MOLECULAR PHYSICS, 10 MARCH 2004, VOL. 102, NO. 5, 499–506
Excited state proton transfer and internal
conversion in o-hydroxybenzaldehyde: new insights
from non-adiabatic ab initio molecular dynamics
NIKOS L. DOLTSINIS*
Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
(Received 25 November 2003; accepted 16 January 2004)
A recently developed non-adiabatic ab initio molecular dynamics method coupling the S1
excited electronic state to the ground state by a surface hopping technique has been applied to
study photoexcited o-hydroxybenzaldehyde. Vertical excitation of the enol tautomer to the pp*
state leads to spontaneous proton transfer (PT) and thus formation of the keto tautomer. The
PT process has been found to be entirely driven by the breathing mode of the H-chelate ring.
In fact, there exists no barrier for PT in the S1 state. Non-radiative decay of the pp* excited
keto tautomer through internal conversion (IC) is observed on a picosecond time scale. The
probability for a non-adiabatic surface hop from the S1 state back to the ground state is seen
to be correlated to the chelate ring breathing mode and to the temporal changes in the
methoxy OH bond length. There are indications of an increased IC rate associated with the
initial PT event.
1. Introduction
Excited state proton transfer (PT) and internal conversion (IC) are two of the most fundamental photochemical processes. They play an important role in
numerous biological systems such as DNA, where PT
causes genetic damage [1] and excited state radiationless
decay is thought to be fast [2–6] in order to prevent
any photochemical reactions. The smallest aromatic
molecule that shows both PT and IC is o-hydroxybenzaldehyde (OHBA) (see figure 1 for the structures of
the two tautomers involved); it is therefore the ideal
candidate for studying these photochemical processes
under well-defined conditions. According to experimental evidence, photoexcitation to the S1 electronic state of
the enol tautomer [7] first results in ultrafast tautomerization leading to the keto form by intramolecular PT
Figure 1. Schematic view of the OHBA enol and keto
tautomers. After photo-excitation of the enol form,
hydrogen HT is transferred from the donor oxygen, OD ,
to the acceptor oxygen, OA .
*e-mail: [email protected]
in less than 50 fs followed by fast IC on the picosecond
time scale [7, 8].
From an experimental point of view it has become
increasingly clear that the excited state reaction barrier
for PT must be either very small or even non-existent
[7, 8] judging by the extremely short time scale measured
for PT. Ab initio electronic structure calculations do,
on the whole, confirm this picture; there remain some
doubts, however, concerning the precise shape of the
excited state potential [9–12]. Beyond these purely static
aspects, interesting questions have been raised by a recent
experimental study [8] as to the dynamical mechanism
of PT, in particular with regard to the role of the skeletal
vibrational modes of the H-chelate ring.
Perhaps even more intriguing is the problem of IC
in OHBA. Although this process is well studied experimentally and excited state lifetimes are known to a
considerable degree of accuracy [7, 8], a coherent account
of the underlying reaction mechanism has yet to emerge.
The most promising reaction scheme so far has been put
forward by Sobolewski and Domcke [9, 11], who have
proposed that de-excitation may proceed via a conical
intersection between the ground state and a dissociative
n * or p * state. In order to reach the conical intersection
the system has to overcome a potential barrier in the pp*
state in the direction perpendicular to the PT coordinate,
i.e. involving hydrogen detachment. This paradigm
has been highly successful in explaining the non-radiative
decay of a number of aromatic molecules [11, 13, 14].
Molecular Physics ISSN 0026–8976 print/ISSN 1362–3028 online # 2004 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/00268970410001668408
500
Nikos L. Doltsinis
However, in the case of OHBA the absence of any
deuteration effects on the measured IC rates hints at
the existence of an alternative mechanism.
