DFT performance for the hole transfer parameters in DNA π stacks

DFT Performance for the Hole TransferParameters in DNA p Stacks

MARTIN FELIX,1 ALEXANDER A. VOITYUK1,2

1Institut de Quımica Computational, Departament de Quımica, Universitat de Girona,17071 Girona, Spain2Institucio Catalana de Recerca i Estudis Avancats, Barcelona 08010, Spain

Received 16 June 2009; accepted 9 July 2009Published online 15 December 2009 in Wiley Online Library (wileyonlinelibrary.com).DOI 10.1002/qua.22419

ABSTRACT: Recently, we showed that unoccupied Kohn-Sham (KS) orbitalsstemming from DFT calculations of a neutral system can be used to derive accurateestimates of the free energy and electronic couplings for excess electron transfer inDNA (Felix and Voityuk, J Phys Chem A 2008, 112, 9043). In this article, we considerthe propagation of radical cation states (hole transfer) through DNA p-stacks andcompare the performance of different exchange-correlation functionals to estimate thehole transfer (HT) parameters. Two different approaches are used: (1) calculations thatuse occupied KS orbitals of neutral p stacks of nucleobases, and (2) the time-dependentDFT method which is applied to the radical cation states of these stacks. Comparison ofthe calculated parameters with the reference data suggests that the best results areprovided by the KS scheme with hybrid functionals (B3LYP, PBE0, and BH&HLYP).The TD DFT approach gives significantly less accurate values of the HT parameters. Inagreement with high-level ab initio results, the KS scheme predicts that the hole in pstacks is confined to a single nucleobase; in contrast, the spin-unrestricted DFT methodconsiderably overestimates the hole delocalization in the radical cations. VC 2009 WileyPeriodicals, Inc. Int J Quantum Chem 111: 191–201, 2011

Key words: electron transfer; DFT calculation; DNA; electronic coupling; Kohn-Shamorbitals

Introduction

B ecause of the biological relevance andpotential use in nanotechnology, the hole

transfer (HT) process in DNA has attracted greatattention of both experimentalists and theoreti-cians [1, 2]. Many factors such as the structuraldisorder, conformational flexibility, dynamics ofcounter-ions, and water molecules, considerablyaffect the charge propagation making DNA a verychallenging HT system. Different computationalapproaches have been applied to understand themechanisms of the HT process [3, 4]. A number of

Correspondence to: A. A. Voityuk; e-mail: [email protected]

Additional Supporting Information may be found in theonline version of this article.

International Journal of Quantum Chemistry, Vol. 111, 191–201 (2011)VC 2009 Wiley Periodicals, Inc.

theoretical investigations of HT in DNA havebeen recently published [5–11].

The key parameters that control the efficiencyof HT are the donor–acceptor energy gap andelectronic coupling [12, 13]. Different approachesto calculate these parameters for DNA p-stackshave been recently reviewed [14]. Different quan-tum-chemical techniques have been used, rangingfrom efficient semiempirical [15–19] and SCC-DFTB schemes [20, 21], to Hartree–Fock [22–26]and DFT [27–33] and then to computationallyvery demanding CASPT2 [34, 35].

As the structural fluctuation of DNA and itsenvironment considerably affect the energetics[36] and donor–acceptor couplings [37, 38], com-putationally efficient methods should be used toaccount for these factors [5–8, 39]. It has beendemonstrated that the semiempirical INDO/Smethod performs well in calculations of the HTparameters, while the MNDO scheme and relatedapproaches (AM1, PM3, etc) considerably under-estimate the couplings [15]. INDO/S has beensuccessfully used to calculate the hole transfer pa-rameters over MD trajectories of DNA [6, 8–11,39].

A number of DFT calculations have been car-ried out to derive CT parameters for DNA pstacks [27–32]. It is well known that the electronicproperties computed by DFT essentially dependon the exchange-correlation functional used in thecalculation [40–42]. Recently, we showed thatquite accurate estimates of the parameters deter-mining the efficiency of excess electron transfer inDNA (migration of radical anion states) can bederived from unoccupied Kohn–Sham orbitals ofneutral systems [33]. The performance of DFTschemes for HT through DNA stacks, however,has not been considered so far. Recently, usingdifferent quantum chemical methods Huang andKertesz calculated the orbital splitting in the eth-ylene p dimer [43]. They found that Hartree–Fockand various forms of density functional theoryprovide very similar values. As we will see, thisresult does not hold for DNA p stacks.

Because the majority of the computational stud-ies on charge transport in DNA has been performedfor HT processes, an assessment of the performanceof different DFT functionals needs to be explored.We evaluate the performance of DFT schemes bycomparing the derived HT parameters with thoseobtained using the CASPT2 results for several DNAp-stacks [34]. As in our previous study [33], two dif-ferent approaches are used to calculate the elec-

tronic properties of the radical cation states. First,we describe the radical cation states of the p-stacksin terms of the occupied Kohn–Sham (KS) orbitalsand their eigenvalues computed for the correspond-ing neutral system. This approach has been provento be quite useful to study radical-cation states oforganic and biological molecules [44, 45]. Forinstance, reasonable estimates of the ionizationpotential of DNA bases were obtained [46, 47]. Thephysical meaning of the energies of the occupiedKS orbitals has been considered in a number ofpapers [48–53]. In particular, it has been shown thatthese energies correspond to approximate butrather accurate relaxed vertical ionization potentials[53].

