Diffuse Vibrational Signature of a Single Proton Embedded in the

Nov 26, 2015 - The main conclusion is that the breadth of the vibrational signature associated with the embedded OH group is due to the displacements ...
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Diffuse Vibrational Signature of a Single Proton Embedded in the Oxalate Scaffold, HO2CCO2− Published as part of The Journal of Physical Chemistry A virtual special issue “Spectroscopy and Dynamics of Medium-Sized Molecules and Clusters: Theory, Experiment, and Applications”. Conrad T. Wolke,† Andrew F. DeBlase,†,‡ Christopher M. Leavitt,† Anne B. McCoy,*,§ and Mark A. Johnson*,† †

Sterling Chemistry Laboratory, Yale University, New Haven, Connecticut 06520, United States Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States § Department of Chemistry, University of Washington, Seattle, Washington 98195, United States ‡

S Supporting Information *

ABSTRACT: To understand how the D2d oxalate scaffold (C2O4)2− distorts upon capture of a proton, we report the vibrational spectra of the cryogenically cooled HO2CCO2− anion and its deuterated isotopologue DO2CCO2−. The transitions associated with the skeletal vibrations and OH bending modes are sharp and are well described by inclusion of cubic terms in the normal mode expansion of the potential surface through an extended Fermi resonance analysis. The ground state structure features a five-membered ring with an asymmetric intramolecular proton bond. The spectral signatures of the hydrogen stretches, on the contrary, are surprisingly diffuse, and this behavior is not anticipated by the extended Fermi scheme. We trace the diffuse bands to very strong couplings between the highfrequency OH-stretch and the low-frequency COH bends as well as heavy particle skeletal deformations. A simple vibrationally adiabatic model recovers this breadth of oscillator strength as a 0 K analogue of the motional broadening commonly used to explain the diffuse spectra of H-bonded systems at elevated temperatures, but where these displacements arise from the configurations present at the vibrational zero-point level. explore this issue is presented by the molecular ion HO2CCO2− displayed in Scheme 1, hereafter denoted Ox-H−. This species can be obtained by deprotonating oxalic acid to yield the singly charged anion, but when viewed in the present context, it is useful to consider the system from the perspective of adding a proton to the dianion (oxalate). The proton can then reside in one of the four equivalent minima according to the calculated attachment motif shown in Scheme 1, corresponding to asymmetrical binding of the proton between the oxygen atoms on opposing CO2− moieties, thereby forming a fivemembered cyclic ionic hydrogen bond (CIHB). This binding motif is thus a cyclic analogue of the OH−·H2O anion, which is similarly best viewed from the perspective of a proton bound between two hydroxide ions (e.g., OH−·H+·OH−).9,30 Because there is only one light atom in the Ox-H− case, however, one can readily isolate the spectral activity due to excitation of the proton using H/D isotopic substitution, whereas the rigidity

I. INTRODUCTION The vibrational signatures associated with “proton defects” in H-bonded networks are remarkably complex due to strong coupling between the proton motions and the weak bonds that support the structure of the surrounding medium.1−14 As a result, the absorption bands associated with the charge center are often broadened over hundreds of wavenumbers even when the system is close to 0 K,15−28 signaling very strong coupling between the excited OH stretching manifold and excited states involving the lower frequency motions of the assembly (as opposed to thermal fluctuations and associated spectral diffusion). Similar behavior has been observed in the spectra of protonated peptides, which feature cyclic intramolecular Hbonding to the charge center.16,29 The latter are typically complicated by overlapping features arising from distant XH groups, however, making it difficult to isolate the band structures due solely to the stretching vibration of the active proton. This raises the important question of whether the fast relaxation dynamics underlying the spectral breadth can be suppressed when a single proton is embedded in a covalently bound substrate of heavy atoms. An archetypal system to © 2015 American Chemical Society

Received: October 30, 2015 Revised: November 24, 2015 Published: November 26, 2015 13018

DOI: 10.1021/acs.jpca.5b10649 J. Phys. Chem. A 2015, 119, 13018−13024

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a

Geometrical parameters were calculated at the B3LYP/6-311+ +G(d,p) level of theory.

