Computational and Theoretical Chemistry 1043 (2014) 31–37

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Computational and Theoretical Chemistry

journal homepage: www.elsevier .com/locate /comptc

Possibility of distinguishing DNA bases and of tracking the keto–enoltautomerism by using high-order harmonic generation

http://dx.doi.org/10.1016/j.comptc.2014.05.0112210-271X/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +84 937671182.E-mail address: tynn@hcmup.edu.vn (N.-T. Nguyen).

Van-Hung Hoang, Cam-Tu Le, Ngoc-Ty Nguyen ⇑, Van-Hoang LeDepartment of Physics, Ho Chi Minh City University of Pedagogy, 280, An Duong Vuong Street, District 5, Ho Chi Minh City, Vietnam

a r t i c l e i n f o

Article history:Received 31 March 2014Received in revised form 20 May 2014Accepted 21 May 2014Available online 2 June 2014

Keywords:Keto–enol tautomerismDNA basesHigh-order harmonic generationUltrashort laser pulses

a b s t r a c t

We point out the possibility to distinguish the DNA bases (adenine, cytosine, guanine and thymine) byusing the high-order harmonics sources. Moreover, we find the intensity peaks of the high-order harmon-ics emitted by thymine base while this molecule is near the stable states (keto and enol) as well as at thetransition state along the chemical reaction path of a tautomerism. This finding shows the possibility oftracking the DNA tautomerism. Our investigation is based on the simulation method. The structures offour DNA bases and the keto–enol tautomerism of thymine are simulated by the molecular dynamicsmethod within the Born–Oppenheimer approximation. High-order harmonics, emitted from the baseswhile molecules are exposed to ultrashort laser pulses are calculated by the strong-field approximationwithin the Lewenstein model. The calculated data then are used as ‘experimental’ high-order harmonicssources for investigation.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Probing dynamic processes in molecules has become one of themost interesting issues due to its potential that helps us under-stand and control chemical or biological reaction [1,2]. Thanks totechnological development of generating ultrashort laser pulses,the physics at the femto and sub-femto second scale allows us totrack dynamic processes in molecules [3–5]. The latest record ofshortest pulse in our knowledge is 67 attosecond that opens newgates for monitoring the electronic motion [6–8]. When atoms,molecules are exposed to an intense laser pulse, several nonlinearphenomena may occur. One of them is the high-order harmonicgeneration (HHG) which can perhaps be understood through thethree-step model in which the ionized electron may return andcollide with the parent ion to emit a photon [9]. HHG is rich inmolecular information because the photon is released at the timeof recombining. Due to that reason, the HHG spectra are usefulresources to extract molecular structure [10,11].

The inspiration of retrieving dynamic structure using HHGcomes from molecular imaging of N2 published in Nature [12].Authors used a laser pulse of 30 fs to reproduce the highest occu-pied molecular orbital (HOMO). That achievement has attractedmuch attention of colleagues to conduct experiments and simula-tion to retrieve molecular dynamic information [13–16]. In [13,14]

images of HOMO and HOMO-1 of N2 are reproduced. Then,dynamic imaging of CO2 is also reported in [15, 16]. Furthermore,probing molecular dynamics has been investigated effervescently[17–21]. In [17–19], authors solve the time-dependent Schrödingerequation (TDSE) for H2

+, H2 exposed to laser fields to obtain theHHG spectra and then claim that nuclear dynamics can be probedby using the ultrashort laser pulses. Recently, by analyzing theHHG spectra electronic dynamics has been studied experimentallyand theoretically [20,21]. In addition, tracking dynamic processesin molecule due to migration of atoms has conducted by investi-gating the dependence of the HHG spectra on molecular configura-tion [22,23]. In [22], by simulating the HHG spectra emitted fromthe molecule during an isomerization process, we concluded thatthe HCN/HNC and acetylene/vinylidene isomerization may betracked. Then the method is extended to track the similarprocesses in the DNA molecule [23].