The second approach is based on TD DFT calcu-lations of the ground and excited states of the radi-cal cation. In many cases, TD DFT offers a goodcompromise between the accuracy of the resultsand the size of treated systems [41, 54]. Thismethod has several known shortcomings, espe-cially when applied to charge-transfer excitations[54–57]. In particular, the incomplete cancellationof the electron self-interaction in odd-electron sys-tems often leads to considerable underestimationof excitation energies and artificial delocalizationof the unpaired electron [32, 58]. Several correctionschemes have been suggested to improve the accu-racy of TD DFT [59, 60].

In this article, we assess the performance of theKS and TD DFT models with different exchange-correlation functionals to compute the HT param-eters in DNA.

Computational Details

p-STACKS

We examine several one-strand B-DNA p stacksconsisting of two and three nucleobases. AmongDNA bases adenine (A), cytosine (C), guanine (G),and thymine (T), G is the most easily oxidized andplays the main role in HT through DNA [1–3].Therefore, we consider five dimers GG, GA, AG,GT, TG, and two trimers GAG and GTG containingone or two guanines. The mutual position of thenucleobases in the p stacks corresponds to thestructure of ideal B-DNA. Because electronic cou-pling is very sensitive to the arrangement of the do-nor and acceptor sites and even relatively smallstructural changes can lead to its considerable vari-ation, the DFT calculations were performed using

FELIX AND VOITYUK

192 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI 10.1002/qua VOL. 111, NO. 1

the same geometries as in the CASPT2 study (theCartesian coordinates of all p-stacks are given inthe Supporting Information [34]). By convention,the base sequence in the dimers and trimers is writ-ten in the 50 ! 30 direction.

ELECTRONIC COUPLINGS

Different schemes can be used to derive the do-nor-acceptor electronic couplings Vda [14, 27, 38,61–64]. The reference data [34] were obtained usingthe Generalized Mulliken–Hush (GMH) method[61, 62, 65]. For sake of consistency, we also usethis scheme to estimate electronic couplings fromKS and TD DFT calculations. Within GMH, theelectronic coupling is expressed via the vertical ex-citation energy DE12, the transition dipole momentl12 and the difference of the diabatic dipolemoments ld � laj j.

V ¼ DE12 l12j jld � laj j (1)

In turn, ld � laj j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðl11 � l22Þ2 þ 4l212

q, where

l11 and l22 are the dipole moments of the groundand excited states. Within the KS approach, DE12

is estimated as a difference of the HOMO andHOMO-1 orbital energies calculated for the neu-tral stack (close-shell system); the difference of theadiabatic dipole moments l11 � l22 and the tran-sition moment l12 can be estimated as

l1 � l2

¼XM

i;j¼1

Ci;HOMOCj;HOMO � Ci;HOMO�1Cj;HOMO�1

� �dij

(2)

l12 ¼ �XM

i;j¼1

Ci;HOMOCj;HOMO�1dij: (3)

Here, dij are the matrix elements of the dipoleoperator defined for AOs i and j.

Alternatively, the TD DFT method can beapplied to a radical cation (open-shell system)consisting of the stacked nucleobases. In this case,DE12, l11, l22, and l12 are calculated directly andlisted in the output of the Gaussian03 program[66]. In the p-stacks, two adiabatic states are ofinterest: the ground and the lowest CT excitedstates. The calculated first excited state of the rad-ical cations often but not always correspond tothe HT state. To estimate the HT parameters cor-

rectly, the character of several low-lying excitedstates of the radical cation has to be explored. Inthe GAG and GTG stacks, the multistate effectsare important [67], and therefore, three-statemodel was applied.

CHARGE DISTRIBUTION

Within the KS approach, the hole charge distri-bution in the radical cation may be derived fromthe corresponding KS orbitals calculated for theneutral stack. For instance, the hole charge on frag-ment F in the ground state of the radical cation iscalculated from HOMO of the neutral system

q Fð Þ ¼Xi2F

Ci;HOMO

XN

j¼1

Cj;HOMOSij (4)

Here, Sij is the overlap of atomic orbitals i and j; iruns over AOs of the fragment F and j over allAO of the system. Similarly, the hole charge dis-tribution in the excited state of the radical cationcan be derived by using coefficients of HOMO-1(or lower occupied orbitals).

QUANTUM CHEMICAL CALCULATIONS

Within the KS approach, we obtained the HTparameters for nonhybrid functionals SVWN [68],BLYP, BP86, and PBE [69–72], and hybrid func-tionals B3LYP, PBE0, and BH&HLYP [73–77]. TDDFT calculations were performed using PBE,PBE0, B3LYP BH&HLYP. Additionally, we per-form KS and TD DFT calculations with a newlydeveloped M05-2X functional [78]. All the calcula-tions were carried out by using the programGaussian03 [66]. We note that PBE and PBE0 showgood performance in the calculation of excitedstates of organic chromophores [41] and providereasonable description of excited states of stackednucleobases [79]; the B3LYP was successfullyapplied to excited states of nucleobases [80].Throughout this study, we used the standard ba-sis set 6-31G*; some additional calculations werecarried out including diffuse function on heavyatoms (6-31þG* basis set).

Results and Discussion

GG STACK

Let us consider the 50-GG-30 stack. The mutualposition of guanines in the stack is shown in

HOLE TRANSFER PARAMETERS IN DNA p STACKS

VOL. 111, NO. 1 DOI 10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 193

Figure 1. This dimer is often used as a hole trap inDNA stacks [1, 2]. According to the CASPT2 cal-culation [34], in the ground state of the radical cat-ion, the hole is localized on the nucleobase 50-G,whereas in the excited state, it is confined to G-30.Thus, the states GþG and GGþ with a hole on thefirst and second G represent the initial and finalstates for HT. The computed data are listed inTable I and shown in Figure 2. The excitation energyDE12 is closely related to the difference of diabatic-state energies Dda and the electronic coupling V.Within the two-state model, DE2

12 ¼ D2da þ 4V2.

