Comment on “Multiwavelength Raman Spectroscopic Study of Silica

COMMENT pubs.acs.org/JPCC

Comment on “Multiwavelength Raman Spectroscopic Study of Silica-Supported Vanadium Oxide Catalysts” A. E. Stiegman* Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States n the recently published paper titled “Multiwavelength Raman Spectroscopy Study of Silica-Supported Vanadium Oxide Catalysts” by Wu, Dai, and Overbury, multiple excitation wavelengths were used to collect both resonant and nonresonant Raman spectra of an isolated V(V) oxide site on a silica support.1 On the basis of a specific analysis of these spectra, including an analysis of the overtones, 18O labeling studies, and arguments based on the mechanism of resonance enhancement, “assignments” of the “vibrational modes” of the silica-bound vanadyl site were made. These assignments included the identification of the intense band at 1032 cm
1 as a “VdO” stretch and the band at 920 cm
1 as a “Si
O
V” stretch. Notably, these conclusions counter completely the results of a detailed normal coordinate analysis that we recently published.2 While a thoughtful, experimentally supported reassignment of spectroscopic bands is an appropriate contribution to the literature, a careful reading of this report indicates that it is highly flawed, suffering as it does from what appears to be a fundamental lack of understanding of the nature of the normal modes of vibration of complex molecules and the importance of these modes in the correct description of a vibrating species bound to the surface. As such, the conclusions drawn in this report are in no way supported by the data. Since our work has been directly impugned in this publication and since we were not provided an opportunity to participate in the reviewing process, we believe that it is incumbent upon us to correct these errors so that other members of the catalysis community are not led astray. In the introduction to the report, Wu et al. outline numerous “controversies” that appear in the catalysis literature concerning the assignment of VdO or V
O
Si vibrational modes to specific bands observed in the vibrational spectra. Consistent with this discussion, the primary goal of their paper appears to be to “resolve” these controversies and correctly “assign” the resolved spectroscopic bands to “VdO” modes or “V
O
Si” modes. As will be discussed, these are not normal modes of the bound vanadyl site and, as such, cannot be meaningfully “assigned” to any spectral features at all. In fact, many of the “controversies” that plague the vibrational literature of heterogeneous catalysis are not controversies at all, but arise from a lack of understanding of the basic physics of molecular vibrations and normal modes. In particular, the belief that bond-unit designators such as VdO and Si
O
V stretches have physical significance and that spectroscopic bands can be meaningfully segregated into them is false. Unfortunately, this misconception, which permeates the literature of vibrational studies of heterogeneous catalysis, has prevented vibrational spectroscopy from providing meaningful information about important issues in

I

r 2011 American Chemical Society

supported heterogeneous catalysts, such as the effect of the support on the catalytic site. For the case of monomeric vanadyl supported on a surface, the assignment of the highintensity, high-energy band occurring around 1032 cm
1 to a VdO stretch originated in early studies by comparison of the spectra to those of small molecule analogues.3 Since the highest frequency bands of many small-molecule oxovanadium model compounds (e.g., VOCl3) occur in the spectral region from ∼960 to 1050 cm
1 and have normal modes dominated by a VdO stretch, the 1032 cm
1 mode for vanadia on silica was assigned purely by analogy to such species as a VdO stretch. This, of course, was an entirely rational place to begin, and we in no way fault these early studies for using such an analogy. However, it would be expected that future work would involve in-depth analysis of the validity of these assignments with the application of appropriate normalmode analysis. This has never been done, and the early, nonrigorous assignments have become ingrained in the literature. In our view, this has been a considerable detriment to the field of heterogeneous catalysis, where a proper characterization of the interactions between the surface and the active site is of paramount importance. Before analyzing the specific arguments put forth by Wu et al., some background is in order. A transition observed in the vibrational spectra (IR or Raman) of polyatomic molecules arises, in the classical treatment, from the excitement of a normal mode of vibration.4,5 The normal modes of vibration are the eigenvectors that diagonalize the product of the potential (F) and kinetic (G) energy matrices, with the eigenvalues being the energies of the modes (i.e., frequencies of the spectral bands). In the standard vibrational treatment, the normal modes are related to the internal coordinates of the molecule, which are the bond-specific stretching and bending operations. A model for the surface-bound vanadyl group, along with the relevant internal coordinates that we used in our analysis, is shown in Figure 1. This model maintains an idealized C3v point group, although it is understood that rather drastic symmetry reduction occurs on the surface that will affect the selection rules for the spectroscopic observations of bands associated with the normal modes. Moreover, it is also understood that the degree to which any small molecule model will accurately describe a vanadyl site bound to what is essentially an infinite silica surface will depend on the degree to which it includes the primary internal coordinates that make up the normal mode. Received: May 18, 2010 Revised: April 13, 2011 Published: May 11, 2011 10917

