Driven Molecular Dynamics Studies of the Shared Proton Motion in the

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Driven Molecular Dynamics Studies of the Shared Proton Motion in the HO .Ar Cluster: The Effect of Argon Tagging and Deuteration on Vibrational Spectra Martina Kaledin, and Deborah T Adedeji J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp511305c • Publication Date (Web): 16 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Driven Molecular Dynamics Studies of the Shared Proton Motion in the H5O2+.Ar Cluster: The Effect of Argon Tagging and Deuteration on Vibrational Spectra Martina Kaledin*, Deborah T. Adedeji Kennesaw State University, Chemistry & Biochemistry, 370 Paulding Avenue NW, Box # 1203, Kennesaw, GA 30144 Submitted: 1/16/2015 ABSTRACT We report IR spectra of H5O2+ and H5O2+. Ar and their deuterium isotopologues using ab initio molecular dynamics. The trajectories were propagated as microcanonical (NVE) ensembles at energies corresponding to temperatures 50 K and 100 K. The potential energy surface is calculated on-the-fly at the MP2/aug-cc-pVDZ level of theory. The calculations show that adding an argon atom to H5O2+ introduces symmetry breaking in the Zundel core ion, causes blueshift in the shared proton vibration by about 200 cm-1, and leads to the splitting of the OH stretch vibrations into four bands. Driven molecular dynamics (DMD) method is used to assign the spectrum by coupling the dipole moment to an external electric field oscillating at frequency ω. The broad feature at 1100 cm-1 in the H5O2+.Ar spectrum is ascribed to the large amplitude shared proton vibration coupled with torsion and wag modes. MD MP2 simulations predict the H/D redshift in the shared proton vibration and water bending vibration to be about 280 cm-1 and 460 cm-1, respectively in good agreement with experimental observations. *Corresponding author, Martina Kaledin: Phone: +1-470-578-6281, Fax: +1-470-578-9137, e-mail: [email protected].

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I.

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Introduction Theoretical simulations are essential to the understanding and assignment of experimental

spectra. Assignment of spectral features is an important step in the structural and dynamical interpretation of spectral fingerprints in gas phase and especially in solution. This is where ab initio calculations can be most helpful, in particular when a full vibrational spectrum, including band assignment, can be computed and directly compared to experimental data. In recent years, the development of new experimental approaches, such as messenger method infrared photon dissociation (IR-PD)1-4 and multi-photon dissociation (IR-MPD)5-10 makes it possible to probe the vibrational properties of molecular systems in the gas phase. Gas-phase spectroscopy combined with ab initio calculations allows to evaluate the forces that control the structure and dynamics of molecules and transfer the information to the liquid phase. The endeavor to explain the mechanism of proton mobility in water is motivated by the role protons play in acid-base reactions, in aqueous solutions, in environmental chemistry, and in bioenergetics.11 Understanding the proton migration in water is essential to explaining the mechanism of charge transport across cell membranes.12,13 Proton transfer in biological systems is thought to often proceed through hydrogen bonded chains of water molecules, the so called water wires, in which any one of the hydrogens in a water cluster can hop forward along the chain. To resolve the complex processes in biological systems, the study of elementary species, e.g. small protonated water clusters is of fundamental importance. Several groups have studied structure and vibrational dynamics of hydrated ions extensively both theoretically14-45 and experimentally.45-59 Theoretical studies of the vibrational dynamics of hydrated ions include numerous ab initio calculations of harmonic normal mode frequencies, molecular dynamics simulations,33-44 and accurate quantum calculations.30-32


