Toward Feasible and Comprehensive Computational Protocol for

Article pubs.acs.org/JPCA

Toward Feasible and Comprehensive Computational Protocol for Simulation of the Spectroscopic Properties of Large Molecular Systems: The Anharmonic Infrared Spectrum of Uracil in the Solid State by the Reduced Dimensionality/Hybrid VPT2 Approach Teresa Fornaro,† Ivan Carnimeo,†,‡ and Malgorzata Biczysko*,†,§ †

Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy Compunet, Istituto Italiano di Tecnologia (IIT), Via Morego 30, I-16163 Genova, Italy § Istituto di Chimica dei Composti OrganoMetallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca CNR, Consiglio Nazionale delle Ricerche, Via G. Moruzzi 1, I-56124 Pisa, Italy ‡

S Supporting Information *

ABSTRACT: Feasible and comprehensive computational protocols for simulating the spectroscopic properties of large and complex molecular systems are very sought after. Indeed, due to the great variety of intra- and intermolecular interactions that may take place, the interpretation of experimental data becomes more and more difficult as the system under study increases in size or is placed in a complex environment, such as condensed phases. In this framework, we are actively developing a comprehensive and robust computational protocol aimed at quantitative reproduction of the spectra of nucleic acid base complexes, with increasing complexity toward condensed phases and monolayers of biomolecules on solid supports. We have resorted to fully anharmonic quantum mechanical computations within the generalized second-order vibrational perturbation theory (GVPT2) approach, combined with the cost-effective B3LYP-D3 method, in conjunction with basis sets of double-ζ plus polarization quality. Such an approach has been validated in a previous work (Phys. Chem. Chem. Phys. 2014, 16, 10112−10128) for simulating the IR spectra of the monomers of nucleobases and some of their dimers. In the present contribution we have extended such computational protocol to simulate spectroscopic properties of a molecular solid, namely polycrystalline uracil. First we have selected a realistic molecular model for representing the spectroscopic properties of uracil in the solid state, the uracil heptamer, and then we have computed the relative anharmonic frequencies combining less demanding approaches such as the hybrid B3LYP-D3/DFTBA one, in which the harmonic frequencies are computed at a higher level of theory (B3LYP-D3/ N07D) whereas the anharmonic shifts are evaluated at a lower level of theory (DFTBA), and the reduced dimensionality VPT2 (RD-VPT2) approach, where only selected vibrational modes are computed anharmonically along with the couplings with other modes. The good agreement between the theoretical results and the experimental findings allowed us to extend the interpretation of experimental data. Our results indicate that hybrid and reduced dimensionality models pave a way for the definition of system-tailored computational protocols able to provide more and more accurate results for very large molecular systems, such as molecular solids and molecules adsorbed on solid supports.

1. INTRODUCTION

hydrogen bonds and stacking interactions, nucleobases can self-assemble, forming monolayers or more complex threedimensional structures in plausible conditions.12 From the prebiotic point of view, such a capability for self-organization has very likely been one of the driving forces that led to the origin of life.13 Recently, nucleobases arouse a great interest also for the development of biosensors, 14−17 and as

A comprehensive analysis of the properties and processes concerning increasingly large and complex chemical systems, starting from molecular clusters, biopolymers, up to condensed phases and macromolecular systems in complex environments like monolayers of biomolecules on solid supports, is of fundamental importance in several fields ranging from materials science, nanotechnology, and surface science to biotechnology, drug designing and delivery, and prebiotic chemistry.1−11 Among the complex chemical systems, DNA and its building blocks, e.g., nucleobases, represent very interesting cases. In particular, due to the possibility to form intermolecular © XXXX American Chemical Society

Special Issue: Jacopo Tomasi Festschrift Received: October 6, 2014 Revised: December 3, 2014

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dx.doi.org/10.1021/jp510101y | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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and their dimers turned out to be the combination of the GVPT2 model, 55−58 with the cost-effective B3LYP-D3 method83−85 in conjunction with the SNSD basis set.54,58 Noteworthy, not only has the B3LYP-D3/SNSD proved a good performance in predicting structural parameters and binding energies for chemical systems governed by dispersion interactions but also it has shown improvements in the case of hydrogen-bonded complexes.54 In the present contribution we have extended the computational protocol developed for the dimers of nucleobases to a larger system, namely, the uracil heptamer, chosen to represent the properties in the solid state. From a theoretical point of view, the main challenge of simulating the spectroscopic properties of supramolecular systems consists in the development of a comprehensive yet feasible computational protocol that would be a compromise between accuracy and computational cost. A quantitative comparison with the experimental measurements can be obtained only treating the vibrational problem beyond the harmonic approximation, but a fully dimensional anharmonic computation of vibrational frequencies (with either perturbative58 or variational approaches86−88) would be very demanding with large molecular systems, due to the increasing number of underlying electronic structure computations (energies, gradients, or Hessians) necessary to describe multidimensional potential energy surfaces (PES). Indeed, theoretical anharmonic simulations of vibrational spectra of very large molecular systems are still far from standard, but few pioneering applications to the systems like chlorophyll35,89 or polypeptides,90,91 glycine,58,89,92 or ammonia93 adsorbed on inorganic surfaces, graphene,91 or water clusters,90,91 have shown promising results. Within the VPT2 framework, with the aim of reducing the computational cost of anharmonic computations, we have considered and combined two approaches applicable to the medium- to large-size molecular systems, namely, the hybrid model,58,82 in which the harmonic frequencies are computed at a higher level of theory with anharmonic corrections obtained by less expensive methods, and the reduced dimensionality VPT2 (RD-VPT2) computations,58,89,92 in which only selected vibrational modes are calculated anharmonically (including the couplings with the other modes), whereas the remaining modes are treated at the harmonic level. In both cases, the B3LYP-D3/N07D has been considered as the highest level of theory, whereas in the case of the hybrid approach VPT2 computations have been performed using the analytical formulation94 of the self-consistent charge density functional tight binding (DFTB) method,95,96 which has already shown promising results for computation of anharmonic corrections.97 Moreover, we have also discussed possible further improvements of the computed vibrational frequencies, by correction of harmonic frequencies of uracil monomer based on the best theoretical estimates,98 while considering the environmental and anharmonic effects at the DFT/DFTB level. The paper is organized as follows: after providing a short description of the theoretical methods applied for the energetic and vibrational computations (section 2), the procedure for selecting the model for uracil in the solid state is described (section 3.1). Then, the hybrid and reduced dimensionality VPT2 computations are validated by comparison with the results from the full-dimensional GVPT2 ones at the B3LYPD3/N07D level for the uracil dimers (section 3.2). Finally, the anharmonic frequencies computed through the hybrid and RDVPT2 approaches for the uracil heptamer are compared with

