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Explaining the Structure of the OH Stretching Band in the IR Spectra of Strongly Hydrogen-Bonded Dimers of Phosphinic Acid and Their Deuterated Analogs in the Gas Phase: A Computational Study Najeh Rekik,*,† Houcine Ghalla,‡ and Gabriel Hanna*,† †

Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada Laboratoire de Physique Quantique, Faculté des Sciences de Monastir, 5000 route de Kairouan, Tunisia

‡

ABSTRACT: We present a simulation of the OH stretching band in the gas-phase IR spectra of strongly hydrogen-bonded dimers of phosphinic acid and their deuterated analogs [(R2POOH(D), with R = CH2Cl, CH3], which is based on a model for a centrosymmetric hydrogen-bonded dimer that treats the high-frequency OH stretches harmonically and the low-frequency intermonomer (i.e., O···O) stretches anharmonically. This model takes into account the following effects: anharmonic coupling between the OH and O···O stretching modes; Davydov coupling between the two hydrogen bonds in the dimer; promotion of symmetry-forbidden OH stretching transitions; Fermi resonances between the fundamental of the OH stretches and the overtones of the in- and out-of-plane bending modes involving the OH groups; direct relaxation of the OH stretches; and indirect relaxation of the OH stretches via the O···O stretches. Using a set of physically sound parameters as input into this model, we have captured the main features in the experimental OH(D) bands of these dimers. The effects of key parameters on the spectra are also elucidated. By increasing the number and strength of the Fermi resonances and by promoting symmetry-forbidden OH stretching transitions in our simulations, we directly see the emergence of the ABC structure, which is a characteristic feature in the spectra of very strongly hydrogen-bonded dimers. However, in the case of the deuterated dimers, which do not exhibit the ABC structure, the Fermi resonances are found to be much weaker. The results of this model therefore shed light on the origin of the ABC structure in the IR spectra of strongly hydrogen-bonded dimers, which has been a subject of debate for decades.

I. INTRODUCTION Systems with multiple hydrogen bonds (H-bonds) are prevalent in chemistry and biology. For example, liquids such as water and alcohols form extended H-bonded networks with different geometries.1 The structure of DNA is dictated by Hbonding between the nucleic acid base pairs and, more generally, protein structures may be stabilized by H-bonding interactions. Over the years there has been much interest in strong H-bonds,2-10 which are characterized by large bond enthalpies (≥10 kcal/mol), short distances, and a low to vanishing barrier to H transfer. Strong H-bonds are encountered in both neutral and ionic complexes of acids and bases.10 The strongest H-bonds in neutral complexes of the O− H···O type are found in dimers of phosphinic and arsenic acids,5,11,12 and, due to their high thermal stability, their IR spectra can be measured in the gas phase at temperatures between 400 and 600 K.13−15 On the other hand, the ionic complexes are found to be more stable in the condensed phase.16 Strong H-bonds have also been found in the active sites of several enzymes and, therefore, may play an important role in catalysis.6−9 © 2012 American Chemical Society

Infrared spectroscopy is a very powerful tool for studying Hbonded systems. The main signature of H-bonding in the IR spectrum of an H-bonded system is the υS(XH) band corresponding to the XH stretch involved in the H-bond (where X = O, N, ...). The interpretation of the unusual width and complicated structure of the υS(XH) band remains a challenging problem in this field. The problem becomes more complex when one goes beyond single, isolated H-bonds to coupled H-bonds in aggregates such as dimers. Nevertheless, the IR spectra of even simple systems such as cyclic, centrosymmetric H-bonded dimers, are still not fully understood, especially when it comes to the origin of the ABC structure arising from very strong H-bonds.5,17−19 The ABC band is composed of three broad peaks whose relative intensities are sensitive to the H-bond length. Several explanations for the origin of the ABC structure have been proposed over the years.17−28 One popular explanation, due to Received: February 17, 2012 Revised: April 9, 2012 Published: April 10, 2012 4495

dx.doi.org/10.1021/jp3016084 | J. Phys. Chem. A 2012, 116, 4495−4509

The Journal of Physical Chemistry A

Article

model and explain the structure of the υS(OH) bands in the gas-phase IR spectra of dimers of two phosphinic acids and their deuterated analogs R2POOH/D: dimethylphosphinic acid (i.e., R = CH3) and bis-(chloromethyl)-phosphinic acid (i.e., R = CH2Cl). In particular, we demonstrate how the ABC structure in the IR spectra of strongly H-bonded acid dimers emerges from the underlying molecular interactions within the context of this approach. The structure of the paper is as follows: Section II contains an overview of the model and the theoretical formulation for calculating the spectra. In section III, we present and discuss the results of our simulations, and concluding remarks are made in section IV.

Claydon and Sheppard,17 is that it is caused by strong Fermi resonances between the XH stretching fundamentals and the overtones or combinations of XH bending modes. Over the last several decades, a theoretical picture of the IR spectroscopy of cyclic H-bonded dimers has emerged, which has proven to be useful for interpreting the main qualitative features in their spectra.29−32 Within this picture, the main factors which influence the shape of the υS(XH) band are the following: anharmonic coupling between the XH and H-bond bridge stretches,33−35 vibrational energy relaxation from the XH stretches to their surroundings,36−40 Davydov coupling between multiple H-bonds,41 Fermi resonances between the first excited state of the XH stretching mode and overtones of the in- and out-of-plane bending modes or combination modes,42−44 and the promotion of symmetry forbidden transitions in centrosymmetric models of H-bonded dimers.45 All of these effects should somehow be taken into consideration when modeling the IR spectra of these systems. Carboxylic acids, which usually form cyclic dimers in both the gas46,47 and condensed phases,48−54 have served as prototypes for understanding the complex spectral signatures of coupled OH stretches in cyclic H-bonded systems. These prototypes were first studied in the pioneering work of Marechal and Witkowski41 and later by several other groups.46−54 In these dimers, the H-bonds are primarily of the weak to medium-strong type, and give rise to noisy υS(OH) bands, in contrast to the more ordered ABC structures observed in the case of very strong H-bonds. In this paper, we focus on the spectroscopy of H-bonds formed by the POOH groups in dimers of phosphinic acids, which are considered to be one of the strongest intermolecular bonds formed by neutral molecules. In crystals, these molecules form infinite chains and, less commonly, cyclic dimers when the O···O separation in the dimer lies between 2.40 and 2.55 Å, whereas in the gas phase these molecules almost always form cyclic dimers.55 Asfin et al. have conducted several experimental studies of the υS(OH) band in the IR spectra of various gasphase phosphinic acid dimers.13,55−57 Their investigation provided some insight into the formation of the ABC structure in the υS(OH) band, stating that the formation of such a broad band is mainly due to the strong H-bonding between the POOH groups, with the interaction between the H-bonds (i.e., Davydov coupling) essentially playing no role in the band shape formation. To date, the only simulations of the IR spectra of gas-phase monomers and dimers of phosphinic acid and dimethyl phosphinic acid have been performed by González et al.,58 using ab initio calculations based on molecular orbital and density functional theories. In this study, they showed that the two monomers form cyclic dimers in the gas phase, which are held together by two H-bonds that are considerably stronger than those in their carboxylic acid analogs. Although their calculated harmonic frequencies (and corresponding intensities) for the various vibrational modes were in qualitative agreement with the experimental gas-phase spectra, their calculations did not take into account anharmonic effects and peak broadening due to relaxation of the vibrational modes. The main goal of this paper is to apply an approach, which takes into account the anharmonic coupling between the highfrequency OH stretches and the low-frequency O···O stretching modes, Davydov coupling, direct/indirect relaxation of the OH stretching modes, and Fermi resonances between the fundamentals of the high-frequency OH stretches and overtones of the bending modes involving the OH groups, to

