Electronic Resonances of Nucleobases Using Stabilization Methods

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Electronic Resonances of Nucleobases Using Stabilization Methods Mark A. Fennimore, and Spiridoula Matsika J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b01523 • Publication Date (Web): 03 Apr 2018 Downloaded from http://pubs.acs.org on April 4, 2018

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The Journal of Physical Chemistry

Electronic Resonances of Nucleobases Using Stabilization Methods Mark A. Fennimore and Spiridoula Matsika∗ Department of Chemistry, Temple University, Philadelphia, PA 19122 USA E-mail: [email protected]

Abstract The interaction of low energy electrons with nucleobases is important because of their potential to damage nucleic acids. In this work we investigate several low lying resonances of nucleobases using quantum chemical methods including static and dynamical correlation coupled with orbital stabilization methods. Specifically, the equation of motion for electron affinities via couple cluster singles and doubles (EOMEA-CCSD) and multireference perturbation theory (XMCQDPT2) methods were used and their performance explored. Low lying π ∗ resonances were calculated and compared to previous theoretical and experimental results, showing good agreement for positions and widths. Feshbach/Core-excited resonances generated by attachment of an electron to a ππ ∗ excited state of the bases were also calculated, providing for the first time accurate information for these resonances. Mixing between configurations corresponding to shape and Feshbach/core-excited resonances is present in all nucleobases, which complicates the theoretical treatment and necessitates multiconfigurational approaches for a proper description.

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Introduction Much is known about the effects of ionizing radiation on the chemical stability of DNA and, more specifically, the stability of the canonical nucleobases. 1,2 A number of experimental and theoretical studies have shown that direct UV absorption by the bases can result in a number of photo-induced reactions that can lead to the formation of lesions like thymine-thymine dimer formation and clustered double strand breaks. 1–4 Damage of this kind can result in cellular death and potentially cancer-causing mutations. 5,6 In addition to direct damage from UV radiation, an indirect effect is damage caused by low energy electrons (LEEs) created after irradiation.In 2000, Sanche and co-workers showed that LEEs in the range of 3 − 20 eV induce strand breaks in lyophilized DNA isolates, 7 while later studies indicate that strand breaks can also occur at substantially lower energies (i.e. 0 − 4 eV). 8 Electron transmission (ET) experiments on the canonical DNA bases and uracil indicate electron attachment within this range of energies. 9 Furthermore, a number of studies suggest that electron attachment can occur to the DNA bases followed by electron transfer to the sugar phosphate backbone leading to C-O bond fission. 8,10–17 Because of these findings many scientists have tried to understand how the breaks occur, and in general how nucleic acids interact with LEEs. 17–24 Much work has been done on understanding electron attachment with electron energies less than 3 eV. 16,25–27 For electrons with energies above 3 eV the situation is not as well understood. In polyatomic molecules (e.g. pyrimidine and purine bases), electrons may be captured by any number of unoccupied σ ∗ or π ∗ molecular orbitals. When such electron attachment occurs in closed shell neutral species, the resultant transient state is a shape resonance. However, electron attachment to an excited state can also occur. The attachment of an electron to the highest occupied orbital in a molecule that has been previously excited manifests as an electronic configuration characterized by an open shell, singly occupied hole, referred to as a core-excited shape or Feshbach resonance. Core-excited shape and Feshbach resonances are differentiated by whether the resonance is above or below the parent 2


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neutral reference state. In shape resonances electron detachment is a Koopmans-allowed one-electron process, while in Feshbach resonances electron ejection is a Koopmans-forbidden two-electron transition and the excited-state decay is governed by electron correlation. Shape and Feshbach resonances are important in gas-phase studies of several biochromophores, and have been discussed for model chromophores such as those of green fluorescent and photoactive yellow proteins. 28,29 From now on we refer to core-excited shape resonances simply as core-excited resonances. In general little is known about these resonances in nucleobases, and the detailed, step by step, mechanisms of subsequent dissociative electron attachments (DEA) in the canonical nucleobases is even less clear. DEA in nucleobases has been extensively studied experimentally. 30–39 However, while a general picture of resonance formation is emerging, detailed theoretical treatment of resonances, let alone DEA processes, still presents significant challenges. These challenges arise mainly due to the nature of resonances, which are comprised of electrons weakly coupled to the continuum and are, therefore, described by wavefunctions that are not square integrable. For this reason, standard electronic structure methods are not applicable. To overcome this, alternative methods have been applied, including scattering and various adaptations to standard quantum chemical codes (e.g. complex absorbing potential (CAP) and orbital stabilization methods). 40–42 Scattering methods have been used to locate resonances in nucleobases 40–49 and in nucleosides and nucleotides. 50–52 Many of the quantum chemistry based theoretical studies have focused primarily on describing the lowest electronic energy of the anion which corresponds to either a valence state, with the electron attached to the lowest π ∗ orbital or to dipole bound states. 16,53–55 A recent study reports shape resonances for all bases using CAP combined with the symmetry adapted cluster-configuration interaction (SAC-CI) method. 24 In addition, the orbital stabilization method has been applied to uracil using DFT and Koopmans’ theorem. 56 Even these studies however did not include core-excited shape or Feshbach resonances, for which very little is known. In our recent work we used the orbital stabilization method coupled with Equation

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of Motion for Electron Affinities via Couple Cluster Singles and Doubles (EOM-EA-CCSD) and multireference perturbation theory methods (XMCQDPT2) to predict both shape and core-excited resonances of uracil. 57,58 Using the results of this study, a subsequent study revealed a viable dissociation channel by tracking the resonances along the minimum energy path of CO loss in uracil followed by H loss to reproduce the 83 m/z fragment identified by Kawarai et al. 59 Both of these works in uracil highlight the importance of configurational mixing between shape and core-excited resonances to reproduce the energetics relevant for DEA. The success of our previous studies demonstrated that the applied approach can be used to provide useful results. In the present study we extend our methodology to the other bases, and predict for the first time both shape and core-excited resonances at an accurate correlated level. In this work we present results on the resonances of nucleobases using quantum chemical methods that include static and dynamical correlation. We compare our results to previous experimental and theoretical results when available. This work helps us reassign some of the observed resonances, and make comparisons between the bases.

