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Details of the Excited-State Potential Energy Surfaces of Adenine by Coupled Cluster Techniques Zsuzsanna Benda and Péter G. Szalay* Laboratory of Theoretical Chemistry, Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518 Budapest, Hungary S Supporting Information *

ABSTRACT: EOM-CCSD and CC2-LR methods were used to study the potential energy surfaces of the three lowest excited states (two ππ* and an nπ*) of adenine. The equilibrium structure could only be obtained for the S1 state, which has n−π* character. It was shown that the topology of the coupled cluster surface is such that no minimum for the S2 and S3 states exists in the Franck− Condon region due to conical intersections between these low-lying states. To understand this topology, relevant cuts of the potential energy surfaces have also been calculated, and conical intersections have been located. Even a three-fold intersection between these three states was found. The crossings of these surfaces can be reached from the bright state barrierlessly without major change in the geometry. Therefore, these might play an important role in the ultrafast deactivation of adenine.

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(vapor-phase absorption spectrum9 and matrix isolation spectrum10), but resonant two-photon ionization (R2PI), laser-induced fluorescence and various double-resonance spectra11−16 show also the low-intensity transitions at around 4.5 eV. The lowest-energy transition is usually assigned to the 1(nπ*) state, while the second is assigned to the Lb (ππ*) transition.11,15,16 These are extremely close to each other; therefore, significant vibronic interaction is assumed.1 Other experiments were carried out (dispersed fluorescence,17 UV− UV, and IR−UV18) in order to help the assignment of the multiphoton ionization spectra. Kim et al. assigned the bands at 4.40 (35503 cm−1) and 4.48 eV (36108 cm−1) to the 0−0 transitions corresponding to the lowest nπ* and ππ* states, respectively.11 The same 0−0 band of the ππ* transition was also observed by Lührs et al.12 and Nir et al.,18 but the position of the 0−0 band of the nπ* transition is controversial; the latest work by the Kleinermanns group assigns it to the 4.47 eV (36602 cm−1) band.16 (Note that they cite ref 15 for this conclusion; however, the latter paper does not state explicitly this assignment.) The onset of the more intense La transition starts at somewhat higher energy. Time-resolved experiments of adenine are usually initiated with an excitation to one of the ππ* states. These show doubleexponential decay6,12,19,20 with time constants varying with the pump wavelength.6,7,12,19,20 As for the deactivation mechanism, it was proposed that excitation populates the bright ππ* state, from which the decay leads to the lowest nπ* state within 100 fs.19 According to Kleinermanns et al., the second relaxation step to the ground state is responsible for the long component

INTRODUCTION What happens with the DNA after UV irradiation? This question is asked not only by scientists, but even public interest is high due to health risks related to increased UV impact on the Earth’s surface. To understand all details of this process, the most logical route, both theoretically and experimentally, should start with the investigation of the nucleobases, the principal building blocks of DNA responsible for the absorbance of UV photons, and then continue with a systematic buildup of the natural DNA with sugar residues, hydrogenbonded Watson−Crick pairing, π stacking, solvent effects, and so forth. Following this line, in a recent paper, Kleinermanns et al.1 reviewed both experimental and theoretical development of the last years, while earlier results have been summarized in refs 2−4. Here, we mention only that all of the nucleobases relax to the ground state extremely fast, within a few picoseconds after excitation,2,5−7 resulting in low fluorescence yield;8 the same relaxation paths are also open in DNA, and the effect of base pairing, neighboring bases, bound sugar, and so forth seem to be small on these.1 However, in this case, other relaxation mechanisms are also possible, like proton transfer between base pairs or excitation of strands.3 In the focus of the present study is adenine, which has been extensively investigated, but so far, there is no definite consensus regarding the relaxation mechanism after excitation.1 We would like to contribute to this debate by investigating the potential energy surfaces of the lowest excited states of adenine at a high level of electronic structure theory in order to set some benchmarks with which to compare. The lowest excited states of adenine are two ππ* and one nπ* states. The ππ* states are often labeled La and Lb; the former carries considerably larger oscillator strength. Of these, most probably only the La transition is seen in the UV spectrum © 2014 American Chemical Society

Received: May 30, 2014 Revised: July 13, 2014 Published: July 15, 2014 6197

dx.doi.org/10.1021/jp505331s | J. Phys. Chem. A 2014, 118, 6197−6207

The Journal of Physical Chemistry A

Article

In connection with the decay mechanism and the details of the potential energy surfaces, it is important to cite here the recent work of Barbatti et al.,26 where the uncertainty introduced by limited accuracy of electronic structure methods has been discussed. In particular, the ordering of the states and the locations and relative positions of conical intersections are found to be highly dependent on the method.26 For a systematic comparison of vertical excitation energies of nucleobases obtained by different methods, see ref 44. One can conclude therefore that the final word on the mechanism can only be declared if reliable potential energy surfaces of the excited states are available. In order to set benchmark values, high-level quantum chemical calculations are needed. The vertical excitation energies have already been studied by coupled cluster methods,44 and the CC2 method has been used for excitedstate optimizations.16,21,22,26,28 In this study, two coupled cluster methods, CC2 and CCSD, were used to investigate the excited-state potential energy surfaces of adenine.