II. MODEL AND THEORETICAL CONSIDERATIONS Experimental studies have suggested that phosphinic and dimethylphosphinic acids form cyclic dimers with two Hbonds in the gas phase.14,56 Therefore, we consider a model in which two phosphinic acid molecules form a cyclic, centrosymmetric acid dimer with two H-bond bridges (see Figure 1). The dimer is assumed to be centrosymmetric

Figure 1. Centrosymmetric, cyclic acid dimer. The fast OH and slow O···O stretching mode coordinates are denoted by qi and Qi, respectively.

because the H-bonds are very strong and homonuclear (i.e., O−H···O). As a result, the two states of each H-bond (i.e., O− H···O ⇋ O···H−O) are isoenergetic. The two degenerate highfrequency OH stretching modes are characterized by position and momentum operators qi and pi and frequency ω, while the two degenerate low-frequency H-bond bridge stretching modes are characterized by position operators Qi and Pi and frequency Ω. The quantum mechanical model used to simulate the υS(OH) line shapes of these strongly H-bonded dimers contains the following features: (i) an adiabatic separation between the high-frequency OH and low-frequency H-bond bridge modes for each H-bond in the dimer (since their time scales differ by a factor of ≈10−3034,35), (ii) within this Born− Oppenheimer picture, a strong anharmonic coupling through the linear dependence of the OH stretching frequency on the H-bond bridge coordinate, (iii) Davydov coupling between the OH stretching modes, (iv) indirect relaxation of the OH stretch via the H-bond bridge vibration, (v) direct relaxation of the OH stretch, (vi) Fermi resonances between the OH stretching modes and overtones of the in- and out-of-plane OH bending modes, and (vii) anharmonicity of the H-bond bridge coordinate. This model has been previously used to simulate the IR spectrum of crystalline adipic acid48 and the polarized IR spectra of the OH stretching mode in medium-strong Hbonded dimers of 2-thiophenic53 and 3-thiophenic acids.54 The IR spectral density, I(ω), corresponding to the fast XH stretch mode in a H-bonded cyclic dimer may be related, within linear response theory,59,60 to the Fourier transform of its dipole moment autocorrelation function (ACF), G(t): 4496


The Journal of Physical Chemistry A I(ω) ∝ Re

∫0

∞

Article

G(t ) exp( −iωt ) exp( −γ ◦t )dt

where C2 is the symmetry operator (which performs an in-plane rotation by 180°) and Qu is a symmetrized variable given by

(1)

where γ° is the parameter responsible for the direct damping. Due to the centrosymmetric nature of the cyclic dimer, the ACF may be split into a symmetric (g) and an antisymmetric (u) part:46 G(t ) = Gg (t )(Gu+(t ) + Gu−(t ))

α

◦

⎣

⎣

× e−i⎡β /

(2)

2

2 ⎤⎦ Ωt

2 ⎤⎦ [⟨n⟩+ 1 ](2e−γt /2 cos Ωt − e−γt ) 2 2

× eiβ

2 −γt /2

e

[H{1}]u± |Ψ±μ⟩ = ωμ±|Ψ±μ⟩

sin Ωt

(3)

|Ψ±μ⟩ =

e

β=α

(4)

−1

(

2 Ω2 +

[H{1}]u± =

γ2 4

)

(6)

where ω° is the frequency of the two degenerate fast modes in the dimer when the H-bond bridge coordinates are at their equilibrium values. Each H-bond bridge is treated anharmonically (in terms of Morse potentials), whereas the OH stretching modes are treated harmonically. Their Hamiltonians are respectively given by ⎛

⎡

⎛

⎝

⎣

⎝

1 2

∑ ⎜⎜Pi2ℏΩ + De⎢⎢1 − exp⎜−βeQ i

1 2

∑ (pi2 + q i2)ℏω(Q i)

Gg (t ) =

2⎞

M Ω ⎞⎤ ⎟ ⎟⎥ ℏ ⎠⎥⎦ ⎟⎠

nu

(15)

where the μth eigenstate of HFermi is given by g |ϕμ⟩g =

∑ ∑ agμ,l ,m|Ψl ,m⟩g l

m

(16)

and the basis states, {|Ψl,m⟩g}, which are used to represent HFermi , are given by44 g |Ψ0, m⟩g = |{1}⟩g |[0]1 ⟩g |[0]2 ⟩g |[0]3 ⟩g ···|[0]nF ⟩g |(m)⟩g

⎡⎣1 ± ( − 1)

nu + 1

|Ψ1, m⟩g = |{0}⟩g |[2]1 ⟩g |[0]2 ⟩g |[0]3 ⟩g ···|[0]nF ⟩g |(m)⟩g

μ ±

+ η⎡⎣1 − ( − 1)nu + 1⎤⎦2 ⎤⎦2 × |Cn±u , μ|2 eiωμ t e−inuΩt

|Ψ2, m⟩g = |{0}⟩g |[0]1 ⟩g |[2]2 ⟩g |[0]3 ⟩g ···|[0]nF ⟩g |(m)⟩g

(8)

