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Nuclear dynamics for a three-state Jahn–Teller model system
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10.1063/1.3677273
/content/aip/journal/jcp/136/3/10.1063/1.3677273
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/3/10.1063/1.3677273

Figures

Image of FIG. 1.
FIG. 1.

(a) 2D adiabatic potential energy surfaces along the e modes, Q ea and Q eb . The potentials are from Eq. (7) using the parameters (in eV). Contour lines correspond to tic marks on the z-axis. Cuts along (b) Q ea , (c) Q eb , and (d) Q tc for all other Q ij = 0. (e) Cut along Q ea for Q eb = 7 and all other Q ij = 0. The grey markings illustrate different initial positions as described in the text.

Image of FIG. 2.
FIG. 2.

Selected dynamical properties for scenario “zero3.” (a) The adiabatic population of the states, and (b) the expectation values of the kinetic energy, 〈E kin, ij 〉, of each mode ij are plotted as a function of time. Marked points at the first maximum in 〈E kin, ij 〉 are denoted as and are used to evaluate coupling dependence, see Fig. 7. The parameters used (in eV) are: .

Image of FIG. 3.
FIG. 3.

(a) Time-dependent adiabatic densities on state 1 along Q ea (left) and Q eb (right) for case “zero3.” Arrows mark positions when wavepackets reach minima at (Q ea , Q eb ) = (3.333, 0) for WP1, and (− 1.666, ± 2.887) for WP2 (cf. Fig. 1(a)). APES cuts along Q ea (left) and Q eb (right) (b) at t = 0 fs going through the three-state CI, (c) going through the minimum (Q ea , Q eb ) = (3.333, 0) reached by WP1 at t = 5.5 fs, (d) going through the minima (−1.666, ± 2.887) reached by WP2 at t = 8 fs. Stars indicate positions of the wavepackets and the arrows schematically show their momentum.

Image of FIG. 4.
FIG. 4.

(a) Time-dependent population as a function of time for different values of coupling magnitudes F e and constant eV for case “zero3.” (b) Detailed view of the initial transition up to t = 5 fs with populations for all couplings superimposed to each other.

Image of FIG. 5.
FIG. 5.

(a) APES cuts along Q ea for when varying F e . (b) Time-dependent adiabatic densities of state 1 along mode Q ea for scenario “zero3.” From left to right: F e = 0.00, 0.155, 0.31, 0.465, 0.62 (in eV).

Image of FIG. 6.
FIG. 6.

(a) APES cuts along Q tc for different coupling magnitudes F e : colored lines show cuts along Q tc for Q ea = 2.5 and , and grey lines show cuts along Q tc for (corresponds to t = 0 fs). (b) Time-dependent adiabatic densities of state 1 for mode Q tc for scenario “zero3” for different coupling magnitudes F e : from left to right in eV: F e = 0.00, 0.155, 0.31, 0.465, 0.62 (in eV).

Image of FIG. 7.
FIG. 7.

Selected points from the kinetic energy data are plotted to show the influence of coupling parameter on forces on the wavepacket. (a) The first maximum point of 〈E kin 〉, , for each mode Q ij is plotted as a function of F e for constant eV. (b) as a function for constant F e = 0.62 eV. Highlighted with bold points is the eV case.

Image of FIG. 8.
FIG. 8.

(a) Time-dependent populations as a function of time for different values of coupling magnitudes and constant F e = 0.62 eV for case “zero3.” (b) Detailed view of the initial transition up to t = 5 fs with populations for all couplings superimposed to each other.

Image of FIG. 9.
FIG. 9.

(a) Time-dependent population as a function of time for case “eb1,” with F e = 0.62 eV and eV. (b) Time-dependent populations for different values of coupling strength F e : 0.155, 0.31, 0.465, and 0.62 eV, and constant eV.

Image of FIG. 10.
FIG. 10.

(a) APES cuts along Q ea and Q eb . Grey lines represent cuts at t = 0 to illustrate the initial positions, while the colored lines represent potential cuts going through the position of the wavepacket at the time of the first nonadiabatic transition (indicated by ①). These cuts are along Q ea for Q eb = 0.0, and along Q eb when Q ea = −3. The stars indicate the initial positions of the wavepacket and the arrows indicate the direction of motion. (b) Adiabatic densities along the modes Q ea and Q eb for states 1 and 2 as a function of time. “eb1” case with (in eV).

Image of FIG. 11.
FIG. 11.

(a) Time-dependent population as a function of time for case “eb2,” with F e = 0.62 eV and eV. (b) Time-dependent populations for different values of coupling strength F e : 0.155, 0.31, 0.465, and 0.62 eV, and with constant eV.

Image of FIG. 12.
FIG. 12.

(a) APES cuts along Q ea and Q eb . Grey lines represent cuts at t = 0 to illustrate the initial positions, while the colored lines represent potential cuts going through the position of the wavepacket at t = 3 fs which is the moment of the first nonadiabatic transition (indicated by ①). These cuts are along Q ea for Q eb = 3, and along Q eb when Q ea = −1.8. The stars indicate the initial positions of the wavepacket and the arrows indicate the direction of motion. (b) Adiabatic densities along the modes Q ea and Q eb for all states as a function of time. “eb2” case with (in eV).

Image of FIG. 13.
FIG. 13.

(a) Time-dependent population as a function of time for case “eb3,” with F e = 0.62 eV, eV. (b) Time-dependent populations for different values of coupling strength F e : 0.155, 0.31, 0.465, and 0.62 eV, and constant eV.

Image of FIG. 14.
FIG. 14.

(a) Selected APES cuts along the modes Q ea and Q eb for all states. Grey lines represent cuts at t = 0 to illustrate the initial positions, while the colored lines represent potential cuts going through the position of the wavepacket at the time of the first nonadiabatic transition (indicated by ①). These cuts are along Q ea for Q eb = 4, and along Q eb when Q ea = 2. The stars indicate the initial positions of the wavepacket and the arrows indicate the direction of motion. (a) Adiabatic densities along the modes Q ea and Q eb for all states as a function of time. “eb3” case with (in eV).

Tables

Generic image for table
Table I.

Initial conditions defining the systems to be studied. E tot is given for the reference system only: (in eV relative to the potential energy at the CI).

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/content/aip/journal/jcp/136/3/10.1063/1.3677273
2012-01-18
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nuclear dynamics for a three-state Jahn–Teller model system
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/3/10.1063/1.3677273
10.1063/1.3677273
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