As can be seen (Table I), the HF method overes-timates DE12 by 20%, whereas the DFT calculationsprovide more accurate values. DE12 derived withother nonhybrid functionals is in good agreementwith the reference value: the SVWN deviation isonly 4%, and the PBE and BP86 energies (0.402 and

0.407 eV) are also very close to the reference value(0.392 eV). Good agreement is provided by theBLYP functional while this scheme is not veryaccurate when predicting ionization energies [40].Somewhat Higher deviations are found for thehybrid functionals. B3LYP and PBE0 overestimateDE12 by about 6%, whereas BH&HLYP by 11%.M05-2X overestimates slightly the reference databy 10%. The deviations increase with a contribu-tion of the HF exchange included in the functional(PBE0, B3LYP, and BH&HLYP, M05-2X include 20,25, and 50, 56% of the HF exchange).

The donor–acceptor coupling V is considerably(62%) overestimated by HF, whereas DFT resultsare more accurate. The SVWN value differs fromthe reference by 33%, the PBE and BLYP devia-tions are about 25%. As expected, including theHF exchange in to DFT leads to further overesti-mation of the coupling value; deviations of B3LYPand PBE0 are about 40%, while the BH&HLYPand M05-2X errors are about 60%.

The hole charge distribution in a stack is animportant feature which determines the mecha-nism of HT. As already mentioned, the high-levelcalculations [34] of the dimer suggest that thehole is almost completely localized on the 50-Gsite in the ground state and on 30-G in the excitedstate of (GG)þ. Both the HF (within Koopmans’approximation) and the KS DFT calculations pre-dict the charge distribution to be in good agree-ment with the CASPT2 data (see Table I). How-ever, spin-unrestricted (SU) DFT calculations ofthe radical cation overestimate the charge delocal-ization significantly. For example, SU B3LYP

FIGURE 1. Arrangement of adjacent guaninenucleobases in the GG p-stack. [Color figure can beviewed in the online issue, which is available atwileyonlinelibrary.com.]

FIGURE 2. Excitation energy (DE) and electronic coupling (V) calculated using different DFT functionals. 1 and 2correspond to the first and second excitation energy in the GAG and GTG. [Color figure can be viewed in the onlineissue, which is available at wileyonlinelibrary.com.]

FELIX AND VOITYUK


predicts the hole to be spread over subunits (0.62and 0.38). PBE0 and B3LYP provide similar holedistributions in the p-stack. BH&HLYP and M05-2X provide better results (0.88 and 0.12; 0.96 and0.04), because both include 50 and 56% percent-age of the exact exchange. Thus, the hole distri-bution in the radical cation derived from the KScalculations of the neutral GG stack is in muchbetter agreement with the reference data than theresults of the SU DFT calculation of the radicalcation. The higher percentage of the exactexchange in the functional the better agreement isfound with reference data.

GTG TRIMER

In this system, hole transfer between donorand acceptor (guanine nucleobases) is mediatedby a bridging nucleobase (thymine). As shownpreviously [67], in addition to the donor andacceptor states where a hole is localized on gua-nines, a state with the hole on the bridging unitshould be treated. The HT parameters calculatedfor this stack are compared in Tables II and IIIand shown in Figure 2. In the radical cation, the

excitation energies DE12 and DE13 are referred tothe adiabatic transitions between the donor andacceptor (DE12) and the donor and bridge (DE13).All the methods including HF exchange provideaccurate estimates of DE12 (the largest deviationof 6% is found for HF). However, DE13 is not well

TABLE IIExcitation energies DE12 and DE13 and electroniccouplings V calculated for the GTG trimer.

Method DE12 DE13 Vda Vdb Vba

CASSCF [35] 0.178 1.239 0.007 0.078 0.082HF 0.188 1.249 0.017 0.126 0.092SVWN 0.186 0.631 0.021 0.079 0.073PBE 0.184 0.655 0.018 0.075 0.072BP86 0.185 0.658 0.018 0.069 0.075BLYP 0.178 0.678 0.017 0.071 0.074B3LYP 0.179 0.771 0.017 0.089 0.075PBE0 0.186 0.774 0.019 0.092 0.076BH&HLYP 0.180 0.939 0.018 0.103 0.083M05-2X 0.188 0.882 0.008 0.114 0.083

All data are in eV.

TABLE IExcitation energy DE12, electronic coupling (V), and hole charge distribution in the 50-GG-30 calculated by usingdifferent DFT functionals.a

Method DE12 V

Ground state Excited state

Q(G1) Q(G2) Q(G1) Q(G2)

CASPT2 [35] 0.392 0.051 0.976 0.024 0.025 0.975HF 0.472 0.083 HOMO 0.965 0.035 0.040 0.960

UHF 0.980 0.020SVWN 0.409 0.068 HOMO 0.969 0.031 0.043 0.957

SU 0.578 0.422PBE 0.402 0.064 HOMO 0.969 0.031 0.040 0.960

SU 0.577 0.423BP86 0.407 0.065 HOMO 0.967 0.033 0.040 0.960

SU 0.574 0.426BLYP 0.398 0.064 HOMO 0.969 0.031 0.040 0.960

SU 0.575 0.425B3LYP 0.413 0.070 HOMO 0.968 0.032 0.041 0.959

SU 0.615 0.385PBE0 0.417 0.072 HOMO 0.967 0.033 0.041 0.959

SU 0.633 0.367BH&HLYP 0.435 0.077 HOMO 0.965 0.035 0.041 0.959

SU 0.884 0.116M05-2X 0.433 0.082 HOMO 0.960 0.040 0.047 0.953

SU 0.806 0.194

aHF and DFT calculations of the neutral systems were carried out by using the 6-31G* basis set.All data are in eV.



reproduced by KS DFT, whereas the HF estimateis in good agreement with the CASSCF value. Asseen from Table II, the nonhybrid functionalsunderestimate DE13 significantly, for example, thePBE and BP86 deviations are �50%. The hybridfunctionals perform better (deviation of ca. 40% isfound for B3LYP and PBE0, 24% for BH&HLYP).We note that the reference energy DE13 is prob-ably somewhat overestimated because the effectsof dynamic electron correlation are not taken intoaccount in the CASSCF calculation.