In an attempt to shed light on the dynamics of
photo-excited OHBA we have carried out non-adiabatic
ab initio molecular dynamics (MD) simulations on coupled S0 and S1 potential energy surfaces (PES). A fulldimensional treatment of a system with many degrees of
freedom, such as the present one, calls for an electronic
structure method which cheaply and reliably provides
excited state energies and nuclear gradients. In order
to further reduce the computational effort it is necessary to employ a so-called on the fly MD scheme whereby
one avoids calculation of the entire PES prior to the
simulation and only solves the electronic structure problem along the classical MD trajectory. These criteria
are fulfilled by the density functional restricted openshell Kohn–Sham (ROKS) [15, 16] method as implemented within the framework of Car–Parrinello MD
(CP-MD) [17, 18]. In the present work, we use a recent
non-adiabatic extension of CP-MD (na-CP-MD) [16, 19,
20] which couples the Kohn–Sham density functional
electronic ground state to the ROKS S1 excited state
by means of a surface hopping scheme [16, 20–24].
2. Theoretical approach
2.1. Car–Parrinello surface hopping
A detailed description of the Car–Parrinello surface
hopping method has been published elsewhere [16, 19,
20]; it shall only be reviewed briefly here. We have
adopted a mixed quantum-classical picture treating
the atomic nuclei according to classical mechanics and
the electrons quantum mechanically. The total electronic wavefunction of the system, C, is taken to be a linear
combination of adiabatic state functions Fj ,
C¼
X
Z
aj Fj exp i Ej dt=
h ,
ð1Þ
where n is half the (even) number of electrons. Separate
variational optimization of the two wavefunctions genand ð1Þ
erally results in the molecular orbitals ð0Þ
l
l
being different. Hence, for the overlap matrix elements,
Sij ¼ hFi jFj i we obtain S01 ¼ S10 S and Sii ¼ 1.
Therefore, the non-adiabatic coupling matrix elements,
Dij ¼ hFi jð@=@tÞjFj i, are Dii ¼ 0 and Dij ¼ Dji . Substitution of (1) into the TDSE and integration over the
electronic coordinates following multiplication by F*i
from the left yields the coupled equations of motion
for the wavefunction coefficients
1
p1
p1
ia
SðE
E
Þ
þ
a
D
a
D
S
1
0
1
1 01
0 10
S2 1
p0
p0
1
p0
a0 D10 a1 D01 S ia1 S2 ðE0 E1 Þ , ð2Þ
a_ 1 ¼ 2
S 1
p1
a_ 0 ¼
R
where pj exp ði Ej dt=hÞ and Hii ¼ hFi jHjFi i ¼ Ei ,
H01 ¼ H10 ¼ E0 S.
In the CP formalism, computation of the nonadiabatic coupling elements, Dij , is straightforward and
efficient, since the orbital velocities, _l , are available at no
additional cost due to the underlying dynamical propagation scheme. If, instead of being dynamically propagated, the wavefunctions are optimized at each point
of the trajectory (so-called Born–Oppenheimer mode),
the non-adiabatic coupling elements are calculated using
a finite difference scheme.