biomaterials forming nanostructures for homogeneous dense surface coatings, bottom-up nanopatterning, and 3D nanoparticle lattices.18 The investigation on the nature, formation, and evolution of such supramolecular structures requires a detailed analysis of the physicochemical interactions taking place among the molecules and between the molecules and the environment, which can be performed by spectroscopic techniques.19−24 For example, isolated or solvated DNA bases, base pairs, nucleosides, or hybrid nucleobases−inorganic supramolecular structures have been investigated on the basis of their vibrational signatures from infrared (IR), Raman, or IR−UV doubleresonance spectroscopies.9,25−31 However, the overall spectroscopic signals ensue from the contribution of all the different kinds of intra- and intermolecular interactions that may take place within the system or between the system and the environment, hampering the interpretation of the experimental outcomes. In this regard, computational spectroscopy techniques have become in the last years effective tools to unravel intricate experimental data for molecular systems of increasing size and complexity.32−35 In particular, for localized spectroscopic phenomena, complex molecular systems can be described by resorting to multiscale or “focused” models, where the system is separated in multiple layers and the target structure is treated at a higher level of theory, whereas the rest of the system is described with less accurate but computationally less demanding approaches.36−43 The overall environmental effects can be often described by means of continuum, polarizable medium44−46 models, which intrinsically take into account long-range bulk effects and statistical averaging of solvent molecules. Moreover, quantum chemical modeling of large biomolecular systems by means of effective fragment potentials42,47 or frozen-density embedding43,48,49 allows to take into account more realistic environmental effects on electronic spectra.50−52 However, for vibrational spectra of molecular systems governed by the specific system−environment interactions (e.g., hydrogen bonds), nearest neighbors (e.g., the surrounding molecules or the first solvation shell) have to be considered explicitly to correctly simulate spectroscopic properties.53 Definition of a suitable molecular model can be achieved through a multistep strategy starting the investigation from the spectroscopic properties of the isolated molecule, and then studying the perturbation induced by the interaction with another molecule (molecular dimers) or a small number of molecules (microsolvation), toward condensed phases like the molecular solid, up to monolayers of biomolecules on solid supports. In particular, in a previous work54 we have performed the study of the IR spectroscopic properties of the isolated nucleobases adenine, hypoxanthine, uracil, thymine, and cytosine, and some of the most stable hydrogen-bonded and stacked dimers of adenine and uracil, identifying a general, reliable, and effective computational procedure based on fully anharmonic quantum mechanical computations of the vibrational wavenumbers and IR intensities through the generalized second-order vibrational perturbation theory (GVPT2) approach.55−58 The second-order vibrational perturbation (VPT2) theory55−57,59−78 is particularly appealing to treat medium-size semirigid systems when combined with a semidiagonal fourth-order normal mode representation of the anharmonic force field.54,58,79−82 The most successful procedure for analyzing and assigning the IR spectra of nucleobases B



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Figure 1. Structures and numbering schemes of the uracil clusters considered in this work, following the crystal structure of uracil.117 The u2a and u2b dimers within the heptamer model are also marked by dotted and dashed gray lines, respectively.

In particular, the energy properties of the hydrogen-bonded and stacked dimers of nucleobases computed at the B3LYPD3/SNSD level have shown a very good agreement with the best theoretical estimates.54 Thus, in this work the energetics of all the cluster models has been evaluated at the B3LYP-D3/ SNSD level, whereas the less-expensive B3LYP-D3/N07D method has been considered for geometry optimizations as well as harmonic and anharmonic frequency computations. The self-consistent-charge density functional tight binding method95,96 (SCC-DFTB, or simply DFTB for conciseness) has been also used as a lower QM level within the hybrid approach (vide inf ra), following the same philosophy proposed in a previous work.97 Indeed, among the other semiempirical methods, the DFTB approach turns out to be suitable for studying the vibrational properties of large systems,108−110 especially when the parameters are fitted to reproduce accurate vibrational frequencies,108,109,111 or when analytical functions (DFTBA94) with continuous first and second derivatives are used to obtain fully analytical second energy derivatives. In particular, the latter version of the method has been employed in this work. 2.2. Anharmonic Vibrational Computations. Both B3LYP-D3/N07D and DFTBA have been applied to anharmonic vibrational frequency computations within the second-order vibrational perturbation theory (VPT2) framework,55−57,59−78 using semidiagonal quartic force fields obtained by numerical differentiation of the analytical second derivatives along each active normal coordinate (with the standard 0.01 Å step) at the geometries optimized with tight convergence criteria. The Fermi resonances have been treated

the experimental data reported in the literature (section 3.3). A summary of the results, general conclusions, and perspectives are given in the last section.

2. COMPUTATIONAL DETAILS A computational protocol for simulating the infrared spectra of large molecular systems like uracil in the solid state has been set up in the present work selecting, first of all, a realistic molecular model of the system under investigation and, then, defining reliable yet feasible quantum mechanical (QM) and VPT2related approaches for vibrational frequency computations at anharmonic level. 2.1. DFT and DFTB. The calculations at the density functional theory (DFT) level have been performed using the B3LYP83 hybrid functional, including also an empirical correction for the treatment of the dispersion effects84,85 (B3LYP-D3), in conjunction with the N07D99−102 and the SNSD58,102,103 basis sets. The B3LYP/N07D and the B3LYP/ SNSD methods have been extensively validated for the prediction of fully anharmonic vibrational frequencies with the accuracy necessary for a quantitative comparison with experimental data for systems of increasing size and complexity (see for instance refs 58, 92, 103, and 104 and references therein). Moreover, it has been shown that the inclusion of the empirical dispersion treatment improves the accuracy of structural parameters and binding energies for the chemical systems involving dispersion interactions,54,58,105−107 retaining the same accuracy of the noncorrected methods for the anharmonic frequencies. C



