This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 6145–6155 6145
Cite this: Phys. Chem. Chem. Phys., 2011, 13, 6145–6155
Photodynamical simulations of cytosine: characterization of the ultrafast
bi-exponential UV deactivationw
Mario Barbatti,*ab
Adelia J. A. Aquino,ac
Jaroslaw J. Szymczak,zaDana Nachtigallova
dand Hans Lischka*
a
Received 27th July 2010, Accepted 27th January 2011
DOI: 10.1039/c0cp01327g
Deactivation of UV-excited cytosine is investigated by non-adiabatic dynamics simulations,
optimization of conical intersections, and determination of reaction paths. Quantum chemical
calculations are performed up to the MR-CISD level. Dynamics simulations were performed at
multiconfigurational level with the surface hopping method including four electronic states.
The results show the activation of four distinct reaction pathways at two different subpicosecond
time scales and involving three different conical intersections. Most trajectories relax to a
minimum of the S1 state and deactivate with a time constant of 0.69 ps mainly through a
semi-planar conical intersection along the nOp* surface. A minor fraction deactivate along pp*regions of the S1 surface. Sixteen percent of trajectories do not relax to the minimum and
deactivate with a time constant of only 13 fs.
1. Introduction
Upon UV excitation, the five naturally occurring nucleobases
return to the ground state by internal conversion at an
ultrafast time scale ranging from half a picosecond to few
picoseconds.1–5 In general, ultrafast decay depends on the
existence of reaction pathways connecting the Franck–Condon
region to the seam of conical intersections between the excited
and ground states where radiationless processes can occur.
The characterization of these pathways has led to a large
amount of theoretical work not only for the five nucleo-
bases,1–14 but also for their isomers,6,15 substituted species,7,16,17
and base models.18,19 Significant progress has been achieved
with photodynamical simulations,20–22 which describe the
excited-state time evolution and the most accessed reaction
pathways explicitly.
Excited-state dynamics simulations are still a major
challenge in computational chemistry requiring a proper
description of multiple electronic excited states and their
non-adiabatic couplings. At the same time, they should keep
computational costs under strict control as to allow dynamics
propagation for thousands of femtoseconds. Despite the
difficulties, ab initio21–25 and semiempirical20,26–31 non-adiabatic
dynamics simulations have been recently reported for all
nucleobases.
In the gas phase, the excited-state lifetime of cytosine
measured by different groups present somewhat divergent
results. Kang et al.32 (pump: 267 nm; probe: 800 nm) reports
a single time constant decay of 3.2 ps. Canuel et al.33 (pump:
267 nm; probe: 2 � 400 nm) reports two time constants, 0.16 ps
and 1.86 ps. Ullrich et al.34 (pump: 250 nm; probe: 200 nm)
distinguishes three time constants, a very fast decay occurring
in less than 0.05 ps, another component of 0.82 ps and a third
component of 3.2 ps. Recently, Kosma and co-workers have
shown that the excited-state lifetime strongly depends on the
excitation wavelength, varying from 3.8 ps to 1.1 ps for pump
wavelengths spanning the range from 260 to 290 nm.35
In common, all these sets of results indicate that cytosine
relaxation takes place within one to three picoseconds after the
excitation. Additionally, Ullrich et al.34 have measured the
time dependent photoelectron spectra of cytosine and other
nucleobases in gas phase. The comparison between the pyrimidine
bases cytosine, uracil and thymine clearly indicates that
cytosine deactivates in a distinct way producing more energetic
photoelectrons.
As typical for species deactivating by internal conversion,
cytosine fluorescence quantum yield is very small in neutral
a Institute for Theoretical Chemistry, University of Vienna,Waehringerstrasse 17, A 1090 Vienna, Austria.E-mail: Mario [email protected],Hans [email protected]
bMax-Planck-Institut fur Kohlenforschung,Kaiser-Wilhelm-Platz 1, D-45470 Mulheim an der Ruhr, Germany
c Institute of Soil Research, University of Natural Resources andApplied Life Sciences Vienna, Peter-Jordan-Straße 82,A-1190 Vienna, Austria
d Institute of Organic Chemistry and Biochemistry,Academy of Sciences of the Czech Republic, Flemingovo nam. 2,CZ-16610 Prague 6, Czech Republic
w Electronic supplementary information (ESI) available: Experimentaltime constants, conical intersection notations, molecular orbitals,geometries and pathways at CASSCF level, Cartesian coordinates.See DOI: 10.1039/c0cp01327gz Present address: Department of Chemistry, University of Basel,Klingelbergstrasse 80, 4056 Basel, Switzerland.
PCCP Dynamic Article Links
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6146 Phys. Chem. Chem. Phys., 2011, 13, 6145–6155 This journal is c the Owner Societies 2011
aqueous solution.36 The quantum yield, however, tends to
increase with the pH and even phosphorescence was observed
in high pH conditions.37 Consistent with the quantum yields
derived from static spectra, time-dependent spectra of cytosine
in water show a time constant of about 1 ps in neutral
solution.38 The time constant is shortened to 0.63 ps in
pH 0.08 and elongated to 13.3 ps in pH 13. (A survey of
experimental time constants for cytosine and cytosine
derivatives under different conditions is given in Table S1 of
the Supplementary Information.)
Also from a theoretical perspective, excited state excitation
and deactivation of cytosine has been subject to several studies
employing different methodologies. There are three well
described S1/S0 conical intersections in cytosine, and the paths
connecting them to the Franck–Condon region and to excited
state minima have been investigated in detail at several
theoretical levels.10,11,16,39–44 A recent review on this topic
can be found in ref. 39.