Numerical integration of (2) yields the expansion
coefficients ai , whose square moduli, ja0 j2 and ja1 j2 ,
could be interpreted as the occupation numbers of
ground and excited states, respectively, if the two adiabatic wavefunctions were orthonormal. However, since
the definition of state populations in this basis is ambiguous, we project the wavefunction C onto an orthonormal set of auxiliary wavefunctions, F0i ¼ c0i F0 þ
c1i F1 , ci ¼ ðc0i , c1i Þ being a solution of the eigenvalue
problem Hci ¼ Sci Ei ,
j
where Ej is the energy expectation value of wavefunction
Fj and the time-dependent expansion coefficients aj are
to be determined such that C is a solution to the timedependent electronic Schrödinger equation (TDSE),
_ . In the present case, our basis functions are
HC ¼ i
hC
the S0 closed-shell KS ground state determinant,
ð0Þ ð0Þ
ð0Þ
F0 ¼ jð0Þ
1 1 n n i
C ¼ d0 F00 þ d1 F01 ¼ b0 F0 þ b1 F1 ,
ð3Þ
where bj ¼ aj pj . Transformation to this orthonormal
basis leads to the square moduli of the expansion
cofficients di
jd0 j2 ¼ jb0 j2 þ S2 jb1 j2 þ 2S < ðb*0 b1 Þ,
2
2
2
jd1 j ¼ ð1 S Þjb1 j ,
ð4Þ
ð5Þ
and the ROKS S1 excited state wavefunction [15],
E E
1 n
ð1Þ ð1Þ
ð1Þ ð1Þ
ð1Þ
ð1Þ ð1Þ
F1 ¼ 1=2 ð1Þ
1 1 n nþ1 þ 1 1 n nþ1 ,
2
which add up to unity and can be regarded as proper
state populations. Following Tully’s fewest switches criterion [22] recipe, the non-adiabatic transition
Excited state proton transfer and internal conversion in o-hydroxybenzaldehyde
ð6Þ
where t is the MD time step. A hop from surface i to
surface j is carried out when a uniform random number
>Pi (and Pi >0), provided that the potential energy Ej
is smaller than the total energy of the system. The latter
condition rules out any so-called classically forbidden
transitions. After each surface jump atomic velocities are
rescaled in order to conserve total energy. In the case of
a classically forbidden transition, we retain the nuclear
velocities, since this procedure has been demonstrated to
be more accurate than alternative suggestions [25].
2.2. Technical details
The above surface hopping algorithm has been
implemented in the CPMD package [18, 26]. For the
example discussed below, the KS and ROKS equations
were solved using the BLYP exchange-correlation
functional [27, 28] in a plane wave basis truncated at
70 Ry in conjunction with Troullier–Martins pseudopotentials [29]. Cut-off radii of 1.05, 1.23 and 0.5 au
were employed for the construction of the 2s, 2p
pseudo-wavefunctions of O and C, and the 1s pseudowavefunction of H, respectively. We chose a periodically
repeated simple cubic unit cell of length 22.68 au.
All MD simulations were carried out in the Born–
Oppenheimer mode with a comparatively small time
step of t ¼ 1 au, the latter being due to the necessity to
compute the wavefunction time derivative from a finite
difference scheme. The state amplitudes ai were integrated using a standard fourth-order Runge–Kutta
scheme [30] with a time step of 0.04 au.
3.
Results and discussion
3.1. Proton transfer
At optimized ground state geometry (enol form),
our ROKS calculation yields a vertical excitation energy
to the S1 (pp* ) state of 3.12 eV. Experimental values
range from 3.8 to 3.9 eV [7, 31–34] suggesting that
ROKS underestimates the vertical excitation energy
by 0.7 to 0.8 eV, in accord with previous observations
[15, 16, 35] regarding ROKS energy gaps. It is believed,
however, that ROKS excited state potential energy
surfaces have qualitatively correct shapes and are merely
subjected to a constant energy shift. Support for this
argument can be found by comparing our calculated
energy gap of 1.65 eV at optimized S1 keto geometry
to the experimental fluorescence maximum between 2.4
and 2.5 eV [7, 31–34]. Thus the ROKS energy shift
at this point of the PES is 0.75 to 0.85 eV, very similar
to the shift for the enol vertical excitation energy,
R(OO) [Å]
d
jdi j2 =jdi j2 ,
dt
R(OH) [Å]
Pi ¼ t
resulting in a theoretical estimate for the Stokes shift
of 1.47 eV in surprisingly good agreement with the
experimental value of 1.4–1.5 eV [7, 31–34].