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Bowman et. al.26 reported a full dimensional ab initio potential energy surface at the CCSD(T)/aug-cc-pVTZ level of theory and dipole moment surface at the MP2/aug-cc-pVTZ level of theory for H5O2+. These surfaces were used in our previous MD and DMD simulations60 of H5O2+ and its deuterium substituted isotopologues,61 and in full quantum calculations.30-32 Currently, there is no full dimensional potential energy surface for the H5O2+.Ar system. Park et al.43 have performed Car-Parrinello ab initio molecular dynamics calculations at the BLYP level of theory for small protonated water clusters with and without argon. However, BLYP is not able to describe weakly bound interactions correctly, and dispersion-corrected methods have to be employed.62 Also the BLYP functional is known to systematically underestimate the experimental OH stretch and H−O−H bending frequencies and therefore the vibrational frequencies were corrected by scaling factors.43 On the other hand, BLYP gives a too high value for the harmonic frequency of the shared proton stretch. Asmis et. al.56 carried out the IRMPD experimental study of the gas-phase vibrational spectroscopy of H5O2+ and D5O2+ between 620 and 1900 cm-1. They observed four bands in the H5O2+spectrum at 921, 1043 cm-1 (assigned to O−H+…O bending vibrations), 1317 cm-1 (O−H+…O stretching vibration), and 1741 cm-1 (H−O−H bending vibration). The assignment of peaks was based on the 4D quantum simulation by Sauer et al. 35 Another IRMPD experiment by Fridgen et al.55 shows bands at 990, 1163, 1337, 1756 cm-1. There appears to be a discrepancy in assignment between the two experiments in the proton-transfer region. Hammer et al.54 reported the vibrational predissociation spectra of the H5O2+ in the presence of argon and neon as messenger atoms. The H5O2+.Ne spectrum is dominated by two intense peaks at 928 cm-1 and 1047 cm-1 and weaker features at 1763 cm-1 and 1878 cm-1. The H5O2+. Ar spectrum is more complex, showing four bands at 975, 1089, 1768, and 1872 cm-1. These experimental spectra


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were compared to full-dimensional vibrational diffusion Monte Carlo (DMC) and multimode/vibrational configuration interaction MM/VCI calculations.54 The theoretical MM/VCI spectrum predicted a dominant transition at 1070 cm-1 assigned to fundamental parallel stretch of the shared proton. However, neither the DMC nor MM/VCI resolved the dominant low energy doublet in H5O2+ spectrum. This doublet was first successfully described as a resonance between the shared proton O−H+…O asymmetric stretch and a combination state involving one quantum of the O-O stretch and two quanta of the water wag by Meyer et al.30-32 H/D isotopic work by McCunn et al.57,58 clarified the assignment of the bridging proton fundamentals in terms of Fermi resonance interaction. Recently Duncan et al.59 studied small argon tagged protonated water clusters. They computed the binding energy of argon to H5O2+ to be 2.74 kcal/mol (959 cm-1) at the MP2/augcc-pVDZ level of theory. Their H5O2+.Ar experimental spectrum in the O-H stretch region has four main bands at 3522, 3616, 3657, and 3696 cm-1 and two weak features at 3748 and 3825 cm-1. The most recent work on protonated water clusters by Kulig and Agmon44 investigated the effect of temperature and dispersion correction on several isomers of H9O4+ cluster. Due to some differences among the various experiments, as well as differences between the theory and experiment for the H5O2+ cluster, the focus of this paper is to analyze an effect of argon tagging and deuteration on vibrational spectra of H5O2+. We reviewed the structural parameters, vibrational frequencies, dissociation energy (H5O2+ H2O+ H3O+), and binding energy of argon to H5O2+ at DFT, MP2, and CCSD(T) levels of theory. We calculated vibrational spectra for protonated water clusters and compared them to experimental spectra. Prominent peaks were analyzed and assigned using the driven molecular dynamics method.60,63-65


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II.

Computational Methods All calculations were carried out using the Gaussian 09 program package.66 We

optimized the geometries of H5O2+ and H5O2+.Ar and their dissociation products H2O, H3O+ at the B3LYP, BLYP, MP2, and CCSD(T) levels of theory with 6-31+G**, aug-cc-pVDZ (AVDZ), and aug-cc-pVTZ (AVTZ) basis sets. The vibrational frequencies for H5O2+, H5O2+.Ar, and their isotopologues D5O2+, D5O2+.Ar were obtained using normal mode analysis (NMA). Once we obtained Cartesian force constants for H5O2+ and H5O2+.Ar, we used them to determine the mass-weighted Hessian matrix for deuterium isotopologues D5O2+ and D5O2+.Ar. We calculated the dissociation energy (De) for H5O2+ H2O+ H3O+ and Ar binding energy (BE). De was corrected for zero-point energy (ZPE). The results from several computational levels are compared in order to select the sufficiently accurate and cost effective method to carry out MD and DMD simulations. IR spectra of H5O2+ , H5O2+. Ar, D5O2+ , and D5O2+. Ar were obtained by running direct molecular dynamics at the MP2/aug-cc-pVDZ level of theory. The trajectories were run at a constant energy (NVE) and J=0 using an interface between the Gaussian 09 program and our own suite of MD codes. A total of 10 trajectories were generated randomly and run up to 10 ps using the velocity Verlet integrator with a time step of 0.5 fs at energies corresponding to temperatures 50 K and 100 K. The time step was determined by the frequency of the fastest mode in the system, corresponding to OH stretch vibrations (~3600-3700 cm-1). It is recommended to use time steps on the order of a femtosecond or less to achieve sufficient accuracy.67 In our previous work we showed that it is sufficient to run ten to twenty trajectories on the order of tens of picoseconds to achieve convergence.68,69


