Quantum-Chemical Investigation of the Structures and Electronic Spectra of the Nucleic Acid Bases at the Coupled Cluster CC2 Level

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1 5482 J. Phys. Chem. A 2007, 111, Quntum-Chemicl Investigtion of the Structures nd Electronic Spectr of the Nucleic Acid Bses t the Coupled Cluster CC2 Level Timo Fleig* nd Stefn Knecht Institute of Theoreticl nd Computtionl Chemistry, Heinrich Heine UniVersity Düsseldorf, UniVersitätsstrsse 1, D Düsseldorf, Germny Christof H1ttig Lehrstuhl für Theoretische Chemie, Ruhr-UniVersität Bochum, UniVersitätsstrsse 150, D Bochum, Germny ReceiVed: October 23, 2006; In Finl Form: Mrch 8, 2007 We study the ground-stte structures nd singlet- nd triplet-excited sttes of the nucleic cid bses by pplying the coupled cluster model CC2 in combintion with resolution-of-the-identity pproximtion for electron interction integrls. Both bsis set effects nd the influence of dynmic electron correltion on the moleculr structures re elucidted; the ltter by compring CC2 with Hrtree-Fock nd Møller-Plesset perturbtion theory to second order. Furthermore, we investigte bsis set nd electron correltion effects on the verticl excittion energies nd compre our highest-level results with experiment nd other theoreticl pproches. It is shown tht smll bsis sets re insuffient for obtining ccurte results for excited sttes of these molecules nd tht the CC2 pproch to dynmic electron correltion is relible nd efficient tool for electronic structure clcultions on medium-sized molecules. 1. Introduction The nucleic cid (NA) bses denine, thymine, gunine, cytosine, nd urcil re essentil building blocks of DNA nd RNA. A profound understnding of their electronic structure nd dynmics is of gret interest, s the NA bses re remrkbly stble with respect to dmging UV irrdition. 1 In recent works, rpid decy pthwys for electronic energy in excited sttes of denine nd lso the other NA bses hve been investigted, 2-8 indicting the importnce of high-ccurcy dt for excited singlet nd possibly lso triplet sttes of the NA bses. With the impressive dvnce of quntum-chemicl methodology nd computtionl power in the pst decde, b initio clcultions of molecules of the size of the NA bses nd lso their dimers hve become possible using lrge bsis sets nd including electron correltion by coupled cluster methods. 9,10 A consistent study of the NA bses using the sme high-level tretment for both full geometry optimiztions nd the clcultion of excited sttes, however, hs not been vilble to the dte. Aprt from pplictions of vrious density functionl theory nd semiempiricl models, only few b initio pproches hve been pplied to the clcultion of excited sttes of the NA bses. Dynmic electron correltion hs either been treted by configurtion interction (CI) theory (e.g., in refs 11 nd 12) or multireference perturbtion theory vi the complete ctive spce perturbtion theory to second order (CASPT2, s in refs 13 nd 14). Shifted CI singles is not rigorous method, s electron correltion is merely ccounted for in n implicit fshion. Moreover, CI pproches generlly suffer from the low compctness of the truncted CI wve function. CASPT2 bsed on CASSCF wve functions hs been the most rigorous pproch * Corresponding uthor. E-mil: timo@theochem.uni-duesseldorf.de. to the electronic spectr of the NA bses so fr. However, this method becomes difficult to pply when the electronic structure of species requires the use of n extensive complete ctive orbitl spce, which for lrger molecules quite frequently is the cse. In coupled cluster theory, on the other hnd, the leding higher excittions representing the multireference spce of the CASPT2 clcultions re contined in the cluster expnsion of the wve function. Using the pproximte coupled cluster model CC2 15 throughout, we pursue the following purposes with this investigtion: (1) Full ground-stte geometry optimiztion of ll 5 NA bses without moleculr symmetry, thus llowing for relxtion to the energeticlly most fvorble nonplnr structures. We use series of one-prticle bsis sets nd systemticlly elucidte bsis set effects nd the influence of electron correltion treted t different levels of sophistiction on moleculr geometries. (2) Verticl excited-stte clcultion of singlet nd triplet sttes of the NA bses using the optimized geometries. We here specificlly focus on bsis set nd electron correltion effects on excittion energies nd the chrcter of excited sttes in terms of contributing orbitls/excittions. (3) Assessment of level of high ccurcy nd profound understnding of the subunits for subsequent investigtion of NA bse dimers. 16 In the following section (2), we summrize the employed computtionl pproches. Section 3 comprises the min body of the pper with ll results nd their discussion, nd in Section 4, we drw conclusions from our studies, with n emphsis on future work concerning lrger relted systems. 2. Computtionl Method nd Bsis Sets The CC2 equtions re n pproximtion to the coupled cluster singles nd doubles (CCSD) equtions, where the singles equtions re retined in the originl form nd the doubles /jp CCC: $ Americn Chemicl Society Published on Web 06/02/2007

