The effect of intermolecular interactions on the electric dipole polarizabilities of nucleic acid base complexes

Chemical Physics Letters 555 (2013) 230–234

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The effect of intermolecular interactions on the electric dipole polarizabilities of nucleic acid base complexes a,⇑ _ _ Zaneta Czyznikowska , Robert W. Góra b,⇑, Robert Zales´ny b, Wojciech Bartkowiak b, Angelika Baranowska-Ła˛czkowska c, Jerzy Leszczynski d a

Department of Inorganic Chemistry, Faculty of Pharmacy, Wrocław Medical University, Szewska 38, PL-50137 Wrocław, Poland ´ skiego 27, PL-50370 Wrocław, Poland Theoretical Chemistry Group, Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wyb. Wyspian Institute of Physics, Kazimierz Wielki University, Plac Weyssenhoffa 11, PL-85072 Bydgoszcz, Poland d Interdisciplinary Nanotoxicity Center, Department of Chemistry and Biochemistry, Jackson State University, Jackson, MS 39217, USA b c

a r t i c l e

i n f o

Article history: Received 25 June 2012 In final form 30 October 2012 Available online 8 November 2012

a b s t r a c t In this Letter, we report on the interaction-induced electric dipole polarizabilities of 70 Watson–Crick BDNA pairs (27 adenine–thymine and 43 guanine-cytosine complexes) and 38 structures of cytosine dimer in stacked alignment. In the case of hydrogen-bonded Watson–Crick base pairs the electrostatic as well as the induction and exchange-induction interactions, increase the average polarizability of the studied complexes, whereas the exchange-repulsion effects have the opposite effect and consistently diminish this property. On the other hand, in the case of the studied cytosine dimers in stacked alignment the dominant electrostatic contribution has generally much larger magnitude and the opposite sign, resulting in a significant reduction of the average polarizability of these complexes. As a part of this model study, we also assess the performance of recently developed LPol-ds reduced-size polarized basis set. Although being much smaller than the aug-cc-pVTZ set, the LPol-ds performs equally well as far as the excess polarizabilities of the studied hydrogen-bonded complexes are concerned. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Much attention has been devoted to analyzing various properties of nucleic acid base complexes in the past and there are still many vital issues to be addressed that facilitate an enormous interest in this subject (cf. [1–4] and references cited therein). The main rationale behind studying structure and stability of DNA (and its model fragments) is mainly due to its biological functions (see, for example, [5–7]). However, recently DNA became also a very interesting material for nanoelectronics and molecular nanotechnology. In fact, this aspect has been extensively studied because of various DNA features including high flexibility, self-assembly, self-recognition and self-replication [8]. Nucleic acids can also be used as a template to align other molecules (due to their ability to form stable aggregates with nanoparticles and proteins [9]) and thus they might serve as parts of assemblies used as molecular switches, memory devices or transistors [10–13]. Successful attempts have been reported to apply DNA as a component in materials of nonlinear optical activity [14–16] and also for holographic inscription [17]. Moreover, DNA potential to serve as a chiral template for second-order nonlinear optical materials has been ⇑ Corresponding authors. _ Czyznikowska), _ E-mail addresses: [email protected] (Z. robert. [email protected] (R.W. Góra). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.10.087

recently demonstrated by Wanapun et al. [18]. Also the linear optical properties of organic dyes, such as photoabsorption and photoemission, are affected by the presence of DNA [19,16]. In general, the (non)linear optical response of such hybrid systems is a result of quite complex interplay of various factors. They include the excess (hyper)polarizabilities resulting from interactions among host/guest and guest/guest molecules. This is particularly important in the case of photoactive dyes intercalated into DNA. Our ultimate goal is to describe linear and nonlinear optical (L&NLO) properties of various assemblies of photoactive systems incorporated into DNA. In an attempt to make a step towards understanding of these properties in DNA-based hybrid systems, in this Letter we focus on investigations of the origins of interaction-induced polarizabilities in nucleic acid base pairs. In particular, we analyze 70 Watson–Crick B-DNA pairs (27 adenine–thymine and 43 guanine-cytosine complexes) and 38 structures representing the cytosine dimer in stacked alignments. All structures have been extracted from the available crystallographic data. The complexes in question, in the very same conformations, have been recently studied by some of us with an eye towards the origins of intermolecular interactions [20,21]. Although the static electric properties of isolated nucleic acid bases have been quite extensively studied [22,23], to the best of our knowledge there is only one study devoted to excess electric properties of nucleic acid base pairs published by Seal et al. [24]. In that paper the authors