explained by a sizable equilibrium well on the nπ* potential energy surface.1 There are also numerous theoretical calculations on the excited states of adenine, but the different methods often give contradicting results.1 In the case of the lowest excited state, the S1 state, the character has been predicted as dominantly n−π*21−25 or, in many cases, a strong mixture of n−π* and π−π* components.16,26−28 The equilibrium structure shows significant pyramidalization around the C2 atom, as predicted by the majority of methods;23−2425,28 however, some other, including most DFT calculations give planar rings for this minimum.26−29 It is controversial whether the darker ππ* state (Lb) has a minimum on its potential energy surface. This state is close to the nπ* state in energy, mixing between them, as well as close-lying conical intersections make the Lb state hard to study. Usually, only a shallow minimum can be located,23−25,30 or a flat region is observed on the potential energy surface.31 Marian27 was not able to locate a ππ* minimum with the TDDFT method, which she attributed to the failure of the B3-LYP functional, which is “biased toward the n−π* excitation”.27 CASSCF predicts a minimum on the Lb surface with planar rings and a pyramidalized NH2 group.23−25 Two different equilibrium structures have been reported from CC2 calculations. Fleig et al.21 report a planar minimum with an adiabatic excitation energy of 4.47 eV, which agrees with the above-cited experimental observation by Kim et al.11 Recently, Engler et al.16 found a nonplanar minimum for this ππ* state, which resembles the nπ* equilibrium structure (see the discussion below). To understand the mechanism of the dynamics, subsections of the potential energy surface were investigated in several papers, and numerous conical intersections could be located. A conical intersection of the πσ* excited state and the ground state has been found by Sobolewski and Domcke,23,32 which could explain a radiationless relaxation to the ground state through the elongation of an NH bond. The most systematic study is published by Barbatti and Lischka,33 who, using the MRCIS method, could find six different minima on the crossing seam (MXS) between the bright La state and the ground state, all of them characterized by puckered structures. It was observed that the Franck−Condon (FC) point is barrierlessly connected to a conical intersection with the ground state, which was also confirmed by others24,25,30,34,35 using different methods. Barbatti and Lischka33 could also find MXS between the ground and the nπ* states. An La−Lb crossing was located at lower energy than the vertical excitation energy of the La state with CASPT2//CASSCF in several studies.24,25,34 An nπ*−ππ* crossing and two different three-state conical intersections at low energies were found by Matsika.36 Theoretical simulations have been used to understand the details of the deactivation mechanism,23,24,26,33,37−41 applying various methods. The involvement of different states is basically confirmed by these calculations (see, e.g., ref 41). Concerning the geometry change, there are three relaxation pathways that might explain the ultrafast decay; two of them involve significant distortions of the six-membered ring at the C2 or C6 atoms,23,24,33 and one is the path of hydrogen detachment from the N9 atom.32,42,43 Because these three relaxation pathways all come from different calculations, it is not clear yet whether these are competing pathways or if any of them is dominating. In any case, all of these mechanisms show a fast conversion to the nπ* state as a first step.

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METHODS As has been shown in a previous study,44 coupled cluster methods (equation of motion (EOM)45−47 or linear response (LR);48−50 for a recent review, see ref 51) provide reliable excitation energies for nucleobases. While the most approximate version, CC2-LR,52 seems to underestimate the nπ* excitation energies, it gives very accurate results for the ππ* states;44 due to error compensation, the excitation energies in this latter case are even closer to EOM-CCSD(T)53 results than EOM-CCSD ones. Therefore, in this study, both EOMCCSD47 and CC2-LR52 methods have been used, augmented with some CC3-LR50,54 single-point calculations to check the accuracy of these. In all calculations, the cc-pVDZ55 basis was used, which was shown44 to give reliable excitation energies, very close to the ccpVTZ basis. However, the missing diffuse functions have two consequences: (i) no Rydberg states will appear; therefore characterization of the states and surfaces are simplified; (ii) excitation energies will be somewhat (by 0.1−0.3 eV) too high.56 In our opinion, this does not affect the conclusions of this paper but largely facilitates the discussion. Geometry optimizations were performed with CCSD and CC2 methods for the ground state and with the corresponding EOM-CCSD and CC2-LR methods for the excited states using analytic gradients57−59 and the GDIIS (geometry optimization by direct inversion in the iterative subspace) algorithm.60 The search for conical intersections was carried out with the algorithm outlined in ref 61 using analytically obtained gradients58,59 and nonadiabatic coupling terms62 at the EOMCCSD level. Close to the degenerate points, corrections suggested by Tajti and Köhn63 were applied to avoid imaginary solutions of the EOM equations. Note that if such a point was reached, the optimization could not be carried out further due to the lack of gradients for the corrected energy. For the representation of the character of excited states, the natural orbitals of the difference density of the ground and excited states were applied. These natural orbitals, along with the corresponding occupation numbers, allow an unbiased characterization of ππ* and nπ* states. The one-dimensional cuts, if not stated otherwise, have been generated by linear interpolation of the Cartesian coordinates between the two terminal points, which first have been brought to maximal overlap. 6198