In the donor bridge-acceptor system GTG,three electronic couplings (Vda, Vdb, Vba) are to bedetermined. Within the KS approach, all the func-tionals can satisfactorily reproduce the couplingsbetween the adjacent bases Vdb and Vba (Table II).HF overestimates while the nonhybrid functionalsunderestimate these matrix elements. As expectedin such situations, the hybrid functionals providerather accurate data. For instance, the B3LYPdeviations are within 14%. As to the matrix ele-ment Vda, both the HF and DFT provide signifi-cantly stronger coupling than CASSCF.

Hole charge distribution in (GTG)þ is shown inTable III. CASSCF predicts that the hole is mostlylocalized on 50-G in the ground state, on 30G in

the first excited state, and on the T bridge in thesecond excited state which is about 1 eV higherthan the ground state. As seen, the KS schemadescribes the hole distribution properly. By con-trast, the spin-unrestricted DFT calculations of theradical cation significantly overestimate delocali-zation of the hole (Table III).

STATISTICAL EVALUATION

Now we consider the results obtained for allsystems (dimers GG, GA, AG, GT, and TG, andtrimers and GAG and GTG). Detailed data foreach system are provided in the Supportinginformation.

ADIABATIC SPLITTING

The calculated excitation energies are listed inTable IV. The reference DE values change from 0.12to 1.24 eV covering the whole range of the HT ener-getics in DNA. Note that crude values of DE12 indimers may be derived from the ionization poten-tials (IPs) of isolated nucleobases. ExperimentalIPs of G, A, and T in the gas phase are 7.77, 8.26,and 8.87 eV, respectively [47]. Neglecting the elec-trostatic and stacking interactions between

TABLE IIIHole charge distribution in the p stacks derived from the CAS(11,12), KS-DFT, and spin-unrestricted (SU) DFTcalculations of radical GTG cation.

Method

Ground state Excited state 1 Excited state 2

Q(G1) Q(T) Q(G2) Q(G1) Q(T) Q(G2) Q(G1) Q(T) Q(G2)

CAS(11,12) 0.991 0.006 0.003 0.006 0.000 0.994 0.016 0.974 0.010HF HOMO 0.982 0.017 0.001 0.002 0.008 0.090 0.021 0.972 0.008

UHF 0.456 0.009 0.535SVWN HOMO 0.963 0.035 0.002 0.004 0.028 0.968 0.033 0.907 0.059

SU 0.427 0.128 0.445PBE HOMO 0.970 0.029 0.001 0.003 0.025 0.972 0.0028 0.909 0.063

SU 0.050 0.046 0.904BP86 HOMO 0.969 0.029 0.001 0.003 0.025 0.972 0.027 0.856 0.117

SU 0.467 0.117 0.416BLYP HOMO 0.972 0.027 0.001 0.003 0.022 0.975 0.027 0.884 0.089

SU 0.837 0.116 0.047B3LYP HOMO 0.974 0.025 0.001 0.002 0.017 0.981 0.026 0.958 0.017

SU 0.503 0.072 0.425PBE0 HOMO 0.973 0.025 0.001 0.002 0.017 0.980 0.026 0.957 0.017

SU 0.517 0.042 0.441BH&HLYP HOMO 0.978 0.021 0.001 0.002 0.012 0.986 0.023 0.965 0.012

SU 0.612 0.039 0.349M05-2X HOMO 0.972 0.026 0.002 0.003 0.015 0.982 0.027 0.958 0.015

SU 0.613 0.041 0.346

FELIX AND VOITYUK


nucleobases, one can infer from these data thatDE12 should be zero in GG, 0.49 in GA and AG,1.10 eV in GT and TG. Such estimations are some-times used when considering HT in DNA. The cal-culations of XY and YX stacks show, however, thatDE12 is quite different in the related dimers (TableIV). For instance, DE12 in GA is found to be twiceas large as in AG. Also, there is a remarkable differ-ence in DE12 of GT and TG. The effects of adjacentnucleobases on hole transfer energetics in DNAhave been systematically discussed elsewhere [81].

As can be seen from Figure 2, the KS approachwith different functionals gives acceptable valuesof DE12. All the methods slightly underestimatethe reference energy in GA. Relatively large devi-ations (�12%) are found for the nonhybrid func-tionals. More accurate data are obtained using thehybrid functionals; for example, the BH&HLYPdeviation is only 3%. Also for other systemsincluding trimers, the hybrid functionals show abetter performance when compared with nonhy-brid functionals. The mean absolute deviations(MAD) are in the range of 0.07–0.19 eV (25–47%,see Table IV). The most accurate values of theadiabatic splitting are obtained using BH&HLYP(MAD ¼ 0.07 eV). PBE0, B3LYP (MAD � 0.10eV), and M05-2X (MAD ¼ 0.09 eV) provide lessaccurate estimates.