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Figure 2. Normalized binding energies for the different uracil cluster models, ⟨EN⟩u (eq 1), with each energy term obtained through single point calculations on the experimental crystallographic structure117 performed at the B3LYP-D3/SNSD (blue squares) and DFTBA (red squares) levels. Computed values are fitted to the functional form shown on the graph along with coefficients of determination (R2). The error bars correspond to the mean absolute errors (MAE) between computed binding energies and the (f(N)).

used to visualize normal modes and analyze in detail the outcome of vibrational computations, i.e., the Duschinsky matrix describing the mixing between the two sets of the normal modes.

within the generalized VPT2 scheme (GVPT2), where the nearly resonant contributions are removed from the perturbative treatment (leading to the deperturbed model, DVPT2) and variationally treated in a second step. 55,64,69,77 This model55,56,77 provided accurate vibrational wavenumbers for several semirigid systems (see for instance ref 58 and references therein). The hybrid approach58,80,82,97,103,104,112,113 has been applied to reduce the computational burden associated with the calculation of the anharmonic frequencies of the largest clusters. Within a hybrid scheme the harmonic part is computed at a higher level of theory and/or with larger basis sets, whereas the anharmonic corrections are evaluated by computationally less demanding models (see ref 58 and references therein). In this work the harmonic part has been evaluated at the B3LYP-D3/N07D level and the anharmonic corrections have been included in an approximate fashion with the DFTBA method (see also ref 97). The reduced dimensionality VPT2 (RD-VPT2) approach58,89,92 has been employed as an alternative for the evaluation of approximate anharmonic frequencies. Within the RD-VPT2 approach, the most demanding computation, namely, the numerical differentiation of analytical Hessian, is performed only along a restricted set of “active modes”. Such selected modes are included into the VPT2 treatment along with the couplings with the other modes which, instead, are treated at the harmonic level. A detailed description of such an approach has been given in refs 58 and 89. Here we just note that the reliability of the RD-VPT2 approach is ensured when the set of active modes is large enough to include all the couplings between the modes contributing to the frequencies of interest. The correct choice of the active modes can be based on the nature of the vibrations and the related energy range, allowing us to take into account all the vibrations of specific functional groups, which have similar frequencies and are likely to be coupled.89 Alternatively, lower level electronic structure computations, resonance conditions, or normal mode similarity (see ref 114 and references therein) can be also applied to define the reduced dimensionality schemes. All calculations have been carried out employing the Gaussian suite of programs.115 A graphical user interface for a virtual multifrequency spectrometer (VMS-Draw)116 has been

3. RESULTS AND DISCUSSION 3.1. Cluster Models. 3.1.1. Energetics. The molecular crystal of uracil is a monoclinic system, belonging to the P21/a space group117 with cell parameters a = 11.938 ± 0.001 Å, b = 12.376 ± 0.0009 Å, c = 3.6552 ± 0.0003 Å, β = 120°54′ ± 0.4′. The uracil molecules in the crystal interact through NH−O and CH−O hydrogen bonds, forming parallel layers along the (001) crystal plane, and such layers are held together by stacking interactions, with a regular spacing of 3.136 Å.117 To study the spectroscopic properties of the uracil crystal,8,30 the symmetry operations of the space group, the cell parameters and the fractionary coordinates of the atoms obtained by crystallographic measurements of uracil in the solid state117 have been used to design different cluster models of increasing size (Figure 1), to take gradually into account all the intermolecular interactions influencing the vibrational frequencies. The monomeric unit of uracil (u1) is the simplest model that we have considered. A slightly more sophisticated model is represented by the two different types of uracil dimers (u2a and u2b) appearing in the crystal (Figure 1), showing two N3−H− O4 and one N1−H−O4 hydrogen bonds, respectively. More accurate cluster models of the infinite layers are the tetramer (u4), the hexamer (u6), the heptamer (u7), the two decamers (u10a) and (u10b) based on (u2a) and (u2b), respectively, and the cluster composed of 14 uracil molecules (u14). Furthermore, for reasons related to the evaluation of the binding energies (vide inf ra), four ring-shaped cluster models (r6, r8a, r8b, r10) have been also employed, obtained by removing the one, two, and four central uracil units from u7, u10a, u10b, and u14, respectively. It is worth noting that in all such cluster models the influence of the stacked layers on energies, geometries and vibrational frequencies has been neglected. The total binding energy of a cluster model composed by N > 1 uracil units can be evaluated as the difference between the total energy of the cluster (EuN) and the total energy of N isolated uracil units at the solid state geometry (Eu1). By D