DNA is a huge molecule consisting of simpler units called nucle-otides. These units are distinguished by carried nucleobases (orbases) that are adenine (A), cytosine (C), guanine (G) and thymine(T). In the present work, our first aim is to distinguish these basesby using the HHG spectra. Our next target is related to trackingmolecular dynamics due to rearranging atoms in bases. Each baseexists in two tautomers: one popular form called the keto state forG, T or amino state for A, C and one rare form called the enol orimino state, respectively. The tautomerism is a process ofswapping two tautomers due to the migration of a hydrogen atomamong stable positions of molecules. Despite living in extremely

32 V.-H. Hoang et al. / Computational and Theoretical Chemistry 1043 (2014) 31–37

short time, if rare tautomers are used during the synthesis of DNAin vivo, mutation may occur that results in changing genetic infor-mation. Therefore probing the tautomerism, in our point of view, isessential. In [23] we used the HHG spectra to track amino-iminotautomerism of cytosine. Another tautomerism is the keto–enolthat has not been investigated yet so in this paper, we developthe method to continue tracking the keto–enol tautomerism inthymine, as a sample.

In the present work, we study the alignment dependence of theHHG spectra emitted from four bases A, C, G, T and point out thepossibility to distinguish them. Then and most important, we focuson the dependence of the intensity harmonics on alignment anglesand structural molecular parameters of thymine, which is on thereaction path of tautomerization and interacts with the intenseultrashort laser pulse. Basing on that result, we continue to pointout the possibility of tracking tautomerisms in DNA.

The rest of this paper is arranged as follows. In Section 2 weintroduce the calculation method used to simulate molecularstructures, the tautomerism and the HHG spectra when moleculesare exposed to the intense laser field. Our results are shown inSection 3. Section 4 is the conclusion.

2. Calculation model

In this section, we use a chemical code to simulate bases struc-ture and the tautomerism. To calculate the HHG intensity for suchbig molecules like DNA, hitherto there has been only the three-stepmodel meeting that requirement. Moreover, the HHG spectra thatare calculated by the model also have characteristics like thosefrom experimental data so from our point of view they can be usedfor our objects.

2.1. Simulation the structure of bases and the keto-enol tautomerismof thymine

We employ the Gaussian software to simulate structures ofbases and the tautomerism of thymine. We use the optimizationjob in the frame of DFT with B3LYP level and the basis set6-31+G(d, p) [24] to calculate structural parameters of bases in sta-ble states. DFT and the basis set 6-31+G(d, p) have been used inmany works and claimed to give the results well consistent withexperimental measurement [25]. With such a complex moleculeas DNA, there are many stable states corresponding to minimaon the hyper potential energy surface (PES) [26]. In the presentwork, we are only concerned about the most popular isomersnamed amino (for A and C base), keto (for G and T base) and rareisomers called imino, enol, respectively. After obtaining structuresof isomers, we continue to simulate the tautomerization betweentwo states. During this process, the molecule will overcome a tran-sition state. Fig. 1 is the illustration the thymine structures withthree states: the keto, enol and transition.

In Fig. 1, states of thymine are described by the position of thehydrogen atom H11, which is characterized by the distance R fromC4 to H11 and the angle hHð\O8� C4�H11Þ. Using the optimiza-tion job in the Gaussian, we obtain three positions of H11corresponding to two stable states called the keto and enol, andan unstable state that is the transition state.

To demonstrate the existence of the keto, enol and the transi-tion state, we investigate the H11 position dependence of thepotential energy. In fact, the dependence of energy on bases struc-ture is extremely complicated. In this work, we focus only on onecertain way to obtain the PES of thymine relying on the H11position. First, we calculate and have the intrinsic reactioncoordinates (IRC) from keto to enol. Then on that path, at eachpoint corresponding to a certain value of hH, we change the

distance R and obtain the respective energy. By that way, we havethe PES of thymine depending on two structural parameters hH andR that contains the keto, enol state and the transition state. Finally,we simulate the keto–enol tautomerism with the BO-MD jobimplemented in the Gaussian. Indeed, tautomerization is thechanging position of H11 from N3 to O8. To excite this process,we supply for H11 initial kinetic energy that is enough to breakthe bond with N3 and move to create the bond with O8. In thissimulation, we do not study mechanism of giving the initial kineticenergy for H11.