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reported only the rough estimates of the first hyperpolarizability obtained within a two-state approximation. In our study, we report on comprehensive ab initio results of interaction-induced properties and their partitioning into physically meaningful components. In doing so, we follow here an approach proposed originally by Heijmen and Moszyn´ski [25] which has been applied only to relatively small atomic and molecular dimers [25–27] and trimers [28]. 2. Computational details The total interaction energy of a dimer, calculated by a supermolecular approach using the second-order Møller–Plesset perturbation theory (MP2), is partitioned into the Hartree–Fock (HF) and the electron correlation interaction energy components:

DEMP2 ¼ DEHF þ DEMP2 corr :

ð1Þ

The HF term can be partitioned into the Heitler–London (HL) and the delocalization (DEHF del ) energy components. The former involves the electrostatic interactions of unperturbed monomer charge denð10Þ sities, el , as well as the associated exchange repulsion DEHL ex and can be calculated after Löwdin [29] as a difference between the expectation value of the Hamiltonian, defined as a sum of the free-monomer Hamiltonians Hi and Hj and the intermolecular perturbation V ij , for the wavefunction given as an antysymmetrized Hartree product of monomers’ wavefunctions and the sum of monomer energies:

  HF HF DEHL ¼ NHL ij hAWi Wj j Hi þ Hj þ V ij j AWi Wj i  Ei þ Ej

ð2Þ

where N HL ij is the normalization constant. The delocalization term is estimated as a difference between the HF and the HL interaction energies and encompasses the induction and the associated exchange effects due to the Pauli exclusion principle: ð10Þ HF DEHF ¼ DEHL þ DEHF þ DEHL del ¼ el ex þ DEdel :

ð3Þ DEMP2 corr ,

The second order electron correlation term, includes the secð20Þ ond order dispersion interaction, disp , as well as the electron correð12Þ lation correction to the first order electrostatic interaction, el;r , and ð2Þ the remaining electron correlation effects (DEex ): ð12Þ ð20Þ ð2Þ DEMP2 corr ¼ el;r þ disp þ DEex :

ð4Þ

The latter term accounts mainly for the uncorrelated exchange-dispersion and electron correlation corrections to the Hartree–Fock exð10Þ ð20Þ change repulsion [30,31]. The el and the disp terms are obtained ð12Þ in the standard polarization perturbation theory, whereas the el;r term is calculated using the formula proposed by Moszyn´ski et al. [32]. The indices in parenthesis denote perturbation orders in intermolecular interaction operator and intramonomer correlation operator, respectively. In order to account for higher-order electron correlation effects, this scheme can be extended to higher orders of perturbation theory or augmented with the supermolecular electron correlation corrections estimated using the coupled-clusters approach. If a molecular complex is embedded in an external uniform electric field, interaction energy and all of its components become field dependent. For interaction-induced tensorial property DPij...n (dipole moment, polarizability, first- and second hyperpolarizabilities, etc.) one obtains:

DPij...n

  @ n DE ¼ : @F i @F j . . . @F n F i ¼F j ¼F n ¼0

ð5Þ

The required derivatives can be estimated in a numerical differentiation procedure, commonly referred to as the finite field (FF) approach, which can be combined with any ab initio method. In this study, we use the Rutishauser–Romberg scheme [33] to compute

231

numerical derivative given by Eq. (5). In case of interaction-induced polarizabilities the diagonal tensor elements can be computed using:

Dap;k ¼

4p  Dap1;k  Dap1;k1 4p  1

ð6Þ

where p is the iteration number and k is related to the distance from DEðF ¼ 0Þ. The values of Da0;k are determined from finite-difference expression for the second derivative of interaction energy (DEð2Þ ðFÞ) ð2Þ or its components (DEi ðFÞ):

DEið2Þ ðFÞ  dð2;kÞ ¼

DEi ð2k F h Þ þ DEi ð2k F h Þ  2DEi ðF ¼ 0Þ ð2k F h Þ2

ð7Þ

where F h is an electric field step equal 0.001 a.u. In all calculations the aug-cc-pVDZ correlation-consistent basis set was used [34–36]. However, in order to establish the basis set extension effects we calculated the contributions to the interaction-induced diagonal polarizability of AT dimer using a selection of other correlation-consistent basis sets (cc-pVXZ and aug-ccpVXZ, where X = D,T) as well as the recently developed polarized LPol-ds basis set [37]. The LPol-ds set is the smallest among the LPol-n (n = ds, dl, fs, fl) property-oriented basis sets, designed for accurate studies of linear and non-linear molecular electric properties. High level of saturation of LPol-n sets with respect to polarization effects induced by external electric field makes them also reliable for calculation of interaction-induced properties. They were developed using method based on the studies of analytic dependence of Gaussian-type orbitals (GTOs) on the external oscillating electric field [38]. Polarized set is obtained from some source set of GTOs through addition of multiple first- (all LPol-n sets) and second-order (LPol-fs and -fl sets) polarization functions. Their contraction coefficients are obtained by simple scaling of the corresponding contraction coefficients in the valence orbitals. Quality of the final set depends strongly on the choice of initial set of functions, and thus the LPol-n sets were developed from the fully optimized large [13s8p] ([10s] in the case of hydrogen) basis sets of van Duijneveldt [39]. To further increase basis set flexibility, the source set was augmented with one diffuse s- and one diffuse p-type function (one s-type function in the case of hydrogen atom). Final LPolds set was contracted to the form [14s9p6d/6s5p3d] ([11s6p/4s3p] for hydrogen). In order to elucidate the relations among the various components of interaction energy and interaction-induced electric properties, in this Letter we use both the Pearson’s and the Spearman’s rank correlation coefficients [40]. The latter coefficient can be estiP 2 mated as: q ¼ 1  6 i di =nðn2  1Þ, where di is the difference between the ranks of each observation for the pair of compared quantities, and n is the number of observations (in this case number of studied complexes in each set). The advantage of using the Spearman’s rank is that it does not assume a normal distribution for the compared quantities and it is based on the order of their rising magnitudes rather than their values. All calculations have been performed using a modified version of the GAMESS (US) program [41]. 3. Results and discussion Regarding evaluation of interaction-induced electric polarizabilities and hyperpolarizabilities in hydrogen-bonded complexes, a considerable improvement of results is observed when using large Dunning’s basis sets [34–36] augmented with diffuse functions. However, due to the size of such sets their use makes the calculations unfeasible for larger complexes [42,43,28]. On the other hand, it has been previously shown that the LPol-n sets are competitive to the larger all-purpose sets of Dunning in the case of