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corresponding values of f(N), have been used as an average estimate of the errors on each point, and have been graphically visualized as the error bars. Despite different absolute values, the trends obtained with the B3LYP-D3/SNSD and the DFTBA methods are quite similar and the energy convergence is reached at the heptamer model. For both B3LYP-D3/SNSD and the DFTBA methods the value of ⟨Ec+r⟩HB remains almost constant in the different cluster models, with the most accurate B3LYP-D3/SNSD result of about 6 kcal mol−1 (average of 5.7 kcal mol−1 and MAE of 0.2 kcal mol−1) despite the size of the system. 3.1.2. Geometries. Geometry optimizations with tight cutoffs on forces and step-size convergence have been performed for u1, u2a, u2b, and u7 models, at the B3LYPD3/N07D and the DFTBA levels. The most relevant structural parameters of the optimized geometry of u2a, u2b, and u7 have been compared with the available experimental crystallographic data,117 to evaluate the effect of the optimization on the overall structures, and the hydrogen bond distances are reported in Tables 4 and 5 in the Supporting Information. For all the three cluster models average errors of about 4% with the B3LYP-D3/ N07D method and 8% at the DFTBA level have been found. 3.1.3. Frequencies. For u1, u2a, and u2b clusters the full VPT2 anharmonic treatment is feasible at the B3LYP-D3/ N07D level. Comparing such frequencies with the experimental spectrum of the uracil crystal, large errors are found for several modes, especially the ones related to the moieties involved in the hydrogen bonds. For example, the errors of both the N1 H1 and N3H3 stretching frequencies of u1 are larger than 350 cm−1, as well as the errors related to the frequency of the CO stretching mode (about 100 cm−1). Moreover, each of the dimers accounts only for specific hydrogen bond interactions (N3HO4 or N1HO4), whereas errors of the same magnitude are found for the frequencies of the other NH stretching modes not involved in the hydrogen bonds. This suggests that the correct inclusion of all the hydrogen bonds of the crystal is required to assign and predict the experimental infrared spectrum in the solid state. In this sense, the uracil heptamer can be viewed as a focused model in which the hydrogen bonds between the central monomer and its surroundings (N1H1O4H3N3 motif) are included consistently with the periodic crystal, leading to a model mimicking the chemical interactions occurring in the solid state uracil. However, such a system involves 84 atoms, resulting in 246 normal modes, and the complete VPT2 treatment requires 493 Hessian computations to obtain the full semidiagonal quartic force field via numerical differentiation of the analytical second derivatives. It should be noted that a general VPT2 framework to compute thermodynamic properties, vibrational energies, and transition intensities developed by Barone and co-workers55−57,77,78 is not limited by the number of nuclear degrees of freedom, as far as the necessary force fields are provided. However, such computations are not feasible at the B3LYP-D3/N07D level with the full VPT2 approach, so that the hybrid B3LYP-D3/N07D:DFTBA scheme and the RD-VPT2 approach with the B3LYP-D3/ N07D method have been applied. 3.2. Validation of Hybrid and Reduced Dimensionality VPT2 Approaches. The hybrid and RD-VPT2 approaches have been first validated by comparison with the B3LYP-D3/ N07D full-dimensional VPT2 results for uracil dimers and, then, used for the computations of anharmonic vibrational frequencies for the heptamer model of uracil in the solid state.

dividing such an energy by N or by the total number of the hydrogen bonds (NHB) occurring in the cluster, the average binding energies per uracil unit (⟨EN⟩u) or per hydrogen bond (⟨EN⟩HB) are obtained as

⟨EN ⟩u =

EuN − NEu1 N

(1)

and ⟨EN ⟩HB =

EuN − NEu1 N HB

(2)

However, both these approaches tend to treat all the uracil units in the same fashion, whereas the clusters are intended to be focused models, providing a more realistic description for the central uracil unit considering the outer ones as an environment. For this reason, in the case of the largest cluster models (u7, u10a, u10b, and u14) a more suitable definition of the average hydrogen bond energy can be formulated by calculating the total binding energy as the difference between the total energy of the cluster and the total energy of the noninteracting central units (Ec: u1, u2a, u2b, and u4, respectively) and rings (Er: r6, r8a, r8b, and r10, respectively) ⟨Ec + r⟩HB =

EuN − (Ec + Er) NcHB +r

(3)

where EuN is related to u7, u10a, u10b, and u14. In this case the normalization is performed by dividing the energy by the number of the hydrogen bonds connecting the central units and the rings (NHB c+r ). It has been also verified that the latter approach is less affected by the basis set superposition error (BSSE).118 All the total energies have been obtained by single point calculations at the B3LYP-D3/SNSD and DFTBA levels, using the experimental crystallographic geometries and without performing any optimization. Figures 2 and 3 report the resulting ⟨EN⟩u, ⟨EN⟩HB, and ⟨Ec+r⟩HB as a function of the cluster size. The convergence of the normalized binding energies is represented by a fit function (f(N)), shown on the graph along with the coefficients of determination (R2). The error bars computed as mean absolute errors (MAE) between the binding energies and the

Figure 3. Mean hydrogen bond energies for the cluster models ⟨E⟩HB: ⟨EN⟩HB (eq 2, squares) and ⟨Ec+r⟩HB (eq 3, circles), evaluated at the B3LYP-D3/SNSD (blue) and DFTBA (red) levels. The average ⟨E⟩HB over all cluster models are shown as a horizontal lines. The error bars correspond to the mean absolute errors (MAE) between computed binding energies and the average ⟨E⟩HB. E



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Figure 4. Graphical representation of the correspondences between normal modes computed with B3LYP-D3/N07D and DFTBA methods for the uracil heptamer. Assignments were performed on the basis of the atomic displacements along normal modes. The JHL matrix and normal modes are visualized using the VMS-Draw tool;116 a gray scale is used to represent the magnitude of each element of the JHL matrix, with a white square for a near-null value and a black square for 1 (equivalent normal modes). Selected modes of the central uracil unit with large and negligible mode mixing are marked by red and green arrows, respectively, and are shown in the insets.

3.2.1. Hybrid Frequencies. The hybrid approach can be appropriately used only when the vibrational modes computed with the two different methods have an univocal correspondence; otherwise, the respective anharmonic force fields should be transformed accordingly, which would be unfeasible for large molecular systems. The similarity between two sets of normal modes can be inferred by analyzing a “Duschinsky-like matrix”119 (JHL). With LH and LL, the rectangular matrices that define the mass weighted Cartesian−mass weighted normal coordinates transformation of the high- and low-level methods, respectively, the JHL matrix is the product matrix LHLL, and it deviates from the identity matrix as far as the normal mode definition is different between the two methods. With such an approach (commonly applied also to vibronic computations120,121 to define a linear transformation between the normal modes of two electronic states), JHL describes the projection of the normal coordinate basis vectors computed at the DFTBA level on those computed at the B3LYP-D3/N07D level. The latter are used for the assignments of molecular vibrations, based on the inspection of the atomic displacements along normal modes, whereas normal modes computed at the DFTBA level are assigned as linear combinations of the B3LYPD3/N07 ones, as derived from the analysis of the JHL matrix coefficients. For example, highlighted DFTBA vibrations (in columns, Figure 4) correspond to the combinations of normal modes assigned as γ(CH) and γ(C4O) (B3LYP-D3/N07D, in rows). Duschinsky transformation has been used also to derive mode-specific anharmonic corrections to be applied to the excited state frequencies122 and can be applied also to the ground state in the spirit of hybrid models. Figure 4 reports JHL related to the B3LYP-D3/N07D and the DFTBA modes of the uracil heptamer, using a color scale for the magnitude of the JHL matrix elements (the darker, the more it is close to unity). In this figure subsets of normal modes that are consistently defined by the two methods can be identified, suggesting that the hybrid approach can be applied.