Methods Geometries The geometry for each nucleobase studied in this work was determined at the MP2/cc-pVDZ level of theory. Because of the intensive nature of the subsequent calculations, the geometries were all restricted to Cs symmetry. Since only thymine naturally has an equilibrium geometry with Cs symmetry, the remainder of the nucleobases were optimized in their nearest laying, planar transition states. These geometries (Presented in Supporting Information (SI)) were used in all subsequent calculations. Additional calculations were performed to determine the true equilibrium geometries for each base, which were also carried out at the MP2/cc-pVDZ level of theory. The difference in 4


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the Cs −C1 Coupled-Cluster reference energies were used to correct for the small error in calculating electron attachment energies for cytosine, adenine, guanine-enol and guanine-keto. These energetic shifts were generally less than 0.01 eV with a few exceptions approaching 0.05 eV. Table S1 shows all the corrections applied.

EOM-EA-CCSD Stabilization Curves As mentioned previously, resonances are described by wavefunctions that are not square integrable and, therefore, cannot be described by standard electronic structure methods; however, resonances may be described by discrete states with complex energy known as the Siegert energy 60 E = Er − iΓ/2.

(1)

Here, Er is the position, which corresponds to the measurable energy of a given resonance, and the width (Γ) is inversely proportional to the lifetime of the attached electron. To determine the resonance parameters Er and Γ, orbital stabilization curves were generated, for the shape and core-excited resonances, using EOM-EA-CCSD. EOM-EA-CCSD is one of the EOM-CCSD family of methods which provide accurate description of excited states, ionization potentials or electron affinities depending on the excitation operator used. 61 EOM-EA-CCSD is an appropriate method to provide accurate electron affinities when coupled with the correct basis set. EOM-EA-CC has been extended previously to treat metastable states via both CAP and complex scaling methods (see Ref. 29 for an overview of recent developments). It should be mentioned that CAP-EOM is a more rigorous (albeit more expensive) way to treat resonances, as compared to the stabilization methods employed here. Stabilization was accomplished through the application of a scaling factor (α) to the diffuse orbital exponents on each atom for a given basis set. At small values of α (i.e. α approaching 0), the orbitals are highly diffuse and the electron affinities converge to the neutral reference. However, at increasing values of α (i.e. 0 < α < 3), the stabilization plots

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show a number of avoided crossings due to the coupling of the resonance states with the discretized approximations to the continuum. 62–66 The real eigenvalues from these avoided crossings may be interpreted using Analytic Continuation (AC) with the General Pad´e Approximation (GPA) to determine the resonance position (Er ) and widths (Γ). The GPA expands the real eigenvalues from the stabilization plot into the complex domain via the quadratic Eq. 2. E 2 P (α) + EQ(α) + R(α) = 0 P (α) = 1 +

ni X

pi α i

(2) (3)

i=1

Q(α) =

nj X

qj α j

(4)

rk αk

(5)

j=0

R(α) =

nk X k=0

Here P (α), Q(α) and R(α) are themselves expansion of the scaling parameter, α, giving rise to 11, 14 and 17 parameters for (ni , nl , nk ) being (3,3,3), (4,4,4) and (5,5,5) GPA, respectively. By convention, Eq. 2 was expanded by keeping ni = nj = nk , and AC was performed centered at the point of nearest approach at each avoided crossing. The solutions for pi , qj and rk were determined by fitting Eq. 2 to the ab initio points, and subsequently the resonances parameters Er and Γ were determined by solving for the stationary points in the usual way, i.e. dE/dα = 0. Real resonances are regarded as those that are invariant with respect to GPA approximant used. Additional details about how we apply this approach may be found in our previous publications. 57–59 The energies at the EOM-EA-CCSD level were converged to 10−9 Hartree in order to have high precision of the GPA approach. Resonances were calculated using the real eigenvalues from the upper and lower roots of an avoided crossing, which by convention is centered at the point of nearest approach. In the results we present the (5,5,5) values, being the most accurate, and whenever there are many avoided crossings corresponding to the same resonance, we average the values of these crossings and report

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these averages. In some cases there is considerable fluctuation in the values obtained from the different avoided crossings and this indicates the uncertainty of the present procedure. SI (Sections S2-S3) reports all the results in detail. For the first shape resonance of the keto tautomer of guanine avoided crossings were not as clearly identified. Therefore, analytic continuation was performed along several points in the resonance curve at low values of α to determine if any complex roots manifest among multiple forms of the GPA. This methodology resulted in consistent complex roots between the positions and widths obtained from the various forms of the GPA suggesting a nonspurious solution (i.e. a resonance). Using data not necessary centered at the point of nearest approach at an avoided crossing has been done before. More specifically, work performed by Moiseyev and coworkers demonstrated that analytic continuation using the stable part of a resonance curve (and not the avoided crossing) resulted in consistent and accurate resonances predictions in test systems. 67 Our previous work demonstrated that the extended augmented basis, aug-cc-pVDZ+1s,1p,1d (which adds a set of s,p,d diffuse functions on each atom to the aug-cc-pVDZ basis in an even tempered manner) provided the best balance between efficiency and accuracy at reproducing the experimental 12 A00 resonance in uracil. This basis set was used for thymine and cytosine. However, this basis proved intractable for the larger purine bases, and we had to use the standard aug-cc-pVDZ instead. Obtaining Feshbach or core-excited resonances using EOM-EA-CCSD is less straightforward. These resonances differ from the ground state by more than one electron and cannot be produced with attachment of an electron to the ground state. Recent work has shown that the positions of Feshbach resonances can be significantly improved when including noniterative triples in the CAP-EOM-EA-CCSD approach 68 An alternative approach can be used, as we showed in our previous work with uracil, in which at least one of these resonances can be obtained using the lowest neutral triplet state as reference. This approach was also applied here. The core-excited resonances were investigated by converging the lowest