⋮

Here, nu = 0, 1, 2, and so on corresponds to the quantum number of the |nu(Qu)⟩ state of the low-frequency H-bond bridge mode obeying C2|nu(Q u)⟩ = ( −1)nu |nu(Q u)⟩

(14)

μ

HFermi |ϕμ⟩g = ℏωgμ|ϕμ⟩g g

Gu±(t )

∑∑e

B

Here, ωgμ and agμ,0,m are the eigenvalues and expansion coefficients of the corresponding eigenvectors, respectively, of the Hamiltonian HFermi :48 g

where M is the reduced mass of each H-bond bridge, De is the dissociation energy of the H-bond, and βe = (ℏΩ/2De)1/2 is the parameter characterizing the width of the H-bond bridge potential. The antisymmetric parts, G±u (t), which are influenced by Davydov coupling, are given by48

∝

μ g

∑ ∑ e−ℏΩm/k T |agμ,0,m|2 eiω t /ℏe−imΩt m

(7)

i

−nuℏΩ / kT

1 2 1 (Pu + Q u2)ℏΩ + αQ uℏΩ ± ℏΩVDC2 2 2

Here, Pu is the conjugate momenta of the symmetrized variable Qu and VD is a parameter that governs the strength of the Davydov coupling,41 which results from the nonadiabatic coupling between the two resonant OH stretching modes. Let us now consider the effects of Fermi resonances, which result from the coupling between the first excited state of the high-frequency OH stretching mode and the second excited states of the in- and out-of-plane bending modes involving the OH groups. Because the overtones of the bending modes giving rise to Fermi resonances are of g symmetry, only the gsymmetrized excited states of the fast mode are considered.48 Thus, in the presence of Fermi resonances, only the symmetric part of the ACF in eq 2 is affected and has the following form:48

(5)

ω(Q i) = ω◦ + αΩQ i

H fast =

(12)

(13)

where T is the absolute temperature. In eqs 3 and 5, α = 1/Ω(dω/dQi) is a dimensionless anharmonic coupling parameter, which describes the linear dependence of the fast mode frequency, ω(Qi), on the H-bond bridge coordinate Qi:41

i

u

and

[4Ω4 + γ 2 Ω2]1/2

Hslow =

∑ Cn±,μ|nu⟩ nu

1 ℏΩ / kT

(11)

where

Here, γ is the parameter responsible for the indirect damping, and the thermal average of the occupation number, ⟨n⟩, and β are given, respectively, by38,39 ⟨n⟩ =

(10)

η is a dimensionless parameter (that ranges from 0 to 1) that controls the strength of the IR transitions between the g states of the OH stretching mode, which are forbidden in centrosymmetric cyclic dimers, thereby accounting for deviations from centrosymmetry.45 ωμ± and Cn±u,μ are the eigenvalues and eigenvector expansion coefficients, respectively, defined by48

In the absence of Fermi resonances, Boulil et al. have shown that Gg(t) can be written in the following closed form:38,39 Gg (t ) = eiω t e−i 2 Ωt e−i⎡β /

1 [Q 1 − Q 2] 2

Qu =

|ΨnF , m⟩g = |{0}⟩g |[0]1 ⟩g |[0]2 ⟩g |[0]3 ⟩g ···|[2]nF ⟩g |(m)⟩g

(17)

where |{n}⟩g, |[n]i⟩g, and |(n)i⟩g are the g states of the highfrequency OH stretching, low-frequency H-bond bridge

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Table 1. Parameters Used for Fitting the Experimental Line Shapes of the (CH2Cl)2POOH and (CH3)2POOH Dimers and Their Deuterated Analogs (CH2Cl)2POOH (CH2Cl)2POOD (CH3)2POOH (CH3)2POOD

T (K)

ω° (cm−1)

Ω (cm−1)

De (cm−1)

α

γ° (Ω)

γ (Ω)

VD (Ω)

η

435 475 530 515

2300 1860 2415 1880

205 202 206 204

2100 2100 2100 2100

0.8 0.25 0.95 0.3

0.4 0.35 0.55 0.65

0.1 0.1 0.1 0.1

1.68 0.55 1.9 0.78

0.9 0.49 0.6 0.29

stretching, and bending modes. For example, |{1}⟩g, |[0]i⟩g, and |(m)⟩g correspond to the first excited state of the OH stretching mode, ground state of the ith bending mode, and the mth state of the H-bond bridge stretching mode, respectively. It should be noted that, in eq 17, it is implied that the size of the basis is N(nF + 1) because m ranges from 0 to (N − 1), where nF is the number of Fermi resonances and N corresponds to the number of H-bond bridge stretching states. In this basis, HFermi , which g incorporates the indirect damping via both the H-bond bridge stretching and bending modes, is given by an N(nF + 1) × N(nF + 1) matrix of the form44

HFermi g ℏ

⎛[H 0] ⎜ ⎜ [F ] ⎜ 1 ⎜ [F2] =⎜ ⎜ ⎜ ⎜ ⋮ ⎜ [F ] ⎝ nF

[FnF ] ⎞ ⎟ [H1] [N ] ··· [N ]⎟ ⎟ [N ] [H 2] ··· [N ]⎟ ⎟ ⋮ ⎟ ⎟ ⋮ ⋮ ⋱ [N ]⎟ [N ] ··· [N ] [H nF]⎟⎠ [F1]

[F2]

where ωδi is the frequency of bending mode δi.

