^{1}, Ivano Tavernelli

^{1,a)}, Ursula Rothlisberger

^{1}, Claudia Filippi

^{2,b)}and Mark E. Casida

^{3,c)}

### Abstract

We present a mixed time-dependent density-functional theory (TDDFT)/classical trajectory surface hopping (SH) study of the photochemical ring opening in oxirane. Previous preparatory work limited to the symmetric CC ring-opening pathways of oxirane concluded that the Tamm-Dancoff approximation (TDA) is important for improving the performance of TDDFT away from the equilibrium geometry. This observation is supported by the present TDDFT TDA/SH calculations which successfully confirm the main experimentally derived Gomer-Noyes mechanism for the photochemical CO ring opening of oxirane and, in addition, provide important state-specific information not easily accessible from experiments. In particular, we find that, while one of the lowest two excited states is photochemically relatively inert, excitation into the other excited state leads predominantly to rapid ring opening, *cyclic*-. This is followed by hopping to the electronic ground state where hot dynamics leads to further reactions, namely, and . We note that, in the dynamics, we are not limited to following minimum energy pathways and several surface hops may actually be needed before products are finally reached. The performance of different functionals is then assessed by comparison of TDDFT and diffusion Monte Carlo potential energy curves along a typical TDDFT TDA/SH reaction path. Finally, although true conical intersections are expected to be absent in adiabatic TDDFT, we show that the TDDFT TDA is able to *approximate* a conical intersection in this system.

We like to acknowledge useful discussions with Professor Todd Martínez, Professor Melvyn Levy, Professor Massimo Olivucci, Professor Felipe Cordova, and M. Mathieu Maurin. C.F. acknowledges the support by the Stichting Nationale Computerfaciliteiten (NCF-NWO) for the use of the SARA supercomputer facilities. Dr. Latévi Max Lawson Daku is thanked for supplying us with equilibrium geometry HOMO energies calculated with ADF and the LB94 and SAOP model exchange-correlation potentials.

I. INTRODUCTION

II. THEORETICAL METHODS

III. TDDFT/SH DYNAMICS

A. Computational details

B. Results

IV. ASSESSMENT OF THE PERFORMANCE OF FUNCTIONALS ALONG THE REACTION PATH

A. Computational details

B. Vertical excitation energies

C. Potential energy curves

V. CONICAL INTERSECTIONS IN TDDFT

A. Computational details

B. Results

VI. CONCLUSION

### Key Topics

- Photochemical reactions
- 45.0
- Excitation energies
- 33.0
- Excited states
- 33.0
- Photochemistry
- 30.0
- Ground states
- 28.0

## Figures

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

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

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

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

(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) .

(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) .

(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).

(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).

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.

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.

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.

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.

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.

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.

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) .

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) .

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, .

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, .

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: .

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: .

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, .

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, .

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.

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.

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, .

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, .

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.

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

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.

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.

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.

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.

Diffusion Monte Carlo energies.

Diffusion Monte Carlo energies.

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

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

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