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laying triplet state of each base followed by application of the stabilization procedure via EOM-EA-CCSD. The following results report the Cs − C1 corrected values. All CCSD calculations were carried out using the QChem ab initio package. 69

CASSCF and XMCQDPT2 Multireference methods are needed to describe the Feshbach/core-excited resonances in a more straightforward way because of the coupling that occurs between them and shape resonances. In this work we employed Extended- Multi-Configurational- Quasi-DegeneratePerturbation-Theory (XMCQDPT2), which proved very useful in our previous studies on uracil. 57 It has also been shown in a recent investigation that this approach can be used very efficiently to describe resonances in combination with CAP. 70 All Complete-Active-Space-Self Consistent Field (CASSCF) and XMCQDPT2 calculations were carried out in Cs symmetry. These calculations were performed using the Firefly computational package, 71 which is partially based on the GAMESS (US) 72 source code, using the 6-31+G* basis set. The active space for each nucleobase was chosen to contain all π and π ∗ orbitals with no less than one highly diffuse π ∗ orbital to promote the formation of orthogonal discretized continuum states. The active spaces for thymine, cytosine, adenine, guanine-enol and guanine-keto were CAS(11,9), CAS(11,10), CAS(13,11), CAS(13,11) and CAS(13,11) respectively, where (n, m) denotes n electrons in m orbitals. An energy shift of 0.02 a.u. was used in the XMCQDPT2 calculations. Because of limitations in the computational resources required for high level multireference electronic structure calculations, increasing the size of both the active space (mainly to include more diffuse, Rydberg-like virtual orbitals) and basis to include more diffuse functions (which is necessary to accurately describe individual couplings between resonance and continuum solutions) is difficult. As a result we do not have enough discretized continuum solutions resulting in a poor representation of their coupling to resonances and a 8


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poor description of the width. However, despite the lack of a suitable description of Γ, the multiconfigurational calculations are invaluable for understanding the behavior of the resonances, especially when configurational mixing between shape and core-excited resonances is present. This effect was highlighted in our previous work on uracil. 57 To examine the effect of configurational mixing in the other nucleobases with their associative impact on Er , the resonances positions, both for the CASSCF and XMCQDPT2, were extracted directly from the stable points (i.e. where the energy was not subject to change) of the stabilization curves. The first resonance for each nucleobase was adjusted to match that of the experimental value. In guanine it has not been established which tautomer is present experimentally so the experimental value was used for both enol and keto tautomeric forms.

Results and Discussion In the following discussion we first present EOM-EA-CCSD results followed by the XMCQDPT2 results. Our results are compared with previous theoretical and experimental studies whenever available. Previous results are mainly on shape resonances. Theoretical results are taken either from scattering calculations or from recent studies using CAP. A brief summary of these studies is as follows. Previous scattering calculations were done for all bases based on R-matrix or Schwinger multichannel calculations (SMC). Dora and Tennyson used four different models in connection with the R-matrix: static exchange (SE), SE plus polarization (SEP), close coupling (CC) and the uncontracted close-coupling (u-CC), which correspond to different levels of theoretical treatment of electron correlation and polarization in the target and the scattering systems. 41,42 In the SE and SEP models the target is represented only by the ground-state Hartree-Fock (HF) wavefunction, while in the CC models several target states, represented at a partially correlated level of a complete active space configuration interaction (CASCI) model. These calculations showed that inclusion of polarization at the SEP level provides a big improvement compared to SE. R-matrix calculations by Tonzani

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and Greene are based on HF theory, so these results are expected to be inferior since they lack correlation. 40 The SMC method was also used with static-exchange plus polarization (SEP) calculations. 50,51 For guanine and cytosine the SMC method with SEP was also used in a very recent study. 73 When comparing to previous scattering calculations it should be pointed out that it appears that the disagreements between the theoretical results are mostly due to the differences between the underlying electronic structure theory used, rather than the differences in the continuum methods or the one-particle basis sets. In addition to the scattering calculations a study using SAC-CI combined with CAP 24 is the closest to our approach where emphasis is given on the electronic structure aspect of the problem trying to include significant dynamical correlation. As will be seen below for all bases our results are in close agreement to the CAP/SAC-CI results.

EOM-EA-CCSD: Shape Resonances We initially focus on the shape resonances for all bases using EOM-EA-CCSD. These results will be compared to previous theoretical and experimental results. In that sense they can be used to benchmark our methodology and compare the performance of this methods to others. EOM-EA-CCSD can be readily used for the shape resonances with the closed shell ground state as the reference. Figure 1 shows the orbital stabilization curves obtained for all the bases studied. The avoided crossings have been used to obtain the positions and widths. Details of the results for each avoided crossing are given in SI. Table 1 summarizes the results for all the bases at the EOM-EA-CCSD level. Results for uracil are taken from our previous work in order to make comparisons between all bases. 57,58 Below we discuss the DNA bases separately and compare to other studies.