Regarding the frequencies, a statistical analysis of the deviations between the ones computed with the DFTBA method and the ones at the B3LYP-D3/N07D level for the uracil monomer and the dimers u2a and u2b is presented in Table 1, whereas the detailed comparison between the B3LYPD3 and DFTBA harmonic and anharmonic vibrational frequencies for the monomer in the whole spectral region and the dimers in the high-frequency spectral region are Table 1. Deviations of Harmonic and Anharmonic Vibrational Frequencies (cm−1) Computed with the DFTBA Method Respect to the B3LYP-D3/N07D Results for the Uracil Monomer and the Dimers u2a and u2ba DFTBA vs B3LYP-D3 Δharme

Δanharmf

Δanharm shiftg

MAEb u u2a u2b

65.3 141.9 133.3

u u2a u2b

−233 −270 −471

u u2a u2b

180 178 166

55.3 155.7 126.3 MINc −198 −580 −456 MAXd 149 146 136

16.7 43.6 (22.1) 27.9 (24.0) −40 −310 (−40) −102 (−40) 39 38 (38) 43 (43)

a

In brackets are the mean absolute errors (MAEs), the minimum negative deviations (MIN), and the maximum positive deviations (MAX) obtained by exclusion of the N3H stretching vibrational modes of both monomeric units in the dimer u2a and of the N1H stretching vibrational mode of monomer 1 in u2b, respectively. bMean absolute error. cMinimum negative deviation. dMaximum positive deviation. eDeviation between harmonic frequencies. fDeviation between anharmonic frequencies. gDeviation of anharmonic shifts. F



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Table 2. Anharmonic Vibrational Frequencies (cm−1) for the Hydrogen-Bonded Uracil Dimers u2a and u2b, Computed at the B3LYP-D3/N07D Level through a Fully Anharmonic and Reduced Dimensionality VPT2 (RD-VPT2) Treatmenta

reported in Tables 6−8 in the Supporting Information. Although the absolute values of the harmonic and anharmonic DFTBA vibrational frequencies show large differences with respect to B3LYP-D3/N07D for both the dimers and the monomer, the anharmonic corrections computed with the DFTBA method are sufficiently close to the ones computed at the B3LYP-D3/N07D level, with MAEs of 16.7 cm−1 for the uracil monomer, 43.6 cm−1 for u2a, and 27.9 cm−1 for u2b. Moreover, the most significant deviations of the anharmonic shifts for the dimers are related to the stretching modes of the NH groups involved in the hydrogen bonds, namely, both the N3H groups of u2a and the N1H group of the monomer M1 in u2b. However, it is worth noting that such strongly anharmonic vibrations usually require accurate description of the underlying PES, 123 which is difficult to achieve especially when approximate approaches such as the DFTBA method are employed. Excluding these modes, the MAEs are lower than about 22−24 cm−1 for both dimers, with maximum deviations of about 40 cm−1. These results indicate that the DFTBA method can be used for the computation of the anharmonic corrections within the hybrid scheme, accordingly to ref 97. 3.2.2. RD-VPT2 Frequencies. As briefly discussed in section 2, the reliability of the RD-VPT2 approach is strongly dependent on the selection of the set of “active modes”. The validation of the active modes has been performed on the basis of the full-dimensional B3LYP-D3/N07D anharmonic computations available in the case of the dimers, comparing those fulldimensional vibrational frequencies with the anharmonic frequencies obtained through the RD-VPT2 treatment. As reported in Table 2, choosing as active modes those corresponding to the high-frequency region, namely, ν(N1H), ν(N3H), ν(C5H), ν(C6H), ν(C2O), ν(C4O), ν(C5C6), δ(N1H), and ν(ring), it is possible to obtain anharmonic frequencies that are in good agreement with the fulldimensional VPT2 ones. It can be noted that the overall deviations between the full-dimensional and RD-VPT2 frequencies are very small, with MAEs of 6.2 and 4.9 cm−1 for u2a and u2b, respectively, and maximum deviations below 35 cm−1. Therefore, we have assumed that such vibrational modes may constitute a minimum “active set” to obtain a reliable prediction of the higher vibrational frequencies for the uracil molecule in the center of the heptamer cluster. 3.3. Comparison with Experiments: Mixed Hybrid and RD-VPT2 Scheme. The hybrid B3LYP-D3/N07D:DFTBA approach has been applied to the heptamer model, providing anharmonic frequencies whose harmonic part has been computed at the B3LYP-D3/N07D level whereas the anharmonic correction has been evaluated by means of the DFTBA method. First, we have selected, among the 246 normal modes, the vibrational frequencies relative to the central uracil molecule, which has been considered as the target for predicting the vibrational frequencies of uracil in the solid state. Due to the inevitable mixing of the contributions of the various atoms to the normal modes occurring in very large systems like the heptamer cluster, the assignment of the normal modes of the central uracil molecule has been performed not only by visual inspection but also by examining in detail the values of the atomic displacements along the normal modes. It can be noted that such a procedure can be facilitated by localized mode approaches90,91,124 or use of other (i.e., mixed Cartesian− internal) coordinate systems. Then, we have analyzed the JHL matrix of the heptamer to verify the correspondences between the modes of the central uracil molecule computed with the

anh mode

FULL-VPT2

RD-VPT2

66 65 62 59 64 63 61 60 58 57 56 55 54 53 52 51 50 49 48 47 MAE MIN MAX

3476 3476 2998 2960 3124 3128 3089 3080 1788 1783 1696 1687 1630 1643 1473 1474 1447 1444 1390 1387

3473 3473 2977 2926 3121 3126 3088 3078 1782 1776 1692 1684 1633 1633 1478 1479 1453 1448 1389 1386 6.2 −34 6

66 63 65 64 62 59 61 60 58 57 56 55 54 53 52 51 50 49 48 47 MAE MIN MAX

3472 3121 3440 3435 3124 3074 3088 3081 1779 1761 1747 1694 1639 1641 1522 1468 1399 1391 1386 1379