Two of the three known conical intersections in cytosine were
first characterized by Ismail and co-workers.11 The first conical
intersection has a semi-planar structure with sp3 hybridization of
C6, shortening of the C2–N3 bond and stretching of the C5–C6
bond relative to the ground state minimum (see numbering in
Fig. 1). It occurs in a region of mixing of the nOp*, pp* and
closed shell states, which ends in a triply degeneracy as shown in
ref. 45–47. Throughout this paper we will refer to this conical
intersection as the semi-planar conical intersection. (Since no
generally accepted scheme for labeling conical intersections has
been proposed so far, we give a cross-referenced summary of
notations for conical intersections in cytosine in Table S2 of the
Supplementary Information for the readers’ convenience.)
The second S1/S0 conical intersection is characterized by
puckering of atom N3, which induces a strong out-of-plane
deformation of the amino group. It has been often assigned as
connected to the nNp* state, but it will be shown in this work
that in fact it is reached by a reaction path of pNp* character,
which is stabilized by a twisting of the N3–C4 bond. We will
refer to this structure as the oop-NH2 conical intersection.
The third conical intersection occurs also with involvement of
a pp* state and is characterized by a strong puckering of the C6
atom induced by a twisting around the C5–C6 bond. We refer
to this structure as the C6-puckered conical intersection. This
conical intersection was found by Sobolewski and Domcke48
when investigating guanine-cytosine pairs and its electronic
structure has been investigated in detail by Zgierski et al.10,40
Because of the barrierless diabatic connection to the ground
state, Merchan, Serrano-Andres43,44 and co-authors have
predicted that cytosine should relax to the ground state
directly through the C6-puckered conical intersection. This
prediction is supported by surface hopping dynamics
simulations performed with the OM2 semi-empirical level.30
Nevertheless, dynamics simulations with multiple spawning24
at CASSCF(2,2) and surface hopping31 at AM1/CI(2,2) levels
have found only small fractions of deactivation at the
C6-puckered conical intersection and a major part of deactivation
at the oop-NH2 conical intersection.
In addition to these three conical intersections, we have
optimized a new S1/S0 conical intersection in cytosine related
to a pOpO* state. It is characterized by a strong out-of-plane
deformation of the O atom analogous to uracil12 and
thymine.9 However, because of its relatively high energy, it is
not expected to play any relevant role in deactivation of
low-energy excited cytosine. It will be referred to as the
oop-O conical intersection.
This large set of theoretical investigations of cytosine have
demonstrated the existence of multiple pathways for internal
conversion available either by direct relaxation to the conical
intersections or by a stepwise process first relaxing into the S1minimum and then moving to the intersection seam. In the
present work the photodeactivation of UV-excited cytosine
has been addressed by non-adiabatic dynamics simulations
with an electronic structure level significantly superior to those
employed in previous simulations, with a detailed control of
the initial conditions as to simulate as closely as possible the
experimental settings, and with extensive comparisons to other
theoretical and experimental results in the literature. Moreover,
optimization of stationary points, conical intersections and
determination of reaction pathways has been performed
up to multireference configuration interaction with singles
and doubles (MR-CISD) level. The results allow drawing a
comprehensive scenario for deactivation of cytosine based on a
bi-exponential sub-picosecond decay involving four distinct
reaction pathways and three different regions of the seam of
conical intersections. The results also show two singular features
in the deactivation process of cytosine: first a fraction of cytosine
population returns to the ground state within 10 fs, one of the
fastest internal conversion among organic molecules; second, the
deactivation at a conical intersection involving three states.
2. Computational details
Mixed quantum-classical dynamics simulations49 were performed
for cytosine at the complete active space self-consistent field
(CASSCF) level. The active space was composed of fourteen
electrons in ten orbitals [CASSCF(14,10)]. At the ground state
Fig. 1 Structures of the ground and S1 minima of cytosine with
selected geometrical parameters optimized at CASSCF(14,10)/6-31G*
and MR-CISD(6,5)/CASSCF(14,10)/6-31G* (in parentheses) levels of
theory. Valence-bond structures based on bond distances. Bond
distances are given in A.
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minimum geometry, these orbitals are three n, four p,and three p* orbitals (see Fig. S1 of the Supplementary
Information). State averaging was performed over four states
(SA-4) and the 6-31G* basis set50 was employed. Analytical
energy gradients and non-adiabatic coupling vectors were
computed by the procedures described in ref. 51–55.
The classical equations were integrated with the Velocity-
Verlet algorithm56 using a 0.5 fs time step. The quantum
equations were integrated with the 5th-order Butcher
algorithm57 with a 0.01 fs time step. The partial coupling
approximation58 was used to reduce the number of non-
adiabatic couplings to be computed every time step. Decoherence
effects were introduced by the model discussed in ref. 59
(a = 0.1 hartree). Non-adiabatic events were taken into
account by the surface hopping fewest-switches algorithm.60,61
Results were analyzed in terms of the Cremer-Pople (CP)
parameters62 using the Boeyen’s conformer classification
scheme.63 The CP parameters quantify the degree (Q) and
the kind (y and f) of ring puckering. In particular, Q = 0 A
indicates planar structures and y and f parameters can be used
to classify the ring conformation as boat (B), envelope (E),
chair (C), half-chair (H), screw-boat (S), and twisted-boat (T).