Thymine In pyrimidine bases there are three unoccupied π ∗ orbitals readily available for electron attachment, leading to three shape resonances. Using the diabatic character of the resulting 10


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Energy/eV

6 5 4 3 2 1 0

0.5

1

1.5

2

8 7 6 5 4 3 2 1 0 0.5

1

α

1.5

2

α

(b) 8 7 6 5 4 3 2 1 0

Energy/eV

(a) Energy/eV

0.5

1 α

1.5

2

(c)

8 7 6 5 4 3 2 1 0

0.5

1 α

1.5

(d) Energy/eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Energy/eV

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8 7 6 5 4 3 2 1 0

0.5

1 α

1.5

(e) Figure 1: Stabilization curves for (a) thymine and (b) cytosine at the EOM-EA-CCSD/augcc-pVDZ+1s1p1d level of theory, and (c) adenine, (d) keto guanine, and (e) enol guanine at the EOM-EA-CCSD/aug-cc-pVDZ level of theory.

Table 1: Summary of resonances for all bases at the EOM-EA-CCSD level. All values are given in eV. 1π ∗ Er uracil 0.61 thymine 0.68 cytosine 0.93 adenine 1.13 keto guanine 1.00 enol guanine 1.34

Γ 0.02 0.02 0.02 0.04 0.74 0.09

2π ∗ Er 2.28 2.32 2.40 2.01 1.70 2.24

Γ 0.07 0.07 0.19 0.05 0.10 0.05

3π ∗ Er 4.98 5.02 5.54 2.96 3.06 3.13

11

4π ∗ Er

Γ Γ 0.34 0.58 0.35 0.14 6.78 0.21 0.09 6.64 0.21 0.12 6.80 0.26


π 1 (π ∗ )2 Er 5.25 4.65 5.23 5.66 5.9

Γ 0.17 0.11 0.11 0.16


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Table 2: Energies Er and widths Γ (in parenthesis) of resonances of thymine obtained in this work at the EOM-EA-CCSD/aug-cc-pVDZ+1s,1p,1d level, and comparisons with previous theoretical and experimental results. All values are given in eV.

this work CAP/SAC-CI 24 R-matrix/u-CC (2012) 42 R-matrix/SEP (2012) 42 SMC/SEP (2007) 51 R-matrix/SE (2006) 40 Expt. 9

1π ∗ Er 0.68 0.67 0.53 0.60 0.30 2.40 0.29

Γ 0.02 0.11 0.08 0.11 0.20 -

2π ∗ 3π ∗ Er Γ Er 2.32 0.073 5.02 2.28 0.15 5.14 2.41 0.10 5.26 2.73 0.11 5.52 0.19 5.70 5.50 0.60 7.90 1.71 4.05

Γ 0.58 0.41 0.57 1.00 -

π 1 (π ∗ )2 Er 4.65

Γ 0.11

resonances we denote them as 1π ∗ , 2π ∗ and 3π ∗ indicating in which orbital the electron is attached. Adiabatically these will be denoted as 12 A00 , 22 A00 and 32 A00 , respectively. It should be noted however that the energetic ordering may change when the core-excited resonances are considered, so we prefer the diabatic notation here. Table 2 shows results obtained for thymine shape resonances using the EOM-EA-CCSD approach with the aug-cc-pVDZ+1s,1p,1d bases set. In the present work using the stabilization procedure, we estimate the first three shape resonances of thymine to be 0.68 eV, 2.32 eV and 5.02 eV. These values, though higher in energy compared to the experimental values, are in excellent agreement with those determined using the CAP/SAC-CI, R-Matrix/u-CC and R-matrix/SEP treatments (See Table 2); importantly, our calculated resonances using the stabilization procedure were able to reproduce the inductive upshift in all three shape resonances of thymine when compared to our previously published uracil results, 57,58 though the relative differences were somewhat small compared to experiment (i.e. 0.07 eV, 0.04 eV and 0.04 eV respectively). Low-energy electron transmission spectra (ETS) experiments have been performed on thymine and have shown that its shape resonances are upshifted compared to uracil to the effect of 0.07 eV, 0.13 eV and 0.22 eV for the 1π ∗ , 2π ∗ and 3π ∗ resonances, respectively. 9 This upshift is posited to arise due to the σ-electron donating property of the C5 methyl in thymine. 24 The resonance widths (Γ) that are obtained for thymine using resonance stabilization are 12


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highly consistent with those determined using other theoretical treatments though the calculated width for the 1π ∗ resonance obtained using the stabilization procedure are somewhat diminished compared to the other methods. Moreover, all theoretical treatments predict comparative large widths for the third shape resonance (i.e. Γ=0.4-0.5 eV) in reference to the 1π ∗ and 2π ∗ in excellent agreement with each other. The character of the resonances can be clearly characterized by Dyson orbitals. In a Koopmans’ theorem framework the Dyson orbitals will resemble the π ∗ unoccupied orbitals where the electron is attached. Dyson orbitals for the shape resonances of thymine (and other bases) are shown in SI (Figures S20-S24). The Dyson orbitals show the characteristics of the π ∗ orbitals, although they are also affected by the lifetime and they appear more diffuse for the higher in energy, less stable, resonances.

