Bifurcated Hydrogen Bond in Lithium Nitrate Trihydrate Probed by ab

Article pubs.acs.org/JPCA

Bifurcated Hydrogen Bond in Lithium Nitrate Trihydrate Probed by ab Initio Molecular Dynamics Francesco Muniz-Miranda,† Marco Pagliai,‡ Gianni Cardini,†,‡ and Roberto Righini*,†,‡ †

European Laboratory for Nonlinear Spectroscopy (LENS), via Nello Carrara 1, 50019 Sesto Fiorentino (Firenze), Italy Dipartimento di Chimica “Ugo Schiff”, Università degli Studi di Firenze, via della Lastruccia 3, 50019 Sesto Fiorentino (Firenze), Italy

‡

ABSTRACT: The hydrogen-bond dynamics of lithium nitrate trihydrate has been studied by a combined approach based on ab initio molecular dynamics simulations and wavelet analysis. The simultaneous bifurcated interaction between one hydrogen atom of water molecules and two oxygen atoms of nitrate ions is the pivotal feature of the crystal structure: this bifurcated interaction has deep effects on the O−H stretching region of the vibrational spectrum. The structural, dynamic, spectroscopic, and electronic properties of the bifurcated hydrogen bond have been investigated computationally, elucidating at the molecular level the differences with weak and strong hydrogen bonds present in the crystal. These studies corroborate the very recent IR experiments performed on the lithium nitrate trihydrate crystal, offering new perspectives to interpreting the vibrational spectra. In fact, this approach allows obtaining two-dimensional plots, which summarize the essential features of both the hydrogen-bond network and IR spectra, resulting in a peculiar “signature” of the bifurcated interaction.

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INTRODUCTION The hydrogen bond occurring in water is closely related to the most peculiar properties of this solvent, and it has been the subject of many experimental1−10 and computational studies.11−15 As a matter of fact, the network of water molecules evolves in time exploring different types of hydrogen bonds (HBs) during their formation and breaking.16−18 This evolution can be viewed as succession of different transient structures occurring in the dynamics of water molecules; recently Laage and Hynes19,20 proposed a bifurcated model to describe the transition state of hydrogen-bonded species as they switch from one HB acceptor to the other. This type of bond is deeply involved in the formation of biologically relevant structures,21 but actually, in pure water bifurcated or strained HBs have extremely short lifetime (∼100 fs as an order of magnitude), as shown by two-dimensional IR studies.22−24 Pandelov et al.25 recently showed that the geometry and dynamics of those peculiar structures are, instead, well accessible for water molecules confined in crystalline ionic hydrates. Lithium nitrate trihydrate is an inorganic salt where the water molecules are constrained by the lattice forces into a characteristic crystalline arrangement.26,27 In this crystal, water is involved in three different types of HBs: a strong one between water molecules, a weak one between water and nitrate anions, and a bifurcated one where the hydroxyl group of water is directed halfway between two N−O bonds of nitrate (see Figure 1). Due to the crystalline nature of this salt, about one-third of water molecules are engaged in bifurcated HBs that persist for quite a long time, in contrast to what happens in pure liquid © 2012 American Chemical Society

Figure 1. Simulation cell. Some selected H-bond interactions are represented with dotted blue lines. Water molecules and nitrate ions, whose interactions are not explicitly shown, are represented with translucent cyan and green colors, respectively.

water. Werhahn et al.28 have recently characterized crystalline LiNO3·(HOD)(D2O)2 by means of IR spectroscopy and interpreted the OH stretching region of the IR spectrum as being due to the superposition of the stretching bands of the hydroxyl Received: December 13, 2011 Published: February 6, 2012 2147

dx.doi.org/10.1021/jp2120115 | J. Phys. Chem. A 2012, 116, 2147−2153

The Journal of Physical Chemistry A

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where ω is the frequency in wavenumbers, μ(t) is the water dipole moment projected along the O−H or O−D unit vector, I(ω) is the IR intensity mainly due to O−H or O−D stretching modes, and - is the Fourier transform. Saving the MLWF centers at ∼3 fs intervals for a ∼17.6-ps-long trajectory, we obtain a resolution of ∼1.9 cm−1 and a maximum accessible frequency of ∼5500 cm−1 for the calculated spectra. The dipole moment has been projected along the unit vectors in order to enhance the contribution to the spectrum due to the OH/OD stretching mode. Wavelet Transform. Differently from the Fourier transform, the wavelet transform (WT) is an integral operator that allows time−frequency analysis. For a discrete time dependent function, WT is expressed in the formalism of Torrence and Compo41 as