We have carried out adiabatic on the fly molecular
dynamics simulations at various temperatures using
the ROKS S1 potential in order to probe the hypothetical barrier for PT. For all temperatures spontaneous
PT was observed, suggesting the non-existence of
such a barrier in accordance with previous CASSCF
and TDDFT calculations of mimimum energy profiles
[11]. Figure 2 (c) shows the S1 energy profile as a
function of the simulation time after vertical excitation
of the ground state optimized enol tautomer at a
constant temperature of 1 K. The S1 energy is seen to
continuously decrease while both donor–acceptor OO
distance, ROD OA , and the distance between the transferring hydrogen (HT ) and the accepting oxygen (OA ),
ROA HT (see also figure 1 for nomenclature) shorten
(figures 2 (a) and (b)). Simultaneously, the original
hydroxyl bond length, ROD HT , steadily grows (figure
2 (b)) and does not, as might have been suspected,
oscillate about any potential enol equilibrium value.
In the present example, the geometrical transition state,
i.e. ROA HT ¼ ROD HT , is reached in roughly T z ¼ 50 fs
(figure 2 (b)). As the new methoxy OH bond is formed,
we notice a sharp drop in energy, which levels off at
about 60 fs (figure 2 (c)). Figure 2 thus demonstrates
that the geometrical PT transition state can give a lower
bound for the PT time, but observable energetic changes
take place with a delay of several femtoseconds. Due
to the absence of an excited state enol minimum it is
not straightforward to define an enol–keto energy
splitting. A purely static estimate may be obtained by
2.6
a)
2.5
1.5
b)
1
E [eV]
probability from state i to any other state is
501
3
2.5
c)
0
time [fs]
100
Figure 2. (a) OD OA distance, (b) OD HT (– –) and OA HT (—)
distances, and (c) excited state energy relative to ground
state minimum as a function of simulation time at a
temperature of 1 K.
Nikos L. Doltsinis
taking the difference between the vertical enol excitation
energy at optimized S0 geometry and the keto S1
minimum yielding a value of 0.78 eV. However, we
have determined a dynamical ensemble average at 300 K
of 0:4 0:1 eV (see end of this section). Experimentally
an enol–keto splitting of approximately 0.5 eV has been
measured [7], whereas CASPT2 and TDDFT ab initio
electronic structure calculations predict 0.52 and
0.29 eV, respectively [11]. A detailed comparison of
ROKS S1 data with previous theoretical as well as
experimental results is given in table 1.
In order to gain insight into the PT process under
laboratory conditions, we have calculated 20 nonadiabatic surface hopping trajectories initially propagating the system in the S1 electronic state at a vibrational
temperature of 300 K. For each run the starting
configuration has been picked at random from a ground
state CP-MD simulation at 300 K.
We observe spontaneous PT in the space of
T z ¼ 25:1 15:4 fs (ensemble average standard deviation), measuring the time between vertical excitation
and the moment the geometrical PT transition state,
i.e. ROD HT ¼ ROA HT is reached. In order to enable
meaningful comparisons with results from photoelectron spectroscopy, however, it is important that we
define PT in terms of changes in electronic structure
which lead to an experimentally observable decrease in
energy once the keto tautomer has been formed. As we
have discussed above, these changes take place several
femtoseconds after the geometrical PT transition state
has been reached. Therefore the time for PT of
T z ¼ 25:1 15:4 fs stated here should be seen as a
lower bound. As figure 2 demonstrates the excited state
energy continues to fall well beyond the geometrical
PT transition state. Experimentally measurable PT times
should therefore lie above 25 fs (an upper limit may
be placed at 50 fs, since the keto minimum is reached
at 2T z in figure 2, but here the system is not allowed
to gather kinetic energy beyond 1 K). Time-resolved
photoelectron spectroscopy places an upper bound
for the PT time at 50 fs [7]. Stock et al. [8] report a
PT time of 45 fs from transient absorption measurements. Considering the limitations of our theoretical
model and the statistical uncertainty the agreement is
remarkable.