2.2. Calculating high-order harmonic spectra by using the Lewensteinmodel

In this paper, we employ the Lewenstein model [27] to calculatethe HHG spectra from bases exposed to the ultrashort intense laserfield. According to the model, the HHG is majorly created fromthree steps. In first step, electrons in HOMO will be ionized by tun-neling and move to the continuum energy region. Second, the elec-trons are accelerated by the electric field and gain energy. In thisstep, in frame of the strong field approximation, the effect ofmolecular Coulomb field is neglected. In final step, when the direc-tion of the electric field of the laser is reversed, the ionized elec-trons are driven back and recombine with the parent molecularion to emit high-order harmonics. The Lewenstein model providesnot only an overall view but also an analytical method for calculat-ing the intensity of harmonics. In our previous papers, we used thismodel so some formulas to calculate harmonics intensity can befound in Ref. [14]. Besides, in [27] author Lewenstein describes cal-culation steps thoroughly so it is not crucial to show formulas here.In the Lewenstein model, only electrons in HOMO contribute toHHG considerably. To obtain the wavefunction of electrons inHOMO, we used the DFT method with the basis set 6-31+G(d, p)and B3LYP level implemented in the Gaussian codes. For the morecorrect HOMO, some advanced methods could be used, for exam-ple using the LB94 (instead of LDA) potential [28]. However, foruse in the simple method such as the one based on the three-stepmodel, the HOMO calculated by the DFT – B3LYP method is quitegood for our purpose.

It should be noted that there are several methods for HHG cal-culations, which are more quantitatively accurate than the oneused in this paper, have been developed in the last decade. The firstones we want to mention are numerical methods of solving theTDSE for H2

+ and some complex molecules based on the single-active electron approximation [29–31]. In [29], there is an interest-ing finding that for minima caused by the electron interferenceeffect in harmonic spectra, the calculation method with usingLCAO approximation for bound state wavefunction is more accu-rate if the acceleration operator is used rather than the dipole form.Nevertheless, the calculation method using the Lewenstein modelin which the dipole form is used is adequate to investigate theangular dependence of HHG. With using strong field approxima-tion (SFA), the three-step model gives qualitatively good resultswith experimental data not only for small molecules as N2, CO2

but also for some large molecules, such as C2H2, C3H4 (see forexample [32]). We also want to mention the modification of meth-ods based on SFA in three-step model. The inaccuracies of SFA withthe plane-wave approximation for the continuum state are modi-fied by using Ehrenfest theorem [33], or improved by using thescattering wave in [34,35]. However, in this work, our purpose isto distinguish the bases from HHG spectra, the basis three-stepmodel with plane-wave approximation is sufficient.

In Fig. 2, we introduce the model describing interactionbetween thymine and the ultrashort intense laser field.

In experiments, a weak laser field is used to align the moleculedue to molecular polarization. In the present work, we assume the

Fig. 1. Thymine in the keto (a), enol (b), and the transition (c) state in dependence on the position of the hydrogen atom H11, described by the structural angle hH and thedistance R. The tautomerism occurs by the motion of H11.

k

Fig. 2. Interaction model of thymine and the laser field. The molecule is aligned insuch a way that its plane is perpendicular to the laser direction, i.e. along the Ozaxis. The alignment angle h is the angle between the bond N1–C2 and thepolarization vector k.

Table 1Structures of thymine corresponding to the keto, transition, and enol state. Distanceunit is Angström whereas angle unit is degree. For the keto state, experimental data[37] are given to compare with our results.