Initial geometries and velocities were generated by a Wigner
distribution treating each nuclear coordinate as a harmonic
oscillator in the ground state. Harmonic frequencies computed
at the CASSCF(14,10)/6-31G* level were scaled by a factor
l = 0.90452, which was derived by comparison to experimental
frequencies given in ref. 64. One thousand random geometries
and velocities were generated. Single point calculations
were performed for each of them and used to compute the
absorption cross section with the semi-classical approximation
described in ref. 65. Three excited states were included and
Lorentzian line shapes with width 0.1 eV were employed. The
simulated spectrum (see Fig. 2) shows a single band dominated
by the first pp* transition and centered at 5.49 eV.
To perform the simulations as closely as possible to the
experimental conditions, it should be taken into account
that time-resolved spectroscopic experiments33,66 have been
performed by pumping cytosine at 267 nm near the center of
the first absorption band located at 260 nm.67 Thus, in the
construction of initial conditions excitation energies have been
restricted to the range 5.25 � 0.25 eV, near the center of the
simulated spectrum. Besides this energy restriction, initial
conditions were randomly selected in terms of transition
probabilities into the three excited states. From the original
3000 possible initial conditions (1000 random points starting
in each of the three excited states), this procedure selected
172 initial conditions, 49 starting in S1, 105 starting in S2, and
18 starting in S3. The number of trajectories finally
computed—30 starting in S1, 64 starting in S2 and 11 starting
in S3—was chosen to keep this proportion. The 105
trajectories were propagated for a maximum time of 1.2 ps.
Trajectories that returned to the ground state and stayed there
for more than 50 fs were terminated.
The relaxation of the initial dynamics was also simulated at
the resolution-of-identity coupled cluster to the second-order
(RI-CC2)68–70 method with the SVP basis set. Initial conditions
were selected from the center of the first band of the absorption
spectrum, within�0.25 eV range around the vertical excitation
into the pp* state (4.88 eV). Fifteen trajectories were computed
for a maximum of 20 fs with time step 0.5 fs.
Minima and conical intersections were optimized at the
CASSCF level described above and also at the MR-CISD
level. The reference space was composed by a complete active
space with six electrons in five orbitals. This space was built
based on the analysis of CASSCF(14,10) calculations for the
minima and conical intersections. Orbitals with natural
occupation lower than 0.1 in all those geometries were moved
to the virtual space and orbitals with natural occupation
higher than 0.9 were moved to the doubly occupied space.
Sixteen orbitals were kept in the frozen space and generalized
interacting space restrictions were adopted.71 TheMR-CISD(6,5)
calculations were performed with the orbitals obtained at
SA-4-CASSCF(14,10)/6-31G* level. Davidson corrections52,72,73
(+Q) were additionally computed for single point calculations.
Cartesian coordinates for all optimized structures are given in
the Supplementary Information.
MRCI and CASSCF calculations were performed with the
COLUMBUS program system74–76 and for the dynamics
simulations the NEWTON-X program77,78 was used. RI-CC2
and DFT calculations were performed with the TURBOMOLE
program.79 Cremer-Pople parameters were computed with
the PLATON program.80
3. Results and discussion
3.1 The potential energy surface of cytosine
3.1.1 Vertical excitation energies. The geometries of the
ground state minimum of cytosine optimized at CASSCF and
MR-CISD levels, both using the 6-31G* basis set, are shown
in Fig. 1. The main differences between the two levels are
found in the N3–C4 and at the C6–N1 bond distances, which
are, respectively, stretched by 0.027 A and shrunk by 0.022 A
when optimized at the higher level.
Vertical excitation energies for the lowest electronic states of
cytosine are given in Table 1. At the CASSCF level employed
in the dynamics calculations as well as in the MR-CISD level,
the np* state is the first singlet excited state and it is closely
followed by the first pp* state. The inclusion of the Davidson
correction (+Q) to the MR-CISD level stabilizes the pp*state, which becomes the first excited state. This result is also
confirmed at the CC2 level. We shall discuss later in this
section that this inversion does not affects the dynamics
results. As usual, the vertical excitation energy of the pp*ionic state is overestimated.81 The effect of this overestimation
on the dynamics results are discussed in the section
‘‘Photophysics of cytosine.’’
The S4 state at the CC2/aug-TZVP level (not shown in
Table 1) is the p3s state. Its transition energy is 5.44 eV and its
oscillator strength is 0.01. Since this state lies 0.8 eV above the
vertical excitation into the pp* state, we do not expect that it
will be involved in the photodynamics of cytosine starting in
the first absorption band.
The simulated spectrum at the CASSCF level is shown in
Fig. 2. The band has a Gaussian profile with amplitude
0.07 A2.molecule�1 and width 1.15 eV, which is in good
agreement with CC2 results65 (0.08 A2.molecule�1, 1.05 eV).
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The np* states are completely hidden by the pp* intense
absorption. The dashed area indicates the range from where
initial conditions for dynamics were selected, just below the
absorption maximum as in the time-resolved experiments.
While in the ground state minimum the pp* state is slightly
above the np* state at the CASSCF level, in the distorted
geometries sampled by the Wigner distribution, the pp* may
be also found below the np* state. Trajectory simulations
starting in either situation show essentially the same results,
which means that the inverted order of the np* and pp* states
at CASSCF level is not important for the dynamics results.
3.1.2 Excited-state minimum and conical intersections. The
geometry of the S1 excited state minimum optimized at
CASSCF and MR-CISD levels is shown in Fig. 1. Energies
of the ground and excited states are given in Table 2 for these
geometries. In both CASSCF andMRCI levels, the S1 minimum
has nOp* character. Although the ring is still planar, hydrogen
atoms connected to N1 and C6 atoms are displaced out of the
plane. Molecular orbitals for both ground and excited state
minima are shown in Fig. S1 of the Supplementary Information.