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The IR spectra were obtained by the Fourier transform of the dipole-dipole correlation function recorded along the trajectories,

I (ω ) =

Re ∞ iωt µr ⋅ µr , ∫ dt e 0 t T π 0

r

where ω is the frequency,

(1)

r

µ0 ⋅ µt

T

is the dipole-dipole time correlation function that is averaged

over the Boltzmann distribution and scaled by an anharmonic correction factor70 equal to ω/[1-exp(-ω/kT)]. The correlation function was also averaged over the length of the trajectory and over the initial conditions. The most prominent spectral features in the H5O2+.Ar spectrum are assigned using the driven MD method.60,63-65 In the DMD method, an external, sinusoidal force is applied and true resonances are obtained by finding absorbing frequencies. The strength of the external driven force determines the amplitude of the motion. An important feature of DMD is the ability to study non-harmonic motion and also mode coupling. At resonant frequencies the molecular motions induced by a weak driven force closely correspond to the normal-modes, while harder driving induces non-harmonic motion and leads to mode-coupling and non-harmonic shifts60,68 which are missing from normal mode analysis. The Hamiltonian of a molecular system in a DMD simulation consists of the molecular Hamiltonian, H0 and a driving term U(q, t; ω)

H (p,q, t; ω) = H0 (p,q) + U (q, t; ω) ,


(2)

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where q and p represent the 3N atomic Cartesian coordinates and momenta, respectively, ω is frequency, t is time. In order to make assignment of vibrational IR spectra, we use the dipoledriving term60

r r U(q,t;ω) = µ(q) ⋅ ε (t;ω) ,

(3)

r r r where ε ( t; ω ) = ε 0 sin(ω t ) determines the direction and strength of the electric field, and µ (q) is the electric dipole of the molecule. The usual equations of motion are modified for the driving term, as follows,

r pi r& ∂H qi = r = ∂pi mi

r r& ∂H r ∂µ r pi = − r = f i − r ⋅ ε 0 sin(ω t ), ∂qi ∂qi

(4)

i = 1, 2 ,K N

r r where, q&i and p& i represent time derivatives of atomic Cartesian coordinates and momenta, r

respectively, and f i represent the forces acting on the nuclei. Following our previous work61 and work by Voth et. al.,71 we approximate the dipole derivative by a flexible point charge model using Mulliken charges.72 Initially, the Cartesian coordinates of the molecules were set at the equilibrium structure, with zero velocities. Corresponding initial temperature is 0 K. At resonant frequencies, applied driven force gradually increases molecular motion and therefore temperature of the system gradually increases. The DMD trajectories were propagated up to 2 ps using the velocity Verlet integrator with a time step 1 fs. In the DMD simulations we used a twice larger time step because the


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maximum target frequency considered is roughly half of the OH stretch frequency. The electric

r field | ε0 | =0.08 mV/bohr was oriented along x, y, and z -axes, and also along the O−O bond. The angular momentum was kept at J=0. To identify resonant frequencies, the average internal energy of the molecule is obtained after a finite time of driving, which is given by60

E =

1t ∫ H 0 (τ )dτ t0

(5)

We also monitored the dipole moment, atomic coordinates, and charges along each driven trajectory. From each driven trajectory, we evaluated atomic displacements and recorded overlaps with the normal mode vectors. We used a similar analysis in our previous work60,68 to assign spectra of hydrated ions. We carried out DMD MP2/aug-cc-pVDZ simulations at normal mode frequencies and scanned the region between 900 − 1300 cm-1 , where the H5O2+.Ar spectrum shows IR activity. Normalized mass-scaled atomic displacements from DMD simulations are calculated after a significant amount of energy is absorbed by the molecule. They are defined as60,68

∆xi (t ) =

mi1 / 2 ( qi ( t ) − qei )  2  ∑ mi ( qi ( t ) − qei )   i =1  3N

1/ 2

.