Electronic Coupling

The calculated data are listed in Table V andshown in Figure 2. As can be seen, in most cases,

the DFT calculations overestimate the referencevalues. The mean absolute deviations are in therange of 0.016–0.031 eV (20–44%, see Table V).Larger deviations are given by the hybrid func-tionals. Overall, the electronic couplings calcu-lated with the KS scheme are in better agreementwith the benchmark results than the HF values.

Hole Charge Distribution

Table VI compares the excess charge distribu-tions derived from the KS [see Eq. (5)] and spin-unrestricted (SU) DFT calculations. As seen, theKS DFT results based on the calculation of neutralsystems can well reproduce the CASSCF chargedistribution in the corresponding radical cations.In XG and GX stacks, a hole is almost completelylocalized on G. The most accurate description isprovided by the hybrid and M05-2X functionals.SU DFT calculations overestimate the hole deloc-alization considerably. As already discussed inthe literature, this deficiency of DFT may bereduced by using long-range corrections [82].

Time-Dependent DFT Calculations

The electronic excitation energy DE12, transitiondipole moment l12, and the change of the dipolemoment by the HT process in a p stack can bedirectly calculated using TD DFT calculations ofthe radical cation. These quantities are required toestimate the coupling matrix element [see Eq. (1)].We carried out TD DFT calculations of the GG,

TABLE IVComparison of HT energy (in eV) calculated by using KS orbitals of neutral systemsa with MS-PT2 results forthe radical cations.

p-stack HF SVWN PBE BP86 BLYP B3LYP PBE0 BH&HLYP M05-2X CASPT2 [35]

GG 0.472 0.409 0.402 0.407 0.398 0.413 0.417 0.435 0.433 0.392GA 0.551 0.490 0.499 0.496 0.493 0.519 0.524 0.544 0.539 0.560AG 0.190 0.211 0.223 0.220 0.220 0.228 0.231 0.226 0.234 0.340GT 1.574 0.906 0.930 0.935 0.952 1.059 1.067 1.241 1.178 1.175TG 1.135 0.494 1.438 0.529 0.551 0.649 0.652 0.821 0.751 0.797GAG DE12 0.185 0.152 0.147 0.149 0.146 0.155 0.158 0.167 0.169 0.118DE13 0.344 0.303 0.307 0.304 0.310 0.328 0.328 0.347 0.346 0.345GTG DE12 0.188 0.186 0.184 0.185 0.178 0.179 0.186 0.180 0.188 0.178DE13 1.249 0.631 0.655 0.658 0.678 0.771 0.774 0.939 0.882 1.239MDb 0.083 �0.151 �0.039 �0.140 �0.135 �0.094 �0.089 �0.027 �0.081MADb 0.118 0.164 0.192 0.152 0.143 0.107 0.106 0.070 0.096MAD (%) 41.2 42.0 47.0 38.7 35.6 29.7 30.6 24.7 25.9

a All calculations were performed with 6-31G* basis set.b Statistical evaluation: mean deviation, MD; mean absolute deviation, MAD.



TABLE VComparison of electronic couplings (in eV) calculated by DFT on the basis of KS orbitals of neutral systemswith MS-PT2 results obtained for the corresponding radical cations.a

p-stack HF SVWN PBE BP86 BLYP B3LYP PBE0 BH&HLYP M05-2X CASPT2 [35]

GG 0.083 0.068 0.064 0.065 0.064 0.070 0.072 0.077 0.082 0.051GA 0.089 0.071 0.066 0.077 0.068 0.073 0.075 0.081 0.089 0.036AG 0.049 0.019 0.019 0.020 0.019 0.026 0.027 0.035 0.032 0.044GT 0.137 0.110 0.093 0.092 0.089 0.101 0.104 0.115 0.121 0.081TG 0.085 0.056 0.030 0.058 0.060 0.070 0.071 0.077 0.079 0.060GAG

GA 0.059 0.067 0.066 0.063 0.062 0.067 0.069 0.069 0.087 0.036AG 0.041 0.014 0.015 0.015 0.015 0.021 0.022 0.030 0.028 0.052GG 0.037 0.015 0.009 0.014 0.014 0.019 0.020 0.025 0.016 0.021

GTGGT 0.126 0.079 0.075 0.075 0.071 0.089 0.092 0.103 0.114 0.078TG 0.092 0.073 0.072 0.070 0.074 0.075 0.076 0.083 0.083 0.082GG 0.017 0.021 0.018 0.018 0.017 0.017 0.019 0.018 0.008 0.007

MDb 0.034 0.010 0.000 0.008 0.006 0.014 0.015 0.023 0.026MADb 0.034 0.022 0.022 0.018 0.016 0.021 0.022 0.026 0.031MAD (%) 66.4 33.7 32.4 22.5 20.4 28.8 30.9 36.7 43.7

aUsing 6-31G* basis set.b Statistical evaluation for dimers: mean deviation, MD; mean absolute deviation, MAD.