groups engaged in strong, weak, and bifurcated HBs. Vibrational analysis is considered to be a prominent tool to investigate HB properties, such as strength, stability, geometry, and lifetime; it can be approached by both spectroscopic and simulation methods. It is well-known that the hydroxyl stretching frequency is strongly affected by the HB network, being shifted to lower frequency as the hydrogen bonding becomes stronger. As the bifurcated HBs lie in crystallographic planes orthogonal to those where the water molecules form weak and strong HBs, Werhahn et al.28 were able to discriminate the three strong peaks occurring in the OH stretching region from polarized IR spectra. Moreover, they measured slightly different lifetimes for these types of HBs, ranging from ∼1 to ∼2 ps. These lifetimes are accessible to ab initio molecular dynamics, as proved in previous works,29 by adopting the Car−Parrinello approach.30 Ab initio molecular dynamics provides reliable structural information, along with an accurate and satisfactory description of intra- and intermolecular forces, including the anharmonic contributions, required for an accurate calculation of vibrational spectra at finite temperatures.31 In addition, the time-dependent data sets will be analyzed by means of the wavelet transform, which we have recently employed to correlate structural and spectroscopic properties.32,33

N−1 n ′= 0

⎛ (n′ − n) δt ⎞ ⎟ f (n′ δt )ψ*⎜ ⎝ ⎠ s

(2)

Here f(n′ δt) is the discrete time series used as input function sampled N times at δt time intervals, and the ψ function, called “wavelet”, is the window of the transform. The wavelet function is translated in time by the n parameter and is stretched by the s parameter. The algorithm adopted in the present study computes the WT in the Fourier (frequency) space as

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COMPUTATIONAL DETAILS Ab Initio Molecular Dynamics Simulation. In this study, our aim is to give a molecular level interpretation of the experimental findings very recently obtained by Werhahn et al.,28 adopting a computational approach based on Car−Parrinello simulations and wavelet analysis. Making use of the CPMD code,34 we have simulated a LiNO3·(HOD)3 crystal composed by 48 water molecules, 16 Li+ cations, and 16 NO3− anions in an orthorhombic box of 13.6036 × 12.7132 × 11.998 Å3 volume, with periodic boundary conditions. The structure reported in the Supporting Information of ref 28 has been chosen as the starting configuration. In this lattice, two “families” of HOD molecules are present: 16 of them are engaged in two bifurcated HBs, whereas 32 molecules form simultaneously one weak and one strong HB. We took care to dispose the HOD molecules so to have an equal number of HBs formed along the O−H and the O−D directions for every type of HB (i.e., 16 weak, 16 strong, and 8 bifurcated HBs along either the O−H or O−D direction). Moreover, HOD molecules are disposed to break the crystal symmetry, in order to avoid spectral contribution from higher K-points for a better comparison with the experimental data. The BLYP35,36 exchange-correlation functional was employed along with GTH pseudopotentials,37 the wave functions were expanded in a plane wave basis truncated at energies of 85 Ry, and the fictitious electronic mass was 400 au. The equations of motion were integrated with a time step of 4 au (∼0.096 fs) over 17.6 ps at a temperature of 224 ± 9 K in the microcanonical ensemble (NVE), after a thermalization of ∼3 ps by velocity rescaling. Dipole Moment Calculation. Maximally localized Wannier functions (MLWF) centers38,39 were calculated every 128 au (∼3.072 fs) to obtain molecular dipole moments. Within the linear response theory, we have calculated the contribution to the IR absorption spectrum due to water molecules by Fourier transforming the molecular dipole time series according to the following relation:40 I(ω) ∝ ω tanh−1(ω) -[μ(t )] -*[μ(t )]