Analysing the changes in the donor–acceptor oxygen–
oxygen distance during PT at room temperature (see
figure 3), it becomes apparent that shortening of the OO
distance by roughly 10% of its enol equilibrium value
is a prerequisite for PT to occur. Therefore, we conclude
that the breathing mode of the chelate ring should be
rate determining, in agreement with previous proposals
[8, 36, 37]. A rough estimate of the corresponding
vibrational frequency can be obtained by measuring the
Table 1. Comparison of ROKS S1 data to CASPT2 and
TDDFT results reported previously in the literature [11]
as well as experimental numbers [7, 31–34]. ROKS is seen
to underestimate the energy gap between ground and
excited states. However, the good agreement with experiment in the case of the Stokes shift and the enol–keto
splitting (the number in parentheses is the relevant
dynamical splitting, see text for details) indicates that
the ROKS S1 potential shape is qualitatively reasonable.
E
CASPT2
TDDFT
ROKS
vertical
3.74
3.97
3.12
adiabatic
fluorescence
3.22
2.41
3.68
3.05
2.34
1.65
Stokes shift
1.33
0.92
1.47
enol–keto
0.52
0.29
0.78
(0.4)
Exp.
3.8
3.9
3.4
2.4
2.5
1.5
1.4
0.5
[34],
[7, 31–33]
[7]
[31, 32],
[33, 34]
[31, 32],
[33, 34]
[7]
3
distance [Å]
502
2
1
0
100
200
time [fs]
300
400
Figure 3. Typical time evolution of the OD OA (- -), OD HT
(– –) and OA HT (—) distances after vertical photoexcitation at time t ¼ 0 for an initial vibrational
temperature of 300 K.
period of the OO oscillation shown in figure 3.
The vibrational energy of 256 cm1 determined this
way is indeed close to transmission oscillation frequencies of 275–296 cm1 observed experimentally by Stock
et al. [8]. Figure 3 further shows that after PT the newly
formed methoxy OH bond is vibrationally excited,
but the kinetic energy rather rapidly dissipates into
other degrees of freedom.
In order to obtain a dynamical estimate for the enol–
keto energy splitting, we have calculated ensemble averages of the difference between the S1 energy at t ¼ 0
(vertical excitation) and at t ¼ 100, 200, 300, 400 and
500 fs (see figure 4 for details). Additional time
averaging over the interval [100, 500] fs gives a dynami-
Excited state proton transfer and internal conversion in o-hydroxybenzaldehyde
0.7
∆E [eV]
0.5
0.3
0.1
0
100
200
300
400
time [fs]
500
600
Figure 4. S1 energy difference between vertical excitation
(t ¼ 0) and t ¼ 100, 200, 300, 400 and 500 fs averaged
over the ensemble of trajectories. The error bars represent
the respective standard deviations and the horizontal
dashed line is the time average.
20
S1 population
15
10
5
0
0
200
400
600
time [fs]
800
1000
Figure 5. S1 population as a function of time from surface
hopping trajectories (). The three exponential fits which
have been obtained (i) imposing that all molecules occupy
the S1 state at t ¼ 0 (—), (ii) without boundary condition
(– –) and (iii) including only the data points at t 300 fs
(- - -), give relaxation times of 333, 405 and 841 fs,
respectively.
cal splitting of 0:4 0:1 eV, in good agreement with the
experimental estimate of approximately 0.5 eV [7].
3.2. Internal conversion
In an attempt to unravel the mechanism by which
radiationless decay of the keto S1 excited state takes
place, we have analysed 20 non-adiabatic surface
hopping trajectories obtained for different initial
503
conditions sampled from a ground state MD run at
300 K. In order to get an estimate of the IC rate, we
have calculated the S1 population as a function of time
(see figure 5) starting from the time of vertical excitation
(t ¼ 0). Similar to the experimental procedure [7] the
time constant for radiationless decay may be obtained
from an exponential fit. Imposing the correct initial
condition that all molecules are in the excited state at
t ¼ 0 thus yields a decay time of 333 fs. However, it is
apparent from figure 5 that this fit does not describe
our data points too well, the short time decay is too slow
whereas the long time decay is too fast. Removing the
boundary condition at t ¼ 0 gives a somewhat better fit
with a decay time of 405 fs. Experimentally, data points
near t ¼ 0 are usually neglected since they are part of the
pulse width limited coherent artefact [7]. Following this
recipe, we have performed a fit taking into account only
the data points at t 300 fs leading to an IC time of
841 fs. It should be stressed here that all our theoretical
values stated above are lower bounds, since we restricted
the length of the trajectories to a maximum of about 1 ps
at which point three molecules had still not undergone
a transition to the ground state. Our lower bound of
841 fs should be compared to the experimental rate [7]
of 0:62 0:15 ps1 determined at an excitation energy
of 4.34 eV, corresponding to a decay time between
1.3 and 2.1 ps. An MD simulation at 300 K corresponds
to a vibrational energy of 0.5 eV and therefore, assuming an electronic excitation energy of 3.9 eV, to an
experimental measurement at 4.4 eV.