3477 3117 3442 3436 3123 3068 3086 3082 1780 1755 1723 1678 1633 1628 1524 1467 1404 1390 1387 1380 4.9 −24 6

assignmentb u2a ν(N1H) (M1,M2) ν(N1H) (M1,M2) ν(N3H) (M1,M2) ν(N3H) (M1,M2) ν(C5H) (M1,M2) ν(C5H) (M1,M2) ν(C6H) (M1,M2) ν(C6H) (M1,M2) ν(C2O) (M1,M2) ν(C2O) (M1,M2) ν(C4O), ν(ring), δ(N3H) (M1,M2) ν(C4O), ν(ring), δ(N3H) (M1,M2) ν(C5C6) (M1,M2) ν(C5C6) (M1,M2) δ(NH) + δ(CH) (M1,M2) δ(NH) + δ(CH) (M1,M2) δ(N3H) (M1,M2) δ(N3H) (M1,M2) ν(ring), δ(N1H) (M1,M2) ν(ring), δ(N1H) (M1,M2)

u2b ν(N1H) (M2) ν(N1H) (M1) ν(N3H) (M1) ν(N3H) (M2) ν(C5H) (M1) ν(C5H) (M2) ν(C6H) (M2) ν(C6H) (M1) ν(C2O) (M2) ν(C2O) (M1) ν(C4O) (M1) ν(C4O) (M2) ν(C5C6) (M1) ν(C5C6) (M2) ν(ring), δ(N1H) (M1) ν(ring), δ(N1H) (M2) δ(NH) + δ(CH) (M1) δ(NH) + δ(CH) (M2) ν(ring), δ(NH) (M2) ν(ring), δ(N1H) (M1)

a

Mean absolute errors (MAEs), minimum negative deviations (MIN), and maximum positive deviations (MAX) with respect to the fully anharmonic VPT2 treatment are also reported. bAbbreviations: ν = stretching; δ = in-plane bending; γ = out-of-plane bending; M1 = monomer 1 in the uracil dimers; M2 = monomer 2 in the uracil dimers.

G



Article

Table 3. Vibrational Frequencies (cm−1) for the Uracil Monomer and Central Uracil Unit in the Heptamer Model, Obtained at Different Levels of Theory Including the Hybrid B3LYP-D3/N07D:DFTBA and the Reduced Dimensionality VPT2 (RDVPT2) Approaches, with Corrections Based on the Best Estimated Harmonic Frequencies Available for the Uracil Monomer Evaluated by the Composite Scheme at the CCSD(T)/CBS(T,Q+aug)+CV levela,b uracil monomer

uracil heptamer

solid uracil

B3LYP-D3

CCSD(T)

CCSD(T)

B3LYP-D3

hybrid B3LYP-D3

RD-VPT2

CC+RD-VPT2

/N07D

/CBS+CVb

/B3LYPb

/N07D

/N07D:DFTBA

+hybrid

+hybrid

harm

harm

anharm

harm

anharm

anharm

anharm

3647

3653

3472

3607 3261 3219 1810

3602 3253 3218 1790

3430 3113 3062 1771

1776 1675 1504 1409 1421 1385 1232 1089 970 990 968 815 770 761 562 544 523

1762 1678 1505 1414 1427 1394 1248 1084 968 995 973 814 765 773 545 541 517

1747 1640 1455 1367 1390 1349 1204 1064 947 978 946 803 748 753 549 534 515

95.1 −47 607

95.0 −42 602

73.2 −89 430

3298 3243 3266 3231 3208 1792 1773 1691 1652 1570 1505 1458 1424 1285 1133 1033 1000 873 851 801 772 592 586 552 542 58.9 −12 266

2999 2904 2935 3109 3005 1803 1781 1634 1624 1520 1481 1436 1276 1115 1019 995

796 762 586 547 554 32.0 (11.8) −202 (−7) 42 (34)

3074 3076 3036 3069 3053 1746 1725 1651 1615 1537 1471 1436 1395 1276 1115 1019 995 781 771 796 762 585 586 547 554 17.3 −47 36

3079 3081 3031 3060 3051 1725 1705 1636 1618 1538 1477 1443 1405 1292 1110 1016 1001 786 770 791 774 569 583 541 548 21.7 −56 50

experimental assignmente 3106 sh

c

ν(N1H)

3000 3088 3040 1761

mc sc md vsd

ν(N3H) ν(C5H), ν(N1H) ν(C6H) ν(C2O)

1652 1616 1509 1456 1421 1391 1242 1099 1006 994 828 807 782 762 585 569 554

md wd sd vsd vsd sd vsd wd vsd sd sd md wd sd sd vsd md

ν(C4O) ν(C5C6) δ(N1H) ν(ring), δ(N1H), δ(N3H) δ(N3H) + δ(CH) δ(CH), ν(ring), δ(NH) ν(ring), δ(NH), δ(CH) ν(ring), δ(CH), δ(N1H) ν(ring), δ(N3H), δ(CH) δ(ring) γ(CH), γ(C4O) γ(CH), γ(C4O) ring breathing γ(C2O) δ(ring) δ(CO), δ(ring) δ(ring) MAE MIN MAX

a

Mean absolute errors (MAEs), minimum negative deviations (MIN), and maximum positive deviations (MAX) of computed vibrational frequencies with respect to the experimental data for uracil in the solid statec,d are also reported. bFrom ref 98. cFrom ref 30. dFrom ref 9. eAbbreviations: ν = stretching; δ = in-plane bending; γ = out-of-plane bending.

in the high-frequency region are excluded (reported in brackets in Table 3), similarly the minimum negative and maximum positive deviations decrease from −202 to −7 cm−1 and from 42 to 34 cm−1, respectively. The hybrid B3LYP-D3/N07D:DFTBA results for the heptamer can be improved by the application of the RDVPT2 treatment. Thus, the RD-VPT2 approach has been used to compute the anharmonic frequencies of the four modes excluded from the hybrid calculation due to their nonunivocal correspondence between the B3LYP-D3/N07D and DFTBA methods (as discussed above) along with the highest vibrational frequencies, largely influenced by the hydrogen bonds, namely, the 11 vibrational modes of the central uracil molecule in the heptamer corresponding to the ν(N1H), ν(N3H), ν(C5H), ν(C6H), ν(C2O), ν(C4O), ν(C5C6), δ(N1H), and ν(ring) vibrational modes, previously validated as the preferential active set. The RD-VPT2 frequencies have been reported in Table 3 (highlighted in bold) and combined with the hybrid B3LYPD3/DFTBA ones within the final hybrid+RD-VPT2 set, which has been compared with the experimental data for uracil in the solid state.9,30 With this approach, a better agreement with the highest experimental frequencies of the solid uracil has been