2 Nucleic Acid Bses t the Coupled Cluster CC2 Level J. Phys. Chem. A, Vol. 111, No. 25, equtions re truncted to first order in the fluctution potentil. 15 We used the implementtion in the TURBOMOLE 20 quntum chemistry progrm pckge. A resolution-of-theidentity (RI) pproximtion is employed for moleculr orbitl two-prticle integrls. The errors mde within this pproximtion re, with optimized uxiliry bsis sets, in generl negligible s compred to errors due to the one-electron bsis set incompleteness. 17,18 All electrons were correlted, i.e., 78 in gunine, 70 in denine, 66 in thymine, nd 58 in cytosine nd urcil. This computtionl level ws retined for both the geometry optimiztions nd the excited-stte clcultions vi coupled cluster response theory. For few molecules nd bsis sets, we lso checked for the effect of forming frozen core from the 1s electrons on structures nd excittion energies. All clcultions hve been crried out in C 1 point-group symmetry. We used sequence of stndrd Gussin bsis sets, the polrized split-vlence SV(P) (C, N, O: 7s4p1d/3s2p1d; H: 4s1p/2s1p), 21 nd the ugmented correltion-consistent sets ugcc-pvdz (C, N, O: 10s5p2d/4s3p2d; H: 5s2p/3s2p), cc-pvtz (C, N, O: 10s5p2d1f/4s3p2d1f; H: 5s2p1d/3s2p1d), ug-ccpvtz (C, N, O: 11s6p3d2f/5s4p3d2f; H: 6s3p2d/4s3p2d), ugcc-pvqz (C, N, O: 13s7p4d3f2g/6s5p4d3f2g; H: 7s4p3d2f/ 5s4p3d2f). 22,23 The corresponding uxiliry bsis sets for the RI pproximtion re documented in refs 24,25. For nlyzing the chrcter of excited sttes, we hve used the MOLDEN progrm suite version Results nd Discussion A. Geometry Optimiztions. The geometries of the nucleic cid bses re sensitive to both the employed bsis sets nd the tretment of electron correltion. For consistency in our study, the geometry t which the single-point clcultions of verticl excittion energies were crried out re optimized using the sme electronic structure method. We therefore optimize ll geometries with the CC2 pproch nd compre the obtined structures employing different bsis sets. Moreover, we elucidte the influence of electron correltion by compring structures obtined with the sme bsis sets but different pproches to electron correltion. 1. Bsis Set Effects. The optimized geometries of ll five nucleic cid bses cn be found in the Supporting Informtion (figures S1-S5) to this rticle. The following discussion is bsed on the CC2 results. Becuse of the high computtionl demnd, only urcil ws treted with the set of qudruple-ζ qulity. For the series ug-cc-pvxz (X ) D,T,Q), we observe tht bonds contrct systemticlly by bout 0.01 Å for DZ to TZ nd by bout Å for TZ to QZ. The smll SV(P) set, which is comprble to the commonly used 6-31G* bsis set in qulity, overestimtes bond lengths in the rnge of 0.01 to 0.02 Å except for CdO bonds, where bond lengths resemble those obtined with the ug-cc-pvqz set. The effect of diffuse ugmenting functions, by comprison with the results for the cc-pvtz for urcil, is to stretch ll bonds by roughly Å. We hve dded these functions for n pproprite description of Rydberg-type excited sttes nd especilly prepring for further study on the NA bse dimers, where they re required for modeling excited sttes of chrge-trnsfer type nd the hydrogen bonds in mny dimer structures. We confirm the trend of the CC2 method to give slightly longer bond lengths thn MP2 (cc-pvtz, ref 27), which hs been estblished erlier for test set of smll molecules. 