It was not possible to optimize the previously reported pp* S1minimum44 at the present CASSCF level, which seems to be
coincident with the S2/S1 minimum on the crossing seam.
Four different minima on the crossing seam (MXSs) have
been optimized at CASSCF and MR-CISD levels. Their
geometries are show in Fig. 3 at MR-CISD level and selected
geometric parameters are given in Table 3. Molecular orbitals
and geometries optimized at CASSCF level are shown in
Fig. S2 and S3 of the Supplementary Information. The lowest
MXS at the CASSCF level (oop-NH2) is characterized by a
strong deformation of the NH2 group out of the ring plane. It
has a screw-boat conformation with puckering of atoms
N3 and C4 (3S4). This conical intersection has been often
characterized as a crossing between the nNp* and closed shell
(cs) states.11,16,24,39,42,44 A closer inspection of the electronic
configurations involved in this conical intersection, however,
indicates that it can be better characterized as a pN3pC4*/cscrossing.46 This can be seen from Fig. 4, where the relevant nN,
p and p* orbitals are displayed for the ground state minimum
and conical intersection geometries. By twisting the N3–C4
bond in moving from the ground-state structure to the
oop-NH2 MXS the lone pair on N3 is rotated out from the
molecular plane, but otherwise keeps its characteristics. It
remains doubly occupied while the single occupied orbital is
indeed the p orbital with a large density at N3. This distinction
is important because it clarifies the origin of this conical
intersection, which corresponds to an ethylenic conical inter-
section arising from the twisting around the N3–C4 bond.
The next MXS in the energetic order of the CASSCF level is
the semi-planar MXS. It is characterized by strong stretching
of the C5–C6 bond accompanied by a strong shrinking of the
C2–N3 bond. A certain degree of pyramidalization is also
observed at the C6 atom. Although the minimum energy
geometry has a twist-boat conformation slightly puckered
(Q = 0.25 A) at atoms N1 and N3 (1T3), we anticipate that
the dynamics simulations will reveal that this section of the
crossing seam spreads over a large region of the conformation
space. Electronically, this MXS is formed by a crossing
between the nOp* and the pp* states, but showing a large
mixing with the closed shell configuration. Indeed, as it has
been discussed in ref. 45 and 47, the S0, S1 and S2 states are
very close to each other for geometries in this region of the
crossing seam space, even forming three state conical
intersections.
The third conical intersection (C6-puckered) is characterized
by a twist around the C5-C6 bond, which leads to a C6
puckering (screw-boat 6S1). This is also an ethylenic conical
intersection with crossing between pC5pC6* and closed shell
states.
The highest energy conical intersection optimized in this
work (oop-O) is characterized by a strong out-of-plane
displacement of the O atom keeping the ring planar or
semi-planar. It is energetically too high in energy to play any
role in the low energy excitation dynamics of cytosine. Besides
Fig. 2 Absorption spectrum into the first band simulated at
CASSCF(14,10)/6-31G* level. Crosses show the oscillator strength
of the vertically excited S1 (nNp*), S2 (pp*) and S3 (nOp*) states. Thedashed area indicates the spectral region where initial conditions were
selected.
Table 1 Theoretical data for the first three vertical excitation levels of cytosine computed with different methods
S1 S2 S3
DE (eV) f DE (eV) f DE (eV) f
CASSCF 5.41 np* 0.002 5.56 pp* 0.085 5.74 np* 0.003MR-CISD 5.72 np* 0.003 5.86 pp* 0.140 7.48 np* 0.019MR-CISD+Q 5.39 pp* 0.003 5.55 np* 0.140 6.80 np* 0.019CC2/SVP 4.88 pp* 0.055 5.04 np* 0.002 5.41 np* 0.001CC2/TZVP 4.71 pp* 0.051 4.95 np* 0.008 5.35 np* 0.009CC2/aug-TZVP 4.61 pp* 0.052 4.87 np* 0.007 5.27 np* 0.010
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that, cytosine should present other S0/S1 crossings for NH
stretching and CN ring opening. The intersection along the
NH stretching should occur by a crossing between the p3s andthe closed shell states.82 Because of its high vertical excitation
energy, the p3s state in cytosine is not expected to play a
relevant role in the photodynamics following excitation into
the first pp* state. In the case of the ring-opening conical
intersections, their activation usually involves the overcoming
of high energy barriers.83 Dynamics simulations will also show
that they also do not play any role in the deactivation of
cytosine excited into the first absorption band.
The geometries of the MXSs optimized at the MR-CISD
level are rather similar to the ones optimized at the CASSCF
level (Table 3). The differences are, however, large enough
to change the conformation classification. Thus, while the
oop-NH2 MXS has a 3S4 conformation at the CASSCF level,
it has an envelope 3E at the MR-CISD level, which implies a
smaller degree of C4 puckering. Similarly, the puckering of the
N1 atom in C6-puckered MXS decreases when it is optimized
at the MR-CISD level. Because of this, the conformation
changes from 6S1 to6E.
The energetic order of the MXSs also changes at the
MR-CISD level, although the state character remains
the same as in CASSCF (Table 2). At MR-CISD + Q level,
the semi-planar MXS is destabilized by about 0.6 eV while
the C6-puckered is stabilized by about 0.3 eV in comparison
to the CASSCF level. Because of this, the energetic order
is altered and the oop-NH2 and C6-puckered MXSs appear
first with very close energies followed by the semi-planar at
higher energy. The implications of this change will be
discussed later. (Note that because the MXSs were optimized
at the MR-CISD level and the energies were computed at
the MR-CISD+Q level, there is a small energy split between
S0 and S1.)