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evaluation of induced electric polarizabilities and first hyperpolarizabilities of such systems [42,43]. It was also demonstrated that the basis set superposition error (BSSE) is considerably reduced when LPol-n sets are used in calculations of induced electric properties [43]. On the basis of these works, we employ in the present study the LPol-ds set to compare its performance with the aug-ccpVTZ basis set of Dunning for larger hydrogen-bonded complexes than previously investigated. The values gathered in Table 1 for the adenine–thymine complex show a considerable improvement of the results upon augmentation of the cc-pVXZ set with diffuse functions. It is also obvious that the use of sufficiently diffuse sets is mandatory to obtain reliable estimations of the investigated induced properties. Depending on the property, the differences between the values calculated using the cc-pVXZ and aug-cc-pVXZ results for a given X are from a few up to about 20%. In the case of the aug-cc-pVXZ basis sets, increase of the cardinal number from X = D to T yields a change in the results well below 2%, while the aug-cc-pVDZ set contains 591 less functions leading to an obvious and substantial decrease of the computing cost. Considering the scope of the present study, the aug-cc-pVDZ basis set proves to be sufficiently saturated and allows to obtain results of quantitative accuracy. Considering the results obtained with LPol-ds set, an almost perfect agreement with the aug-cc-pVTZ results is observed. The error with respect to the largest of the employed sets is in the order of 1%, with the only exception being the DaHL ex term (1.6%). Thus, the LPol-ds set, containing 300 functions less than the aug-cc-pVTZ set, can be also recommended for accurate calculations of investigated properties. However, due to a large number of complexes investigated within this project, the aug-cc-pVDZ set was chosen, since it represents the best compromise between the computing cost and the quality of the results. In order to analyze the interaction-induced polarizabilities in nucleic acid base complexes, we have chosen a large set of Watson–Crick pairs represented by geometries taken from crystallographic data. Such selection ensures that one deals with a large spread of values of base-pair parameters, namely buckle, stretch, stagger, shear, propeller, opening. However, we do not intend to analyze the directionality of interaction-induced electric properties; rather we want to make sure that our conclusions do not dependent upon the particular selection of geometries of complexes. Moreover, in doing so we also scan the whole range of plausible alignments and hence determine the range of possible interaction-induced properties. In the case of Watson–Crick nucleic acid base pairs it has been shown that their stabilization is mainly due to the first-order electrostatic and induction effects [20,44]. In the variationalperturbational interaction energy decomposition scheme, the latter contributions are encompassed in the charge delocalization component. For a set of studied here hydrogen-bonded adenine– thymine and guanine-cytosine complexes, in conformations mimicking those appearing in B-DNA, the average value of the DEHL term is 12 kcal/mol and 24 kcal/mol, respectively. Although

Table 1 Contributions due to various interaction energy terms to the diagonal excess polarizability ðDayy Þ estimated for the AT complex (hydrogen bonds were oriented along y-axis). All values of electric properties are in au. N CGTO is the total number of contracted spherical harmonic Gaussian functions.

cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ LPol-ds

N CGTO

Dayy;el

DaHL yy;ex

DaHF yy;del

DaHF yy

321 536 724 1127 827

25.54 28.59 27.46 28.51 28.45

13.71 13.32 13.26 13.16 13.02

7.34 8.81 8.13 8.73 8.59

19.17 24.08 22.33 24.08 24.02

ð10Þ

Figure 1. Decomposition of interaction-induced electric-dipole polarizability for Watson–Crick guanine-cytosine pairs. Da ¼ 13 ðDaxx þ Dayy þ Dazz Þ.

Figure 2. Decomposition of interaction-induced electric-dipole polarizability for Watson–Crick adenine–thymine pairs. Da ¼ 13 ðDaxx þ Dayy þ Dazz Þ.

the average value of electrostatic energy is two times larger (i.e. 28 kcal/mol and 49 kcal/mol), it is substantially quenched by the associated exchange repulsion term (average values for both types of complexes are 34 kcal/mol and 60 kcal/mol). For comparison, higher-order contributions are less important. As it was shown by Toczyłowski and Cybulski [44] and by some of us [20] dispersion interactions contribute only a few kcal/mol to the stability of Watson–Crick A-T and G-C pairs. As far as the interaction-induced electric dipole polarizabilities are concerned, the qualitative agreement for the two types of hydrogen-bonded complexes is found (cf. Fig. 1 and 2). In particular, in both cases a posiP tive contribution to the average polarizability ðDa ¼ 13 i¼x;y;z aii Þ is found due to the first-order electrostatic and delocalization terms. Negative contribution, on the other hand, is observed due to fieldinduced exchange repulsion effects. A qualitatively similar picture of excess polarizabilities is also revealed for the other hydrogenbonded complexes studied previously [27,28]. Interestingly, the same is also true for induced polarizabilities of interacting inert gas atoms. In which case the electrostatic and induction terms tend to increase the polarizability of diatom, whereas the overlap effects lead to its substantial reduction [45,25]. However, in the inert gas dimers the exchange contributions dominate the overall effect at distances close to equilibrium and shorter, while for the hydrogen-bonded complexes considered here the electrostatic and induction effects seem to prevail. Since the influence of all