TABLE VIHole distribution in p stacks derived from the KSa and spin unrestricted (SU) DFT calculations.a

Method

AA GA AG GT TG

Q(A) Q(A) Q(G) Q(A) Q(A) Q(G) Q(G) Q(T) Q(T) Q(G)

CASSCF [35] 0.010 0.990 0.992 0.008 0.024 0.976 0.992 0.008 0.008 0.992HF HOMO 0.186 0.814 0.971 0.029 0.075 0.925 0.988 0.012 0.008 0.992

UHF 0.018 0.982 0.982 0.018 0.016 0.984 0.984 0.016 0.009 0.991SVWN HOMO 0.027 0.973 0.975 0.025 0.013 0.987 0.983 0.017 0.024 0.976

SU 0.004 0.996 0.608 0.392 0.448 0.552 0.722 0.278 0.388 0.612PBE HOMO 0.023 0.977 0.979 0.021 0.012 0.988 0.983 0.017 0.021 0.979

SU 0.429 0.571 0.615 0.385 0.429 0.571 0.721 0.279 0.370 0.630BP86 HOMO 0.020 0.980 0.978 0.022 0.013 0.987 0.981 0.019 0.020 0.980

SU 0.030 0.970 0.615 0.385 0.436 0.564 0.708 0.292 0.374 0.626BLYP HOMO 0.021 0.979 0.979 0.021 0.013 0.987 0.984 0.016 0.019 0.981

SU 0.510 0.490 0.617 0.383 0.439 0.561 0.729 0.271 0.373 0.627B3LYP HOMO 0.007 0.993 0.977 0.023 0.017 0.983 0.985 0.015 0.015 0.985

SU 0.525 0.475 0.662 0.338 0.413 0.587 0.826 0.174 0.304 0.696PBE0 HOMO 0.007 0.993 0.976 0.024 0.018 0.982 0.985 0.015 0.015 0.985

SU 0.470 0.530 0.686 0.314 0.398 0.602 0.860 0.140 0.283 0.717BH&HLYP HOMO 0.334 0.966 0.975 0.025 0.029 0.971 0.986 0.014 0.011 0.989

SU 0.584 0.416 0.927 0.073 0.187 0.813 0.970 0.030 0.027 0.973M052X HOMO 0.012 0.988 0.969 0.031 0.023 0.977 0.984 0.016 0.014 0.986

SU 0.445 0.555 0.858 0.142 0.243 0.757 0.960 0.040 0.053 0.947

a The calculations were performed by using 6-31G* basis set.

FELIX AND VOITYUK


GA, AG, GT, and TG stacks using PBE, PBE0,B3LYP and BH&HLYP and M05-2X functionalsand the 6-31G* basis set (Table VII). The dataobtained with the 6-31þG* basis set are collectedin Table S8 of the Supporting Information. As canbe seen from Figure 3, TD DFT considerablyunderestimates DE12 in TG and especially in GT.More accurate energies are obtained for otherdimers (GG, GA, and AG).

The estimated electronic couplings are in rea-sonable agreement with the reference data (TableVII). Because the transition dipole momentsdepend significantly on the exchange-correlationfunctional, the derived couplings are quite sensi-tive to the DFT scheme. As seen from Figure 3,the best results are provided by BH&HLYP(MAD ¼ 30%). PBE, PBE0, and B3LYP give lessaccurate coupling values. Including diffuse func-tions (6-31G* ! 6-31þG*) does not practicallyaffect the calculated excitation energies whileleads to some variations in the electronic cou-plings (see Fig. 3). Overall, the quality of the HTparameters remains unchanged, and the diffusefunctions can be excluded from the basis.

From Figure 3, one can conclude that inde-pendent of the functional, the KS estimates are inbetter agreement with the CASPT2 results thanthe data derived from TD DFT. Because both theCASPT2 and TD DFT calculations are carried outfor radical cation states, the better performance ofthe KS scheme, which is based on the calculation

of neutral systems, appears quite unexpected.Obviously, the fortunate compensation of errorswithin the KS approach leads to its very goodperformance and offers a pragmatic way to calcu-late the HT parameters.

Conclusions

The DFT method has been used to calculatedifferent electron transfer reactions including holetransfer in DNA. We have compared the perform-ance of the Kohn-Sham and TD DFT approachesto estimate the energetics and electronic couplingsfor the hole migration in DNA p stacks. SevenDFT schemes, SVWN, three GGA (PBE, BP86 andBLYP), and four hybrid functionals (PBE0, B3LYP,BH&HLYP, and M05-2X) have been tested. Thecalculated HT parameters have been comparedwith the reference data derived from CASPT2 cal-culations [34].

We found that independent of the exchange-correlation functional used in the calculation, theKohn-Sham approach provides better estimationof HT parameters and hole distribution than TDDFT. The BH&HLYP and M05-2X functionals(with 50% of the HF exact exchange) show thebest performance. The hybrid functionals PBE0and B3LYP with smaller portions of the HFexchange give less satisfactory results.

TABLE VIIComparison of excitation energy (DE12) and electronic coupling (V) estimated by TD DFT of the radical cation.

DE12 (eV) V (eV)

p-stack PBE PBE0 B3LYP BH&HLYP M05-2X CASPT2 PBE PBE0 B3LYP BH&HLYP M05-2X CASPT2

GG 0.413 0.430 0.457 0.285 0.296 0.392 0.024 0.096 0.104 0.066 0.081 0.051GA 0.364 0.436 0.462 0.386 0.347 0.560 0.012 0.062 0.105 0.067 0.083 0.036AG 0.279 0.259 0.273 0.165 0.172 0.340 0.041 0.019 0.049 0.039 0.043 0.044GT 0.101 0.513 0.533 1.081 0.893 1.175 0.0015 0.097 0.113 0.094 0.100 0.081TG 0.150 0.463 0.491 0.523 0.404 0.797 4.4E-4 0.084 0.105 0.068 0.075 0.060

MDa �0.391 �0.233 �0.210 �0.165 �0.230 �0.039 0.017 0.041 0.012 0.022MADa 0.399 0.248 0.236 0.165 0.230 0.039 0.027 0.041 0.014 0.022MAD (%) 46.2 30.8 29.4 30.4 37.0 64.8 55.4 84.3 31.3 48.0

a Statistical evaluation: mean deviation, MD; mean absolute deviation, MAD.

The calculations presented were carried out for PBE, PBE0, B3LYP, BH&HLYP, and M05-2X functionals, and using 6-31G*basis set.



