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Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry
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10.1063/1.2978380
/content/aip/journal/jcp/129/12/10.1063/1.2978380
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/12/10.1063/1.2978380

Figures

Image of FIG. 1.
FIG. 1.

Mechanism proposed by Gomer and Noyes (Ref. 57).

Image of FIG. 2.
FIG. 2.

Ground-state orbitals obtained using the PBE functional at the equilibrium geometry: (a) HOMO , (b) LUMO , (c) , and (d) .

Image of FIG. 3.
FIG. 3.

(a) Cut of potential energy surfaces along the reaction path of a LZ (--) and a FS (—) trajectory (black, ; blue, ; green, ; magenta, ). Both trajectories were started by excitation into the state, with the same geometry and same initial nuclear velocities. The running states of the LZ and the FS trajectory are indicated by the red crosses and circles, respectively. (b) State populations (black, ; blue, ; green, ; magenta, ) and FS hopping probability (dashed) as a function of time for the FS trajectory shown in (a). The corresponding LZ probability is 98% for at the point of the minimum of the gap. The geometries of the LZ trajectory are shown at time a) 243, b) 284, and c) .

Image of FIG. 4.
FIG. 4.

(a) Cut of potential energy surfaces along reaction path of a LZ (--) and a FS (—) trajectory (black, ; blue, ; green, ; magenta, ). Both trajectories were started by excitation into the state, with the same geometry and same initial nuclear velocities. The running states of the LZ and the FS trajectory are indicated by the red crosses and circles, respectively. The geometries of the LZ trajectory are shown at time a) 0, b) 10, and c) . (b) State populations (black, ; blue, ; green, ; magenta, ) as a function of time for the FS trajectory shown in (a).

Image of FIG. 5.
FIG. 5.

Change of character of the active state along the reactive LZ trajectory, shown in Fig. 4. Snapshots were taken at times (a) 2.6, (b) 7.4, (c) 12.2, and (d) . For (a) and (b), the running state is characterized by a transition from HOMO to , while for (c) and (d) it is characterized by a HOMO-LUMO transition due to orbital crossing. HOMO remains all the time the oxygen nonbonding orbital.

Image of FIG. 6.
FIG. 6.

A swarm of ten trajectories, starting in the state (black, ; blue, ; green, ; magenta, ; red, running state). (a) LZ SH. The trajectory marked with an asterisk corresponds to the oxygen abstraction reaction. The other trajectories all lead the unsymmetric CO bond rupture. (b) FS SH. In the trajectory marked with an asterisk, the molecule is trapped in the unreactive state. The other trajectories all lead the unsymmetric CO bond rupture.

Image of FIG. 7.
FIG. 7.

Fragmentation to and . PES of the running state and its time average are shown in red and black, respectively. If is not the running state, it is shown in blue. Structures were taken at times (a) 31, (b) 56, (c) 72, (d) 122, and (e) . CC distances (Å) are indicated.

Image of FIG. 8.
FIG. 8.

Formation of and CO (colors as in Fig. 7). Structures were taken at times (a) 32, (b) 70, (c) 474, (d) 1151, (e) 1705, and (f) .

Image of FIG. 9.
FIG. 9.

Comparison of the DMC (dashed, triangles) potential energy curves, TDPBE/TDA (circles), and TDPBE/LR (squares). Also shown are the PBE curve (black, circles), the HOMO-LUMO gap (, red), and the TDPBE ionization threshold at (, dotted, open circles). The (TD)PBE calculations were carried out with TURBOMOLE using the aug-cc-pVTZ basis. Black, ; blue, , green, .

Image of FIG. 10.
FIG. 10.

Comparison of the potential energy curves of TDPBE/TDA (circles) and TDPBE0/TDA (squares). Also shown are the PBE (black, circles) and PBE0 (black, squares) curves, and the PBE (red, circles) and PBE0 (red, squares) HOMO-LUMO gap (, red). The (TD)PBE and (TD) PBE0 calculations were carried out with TURBOMOLE using the aug-cc-pVTZ basis. DMC results (dashed) are also shown. Black, ; blue, ; and green: .

Image of FIG. 11.
FIG. 11.

Comparison of the TDPBE/TDA (circles) and TDLDA/SAOP (solid) potential energy curves to DMC (dashed). Also shown is the TDPBE ionization threshold (dotted). Black, , blue, green, .

Image of FIG. 12.
FIG. 12.

symmetry CASSCF conical intersection structure. (a) The DC vector corresponds to a sort of twisting in opposing directions of the CO and the group to which it is joined. (b) The UGD vector corresponds to the opening of the CCO angle while maintaining symmetry.

Image of FIG. 13.
FIG. 13.

On the left hand side, shown are the and PESs for each method computed as described in the text. On the right hand side, shown are the corresponding energy difference, .

Image of FIG. 14.
FIG. 14.

A selection of representative geometries and their CCO angles for the coordinates in Fig. 13. The symmetry CASSCF conical intersection structure is at the origin.

Tables

Generic image for table
Table I.

DMC and experimental excitation energies (eV). DMC energies were computed for the PBE-optimized ground state symmetric structure. Assignment of the experiment is our own.

Generic image for table
Table II.

TDDFT/TDA excitation energies , deviations from corresponding DMC value , oscillator strengths , and assignment. Computations were carried out using a plane wave basis, except for the TDPBE0 calculations where the aug-cc-pVTZ basis was used.

Generic image for table
Table III.

Diffusion Monte Carlo energies.

Generic image for table
Table IV.

Geometries for the Diffusion Monto Carlo energy calculations (Å).

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/content/aip/journal/jcp/129/12/10.1063/1.2978380
2008-09-25
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/12/10.1063/1.2978380
10.1063/1.2978380
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