∑

>n(s) =

N−1

∑

>n(s) =

fk̂ ψ̂ *(s ωk )ei ωkn δt

k=0

(3)

where k is the frequency index, ωk is the angular frequency, and fk̂ and ψ̂ are the Fourier transforms of the time series f and of the adopted wavelet ψ, respectively. The choice of the functional form of the wavelet window ψ affects the resulting power spectra; however, Kirby42 proved that, in employing the Gaussian-modulated plane wave window reported in the following equation, the Fourier power spectrum is best reproduced: ψ(t ) =

1 1/4

π

2 2 ei ω0t e−t /2σ

(4)

The ω0 parameter was set at 2π, since with this choice the Fourier frequency is simply ω ≃ 1.01/s.41 The σ parameter tunes the frequency−time resolution according to an Heisenberg-like uncertainty relation:43 a small value of σ provides good time accuracy, albeit with poor frequency localization, whereas a high value of σ best reproduces the Fourier frequency but has low accuracy in the time localization. An extensive report in this regard is available in ref 33. In this work WT calculations have been performed with values of 24π and π, depending on whether we are more interested in frequency or time resolution, respectively.

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RESULTS AND DISCUSSION We have calculated the IR spectrum of LiNO3·(HOD)3 by Fourier transform of the dipole moment of the whole simulation cell. The result is presented in Figure 2 a; in Figure 2b we report a magnification of the OD and OH stretching region, in order to sort out the high intensity peaks due to lattice modes and those at 1100−1500 cm−1, which are due to the vibrations of nitrate anions.44−46 These latter modes are clearly separated from the rest of the spectrum; however, their analysis is difficult due to the congestion of spikes and peaks that make it difficult to extract the actual band shapes. Therefore, we have

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Figure 2. (a) IR spectrum of the simulation cell; (b) magnification of the 2000−4000 cm−1 region. Frequencies are uniformly scaled by a factor of ∼1.027.

Figure 4. Libration angle distribution for every water molecule interacting with bifurcated HBs along the simulation run.

Figure 5. (A) ELF projected onto the plane containing weak and strong H-bonds. (B) ELF projected onto the plane containing bifurcated H-bonds.

Figure 3. (a) Experimental IR spectra28 of LiNO3·(HOD)(D2O)2 for perpendicular (blue line) and parallel (red line) polarization, and their sum (green line). (b, c) Calculated IR spectra of LiNO3·(HOD)3 for water molecules interacting with weak and strong HBs (blue lines), bifurcated bonds (red lines), and their sum (green lines) in the spectral region of both OH (b) and OD (c) stretching modes. Frequencies are uniformly scaled by a factor of ∼1.027.

Figure 6. In the wavelet spectrograms, the OH stretching frequency has been correlated with the instantaneous intermolecular distances between the OH group and its two nearest oxygen atoms.

calculated the IR spectrum for O−H and O−D stretching adopting MLWF centers, as explained under Computational Details: projecting the dipole moment along the O−H and O−D unit vectors is equivalent to the well-established onephonon approximation (see, for example, Cardini et al.47), which is adopted here to discriminate and highlight the contributions due to a specific normal mode (the OH or OD stretching mode). The experimental spectrum28 for LiNO3· (HOD)(D2O)2 is reported in Figure 3a: Werhahn et al. assigned the peak centered at ∼3380 cm−1 to the OH stretching mode of water molecules forming strong HBs, the

intermediate one at ∼3480 cm−1 to the OH stretching of molecules forming bifurcated HBs, and that at ∼3535 cm−1 to the OH stretching of molecules that form weak HBs. As the weakly and strongly interacting OH groups lie on the same crystallographic plane, orthogonal to that of the bifurcated HBs, they measured the contributions of weakly and strongly bonded water in parallel polarized IR spectra, while that due to bifurcated hydrogen-bonded water molecules appears only in the perpendicular polarization. The same separation of the peaks is obtained in our calculated spectra (shown in panels b 2149



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Figure 7. Distribution of the most intense frequency of the IR wavelet spectrum with the change of the two shortest H···O intermolecular distances; (a) weakly and strongly hydrogen-bonded water molecules; (b) bifurcated hydrogen-bonded water molecules. Panels c and d show the same distribution reported in (b) split between the first and second neighbors. Wavelet plots are calculated with σ = 24π. Frequencies are uniformly scaled by a factor of ∼1.027.