Having made sure that our calculated relaxation times
are in line with experiment, we shall now discuss in
detail the underlying mechanism. As a first step, we have
monitored the energy gap between the S0 and S1
electronic states in order to detect any conical intersections or avoided crossings (see figure 6). Perhaps
somewhat unexpectedly, the energy gap remains larger
than 1 eV over the whole length of the simulation. The
dominant energetic changes are seen to occur during the
initial PT phase, where the energy separation is reduced
by almost 2 eV. Our findings present an alternative to
the decay mechanism proposed by Sobolewski and
Domcke [10, 11], who have shown that a conical intersection between an n * or p * excited state and the
ground state can be reached if a potential barrier in the
S1 state along the hydrogen HT dissociation coordinate
is overcome. We have verified that the Sobolewski–
Domcke scenario is plausible and, more importantly,
that our ROKS approach is capable of describing
such a case. Figure 7 demonstrates that the ROKS
lowest singlet excited state indeed adopts n * character
when hydrogen atom HT is moved to a distance of
ROD HT ¼ ROA HT ¼ 1:99 A (otherwise assuming ground
state geometry). For the sake of completeness, we
504
Nikos L. Doltsinis
energy [eV]
3
2
1
0
0
200
400
600
time [fs]
Figure 6. Ground (- -) and first excited state (—) energies
relative to the initial S0 energy and the corresponding
energy gap (—) as a function of time for an initial
vibrational temperature of 300 K.
Figure 7. ROKS S1 singly occupied molecular orbitals (a) at
enol S0 equilibrium geometry (pp* character) and (b) at
ROD HT ¼ ROA HT ¼ 1:99 A (n * character).
mention that for ROD HT ¼ ROA HT ¼ 1:65 A ROKS still
yields the pp* state. These observations are compatible
with the CASPT2 calculations on malonaldehyde by
Sobolweski and Domcke [10, 11]. However, our
dynamical treatment shows that a vibrational temperature of 300 K in the S1 state is not sufficient to cross the
dissociative barrier and thus reach the conical intersection. Nevertheless, at higher excitation energies this
decay channel may still play a dominant role in the IC
process.
Our preliminary conclusion is that since the
Sobolewski–Domcke decay channel is not accessed in
our simulations there must be another efficient decay
mechanism. In the following, we shall establish which
OHBA vibrational modes in the pp* excited state couple
non-adiabatically to the ground state and thus provide an alternative IC mechanism. For this purpose,
we compare the time evolution of the non-adiabatic
transition probability to that of various geometric
variables.
In figure 8 the probability for a non-adiabatic surface hop from the excited state to the ground state (see
equation (6)) and the donor–acceptor OO distance are
plotted as a function of the simulation time. Clearly,
the two are correlated: small OO distances coincide with
peaks in the transition probability envelope, whereas
large OO distances coincide with small transition
probabilities. Furthermore, for all our trajectories the
decay probability is highest at the moment of PT (see
figure 8 for a typical example). Partially, this can be
explained by our observations for PT in the previous
subsection, where we have seen that PT occurs at short
OO distances close to the OO turning point. Thus if
the condition for PT is fulfilled the non-adiabatic decay
probability is automatically large. On the other hand,
there are points of the trajectory where in spite of the
OO distance being clearly shorter than during PT the
transition probability does not reach the same level.