Enol TS Keto Keto [37]

r(N1–C2) 1.418 1.422 1.388 1.340r(C2–N3) 1.380 1.372 1.385 1.420a

r(N3–C4) 1.307 1.351 1.407 1.384a

r(C4–C5) 1.438 1.431 1.468 1.457r(C5–C6) 1.365 1.368 1.354 1.370r(C6–N1) 1.361 1.367 1.381 1.355r(C5–C7) 1.504 1.502 1.502 1.501\N1� C2� N3 115.2 111.5 112.8 113.7\C2� N3� C4 120.1 124.6 127.9 126.0\N3� C4� C5 126.4 123.5 114.8 115.5\C4� C5� C6 113.5 112.9 118.0 117.3\C5� C6�N1 121.0 122.7 122.7 122.8\C6� N1� C2 123.8 124.9 123.7 124.3\C7� C5� C6 124.2 125.0 123.9 124.3\C4� C5� C7 122.3 122.1 118.2 118.4\C2� N1� H12 115.1 114.6 115.2 114.3\C2� N3� H13 176.6 161.7 115.8 117.0

a There are perhaps two misplaced distances C2–N3 and N3–C4 in [37].

V.-H. Hoang et al. / Computational and Theoretical Chemistry 1043 (2014) 31–37 33

molecule is perfectly aligned. We define the alignment angle h isthe angle between the bond N1–C2 and the polarization vector kof the intense laser. By changing the angle h we investigate thedependence of harmonics intensity on the alignment angle. Thatresult is used as an evidence to distinguish bases in DNA usingthe HHG spectra. In principle, we have to change the alignmentangle from 0� to 360�. However, the direction of the electric fieldis reserved after each half period so it is adequate to consider thealignment angle in the range of 0�–180�.

3. Results

3.1. Bases structure and potential enegry surface

Using the optimization job with the DFT method, we calculateand obtain the structures of three states of DNA bases. In Table 1,we list some parameters of bond lengths and angles of thymine.Our results well agree with other simulation [36] and experimentalvalues [37]. We notice that experimental data of C2–N3 and N3–N4are different from our results and those of others as well. We guessthat in paper [37], perhaps these values are misplaced.

In Table 1, we only show some parameters to compare withmeasured data although we have all values of positions of eachatom of thymine. In above values, we particularly pay attentionto coordinates of H11 corresponding to two equilibrium statesand the transition state as follows: (i) the keto state(R ¼ 2:07Å; hH ¼ 94:0�); (ii) the enol state (R ¼ 1:87Å; hH ¼ 29:8�);

(iii) and the transition state (R ¼ 1:61Å; hH ¼ 53:4�). The optimiza-tion job also allows us to have the potential energy gap betweenstates. For the keto and enol states, we obtain the energy gap of0.553 eV, which well agrees with experimental result 0.570 eV[38]. Also, an energy gap of 1.920 eV between the keto and thetransition state is obtained. In addition, the ionization potentialof thymine also calculated by this method is 9.010 eV, which isconsistent with measurement [39]. Similarly, structural parame-ters of the other bases are obtained as well. Thus, we conclude thatstructural information of bases calculated by the optimization jobis reasonable and also can be used for further calculation.

Continuously, using the scan job implemented in the Gaussian,we obtain the PES of thymine with respect to H11 position. InFig. 3, we show the PES of thymine as a function of the distanceH11–C4 and the angle hHð\O8� C4�H11Þ.

As mentioned above, the dependence of energy on positions ofall atoms is very complicated and has many local minima describ-ing 13 equilibrium states [38]. The PES is shown in Fig. 3 only aslice containing two tautomers and the transition state we areconcerned about. In Fig. 3 we also add the IRC that describes theketo–enol tautomerism through the transition state.