19,28 The effect of ugmenting bsis functions becomes prticulrly interesting when considering the cc-pvdz geometries of urcil, which re the sme up to Å s those with the cc-pvtz bsis set. The contrction from incresing the TABLE 1: Sum of Bond Angles C-N-H 1,C-N-H 2, H 1 -N-H 2, in deg t the Amino Group with Different Bsis Sets nd Levels of Electron Correltion method/bsis set denine gunine cytosine RI-CC2/SV(P) RI-CC2/ug-cc-pVDZ RI-CC2/ug-cc-pVTZ RI-CC2/ug-cc-pVTZ (fc) MP2/ug-cc-pVTZ HF/ug-cc-pVTZ (fc) denotes n optimiztion with ll 1s electrons forming frozen core. The devition from 360 is mesure of the nonplnrity of the mino group. crdinl number is only observed with ugmenting functions. In totl, the elongtion due to ugmenting bsis functions nd this contrction hppen just to level out so tht cc-pvdz nd ug-cc-pvqz geometries of urcil re lmost exctly the sme. In view of the very smll chnges from going to the QZ bsis set nd the generl fct tht the error from the limited tretment of electron correltion surpsses the bsis set error lredy t the ug-cc-pvtz level, 29 we consider our results converged with respect to the extent of the one-prticle bsis set. Regrding the nonplnrity of mino groups in denine, gunine, nd cytosine, we confirm erlier findings. 27,30,31 Tble 1 gives the sum of the three optimized bond ngles round the mino nitrogen tom in denine, gunine, nd cytosine. The individul bond ngles cn be found in the Supporting Informtion for this rticle. The lrgest nonplnrity is found for gunine. The nonplnrity decreses with incresing size of the bsis sets, where the smllest SV(P) does not follow this trend. It is interesting to note tht, for given pproch to electron correltion, bsis set of incresing size leds to more plnr structure. This finding is in line with the results of study on the plnrity of formmide by Fogrsi et l Effects of Electron Correltion. For obtining informtion on the effect of electron correltion on the moleculr geometries, we hve crried out Hrtree-Fock geometry optimiztions nd, furthermore, compre with the MP2 results by Wng et l. 27 Commencing with the effect on nonplnrity, the inclusion of electron correltion leds to considerble increse for the mino groups. However, the perturbtive optimiztions revel tht MP2 nonplnrities re slightly lrger thn those obtined with CC2, s cn be seen in Tble 1. This indictes tht the prtil sp 3 chrcter of the mino nitrogen toms is decresed by including single excittions in the wvefunction t the CC2 level. As expected, due to the shift of electron density into ntibonding orbitls, bonds re stretched upon ccounting for electron correltion (Figures S1-S5 in the Supporting Informtion). This increse rnges from to 0.04 Å, with the exception of one C-C ring bond per system, which is slightly contrcted. The contrcted bond is lwys the longest ring bond with the lrgest σ-bonding chrcter. The elongtion of CdO bonds is most pronounced compred to other elongtions nd t the upper limit of the rnge of CdO bond lengths in smller molecules. 28 We hve furthermore investigted the correltion contributions due to the 1s electrons by optimizing geometries using respective frozen core. The effects on bond lengths re very smll, with elongtion of bonds due to the frozen core pproximtion in the order of Å. For gunine nd the ug-cc-pvtz bsis set, we observe the lrgest effects. B. Excited Sttes. Tbles 2 through 6 contin the verticl excittion spectr of the five molecules, qulittive chrc-

3 5484 J. Phys. Chem. A, Vol. 111, No. 25, 2007 Fleig et l. Figure 1. Urcil: CC2 verticl singlet excittion energies with different bsis sets, t corresponding ground-stte optimized geometries; oscilltor strengths of the trnsitions re given in itlics. teriztion of the electronic trnsitions nd the involved moleculr orbitls, nd the oscilltor strengths for singlet sttes, obtined with the most extensive of the investigted bsis sets, respectively. The comprison of results with vrious bsis sets hs been crried out for ll five molecules nd is displyed grphiclly in Figure 1 for urcil s representtive exmple. 49 All results hve been obtined from clcultions t the optimized geometry with the respective bsis set. 1. Bsis Set Effects. For urcil, it ws computtionlly fesible to increse the bsis set crdinl number up to 4 nd beside SV(P) nd cc-pvtz compre the series ug-cc-pvxz (X ) D,T,Q). The most striking observtion is the indequcy of the very smll split-vlence bsis set for giving ccurte verticl excittion energies in CC2 clcultions. The devitions my become s lrge s 1.0 ev when compring to the ug-cc-pvdz set. Both the ordering nd the chrcter of the excited sttes, on the other hnd, remin essentilly unchnged. Excittion energies increse slightly with incresing crdinl number, but the observed chnges re well within the expected error mrgins from the incomplete tretment of dynmic electron correltion due to the truncted coupled cluster expnsion. A fvorble error compenstion, i.e., the incresing excittion energies through incresing crdinl number combined with decresing energies when the inherent correltion error is ccounted for, lets us nticipte tht the ug-cc-pvdz level provides results closest to experimentl vlues. This sttement finds support in the direct comprison with experimentl results in the following subsection (3.B.2). The generl trends for urcil re lso observed for the other NA bses nd triplet excited sttes. The indequcy of smll bsis sets my be of prticulr relevnce for the relibility of detiled studies (e.g., dectivtion nd other photophysicl processes) lso with other pproches to dynmic electron correltion when such smll bsis sets re employed, quite