Figure 1. Potential energy surface for proton transfer between the two equivalent minima in Ox-H− (black curve) with the ground state probability superimposed (green curve, see text for details of DVR calculation). The angle between the proton, the center of the CC bond, and one carbon is denoted by θ. On the basis of this onedimensional model, the zero-point energy is 410 cm−1.

and structure of the supporting scaffold can be established through analysis of the lower frequency CO stretching modes. Here we explore how key intramolecular distortions of the scaffold drive the spectral signatures of the O−H(D) stretching motions with a simple model in which the OH stretch is adiabatically separated from the remaining vibrational degrees of freedom. With it, we quantify the degree to which the vibrations associated with proton displacement are modulated by the geometry changes in the scaffold that are present in the zero-point vibrational wave function.

Because the barrier in Ox-H− is much smaller than the harmonic level OH stretching fundamental (∼3200 cm−1), it is not immediately obvious whether such vibrational averaging would also act to symmetrize this system as was found in OH−· H2O.9,30 We can address this question directly, however, by analyzing the bands associated with the two CO2− groups. These would be expected to split, for example, in the event that the ground state configuration remained asymmetrical at the vibrational zero-point level. To isolate these bands, we focus on the deuterium isotopologue, Ox-D−, as anharmonic effects are less pronounced than those observed in the Ox-H− spectrum (vide inf ra). The top two traces in Figure 2 present the harmonic predictions [B3LYP/6-311++G(d,p)] for the lowfrequency region of the spectrum when a deuteron is constrained to lie between the oxygen atoms to yield the C2v symmetry transition state (TS) structure (Figure 2a) as well as that corresponding to the Cs symmetry minimum (MIN) energy geometry (Figure 2b). As expected, the high-symmetry structure yields fewer strong transitions, with the highest energy feature at 1799 cm−1 composed of two nearly degenerate, inand out-of-phase CO displacements (blue), with the former dominating the oscillator strength. This near-degeneracy is lifted in the lower symmetry (Cs) minimum energy structure such that the four CO oscillators yield a widely split pair of doublets centered at 1250 and 1700 cm−1. The experimental Ox-D−·(H2)2 predissociation spectrum, presented in Figure 2d, closely corresponds to the open doublet pattern predicted for the asymmetric minimum energy structure. Figure 3 presents a comparison of the Ox-D− and Ox-H− predissociation spectra in Figure 3b,c, respectively. Note that the band assigned to the in-plane bending mode of the OD group (νip near 1200 cm−1 in Figure 3b) dramatically blue shifts in the light isotopologue and appears as a doublet near 1400 cm−1 (green peaks in Figure 3c). To address the origin of this doubling, as well as several weaker extra bands in both isotopologues indicated by * that are not predicted at the harmonic level, we first turned to the second-order vibrational perturbation theory (VPT2) approach (as implemented in Gaussian 09), which includes the cubic terms by perturbation theory rather than by direct diagonalization.36 Interestingly this method does not recover these features. The resulting spectrum is shown in Figure S2 of the Supporting Information.