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Table 1. Equilibrium Structural Parameters for the S0 and S1 States of Adenine Calculated at the CC2 (CC2-LR) and CCSD (EOM-CCSD) Levels Using the cc-pVDZ Basis Seta CC2

a

CCSD

internal coordinate

S0 min

S1 min

S0 min

S1 min

R(N1−C2) R(C2−N3) R(N3−C4) R(C4−C5) R(C5−C6) ∠(N1−C2−N3) ∠(C2−N3−C4) ∠(C6−N10−H11) τ(H12−N10−C6−N1) τ(H11−N10−C6−C5) τ(C6−N1−C2−H2) τ(N1−C2−N3−C4) τ(C4−C5−C6−N1) τ(C4−C5−N7−C8) τ(H9−N9−C4−N3) out-of-plane ∠(C6−H12−H11−N10) out-of-plane ∠(H2−N1−N3−C2)

1.358 1.350 1.349 1.409 1.415 130 110 115 −21 22 180 0 −1 0 0 37 0

1.392 1.430 1.331 1.428 1.446 112 118 111 −30 23 164 −23 1 0 3 46 −35

1.354 1.338 1.347 1.399 1.414 130 111 116 −21 23 180 0 −1 0 0 37 0

1.383 1.411 1.332 1.412 1.445 113 118 112 −30 23 170 −24 0 0 3 45 −30

Bond lengths are given in Å and angles in degrees. For the numbering of the atoms, see Figure 1.

All calculations were performed with the CFOUR64 program package.

very small, only 0.02 eV in the case of the ground state using the CCSD method with the cc-pVDZ basis. The effect on excitation energies will be discussed when appropriate. The four lowest excited states of adenine include two ππ* and two nπ* states. The calculated excitation energies obtained in this work by the CC2-LR and EOM-CCSD methods are given in Table 2, while the characters of these excited states are

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RESULTS AND DISCUSSION The geometry of the ground state (S0) was optimized at the CC2 and CCSD levels. Some of the optimized parameters are listed in Table 1, and the full geometry is given as Supporting Information. Numbering of the atoms can be seen in Figure 1.

Table 2. Vertical Excitation Energies (eV) and Oscillator Strengths of Adeninea CC2

MRCISb

CCSD

state

ΔE

f

ΔE

f

ΔE

1(ππ*) 1(nπ*) 2(ππ*) 2(nπ*)

5.30 5.23 5.47 5.89

0.001 0.006 0.314 0.002

5.43 5.54 5.78 6.17

0.000 0.005 0.284 0.002

5.68 5.85 6.55 6.30

a

The cc-pVDZ basis set has been used in the CC2-LR and EOMCCSD calculations. bSee cc-pVDZ results from reference 36.

shown in Figure 2. In Table 2, the MRCIS data from ref 36 are also given because these will be used in later discussion. For a more detailed comparison of different theoretical results, see ref 44. In particular, the first three states, two ππ* and an nπ*, are very close in energy, and various methods give quite diverse ordering, where one also needs to consider the different geometries used in the different studies. The present EOMCCSD/cc-pVDZ calculations predict the order 1(ππ*), 1(nπ*), and 2(ππ*). However, augmentation of the basis set by diffuse functions reduces the energy of the 2(ππ*) state, which then becomes the second state at this geometry.44 On the other hand, inclusion of triple excitation effects (e.g., at the EOM-CCSD(T) level) does not change the order anymore.44 Note that planarity of the NH2 group does not change the ordering of the states; the ππ* transition energies change only by 0.02 eV the most, while the change is smaller than 0.1 eV in the case of nπ* transitions. In general, CC2-LR transition energies are smaller than CCSD ones; the difference is the largest for the nπ* transition. This results in a different ordering

Figure 1. Numbering of the atoms of the adenine molecule.

Although no planarity constraint was applied, in the resulting structure the rings are practically planar at both CCSD and CC2 levels (see Table 1). On the other hand, the NH2 group is not planar. The question of the nonplanarity of adenine (and other nucleobases) has been discussed in detail recently by Wang and Schaefer65 and by Zierkiewicz et al.;66 these papers show that the energy difference between structures with a planar and nonplanar amino group is very small, and with increasing basis set, it even decreases. See also the systematic study by Fogarasi67 on the strong dependence of the planarity of the amino group on the basis set size and the level of electron correlation included in the calculations. In any case, for the discussion below, the uncertainty about the nonplanarity of the NH2 group does not pose any problem because the energy difference between the planar and pyramidalized structures is 6199



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Figure 2. Characterization and CCSD excitation energies of the first four excited states at the ground-state equilibrium geometry. Occupation numbers are also given for the natural orbitals of the difference density.

