3D15A Theoretical Study on the Wavepacket Dynamics in the Excited States of Aromatic Biomolecules(Graduate School of Science, Tohoku University) {Wilfredo Credo Chung, Yukiyoshi Ohtsuki, Yuichi Fujimura(Institute of Physical and Theoretical Chemistry, Technical University of Munich, Germany) Wolfgang Domcke

Introduction. DNA bases have very low quantum yield
Hfor fluorescence. 1 In effect, photo-induced reactions inHNNHN
9 4 3N92living cells are diminished despite the observation that the324H 81H 8lowest light-absorbing ππ* excited states of DNA bases lie
N1
N7 5N
6N7 5 6 1
approximately 5 eV above their respective ground states.
HN
This significant energy deposited in the molecule couldNHHH
H
have triggered a variety of photoreactions, presumably withharmful consequences to the organisms which these bases
7H‑adenine
9H‑adenine
make up. Fortunately, ultrafast nonradiative decay processes seem to quench reactive decay channels back to theFigure 1 . Tautomers of adenine.
electronic ground state providing DNA with a high level ofphotostability.1,2
The fluorescence quantum yield for adenine is only about 0.0003.1,3 Wilson and Callis previously reported that the major part of the fluorescence is due to the minor tautomer 7H-adenine.4 In this report, weaim to present a detailed picture on the mechanism of nonradiative decay of 9H-adenine.
Methodology. Geometry optimizations were performed with the complete-active-space
self-consistent-field (CASSCF) method5.
The basis set combination proposed by Sobolewski and Domcke6 was used all throughout. For all atoms except the nitrogen atom at position 9 (Fig. 1) and the hydrogen atom of the azine (NH) group, thestandard 6-31G(d,p) split-valence double-zeta Gaussian basis set with polarization functions for all atoms7
was used. In order to allow for greater flexibility for the description of the diffuse σ* orbital, the azine
nitrogen 6-31G(d,p) basis set was supplemented with a standard set of s and p Gaussian diffuse function[6-31+G(d,p)]. For the azine hydrogen atom, an additional set of s and p Gaussian diffuse function ofexponent ζ = 0.02 was added to 6-31G(d,p).
The CASSCF active space used throughout consists ofthe three highest π orbitals, two lowest π* orbitals and theσ*orbital
effectively
affectingalowest
six-electrons-in-six-orbitals calculation.
Diabatic potentials, non-adiabatic coupling matrix elements and transition dipole moments were calculated byusing the MOLPRO8 package of quantum-mechanical routines. Diabatization was done using the procedure proposedby Werner and co-workers 9 and implemented inMOLPRO.
In order to construct a two-dimensional potential energy(a)function for the description of the azine hydrogen detachment in adenine, we have chosen the azine NH bondlength―a natural choice―for the tuning coordinate. The
out-of-plane angle of the dissociating H atom, identified bySobolewski and Domcke6 as the primary coupling coordinate of the conical intersections, was chosen as the coupling mode. The tuning and coupling modes are hereinafterreferred to as r and θ, respectively.
In order to have a clear distinction among the states, themolecule was constrained to be planar (Cs). Geometry optimization at the ground state yields a slightly nonplanaramino group.10 The energy difference, however, is only afraction of a kcal/mol and is deemed negligible for the present purpose.
Results and Discussion. At least two conical intersectionsin the potential energy surfaces (PES) are found to be involved(b)Figure 2. (a) 1ππ*-1πσ* (b) S0-1πσ*intersections in the adiabatic representation.

conical(a)(b)
Figure 3. (a) 1ππ*-1πσ* (b) S0-1πσ* PES crossings in the diabatic representation.

in the three-state (S0-1ππ*-1πσ*) two-dimension (r,θ) system assumed in this study. The first conical intersection
involves the two excited states and is located at coordinates (0.988 Ǻ, 0°). The second conical intersection involves the dark 1πσ* and S0. It is found at coordinates (1.722 Ǻ, 0°) in the PES. The conical intersections in theadiabatic PES are shown in Figure 2. These intersections turn into real crossings in the diabatic representation(Figure 3).
These intersections are also marked by singularities that are typical features around the point of intersectionof adiabatic surfaces. Shown in Figure 4 is the diabatic-to-adiabatic mixing angle near the S0-1πσ* conical intersection. The 1ππ*-1πσ* conical intersection also exhibits a similar feature.

Figure 4. S0-1πσ* diabatic-to adiabatic mixing angles.

Figure 5. S0-1πσ* nonadiabatic coupling matrix elements.

Nonadiabatic couplings in the adiabatic representation likewise show rapid variation near the crossing. This
singularity represent the microscopic origin of ultrafast nonadiabatic transition near the conical intersection. Figure 5 is a plot of the non-Born-Oppenheimer coupling elements in the vicinity of the S0-1πσ* conical intersection.
Calculated adiabatic transition dipole moments also demonstrate rapid variation at the point of intersection.
The time evolution of an optically-prepared Franck-Condon wave packet initially at rest in the lowest optically-allowed excited state will be calculated using the standard split-operator method11 with off-diagonal dipoleand diabatic coupling terms represented as Pauli matrices12.
The molecular dynamics calculations will be limited to the ground-state, the lowest optically active 1ππ*state and the lowest 1πσ*.
Conclusion. The dark 1πσ* state of 9H-adenine intersect both the ground state and the lowest optically accessible 1ππ* state. Initial results indicate that explicit assumption of a two-dimension (tuning and coupling),
three-state (S0, 1πσ* and 1ππ*) model may be necessary to adequately describe the femtosecond dynamics of theultrafast nonradiative relaxation through at least two conical intersections.
1Callis, P., Annu. Rev. Chem., 1983, 34, 329.
M. Daniels, in Photochemistry and Photobiology of Nucleic Acids, edited by S.Y. Wang (Academic Press, New York, 1976), Vol. 1, p. 23; J. Cadet, P.
Vigny, in Bioorganic Photochemistry, edited by H. Morrison (Wiley, New York, 1990), Vol. 1, p. 1.
3
Fletcher, A., J. Mol. Spectrosc., 1967, 23, 221.
4Wilson, R.; Callis, P., Photochem. Photobiol., 1980, 31, 323.
5Roos, B., Adv. Chem. Phys., 1987, 69, 399.
6
Sobolewski, A; Domcke, W., Eur. Phys. J. D, 2002, 20, 369.
7
Gordon, M. et al.., J. Am. Chem. Soc., 1982, 104, 2797.
8
MOLPRO, a package of ab initio programs designed by H.-J. Werner et al., version 2002.1.
9D. Simah, B. Hartke, and H.-J. Werner, J. Chem. Phys. 1999, 111, 4523.
10B. Mennucci, A. Toniolo, J. Tomasi, J. Phys. Chem. 2001, 105, 4749.
11M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 1982, 47, 412.
12Gross, P., Neuhauser, D and Rabitz, H, J. Chem. Phys., 1992, 96, 2834.
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