II. EXPERIMENTAL METHODS Vibrational spectra of mass-selected gas-phase ions were acquired by predissociation of weakly bound H2 molecules using the Yale tandem time-of-flight photofragmentation mass spectrometer described previously.31 Deprotonated oxalic acid was generated using a custom electrospray ionization source, where the detailed experimental parameters involving ion generation and H2-tagging have been discussed at length in previous reports.32,33 The temperature of the bare NH4+H2O ion prepared under similar trapping conditions has been determined to be on the order of 30 K.34 Deuteration of the ions was efficiently carried out by introducing D2O vapor through a bleed valve into the second differentially pumped stage, nominally at ∼0.20 mbar, resulting in a pressure increase of ∼0.13 mbar in this region. The mass spectra signaling the exchange of the lighter hydrogen for a deuterium under these conditions is presented in Figure S1 of the Supporting Information, where >95% of the bare parent ions were converted into Ox-D−. III. RESULTS AND DISCUSSION IIIA. Asymmetrical Minimum Energy Structure of HO2CCO2−. The calculated [B3LYP/6-311++G(d,p)] structure of Ox-H− features asymmetric accommodation of the proton in the double minimum situation depicted in the potential energy surface presented in Figure 1 (black trace). The height of the barrier depends strongly on the level of theory as shown explicitly in Table S1 of the Supporting Information and is on the order of 1000 cm−1 on the Born−Oppenheimer surface. This value drops considerably (more than a factor of 2), however, upon inclusion of zero-point energy corrections. We note that the linearly H-bonded OH−·H2O anion also displays such a barrier,35 but that system becomes effectively symmetrical due to large amplitude zero-point motion that delocalizes the proton across the two minima. 13019

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vibrational configuration interaction matrix, which has the advantage that it can accurately treat coupling between nearly degenerate levels, as is the case in Fermi-resonance type interactions. Here we follow the approach described in a previous study16,37 where we assume that the fundamental transitions (i.e., in the harmonic basis) carry all of the oscillator strength to the mixed states that arise after matrix diagonalization. These mixed states are written in the harmonic basis (ϕi) as Ψanh = cbright,1ϕbright,1 + ... + cbright,3N − 6ϕbright,3N − 6 j + cdoor,1ϕdoor,1 + ... + cdoor,mϕdoor,m

(1)

where the “bright states” correspond to the 3N − 6 harmonic fundamentals. The size of the matrix was increased until the resulting eigenvalues were stable. This led to matrices with 90 states (fundamentals, overtones, and combination bands) in the range 204−5020 cm−1 for Ox-H− and 89 states in the range 102−4138 cm−1 for Ox-D−. The coefficients associated with the “bright states” are denoted cbright,n, whereas the coefficients associated with the nominally forbidden transitions “doorway states” (i.e., overtones and combination bands) are denoted cdoor,m. Thus, we can identify the “bright state” and “doorway state” that have the greatest contribution to a particular transition by comparing the squares of the coefficients cbright,n2 and cdoor,m2. This approach can be viewed as an extended version of the usual Fermi resonance analysis and, as such, will be referred to as the extended Fermi analysis in the discussion that follows. The cubic force constants were obtained by carrying out a VPT2 calculation as implemented in Gaussian 09.36 The small additional splitting of the 1319 cm−1 band and the extra feature at 1718 cm−1 (both indicated by *) in both isotopologues are accurately recovered by the extended Fermi analysis (Figure 2c). Specifically, the transitions at 1396 and 1445 cm−1 (Figure 3c) are traced to a coupling between the inplane bend and a combination band involving the out-of-plane OH bend (ν12) with a low-energy (482 cm−1) out-of-plane skeletal vibration (ν14). The assignments are described in detail in Tables S2 and S3 of the Supporting Information for Ox-H− and Ox-D−, respectively. As noted above, the VPT2 calculations do not recover these features. These results indicate that the oxalate system is asymmetric even though the barrier (∼1000 cm−1) is calculated to be much lower than the zero-point energy in the OH stretching mode. In part this is due to the fact that simple extension of the OH bond (i.e., along the normal mode displacement) does not take the system from the minimum energy structure to the transition state. The path between the potential minimum and transition state also requires a significant displacement of the COH/D angle along with deformation of the skeletal structure, as is illustrated in the structures at the top of Figure 2.38,39 To address this more quantitatively, we return to the one-dimensional scan of the potential surface displayed in Figure 1. The proton transfer coordinate corresponds to collective displacements that occur as the angle (θ) (defined as the angle between the vector connecting the hydrogen atom to the center of the CC bond and the vector that lies along the CC bond) evolves from one minimum at θ = 78.5° to the other minimum at θ = 102.5° with all other coordinates relaxed along the scan. The probability density was calculated using a discrete variable representation40 based on 100 DVR points between