4 Nucleic Acid Bses t the Coupled Cluster CC2 Level J. Phys. Chem. A, Vol. 111, No. 25, Figure 2. CC2 verticl singlet excittion energies with the ug-cc-pvtz bsis set, t corresponding ground-stte optimized geometry; oscilltor strengths of the trnsitions re given in itlics. () Two excited sttes re obtined s conjugted pir of degenerte roots with complex eigenvlues (see text for detils). frequently 6-31G(*) (e.g., in refs 3, 33). Moreover, the inclusion of ugmenting diffuse bsis functions (ug-cc-pvtz compred with cc-pvtz) not only opens for the description of Rydbergtype sttes but lso improves the excittion energies of vlenceexcited sttes significntly (Figure 1). We scribe this finding to the fct tht the one-prticle bsis sets we re discussing hve been optimized for tomic ground sttes nd tht the dditionl diffuse bsis functions ply non-negligible role in the description of moleculr excited sttes, even if these re vlenceexcited sttes like in the present cse. A specific observtion of Neiss et l. for the urcil molecule, 34 nmely tht nπ* trnsitions re supposed to be rther insensitive to the size of the bsis set is not supported by our study. As shown in Figure 1, we find the sme trend in the sme order of mgnitude for singlet excittion energies with vrying bsis sets, irrespective of the chrcter of the trnsition. Conclusively, we consider ug-cc-pvdz relible bsis set qulity for the study of lrger systems involving the NA bse monomers. From systemtic investigtions, it is known tht the errors due to incomplete tretment of electron correltion typiclly surpss the bsis set error t the ug-cc-pvtz level, 18,35,36 which underlines our judgment. 2. Excittion Energies nd Chrcter of Excited Sttes. Verticl excittion energies of ll five NA bses, both for singlet nd triplet sttes, nd using the ug-cc-pvtz bsis set throughout (the lrgest common set for ll studies), re displyed in Figures 2 nd 3. In the following, we discuss the NA bses seprtely, but refrin from repeting ll reference vlues reported in the literture, s very extensive overview hs been given by Crespo-Hernández et l. 1 Insted, we compre our results selectively with vilble experimentl vlues nd some recent studies from the theoreticl literture. An overview is given in Tble 7. Adenine. Despite the fct tht denine hs received considerble ttention by both theoreticins nd experimentlists, there does not seem to be consensus on the chrcter of the lowest singlet-excited stte. Our most sophisticted clcultion (CC2/ ug-cc-pvtz, Tble 2) predicts nπ* s the S 1 stte, with two close-lying ππ* sttes 0.13 ev bove the S 1 stte. We obtin the two low-lying ππ* sttes s degenerte complex eigenvectors within response theory, n rtifct which my be ttributed to the nonsymmetric Jcobi mtrix for CC2, leding in the respective region of the potentil hypersurfce to conjugted pir of degenerte roots with complex eigenvlues 37 insted of

5 5486 J. Phys. Chem. A, Vol. 111, No. 25, 2007 Fleig et l. Figure 3. CC2 verticl triplet excittion energies with the ug-cc-pvtz bsis set, t corresponding ground-stte optimized geometry. two lmost degenerte rel eigenvlues. We re confident, however, tht the two sttes correspond to the lowest ππ* sttes identified previously both by experiment nd theory (e.g., refs 4,33,38), s the orbitl chrcter nd the oscilltor strengths we obtin re in greement with erlier findings. From the work of Clrk et l., 39 which llows for direct comprison with most theoreticl work, it cnnot be deduced whether S 1 is of ππ* (t 4.98 ev) or nπ* chrcter. Our prediction is, however, in generl greement with the experimentl work of Kim et l., 38 from which vibrtion-corrected (E 0-0 ) excittion energies of 4.40 ev for nπ* nd 4.48 ev for ππ*, respectively, cn be deduced. Vibronic coupling between the respective electronic sttes is known to be lrge, 40 but the proximity effect would led to further lowering of the nπ* stte reltive to the ππ* excited sttes if considered in our clcultions. For denine, we hve lso crried out geometry optimiztion in the lowest (π-π*) excited stte t the CC2/ ug-cc-pvdz level, yielding n dibtic excittion energy of 4.47 ev (ls electrons frozen). This vlue is in perfect greement with the vibrtion-corrected experimentl result of Kim et l. 38 CC2 excittion energies re typiclly up to few tenths of n ev too high, 17 nd this is rther systemtic for ll excited sttes. Therefore, we cnnot support n nπ* excittion energy in denine of 6.15 ev s obtined by Fülscher et l. with CASSCF/CASPT2. 