pure water. This could suggest that water molecules involved in bifurcated HBs at finite temperature oscillate between two slightly displaced positions, symmetrically closer to one of the two nitrate groups. Electron localization functions48 (ELFs) have been calculated and projected onto two normal planes of the lithium nitrate trihydrate lattice, as reported in Figure 5 for the optimized structure:28 weak, strong (both panel A), and bifurcated (panel B) hydrogen bonds are displayed. For the strong interaction, a larger charge transfer occurs, as can be appreciated from the fact that the ELF isosurfaces of strongly bonded water pairs overlap slightly, whereas for weak and bifurcated interactions there is a clear separation. The analysis of the dipole moment dynamics by means of wavelet transforms is of help in the interpretation of the strong and broad band attributed to bifurcated HB. Exploiting the wavelet ability to localize a signal both in time and in frequency, we can correlate in time, with steps of ∼3 fs, the most intense frequency of the IR wavelet spectrum (calculated replacing with >n in eq 1) with the H···O intermolecular distance of the two nearest neighbors of each water molecule, as illustrated in Figure 6. The result of this analysis is reported in Figure 7a,b, where the correlation is displayed as two-dimensional contour plot. In previous works, wavelets have been employed to recover from molecular dynamics simulation the intermolecular structure−frequency correlation of the O−D/O−H stretching band9,16,49 for water50−52 and glycols,33 leading to “banana-like”

and c of Figure 3 for O−H stretching and O−D stretching, respectively): in fact, we have calculated the dipole moment time series for each water molecule, and grouped the spectral contribution according to the strength of the HB: every molecule forming a strong HB with one of its hydroxyl groups has the other OH group engaged in a weak HB. These two contributions then appear together in the calculated spectrum (blue lines in Figure 3b,c), whereas the contribution of the water molecules forming bifurcated HB appears separated (red lines in Figure 3b,c). Our results fully confirm the assignment28 of the three spectral components for both OH and OD stretching modes, in order of increasing frequency, to strong, bifurcated, and weak hydrogen bondings. Also the relative bandwidths agree with the experiment, with the central peak being substantially broader (for both OH and OD stretching modes) than the lateral ones. Werhahn et al.28 tentatively attributed the large bandwidth (80 cm−1) of the central peak to librations of bifurcated hydrogen-bonded water molecules in the plane defined by the two nearest NO3− anions. From static ab initio calculations they obtained a potential energy profile along the librational coordinate with a 1 kcal/mol deep well centered at 0°. We have extracted the distribution of this angle from our simulated CPMD trajectory: the result is summarized in Figure 4. The main feature reported by Werhahn et al.28 is recovered, but the maxima of the probability distribution are centered at ±8°. We notice that this value agrees with that obtained by Ramasesha et al.24 from simulations and two-dimensional IR experiments on 2150



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Figure 8. Distribution of the most intense frequency of the IR wavelet spectrum with the change of the two shortest H···O intermolecular distances; (a) weakly and strongly hydrogen-bonded water molecules; (b) bifurcated hydrogen-bonded water molecules. Panels c and d show the same distribution reported in (b) split between the first and second neighbors. Wavelet plots are calculated with σ = π. Frequencies are uniformly scaled by a factor of ∼1.027.

supports this finding. Moreover, with WT we calculate the distribution of the OH stretching frequency as a function of the HB length. Our calculation (Figure 7) confirms the hypothesis of Loparo et al.,17 if the probability distribution of frequencies is adopted in place of the free-energy profile and if the H···O distance replaces the fictitious “HB coordinate”. In Figure 7c,d, the same distribution of probability is reported for the nearest (Figure 7c) and second nearest neighbors (Figure 7d) separately, in order to avoid cancellation effects in the plot relative to the bifurcated interaction due to the two nearest neighbors simultaneously. In the present case the shape of the two distributions is less extended along the H···O coordinate, since the mobility of molecules in a crystalline salt is much less than in a liquid. Moreover, the value adopted for the σ parameter (24π) in Figure 7 is optimal for frequency localization,33 but has poor time-localization accuracy due to a Heisenberg-like uncertainty.43 Therefore, we set σ at a much lower value (π) to improve time accuracy, as reported in Figure 8: with this choice the relationship between the time-dependent distances and the time-dependent frequency is more apparent, albeit with a larger spread along the frequency axis due to time−frequency uncertainty. In particular, the “banana shape” of the distribution33,50−52 is largely recovered in bifurcated-bonded molecules for the interaction with the first neighbor (Figure 8c), while for the interaction with the second neighbor (Figure 8b) the change of frequency with the distance appears to be the