Figure 2. Frequency spectra of Ox-D− (a) transition state and (b) minimum energy structures, with corresponding calculated geometrical parameters [B3LYP/6-311++G(d,p)] present at the top. The predissociation spectrum of Ox-D−·(H2)2 in the 2 H2 loss channel is given in (d). Transitions are color-coded according to their dominant normal mode displacements, e.g., the in-plane bend of the OH group (νip) and the various C−O stretching motions associated with the oxalate (C2O4)2− backbone. Trace c presents the spectrum calculated using the extended Fermi approach described in the text, which indeed recovers the extra bands (marked by *).

Figure 3. Comparison between the vibrational predissociation spectra of (b) Ox-D−·(H2)2 and (c) Ox-H−·(H2)2. Broad envelopes highlighted in red are assigned to spectral signatures of the cyclic intramolecular H-bond [CIH(D)B]. Traces a and d present the calculated anharmonic spectra using the extended Fermi approach. The * symbols denote doublets assigned to Fermi resonances that are also described in Tables S2 and S3 of the Supporting Information. The red arrows mark the positions of the OH(D) stretches at the harmonic level [B3LYP/6-311++G(d,p)]. The feature labeled ν12 denotes the out-of-plane bend in Ox-H−.

An alternative way to address mode coupling caused by inclusion of cubic terms in the potential is to construct a 13020

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structures to obtain the OH stretching frequency and transition moment for this configuration. More specifically, within this adiabatic treatment the vibrational wave function is expressed as

15° and 165°. For these calculations, the coordinate-dependent mass was given by 1/(2mHR2), where R represents the distance between the hydrogen atom and the center of the CC bond. Figure 1 displays the resulting distribution in green, superimposed on the potential curve (black) that controls this motion. Note that there is little amplitude near the transition state, thus demonstrating that the system adopts an asymmetric geometry despite the large harmonic zero-point energy. By performing a one-dimensional calculation, we have neglected contributions to the effective mass from displacements of the heavy atoms. This will increase the mass and thereby decrease the zero-point energy and lead to further localization of the ground state amplitude. IIIB. Identification of the CIH(D)B Band in the Ox-D− and Ox-H− Ions. Returning to the spectra shown in panels b and c of Figure 3, which correspond to the D and H isotopologues of deprotonated oxalic acid, we note that there are no strong features in the vicinity of the calculated harmonic fundamentals of the O−H(D) stretches (red arrows). Closer inspection, however, reveals a diffuse background absorption appear in both the Ox-D− and Ox-H− spectra that are displaced relative to one another by the amount appropriate for the reduced mass change expected for the O−H(D) oscillators. We note that similarly broad NH fundamentals were found in the GlyGlyH+ and SarGlyH+ dipeptides and were traced to the intrinsic character of the intramolecular H-bonds involving the excess proton.16 We therefore assign the broad structures (colored red) in the Ox-H(D) spectra to the corresponding O−H(D) stretching displacements. To put the scope of this broadening in context, we note that the density of states is estimated to be 0.5 and 6 states/cm−1 at 1300 and 2500 cm−1, respectively, using the direct sum method41,42 for separable vibrational degrees of freedom. As such, the near continuum nature of the features implies that the O−H(D) oscillator strengths are massively redistributed to most of the nominally IR forbidden background states in the molecule. IIIC. Adiabatic Treatment of the OH/D Stretch. We remark that inclusion of the cubic couplings as a perturbation leads to much less complexity than is observed, as evidenced by the red features in the calculated anharmonic traces displayed in Figure 3a,d. To address the breadth of the O−H(D) stretches in the oxalate anions, we adopt a perspective that was established in several earlier studies15,43,44 to understand the origin of diffuse OH spectra in ions that persist even as the temperature approaches 0 K. The key to this behavior involves the occurrence of a very strong dependence of the OH stretch frequency on displacements of the lower frequency normal mode coordinates that are available at the zero-point level. To quantify the implications of such mode coupling in the present context, we adopt the approach taken in our recent study of CaOH+ and MgOH+ with up to five water molecules.15 As in that report (and similar work by Petersen and co-workers on bridging double H-bonded systems21,22), we first evaluated the range of OH(D) stretching frequencies that would be sampled by the OH(D) stretching motion at the various zero-point displacements available to the lower frequency normal modes in Ox-H(D)−. To evaluate this behavior, geometries were sampled from the probability distribution associated with the ground vibrational level. The energy of each of the displaced geometries was then minimized with respect to only the OH(D) bond length while all of the other internal coordinates were frozen. A one-dimensional harmonic frequency calculation was then performed on each of these partially optimized