Therefore, although the chelate ring breathing mode
is certainly chiefly responsible for non-adiabatically
coupling the S1 and S0 electronic states, there must be
additional modes causing modulations of the decay
probability.
Figure 9 reveals that there is also correlation, on a
somewhat smaller time scale, between the surface
hopping probability and the velocity of the OA HT
stretching motion. In essence, the faster the hydrogen
atom HT moves, the higher the probability for a surface
jump. Again, this is certainly another factor contributing to the large peak in the non-adiabatic
transition probability in the vicinity of the PT event.
Generally speaking, the non-adiabatic coupling elements Dij ¼ hFi jð@=@tÞjFj i become large when at least
one of the adiabatic wavefunctions involved changes
rapidly as the nuclear configuration changes. This is
clearly the case during the PT reaction when the excited
state wavefunction has to adjust from the enol to the
keto electronic structure. Non-adiabatic coupling should
be additionally enhanced by the momentum gathered as
the system falls into the keto potential well, in particular
as a large portion is initially deposited in the two
main coupling modes, i.e. the OO and OH vibrations.
We believe that this increased non-adiabatic transition
probability caused by the initial tautomerization is
responsible for the higher IC rate in the first few
hundred femtoseconds compared to the long time decay
(cf. figure 5).
It is worth pointing out that the proposed main
decay mechanism via the chelate ring breathing
Excited state proton transfer and internal conversion in o-hydroxybenzaldehyde
3.1
PT
0.001
2.7
R(OO) [Å]
P21
2.9
2.5
–0.001
0
200
time [fs]
2.3
400
Figure 8. Time evolution of the probability (equation (6))
for a non-adiabatic surface jump from the S1 to the S0
PES (—) and the OD OA distance (—). The vertical dashed
line indicates the moment the geometric PT transition
state is reached, i.e. ROD HT ¼ ROA HT .
0.1
0
v(OH) [Å/fs]
P21
0.001
–0.001
20
40
60
time [fs]
80
100
–0.1
Figure 9. Time evolution of the probability (equation (6)) for
a non-adiabatic surface jump from the S1 to the S0 PES
(—) and the time derivative, i.e. velocity, of the OA HT
distance (—).
vibration should be influenced only little by deuteration.
This is in accord with the absence of any isotope effects
in photoelectron spectroscopic measurements [7].
4. Conclusions
We have performed non-adiabatic ab initio molecular
dynamics simulations of the OHBA photocycle coupling
the standard density functional ground state and
the ROKS S1 excited state using a surface hopping
scheme. Ultrafast proton transfer interconverting the
enol and keto tautomers has been observed driven by
the H-chelate ring breathing mode, which modulates
the donor–acceptor oxygen–oxygen distance. We have
determined the time at which the geometrical PT
transition state is reached to be 25:1 15:4 fs. During
505
the proton transfer reaction, the oxygen–oxygen distance is seen to shorten by about 10%.
Radiationless decay of the S1 excited state has been
found to be fast, taking place on a picosecond time
scale in the absence of any conical intersections. We
have been able to demonstrate that the n * conical
intersection decay channel, although being present in the
direction orthogonal to the PT mode, is not accessible at
moderate excitation energies. Rather, it is primarily the
chelate ring breathing mode that is responsible for the
non-adiabatic coupling between the pp* excited state
and the ground state. The secondary coupling mode
is found to be the OH stretching vibration. Moreover,
there are indications for an increased decay rate in the
first few hundred femtoseconds caused by the enol–keto
tautomerization.
The author is indebted to D. Marx for his ongoing
support. W. Domcke and S. Lochbrunner are kindly
acknowledged for informative discussions. Computational resources were provided by the computing
centres of RUB and Rechenverbund NRW. This project is partially funded by the Deutsche Forschungsgemeinschaft.
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