of the states; with CC2, the 1(nπ*) becomes the lowest transition at the FC geometry. Because all three states are very close in energy, the relevance of this different ordering at this geometry is not immediate and will be discussed in more detail later. Our primary goal was to obtain equilibrium geometries for relevant excited states of adenine, in particular, S1, S2, and S3. Minimum for the S1 State. The geometry optimization of the 1(nπ*) state leads to the lowest-energy equilibrium structure; therefore, we refer to this state as S1, although at the FC geometry, the higher-level coupled cluster methods predict 1(nπ*) as the second or even the third excited state. At both EOM-CCSD and CC2-LR levels, the optimization was straightforward and led to a minimum in a few steps. While for nonplanar geometries the distinction of lone pair and π orbitals is somewhat arbitrary, both theoreticians and experimentalist like to distinguish nπ* and ππ* excitations for qualitative argumentation. Therefore, we also try to perform this assignment using the natural orbitals of the difference density. The two most relevant natural orbitals of the S1 state at its equilibrium geometry are depicted in Figure 3, showing that this state has indeed a dominantly nπ* character. This contradicts the interpretation of some recent calculations, for

Figure 3. Natural orbitals of the difference density and the corresponding occupation numbers for the first (nπ*) transition in the S1 minimum.

example, refs 16 and 26, which predict strong mixing of nπ* and ππ* character, but agrees with others.21,22,24,25,32 The disagreement can have several reasons. First is the geometry; as will be discussed below, we also see some mixing of nπ* and ππ* characters along the potential energy surfaces after distorting from the S1 minimum. Second, according to our experience, the natural orbitals of the difference density give an unambiguous tool for identifying the character of the transition, while simple inspection of the orbitals involved in the excitation might be misleading in some cases. 6200



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theory. Using this correction (−0.16 eV), the estimated 0−0 (T0) value becomes 4.39 and 4.71 eV at the CC2 and CCSD levels, respectively. The CC2 result is in good agreement with the recently published experimental value of 4.41 eV.22 Because triple excitations have been proven to contribute significantly to the excitation energy,44,53 we have also calculated Te with the CC3-LR method and obtained Te = 4.64 eV. Using the ZPE correction from the CC2 calculations, this results in a T0 value of 4.48 eV. There are several values in the literature for the band origin of the S1 excitation. Among the recent ones, Kim et al.11 assigned the A band at 4.40 eV (35503 cm−1) in their R2PI and LIF spectra to the nπ* 0−0 transition, while Engler et al.16 refer to the band at 4.47 eV (36062 cm−1) as the nπ* origin. Both CC2-LR and CC3-LR values are in good agreement with these numbers, and the close agreement does not allow us to give a definite answer to which of the two above assignments should be preferred. Other theoretical methods give similar results; CASPT2 values are in the range of 4.35−4.52 eV23−25 CC2 and the related ADC(2) gave 4.3−4.4 eV,22,28 while DFT values, depending on the functional, are 4.2−4.7 eV.22,28 In a forthcoming paper, we will present a simulated vibronic spectrum of adenine also for the low-intensity region, which should shed more light on this problem. In their recent paper, Plasser et al.28 also compare the CC2 and ADC(2) results to an experiment detecting low-intensity fluorescence of adenine8 at 3.68 eV. CC2 and ADC(2) give considerably lower energy. Note that the highest-level calculations of the present study, CCSD and CC3, give values (calculated from data in Table 3 for the S1 state) of 3.75 and 3.59 eV, respectively, which are in better agreement with those from this experiment. Figures 5 and 6 show the CCSD and CC2 one-dimensional cuts of the potential energy surfaces connecting the S0 and S1

The most important structural parameters for both the EOM-CCSD and CC2-LR optimized geometries are listed in Table 1; the Cartesian coordinates of these structures are given in the Supporting Information. The structure obtained at the CCSD level is also depicted in Figure 4.

Figure 4. Equilibrium structure of the S1 state obtained at the CCSD level.

A mere visual inspection of Figure 4 shows that, contrary to the ground state, the ring structure is not planar; an out-ofplane distortion of the six-membered ring can be observed. Quantitatively (see Table 1), the C2 atom moves out of the plane of the H2−N1−N3 atoms as much as 30°. Comparing the CC2-LR and EOM-CCSD structures, they are quite similar, although in the former case, the distortion around the C2 atom is somewhat larger (35 versus 30°), and the C4−C5 bond is longer by 0.016 Å. Compared to the ground-state structure, besides the discussed pyramidalization around the C2 atom, the N1−C2 and C2−N3 bonds elongate considerably, and the N1−C2−N3 angle decreases. This can be explained by the antibonding character of the LUMO π* orbital for these bonds. The pyramidalization of the amino group also increases somewhat. However, the five-membered ring remains practically planar. The equilibrium geometry of the S1 state qualitatively agrees with results of earlier calculations. Most of the previous communications at the CASSCF23−25 and CC216,21,28 levels predict a puckered geometry around the C2 atom, while DFT calculations result in a planar ring.26,28 Table 3 lists the relative energies of the different states at the S1 minimum with respect to the S0 energy at its equilibrium Table 3. Relative Energies (eV) of the Different States at the S1 Minimum with Respect to the S0 Energy at Its Equilibrium Structure state

CC2

CCSD

CC3

S0 1(nπ*) 1(ππ*) 2(ππ*) 2(nπ*)