plots, whose global shape is not very sensitive to the specific molecular system. Conversely, since we include both first and second neighbors (in view of the ambiguity of such a definition for the water molecules interacting with bifurcated HBs) in the present analysis major differences appear between weak and strong (Figure 7a) and bifurcated (Figure 7b) hydrogen-bonding interactions. The wavelet plot of the former clearly shows two separated spatial regions: hydrogen-bonded molecules are within the first 2.4 Å, where the IR activity thickens at frequencies of around 3540 and 3380 cm−1 due to weak and strong HBs, respectively; a second region at distances larger than 2.4 Å contains slightly broader peaks at the same frequencies, but no overlap between the IR activities of the two zones occurs. On the other hand, wavelet analysis shows a definite continuous pathway between the two regions for the bifurcated-bonded water molecules, corroborating the assumption that the IR profile of those molecules is modulated in time not by one of the two H···ONO3− distances, but by both of them. These graphs can be seen as an evident “signature” of bifurcated hydrogen bonding. Loparo et al.17 proposed two different schematic free-energy surfaces that describe the changes of OH stretching frequency in liquid water during the switch of HB partners along a fictitious “HB coordinate”. Their experiments are consistent with the assumption that bifurcated HB configurations are visited only transiently during the switch of bonding acceptor. Our calculated angle distribution (Figure 4) 2151



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molecules in ionic environments, allowing calculation of structural, dynamic, and electronic properties. We also proved that wavelet analysis makes it possible to extract correlations between the structural and spectroscopic properties, elucidating the physical origin of the experimental findings. This computational approach, based on time−frequency localization, could be applied to pinpoint the contribution of bifurcated interactions to the vibrational spectra of different molecular systems, even when characterized by fast hydrogen-bonding dynamics as in liquid water.

opposite. In fact, when the second neighbor moves away from the OH group, the first neighbor comes closer and the hydroxyl stretching mode shifts to lower frequencies. This proves that the two structure−frequency distributions are actually anticorrelated, an effect that in previous studies in liquid solutions50−52 was not observable due to the mobility of the first and (in particular) the second solvation shells. The lifetimes of the three types of HB have been obtained calculating the autocorrelation functions adopting the procedure of Pagliai et al.53 These correlation functions do not show a single exponential decay. The integral lifetimes, albeit with a significant uncertainty, range in the 1.6−2.1 ps interval, which is of the same order of magnitude of those reported by Werhahn et al.28 Differences between weak/strong hydrogen-bonded molecules and bifurcated ones do not occur only in structural and vibrational properties, but also in the electronic structure, as analyzed by MLWF centers. As a matter of fact, dipole moment distribution for the two families of water molecules leads to two different profiles, as reported in Figure 9: the distribution of the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ACKNOWLEDGMENTS This work was supported by the CINECA supercomputing center through a grant of computer time within projects AIMSUP and MOLD2D.