We note that within the KS approach, the holedistribution in the ground and excited states of aradical cation is derived from HOMO andHOMO-k of a neutral stack. These data correctlyreproduce the excess charge localization found

using CASPT2. In all p stacks considered in thearticle, the hole is confined to a single nucleobase.By contrast, the spin-unrestricted DFT calculationsof the radical cations overestimate the delocaliza-tion of the excess charge.

Thus, the KS model which is computationallymuch less expensive than TD DFT can be used togain quite accurate estimates of the HT energetics,electronic couplings, and hole distribution inDNA p stacks. This approach should also providea reliable description of hole transfer in organicmaterials.

References

1. Schuster, G. B., Ed. Topics in Current Chemistry; Springer:Berlin, 2004; Vols. 236, 237.

2. Wagenknecht, H.-A., Ed. Charge Transfer in DNA; Wiley-VCH: Weinheim, 2005.

3. Berlin, Y. A.; Kurnikov, I. V.; Beratan, D. N.; Ratner, M. A.;Burin, A. L. Top Curr Chem 2004, 237, 1.

4. A. A. Voityuk, In Computational Studies of RNA andDNA, Sponer, J.; Lankas, F., Eds.; Springer: Dordrecht,2006; pp 485–512.

5. Berlin, Y. A.; Grozema, F. C.; Siebbeles, L. D. A.; Ratner,M. A. J Phys Chem C 2008, 112, 10988.

6. Siriwong, K.; Voityuk, A. A. J Phys Chem B 2008, 112, 8181.

7. Kubar, T.; Elstner, M. J Phys Chem B 2008, 112, 8788.

8. Hatcher, E.; Balaeff, A.; Keinan, S.; Venkatramani, R.;Beratan, D. N. J Am Chem Soc 2008, 130, 11752.

9. Woiczikowski, P. B.; Kubar, T.; Gutierrez, R.; Caetano,R. A.; Cuniberti, G.; Elstner, M. J Chem Phys 2009, 130,215104.

10. Mantz, Y. A.; Gervasio, F. L.; Laino, T.; Parrinello, M. PhysRev Lett 2007, 99, 58104.

11. Paul, A.; Bezer, S.; Venkatramani, R.; Kocsis, L.; Wierzbin-ski, E.; Balaeff, A.; Keinan, S.; Beratan, D. N.; Achim, C.;Waldeck, D. H. J Am Chem Soc 2009, 131, 6498.

12. Marcus, R. A.; Sutin, N. Biochim Biophys Acta 1985, 811,265.

13. Newton, M. D. Chem Rev 1991, 91, 767.

14. Rosch, N.; Voityuk, A. A. Top Curr Chem 2004, 237, 37.

15. Voityuk, A. A. Chem Phys Lett 2006, 427, 177.

16. Beljonne, D.; Pourtois, G.; Ratner, M. A.; Bredas, J. L. J AmChem Soc 2003, 125, 14510.

17. Voityuk, A. A. J Chem Phys 2005, 122, 204904.

18. Reha, D.; Barford, W.; Harris, S. Phys Chem Chem Phys2008, 10, 5436.

19. Hatcher, E.; Balaeff, A.; Keinan, S.; Venkatramani, R.;Beratan, D. N. J Am Chem Soc 2008, 130, 11752.

20. Kubar, T.; Woiczikowski, P. B.; Cuniberti, G.; Elstner, M.J Phys Chem B 2008, 112, 7937.

21. Gutierrez, R.; Caetano, R. A.; Woiczikowski, P. B.; Kubar, T.;Elstner, M. J.; Cuniberti, G. Phys Rev Lett 2009, 102, 208102.

FIGURE 3. Comparison of excitation energies (DE)and electronic couplings calculated using TD DFT, KSDFT and CASPT2 methods. The HT parameters are cal-culated with the PBE, PBE0, B3LYP, and BH&HLYPfunctionals. 6-31G* and 6-31þG* basis sets wereemployed for TD DFT (TD and TDþ, respectively).[Color figure can be viewed in the online issue, which isavailable at wileyonlinelibrary.com.]

FELIX AND VOITYUK


22. Voityuk, A. A.; Rosch, N. J Phys Chem B 2002, 106, 3013.

23. Olofsson, J.; Larsson, S. J Phys Chem B 2001, 105, 10398.

24. Voityuk, A. A.; Bixon, M.; Jortner, J.; Rosch, N. J ChemPhys 2001, 114, 5614.

25. Lipparini, F.; Mennucci, B. J Chem Phys 2007, 127, 144706.

26. Tong, G. S. M.; Kurnikov, I. V.; Beratan, D. N. J PhysChem B 2002, 106, 2381.

27. Senthilkumar, K.; Grozema, F. C.; Guerra, C. F.; Bickel-haupt, F. M.; Lewis, F. D.; Berlin, Y. A.; Ratner, M. A.;Siebbeles, L. D. A. J Am Chem Soc 2005, 127, 14894.

28. Grozema, F. C.; Siebbeles, L. D. A.; Berlin, Y. A.; Ratner,M. A. Chem Phys Chem 2002, 3, 536.

29. Grozema, F. C.; Tonzani, S.; Berlin, Y. A.; Schatz, G. C.; Sieb-beles, L. D.; Ratner, M. A. J Am Chem Soc 2008, 130, 5157.