B3LYP-D3/N07D method and the ones computed at DFTBA level. In particular, we have found four modes for which the correspondence is not unique, namely, the δ(CH), ν(ring), and δ(NH) modes at 1424 cm−1, the γ(CH) and γ(C4O) modes at 873 and 851 cm−1, and the δ(ring) mode at 592 cm−1 (all frequency values and assignments refer to the B3LYP-D3/ N07D harmonic computations). Thus, such modes have been excluded from the hybrid calculation and afterward treated with a RD-VPT2 approach. Table 3 reports the anharmonic frequencies of the central uracil unit in the heptamer model computed with the hybrid B3LYP-D3/N07D:DFTBA approach. As shown, such an approach provides anharmonic vibrational frequencies that are in rather good agreement with the experimental ones, with particular exception for those corresponding to the stretching of the amino groups and, to some extent the carbonyl groups, which are involved in the hydrogen bonds. As discussed above for uracil dimers, vibrations involved in hydrogen-bonded bridges are characterized by an underlying strongly anaharmonic PES, which is poorly described by the less accurate DFTBA method. Indeed, although the MAE is 32.0 cm−1 when all the vibrational modes are taken into account, it lowers to 11.8 cm−1 when the modes H



Article

Table 4. Shifts of the Experimental Frequencies (cm−1) of Uracil in the Solid Statea with Respect to Uracil Isolated in Argon Matrix,b Compared with the Shifts (cm−1) Obtained by B3LYP-D3/N07D Computations for the Uracil Dimers u2a and u2b (Fully Anharmonic Frequencies) and the Heptamer (RD-VPT2 Frequencies) with Respect to the Fully Anharmonic Frequencies of the Uracil Monomer

achieved and the overall MAE, obtained by mixing the RDVPT2 frequencies with the hybrid ones, turns out to be of 17.3 cm−1. Such an error can be considered sufficiently accurate, in particular taking into account the size of the system and some uncertainties of the experimental frequencies related to the N− H stretching vibrational modes.9,30,125 Then, it is also possible to further extend the computational model (based on additivity assumptions) by applying corrections to the harmonic frequencies of the central unit, based on the best theoretical estimates for the uracil monomer, along with the anharmonic and complexation effects at the hybrid+RD-VPT2 level as described above. In the present case we have used the harmonic frequencies of the uracil monomer evaluated by a composite scheme at the coupled cluster (CC) level (CCSD(T)/CBS(T,Q+aug)+CV),98 and the results are reported in the last column of the uracil heptamer in Table 3. It can be noted that, in the present case, such correction leads to some improvement for the highest frequency modes, related to the N−H stretching vibrations, but on the whole it does not improve over the B3LYP-D3/N07D:DFTBA results, highlighting the good accuracy of the latter. Finally, our anharmonic results for uracil heptamer can be compared with harmonic and anharmonic frequencies for uracil monomer and harmonic B3LYP/N07D values for uracil heptamer, also listed in Table 3. It is clear that neither harmonic values nor best anharmonic estimates for monomer are adequate for the assignment of experimental data, showing discrepancies as large as several hundreds of wavenumbers for modes involved in hydrogen-bonding interactions in solid uracil. The situation is improved once the complexation effects are accounted for in the uracil heptamer, but clearly, only including hydrogen bonding in molecular cluster and anharmonic effects makes it possible to obtain sufficiently accurate results. Moreover, to verify the reliability and accuracy of our computational model, Table 4 compares the shifts of the experimental frequencies of uracil in the solid state9,30 with respect to uracil isolated in an argon matrix25−27 and the corresponding shifts obtained from the simulations for the uracil dimers and the heptamer, i.e., the shifts of the fully anharmonic frequencies of the dimers and the RD-VPT2 anharmonic frequencies of uracil in the heptamer with respect to the fully anharmonic frequencies for the uracil monomer, computed at the B3LYP-D3/N07D level.54 The results show that the heptamer model is more suitable than the dimers for assigning the IR bands of the solid uracil. Indeed, both models based on the dimers provide only a partial description of the multiple interactions involving the uracil molecules in close contact in the solid phase, whereas in the heptamer model the central molecule is completely surrounded by other uracil molecules, simulating more realistically the actual environment of each uracil molecule in the crystal structure. Experimentally, the remarkable effect of the intermolecular interactions taking place through strong hydrogen bonds between the proton donor and acceptor moieties is rather evident, with the most significant red shifts with respect to isolated uracil of about 376 cm−1 for ν(N1H1), 433 cm−1 for ν(N3H1), 42 cm−1 for ν(C5H5), and 81 cm−1 for ν(C4O4). These findings are all well reproduced by the anharmonic computations, using the heptamer as a molecular model. Considering the accuracy of fully anharmonic frequencies of the uracil monomer of about 10 cm−1, these results indicate that the B3LYP-D3/N07D RDVPT2 treatment provides a good prediction of the vibrational

Δν calculated assignmentc

Δν experimental

ν(N1H)

−376

ν(N3H)

−433

ν(C5H)

−42

ν(C2O)

−1

ν(C4O)

−81

ν(C5C6)

−28

u2a 3 3 −432 −470 15 20 18 13 −53 −62 −9 5

(M1,M2) (M1,M2) (M1,M2) (M1,M2) (M1,M2) (M1,M2) (M1,M2) (M1,M2) (M1,M2) (M1,M2) (M1,M2) (M1,M2)

u2b −1 −351 11 5 15 −35 9 −10 −2 −55 0.3 2

(M2) (M1) (M1) (M2) (M1) (M2) (M2) (M1) (M1) (M2) (M1) (M2)

u7 −399 −393 −40 −24 −98 −23

From refs 9 and 30. bFrom refs 25−27. cAbbreviations: ν = stretching; δ = in-plane bending; γ = out-of-plane bending; M1 = monomer 1 in the uracil dimers; M2 = monomer 2 in the uracil dimers.

a

frequencies for the heptamer. Thus, we have also attempted to assign some of the experimental bands of the most recent experiment by some of us, not assigned previously due to the lack of reliable computational data for the comparison.9 Figure 5 shows the experimental spectrum of solid uracil from ref 9 providing the most complete assignment up to date for this molecular system.