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The Journal of Physical Chemistry C

COMMENT

coordinates, R are the internal coordinates, and U is the symmetry transformation matrix.5 Q ¼ L
1 S ¼ L
1 UR

ð1Þ

1 qA1 1 ¼ l11 ðΔrt Þ þ l12 pffiffiffiððΔr11 Þ þ ðΔr12 Þ þ ðΔr13 ÞÞ 3

1 1 þ l13 pffiffiffiððΔr21 Þ þ ðΔr22 Þ þ ðΔr23 ÞÞ þ l14 pffiffiffiððβ11 Þ þ ðβ21 ÞÞ 3 3 1 1 þ l15 pffiffiffiððβ12 Þ þ ðβ22 Þ þ ðβ32 ÞÞ þ l16 pffiffiffiððβ13 Þ þ ðβ23 Þ 3 3 1 3 1 2 3 ð2Þ þ ðβ3 ÞÞ þ l17 pffiffiffiððβ4 Þ þ ðβ4 Þ þ ðβ4 ÞÞ 3 1 qA2 1 ¼ l21 ðΔrt Þ þ l22 pffiffiffiððΔr11 Þ þ ðΔr12 Þ þ ðΔr13 ÞÞ 3 1 1 þ l23 pffiffiffiððΔr21 Þ þ ðΔr22 Þ þ ðΔr23 ÞÞ þ l24 pffiffiffiððβ11 Þ 3 3 1 1 2 1 2 3 þ ðβ1 ÞÞ þ l25 pffiffiffiððβ2 Þ þ ðβ2 Þ þ ðβ2 ÞÞ þ l26 pffiffiffiððβ13 Þ 3 3 1 ð3Þ þ ðβ23 Þ þ ðβ33 ÞÞ þ l27 pffiffiffiððβ14 Þ þ ðβ24 Þ þ ðβ34 ÞÞ 3

Figure 1

In the case of the eight-atom model that we have employed, it possesses the primary bond connecting the five-atom vanadyl group to the surface and has internal coordinates commensurate with the number of observed resolved vibrational bands so that a force field can be determined. Obviously, the inclusion of Si
O and Si
O
Si bonds further in the silica surface would improve the model, although, as we will point out, it would not be expected to shift the normal coordinate change to one that is in agreement with longstanding “assignments”. The eight-atom model will have 18 vibrational modes (5A1 þ A2 þ 6E). Since the assignments in question involve primarily stretching modes, we note that seven of the normal modes will formally be stretching modes, three singly degenerate A1 modes, and two doubly degenerate E modes. It is customary to use the symmetry of the molecule to simplify the vibrational problem through symmetry factoring of the internal coordinates.5,6 The internal coordinates, symmetry factored in the totally symmetric A1 representation, are shown in Figure 1b. As can be seen, all the internal coordinates span the totally symmetric A1 representation and will, therefore, contribute to those modes. While not shown, the terminal VdO internal coordinate does not span the E irreducible representation and, hence, will not formally contribute to stretching modes of that symmetry. As such, there would be some justification in referring to the modes originating from E symmetry vibrations as V
O
Si modes. As mentioned, however, the symmetry reduction that occurs upon binding to the surface will profoundly lift that restriction. The relationship between the normal modes and the symmetrized and internal coordinates is given by the following matrix equation, where Q are the normal coordinates, S are the symmetry