1.22 4.55 5.82 6.00 6.35

1.12 4.87 6.07 6.26 6.52

1.05 4.64

Figure 5. Energy of the five lowest states of adenine calculated at the CCSD level along the cut of the potential energy surfaces between the S0 and S1 minima. Structures have been generated by linear interpolation of the Cartesian coordinates between the two terminal points. Points are connected diabatically, following the character of the transitions.

structure. The ground-state energy is more than 1 eV larger than at the S0 minimum, the 1(nπ*) state stabilizes by 0.7 eV, while the ππ* states destabilize by about 0.5−0.7 eV. The relative changes of the excitation energies of the individual transitions are quite parallel at CC2 and CCSD levels. Due to the increased energy difference between the 1(nπ*) and the ππ* excitations, now the former is the lowest excited state at both levels of theory. In the case of the S1 state, the value in Table 3 corresponds to the minimum-to-minimum (Te) excitation energy. To compare with experiment, we have also calculated the zero-point energy (ZPE) in the harmonic approximation (for frequencies, see the Supporting Information) for both S0 and S1 states at the CC2(CC2-LR) level of

minima. The two methods give semiquantitatively the same result; the curves originating from the different calculations run quite parallel, CC2-LR excited-state curves being about 0.3 eV lower than those calculated at the EOM-CCSD level. A significant difference is that at the FC point, the nπ* state is the second lowest state with the EOM-CCSD method, while it is the lowest at the CC2-LR level. Note that higher-level calculations including triple excitations (e.g., EOM-CCSD(T)) give the same order of the first ππ* and nπ* states at the FC point as does EOM-CCSD.44 Whether this slight difference in 6201



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two excited states are plotted along with hole orbitals, which allows the tracking of the character change. It can be seen from this cut that the gap between the two states gets larger away from the planar structure. At the planar structure, the lower state has a clearly π-type hole orbital, while the second has an ntype one. The character changes, however; while the π character remains on the NH2 group, a lone pair character starts to grow on the N3 atom. From the lowest-energy point of the lower curve (x = 0.225 in Figure 7), the steepest descent was followed. The corresponding curves can be seen in Figure 8. The energy of the lower transition decreases further, but at the same time, the character gradually changes, and at geometries with the largest displacement, the hole orbital belonging to the lower curve becomes n-type, pretty much resembling the orbital of the second excited state at the planar geometry. This means that, coming from the planar geometry, the character of the lower excitation changes from π−π* to n−π* even though the two states never get close in energy; in fact, they are the closest at the planar structure. This character change indicates of course that there must be an intersection close by, which could be reached by moving along the remaining coordinates. To locate the intersection of these two states, a onedimensional cut connecting the S1 minimum and the planar saddle point has been obtained. Figures 9 and 10 show the corresponding CCSD and CC2 diabatic curves, respectively. Indeed, an S1−S2 crossing has been found quite close to the saddle point. The estimated energy and some structural parameters of this crossing are listed in corresponding columns of Tables 4 and 5. As will be seen later, this crossing belongs to the 1−2 crossing seam; in fact, the estimated energy is only slightly above the energy of the optimized structure (MXS 1− 2). The existence of this crossing explains why no minimum for the ππ* state could be found in the optimization procedure. According to the calculations presented here, it seems to be quite likely that no equilibrium structure exists on the S2(ππ*) potential energy surface of adenine. The topology is such that before reaching a minimum, there is a conical intersection with the S1 state. Some of the previous calculations report a minimum for the ππ* state, but it is Marian27 who, based on her TDDFT calculations, reports that the equilibrium structure for the ππ* state could not be located. She explained this, however, as a failure of the B3-LYP functional and did not conclude that this minimum does not exist at all. Earlier CASSCF optimizations report an S2 minimum with ππ* character23−25 that is slightly (0.2−0.4 eV) above the S1 minimum. The ring system is planar, and only the NH2 group stands off of this plane. Note that these structures are similar to the planar saddle point found in this work by the CC methods, differing obviously in the position of the NH2 group. Note, however, that on the CC

Figure 6. Energy of the five lowest states of adenine calculated at the CC2 level along the cut of the potential energy surface between the S0 and S1 minima. Structures have been generated by linear interpolation of the Cartesian coordinates between the two terminal points. Points are connected diabatically, following the character of the transitions.

the topology of the surfaces has an effect on the final outcome of the dynamics, it cannot be predicted from the present calculations. One can state, however, that at the EOM-CCSD level, an S1−S2 crossing can be observed that is quite close to the FC point and has lower energy than the vertical excitation energies (Table 4). Some structural parameters of this crossing point are listed in Table 5, and its further properties will be discussed later. This crossing is not present at the CC2-LR case, but the nπ* and ππ* states are also very close in energy in the FC region. Search for the Minimum of the S2 State. Optimizing the geometry of the 1(ππ*) state did not lead to an S2 minimum; during the optimization, the character of the excitation gradually became n−π*, and after a while the molecule relaxed into the S1 minimum. In one of the attempts to avoid this collapse, a planar geometry was found, at which the 1(ππ*) state has the lowest energy at the CC2 level as well. It turned out that this planar geometry is a saddle point on the surface. In order to find the minimum, we have started the optimization from points distorted along the mode with imaginary frequency. Unfortunately, these optimizations ended up again in the S1 minimum. To understand how and why this character change occurs, different cuts of the potential energy surfaces were investigated. The energy of the first two excited states, that is, 1(nπ*) and 1(ππ*), was inspected. Note that the character of the hole orbitals (see Figure 2) differs for these two transitions, but they share the orbital to where the excitation goes; it is the LUMO π* orbital. This fact makes the mixing of the two states more feasible when the symmetry restriction is removed. The first cut was generated along the mode with the imaginary frequency belonging to the lowest-energy state (ππ*) at the planar geometry. Figure 7 shows the path from the planar saddle point in the direction of the decreasing energy. Energies of the first