30. Kummar, A.; Sevilla, M. D. J Phys Chem B 2006, 110,24181.

31. Adhikary, A.; Kumar, A.; Sevilla, M. D. Radiat Res 2006,165, 479.

32. Mantz, Y. A.; Gervasio, F. L.; Laino, T.; Parrinello, M.J Phys Chem A 2007, 111, 105.

33. Felix, M.; Voityuk, A. A. J Phys Chem A 2008, 112, 9043.

34. Blancafort, L.; Voityuk, A. A. J Phys Chem A 2006, 110,6426.

35. Blancafort, L.; Voityuk, A. A. J Phys ChemA 2007, 111, 4714.

36. Voityuk, A. A.; Siriwong, K.; Rosch, N. Angew Chem IntEd 2004, 43, 624.

37. Voityuk, A. A.; Siriwong, K.; Rosch, N. Phys Chem ChemPhys 2001, 3, 5421.

38. Troisi, A.; Orlandi, G. J Phys Chem B 2002, 106, 2093.

39. Voityuk, A. A. J Chem Phys 2008, 128, 115101.

40. Zhang, G.; Musgrave, C. B. J Phys ChemA 2007, 111, 1554.

41. Jacquemin, D.; Perpete, E. A.; Scuseria, G. E.; Ciofini, I.;Adamo, C. J. J Chem Theory Comput 2008, 4, 123.

42. Kohn, W.; Becke, A. D.; Parr, R. G. J Phys Chem 1996, 100,12974.

43. Huang, J.; Kertesz, M. J Chem Phys 2005, 122, 234707.

44. Dreuw, A.; Head-Gordon, M. Chem Rev 2005, 105, 4009.

45. Wu, Q.; Van Voorhis, T. J Chem Theory Comput 2006, 2, 765.

46. Close, D. M. J Phys Chem A 2004, 108, 10376.

47. Crespo-Hernandez, C. E.; Close, D. M.; Gorb, L.; Leszczyn-ski, J. J Phys Chem B 2007, 111, 5386.

48. Perdew, J. P.; Parr, R. G.; Levy, M.; Balduz, J. L. Phys RevLett 1982, 49, 1691.

49. Almbladh, C.-O.; von Barth, U. Phys Rev B 1985, 31, 3231.

50. Janak, J. F. Phys Rev B 1978, 18, 7165.

51. Tozer, D. J.; Handy, N. C. J Chem Phys 1998, 108, 2545.

52. Baerends, E. J.; Gritsenko, O. V. J Phys ChemA 1997, 101, 5383.

53. Chong, D. P.; Gritsenko, O. V.; Baerends, E. J. J Chem Phys2002, 116, 1760.

54. S. Grimme. Reviews in Computational Chemistry; Lipko-witz, K. B.; Larter, R.; Cundari, T. R. Eds.; Wiley-VCH: Ber-lin, 2004; p 153.

55. Dreuw, A.; Weisman, J. L.; Head-Gordon, M. J Chem Phys2003, 119, 2943.

56. Dreuw, A.; Fleming, G. R.; Head-Gordon, M. J Phys ChemB 2003, 107, 6500.

57. Dreuw, A.; Dunietz, B. D.; Head-Gordon, M. J Am ChemSoc 2002, 124, 12070.

58. Cohen, A. J.; Mori-Sanchez, P.; Yang, W. Science 2008, 321,792.

59. Dreuw, A.; Head-Gordon, M. J Am Chem Soc 2004, 126,4007.

60. VandeVondele, J.; Sprik, M. Phys Chem Chem Phys 2005,7, 1363.

61. Cave, R. J.; Newton, M. D. J Chem Phys 1997, 106, 9213.

62. Cave, R. J.; Newton, M. D. Chem Phys Lett 1996, 249, 15.

63. Voityuk, A. A.; Rosch, N. J Chem Phys 2002, 117, 5607.

64. Voityuk, A. A. Chem Phys Lett 2008, 451, 153.

65. Lappe, J.; Cave, R. J.; Newton, M. D.; Rostov, I. J PhysChem B 2005, 109, 6610.

66. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.;Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.;Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi,M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.;Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.;Kiene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.;Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.;Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski,J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador,P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.;Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.;Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.;Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov,B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C.Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; John-son, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A.Gaussian 03; Gaussian, Inc.: Pittsburgh PA, 2003.

67. Voityuk, A. A. J Phys Chem B 2005, 109, 17917.

68. Vosko, S. H.; Wilk, L.; Nusair, M. Can J Phys 1980, 58, 1200.

69. Becke, A. D. Phys Rev A 1988, 38, 3098.

70. Lee, C.; Yang, W.; Parr, R. G. Phys Rev B 1988, 37, 785.

71. Perdew, J. P. Phys Rev B 1986, 33, 8822.

72. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys Rev Lett 1996,77, 3865.

73. Handy, N. C.; Cohen, A. J Mol Phys 2001, 99, 403.

74. Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M.J. J Phys Chem 1994, 98, 11623.

75. Hoe, W. M.; Cohen, A. J.; Handy, N. C. Chem Phys Lett2001, 341, 319.

76. Adamo, C.; Barone, V. J Chem Phys 1999, 110, 6158.

77. Ernzerhof, M.; Scuseria, G. E. J Chem Phys 1999, 110, 5029.

78. Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J Chem TheoryComput 2006, 2, 364.

79. Santoro, F.; Barone, V.; Improta, R. J Comput Chem 2008,29, 957.

80. Varsano, D.; Di Felice, R.; Marques, M. A. L.; Rubio, A.J Phys Chem B 2006, 110, 7129.

81. Voityuk, A. A.; Jortner, J.; Bixon, M.; Rosch, N. Chem PhysLett 2000, 324, 430.

82. Mantz, Y. A.; Gervasio, F. L.; Laino, T.; Parrinello, M.J Phys Chem A 2007, 111, 105.



Documents

DFT performance for the hole transfer parameters in DNA π stacks