1 qA3 1 ¼ l31 ðΔrt Þ þ l32 pffiffiffiððΔr11 Þ þ ðΔr12 Þ þ ðΔr13 ÞÞ 3 1 1 1 þ l33 pffiffiffiððΔr2 Þ þ ðΔr22 Þ þ ðΔr23 ÞÞ þ l34 pffiffiffiððβ11 Þ 3 3 1 1 þ ðβ21 ÞÞ þ l35 pffiffiffiððβ12 Þ þ ðβ22 Þ þ ðβ32 ÞÞ þ l36 pffiffiffiððβ13 Þ 3 3 1 2 3 1 2 3 ð4Þ þ ðβ3 Þ þ ðβ3 ÞÞ þ l37 pffiffiffiððβ4 Þ þ ðβ4 Þ þ ðβ4 ÞÞ 3 The L matrix is the linear transformation matrix, which takes the symmetrized internal coordinates into the normal coordinates; its columns are the eigenvectors of the GF matrix product, which have been properly normalized. Since the modes brought into question by Wu et al. are those responsible for the 1032 cm
1 and the 920 cm
1 spectroscopic bands, both of which are totally symmetric, we point out that the normal coordinates of those modes will necessarily be linear combinations of the symmetrized coordinates spanning A1 (Figure 1), the normal coordinates of which will be given by eqs 2
4. Since the columns of the L matrix are eigenvectors of the GF product, coefficients lij will be the matrix elements, which will be the products of the elements of these matrices, specifically the force constants from the F matrix and the atomic masses, bond lengths, and angles from the G matrix. As such, a normal mode will necessarily be composed of contributions from all the internal coordinates present in the symmetrized coordinates. The degree to which each internal coordinate contributes to the normal mode is determined by the magnitude of the lij values. The designation of a normal mode in terms of a characteristic bond vibration is well established in vibrational spectroscopy as are the parameters by which the assignment of a characteristic frequency to a normal mode is correctly carried out. Among trained vibrational spectroscopists, such characteristic mode descriptors simply indicate the internal coordinate that makes the largest single contribution to the normal mode, although it may not necessarily dominate the vibration to the exclusion of 10918

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The Journal of Physical Chemistry C

COMMENT

other V ¼

∑

∑

1 1 Fi, j Ri Rj ¼ Q 2 k li, k lj, k Fi, j 2 i, j 2 i, j

ð5Þ

oscillators. Historically, the internal coordinate that contributes the largest displacement to the normal coordinate change can usually be designated as the characteristic vibration for the modes, and this, in fact, is often the case.7,8 However, as pointed out in the classic paper by Morino and Kuchitsu, there are modes where this method of designation does not hold, and a more correct assignment of a characteristic frequency is to be derived from the potential energy contribution of a particular oscillator to the total potential energy of the normal modes.9 This is shown in eq 5, where F are the individual force constants from the Wilson F matrix and R, Q, and l are defined as before. The characteristic frequency of a normal mode, Q, will be the internal coordinate, R, that provides the largest contribution to the potential energy. This is the established requirement for the proper assignment of a normal mode to a specific internal coordinate change or characteristic frequency in vibrational spectroscopy. While well-executed and properly interpreted spectroscopy studies can aid in a normal mode assignment, the accurate assignment can only be carried out by a proper normal coordinate analysis from a reliable force field using a proper set of internal coordinates. For reasons that are unclear, prior density functional studies of the vanadyl site have determined the “normal modes” by calculating the kinetic energy distribution of the oscillators, not the potential energy distribution.10 In these studies, the oscillator that provides the largest kinetic energy is deemed to be the characteristic vibration of the normal mode. As is clear from the previous discussion, this is not a definition of a normal mode that is recognized anywhere in vibrational spectroscopy. Since assignments obtained from the kinetic energy values are likely to differ significantly from the normal mode designations determined properly from the potential energy distribution, the normal mode assignment made in these papers is, in our view, not valid. Inherent in the assignment of the 1032 cm
1 spectral band to a VdO stretch is the assumption that this internal coordinate makes the largest contribution to the potential energy of the normal mode in question. In the study of Wu et al., as well as many other spectroscopic studies in this field, no discussion of normal modes or the relative contributions of internal coordinates to a normal mode is presented. Instead, in both the description of the vibration and, more importantly, the quantitative treatment of the experimental data, the vibration is assumed to act rigorously as an isolated diatomic (VdO) or triatomic (V
O
Si) oscillator. The assumption that a rigorous diatomic oscillator accounts for the 1035 cm
1 stretch essentially assumes that all of the coefficients in eq 2 except l11 are zero or very nearly zero. In point of fact, this can occur only under a specific set of conditions, none of which are realized for supported vanadium oxide. One condition that leads to isolation of a single internal coordinate is a large frequency difference between it and adjacent oscillators, which is brought about by large mass and/or force constant differences. This condition is met, for example, in chloroform, in which the C
H oscillator behaves as a pseudodiatomic oscillator because it is decoupled from the C
Cl due to the large frequency difference.11 It also is met in small molecule vanadyl analogues such as the oxo halides VOCl3 and VOBr3.12