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Table 2 Contributions due to various interaction energy terms to the average incremental polarizability ðDaMP2 Þ estimated for the selected AT, GC and CC complexes using augcc-pVDZ basis set. The corresponding average polarizabilities of the complex are given in parentheses. All values of electric properties are in au. Complex

Dael

DaHL ex

DaHF del

Dael;r

Dadisp

Daex

DaMP2

AT GC CC

2.44 2.83 6.33

4.20 8.06 0.80

3.63 6.70 1.46

1.85 2.40 1.89

1.24 1.97 0.76

2.02 3.06 0.07

2.94 (186.66) 2.78 (188.76) 6.89 (150.81)

ð10Þ

ð12Þ

ð20Þ

ð2Þ

Hartree–Fock terms is qualitatively consistent for all the investigated Watson–Crick base pairs, we decided to estimate the computationally demanding electron correlation terms only for selected complexes. The results reported in Table 2 were calculated for complexes whose DaHF was close to the arithmetic mean for each set. They show that the electron correlation correction to the ð12Þ first-order electrostatics Dael;r enforces further their effect. The dispersion contribution also enhances the average polarizability ð2Þ of both hydrogen-bonded complexes. And although the Daex reduces to a large extent these effects, the overall electron correlation contribution is quite significant (36–47% of DaMP2 ) and positive. In order to reveal the physical origins of interaction-induced polarizabilities in nucleic acid base complexes in stacked configurations, we also present the results of calculations for cytosine dimer (CC). It has been shown that the sources of stabilization in this system are different from those found for hydrogen-bonded Watson–Crick base pairs [21]. Average values of interaction energy components for the set of 37 CC complexes studied in the present ð10Þ Letter are following: el = 1.6 kcal/mol, DEHL ex = 1.4 kcal/mol, ð12Þ DEHF = 0.7 kcal/mol,  ð20Þ del el;r = 0.6 kcal/mol, disp = 4.4 kcal/mol and DEð2Þ ex = 0.5 kcal/mol. As expected, a key contribution is due to the dispersion term of interaction energy which in this system is by far the largest in terms of magnitude. Before we proceed to discussion of our results we would like to address the reliability of MP2 method for the intended purpose. The results obtained by Maroulis for water dimer [46] indicate that MP2 method reproduces very closely the CCSD(T) interaction-induced polarizabilities for hydrogen-bonded complexes. It is also well established that while the Watson–Crick base pairs can be described adequately using this approach, it accounts only for the uncoupled Hartree–Fock dispersion energy which often considerably overestimates the dispersion attraction in p–p complexes [47–49]. Although it may be generally true for the interaction energy itself it is not necessarily true for its derivatives with respect to external electric field. For instance, considering the results shown in the present manuscript, one may notice that there is generally no correlation between the magnitude of particular interaction energy term and the corresponding contribution to the interaction-induced polarizability. An even more spectacular example would be the composition of interaction-induced polarizability in helium diatom, whose stabilization is governed by dispersion and exchange-dispersion effects, whereas Da is primarily electrostatic in nature [25]. Nevertheless, we calculated the induced polarizabilities along the z-axis (being the out-of-plane, i.e. intermolecular axis) at CCSD/aug-cc-pVDZ level. The DaCCSD of zz 7.22 au compares well with DaMP2 of 7.67 au and we expect that zz inclusion of noniterative triples would bring CCSD(T) value even closer to the MP2 estimate. Thus we consider our results to be of, at least, semi-quantitative accuracy. Interestingly, Fig. 3 shows that contrary to hydrogen-bonded Watson–Crick pairs electrostatic interactions make a negative and leading contribution to Da. However, since the variability of HF terms was in this case much larger and the complexes were smaller

Figure 3. Decomposition of interaction-induced electric-dipole polarizability for cytosine dimer in stacked alignments. Da ¼ 13 ðDaxx þ Dayy þ Dazz Þ.