13 In more recent study with CASSCF/ CASPT2, 2 vlue of 4.96 ev is reported tht grees well with our result. The defect of the erlier clcultion ws there explined by the use of n ctive orbitl spce in ref 13 insufficient for describing the nπ* excittion properly. Two quite recent LDA/TDDFT studies on the NA bses nd lso their dimers report the ππ* excited sttes t lower energies, nd this pplies to ll NA bses s compred to our results. Tsoklidis et l. 41 find the lowest ππ* sttes t 4.52 nd 4.95 ev, nd Vrsno et l. 42 t 4.51 nd 4.88 ev, respectively. Their results re generlly in good greement with experiment, but devitions my be in both directions, in contrst to our vlues where the excittion energies re systemticlly overestimted. For higher excited sttes, we observe considerble Rydbergvlence mixing when the ugmented bsis sets re used. This pplies lso to the triplet-excited sttes of denine in Tble 2, for which there is firly good greement in the lower prt of the spectrum with erlier DFT/MRCI clcultions. 4 Thymine. Owing to the double keto group in this NA bse, we find low-lying nπ* singlet stte involving the nonbonding oxygen electrons, shown in Tble 3. The lowest excited sttes re well seprted energeticlly, which lso pplies to the tripletexcited sttes in Tble 3 nd in Figure 3. The excittion energies re in generl greement with those obtined with other methods, 1 in prticulr, the TD-DFT(B3LYP) clcultions of Crespo-Hernández et l. (in ref 1). Our best vlue of 5.20 ev for the lowest ππ* excittion energy exhibits bout the sme devition from experimentl results (obtined in gs phse nd

6 Nucleic Acid Bses t the Coupled Cluster CC2 Level J. Phys. Chem. A, Vol. 111, No. 25, TABLE 2: Excited Singlet nd Triplet Sttes of Adenine nd Their Chrcter (ug-cc-pvtz); Oscilltor Strengths f for Trnsitions stte trnsition E (ev) t 1/ t (%) f S 1 n f π* (49.6) (24.8) S 2 π f π* (20.5) π f Ryd (16.3) π f π* (11.3) S 3 π f π* (28.5) (19.7) π f Ryd (11.4) S 4 π f Ryd (46.9) π f Ryd (16.0) S 5 n f Ryd (28.4) (27.0) n f π* (20.1) S 6 π f Ryd (44.6) π f Ryd (22.8) S 7 n f Ryd (58.1) S 8 n f π* (46.6) (24.9) T 1 π f π* (49.3) (22.2) T 2 n f π* (48.2) (23.6) T 3 π f Ryd (29.0) (23.4) π f π* (17.9) T 4 π f π* (22.7) (16.2) T 5 π f Ryd (31.7) π f Ryd (16.9) T 6 n f Ryd (21.2) (21.1) n f π* (13.2) T 7 π f Ryd (22.6) π f π* (19.4) π f Ryd (14.2) π f π* (10.2) T 8 π f Ryd (18.0) π f Ryd (14.0) t 1/ t denotes the reltive weight of the single-excittion mplitudes (t 1) in the CC expnsion. solution, s shown in Tble 7) s those for the other NA bses. For both the singlet- nd the triplet-excited sttes, Rydbergvlence mixing is fr less pronounced thn in denine. Gunine. Gunine comprises n exception in our series of clcultions, in the sense tht it is the only molecule where the ordering of lower excited sttes vries with the extent of the bsis set. Minly for this reson, we include more detils on this molecule, which re shown in Figure 4. When using the ug-cc-pvtz bsis nd frozen-core (fc) pproximtion for the 1s electrons, the S 1 stte hs the expected ππ* chrcter, nd the second ππ* s well s the nπ* sttes reported in the literture 1 re found t significntly higher energies. The identifiction of these sttes is, however, unmbiguous due to the oscilltor strengths, which re in good greement, e.g., with the vlues of Fülscher et l. with CASSCF/CASPT2. 13 We obtin low-lying dditionl stte, though, which we scribe strong Rydberg chrcter nd which does not pper when using bsis set without diffuse functions (Figure 4). In comprison with experiment (in ref 13), our excittion energies pper to be somewht too high, in this cse with devitions up to 0.5 ev for the low-lying ππ* stte. Our oscilltor strength of from the verticl clcultion for this stte, however, grees quite well with the experimentl vlue of 0.16 (in ref 13). Most of the excited sttes re mixed both with respect to Rydberg contributions s well s the pproximte designtion in terms TABLE 3: Excited Singlet nd Triplet Sttes of Thymine nd Their Chrcter (ug-cc-pvtz); Oscilltor Strengths