Table 2 Vertical excitation energies (eV), energies at the S1 minimum and at the S1/S0 MXSs for cytosine obtained with CASSCF and MR-CISDmethods. Values with Davidson correction are given in parentheses. cs—closed shell
Geom. Conform. S0 S1 S2 S3
SA-4-CASSCF(14,10)/6-31G*Min S0 Planar 0.00a cs 5.41 nNp* 5.56 pp* 5.74 nOp*Min S1 Planar 2.25 cs 3.73 nOp* 4.14 pp* 6.07 nOp*MXS oop-NH2 (
3S4) 3.84 cs 3.84 pN3pC4* 6.73 nNp* 7.16 pp*MXS Semi-planar (1T3) 4.09 nOp* + cs 4.09 pp* 4.53 cs + nOp* 7.19 nOp*MXS C6-puckered (6S1) 4.34 cs 4.34 pC5pC6* 6.43 pp* 7.17 nNp*MXS oop-O (3S2) 5.99 cs + nOpO* 5.99 pOpO* 7.87 cs + nOp* 9.83 nOp*MR-CISD(6,5)/SA-4-CASSCF(14,10)/6-31G*Min S0 Planar 0.00b (0.00c) cs 5.72 (5.55) nNp* 5.86 (5.39) pp* 7.48 (6.80) nOp*Min S1 Planar 2.04 (1.66) cs 4.40 (4.53) nOp* 5.89 (4.97) pp* 6.63 (6.64) nOp*MXS oop-NH2 (
3E) 4.12 (3.99) cs 4.12 (4.08) pN3pC4* 6.98 (6.89) nNp* 7.46 (7.23) pp*MXS Semi-planar (1T3) 4.85 (4.79) cs + nOp* 4.85 (4.65) pp* 6.75 (5.93) nOp* 8.47 (8.42) nOp*MXS C6-puckered (6E) 4.17 (3.91) cs 4.17 (4.22) pC5pC6* 6.94 (6.87) pp* 8.03 (7.74) nNp*MXS oop-O (B4,1) 5.65 (5.06) cs 5.65 (5.53) pOpO* 8.31 (7.82) ppO* 8.21 (8.61) (pO*)
2
a E0 = �392.671177 au. b E0 = �393.153516 au. c E0 = �393.234586 au.
Fig. 3 Geometry of four minima on the S1/S0 crossing seam of
cytosine optimized at MR-CISD level. Geometries optimized at
CASSCF level are shown in the Supplementary Information.
Table 3 Characterization of the S1/S0 minima on the crossing seamoptimized at CASSCF and MRCI levels in terms of the Cremer-Popleparameters Q (A), y (1), and f (1) and of selected bond distances (A)
oop-NH2 Semi-planar C6-puckered oop-O
Conf. CASSCFa 3S41T3
6S12S3
MRCIb 3E 1T36E B4,1
Q CASSCF 0.50 0.25 0.52 0.09MRCI 0.52 0.44 0.47 0.18
y CASSCF 62 80 119 114MRCI 58 81 120 100
f CASSCF 140 322 146 272MRCI 125 324 132 185
N1–C2 CASSCF 1.377 1.339 1.589 1.358MRCI 1.377 1.348 1.562 1.454
C2–N3 CASSCF 1.418 1.240 1.319 1.369MRCI 1.422 1.243 1.349 1.364
N3–C4 CASSCF 1.410 1.455 1.355 1.280MRCI 1.439 1.455 1.331 1.291
C4–C5 CASSCF 1.470 1.338 1.381 1.485MRCI 1.456 1.347 1.446 1.465
C5–C6 CASSCF 1.361 1.481 1.471 1.337MRCI 1.358 1.466 1.452 1.359
C6–N1 CASSCF 1.406 1.403 1.335 1.408MRCI 1.412 1.449 1.358 1.356
C2–O7 CASSCF 1.190 1.399 1.197 1.632MRCI 1.196 1.379 1.186 1.385
C4–N8 CASSCF 1.397 1.392 1.379 1.351MRCI 1.401 1.413 1.347 1.352
a CASSCF: SA-4-CASSCF(14,10)/6-31G*. b MRCI: MR-CISD(6,5)/
SA-4-CASSCF(14,10)/6-31G*.
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3.1.3 Reaction paths. Reaction pathways for internal
conversion of cytosine at the three lowest energy conical
intersections have been computed at the CASSCF (Fig. S4
in the Supplementary information) andMR-CISD+Q (Fig. 5)
levels. All these conical intersections are energetically accessible
after excitation into the pp* state. The reaction paths were
computed from the ground state minimum geometry to the
conical intersections (upper graphs in Fig. S4 and Fig. 5) and
from the ground state minimum geometry to the excited state
minimum and from there to the conical intersections (bottom
graphs). In all cases, they were obtained by linear interpolation
of internal coordinates between optimized structures at the
CASSCF and MR-CISD levels.
The pathways computed at both levels of theory present
essentially the same qualitative features, what should lead to
similar dynamical behaviors. One main difference between the
CASSCF and MR-CISD+Q pathways is related to the S2state of the pathway going to the semi-planar conical inter-
section (Fig. S4 and Fig. 5, top-left). At CASSCF level,
the minimum on the crossing seam is much closer to the
three-state crossing region45 than at MR-CISD+Q level, but
since the initial relaxation should follow the pp* state, which
remains in similar positions for both methods, this feature
should not affect the outcome of the dynamics.