Ψ(qOH ,q) ≈ ψ (qOH ;q) χ (q)

(2)

in which the high-frequency OH stretch (qOH) is separated from the other 3N − 7 lower frequency modes (q). Within this approximation to the wave function, the transition strength and location of the OH stretch fundamental are given by S1 ← 0(ν) ∝ 2

ΨvOH = 1(qOH ,q) μ ⃗ (qOH ,q) δ(ν−νOH) ΨvOH = 0(qOH,q) (3)

If we approximate μ ⃗ (qOH ,q) ≈ μ ⃗ (qOH=0,q) +

dμ ⃗ (qOH ,q) dqOH

qOH qOH = 0

(4)

and treat ψn(qOH) as a harmonic oscillator, ΨvOH = 1 μ ⃗ (qOH ,q) δ(ν−νOH) ΨvOH = 0 = χ0

ℏ

dμ ⃗ (qOH=0,q)

2νOH(q)

dqOH

δ(ν−νOH(q)) χ0 qOH = 0

(5)

Substituting eq 5 into eq 3 and replacing the integral over the 3N − 7 normal modes with a sum over the nMC Monte Carlo sampled points, qi, based on the harmonic ground state probability amplitude in these coordinates, we obtain S1 ← 0(ν) ∝ 2 nMC

∑ i=1

dμ ⃗ (qOH ,q i) ℏ 2νOH(q i) dqOH

δ(ν−νOH(q i)) qOH = 0

(6)

Operationally, this was achieved by performing a normalmode analysis at the minimum energy geometry of the molecule at the chosen level of electronic structure theory. Here we used density functional theory (B3LYP) with a 6-311+ +G(d,p) basis set. We then generated a series of geometries of the molecule by sampling normal mode displacements at random from this (3N − 6)-dimensional Gaussian distribution and refined the resulting structures with respect to only the OH bond length. All of the other internal coordinates were constrained to their values from the displaced geometry. The Hessian and dipole derivatives obtained for these partially optimized geometries provide dμ⃗(qOH,q)/dqOH and νOH(q) in eqs 5 and 6. To ensure that the molecules are oriented the same way (so differences in the components of the dipole moment vector reflect changes in its structure rather than its orientation in space), we rotated all of the generated geometries into an Eckart frame, which is based on its equilibrium geometry. The line width of each q-dependent OH(D) fundamental transition is represented as a Gaussian function with a fwhm of 10 cm−1 and the global spectra reflects the average of the results from 2000 selected geometries (i.e., q values), scaled by a factor of 0.911. 13021

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Figure 4. Vibrational predissociation spectra of (a) Ox-H−·(H2)2 and (c) Ox-D−·(H2)2, with the corresponding calculated line shapes for the OH and OD stretches presented in traces b and d, respectively. These line shapes represent the convolutions of the harmonic spectra, evaluated at the geometries sampled from the ground state probability distribution.