III. RESULTS AND DISCUSSION We have applied the theoretical formulation described above for simulating the υS(OH)/υS(OD) bands in the IR spectra of Table 2. Fermi Resonance Parameters Used for Fitting the Experimental Line Shapes of the (CH2Cl)2POOH and (CH3)2POOH Dimers and Their Deuterated Analogsa

···

Δ2 (cm−1)

f1 (cm−1)

f2 (cm−1)

γδ1 (Ω)

γδ2 (Ω)

380 225 −255 5

320 115 −220 25

96 30 110 15

120 10 120 20

0.02 0.02 0.02 0.02

0.02 0.02 0.02 0.02

(CH2Cl)2POOH (CH2Cl)2POOD (CH3)2POOH (CH3)2POOD a

(18)

[Fi] = fi N

(19)

[N ] = 0 × N

(20)

In all cases, nF = 2.

dimers of two phosphinic acids [R2POOH(D)] in the gas phase: dimethylphosphinic acid (R = CH 3 ) and bis(chloromethyl)-phosphinic acid (R = CH2Cl). The experimental spectra of these phosphinic acids have previously been measured over the temperature range 400−550 K.13−15 We computed the spectra using eq 1, after constructing and diagonalizing the Hamiltonians [H{1}]u± (in the {|nu⟩} basis) and HFermi (in the {|Ψl,m⟩g} basis). The Fourier transform was g calculated numerically via a discrete FFT routine using 8192 points. The convergence of the computed spectra was checked with respect to the size of the basis sets. To make the calculation of the matrix elements of the Morse potential more tractable, the exponential was Taylor expanded with respect to the slow-mode coordinate, Q, and thus it was also necessary to check for the convergence of the expansion. Good agreement between the simulated and experimental υS(OH)/υS(OD) line shapes of dimers of (CH3)2POOH and (CH3)2POOD at 530 and 515 K, respectively, and dimers of (CH2Cl)2POOH and (CH2Cl)2POOD at 435 and 475 K, respectively, was obtained using a set of physically sound parameters (see Tables 1 and 2), as depicted in Figures 2 and 3. The (CH3)2POOH and (CH2Cl)2POOH line shapes exhibit an ABC structure, which is characteristic of strongly H-bonded dimers. The υ S (OD) bands for (CH 3 ) 2 POOD and (CH2Cl)2POOD are narrower and red-shifted compared to the corresponding υS(OH) bands and virtually structureless. Overall, the positions of the minima and maxima in the ABC structure do not depend strongly on the nature of the R group. For example, the high-frequency minima between the A and B peaks are located at 2475 and 2415 cm−1 for the (CH3)2POOH and (CH2Cl)2POOH dimers, respectively, and the lowfrequency minima between the B and C peaks are located at 1905 and 1850 cm−1, respectively. However, a significant change in the relative intensities of the A, B, and C peaks is observed upon switching the R group from CH2Cl to CH3. As seen in Figures 2 and 3, there is a redistribution of the intensity

where

and

Here, [H0] and [Hi]1≤i≤nF, respectively, are the adiabatic Hamiltonians corresponding to the first excited and ground states (after subtracting ω°N) of the OH stretching mode, {f i} are the parameters that govern the Fermi coupling between the OH stretching and bending modes, γ−1 δi is the excited-state lifetime of bending mode δi (where i = 1, 2, ..., nF), and the frequency gap, Δi, corresponding to bending mode δi is given by

Δi = 2ω δi − ω°

Δ1 (cm−1)

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Figure 2. Upper panel: Comparison between the experimental (black line) and theoretical (red line) υ S (OH) line shapes for (CH2Cl)2POOH at 435 K. Lower panel: Comparison between the experimental (black line) and theoretical (red line) υS(OH) line shapes for (CH2Cl)2POOD at 475 K. In both cases, nF = 2.

Figure 3. Upper panel: Comparison between the experimental (black line) and theoretical (red line) υS(OH) line shapes for (CH3)2POOH at 530 K. Lower panel: Comparison between the experimental (black line) and theoretical (red line) υS(OH) line shapes for (CH3)2POOD at 515 K. In both cases, nF = 2.

Table 3. Comparison of the First Moments of the Simulated and Experimental Line Shapesa

toward lower frequencies in the case of R = CH3 as compared to R = CH2Cl, leading to a relative enhancement of the C peak. Consequently, the center of gravity of the (CH3)2POOH band is red-shifted with respect to that of the (CH2Cl)2POOH band (see Table 3). Because there is a decrease in the dimerization enthalpy (associated with the formation of two H-bonds) in going from ΔH = −24 kcal/mol for R = CH3 to ΔH = −35 kcal/mol for R = CH2Cl, but there is no significant effect on the position/shape of the υS(OH) band, one may deduce that the change in the relative intensities of the peaks is due to their differing H-bond strengths. A possible explanation for this difference is that in the case of R = CH2Cl, there is a larger partial positive charge on the P atom due to the large electronegativity of the Cl group, which consequently leads to a greater attraction between the P and O (i.e., a stronger bond) on both sides of the dimer. This reduces the O···O distance in both H-bonds, giving rise to an increase in the strength of the H-bonds (as compared to the R = CH3 case). To validate the employed model for a centrosymmetric cyclic dimer, we must

⟨ω⟩calc (cm−1) (CH2Cl)2POOH (CH2Cl)2POOD (CH3)2POOH (CH3)2POOD a

2266 1968 2321 2007

⟨ω⟩exp (cm−1) 2313 1981 2364 1974

(2150) (1980) (2320) (2000)

The values in brackets were obtained from ref 57.

discuss the physical basis of the parameters used to fit the spectra (see Tables 1 and 2). The frequency of the OH stretching mode is taken to be ω° = 2415 cm−1 and ω° = 2300 cm−1 for the (CH3)2POOH and (CH2Cl)2POOH dimers, respectively. On the other hand, the frequency of the fast OD stretching mode is taken to be ω° = 1880 cm−1 and ω° = 1860 cm−1 for the (CH3)2POOD and (CH2Cl)2POOD dimers, respectively. Therefore, the ratio ω°H/ω°D is 1.28 and 1.24 for the (CH3)2POOH and (CH2Cl)2POOH dimers, respectively, which is different from 4499



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Figure 4. The effect of increasing the value of the Davydov coupling parameter, VD, on the υS(OH) line shapes for the dimers of (CH2Cl)2POOH at 435 K (upper panel) and (CH3)2POOH at 475 K (lower panel). The experimental results are given by the black lines.

Figure 5. Effect of increasing η on the υS(OH) line shapes for the dimers of (CH2Cl)2POOH at 435 K (upper panel) and (CH3)2POOH at 475 K (lower panel). The experimental results are given by the black lines.