Table 4. Relative Energiesa at Various Crossing Points of the Potential Energy Surfaces of Adenine CCSD

MRCISe

CC2

state

1−2b

1−2c

MXS 1−2

MXS 1−2−3

MXS 1−2d

MXS 1−2−3d

MXS 1−2

MXS 1−2−3

S0 1(nπ*) 1(ππ*) 2(ππ*)

0.04 5.39 5.39 5.68

0.51 5.34 5.34 5.78

0.18 5.28 5.28 5.65

0.28 5.44 5.45 5.46

0.13 4.95 5.15 5.43

0.20 5.06 5.18 5.33

0.27 5.52 5.52 6.44

0.85 6.24 6.24 6.24

Energies with respect to the S0 state at its equilibrium geometry, in eV. bEstimated from the S0 min − S1 min cut (Figure 5). cEstimated from the S1 min − saddle point cut (Figure 9). dSingle-point energies at the crossings on the CCSD surface. eReference 36. a

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Table 5. Structural Parameters of the Ground-State Minimum and Various Crossing Points of the Potential Energy Surfaces of Adeninea MRCISd

CCSD b

c

internal coordinate

S0 min

1−2

1−2

MXS 1−2

MXS 1−2−3

S0 min

MXS 1−2

MXS 1−2−3

R(N1−C2) R(C2−N3) R(N3−C4) R(C4−C5) R(C5−C6) ∠(N1−C2−N3) ∠(C2−N3−C4) τ(H9−N9−C4−N3) τ(H12−N10−C6−N1) τ(H11−N10−C6−C5) τ(C6−N1−C2−H2) τ(N1−C2−N3−C4) τ(C4−C5−C6−N1) τ(C4−C5−N7−C8)

1.354 1.338 1.347 1.399 1.414 130 111 0 −21 23 180 0 −1 0

1.358 1.356 1.347 1.411 1.418 128 111 0 −22 23 178 −3 0 0

1.391 1.435 1.313 1.447 1.434 124 114 1 −8 7 175 −7 0 0

1.378 1.390 1.335 1.440 1.425 126 113 0 −22 21 180 0 0 0

1.324 1.410 1.328 1.435 1.455 129 111 −1 −19 23 180 0 0 −1

1.340 1.332 1.329 1.383 1.405 129 111 7 15 −14

1.386 1.393 1.318 1.417 1.417 124 114 −4 3 −1

1.351 1.452 1.323 1.458 1.493 133 104 0 1 −1

Bond lengths are given in Å, and angles are in degrees. bEstimated from the S0 min − S1 min cut (Figure 5). cEstimated from the S1 min − saddle point cut (Figure 9). dReference 36.

a

Figure 8. Energy of the two lowest excited states along the steepest descent path. The zero value of the coordinate corresponds to the minimum (x = 0.225) of the lower curve in Figure 7, and displacement is given in arbitrary units. The figure also shows the character of the natural orbital of the difference density representing the hole orbital (where the excitation comes from). Calculations have been performed at the CC2-LR level.

Figure 7. Energy of the two lowest excited states along the normal coordinate with imaginary frequency belonging to the lowest energy state (ππ*) at the planar geometry. The zero value of the coordinate corresponds to the planar saddle point on the ππ* surface; displacement is given in reduced units. The figure also shows the natural orbitals of the difference density representing the hole orbitals (where the excitation comes from). Calculations were performed at the CC2-LR level.

surface, moving the NH2 group out of the plane requires energy, and the corresponding normal mode is, although low, about 300 cm−1 but real; the mode with imaginary frequency moves instead the C2 atom out of the plane and therefore obviously brings the structure toward the nπ* minimum. We conclude that the different answers by CASSCF and CC methods result from the different surfaces that these methods give. It is not possible to decide for one or for the other, but it is worth remembering that the CC methods include more dynamic correlations. There are, however, two other papers with CC2 calculations that report a ππ* minimum. Fleig et al.21 reported a planar structure as the equilibrium for the 1(ππ*) state at the CC2-LR level. However, no frequency analysis was performed in ref 21. Because the structure (private communication) is very similar to the planar saddle point that we have found, it is suspected

Figure 9. Cut of the potential energy surfaces between the S1 minimum and the saddle point of the π−π* state. Structures have been generated by linear interpolation of the Cartesian coordinates between the two terminal points. The energies of the five lowest states were obtained at the CCSD level. Points are connected diabatically, following the character of the transitions.