Figure 5. Frequency dependence of the OH stretch with respect to (a) the OO bond distance (rOO) and (b) the COH angle (∠COH) obtained from 2000 geometries sampled from the probability distribution of the harmonic zero-point level.

Application of this scheme to the O−H(D) stretching manifold in the oxalate anions is presented in Figure 4, where Figure 4b depicts the calculated spectrum in the OH stretching region of Ox-H−. The results of the analogous calculation for Ox-D− are presented in Figure 4d. The calculated envelopes qualitatively reproduce the observed breadths in both experimental spectra (Figure 4a,c), indicating that the vibrational zero-point displacements are indeed expected to distribute the oscillator strength derived from the O−H(D) stretches over hundreds of cm−1. Note that in the limit that the q-dependent O−H(D) stretch quanta yield a widely spaced set of vibrationally adiabatic potential curves that govern the motion of the soft modes, this oscillator strength is distributed into well-defined combination bands with intensities expected from the vibrational overlap between the ground state wave function and those associated with the v = 1 levels of the O− H(D) potential curves.20,45,46 In the present case, however, we estimate these curves to be too closely spaced, and involve too many modes to yield the type of textbook examples of vibrationally adiabatic progressions found in HCO2−(H2O) and related systems.20,43,45,46 Further analyses of the sampled geometries provide additional insight into the origin of the breadth associated with the O−H stretch in Ox-H−. In particular, the O−O distance and COH angle seem obvious candidates for displacements that control the frequency of the OH stretch. Figure 5 presents the distributions of the calculated OH stretching frequencies as a function of these deformations. Whereas the O−O distance (Figure 5a) is essentially uncorrelated with the OH frequency, the COH angles accessible at the zero-point level are strongly correlated with it and yield changes in the local OH stretching quantum over the range 2000−3500 cm−1 (Figure 5b). Specifically, when the angle moves toward a linear H-bond (i.e., the COH angle becomes closer to 90°) the frequency red shifts, as would be expected for a linear ionic hydrogen bond between two proton acceptors.9

IV. CONCLUSIONS The vibrational predissociation spectrum of deprotonated oxalic acid indicates that, although all other bands appear as expected at the anharmonic level (with cubic corrections to the potential), the OH stretching fundamental of the positively charged group involved in the cyclic intramolecular H-bond to the proximal CO is uniquely broadened over hundreds of wavenumbers. Interestingly, neither the additional features in the fingerprint region nor the broad features in the OH or OD stretch region are recovered with a VPT2 calculation. To understand the origin of this broadening, we convoluted each OH/D stretch spectrum resulting from the structures obtained by sampling the ground state probability amplitude in the lowfrequency motions. The main conclusion is that the breadth of the vibrational signature associated with the embedded OH group is due to the displacements of the other modes at the vibrational zero point. In essence, this is a 0 K, quantum mechanical extension of the motional broadening that is often invoked2,10 to explain the broad envelopes associated with Hbonded systems (like water) at elevated temperatures.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b10649. Tables with barriers for proton transfer and vibrational transitions, harmonic frequency spectra, IR spectra, and mass spectra (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*A. B. McCoy. E-mail: [email protected]. *M. A. Johnson. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 13022

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ACKNOWLEDGMENTS M.A.J. thanks the Air Force Office of Scientific Research (AFOSR Grant: FA9550-13-1-0007), in particular for funding our focus on the introduction of protons to anionic CO2 motifs. A.B.M. acknowledges financial support from the National Science Foundation (NSF Grants CHE-1213347 and CHE1465001) and the Ohio Supercomputing Center for an allocation of computer resources on the Oakley Cluster. We also thank Christopher J. Johnson and Leif D. Jacobson for useful discussions in the preparation of an earlier version of this manuscript.

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