√261 because the fast mode is anharmonically coupled to the slow mode. The frequency of the H-bond bridge vibration, Ω, is almost the same for all dimers considered and ranges from 202−206 cm−1, which is slightly higher than the experimental frequency range of 170−180 cm−1 found for acetic acid dimers,62−64 which contain medium-strong H-bonds. Deuteration leads to a slight decrease (by 2−3 cm−1) in Ω, which is in agreement with ≈4 cm−1 found by Cummings and Wood,65 who explained that this effect is due to the anharmonicity of the slow mode and to the anharmonic coupling between the fast and slow modes. The dissociation energy of the H-bond bridge, De, is taken to be 2100 cm−1 for all dimers. This value has been used previously in several computational studies of H-bonded dimers.53,54,66 It should be noted that the ratios ω°/Ω for the (CH2Cl)2POOH and (CH3)2POOH dimers are 11.21 and 11.72, respectively, whereas for the (CH2Cl)2POOD and (CH3)2POOD dimers, they are 9.20 and 9.21. These ratios are sufficiently large to justify the adiabatic separation between the OH and O···O stretching modes. However, in the case of weaker H-bonded systems, it has been found that the ratios range from 15 to 30,34,35,41,50 which suggests that the adiabatic approximation is even more valid.

The anharmonic coupling parameters, α, are similar for the hydrogenated dimers (i.e., 0.8 and 0.95 for (CH2Cl)2POOH and (CH3)2POOH, respectively). It has been observed previously that for weak to medium-strong H-bonded systems, α lies in the range 0.88−1.5 when Fermi resonances are taken into account.44,48,50,67,68 Upon deuteration, the anharmonic coupling parameter decreases by factors of 3.2 and 3.16 for the (CH3)2POOD and (CH2Cl)2POOD dimers, respectively. This trend was also observed in the cases of crystalline adipic acid,48 gaseous acetic acid dimer,50 propynoic acid dimer,47 and acrylic acid dimer.47 This decrease may be explained by the fact that the fast-mode frequency is more sensitive to changes in the slow-mode coordinate in the case of the OH stretch due to the lighter mass of H. To quantify the change in the spectrum due to deuteration, we have calculated κ = ⟨ω⟩H/⟨ω⟩D, where ⟨ω⟩H/D =

∫ ωIH/D(ω)dω ∫ IH/D(ω)dω

(24)

are the first moments of the H and D lineshapes and IH/D(ω) is the intensity at frequency ω. κ values of 1.16 and 1.15 were 4500



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model employed in this paper may be applied to both gas-phase and condensed phase cyclic, centrosymmetric dimers by varying the values of the direct (γ°) and indirect (γ) relaxation parameters. The values of these parameters used in this study are given in Table 1. The values of γ° for the (CH2Cl)2POOH and (CH2Cl)2POOD dimers are similar (i.e., 0.4Ω and 0.35Ω, respectively). Likewise, the γ° values for (CH3)2POOH and (CH3)2POOD are also similar (i.e., 0.55Ω and 0.65Ω, respectively). Therefore, the value of γ° does not exhibit a significant isotope effect, but depends on the nature of the R group. To explain the difference between the γ° values for the (CH3)2POOH/D and (CH2Cl)2POOH/D dimers, a detailed investigation would be required. Our γ° values correspond to population relaxation times ranging from 0.25 to 0.47 ps, which are in good agreement with the value of 0.2 ps reported by Heyne et al.77 in an ultrafast pump−probe experiment on acetic acid dimers in the liquid phase. For all of the dimers studied, γ = 0.1Ω. It should be noted that the spectra are insensitive to variations of γ in the range 0.1 ≤ γ ≤ 0.4, suggesting that the indirect relaxation is independent of both the nature of the R group and deuteration. In previous computational studies on crystalline adipic acid,48 liquid acetic acid,50 and gaseous acetic acid dimers,50 γ was taken to be 0.35Ω, 0.24Ω, and 0.24Ω, respectively. These results suggest that the indirect relaxation is independent of the phase in which the dimer exists, which may be due to the fact that it arises from the immediate coupling between the OH stretch and the Hbond bridge mode. Our γ value of 0.1 corresponds to a relaxation time scale of 1.6 ps, which is in good agreement with the range of 1 to 2 ps found by Heyne et al.,77 corresponding to the dephasing time scale associated with the anharmonic coupling to low-frequency modes in the dimers. The values of the Davydov coupling parameter, VD, used in this study range from 0.55 to 1.9. The effect of varying the strength of the Davydov coupling is illustrated in Figure 4. We see that, as VD increases, the band becomes broader and the ABC structure becomes more apparent. Furthermore, the VD values of the hydrogenated compounds are larger than those of the deuterated ones, in agreement with previous studies on acid dimers.46−48,50,53,54 This is consistent with the fact that the H states are more delocalized than the D states, giving rise to a more pronounced excitonic coupling in the case of the hydrogenated compounds. To improve the agreement with the experimental spectra, we have chosen η values of 0.9, 0.49, 0.6, and 0.29 for the (CH 2 Cl) 2 POOH, (CH 2 Cl) 2 POOD, (CH 3 ) 2 POOH, and (CH3)2POOD dimers, respectively. Recall that η controls the strength of the transitions between the g states of the OH stretching mode, which are known to be forbidden in centrosymmetric cyclic dimers.45 Therefore, nonzero values of η reflect departures from centrosymmetry. This way of accounting for selection rule breaking in cyclic dimers has been used previously to reproduce the spectra of a variety of crystalline H-bonded dimers of carboxylic acids such as glutaric,78 pimelic,79 benzoic,80 phenyl acetic 1- and 2napthyl,81 and cinnamic82 acids, and of gas-phase H-bonded dimers of acetic acid.46 Figures 5 and 6 illustrate the effect of η on the (CH3)2POOH and (CH2Cl)2POOH dimer spectra. In Figure 5, we see that as η is increased from 0 (i.e., where the transitions between the g states are forbidden), the predominant change is an increase in the C peak intensity, with a minor increase in the B peak intensity. To disentangle the effects of η and Fermi resonances

Figure 6. Effect of increasing η on the υS(OH) line shapes for the dimers of (CH2Cl)2POOH at 435 K (upper panel) and (CH3)2POOH at 475 K (lower panel) in the absence of Fermi resonances. The experimental results are given by the black lines.