(6)

Then the inner product of the DMD displacement ∆x(t) and normal mode, j is obtained as60,68 3N

O j (t ) = ∆x(t ) ⋅ u j = ∑∆xi (t ) uij ,

(7)

i =1


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where uj is the j-th normal-mode vector. The overlap is close to 1 if the two sets of modes are identical and 0, if they are orthogonal. Recently similar techniques probing and decomposing the dynamics data in terms of harmonic normal modes were proposed,41 which also enable mode assignment. III.

Results and Discussion

A. Structural properties of H5O2+ and H5O2+.Ar Labeling of atoms and molecular orientation are shown in Figure 1. The structural parameters of H5O2+ and H5O2+.Ar are available in Supporting Information in Table 1S and Table 2S, respectively. The global minimum of the H5O2+ is of C2 symmetry. MP2 and CCSD(T) structural

parameters are very similar. The O−H and O−H+…O distances in H5O2+ agree within 0.005 Å, yet at the BLYP level of theory these distances are significantly longer. Adding an Ar atom to H5O2+ introduces symmetry breaking in the Zundel core ion. Rather than attaching to the shared proton of H5O2+, Ar prefers to attach to OH (spectator groups).54 In the H5O2+.Ar complex, the shared proton shifts toward the water molecule closest to Ar by about 0.15 Å. The corresponding O−H+…O distances are 1.1282 Å and 1.2781 Å respectively at the MP2/aug-cc-pVTZ level of theory. O−H bond lengths change in the presence of Ar, with the longest O−H bond being attached to Ar. The DFT calculations with B3LYP and BLYP functionals predict H5O2+ moiety in H5O2+.Ar to be less asymmetric.54 H−O−H bond angles in the Ar tagged H5O2+ versus untagged H5O2+ change only slightly. Since argon binding energy is significantly underestimated at the B3LYP level of theory (see section below), the Ar…H distance is predicted to be longer at the B3LYP level of theory comparing to the MP2 value. B. Bond dissociation energy and Ar binding energy


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The bond dissociation energies for H5O2+ H2O+ H3O+ and the binding energy of Ar to H5O2+ are shown in Table 1. The De dissociation energies are 34.0, 34.6, 34.1 kcal/mol at MP2/aug-ccpVDZ, MP2/aug-cc-pVTZ, and CCSD(T)/aug-cc-pVTZ levels of theory, respectively. The corresponding ZPE corrected values, Do are 33.5, 33.7, 33.3 kcal/mol, which agree well with the experimental value of 32.4 kcal/mol reported by Dalleska et al.47 DFT calculations overestimate the dissociation energy by about 2 kcal/mol at BLYP and 6 kcal/mol at B3LYP levels of theory. The binding energy of argon to H5O2+ is very sensitive to the computational method and the basis set. B3LYP and BLYP underestimate the binding energy. The binding energy of argon to H5O2+ at the MP2/aug-cc-pVDZ level of theory is 959 cm-1, while it is 1104 cm-1 at the MP2/aug-cc-pVTZ level of theory. Binding energy obtained from single point energy calculation using CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ is 1121 cm-1. Even though the DFT method was used by others to simulate H5O2+ spectra,43,61 a comparison of bond dissociation energy and Ar binding energy to experiment and higher level of theory values shows that the DFT is not as reliable in describing these weakly bound systems, while MP2/aug-cc-pVDZ is much more qualitatively consistent with CCSD(T)/aug-cc-pVTZ, while being a fraction of its computational cost. Therefore, in the present study we use MP2/aug-cc-pVDZ to simulate and assign IR spectra of H5O2+.Ar. C. IR spectra The harmonic vibrational frequencies of H5O2+ and H5O2+.Ar, their D-substituted isotopologues, dominant MD MP2/aug-cc-pVDZ peaks, and experimental observations in the range from 600 to 4000 cm-1 are listed in Table 2 and Table 3, respectively. The complete list of frequencies is given in Supporting Information in Table 3S and Table 4S. H5O2+ vibrational frequencies are very similar for MP2/aug-cc-pVDZ and CCSD(T)/aug-cc-pVTZ26 methods, one notable