f for Trnsitions stte trnsition E (ev) t 1/ t (%) f S 1 n f π* (36.7) (32.9) S 2 π f π* (39.6) (29.1) S 3 π f Ryd (68.4) (10.2) S 4 n f π* (16.7) (16.0) (14.9) S 5 π f π* (31.5) (30.9) S 6 n f Ryd (51.5) (15.60) S 7 π f Ryd (31.9) (22.6) (13.0) S 8 π f π* + Ryd (34.9) (21.0) (13.0) T 1 π f π* (41.6) (31.2) T 2 n f π* (35.9) (31.4) T 3 π f π* (28.1) (23.3) (11.2) T 4 π f Ryd (66.5) (10.6) T 5 π f π* + Ryd (24.1) (15.8) (13.2) T 6 n f π* (18.0) (12.4) (10.7) T 7 n f Ryd (52.3) (21.7) T 8 π f Ryd (36.9) (15.7) (12.5) t 1/ t denotes the reltive weight of the single-excittion mplitudes (t 1) in the CC expnsion. of ngulr momentum projection (σ, π, etc.). The Rydbergvlence mixing is especilly pronounced when ll electrons re correlted, in which cse we find strong contributions of Rydberg-type excittions to ll excited sttes (ug-cc-pvtz). For some of the higher triplet sttes in Figure 3, this mixing does not even llow precise ssignment. Beside the oscilltor strengths, which should be lrgest for sttes of ππ* chrcter, we used r 2 expecttion vlues for the involved orbitls to identify vlence nd Rydberg chrcters of excited sttes. This led us to the ssignments s given in Figure 4. A pronounced feture of the gunine spectrum when lrger bsis sets re used is the occurrence of groups of excited sttes seprted by significnt energy gps. The groups rise through chnges of the prticipting virtul orbitls, wheres the occupied orbitls from which the excittions re performed remin essentilly the sme (Tble 4). Cytosine. For the singlet-excited sttes of cytosine, we cn support the consensus 1 tht S 1 is of ππ* nd S 2 of nπ* chrcter, with the two sttes locted quite close in energy (Tble 5). With respect to the oscilltor strengths of the respective trnsitions, however, our results gree very well with the CASSCF/CASPT2 vlues of Merchn et l. 43 nd Fülscher et l., 44 wheres the result for the lowest ππ* trnsition obtined with shifted CIS clcultion 11 devites from these by fctor of 2. Most

7 5488 J. Phys. Chem. A, Vol. 111, No. 25, 2007 Fleig et l. Figure 4. Gunine: CC2 verticl singlet excittion energies with different bsis sets, t corresponding ground-stte optimized geometry; oscilltor strengths of the trnsitions re given in itlics. [fc] denotes clcultion with frozen core of 1s electrons. experimentl vlues for the S 1 excittion energy (in ref 44) re round 4.6 ev, in perfect greement with our highest-level vlue (CC2/ug-cc-pVTZ). The gs-phse result of Clrk et l., 39 however, with mximum t 4.28 ev, is significntly lower. Prticulrly interesting is the comprison of our triplet excittion energies for cytosine with those of Nguyen et l. 45 For the T 1 stte, Nguyen et l. obtin 3.63 ev with DFT/B3LYP (lrgest bsis set reported), 3.83 ev with CCSD, nd 3.75 ev with CCSD(T). Our RI-CC2/ug-cc-pVTZ vlue of 3.88 ev (Tble 5) grees quite well with their CC results, but the DFT vlue ppers to be somewht too low. In the following subsection on urcil, we will look more closely into electron correltion errors rising from truncted CC expnsions. Urcil. As shown in Tble 6 nd Figure 1, two low-lying excited singlet sttes re found for urcil, the lower identified s n nπ* trnsition, the higher s ππ*, in ccord with most previous studies. 1,14,45 The excittion energy of 5.35 ev for the ππ* stte grees firly well with the gs-phse result of Clrk et l. 39 (5.08 ev), nd the corresponding oscilltor strengths of the two sttes closely resemble those obtined by Lorentzon et l. 14 The lowest ππ* excittion energy of Vrsno et l. 42 from LDA/TDDFT t 4.69 ev ppers to be somewht too low. All excittions involve electrons from occupied moleculr orbitls with strong oxygen prticiption, nd the energy gp in the spectrum rises from the chrcter of virtul orbitls, which re higher lying for the upper prt of the spectrum. Especilly the lower-energy prt of the clculted spectrum closely resembles tht obtined for thymine, both with respect to the ordering/ chrcter of the excited sttes nd the excittion energies. Our triplet excittion spectrum in Tble 6 grees well with tht obtined erlier with the DFT/MRCI method. 46 Finlly, we hve been ble to ssess electron correltion errors through clcultions of higher ccurcy on urcil. In Tble 8, we report coupled cluster excittion energies obtined with the smllest bsis set used here, SV(P), nd the DALTON 47 progrm pckge. For very smll model systems, the errors for excittion