4. CONCLUSIONS Computational spectroscopy has become in the last years an effective tool for the interpretation of the spectroscopic features of molecular systems of increasing size and complexity, in a wide range of boundary conditions simulating different environments. Indeed, the experimental outcomes become more and more intricate as the system under study increases in size and complexity, such as in the condensed phases, due to the variety of intra- and intermolecular interactions that may take place for example between solute and solvent molecules in the liquid phase or among the molecules in close contact in the crystal structure of a molecular solid or between molecular adsorbates and solid substrates and so on. In such cases, computational simulations may be crucial to dissect the various molecular contributions to the spectroscopic signals, allowing a deeper understanding of the underlying phenomena. Nevertheless, it is quite challenging to develop a comprehensive, reliable, and effective computational protocol for simulating the spectroscopic properties of large complex molecular systems. We are working along these lines to set up feasible computational models for anharmonic computation of vibrational frequencies within the VPT2 framework. In particular, in this work we have calculated at the anharmonic level the vibrational frequencies of uracil in the solid state, choosing a heptamer unit as model system (which is repeated on each layer in the uracil crystal structure) and combining the following methods: (i) the hybrid B3LYP-D3/N07D:DFTBA I



Article

Figure 5. Experimental IR spectrum of solid uracil in the 550−1900 cm−1 range9 along with experimental (blue) and theoretical (black, in parentheses) wavenumbers. The asterisk corresponds to the tentative assignment as a nonfundamental transition. The band assignment proposed in this work is marked in red.

solid state. Indeed, the shifts of the vibrational frequencies due to the hydrogen bonds between proton donor and acceptor moieties are particularly large, up to about 400 cm−1 for the N− H stretching modes, and assignments of the IR bands of molecules like nucleobases in condensed phases based on gasphase spectroscopic data may be misleading. More generally, we have presented a reliable and feasible computational protocol for simulating the IR spectra of quite large systems at anharmonic level, combining the hybrid B3LYP-D3/N07D:DFTBA approach with the RD-VPT2 one. Such a protocol is particularly promising to analyze and assign the IR spectroscopic features and, hence, to investigate the properties and processes of large systems, ranging from molecular clusters and biopolymers to macromolecular systems in complex environments like monolayers of biomolecules on solid supports, therefore finding numerous applications in different areas such as materials science, surface science, catalysis, nanotechnology, biosensing, biotechnology, and astrobiology.

method, in which the harmonic frequencies are computed at the B3LYP-D3/N07D level of theory and the anharmonic shifts are evaluated at a lower level of theory, namely DFTBA, and (ii) the reduced dimensionality VPT2 (RD-VPT2) approach, using the B3LYP-D3/N07D method, where only selected vibrational modes are computed anharmonically (including the couplings with other modes) whereas the remaining modes are treated at the harmonic level. Using the hybrid B3LYP-D3/N07D:DFTBA approach for the heptamer model, we have obtained anharmonic vibrational frequencies quite close to the experimental ones for uracil in the solid state,9,30 except the high-frequency region where the stretching modes of the functional groups involved in the hydrogen bonds are present. Indeed, although the MAE is 32.0 cm−1 when all the vibrational modes are taken into account, it lowers to 11.8 cm−1 when the modes in the high-frequency region are excluded. Such strongly anharmonic vibrations within hydrogen-bonded bridges are, as expected, poorly described by the less accurate DFTBA method, requiring QM models that allow us to take into account correlation effects, in line with what is observed for other hydrogen-bonded systems.123 Therefore, the highest vibrational frequencies of the heptamer, with the addition of the modes that do not show an univocal correspondence between the B3LYP-D3 and DFTBA methods, have been computed at the anharmonic level through a reduced dimensionality VPT2 (RD-VPT2) approach. In this way, we have obtained an overall accurate description of the vibrational frequencies of uracil in the solid state with a MAE of 17.3 cm−1. These theoretical results reproduce very well the significant experimental shifts of the vibrational frequencies of uracil due to the intermolecular hydrogen bonds in the solid state with respect to uracil isolated in an argon matrix,25−27 allowing us also to provide some new assignments of the experimental spectrum of uracil in the solid state.9 Results reported in this work suggest that the vibrational frequencies of uracil in the solid state can be reliably simulated with a molecular model based on a heptamer cluster that is repeated in the uracil crystal structure. In particular, such an extended molecular model is more suitable with respect to the dimers and especially the monomer for simulating uracil in the

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ASSOCIATED CONTENT

S Supporting Information *

(i) Normalized B3LYP-D3/SNSD and DFTBA binding energies and mean hydrogen bond energies for the different uracil cluster models. (ii) Comparison between hydrogenbonded dimer structures optimized with the B3LYP-D3/N07D and DFTBA methods. (iii) Harmonic and anharmonic vibrational frequencies for the uracil monomer and dimers computed with B3LYP-D3/N07D and DFTBA methods. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*M. Biczysko. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/ 2007-2013) under grant agreement No. ERC-2012-AdGJ



Article

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320951-DREAMS and from Italian MIUR (under the project PON01-01078/8). The authors gratefully thank Prof. Vincenzo Barone and Dr. Julien Bloino for fruitful discussions. The highperformance computer facilities of the DREAMS center (http://dreamshpc.sns.it) are acknowledged for providing computer resources. I.C. acknowledge Compunet of IIT for the financial support. The authors thank Dr. John Robert Brucato of the INAF-Astrophysical Observatory of Arcetri for providing the experimental data of IR spectroscopic measurements of uracil in solid state. The support of the COST CMTSAction CM1002 “COnvergent Distributed Environment for Computational Spectroscopy (CODECS)” is also acknowledged.

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