Adjacent oscillators can also decouple as bond angles approach 90
, which sends the cosine dependent off-diagonal coupling terms in the G matrix to zero. None of these conditions are met for a vanadium oxide site on silica (or any other oxide support). There is not a disparity in the masses, as all are oxygen atoms vibrating against metals that are relatively close in mass. Moreover, there are no 90
angles that would serve to completely decouple them. As mentioned above, the only way to quantitatively determine the contribution that each oscillator makes is by a complete normal coordinate analysis using a reliable force field. As far as we know, we are the only ones who have performed such an analysis for the silica-supported vanadyl group. In our report, which was limited to the primary stretching modes, an empirical force field was derived from the spectra and then used to perform a thorough normal coordinate analysis of the stretching modes of vanadyl supported on silica.2 As would be expected from the arguments given above, all the modes showed a significant contribution from all of the coupled oscillators of appropriate symmetry. In the particular case of the 1032 cm
1 band, we determined that while the terminal oxygen stretch was indeed a component of the normal mode the V
O and Si
O oscillators contributed a much larger contribution to the potential energy and, hence, to the mode. These conclusions are, of course, dependent on our particular force field, and a similar analysis carried out using a different force field would likely yield a different contribution of each oscillator to the normal mode.5 It is highly unlikely, however, that any reasonable force field will generate a normal mode consistent with separate pseudodiatomic VdO stretch and -triatomic V
O
Si stretches. For these reasons, the conclusions reached by Wu et al., which purport to restore the VdO assignment to the 1032 cm
1 band and the V
O
Si mode to the 920 cm
1 band, are incorrect. The arguments put forth by Wu et al. that attempt to establish the 1032 cm
1 band as a VdO stretch and the 920 cm
1 band to the V
O
Si stretch can be divided into several categories of spectral analysis that we will critically discuss.

’ ARGUMENTS BASED ON DIATOMIC OSCILLATOR APPROXIMATION AND OVERTONE ANALYSIS Wu et al. observe an overtone/combination-band progression up to n5 for the 1032 and 920 cm
1 totally symmetric fundamentals. The observation of such a progression is νm ðnÞ ¼ nωn
nðn
1Þχmm

ð6Þ

not unusual in the resonance Raman spectroscopy of inorganic complexes, and it arises in the silica-bound vanadyl spectrum because the two totally symmetric modes are close in energy.13 The coupling mechanism occurs through two-dimensional Franck
Condon factors in the A-term of the Kramers
Heisenberg dispersion relationship. While the authors claim that “this is the first resonance Raman showing overtones in the vanadyl stretch”, in point of fact the overtones belong to two totally symmetric normal modes, the assignment of which cannot be made through analysis of the overtones. Notwithstanding this, the authors analyze the progression to support their presupposition that the 1032 cm
1 A1 fundamental is a VdO stretch. The analysis proceeds by first determining the anharmonicity constant using the expression (eq 6) given by Clark and Stewart in which the spectroscopically observed frequency, νm(n), is related 10919