The dynamics simulations at CASSCF level discussed in the
next sections will show that a pathway similar to Fig. S4
(top-left) is initially followed by cytosine. At the conical
intersection a small fraction of the trajectories return to the
ground state, but most of them relax to the minimum of S1state and can later convert to the ground state by any of the
three pathways shown in Fig. S4 (bottom). Naturally, the
fraction of trajectories that will follow each pathway will
depend on topographical details of the surfaces, mainly the
height of the energy barriers separating the minimum and
Fig. 4 Electronic configurations of the nN, p and p* orbitals at (a) theground state minimum geometry (S0 state) and at (b) the oop-NH2
MXS (S0 and S1 states).
Fig. 5 Linearly interpolated pathways between the Franck–Condon (FC) region and the three lowest-energy MXSs (top) and between the FC
region, the S1 minimum and the three MXSs (bottom). Computed at MR-CISD(6,5)+Q/SA-4-CASSCF(14,10)/6-31G* level with geometries
optimized at MR-CISD level. Only three states are shown for clarity. The same pathways computed at CASSCF level are shown in the
Supplementary Information.
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conical intersection. As it has been discussed by Blancafort42
the differences between barriers along CASSCF pathways and
pathways computed at higher levels, in this case CASPT2, are
of about 0.2 eV, which are in the accuracy limit of not only
CASSCF but also of most of the other methods.
3.2 Dynamics results
Fig. 6 shows the time evolution of the occupation of each
adiabatic state. At time zero, cytosine is in the pp* state, whoseintensity is distributed as 29% to S1, 61% to S2 and 10% to S3(see discussion about initial conditions in the ‘‘Computational
details’’ section). Non-adiabatic events take place already in
the first 10 fs. S2, the initially most strongly occupied state,
transfers part of the population to S1 and to S3, reflecting the
exchange of the diabatic character of the three states. S3 is
quickly depopulated within 20 fs. The occupation of the first
excited state reaches a maximum of about 60% in 20 fs and
remains oscillating around this level during the first 100 fs.
After 100 fs, the transfer to the ground state is intensified.
The ground state is populated bi-exponentially. Its
occupation can be fitted with the three-parameter function:
f2(t) = 1 � a exp(�t/t1) � (1 � a)exp(�t/t2),
where t is the time and t1 and t2 are the two time constants.
The amplitude a is the fraction of the initial excited state
population following the pathways with time constant t1,while (1 � a) is the fraction following the pathways with t2.The fitting procedure results in a very fast t1 = 13 fs decay
component followed by a = 16% of the population and a
slower t2 = 0.7 ps component followed by (1 � a) = 84% of
the population (Table 4). This gives an average lifetime of
hti = at1 + (1 � a)t2 = 0.58 ps.
In this analysis, we assumed that trajectories that were still
in the excited state at the end of the simulation (1.2 ps) should
deactivate within the exponential decay t2. An alternative
interpretation is that these trajectories are not part of the
second exponential decay and they will deactivate with a
longer time constant. In this case, the ground state population
can be fitted with the function:
f3(t) = 1 � a1 exp(�t/t1) � a2 exp(�t/t2)� (1 � a1 � a2)exp(�t/t3).
With this procedure, 13% of trajectories decay with the
shortest time constant t1 = 9 fs, 74% decay with
t2 = 0.53 ps and the remaining 13% decay with t3 = 3.1 ps
(Table 4). The average lifetime becomes hti= a1t1 + a2t2 +(1 � a1 � a2)t3 = 0.79 ps.
With exception of oop-O, all other conical intersections
described in the previous sections were origin of S1/S0 hopping
events during the dynamics. oop-NH2 conical intersection was
observed with 3S4 and3H4 conformations. It was responsible
for deactivation of 7% of the trajectories (Table 5).
C6-puckered conical intersection was observed in 8% of the
trajectories. They were associated with puckering at the C6
atom, being formed with 6S1,6E, 6,3B, and 6S5 conformations.
The major fraction of trajectories, 68%, deactivated at the
semi-planar conical intersection, with a large variety of
conformations and puckering degrees. From this amount,
16% occurred within 10 � 2 fs giving origin to the t1 time
constant, while 52% contributed to the t2 time constant. When
the semi-planar intersection occurred with larger degree of
puckering, they were concentrated around the 6E conformation.
The 1T3 conformation, corresponding to the minimum on the
crossing seam of this region, was observed in only few cases.
When the degree of puckering was small, these intersections
were concentrated at the 6T2 and 4T2 conformations. The
large variety of puckering conformations observed in the
C6-puckered conical intersections is a consequence of the fact
that these intersections are mainly formed by in-plane rather
than out-of-plane ring deformations. The remaining 17% of
trajectories did not return to ground state within the 1.2 ps
simulation time. About 20% of S1/S0 hopping events took
place with a degree of puckering smaller than 0.15 A (see Fig. 6
bottom), corresponding to structures with planar or quasi
planar rings. Because of the proximity between S0, S1 and S2in the region of semi-planar conical intersection, 21% of all
trajectories returned to the ground state in a S2 - S0 hopping
event (pp* - cs, with np* between them). This enforces the
importance of a proper multistate treatment of the surface
hopping algorithm in the case of cytosine, which is often
restricted to two-states approximations.