3.2. Distinguishing bases by HHG

In this section, we show our HHG calculation for bases with dif-ferent alignment angles. As mentioned in Section 2, the alignment

Fig. 3. Potential energy surface (PES) of thymine. The positions of minimal energy correspond to equilibrium states: the keto (R ¼ 2:07Å; hH ¼ 94:0�), and enol(R ¼ 1:87Å; hH ¼ 29:8�). The saddle point corresponds to the transition state (R ¼ 1:61Å; hH ¼ 53:4�). Intrinsic reaction coordinates (dark blue line) are also shown to gothrough the equilibrium states of thymine. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

34 V.-H. Hoang et al. / Computational and Theoretical Chemistry 1043 (2014) 31–37

angle is changed in the range of 0� ? 180� when the molecule isinteracting with the intense laser field. In this work, a laser withpeak intensity of 2 � 1014 W cm�2, wavelength of 800 nm andduration of 5 fs is used. To distinguish four bases, we calculatethe HHG spectra emitted from bases that are in stable states (theketo or amino state). Fig. 4 shows the dependence on alignmentangles of 19th and 23rd harmonics from four bases.

In Fig. 4, one can see that HHG spectra emitted from adenineand guanine have peaks at the alignment angle of 35�–40� and145�–150�. Two other bases are cytosine and thymine whose theHHG spectra reveal maxima when the alignment angle is about60�–65�. The similar results are also found for other harmonics.Hence, basing on the alignment angle dependence of the HHG

Fig. 4. The dependence of HHG intensity on the alignment angles for harmonicorders 19 (a) and 23 (b) of four bases adenine (black line), cytosine (red line),guanine (green line) and thymine (blue line). (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

spectra, we can distinguish four bases into two groups: adenine,guanine and cytosine, thymine.

3.3. Tracking keto–enol tautomerism of thymine

To track the keto–enol tautomerism, we start to study the align-ment angle dependence of the HHG spectra generated from twostable states and the transition state of thymine. The dependenceon the alignment angle of HHG from the keto, enol state and thetransition state of thymine are illustrated in Fig. 5. In Fig. 5, we onlyshow the dependence of the 21st, 23rd and 25th order in plateauregion whose cut off is 33rd.

In Fig. 5, one can see that HHG takes maxima at the alignmentangle of 60� and 140� for all three states. The result can beexplained by using the images of HOMO added on the right ofcurves. It is obvious that the difference of three HOMOs is negligi-ble so the alignment angle dependence of the HHG spectra emittedfrom three states are almost the same due to the strong influenceof HOMO on generated harmonics. We continue investigating thealignment dependence of harmonics generated from all stateswhile the molecule is on the reaction path of a tautomerism.

To stimulate a tautomerism, we supply for H11 initial kineticenergy of 2.9 eV and the initial angle between the initial velocityand the bond N3–H11 is 95�. In fact, we tried simulating withmany different values of the initial kinetic energy and the initialangle. A set of 2.9 eV and 95� is only one of many cases of the initialvalues that are enough for H11 to overcome the potential barrier tofinish the tautomerism. That means thymine transfer from the ketoto enol state. The trajectory of H11 during the tautomerization iscalled the chemical reaction path (CPR) on which each point corre-sponds to a certain molecular structure and energy. At every pointon CRP, the molecule interacts with the intense laser field to radi-ate the high-order harmonics. The alignment angle value is chan-ged in the range of 0�–180�.

Fig. 6 shows the dependence of the 21st and 25th on the align-ment angles from 0� to 90� and the structural angle hH. In similar,the results for alignment angles from 90� to 180� are shown inFig. 7.

Fig. 5. The dependence of HHG intensity emitted from thymine on the alignment angles for harmonic orders 21st (blue line), 23rd (red line), and 25th (green line) for thecases of (a) enol state (b) transition state, and (c) keto state. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thisarticle.)

Fig. 6. The dependence of HHG intensity on the alignment angle h from 0� to 90� and on the structural angle hH during the tautomerism for harmonic orders 21 (a) and 25 (b).

V.-H. Hoang et al. / Computational and Theoretical Chemistry 1043 (2014) 31–37 35

Fig. 7. The same Fig. 6 for the alignment angle h from 90� to 180�.