Cytosine In the present work, the first three shape resonances of cytosine were determined to be 0.93 eV, 2.40 eV and 5.54 eV, respectively (see Table 3). Because cytosine only has one electron withdrawing carbonyl, its 1π ∗ and 3π ∗ resonance have been experimentally measured to be higher than either uracil or thymine, 9 and this effect is qualitatively reproduced in our work. Our values for the 1π ∗ are 0.6 eV too high compared to experiment, but the error decreases when comparing energy gaps between resonances. As with our results with uracil and thymine, the measured width for the first resonance of cytosine using the stabilization procedure was somewhat smaller compared to that obtained by CAP/SAC-CI 24 but was in excellent agreement with those found using both the Rmatrix/u-CC and SEP procedures (See Table 3). 24,42

Adenine In purine bases there are four π ∗ orbitals available for electron attachment leading to four shape resonances. The results obtained for adenine using the stabilization method at the

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Table 3: Energies Er and widths Γ (in parenthesis) of resonances of cytosine obtained in this work at the EOM-EA-CCSD/aug-cc-pVDZ+1s,1p,1d level, and comparisons with previous theoretical and experimental results. All values are given in eV.

this work CAP/SAC-CI 24 R-matrix/u-CC (2012) 42 R-matrix/SEP (2012) 42 SMC/SEP (2007) 51 R-matrix/SE (2006) 40 SMC 73 Expt. 9

1π ∗ Er Γ 0.93 0.017 0.70 0.16 0.36 0.016 0.71 0.05 0.50 1.7 0.5 0.61 0.24 0.32 -

2π ∗ Er 2.40 2.18 2.05 2.66 2.40 4.3 1.74 1.53

Γ 0.19 0.30 0.30 0.33 0.7 0.66 -

3π ∗ Er Γ 5.54 0.35 5.66 0.63 5.35 6.29 0.72 6.30 8.1 0.8 5.5 4.50 -

π 1 (π ∗ )2 Er 5.23

Γ 0.11

EOM-EA-CCSD/aug-cc-pVDZ level of theory (shown in Table 4) predict the four first shape resonances to be 1.13 eV, 2.01 eV, 2.96 eV and 6.78 eV, respectively. These results, again, compare very well with those determined using the CAP/SAC-CI 24 and R-matrix/SEP 41 methods. The experimental ETS results have shown that the vertical attachment energies (VAEs) of purine bases are approximately 0.2 eV above that of pyrimidine analogs. 9 In our calculations, we also predict an increase in the VAEs of purines compared to pyrimidines; however, the effect is larger at 0.42 eV. In contrast, the average difference between the purine and pyrimidine bases calculated using the CAP/SAC-CI, R-matrix/u-CC and R-matrix/SEP were determined to be 0.44 eV, 0.83 eV and 0.91 eV respectively. As with the previous bases, the calculated width for the 1π ∗ shape resonance of adenine using the stabilization procedure (Γ=0.04 eV) was markedly narrow in comparison to the other methods examined in this work. However, because of the lack of experimental knowledge about the width, and associative lifetimes of these ETS measured resonances, it is challenging to comment on the accuracy of any given method.

Keto-Guanine and Enol-Guanine As with adenine, resonance stabilization for both tautomeric forms of guanine were computed at the EOM-EA-CCSD/aug-cc-pVDZ level of theory. The ETS measurements on gas phase 14


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Table 4: Energies Er and widths Γ (in parenthesis) of resonances of adenine obtained in this work at the EOM-EA-CCSD/aug-cc-pVDZ level, and comparisons with previous theoretical and experimental results. All values are given in eV.

this work CAP/SAC-CI 24 R-matrix/u-CC (2012) 41 R-matrix/SEP (2012) 41 SMC/SEP (2007) 50 R-matrix/SE (2006) 40 Expt. 9

1π ∗ Er 1.13 0.89 1.58 1.30 1.10 2.40 0.54

Γ 0.04 0.13 0.22 0.14 0.20

2π ∗ Er 2.01 1.93 2.44 2.12 1.80 3.20 1.36

Γ 0.05 0.29 0.14 0.09 0.20

3π ∗ Er 2.96 2.72 4.38 3.12 4.10 4.40 2.17

Γ 0.14 0.17 0.67 0.28

4π ∗ Er 6.78 6.65 7.94 7.07

Γ 0.21 0.57 0.57 0.24

π 1 (π ∗ )2 Er 5.66

Γ 0.16

0.30

guanine place the measured shape resonances at 0.46 eV, 1.37 eV and 2.36 eV. In that work, which forms the basis for the majority of how theoretical methods are benchmarked on DNA nucleobases, Aflatooni and Burrow concluded that the enol tautomer was the major contributor to the spectral features observed in their experiments. 9 That conclusion was based on low-level calculations of the vertical attachment energies between the two tautomers; their conclusion from their calculations were: a) the VAE for the 1π ∗ resonance was more stable in enol compared to keto to the effect of ca. 0.28 eV and b) the spacing between the two lowest laying resonances in enol was more consistent with the experimental results. In the present work, we estimate the three lowest laying resonances of enol to be 1.34 eV, 2.24 eV and 3.13 eV respectively. These results are in excellent agreement with those determine using CAP/SAC-CI both in terms of resonance positions and widths (See Table 5). To our knowledge, no other high level electronic structure methods have been used to compute the VAEs of enol. Moreover, our calculations on keto place the first three resonance positions at 1.00 eV, 1.70 eV and 3.06 eV, the positions of which are again in very good agreement with those obtained using the CAP/SAC-CI formalism though the widths diverge somewhat, particularly for the 3π ∗ resonance. The calculated positions using R-matrix/u-CC are also in reasonably good agreement with those determine in this work; however, Γ for the first shape resonance diverges strongly (i.e. 0.74 eV vs. 0.006 eV). It should be mentioned that the resonance stabilization procedure on keto resulted in atypical behavior associated with 15