Typically, trajectories quickly relaxed along the pp* state as
illustrated in Fig. 7. The closed shell state is strongly destabilized
during this initial process and after about only 10 fs cytosine is
brought to a region of crossing between pp*, nOp* and cs
states. There, it can be either non-adiabatically transferred
to the S0 state (Fig. 7 top), which happened in 16% of
trajectories, or to remain excited (Fig. 7 bottom) as in the
remaining 84%. Note that a hopping algorithm based on
energy thresholds instead of based on non-adiabatic transition
probabilities would completely fail to describe this process.
Fig. 6 Time evolution of the population of the ground and excited
states of cytosine (top). Degree of ring puckering at the S1/S0 hopping
time (bottom).
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The trajectories that remained in the excited state after this
first encounter with S0 were transferred to the nOp* state
within the next 100 fs. They relaxed to the energy minimum
of this state and remained there for an average time of about
0.6 ps before being finally deactivated. During this time,
small energy gaps to the ground state often occurred. The
non-adiabatic transition probability is small enough to
guarantee that multiple of such encounters occur without
returning to the ground state. The reason for this rests on
the shape of the potential energy surface in the region between
the S1 minimum and the semi-planar conical intersection. The
sloped conical intersection is reached in an up-hill motion,
which decreases the efficiency of the non-adiabatic transitions.
Because of this, other pathways to the ground state through
pp*/cs conical intersections (oop-NH2 and C6-puckered
conical intersections) start to compete with the nOp*/cspathway. As discussed in section ‘‘Reaction paths,’’ the
activation of the pp*/cs pathways starting from the nOp*minimum depends on overcoming energetic barriers to the
biradical pp* states. When this is achieved, the conical inter-
section to the ground state can be easily accessed because of its
peaked shape and the internal conversion occurs quickly,
usually in less than 100 fs after the barrier is overcome.
The occurrence of a conical intersection with the ground
state as soon as 10 fs after the photoexcitation is an unexpected
feature for a large molecule like cytosine. It is certainly one of
the fastest internal conversion processes among organic
molecules, even faster than the exceptionally fast decay of
ethylene whose lifetime is about 38 fs.84 To check whether this
was not an artifact of the CASSCF method induced by
artificially large energy gradients in the Franck–Condon
region, we have simulated the initial relaxation of cytosine
with dynamics simulations performed with the RI-CC2/SVP
method. Exactly as predicted at CASSCF level, all CC2
trajectories moved into the semi-planar S1/S0 crossing within
about 10 fs. The average potential energy over all trajectories
plotted as a function of time is shown in Fig. 8. This figure also
shows the shortening of the C2-N3 bond length in the beginning
of the dynamics typical for the semi-planar conical intersection.
3.3 Photophysics of cytosine
Fig. 9 schematically illustrates our main findings concerning
the photodynamics of cytosine excited into the first singlet pp*
Table 4 Time constants for cytosine relaxation after UV excitation in gas phase. SH—surface hopping; MS—multiple spawning. Results fromref. 35 are those for pump wavelength 280 nm, which has the closest correspondence to the spectral region excited in the present work
t1 (ps) t2 (ps) t3 (ps)
ExperimentalRef. 32 — 3.2Ref. 34 o0.05 0.82 3.2Ref. 33 0.16 � 0.02 1.86 � 0.19Ref. 35 o0.1 1.2 55TheoreticalSH/OM2 ref. 30 0.04 0.37MS/CAS(2,2) ref. 24 o0.02 B0.8SH/CAS(14,10), present worka 0.013 � 0.001 0.688 � 0.002SH/CAS(14,10), present workb 0.009 � 0.001 0.527 � 0.005 3.08 � 0.04
a Bi-exponential fitting: a = 0.16, (1 � a) = 0.84. b Tri-exponential fitting: a1 = 0.13, a2 = 0.74, (1 � a1 � a2) = 0.13.
Table 5 Main conical intersections accessed for S1/S0 deactivation. Conical intersection energies computed at same level as the dynamicssimulations are given in parentheses. SH—surface hopping; MS—multiple spawning; nr—not reported
Semi-planar (early) Semi-planar (late) oop-NH2 C6-puckered
SH/OM2a 0% (4.34) 0% (4.34) 0% (nr) 100% (3.64)MS/CAS(2,2)b 15% (5.25) 0% (5.25) 65% (4.35) 5% (3.98)SH/CAS(14,10)c 16% (4.09) 52% (4.09) 7% (3.84) 8% (4.34)
a Ref. 30. b Ref. 24. c Present work.
Fig. 7 Time evolution of the potential energy of the ground and
excited states of cytosine in the beginning of the dynamics for two
selected trajectories. The circles indicate the current state in each time
step. Full circles—pp* state; open circles—closed shell state (cs).
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state. Initially, cytosine relaxes along the pp* state quickly
reaching a region of strong mixing of the pp*, np* and closed
shell states. In this first approach to the ground state, 16% of
the trajectories are deactivated within a 13 fs time constant
(Fig. 9-1). Although the semi-planar minimum on the crossing
seam mixes the nOp* and the pp* states (Table 2), the actual
transitions took place in higher energy regions of the crossing
seam mainly involving the pp* and the closed shell states. Due
to limitations of surface hopping method, the value for this
very short time constant should be taken cautiously. Note,
however, that this semi-instantaneous deactivation of
cytosine through the semi-planar conical intersection was also
observed in the multiple spawning dynamics performed at
CASSCF(2,2) level.24 On the other hand, it was not observed
in surface hopping dynamics simulations at the semiempirical
OM2 level.30 In this case, the very short time constant reported
(0.04 ps) corresponds to a S2 - S1 deactivation process.
(A comparative summary of the results obtained in different
dynamics simulations of cytosine is given in Table 5.)