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mechanism described in ref 63 can only correct the energy but does not give eigenvectors required for the calculation of gradients and nonadiabatic coupling. Therefore, the MXSs reported here should be considered approximate; however, as the results show, the present searches always ended up in points where degeneracy was fulfilled within 0.01 eV. Relative energies of the different states and some structural parameters are compared in Tables 4 and 5 for the optimized structure of MXS 1−2 and estimated crossing points obtained from Figures 5 and 9. The data in these tables support the idea that these points belong to the same seam; they are quite close energetically, and the geometry parameters at the MXS are in between those at the two estimated points. The rings are planar, like at the FC point, and pyramidalization of the NH2 group is present as well. The largest change in the geometry with respect to the S0 equilibrium structure can be observed for the C2−N3 and N1−C2 bond lengths. This can be explained by the antibonding character of the LUMO π* orbital between these atoms. The MXS between the S1 and S2 states was also obtained by Matsika36 at the MRCIS level. The corresponding structure (see Table 5) is similar to ours; the difference is not larger here than that of the S0 structure. The relative energy of this MXS is somewhat higher (by 0.24 eV) at the MRCIS level than that at the EOM-CCSD (see Table 4). The search for the S2−S3 MXS led incidentally to a threestate crossing. Analyzing the steps, it turned out that the energy of the three states became almost degenerate already after the first couple of steps, and then, the 1(ππ*) and 1(nπ*) states often changed their order. Because the algorithm searched for the crossing of the second and third states in every step, the gradients and the coupling vector did not always belong to the same pair. This caused the extrapolation procedure61 to fail, of course. After turning it off, the procedure luckily led to a point where all three states were, with good approximation, degenerate. Although the optimization procedure stopped after a few steps, the three states were closely degenerate at this last point, the energy difference was only 0.0041 eV between the first and second states and 0.017 eV between the second and third. This approximate MXS (denoted by MXS 1−2−3) is about 0.15 eV higher in energy than MXS between S1 and S2 states. In the corresponding structure, the ring system is planar again, and the NH2 group is pyramidalized. There are substantial differences between the two MXSs in bond lengths; in particular, the N1−C2 bond is shorter by 0.05 Å in MXS 1− 2−3. Note that it is much shorter than the corresponding equilibrium bond length in the ground state. Figure 11 demonstrates the differences between the ground-state equilibrium structure and MXS 1−2−3. The largest difference is in the C2−N3 bond, which is stretched by 0.07 Å, while the C5−C6 bond length is also substantially longer. Matsika36 has also located the three-state conical intersection using the MRCIS method. The energies and structural parameters are also given in Tables 4 and 5, respectively. Most of the bond lengths are substantially longer, and deviation from planarity is smaller at the MRCIS level compared to the EOM-CCSD results. More importantly, the CCSD three-state conical intersection is located at a significantly lower energy than the MRCIS one. Because the nonadiabatic coupling vector is not available at the CC2 level, the search algorithm for intersections could not be applied. Instead, CC2-LR single-point energies were

Figure 10. Cut of the potential energy surface connecting the S1 minimum and the saddle point of the π−π* state. Structures have been generated by linear interpolation of the Cartesian coordinates between the two terminal points. The energies of the five lowest states were obtained at the CC2 level. Points are connected diabatically, following the character of the transitions.

that it is the same saddle point and not a minimum. More recently, Engler et al.16 also reported equilibrium structures for both S1 and S2 states. Note, however, that the two structures that they report in their Table 2 are very similar; the rotational constants differ only by 3−4 cm−1, while the T0 values differ only by 200 cm−1. It is very unlikely to have two states with such similar structures so close in energy; therefore, we suspect that their optimization of the 1(ππ*) state also lead to the 1(nπ*) state just like in our calculations; therefore, the former does not represent a real minimum on the ππ* surface. For this region of the potential energy surfaces, the CCSD and CC2 results are semiquantitatively the same. There is a planar geometry with the 1(ππ*) as the lowest state; from here, a barrierless path leads to the S1 minimum, which corresponds to the 1(nπ*) state, and there is a crossing between the 1(ππ*) and 1(nπ*) states. Relative energies are also very similar, but the curve of the 1(nπ*) state is somewhat lower at the CC2 level, moving the position of the crossing farther away from the saddle point. Search for the Minimum of the S3 State. Searching for the equilibrium structure of the 2(ππ*) state was also unsuccessful; optimization led rapidly to the vicinity of a three-state conical intersection and stopped. Considering all of the findings described in the last two subsections, we conclude that most probably there is no minimum either for the S2 (1(ππ*)) or for the S3 (2(ππ*)) state of adenine, at least in the relevant (FC) region; both states connect barrierlessly to the minimum of the 1(nπ*) state. In the following, the corresponding intersections will be studied in more detail. Conical Intersections. Basically, two types of crossings were identified during the search for equilibrium structures, one between the S1 and S2 states and one between the S2 and S3 states. There are two cuts of potential energy surfaces (see Figures 5 and 9 in the case of CCSD) where a crossing between the two lowest excited states can be observed. These are close in energy and also have similar structures. Therefore, most probably, they belong to the same crossing seam. To locate the minimum on this crossing seam (MXS), we performed an EOM-CCSD search using analytically calculated gradients and the nonadiabatic coupling vector.62 Note that such a search cannot lead to the exact minimum because EOM-CCSD might give imaginary energies near the degenerate points;63 in this case, the procedure need to be stopped because the correction 6204



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Figure 13. EOM-CCSD energies of the first three excited states along the one-dimensional cut from the S1−S2−S3 conical intersection to the S1−S2 conical intersection. Structures have been generated by linear interpolation of the Cartesian coordinates between the two terminal points. Points are connected diabatically, following the character of the transitions.