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REFERENCES

(1) Iglev, H.; Schmeisser, M.; Simeonidis, K.; Thaller, A.; Laubereau, A. Nature 2006, 439, 183−186. (2) Stillinger, F. H. Science 1980, 209, 451−457. (3) Corcelli, S. A.; Skinner, J. L. J. Phys. Chem. A 2005, 109, 7725− 7729. (4) Cowan, M. L.; Bruner, B. D.; Huse, N.; Dwyer, J. R.; Chugh, B.; Nibbering, E. T. J.; Elsaesser, T.; Miller, R. J. D. Nature 2005, 434, 199−202. (5) Loparo, J. J.; Roberts, S. T.; Tokmakoff, A. J. Chem. Phys. 2006, 125, 194521. (6) Kraemer, D.; Cowan, M. L.; Paarmann, A.; Huse, N.; Nibbering, E. T. J.; Elsaesser, T.; Miller, R. J. D. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 437−442. (7) Cho, M. Chem. Rev. 2008, 109, 1331−1418. (8) Paarmann, A.; Hayashi, T.; Mukamel, S.; Miller, R. J. D. J. Chem. Phys. 2008, 128, 191103. (9) Roberts, S. T.; Ramasesha, K.; Tokmakoff, A. Acc. Chem. Res. 2009, 42, 1239−1249. (10) Bakker, H. J.; Skinner, J. L. Chem. Rev. 2010, 110, 1498−1517. (11) Ohmine, I.; Tanaka, H. Chem. Rev. 1993, 93, 2545−2566. (12) Chen, B.; Ivanov, I.; Klein, M.; Parrinello, M. Phys. Rev. Lett. 2003, 91, 215503−215507. (13) Kuo, I. F. W.; Mundy, C. J.; McGrath, M. J.; Siepmann, J. I.; VandeVondele, J.; Sprik, M.; Hutter, J.; Chen, B.; Klein, M. L.; Mohamed, F.; Krack, M.; Parrinello, M. J. Phys. Chem. B 2004, 108, 12990−12998. (14) Paesani, F.; Xantheas, S. S.; Voth, G. A. J. Phys. Chem. B 2009, 113, 13118−13130. (15) Zhang, C.; Donadio, D.; Galli, G. J. Phys. Chem. Lett. 2010, 1, 1398−1402. (16) Lawrence, C. P.; Skinner, J. L. J. Chem. Phys. 2003, 118, 264− 272. (17) Loparo, J. J.; Roberts, S. T.; Tokmakoff, A. J. Chem. Phys. 2006, 125, 194522. (18) Stirnemann, G.; Laage, D. J. Phys. Chem. Lett. 2010, 1, 1511− 1516. (19) Laage, D.; Hynes, J. T. Science 2006, 299, 1367−1372. (20) Laage, D.; Hynes, J. T. J. Phys. Chem. B 2008, 112, 14230− 14242. (21) Zheng, Y. J.; Merz, K. M. J. Comput. Chem. 1992, 13, 1151− 1169. (22) Fecko, C. J.; Eaves, J. D.; Loparo, J. J.; Tokmakoff, A.; Geissler, P. Science 2003, 301, 1698−1702. (23) Eaves, J. D.; Loparo, J. J.; Fecko, C. J.; Tokmakoff, A.; Geissler, P. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 13019−13022.

Figure 9. Dipole moment distribution for water molecules. Blue and red histograms correspond to the distributions of weakly/strongly and bifurcated hydrogen-bonded molecules, respectively. Both histograms are normalized to 100%.

32 weakly and strongly hydrogen-bonded molecules display a Gaussian-shaped profile centered at ∼3 D, a value coincident with that previously calculated by Silvestrelli and Parrinello54 and by Gubskaya and Kusalik55 in liquid water. On the other hand, the population of the remaining 16 bifurcated hydrogenbonded molecules shows a bimodal profile of the molecular dipole moment distribution. We tentatively associate the two maxima occurring in the red distribution of Figure 9 to the instantaneous presence of distorted bifurcated HBs, with two of the four H···ONO3− distances being significantly longer (i.e., >0.5 Å) than the others, and we attribute the central minimum to a perfectly bifurcated arrangement.

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CONCLUSIONS We have shown how a combined approach of computational methods provides new significant insights on a somewhat elusive topic such as bifurcated hydrogen bonding. Our results quantitatively confirm the tentative interpretation of the experimental data proposed in ref 28. Ab initio molecular dynamics simulations account for accurate trajectories for small 2152