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exception is the O−H+…O asymmetric stretch vibration that is particularly sensitive to the basis set and the method. The direct comparison of H5O2+ and H5O2+.Ar spectra is shown in Figure 2a. These spectra were calculated from MD/MP2 simulations at temperatures 50 K and 100 K. The H5O2+ spectrum at T=50 K shows a doublet at 790 and 890 cm-1. Our previous MD/CCSD(T) simulations60,61 predicted the doublet at 860 cm-1 and 980 cm-1. The doublet was assigned using the DMD method to shared proton vibration coupled with torsion motion.60 MCTDH quantum calculations30-32 placed the doublet at 910 and 1025 cm-1, which agrees well with the H5O2+.Ne spectrum.54 In our previous work,61 we have concluded that MD simulations underestimate the shared proton vibration due to incomplete recovery of the anharmonicity of the potential energy surface. The MD MP2 simulations of IR spectra predict a blueshift in the shared proton vibration due to Ar to be about 200 cm-1. Based on normal mode analysis, adding Ar to H5O2+ changes the O−H+…O asymmetric stretch frequency from 808 cm-1 to 1262 cm-1 (a 454 cm-1 shift). This anharmonic region in the spectrum is assigned using the DMD method to better understand anharmonic shifts and argon interactions with H5O2+. As noted in the Introduction, the H5O2+.Ne spectrum displays a doublet at 928 cm-1 and 1047 cm-1, while the H5O2+.Ar spectrum shows each of the doublets split into a pair of subdoublets centered at 975 cm-1 and 1089 cm-1.54 The most intense peak in the experimental H5O2+. Ar spectrum at 1089 cm-1 was previously assigned to the O−H+…O asymmetric stretch vibration54. In the present MP2 spectrum of H5O2+.Ar at 50 K, the most intense peak at 1790 cm-1 corresponds to an out-of-phase H−O−H bending vibration. This vibration is not greatly


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affected by the presence of argon (blueshift is only 30 cm-1). The in-phase H−O−H bending vibration at 1693 cm-1 is IR inactive despite the presence of the argon atom. In the shared proton region, there is a broad band with overlapping peaks at 1100, 1170, 1210, 1262 cm-1, and weak features at 1390 and 1560 cm-1. The 1210 and 1262 cm-1 peaks are close to the harmonic O−H+…O asymmetric stretch. Using the DMD method (see below) we verify that the 1390 and 1560 cm-1 peaks correspond to the O−H+…O bending vibrations. However, O−H+…O bending vibrations were not observed in the H5O2+.Ar experimental spectrum.54 McCoy et. al.68 calculated their oscillator strengths and confirmed that intensities of O−H+…O bending vibrations are small. Non-harmonic peaks cannot be assigned by normal mode analysis, and therefore we attempt to assign them using driven molecular dynamics. Here we inspected the role argon plays in the H5O2+ spectrum at low and slightly elevated temperature. We monitored the internuclear distances along the MD MP2 trajectories. The average separation of Ar from one of the terminal H atoms (atom number 5, see Figure 1) is about 2.30 Å at 50 K. However at 100 K, the Ar…H distance fluctuates between 2.5-3.0 Å, in several instances reaching 4.0 Å, with Ar freely switching between the two equivalent H atoms (atoms number 4 and 5, see Figure 1). We can say that at higher temperatures the binding of argon to H5O2+ is less structured. In our previous study61 we discussed the H5O2+ spectrum as a function of temperature where we concluded that Ne and Ar tagged clusters must be very cold, otherwise the messenger atoms would be lost prior to photon absorption. Although analysis of the OH (OD) stretch vibrations is not the main focus of this paper, Figure 2b shows H5O2+ and H5O2+.Ar spectra and their deuterium substituted isotopologues in the OH (OD) stretch region compared to harmonic frequencies. Our spectra show correct


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splitting of symmetric and asymmetric OH (OD) stretches in H5O2+ into four distinct bands in the presence of Ar (two bands correspond to vibrations in water attached to the Ar atom and two bands correspond to vibrations in an isolated water) similar to experimental spectra.57-59 The splitting of the OH stretch vibrations into four bands can be seen even within the harmonic approximation.40,59 However, previous CPMD simulations43 of H5O2+.Ar do not show four distinct peaks in the OH stretch region at low temperature.