Page 16 of 33

the 1π ∗ and 2π ∗ resonances in the stabilization curve (Ref SI Figure S9). In this case we used the approach by Moiseyev and coworkers 67 as discussed in the Methodology in order to obtain the resonances. The large width (Γ=0.8) coupled with being localized in the highly diffuse region of the stabilization curve (i.e. α < 1) in which the electron auto-detaches in the vicinity of the neutral ground state may explain the unusual behavior. Our results cannot make an unambiguous assignment about whether the enol or keto tautomer is the one observed experimentally. The first resonance is too high for both enol and keto tautomers compared to the ETS first peak although it is somewhat lower for the keto tautomer. Even when examining the gap between resonances both tautomers predict these values to be in reasonable agreement with the experimental ETS values, and in this case it is the enol tautomer that approaches the experimental value closer. As will be discussed below the XMCQDPT2 results agree better with an assignment of the enol form being the experimentally observed tautomer. Table 5: Energies Er and widths Γ (in parenthesis) of resonances of guanine obtained in this work at the EOM-EA-CCSD/aug-cc-pVDZ level, and comparisons with previous theoretical and experimental results. All values are given in eV. 1π ∗ Er Keto this work CAP/SAC-CI 24 R-matrix/u-CC (2012) 41 R-matrix/SEP (2012) 41 SMC/SEP (2007) 50 R-matrix/SE (2006) 40 SMC 73 Expt. 9 Enol this work CAP/SAC-CI 24

Γ

2π ∗ Er

Γ

1.00 0.74 1.70 0.10 1.11 0.64 1.66 0.34 0.97 0.006 2.41 0.15 1.83 0.16 3.30 0.24 1.55 2.40 2.00 0.20 3.80 0.25 0.90 0.51 1.55 0.7 0.46 1.37 1.34 1.26

0.09 0.15

3π ∗ Er 3.06 3.21 3.78 4.25 3.75 4.80 2.75 2.36

Γ

4π ∗ Er

Γ

0.09 0.55 0.29 0.33

6.64 6.50 6.42 7.36

0.21 0.92 0.72 0.27

0.35 8.90 0.60

2.24 0.05 3.13 0.12 6.80 0.26 2.19 0.09 3.13 0.33 6.61 0.72

16


π 1 (π ∗ )2 Er

5.9

Γ

Page 17 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


EOM-EA-CCSD: Core-Excited Resonances The lowest energy core-excited resonance for each nucleobase was calculated by performing EOM-EA-CCSD on the lowest laying π − π ∗ triplet excited state of each nucleobase. Several neutral triplet states were calculated and compared to previous results in order to confirm that this is the lowest triplet state energetically. The 13 ππ ∗ vertical excitation energies (VEEs) calculated in this work were 3.48, 3.73, 3.92 and 4.19 eV for thymine, cytosine, adenine and keto-guanine,respectively. These values, which form the basis for our core-excited calculations, were in excellent agreement with the VEEs calculated at the EOM-CCSD level of theory by Wiebeler and co-workers. 74 Table S13 shows the results of triplet states obtained in our work in comparison with high level multireference configuration interaction with Davidson correction (MRCI+Q) results. It can be seen that in all canonical nucleobases the 23 ππ ∗ and the 3 nπ ∗ excited states are well separated in energy from the 13 ππ ∗ supporting our focus on 13 ππ ∗ . Guanine is the only base where the energies of the triplet states are in close proximity, and this likely explains the difficulty we had to converge the core-excited resonance in that molecule. The VEEs differ somewhat from the highly accurate MRCI+Q benchmark values, but the qualitative ordering is the same. Results for the core-excited resonances are given in Tables 2, 3, 4, and 5, while a summary for all bases in given in Table 1. The orbital stabilization curves used to obtain the results are given in SI. It should be noted that despite the potential of this approach to provide core-excited resonances, it does not always work smoothly. In this case, calculations of the core-excited resonances for keto and enol guanine proved difficult at the EOM-EA-CCSD level. The resonance stabilization curve of enol failed to result in an identifiable avoided crossing by which analytic continuation could be performed. However, the stabilization curve did produce a stabilization (i.e. a state whose energy did not change appreciably with α) that exhibited the desired π 1 (π ∗ )2 configuration. Therefore, the Er given for enol in Table 5 should be taken only as an approximation. Further, the triplet ground state of keto guanine failed to converge at many values of α (because of the energetic proximity of 17



at least two triplet states as noted above) - making even an estimation of its core-excited resonance at the EOM-CCSD level unjustifiable. In all bases the resonance is energetically above the neutral triplet state highlighting that it is a core-excited resonance rather than a Feshbach resonance. Since these resonances can decay to the triplet state which is in close proximity they have widths that are smaller than the widths of the shape resonances at the same energy range (third or fourth shape resonances), between 0.11-0.17 eV. In uracil the core-excited state is predicted to be 0.27 eV above the third shape resonance. In thymine and cytosine however it is predicted to be below the third shape resonance. This result is particularly remarkable for the difference between thymine and uracil. These bases only differ by a methyl group, yet the energy of the core-excited resonance in thymine is 0.8 eV lower than in uracil. The difference in the energy of the neutral triplet states of uracil and thymine obtained at the EOM-CCSD level appears to explain some of the energetic difference between the core-excited resonances since the triplet states differ by 0.3 eV at the CCSD level. But this explains only part of the difference in core-excited resonances. In purine bases there are four shape resonances and the first core-excited resonance is between the third and fourth shape resonance in these systems. EOM-EA-CCSD predicts the core-excited resonances to be well separated from both third and fourth shape resonances. The experimental information on core-excited resonances is indirect, coming from DEA measurements, although often a range of values is observed. It should be noted that while ETS reflects the initial Frank-Condon transition, in DEA the energy dependent decomposition probability can considerably shift the resonance maximum, so it is not straightforward to use these experimental values. Nevertheless, DEA studies in pyrimidine bases thymine and cytosine suggest resonances at energies around 5.2-5.5 eV. 75,76 DEA in adenine 34 also shows several fragments with peaks around 5.6-5.8 eV, indicating that the core-excited resonance may be around that region.