obtained for (CH3)2POOH and (CH2Cl)2POOH, respectively, which are in good agreement with 1.16 for (CH3)2POOH and 1.08 for (CH2Cl)2POOH obtained by Asfin et al.57 It is important to note that these values lie in the interval 1.05 < κ < 1.20, which corresponds to H-bonds involving POOH and AsOOH groups.61,69 These values are also in good agreement with the experimental results of Iogansen et al.70 for strong Hbonded complexes of carboxylic acids and with values reported in a theoretical study of the H/D isotopic effects on the spectra of systems with different H-bond strengths.71 In a series of experimental studies of weak to strong H-bonded complexes, it was observed that κ depends on the H-bond strength: for complexes with weak H-bonds, κ is close to √2 and decreases with increasing H-bond strength, reaching a value of κ ≈ 0.9 for complexes with strong H-bonds.72−76 Let us now consider the coupling between the OH stretches in the dimer and their environments via direct and indirect damping. Direct relaxation of the XH stretch is caused by the interaction of the dipole of the XH stretch with the electric field induced by the dipoles in its local environment, whereas indirect relaxation results from the interaction of the XH stretch with its environment via the H-bond bridge mode. The 4501



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Figure 7. Effect of increasing the number of Fermi resonances from nF = 0 to 4 on the υS(OH)/υS(OD) line shapes for the dimers of (CH3)2POOH (top left), (CH3)2POOD (bottom left), (CH2Cl)2POOH (top right), and (CH2Cl)2POOD (bottom right). The experimental results are given by the black lines.

on the spectra, we report in Figure 6 the variation of η in the absence of Fermi resonances. Because the B peak is now absent, we see clearly that the increase in η is directly correlated to the increase in the C peak intensity (with the development of a shoulder which contributes to the low-frequency edge of the B peak in the presence of Fermi resonances). This suggests that the B peak is caused by Fermi resonances, as will be further explained below. These arguments are based on the fact that η is solely involved in G±u (see eq 8) and the Fermi resonance parameters are solely involved in Gg (see eq 14), that is, their effects on the spectra are independent of one another. Our results suggest that the transitions between the g states play a significant role in the spectra of the hydrogenated dimers (with the transition strength being greater in the case of the (CH2Cl)2POOH dimer). In the case of the deuterated dimers, the η values are both lower than those of the hydrogenated ones, suggesting that the transitions between the g states are less important for the deuterated dimers. As in the case of the hydrogenated dimers, the transition strength is greater for the (CH2Cl)2POOH dimer than for the (CH3)2POOH dimer. The observation that η affects only the low-frequency end of the band is consistent with what has been observed previously in the case of liquid and gaseous acetic acid.47 In ref 47, the predominant form of acetic acid was purported to be a cyclic centrosymmetric structure in both the gas and liquid phases, for which the authors claimed that the forbidden transition sub-

band occurs in the low-frequency portion of the band. The authors went on to say that if extended linear structures dominate in the liquid phase, then the forbidden transition subband would occur in the high-frequency portion of the band. Figure 7 show the effects of adding Fermi resonances to the simulated spectra of the (CH3)2POOH/D and (CH2Cl)2POOH/D dimers. In each panel, the number of Fermi resonances, nF, is increased from 0 to 4. As can be seen in the cases of the hydrogenated and deuterated species, good agreement between the simulated and the experimental spectra is obtained with nF = 2 and 0, respectively, with additional Fermi resonances having a slight effect in each case. However, in the case of the (CH2Cl)2POOD dimer, passing from nF = 0 to 2 leads to a slight improvement in the low-frequency peak. These results imply that there are Fermi resonances between the fundamental of the OH stretch and overtones of two (inand out-of-plane) bending modes involving the OH groups that affect the shape of the spectra, whereas in the case of the deuterated dimers, the signatures of these two Fermi resonances on the spectra are not as pronounced. We now discuss the roles played by the frequency gap, Δi, between the first excited state of the fast mode and the second excited state of bending mode i and the Fermi coupling parameter, f i, on the shape of the spectra. The panels on the left in Figures 8 and 9 show the effect of varying Δi from Δi = 0 cm−1 (i.e., resonance conditions) to the optimal values of Δi, 4502



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Figure 8. Left column: The effect of increasing Δi from 0 to the optimal values on the υS(OH) line shape for the (CH2Cl)2POOH dimer at 435 K. Right column: The effect of increasing f i on the υS(OH) line shape for the (CH2Cl)2POOH dimer at 435 K. The experimental results are given by the black lines.

other. Inspection of these panels leads to the following

which reproduce the spectra (using the optimal values of the f is). Our simulations give rise to positive and negative Δi optimal values for (CH2Cl)2POOH and (CH3)2POOH, respectively (see Table 2). In both cases, the first excited state of the fast mode and the second excited state of the bending modes are considerably out of resonance with each

observations: • In Figure 8, as the Δi values are increased from {Δ1 = 0 cm−1,Δ2 = 0 cm−1} to the optimal values, {Δ1 = 380 cm−1,Δ2 = 320 cm−1}, for the (CH2Cl)2POOH dimer, there is an overall red-shift of the intensities of the 4503



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Figure 9. Left column: The effect of decreasing Δi from 0 to the optimal values on the υS(OH) line shape for the (CH3)2POOH dimer at 530 K. Right column: The effect of increasing f i on the υS(OH) line shape for the (CH3)2POOH dimer at 530 K. The experimental results are given by the black lines.

cm−1,Δ2 = −220 cm−1}, for the (CH3)2POOH dimer, there is an overall blue-shift of the intensities of the subpeaks within the band. This is consistent with the picture that for negative Δi, there is an energy transfer from the bending modes to the first excited state of the OH stretching mode, thereby leading to a blue-shift of the υS(OH) band.

subpeaks within the band. This is consistent with the picture that for positive Δi, there is an energy transfer from the first excited state of the OH stretching mode to the bending modes, thereby leading to a red-shift of the υS(OH) band. • In Figure 9, as the Δi values are decreased from {Δ1 = 0 cm−1,Δ2 = 0 cm−1} to the optimal values, {Δ1 = −255 4504



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Figure 10. Effect of increasing Ω on the υS(OH) line shape for the (CH2Cl)2POOH dimer at 435 K with (right column) and without (left column) Fermi resonances. The experimental results are given by the black lines.