We do not observe the two weak

features at 3748 and 3825 cm-1 found experimentally by Duncan et. al.59 D. Deuterium isotopic substitution Introducing deuterium isotopic substitution, we examined the spectra of D5O2+ and D5O2+. Ar shown in Figure 2. To our knowledge, this is the first report of D5O2+. Ar spectrum calculated using either classical MD or quantum simulations. The D5O2+ spectrum has a sharp peak at 610 cm-1 and a weaker feature at 760 cm-1. The MP2/aug-cc-pVDZ harmonic frequency for O−D+…O asymmetric stretch vibration is 591 cm-1 (Table 2). Because the asymmetric stretch of the bridging hydrogen is mostly parallel to the O-O axis, the H/D red shift is close to a

1/ 2

ratio. The doublet in the shared proton stretch region of D5O2+ is recovered by MP2, although the H/D redshift is slightly underestimated compared to our previous MD CCSD(T)61 and the quantum dynamical MCTDH CCSD(T) calculations.30-32 The MD MP2 spectrum of D5O2+. Ar in the shared proton region has an intense nonharmonic feature at 890 cm-1 and two peaks that are consistent with the harmonic O−D+…O stretch and O−D+…O bending vibrations at 927 and 1007 cm-1. Recalling the

1 / 2 factor, the

D5O2+ peak at 890 cm-1 closely relates to the non-harmonic peak at 1170 cm-1 in H5O2+.Ar spectrum. Our MD MP2 simulations predict the H/D redshift of shared proton vibration to be


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about 280 cm-1. The vibrational predissociation spectrum of D5O2+.Ar58 displays intense peaks near 708 and 817 cm-1 which is about 270 cm-1 to the red of the corresponding doublet in the predissociation spectrum of H5O2+.Ar.54 The D−O−D bending mode appears at 1330 cm-1 in MD MP2 spectrum and at 1300 cm-1 in experiment.58 The corresponding MP2 and experimental values for H/D redshifts are 460 cm-1 and 468 cm-1, respectively. We thus may conclude that MP2 combined with molecular dynamics captures the H/D redshifts in the shared proton and water bending vibrations in H5O2+.Ar and D5O2+.Ar spectra in good agreement with experiment.54,58 E. Driven molecular dynamics DMD simulations were run for H5O2+.Ar molecule in order to assign the dominant spectral features. The atomic displacements along the trajectory (Eq. 6) and overlaps with the normal mode vectors (Eq. 7) were evaluated. The absorbed energy as a function of time is shown in Figure 3. Driving each frequency with the electric field aligned with the x-, y-, and z-axes, respectively, enabled us to distinguish between O−H+…O stretch (in xy-plane) and O−H+…O bending modes (in/out of the xy-plane). DMD trajectories at 1385 cm-1 and 1587 cm-1 absorbed 15 kcal/mol and 10 kcal/mol, respectively. Based on overlaps with normal mode vectors these two frequencies were assigned to the O−H+…O bending modes. Non-harmonic frequency at 1100 cm-1 absorbed up to 5 kcal/mol. To elucidate the spectral assignment of this non-harmonic peak, we examined structural parameters along the DMD trajectories. H+ displacement from two oxygen atoms and the O−H+…O angle as a function of time are shown on Figures 4 and 5, respectively. The H+ displacements for O−H+…O stretch harmonic mode 1262 cm-1 are relatively small and oscillatory for each x, y and z electric field orientation. At 1385 and 1587 cm-1, H+ displacements, as well as O−H+…O angles are much larger, therefore these two