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Description of Resonances at the XMCQDPT2 Level Stabilization curves from the XMCQDPT2 calculations are shown in SI (section S3). Using the stable part of the curves we extracted values for the position of resonances but we do not extract information about the width as discussed in the methodology. A summary of the XMCQDPT2 results for all bases is shown in Table 6. Uracil results are taken from previously published stabilization curves (even though in the previous publication we used a different procedure to extract positions, so the values reported here are not exactly the same as previously reported). 57,58 The first resonance in all bases has been shifted to the experimental value as explained in the methodology. A main advantage of the XMCQDPT2 approach compared to EOM-EA-CCSD is that both shape and core-excited resonances are produced in one calculation and thus couplings between these two types of resonances are included. Our work on uracil showed that this coupling is actually very strong and has a profound effect on the DEA processes. 57–59 The current work on the bases also demonstrates a strong coupling between the third or fourth shape resonance and the first core excited resonance in all bases. The resonances in Table 6 are ordered according to their diabatic character in order to facilitate comparisons with EOM-EA-CCSD. Because of the mixing however the assignment is not as strict as in EOM-EA-CCSD, and the predominant character in the wavefunction is used. Furthermore, this ordering is not always in agreement with the energetic ordering. Both EOM-EA-CCSD and XMCQDPT2 predict that in uracil the core excited resonance is above the third shape resonance, while the opposite is true for thymine and cytosine, i.e. the core-excited resonance is below the shape resonance. This ordering should be taken into account when considering the assignment of resonances observed experimentally. In their experimental work, Alfatooni and co-workers assigned the third feature in the ET spectra of thymine to the 3π ∗ resonance. They tentatively confirmed that assignment with lowlevel electronic structure calculations, while proposing that the assignment of higher energy resonances would be difficult because of mixing between shape and core-excited resonances. 19



This work indicates that not only is the core-excited resonance in the vicinity of the 3π ∗ but it is also heavily mixed with configuration interaction (CI) coefficients indicating that the core-excited configuration dominates the lower energy assignment (Ref SI Table S8). In fact, the relative assignments of all three lowest laying resonances using XMCQDPT2 (i.e. 1π ∗ , 2π ∗ and π 1 (π ∗ )2 /3π ∗ ) agree well with the experimental ETS results (reference Table 6). The assignment is indicated in Table 6 by providing the experimental value in parenthesis next to the assigned resonance. The XMCQDPT2 calculations offer an illuminating perspective to the differences between uracil and thymine observed at the EOM-EA-CCSD level. In that case the core-excited states are very different between the two bases. While the single reference EOM-CCSD places the core-excited in uracil 0.6 eV above that of thymine, the XMCQDPT2 results are more subtle, indicating that all four major resonances are energetically similar between uracil and thymine. The only difference is the degree of mixing between the 3π ∗ and core-excited resonances. In uracil, the third resonance is slightly dominated by the 3π ∗ shape resonance, whereas in thymine the converse is true. Close inspection of Table 6 indicates that at the XMCQDPT2 level no other major differences are observed. As with the other pyrimidine bases uracil and thymine, the XMCQDPT2 results in cytosine indicate heavy mixing between the 3π ∗ and π 1 (π ∗ )2 resonances with the latter, again, dominating the lower energy assignment (Ref SI Table S9). The resultant XMCQDPT2 energies, as with uracil and thymine are in good agreement with the ETS results (see Table 6). The core-excited resonance of cytosine was found to be energetically lower than its associative 3π ∗ resonances at the XMCQDPT2 level similarly to what was seen using EOMEA-CCSD. Moving to the purine bases, similarly, heavy mixing between the 4π ∗ and π 1 (π ∗ )2 was also observed in adenine and guanine (Ref SI Tables S10-S12). It should be noted here that the 4π ∗ resonance at this level is predicted to be much lower than at the EOM-EA-CCSD level. Furthermore, the gap between 4π ∗ and core-excited resonances is much smaller compared to

20


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EOM-EA-CCSD. Using XMCQDPT2 the enol tautomer of guanine shows a much better agreement with experiment, so according to these results it is the enol tautomer that is observed experimentally, in agreement with previous assignments. Table 6: Summary of resonances for all bases at the XMCQDPT2/6-31+G(d) level. The lowest laying resonance values for each nucleobase is set to the experimental value. 9 Higher resonances are compared with the experimentally determined values in parenthesis. All values are given in eV. 1π ∗ uracil 0.22 thymine 0.29 cytosine 0.32 adenine 0.54 keto guanine 0.46 enol guanine 0.46

2π ∗ 3π ∗ 4π ∗ π 1 (π ∗ )2 1.59 (1.58) 4.29 (3.83) 4.83 1.76 (1.71) 4.82 4.30 (4.05) 1.68 (1.53) 5.24 4.35 (4.50) 1.21 (1.36) 1.98 (2.17) 5.11 4.74 0.56 1.63 4.59 5.29 1.24 (1.37) 1.98 (2.36) 5.13 4.63