To study the effect of the Fermi coupling strength on the υS(OH) band, we proceeded to vary the f is. The panels on the right in Figures 8 and 9 show the effect of varying f i from {f1 = 0 cm−1,f 2 = 0 cm−1} to the optimal values, {f1 = 96 cm−1,f 2 = 120 cm−1}, for the (CH2Cl)2POOH dimer and from {f1 = 0 cm−1,f 2 = 0 cm−1} to the optimal values, {f1 = 110 cm−1,f 2 = 120 cm−1}, for the (CH3)2POOH dimer (using the optimal

Therefore, one can make a connection between the relative intensities of the peaks and the signs/magnitudes of the Δi values through fitting, and thereby gain insight into the nature of the energy transfer due to Fermi coupling. It should be noted that upon deuteration, the Δi values become smaller in magnitude than for the hydrogenated species and, hence, closer to resonance conditions. 4505



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Figure 11. Effect of increasing Ω on the υS(OH) line shape for the (CH3)2POOH dimer at 530 K with (right column) and without (left column) Fermi resonances. The experimental results are given by the black lines.

values of the Δis). As seen in these figures, as the f is are increased toward their optimal values, the peak centered at 2500 cm−1 splits, leading to the formation of an Evans window and thereby giving rise to the AB diad. Moreover, as in the case of Δi, the f i values become much smaller upon deuteration, which suggests that the interaction between the OD stretch and

the bending modes is weaker and therefore Fermi resonances do not play a significant role in the D spectra. The effect of the intermonomer streching frequency, Ω, on the lineshapes of the (CH2Cl)2POOH and (CH3)2POOH dimers is shown in Figures 10 and 11, respectively. The left panels correspond to the case in which Fermi resonances are not included, whereas the right panels correspond to the case in 4506



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Evans windows are observed when f i ≫ γδi , which is consistent with the parameters we obtained (i.e., f i = 96−120 cm−1 and γδi = 4.12 cm−1). The task of fitting the experimental IR spectra of H-bonded dimers is difficult due to both the number and complexity of physical effects that need to be taken into account. For this reason, the small discrepancies between the simulated and experimental spectra may be due to neglecting certain effects or to making simplifying assumptions. The model used in this study assumes the following: the linear dependence of the frequency of the fast mode on the H-bond bridge coordinate, the independence of the equilibrium position of the fast mode on the H-bond bridge coordinate, a constant Davydov coupling parameter, and an adiabatic separation between the OH stretches and the O···O coordinates. It also neglects the following: electrical anharmonicity, tunneling through a barrier separating the two H-bond bridge minima (because the fast mode is described by a harmonic potential and not by a doublewell potential), and nonadiabatic relaxation mechanisms. However, these approximations are sufficiently justified for the systems studied herein. The fact that the ratio of the fast- to slow-mode frequencies justifies the use of the adiabatic approximation and, hence, the neglect of nonadiabatic relaxation mechanisms. Neglecting the second order dependencies of the frequency and equilibrium position of the fast mode on the H-bond bridge coordinate most likely only leads to small discrepancies, because it has been shown in the case of systems with a single H-bond that accounting for them affects the fine structure of the spectra.71 As in the case of other theoretical studies of H-bonded systems based on similar models,41,46−48 we have used a constant Davydov coupling parameter. However, it should be noted that, in general, the Davydov coupling between two H-bonds in a dimer depends on the H-bond bridge coordinates and may consequently vary for other types of H-bonds. The neglect of the anharmonicities of the fast modes, which amounts to neglecting tunneling effects, may be justified by the fact that the potential barrier between the two symmetric H-bond bridge minima is very low in the case of these very strong H-bonds. Finally, the neglect of electrical anharmonicity may be justified by the fact that the relative intensities of the peaks are well-reproduced without considering second-order terms in the dipole moment expansion.

Figure 12. Effect of increasing both γδi s on the υS(OH) line shape for the (CH2Cl)2POOH (upper panel) and (CH3)2POOH (lower panel) dimers. The experimental results are given by the black lines.

which Fermi resonances are taken into account. In the case of no Fermi resonances, we see that a nonzero Ω leads to a splitting of the υS(OH) band, which increases as Ω increases, giving rise to two of the peaks (i.e., A and C) in the ABC structure. Upon addition of Fermi resonances, the band undergoes further splitting. However, in order properly capture the Evans windows in the experimental spectrum, Ω values corresponding to such strong H-bonds found in these dimers must be used. In doing so, the A peak in the absence of Fermi resonances becomes the AB diad in their presence. Figure 12 illustrates the effect of varying the parameters responsible for relaxation via the bending modes, γδi , on the lineshapes of the (CH2Cl)2POOH and (CH3)2POOH dimers. We observe that only the AB diad is affected by variations in these parameters, and that by increasing their values, the Evans window gradually becomes smaller and eventually disappears. This indicates that, in addition to the strengths of the Fermi couplings between the OH stretch and the bending modes, the relaxation via these bending modes plays an important role in the formation of the AB diad. The optimal relaxation parameters for the two bending modes were found to be γδ1 = γδ2 = 0.02 Ω. According to Chamma and Henri-Rousseau,67

IV. CONCLUDING REMARKS The model adopted in this study has been applied for the first time to very strongly H-bonded acid dimers in the gas phase in order to elucidate the origin of the ABC structure of the υS(OH) band in their IR spectra. This model is based on a strong anharmonic coupling theory in which the high-frequency mode and the H-bond bridge are anharmonically coupled through a linear dependence of the frequency of the OH stretch on the H-bond bridge coordinate and takes into account Davydov coupling, Fermi resonances, anharmonicity of the Hbond bridge, and direct/indirect relaxation. Using this model, we have simulated the υS(OH) band of strongly H(D)-bonded cyclic dimers of phosphinic acid [R2POOH(D), with R = CH2Cl, CH3] in the gas phase. Good agreement with the experimental line shapes of these compounds was obtained by fitting with a set of physically reasonable parameters. The validity of these parameters was discussed on the basis of experimental and/or theoretical grounds. 4507