8 Nucleic Acid Bses t the Coupled Cluster CC2 Level J. Phys. Chem. A, Vol. 111, No. 25, TABLE 4: Excited Singlet nd Triplet Sttes of Gunine nd Their Chrcter (ug-cc-pvtz); Oscilltor Strengths f for Trnsitions stte trnsition E (ev) t 1/ t (%) f S 1 π f π* + Ryd (20.0) (16.0) (13.0) (10.0) S 2 π f Ryd (48.4) S 3 n f Ryd + π* (13.5) (11.3) S 4 π f Ryd (41.7) S 5 π f Ryd + π* (35.3) (11.2) S 6 π f Ryd (57.0) S 7 n f Ryd (19.8) (11.0) S 8 n f Ryd (13.0) T 1 π f π* + Ryd (27.0) (16.9) (16.2) (11.1) T 2 π f π* (22.1) π f Ryd (14.1) T 3 π f Ryd + π* (62.2) T 4 n f Ryd + π* (14.2) (10.6) T 5 π f Ryd (26.8) π f π* (12.3) (11.0) T 6 π f Ryd (46.7) T 7 mix T 8 π f Ryd (49.4) t 1/ t denotes the reltive weight of the single-excittion mplitudes (t 1) in the CC expnsion. energies re known to decrese long the series CC2-CCSD- CC3, where CC3 provides very high level of ccurcy close to the exct bsis set energies from full configurtion interction (FCI) clcultions. 48 For more relistic systems such s benzene, however, CCSD excittion energies tend to overshoot for mny low-lying sttes of π-π* chrcter, 35 nd CC2 excittion energies re in fct closer to the exct verticl electronic excittion energies. We mke precisely this finding for two selected excited sttes of urcil, from which the CC2 correltion errors re seen to be round +0.1 ev. This is lso in line with erlier findings, tht CC2 errors re smll if the double replcement chrcter of given excited stte is well below 10%, 35 which is the cse here. It ws not possible to crry out the sme study using lrger bsis set due to the steep increse in computtion time. The results in Tble 8 lso substntite tht errors from the RI pproximtion re negligible. We gin confidence tht the obtined verticl RI-CC2 excittion energies lso for the other NA bses, which hve similr electronic structure, re of high ccurcy. As fr s the present studies re concerned, we recommend the computtionl level RI-CC2/ug-cc-pVDZ s the most beneficil CC electronic structure level for the clcultion of verticl electronic excittion energies of medium-sized molecules. 4. Concluding Remrks Our systemtic series of geometry optimiztions for the NA bses suggests tht n ccurcy of up to 0.01 Å for equilibrium bond lengths cn only be obtined with bsis sets of t lest triple-ζ qulity. Such bsis sets cn be used for the monomer studies here, but for lrger systems (like, e.g., the corresponding dimers), one hs to compromise. Furthermore, we show the trends of electron correltion on moleculr geometries nd TABLE 5: Excited Singlet nd Triplet Sttes of Cytosine nd Their Chrcter (ug-cc-pvtz); Oscilltor Strengths f for Trnsitions stte trnsition E [ev] t 1/ t (%) f S 1 π f π* (31.5) (19.0) (12.5) S 2 n f π* (31.4) (19.4) (13.2) S 3 n f π* (29.9) (20.0) (13.1) S 4 π f Ryd (64.0) S 5 π f π* (29.2) (16.0) (14.5) S 6 n f π* (22.6) (15.1) (10.7) S 7 n f Ryd (43.2) S 8 π f Ryd (30.4) (24.0) T 1 π f π* (38.7) (14.0) (12.9) T 2 π f π* (25.9) (17.5) (10.4) T 3 n f π* (27.9) (17.2) (11.7) T 4 n f π* (31.2) (21.2) (13.5) T 5 π f π* (29.5) (20.0) (10.7) T 6 π f Ryd (62.7) (10.3) T 7 n f π* (20.7) (14.1) (12.1) T 8 n f Ryd (39.0) t 1/ t denotes the reltive weight of the single-excittion mplitudes (t 1) in the CC expnsion. estblish the expected behvior of MP2 s compred to our CC2 results, where the ltter typiclly come out slightly too long nd vice vers for the former. However, the devitions re quite smll overll, mking both MP2 nd CC2 geometries relible strting points for further studies of verticl excittion spectr. For both singlet nd triplet verticl excittion energies, we obtin relible results with the CC2/response method. The description of vrious excited sttes is blnced nd we ssign errors in rnge of ev, the obtined energies overshooting the expected experimentl results. Upon investigting electron correltion errors nd regrding bsis set errors, we observe fvorble error cncelltion from bsis set limittions nd limited correltion tretments t the CC2/ugcc-pVDZ level. In these studies, the use of high-level pproch to electron correltion like the CC2 method nd the use of extensive bsis sets becomes mjor issue in obtining ccurte results. In prticulr, smll bsis sets like the split-vlence set with polriztion functions (SV(P)) in combintion with the CC2 pproch is clerly insufficient in describing the excited sttes of NA bses stisfctorily. We consider it rther importnt to note tht the ddition of diffuse functions (ug) to one-prticle bsis sets yields significntly lower nd more precise excittion energies thn clcultions without such functions. For geometry