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frequencies are assigned to O−H+…O bending vibrations. For an 1100 cm-1 unassigned nonharmonic spectral feature, there was neither energy absorption nor H+ displacements, nor O−H+…O angle change for the electric field aligned with z-axis. Rapid energy absorption, large H+ displacements, and O−H+…O angles were observed for x and y directions of the electric field. Therefore, this frequency is tentatively assigned to the O−H+…O asymmetric stretch. Torsion angle evolution along the DMD trajectories is seen in Figure 6. At 1100, 1385, and 1587 cm-1 frequencies, the torsion angle changes significantly suggesting strong coupling of the shared proton vibration to torsion and wag modes. At 1100 cm-1 there is a time delay in torsion angle fluctuations, suggesting there is an energy threshold of about 2 kcal/mol (see energy profile on Figure 3) that the system must absorb in order to activate this vibration. In similar fashion, the two O−H+…O bending vibrations at 1385 cm-1 and 1587 cm-1 are coupled to torsion and wag modes. To distinguish between fundamental and combination frequencies and to identify possible mode mixing, we analyzed the average overlaps of the normal modes with the atomic displacements along the trajectories. Figure 7a shows the overlap map for the DMD trajectories driven with the field aligned along the O−O bond. The high overlaps (red) represent two sets of modes (NMA and DMD) that are very similar and zero (blue), if they are unrelated. Large overlaps were found for modes with large atomic displacements along the O−O bond, in particular H−O−H bending as well as O−H+…O asymmetric stretch modes. Overlaps evaluated separately for the specific orientation of the electric field aids to visualize atomic displacements during vibration. The same pattern was observed for the electric field orientation along x, y, and z axes (Figures 7b-d). Diagonal elements of the overlap matrix for harmonic frequencies 1385,


15


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Page 16 of 35

1587, 1693, and 1795 cm-1 have values between 0.3 and 0.5. At 1385 cm-1 and 1587 cm-1 offdiagonal elements of the overlap matrix for low frequency modes such as torsion, and wag are about 0.2. This confirms mode coupling of O−H+…O bending modes with low frequency torsion and wag modes. IV.

Conclusions In this work we present IR spectra of H5O2+ and H5O2+.Ar and their deuterium substituted

isotopologues calculated at the MP2/aug-cc-pVDZ level of theory. MP2 spectra reproduce the experimentally observed IR patterns, such as the doublet in the shared proton region of H5O2+. The difference in the position of the doublet is consistent with the difference in the harmonic O−H+…O asymmetric stretch vibrations calculated at MP2 and CCSD(T) levels of theory. This work provides the first report of IR spectra for D5O2+.Ar at the MP2/aug-cc-pVDZ level of theory. MD MP2 simulations predict the H/D redshift in the shared proton vibration and in water bending vibration to be about 280 cm-1 and 460 cm-1, respectively, in good agreement with experimental observations.54,58 We used DMD simulations to assign the non-harmonic spectral feature in the shared proton region of the H5O2+.Ar spectrum. Based on atomic displacements along the DMD trajectory and overlaps of atomic displacements with normal mode vectors, we concluded that spectral feature at 1100 cm-1 consists of an O−H+…O asymmetric stretch vibration coupled with low frequency torsion and wag modes. O−H+…O bending modes were also coupled with torsion and wag modes based on DMD analysis. Driven molecular dynamics simulations can also be used to identify and assign two weak spectral features in the high frequency region above OH


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stretches, which were observed in the experimental spectrum.59 Hard driving of these weakly absorbing peaks can stimulate combination modes that are absent in MD simulations. MP2/aug-cc-pVDZ level of theory provides a good quality potential energy surface for the weakly bound rare-gas complexes at a relatively low computational cost. Further studies including two and more rare-gas atoms bound to protonated water clusters are presently being pursued in our laboratory. Acknowledgement We thank Advanced Computer Services at Kennesaw State University for providing a high performance computer system to carry out simulations.

Supporting Information Supporting information is available. This material is available free of charge via the Internet at http://pubs.acs.org.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1: H5O2+ H3O+ +H2O dissociation energies (De), zero point energy corrected values (Do), and binding energies (BE) of argon to H5O2+. De

Do

BE

(kcal/mol)

(kcal/mol)

(cm-1)

B3LYP/6-31+G**

37.6

36.6

538

BLYP/AVDZ

35.4

34.4

843

MP2/AVDZ

34.0

33.5

959

MP2/AVTZ

34.6

33.7

1104

CCSD(T)/AVTZ

34.1

33.3

1121b

Exp a

32.4

a

Ref. 47

b

Single point calculation at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ level of theory.


