltonians are reported, together with the percent relative error (in parenthesis) with respect to the exact value. The value of the first cumulant has been diminished by the zero-point energy of the ground state E ZPE , so to obtain the energy of the center of gravity of the corresponding spectrum.

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/content/aip/journal/jcp/136/24/10.1063/1.4729049
2012-06-25
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hierarchical transformation of Hamiltonians with linear and quadratic couplings for nonadiabatic quantum dynamics: Application to the ππ*/nπ* internal conversion in thymine
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/24/10.1063/1.4729049
10.1063/1.4729049
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