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(8) Kim, K. S.; Oh, K. S.; Lee, J. Y. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 6373−6378. (9) Katz, B. A.; Spencer, J. R.; Elrod, K.; Uong, C. L; Mackman, R. L.; Rice, M.; Sprengeler, P. A.; Allen, D.; Janc, J. J. Am. Chem. Soc. 2002, 124, 11657−11668. (10) Grech, E.; Malarski, Z.; Sawka-Dobrowolska, W.; Sobczyk, L. J. Mol. Struct. 1997, 416, 227−234. (11) Thomas, L. C.; Chittenden, R. A.; Hartley, H. E. Nature 1961, 192, 1283−1284. (12) Walmsley, J. A. J. Phys. Chem. 1984, 88, 1226−1231. (13) Asfin, R. E.; Denisov, G. S.; Tokhadze, K. G. J. Mol. Struct. 2002, 608, 161−168. (14) Denisov, G. S.; Tokhadze, K. G. Doklady Phys. Chem. 1994, 337, 117−119. (15) Tokhadze, K. G.; Denisov, G. S.; Wierzejewska, M.; Drozd, M. J. Mol. Struct. 1997, 404, 55−62. (16) Novak, A. Struct. Bonding (Berlin, Ger.) 1974, 18, 177−216. (17) Claydon, M. F.; Sheppard, N. Chem. Commun. 1969, 1431− 1433. (18) Hadzi, D. Pure Appl. Chem. 1965, 11, 435−453. (19) Hadzi, D.; Bratos, S. The Hydrogen Bond. In Recent Developments in Theory and Experiments; Schuster, P., Zundel, G., Sandorfy, C., Eds.; North-Holland: Amsterdam, 1976; Vol. 2, Chapter 12. (20) Bratos, S.; Ratajczak, H.; Viot, P. In Hydrogen Bonded Liquids; Dore, J. C., Teixeira, P., Eds.; Kluwer: New York, 1991; pp 221−235. (21) Baran, J. J. Mol. Struct. 1988, 172, 1−13. (22) Baran, J.; Lis, T.; Drozd, M.; Ratajczak, H. J. Mol. Struct. 2000, 516, 185−202. (23) Marchewka, M. K.; Baran, J. Spectrochim. Acta 2004, A60, 201− 210. (24) Ratajczak, H.; Yaremko, A; Baran, J. J . Mol. Struct. 1992, 275, 235−247. (25) Videnova-Adrabinska, V.; Baran, J. J. Mol. Struct. 1987, 156, 1− 14. (26) Videnova-Adrabinska, V. J. Mol. Struct. 1988, 177, 477−486. (27) Soptrajanov, B.; Stefov, V.; Kuzmanovski, I.; Jovanovski, G. J. Mol. Struct. 1999, 103, 482−483. (28) Soptrajanov, B.; Jovanovski, G.; Kuzmanovski, I.; Stefov, V. Spectrosc. Lett. 1998, 31, 1191−1205. (29) Nibbering, E. T. J.; Elsaesser, T. Chem. Rev. 2004, 104, 1887− 1914. (30) Czarnik-Matusewicz, B.; Rospenk, M.; Koll, A.; Mavri, J. J. Phys. Chem. A 2005, 109, 2317−2324. (31) Denisov, G. S.; Mavri, J.; Sobczyk, L. In Hydrogen Bonding New Insights; Grabowski, S., Ed.; Springer: Berlin, 2006; Chapter 12. (32) Stare, J.; Panek, J.; Eckert, J.; Grdadolnik, J.; Mavri, J.; Hadzi, D. J. Phys. Chem. A 2008, 112, 1576−1586. (33) Hofacker, G.; Maréchal, Y.; Ratner, M. In The Hydrogen Bond Theory; Schuster, P., Zundel, G., Sandorfy, C., Eds.; North-Holland: Amsterdam, 1976; p 297; see also pp 567 and 616. (34) Henri-Rousseau, O.; Blaise, P. Infrared Spectra of Hydrogen Bonds: Basic Theories. In Indirect and Direct Relaxation, Theoretical Treatment of Hydrogen Bonding; Hadzi, D., Ed.; Wiley: New York, 1997; p 165. (35) Henri-Rousseau, O.; Blaise, P. The Infrared Spectral Density of Weak Hydrogen Bonds within the Linear Response Theory. In Adv. Chem. Phys.; Prigogine, I., Rice, S. A., Ed.; Wiley: New York, 1998; Vol. 103, p 1. (36) Rosch, N. Chem. Phys. 1973, 1, 220−231. (37) Rosch, N.; Ratner, M. J. Chem. Phys. 1974, 61, 3344−3351. (38) Boulil, B.; Henri-Rousseau, O.; Blaise, P. Chem. Phys. 1988, 126, 263−290. (39) Boulil, B.; Blaise, P.; Henri-Rousseau, O. J. Mol. Struct.: THEOCHEM 1994, 314, 101−112. (40) Rekik, N.; Ouari, B.; Blaise, P.; Henri-Rousseau, O. J. Mol. Struct.: THEOCHEM 2004, 687, 125−133. (41) Maréchal, Y.; Witkowski, A. J. Chem. Phys. 1968, 48, 3697− 3705.

Within the context of this model, we have shown that the ABC structure arises as a consequence of both Fermi resonances and the promotion of forbidden transitions for centrosymmetric H-bonded dimers that result from coupling to the slow mode. In the case of the D-bonded dimers, we have shown that Fermi resonances do not play a significant role, which explains the lack of Evans windows in their spectra. It should be emphasized that the ABC structure is a spectral signature of very strong H-bonded dimers, whereas in the case of weak to moderately strong H-bonded acid systems such as dimers of 2-thiophenic53 and 3-thiophenic54 acids (which do not exhibit an ABC structure), it was found that Fermi resonances do not play an important role. Owing to the decent agreement between the theoretical and experimental line shapes, we believe that the model applied herein can be useful for simulating and interpreting the line shapes of very strongly H-bonded dimers. However, whether or not this approach is generally applicable to this class of Hbonded systems remains an open question. Several refinements may need to be made to the model in order to generalize it. For example, in the solid phase at 80 and 300 K, the υS(OH) band shapes of the (CH2Cl)2POOH and (CH3)2POOH dimers are significantly different from those measured in the gas phase at higher temperatures.13,57 Namely, one observes a redistribution of the intensities of the A, B, and C peaks, with the C peak becoming more intense as the temperature is decreased. It would be interesting to see if it is possible to simulate the temperature dependence of the bands by introducing temperature dependence into the η and Δi parameters or if a model such as that recently proposed in ref 83 would be more appropriate. Also, in the case of other strongly H-bonded systems whose ABC trio is further split into several submaxima,18 it is necessary to take into account the protonic tunneling in a double-well potential (as opposed to a harmonic potential) in order to split the vibrational levels. The effects of extending the current model on the IR spectra of these systems will be the subject of future work.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by grants from the University of Alberta and the Natural Sciences and Engineering Research Council of Canada. The authors would like to thank Professor Ruslan E. Asfin from the Institute of Physics at St. Petersburg State University for providing the experimental spectra for the (CH3)2POOH(D) and (CH2Cl)2POOH(D) dimers.

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REFERENCES

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