36 V.-H. Hoang et al. / Computational and Theoretical Chemistry 1043 (2014) 31–37

As mentioned above, the distance R and the structural angle hH

characterize the position of H11. However, in a certain tautomer-ism, the trajectory of H11 is the CRP so there exists a relationR(hH). Thus, during the process we need only hH instead of twoparameters to describe the position of H11 while thymine is inter-acting with the intense laser field.

In Fig. 6 one can see the intensity of HHG takes maxima at thealignment of 60� and that of 140� in Fig. 7. These results are wellconsistent with those shown in Fig. 5.

Continuously we analyze the dependence of HHG on the struc-tural angle hH. In Fig. 6, at the alignment angle of 60�, the HHGspectra reveal peaks at the structural angle of 30� and 75�. Thestructure corresponding to the value of 30� is enol state but thereis no special structure to value 75�. However, with the alignmentangle of 140�, we obtain the interesting results. In Fig. 7, it is obvi-ous that peaks of HHG appear at values of 30�, 55� and 94� of thestructural angle corresponding to the enol, transition and ketostate, respectively. With other harmonics, we also obtain similarperformance of the HHG spectra. Those results can be used as evi-dences to recognize the states when thymine is in a tautomerism.

Hence, by analyzing the dependence of HHG radiated from thy-mine on the alignment angle and the structural angle, we point outthe possibility of tracking the tautomerism using the ultrashortintense laser. The existence of peaks in HHG needs to be explainedphysically. The explanation will be carried in our next works, per-haps basing on simple models. At this time we guess that at stablestate, the electron is ionized easier than other states and that leadsto the emitted harmonics to be more intense.

3.4. Conclusions

In this paper, using the DFT method with B3LYP level theoryand the basis set 6-31G+(d, p) implemented in the Gaussian codes,we have simulated the partial structures as well as the potentialenergy of equilibrium states such as keto/amino, enol/imino andtransition states for four bases of DNA. Our results are consistentwith experimental data and theoretical simulations of other

authors. Using the Born–Oppenheimer approximation with themolecular dynamics method we have also simulated a tautomer-ism from the keto state to the enol state for thymine.

High-order harmonic spectra emitted when four bases interactwith infrared 800 nm laser pulses of duration 5 fs, peak intensity of2 � 1014 W cm�2 have been calculated by a method based on theLewenstein model. The dependence of HHG intensity from fourbases on the alignment angle allows us to distinguish two groupsadenine, guanine and cytosine, thymine.

The dependence of HHG intensity from thymine on the align-ment angle for the two equilibrium states (keto and enol) andthe transition state has been found. There are not much differencesfor these three states in which the HHG intensity have peaks at thealignment angles of 60� and 140�. This circumstance can be inter-preted by the slight dependence of the HOMO electron density onthe movement of the hydrogen atom during tautomerism. Withthat we can (but not easily) use the dependence of HHG on align-ment for distinguishing the tautomers.

High-order harmonic spectra emitted when thymine interactswith ultrashort laser pulses during the tautomerism have been cal-culated. The dependence of the HHG intensity on the alignmentand structural angles has been analyzed. For the alignment angleof 140�, the HHG intensity has peaks at the equilibrium (keto, enol)and the transition states. This result opens a possibility of trackingthe tautomerism by ultrashort laser pulses using the HHG. In theconsequent works, we will apply the procedure to other basesand try to interpret the physical meaning of the HHG intensitypeaks, perhaps for a simpler molecule.

Acknowledgments

This Project is financially supported by Vietnam’s NationalFoundation for Science and Technology Development (NAFOSTED),Grant No. 103.01.20.09. We would like to thank Dr. Anh-Thu Le(Kansas State University, USA) for helpful consultancy on the calcu-lation method and for permission to use and modify his polyatomicHHG codes.

V.-H. Hoang et al. / Computational and Theoretical Chemistry 1043 (2014) 31–37 37

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