Conclusions In this work we examined both shape and core-excited resonances of nucleobases. Figure 2 summarizes both the EOM-EA-CCSD and XMCQDPT2 results. In order to make equivalent comparisons, the first resonance for all bases in both methods has been shifted to the experimental values. These results clearly show that pyrimidine bases have three shape resonances, while purine bases have four shape resonances. In pyrimidine bases the third shape resonance is well separated from the first two shape resonances, and it is very close energetically to the core-excited resonance. In purine bases there are four shape resonances, with three of them grouped together while the fourth one is much higher in energy. All bases have a core-excited resonance at comparable energies to the highest shape resonance, which leads to mixing between them. XMCQDPT2 predicts the third and fourth resonances to have lower energies compared to EOM-EA-CCSD. It also predicts considerable mixing between them. Both EOM-EA-CCSD and XMCQDPT2 predict that in uracil the

21


Energy/eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy/eV


7 6 5 4 3 2 1 0 U

T

C

A kG eG

U

T

C

A kG eG

7 6 5 4 3 2 1 0

Figure 2: Resonance energies for the nucleobases (uracil (U), thymine (T), adenine (A), keto guanine (kG), and enol guanine (eG)) calculated using an orbital stabilization approach combined with the EOM-EA-CCSD/aug-cc-pVDZ (top) and XMCQDPT2/6-31+G(d) (bottom) methods. The first resonance in all cases has been shifted to the experimental value. 9 Red: 1π ∗ , Blue: 2π ∗ , Yellow: 3π ∗ , Green: π 1 (π ∗ )2 , Gray: 4π ∗

22


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core-excited state is above 3π ∗ but this ordering switches in thymine and cytosine bringing the core-excited state below the shape one. EOM-EA-CCSD predicts that the 4π ∗ resonance is well separated from the core-excited being about 1 eV higher in energy. In XMCQDPT2 however this gap is much smaller, and in keto guanine the core-excited is predicted to be higher than the fourth shape resonance. In all cases XMCQDPT2 predicts that the highest shape resonance mixes significantly with the core-excited resonance. This can have significant implications in DEA as we have seen for uracil. These results further reinforce our previous hypothesis that a multi-configurational approach is necessary to accurately determine the properties of higher energy shape (i.e. 3π ∗ in pyrimidine and 4π ∗ in purine bases) and core-excited resonances. However, the multiconfigurational approach suffers in the determination of the first shape resonance. Because of the inadequacies of both single and multi-reference methods, we believe that presently a combination approach is required to give the best overall picture of resonances of canonical nucleobases. This work presents the first study that describes both shape and core-excited resonances of bases using high level electronic structure methods including both static and dynamical correlation, and it should be an important guide and first step in interpreting how electrons with energies up to 6 eV interact with nucleobases.

Acknowledgements This material is based upon work supported by the National Science Foundation under grant CHE-1465138. MAF acknowledges Quaker Chemical Corporation for support. Supporting Information. Details of the methodology not discussed in the main text; details of the EOM-EA-CCSD and XMCQDPT2 results; neutral excitation energies; and cartesian coordinates.

23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy/eV


7 6 π1(π*)2 5 4 3π* 3 2π* 2 1π* 1 0 U T

4π*

C

A kG eG

24


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References (1) Crespo-Hernandez, C. E.; Cohen, B.; Hare, P. M.; Kohler, B. Ultrafast Excited-State Dynamics in Nucleic Acids. Chem. Rev. 2004, 104, 1977–2020. (2) Improta, R.; Santoro, F.; Blancafort, L. Quantum Mechanical Studies on the Photophysics and the Photochemistry of Nucleic Acids and Nucleobases. Chem. Rev. 2016, 116, 3540–3593. (3) Barbatti, M.; Aquino, A.; Jaroslaw,; Szymczak, J.; Nachtigallov, D.; Hobza, P.; Lischka, H. Relaxation Mechanisms of UV-photoexcited DNA and RNA Nucleobases. PNAS 2010, 107, 21453–21458. (4) Middleton, C. T.; de La Harpe, K.; Su, C.; Law, Y. K.; Crespo-Hernandez, C. E.; Kohler, B. DNA Excited-State Dynamics: From Single Bases to the Double Helix. Annu. Rev. Phys. Chem. 2009, 60, 217–239. (5) Vignard, J.; Mirey, G.; Salles, B. Ionizing-radiation Induced DNA Double-Strand Breaks: A Direct and Indirect Lighting up. Radiotherapy and Oncology 2013, 108, 362–369. (6) Lomax, M.; Folkes, L.; O’Neill, P. Biological Consequences of Radiation-induced DNA Damage: Relevance to Radiotherapy. Clinical Oncology 2013, 25, 578–585. (7) Bouda¨ıffa, B.; Cloutier, P.; Hunting, D.; Huels, M. A.; Sanche, L. Resonant Formation of DNA Strand Breaks by Low-Energy (3 to 20 eV) Electrons. Science 2000, 287, 1658–1660. (8) Martin, F.; Burrow, P. D.; Cai, Z.; Cloutier, P.; Hunting, D.; Sanche, L. DNA Strand Breaks Induced by 0 - 4 eV Electrons: The Role of Shape Resonances. Phys. Rev. Lett. 2004, 93, 068101.

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(9) Aflatooni, K.; Gallup, G. A.; Burrow, P. D. Electron Attachment Energies of the DNA Bases. J. Phys. Chem. A 1998, 102, 6205–6207. (10) Barrios, R.; Skurski, P.; Simons, J. Mechanism for Damage to DNA by Low-Energy Electrons. J. Phys. Chem. B 2002, 106, 7991–7994. (11) Berdys, J.; Anusiewicz, I.; Skurski, P.; Simons, J. Damage to Model DNA Fragments from Very Low-Energy (

Electronic Resonances of Nucleobases Using Stabilization Methods

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