The remaining 84% of trajectories that did not deactivate in
this first encounter with the ground state relaxes to the nOp*state (Fig. 9-2). A second time constant of 0.69 ps appears
in the simulations corresponding to the time for internal
conversion of these trajectories. Three different reaction
pathways were observed at this time scale. The main one
was again the deactivation at the semi-planar region of the
crossing seam, which could occur every time the motion of the
molecule in the nOp* well brings it near this intersection. This
was the pathway followed by 52% of the trajectories (Fig. 9-3).
This finding is in strong contrast with the surface hopping
dynamics performed at OM2 level30 and the multiple spawning
dynamics performed at the CASSCF(2,2) level,24 where no
deactivation in this region of the crossing seam was observed
at the long time scale. The results of surface hopping dynamics
at CASSCF(12,9) are similar to the present results and show
predominance of the semi-planar conical intersection.85
The sloped shape of the conical intersection at this region
decreases its efficiency and opens the possibility of internal
conversion through other channels. A total of 15% of
trajectories escaped from the nOp* well by crossing the barrier
to biradical pp* states. Eight percent of them deactivated at
the C6-puckered conical intersection (Fig. 9-4). Other seven
percent deactivated at the oop-NH2 conical intersection
(Fig. 9-5). Again the present results are not in agreement with
previous dynamics simulations. While the oop-NH2 conical
intersection was the most accessed conical intersection in the
Fig. 8 Average potential energies during the dynamics simulations
computed at RI-CC2/SVP level. The inset shows the average C2–N3
bond length as a function of time. The gray area indicates the standard
deviation.
Fig. 9 Reaction pathways and time constants for dynamics of cytosine in the excited state.
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CASSCF(2,2) multiple spawning simulations, the C6-puckered
was the unique conical intersection observed in the OM2
surface hopping simulations (Table 5).
The remaining 17% of trajectories did not deactivate within
the 1.2 ps simulation time. They may still be part of the t2exponential decay or at least a fraction of them may decay
with a third and longer time constant of 3 ps. The duration
of our dynamics simulation is not sufficiently extended to
distinguish between the two possibilities. If the longer decay
time constant is assumed, the previous discussion is still valid,
but the numerical values for the time constants are slightly
modified to t1 = 9 fs and t2 = 0.53 ps (Table 4).
Different from our results, the analysis of reaction pathways
performed in ref. 42 at CASPT2 level disfavored the
semi-planar intersection and indicated a dominance of the
C6-puckered and oop-NH2 conical intersections. However,
comparison of the energy of the semi-planar conical inter-
section not only with present results based on full optimiza-
tion, but also with those of other CASPT2 and MRCI
investigations44,46 shows that the semi-planar structure is
probably computed too high in energy in ref. 42.
The different results obtained by several simulations are
expression of the discrepancies between the potential energy
surfaces computed at diverse levels. All of them predict
internal conversion occurring in sub-picosecond time scale
but with different populations of each deactivation pathway.
The CAS(2,2) employed in the multiple spawning dynamics is
likely a too small space to adequately describe the potential
energy surfaces of cytosine and it should be especially taken
with care for the description of the three state region of the
crossing seam, leading to a underestimation of the role of the
semi-planar conical intersection. Nevertheless, similar to our
results, it predicts a dominant trend of relaxation to the S1minimum from where cytosine escapes to different conical
intersections. In the case of the OM2 method, the lack of
activation of different conical intersections in any proportion
may be an indication of an overstabilization of the pathway
leading to the C6-puckered conical intersection. In comparison
to our results, a qualitatively different mechanism is predicted,
with direct deactivation along the pp* state without relaxing tothe S1 minimum. The CAS(14,10) active space used in our
simulations tends to predict the energy of the pp* state
relatively too high in comparison with the np* state. Because
of this, we believe that the proper stabilization of the pp* stateby inclusion of dynamical electron correlation should bring to
an increase of deactivation at the pp* channels.
4. Conclusions
We have investigated the photophysics of cytosine by non-
adiabatic dynamics simulations, optimization of stationary
points and conical intersections, and determination of reaction
paths. Optimizations have been performed at CASSCF and
MR-CISD levels and the dynamics simulations were performed
at CASSCF level with the surface hopping method including
four electronic states.
The results show the activation of multiple reaction
pathways in up to three different time scales, which correlates
well with the experimental results. Most of trajectories relax to
the np* S1 minimum. From this minimum, cytosine deactivates
mainly via a semi-planar conical intersection between the nOp*and the ground state in a region of the crossing seam near
a triple degeneracy. In fewer cases, it deactivates via two
different conical intersections involving crossings between
pp* states and the ground state. Dynamics of cytosine presents
a singular feature that is a semi-instantaneous internal
conversion of a minor fraction of the population within only
10 fs. The competition between reaction paths is controlled by
excited state barriers, and comparison to results of other
dynamics simulations shows that details of the potential
energy surfaces are important for the exact determination of
the role of each deactivation path.
Acknowledgements
This work has been supported by the Austrian Science Fund
within the framework of the Special Research Programs F41
(ViCoM) and of the German Research Foundation, Priority
Program SPP 1315, project No. GE 1676/1-1. This work was
part of the research project Z40550506 of the Institute of
Organic Chemistry and Biochemistry of the Academy of
Sciences of the Czech Republic. Support by the grant from
the Ministry of Education of the Czech Republic (Center for
Biomolecules and Complex Molecular Systems, LC512) and
Computer time at the Vienna Scientific Cluster (project nos.
70019 and 70151) is gratefully acknowledged.
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