9 5490 J. Phys. Chem. A, Vol. 111, No. 25, 2007 Fleig et l. TABLE 6: Excited Singlet nd Triplet Sttes of Urcil nd Their Chrcter (ug-cc-pvqz) nd Oscilltor Strengths f for Trnsitions stte trnsition E [ev] t 1/ t (%) f S 1 n f π* (37.4) (25.9) (13.5) S 2 π f π* (41.6) (20.7) (16.4) S 3 π f Ryd (60.7) (15.4) S 4 n f π* (32.0) (15.3) S 5 π f π* (39.7) (24.6) (17.5) S 6 n f Ryd (55.4) (16.0) S 7 n f π* (35.5) (25.6) (13.2) S 8 π f π* (67.0) T 1 π f π* (44.2) (21.6) (16.6) T 2 n f π* (36.1) (25.1) (12.4) T 3 π f π* (30.5) (17.4) (16.7) (11.5) T 4 n f π* (34.0) (13.7) (13.6) T 5 π f Ryd (62.3) (16.7) T 6 π f π* (46.4) (16.1) T 7 n f Ryd (53.6) (19.0) T 8 n f π* (30.8) (28.2) (14.7) t 1/ t denotes the reltive weight of the single-excittion mplitudes (t 1) in the CC expnsion. TABLE 7: Selected Verticl Excittion Energies of the NA Bses from Present CC2 Clcultions (ug-cc-pvtz Bsis Set, ug-cc-pvqz for Urcil) nd Comprison with Experimentl Dt NA bse stte (trnsition) RI-CC2 T V [ev] experimentl denine S 1 (n-π *) b S 2 (π-π*) thymine S 1 (n-π*) 4.82 S 2 (π-π*) c 4.7 d gunine S 1 (π-π*) e cytosine S 1 (π-π*) b urcil S 1 (n-π*) 4.80 S 2 (π-π*) b E 0-0, vibrtion corrected. 38 b Vpor phse. 39 c 1,3-Dimethylurcil, gs phse. 39 d In wter nd TMP. 39 e From ref 13. optimiztions in both ground nd excited sttes, on the other hnd, one-prticle bsis sets without diffuse functions my be more fvorble s bsis set superposition errors re smller. For thymine (SV(P), ug-cc-pvdz, nd ug-cc-pvtz), gunine (SV(P) nd ug-cc-pvtz), nd urcil (SV(P), ug-ccpvdz, nd ug-cc-pvtz), we compred our clcultions with frozen-core (ll 1s electrons) pproximted ones nd found very TABLE 8: Lowest π-π* Excittion Energies of Urcil, SV(P) Bsis Set stte RI-CC2 CC2 CCSD CC3 S S RI-CC2 from TURBOMOLE, ll others from DALTON. smll devitions for both geometries (mx of Å) nd excittion energies (mx of 0.01 ev, 0.03 ev for gunine) which re much smller thn the other errors discussed here. In ongoing studies, we exploit the obtined knowledge nd investigte prticulrly chrge-trnsfer sttes of the NA bse dimers t the CC2/ug-cc-pVDZ level. Here TDDFT is no longer pplicble with stndrd density functionls nd the ppliction of the CASSCF/CASPT2 pproch is hmpered by the computtionl demnd rising especilly from the requirement for extensive complete ctive orbitl spces. We expect tht the CC2 method is significnt nd ccurte tool for the investigtion of excited singlet nd triplet sttes of systems of incresing size like the mentioned NA bse dimers or cged compounds. Acknowledgment. T.F. nd S.K. cknowledge support from the Collbortive Reserch Center (SFB) 663, Moleculr Response fter Electronic Excittion (Düsseldorf). We thnk the reviewers for number of helpful comments nd suggestions. Supporting Informtion Avilble: Detiled tbles nd dditionl figures. This mteril is vilble free of chrge vi the Internet t References nd Notes (1) Crespo-Hernández, C. E.; Cohen, B.; Hre, P. M.; Kohler, B. Chem. ReV. 2004, 104, (2) Serrno-Andrés, L.; Merchán, M.; Borin, A. C. Chem.sEur. J. 2006, 12, (3) Perun, S.; Sobolewski, A. L.; Domcke, W. J. Am. Chem. Soc. 2005, 127, (4) Mrin, C. M. J. Chem. Phys. 2005, 122, (5) Cnuel, C.; Elhnine, M.; Mons, M.; Piuzzi, F.; Trdivel, B.; Dimicoli, I. Phys. Chem. Chem. Phys. 2006, 8, (6) Chen, H.; Li, S. J. Chem. Phys. 2006, 124, (7) Blncfort, L. J. Am. Chem. Soc. 2006, 128, 210. (8) Mtsik, S. J. Phys. Chem. A 2005, 109, (9) Fogrsi, G. J. Phys. Chem. A 2002, 106, (10) Dbkowsk, I.; Jurečk, P.; Hobz, P. J. Phys. Chem. A 2002, 106, (11) Shukl, M. K.; Mishr, P. C. Chem. Phys. 1999, 240, 319. (12) Mennucci, B.; Toniolo, A.; Tomsi, J. J. Phys. Chem. A 2001, 105, (13) Fülscher, M.; Serrno-Andrés, L.; Roos, B. O. J. Am. Chem. Soc. 1997, 119, (14) Lorentzon, J.; Fülscher, M.; Roos, B. O. J. Am. Chem. Soc. 1995, 117, (15) Christinsen, O.; Koch, H.; Jørgensen, P. Chem. Phys. Lett. 1995, 243, 409. (16) Fleig, T. 2006, unpublished. (17) Hättig, C.; Weigend, F. J. Chem. Phys. 2000, 113, (18) Hättig, C.; Köhn, A. J. Chem. Phys. 2002, 117, (19) Hättig, C. J. Chem. Phys. 2003, 118, (20) Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H. Kölmel, C. Chem. Phys. Lett. 1989, 162, 165. (21) Schäfer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, (22) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, (23) Kendll, R. A.; Dunning, T. H., Jr.; Hrrison, R. J. J. Chem. Phys. 1992, 96, (24) Weigend, F.; Köhn, A.; Hättig, C. J. Chem. Phys. 2002, 116, (25) Weigend, F.; Häser, M.; Ptzelt, H.; Ahlrichs, R. Chem. Phys. Lett. 1998, 294, 143. (26) Schftenr, G.; Noordik, J. H. J. Comput. Aided Mol. Des. 2000, 14, 123.

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