23


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Table 2: Experimental and calculated vibrational frequencies of H5O2+ and D5O2+ (in cm-1). H 5O 2+

D 5O 2+

B3LYP

BLYP

MP2

MP2

CCSD(T)a

MD/MP2

MP2

MP2

CCSD(T)

MD/MP2

6-31+G**

AVDZ

AVDZ

AVTZ

AVTZ

AVDZ

AVDZ

AVTZ

AVTZ

AVDZ

591

660

627

610/760b

b

1004

973

808

912

861

790/890

1476

1392

1464

1473

1494

1460

1063

1069

1084

1060

1523

1449

1528

1550

1574

1530

1110

1126

1145

1110

1678

1624

1691

1706

1720

1237

1248

1257

1764

1692

1747

1761

1770

1760

1281

1292

1298

1290

3745

3584

3718

3733

3744

3740

2677

2687

2694

2680

3754

3591

3725

3741

3750

2687

2698

2703

3851

3681

3832

3837

3832

2813

2817

2811

3851

3681

3832

3837

3832

2813

2817

2811

a

Ref

b

Doublet.

3850

2815

26


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 3: Experimental and calculated vibrational frequencies of H5O2+.Ar and D5O2+.Ar (in cm-1). H5O2+.Ar MD/MP2 B3LYP BLYP MP2 MP2 6-31+G** AVDZ AVDZ AVTZ AVDZ(50K)

1120 1438 1558 1678 1777 3664 3762 3814 3864 a Doublet.

1160 1343 1491 1625 1712 3433 3606 3641 3701

1262 1385 1587 1693 1795 3632 3746 3782 3859

1235 1411 1597 1707 1793

3624 3757 3794 3860

1100, 1170, 1210, 1262 1390 1560

Exp.54

Exp.59

975/1089a

1790

1768/1872a

3660 3770 3805 3880

3520 3615 3660 3695

3522 3616 3657 3696b

D5O2+. Ar MP2 MD/MP2 Exp.59 MP2 AVDZ AVTZ AVDZ(50K)

Exp.57,58

929 1007 1151 1235 1330

921 1024 1161 1245 1329

890/ 929a 1007 1160

708/817a

1330

1300c

2624 2700 2772 2832

2619 2707 2776 2833

2635 2705 2780 2830

b

Additional weak intensity peaks were observed experimentally59 at 3748, 3825 cm-1.

c

D−O−D bending and OD stretch bands were not tabulated in refs.57,58


2563 2633 2703 2742

2580c 2650c 2710c 2750c

25


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Page 26 of 35

Figure 1. The atom labeling (oxygen red, hydrogen white, argon blue) and molecular orientation of H5O2+ and H5O2+.Ar.


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Figure 2. Temperature dependence of the MD-MP2/aug-cc-pVDZ IR spectra for H5O2+ and H5O2+.Ar and their deuterium substituted isotopologues at T= 50 K (red line) and at T=100 K (green line). The harmonic frequencies are shown as sticks in the spectrum. a)

b)


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Page 28 of 35

Figure 3. DMD MP2/aug-cc-pVDZ simulations: average absorbed energy in kcal/mol as a function of time. The electric field |ε| 80 mV/bohr was oriented along the x- (red line) , y- (green line), and z- (black line) axes, respectively.


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Figure 4. Results of DMD MP2/aug-cc-pVDZ simulations: time dependence of the H+ displacement R(O1-H3)-R(O2-H3). Atom numbering is shown in Figure 1. For each driven frequency ω, the electric field was oriented along x-, y-, z-axes.


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Figure 5. Results of DMD MP2/aug-cc-pVDZ simulations: time dependence of the O−H+…O bond angle (O1-H3-O2).


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Figure 6. Results of DMD MP2/aug-cc-pVDZ simulations: time dependence of the torsion angle between two planes formed by atoms H6-O1-H7 and H4-O2-H5.


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Figure 7. Average overlaps of the atomic displacements along the trajectory (ωDMD ) with the normal modes (ωNMA). DMD trajectories were run up to 250 fs with a time step 1 fs. The electric field |ε| 80 mV/bohr was aligned along the O−O bond and x-, y-, z- axes respectively.

a) O-O bond

b) x axis

c) y axis

d) z axis


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Table of Contents Graphic


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Driven Molecular Dynamics Studies of the Shared Proton Motion in the

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