we calculated the electron correlation terms for the whole set. In the case of all considered conformations of cytosine dimer the contribution to Da related to electron correlation interactions is also negative. Only the delocalization and exchange components have qualitatively the same effect in all studied systems. The magnitude of electrostatic term reproduces quite accurately the overall Da value estimated using both HF and MP2 methods. The latter, however, is largely due to the net correlation contributions being relatively small in this set (average DaMP2 corr amounts to 1.19 au). Nevertheless, one may conclude that the electrostatic component represents a reasonable estimate of incremental polarizabilities essentially in all the studied complexes, since also in the case of Watson–Crick base pairs it is quite close to the total value of Da. However, only for the studied set of CC dimers one finds nearly linear correlation of these two quantities (Pearson’s correlation coefficient amounts to 0.991). This is particularly interesting, since the electrostatic term should in principle be quite accurately rendered by the estimates of an approximate multipole-induced-multipole model [50]. Although at first sight a comparison of the field-free interaction energy terms and the corresponding contributions to interactioninduced polarizability does not reveal any obvious dependencies, estimation of Pearson’s and Spearman’s rank correlation coefficients indicates a few quite intriguing relations. Perhaps the clearest picture is found for the studied set of cytosine dimers in stacked alignments for which there is a strong correlation of DaMP2 and the ð20Þ field-free DEHL ex and disp . The corresponding Spearman’s ranks amount to 0.94 and 0.97, respectively. Thus for these complexes one finds that following the increase of induced polarizability, the field-free dispersion interaction also increases. Whereas, DaMP2 de-

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creases with an increase of the exchange-repulsion between monomers. It should be noted, however, that even though the former effect could be easily rationalized considering the Casimir–Polder formula for dispersion interaction (cf. [26]), we did not observe any such obvious correlations for the studied hydrogen-bonded complexes. 4. Conclusions In this Letter we analyze the interaction-induced polarizabilities of 70 hydrogen bonded Watson–Crick B-DNA pairs and in 38 structures of cytosine dimer in stacked alignments. This selection of the structures, extracted from the available crystallographic data covers the whole range of plausible alignments and hence the variety of possible interaction-induced properties. In the case of hydrogen-bonded Watson–Crick base pairs the electrostatic as well as the induction and exchange-induction interactions, constituting the electron-delocalization component, increase the average polarizability of the studied complexes, whereas the exchange-repulsion terms have the opposite effect and consistently diminish this property. The former, however, are in excess and the average polarizability of the hydrogen-bonded complexes is larger by about 1.5–2.0 au (which is roughly 2%) than that of the sum of its isolated constituents. On the other hand, in case of the studied cytosine dimers in stacked alignments the dominant electrostatic contribution has generally much larger magnitude and the opposite sign, resulting in overall reduction of the average polarizability of these complexes (by about 6.4 au or 4%). Interestingly, in the case of cytosine complexes we found that the magnitude of induced polarizability increases with an increasing field-free dispersion interaction, and that its magnitude decreases for an increasing exchange-repulsion between monomers. As a part of this model study, we also investigated the performance of recently developed LPol-ds reduced-size polarized basis set. Even though it is much smaller than the aug-cc-pVTZ set, LPol-ds performs equally well as far as the excess polarizabilities of the studied hydrogen-bonded complexes are concerned. Acknowledgments One of us (Z.C.) acknowledges financial support within a statutory activity subsidy for Wroclaw Medical University. Part of the work, regarding assessment of newly developed basis set, was supported by the Foundation for Polish Science within the Homing Plus programme (Homing Plus/2010–1/2), co-financed from European Regional Development Fund within Innovative Economy Operational Programme. W.B. acknowledges a statutory activity subsidy from the Polish Ministry of Science and Higher Education for the Faculty of Chemistry of Wrocław University of Technology. J.L. thanks for the support from the National Science Foundation (Grant NSF/CREST HRD 0833178). This work was also supported by computational grant from Wroclaw Centre for Networking and Supercomputing (WCSS). The allocation of computing time is greatly appreciated. Authors declare no competing financial interest.

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