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(24) Ramasesha, K.; Roberts, S. T.; Nicodemus, R. A.; Mandal, A.; Tokmakoff, A. J. Chem. Phys. 2011, 135, 54509. (25) Pandelov, S.; Pilles, B. M.; Werhahn, J. C.; Iglev, H. J. Phys. Chem. A 2009, 113, 10184−10188. (26) Hermansson, K.; Thomas, J. O.; Olovsson, I. Acta Crystallogr., B 1977, 33, 2875−2861. (27) Hermansson, K.; Thomas, J. O.; Olovsson, I. Acta Crystallogr., B 1980, 36, 1032−1040. (28) Werhahn, J. C.; Pandelov, S.; Xantheas, S. S.; Iglev, H. J. Phys. Chem. Lett. 2011, 2, 1633−1638. (29) Candelaresi, M.; Pagliai, M.; Lima, M.; Righini, R. J. Phys. Chem. A 2009, 113, 12783−12790. (30) Car, R.; Parrinello, M. Phys. Rev. Lett. 1985, 55, 2471−2474. (31) Marx, D.; Hutter, J. Ab Initio Molecular Dynamics; Cambridge University Press: Cambridge, U.K., 2009. (32) Pagliai, M.; Muniz-Miranda, F.; Cardini, G.; Righini, R.; Schettino, V. J. Phys. Chem. Lett. 2010, 1, 2951−2955. (33) Muniz-Miranda, F.; Pagliai, M.; Cardini, G.; Schettino, V. J. Chem. Theory Comput. 2011, 7, 1109−1118. (34) CPMD; Copyright IBM Corp. 1990−2008; Copyright MPI für Festkörperforschung Stuttgart 1997−2001. http://www.cpmd.org. (35) Becke, A. D. Phys. Rev. A 1988, 38, 3098−3100. (36) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785−789. (37) Goedecker, S.; Teter, M.; Hutter, J. Phys. Rev. B 1996, 54, 1703−1710. (38) Marzari, N.; Vanderbilt, D. Phys. Rev. B 1997, 56, 12847−12865. (39) Silvestrelli, P. L.; Marzari, N.; Vanderbilt, D.; Parrinello, M. Solid State Commun. 1998, 107, 7−11. (40) Pagliai, M.; Cavazzoni, C.; Cardini, G.; Erbacci, G.; Parrinello, M.; Schettino, V. J. Chem. Phys. 2008, 128, 224514−224521. (41) Torrence, C.; Compo, G. P. Bull. Am. Meteorol. Soc. 1998, 79, 61−78. (42) Kirby, J. F. Comput. Geosci. 2005, 32, 846−864. (43) Chui, C. K. An Introduction to Wavelets; Wavelet Analysis and Its Applications; Academic Press, Inc.: San Diego, CA, 1992. (44) Wilmshurst, J. K.; Senderoff, S. J. Chem. Phys. 1961, 35, 1078− 1084. (45) Wait, S. C.; Ward, A. T.; Janz, G. J. J. Chem. Phys. 1966, 45, 133−137. (46) Waterland, M. R.; Stockwell, D.; Kelley, A. M. J. Chem. Phys. 2001, 114, 6249−6258. (47) Cardini, G.; O’Shea, S. F.; Klein, M. L. Faraday Discuss. Chem. Soc. 1985, 80, 227−238. (48) Becke, A. D.; Edgecombe, K. E. J. Chem. Phys. 1990, 92, 5397− 5403. (49) Møller, K. B.; Rey, R.; Hynes, J. T. J. Phys. Chem. A 2004, 108, 1275−1289. (50) Mallik, B.; Semparithi, A.; Chandra, A. J. Phys. Chem. A 2008, 112, 5104−5112. (51) Mallik, B.; Chandra, A. J. Phys. Chem. A 2008, 112, 13518− 13527. (52) Muniz-Miranda, M.; Pagliai, M.; Muniz-Miranda, F.; Schettino, V. Chem. Commun. 2011, 47, 3138−3140. (53) Pagliai, M.; Cardini, G.; Righini, R.; Schettino, V. J. Chem. Phys. 2003, 119, 6655−6662. (54) Silvestrelli, P. L.; Parrinello, M. Phys. Rev. Lett. 1999, 82, 3308− 3311. (55) Gubskaya, A. V.; Kusalik, P. G. J. Chem. Phys. 2002, 11, 5290− 5302.

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Bifurcated Hydrogen Bond in Lithium Nitrate Trihydrate Probed by ab

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