Figure 11. Geometries in the ground-state minimum and the S1−S2− S3 conical intersection.

calculated at the crossing points obtained at the CCSD level, and these are also listed in Table 4. Degeneracy of the states is lifted, showing that the CC2 crossing points differ from those at the CCSD level. Relative energies are somewhat smaller at the CC2 level; the difference seems to be a bit larger than that at the FC point. In order to see how the observed intersections can be reached from the FC point, a one-dimensional cut between the FC point and MXS 1−2−3 has been generated. The corresponding energy curves at the CCSD level can be seen in Figure 12. A shallow minimum for the 1(nπ*) state can be

In summary for this subsection, an intersection seam between the two lowest excited states (1(nπ*) and 1(ππ*)) of adenine has been found. The estimated energy of the MXS corresponding to this seam is lower than the vertical excitation energies. This MXS is further connected to a three-fold intersection including also the 2(ππ*) state. This latter point is about 0.16 eV higher than the former one, and they connect barrierlessly. The cuts calculated at the CC2 and CCSD levels are in good agreement. However, it seems to be an important difference that the CC2 potential curves of the 1(nπ*) and 1(ππ*) states do not cross between the ground-state minimum and S1 minimum.

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CONCLUSIONS In this paper, EOM-CCSD and CC2-LR methods were used to study the potential energy surfaces of the three lowest excited states of adenine to obtain the equilibrium structures of the excited states and study relevant cuts of the potential energy surfaces. From the three lowest excited states, only the S1 state has a proper equilibrium geometry. This structure is nonplanar and can be characterized as an n−π* transition. For the other two ππ*-type excited states, no minimum could be located. In the case of the S2 state, the character gradually turns into that of the S1 state, and the optimization procedure leads to the S1 equilibrium structure. In the case of the S3 state, the optimization leads to the vicinity of a three-fold seam. In this respect, both EOM-CCSD and CC2-LR give the same results, with only slightly different structures and energies. Assignment of the spectra of adenine always operates with n−π*- and π−π*-type transitions. The present results, and in particular the missing equilibrium structures of the S2 and S3 states, show that the coupling between these states is very strong, and this vibronic coupling does not necessarily allow assignment based on adiabatic states. On the other hand, the S1 has an equilibrium structure, and its lowest-level vibrational state(s) is (are) probably accessible. Indeed, the calculated T0 value for the nπ* state is in good agreement with experiment.11,16 Two-fold S1−S2 and three-fold S1−S2−S3 conical intersections could be located at low energies. The corresponding structures are similar to the ground-state equilibrium structure and can be reached barrierlessly; therefore, they might play an important role in the ultrafast deactivation of adenine.

Figure 12. EOM-CCSD energies of the first three excited states along the one-dimensional cut from the S0 minimum to S1−S2−S3 conical intersection. Structures have been generated by linear interpolation of the Cartesian coordinates between the two terminal points. Points are connected diabatically, following the character of the transitions.

observed, but there is practically no minimum for the 1(ππ*) state, and the bright 2(ππ*) state has a monotonically decreasing energy. The figure shows clearly that there is a barrierless path from both ππ* states to MXS 1−2−3, where conversion into the dark 1(nπ*) state can occur. Finally, we were curious about the path between MXS 1−2− 3 and MXS 1−2. In Figure 13, the corresponding onedimensional cut of the potential surfaces is shown. This path is practically on the seam of the S1−S2 intersection because the two curves run very close to each other. The energy of these two states decreases monotonically. On the other hand, the energy of the third state S3 increases along this cut, that is, degeneracy with the other two states is lifted. Again, one can conclude that the low-energy MXS 1−2 can be reached from MXS 1−2−3 barrierlessly. 6205



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Concerning the reliability of the methods, in the case of the nπ* and ππ* states, we do not observe as large of a discrepancy between CC2 results and those including triples effects as in our previous paper.44 Concerning the 0−0 excitation energies, CC2 and CC3 results in fact envelop the experimental value.11 Nevertheless, the relative energies of nπ* and ππ* states are not the same at CC2 and triples including levels (see in ref 44), which might have an effect on the location of conical intersections and the outcome of dynamics simulations.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates of the optimized ground and excited state structures, those of the MXSs, as well as the vibrational frequencies at some geometries are given. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by Orszagos Tudomanyos Kutatasi Alap (OTKA; Grant No. 104672). The authors thank Dr. A. Tajti for continued discussions and for his help to get the conical intersection search algorithm to work. We also thank Prof. Fleig for providing his S2 state structure.

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REFERENCES

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