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The Journal of Physical Chemistry C to the nth harmonic frequency, ωn, adjusted by the anharmonicity, χ. Importantly, though apparently unrealized by the authors, the index m designates the normal mode of the vibration for a polyatomic molecule (a point made quite clear by Clark and Stewart), with the anharmonicity term being a measure of the deviation from the harmonic approximation of the entire normal mode. As such, the anharmonic constant calculated from the overtone of the 1032 cm
1 normal mode using eq 1 gives the deviation from harmonic behavior of the coupled oscillators that make up the normal mode. In short, neither the analysis of the overtones using eq 1 nor the value of the anharmonicity constant obtained can in any way be interpreted as supporting the assignment of a decoupled VdO mode to the 1032 cm
1 spectra band. In subsequent analysis, Wu et al. treat the 1032 cm
1 band quantitatively as a diatomic VdO oscillator. This is done through the well-known analytical expression, ν  (f/m)1/2, where ν is the frequency, f is the force constant, and m is the reduced mass. (It should be noted that this equation is reproduced incorrectly in Wu et al.)14 The supposition is that values of the force constant, calculated using this approximation, can be compared to other molecular species for which the diatomic oscillator approximation may be more justified, and if the values are close to each other, then the assignment of the 1032 cm
1 band to a diatomic VdO stretch must be valid. The value of any force constant, however, will depend on the force field used. Consequently, the value of the force constant generated in an inappropriate approximation (i.e., a diatomic oscillator) will have no particular meaning irrespective of any cursory agreement with model compounds. In this particular case, what they are actually calculating is the force constant for a fictitious diatomic molecule with a frequency at 1032 cm
1 and a reduced mass composed in some way of V and O atoms. In fact, a considerable amount of ambiguity in the value of the force constant comes from the act of approximating the normal mode associated with the 1032 cm
1 stretch as a diatomic oscillator. In particular, the authors report a force constant of 7.99 mdyn/Å, but we have not been able to reproduce that value. If the site is treated as a diatomic oscillator, using V and O for the reduced mass (μ=12.175 amu), the force constants are 7.63 and 7.77 mdyn/Å for 1032 and 1041 cm
1 frequencies, respectively (the anharmonically corrected fundamental frequency determined by Wu et al. is 1041 cm
1). To generate a force constant of 7.99 mdyn/Å, the reduced mass would have be 12.73 and 12.51 amu for 1032 cm
1 and 1041 cm
1, respectively, neither of which correspond to a possible reduced mass for the vanadyl system. However, since the VdO internal coordinate is attached to a surface through three oxygen linkages, one could easily justify the use of a larger reduced mass to account for this. When a reduced mass defined by (O3V) and the O are used (μ = 13.772 a.m.), a force constant of 8.80 mdyn/Å is determined, respectively, for 1032 and 1041 cm
1. Clearly, the crudeness of the approximation results in a range of possible force constants, depending on the assumptions made, and, as a result, makes comparative arguments less than compelling. Wu et al. first compare the value they get to the value to the VdO force constants from vanadium oxohalides, VOX3 (X = Br, Cl), which have often served as models for the surface-bound vanadyl group. In these species, the highest energy A1 symmetric stretch is justifiably referred to as the VdO stretch since that

COMMENT

oscillator does dominate the normal mode. For the complexes VOX3 (X = Cl, Br), the diatomic approximation yields force constants of 7.64 and 7.70 mdyn/Å for Br and Cl, respectively, which are comparable to the values estimated for silica-bound vanadyl. This comparison can be justifiably carried further by considering VOF3, which has an A1 mode at 1058 cm
1 that can be designated as the VdO stretch.15 In the diatomic oscillator approximation, using the V, O reduced mass of 12.17 amu, the force constant is 8.04 mdyn/Å. While this is arguably a better approximation to the surface-bound vanadyl due to the similarity in masses between F and O, the force constant agrees much less convincingly. In short, while all of these estimates for the VdO force constant fall into a range between ∼7.5 and 8.1, this in fact constitutes a large variation considering that, implicit in the single-force force field of the diatomic approximation, there should be one independent value for the force constant. The origin of the variation in the values arises from the fact that, even for these small molecules, the diatomic approximation is, at best, a crude one that does not properly take into account the contribution to the normal modes from the other internal coordinates. When moving to a more complex system such as silica-bound vanadyl, in which there are many more internal coordinates, all having fairly large force constants (F(Si
O) is ∼5.9 mdyn in quartz and ∼4.5 mdyn in amorphous silica), the diatomic oscillator approximation is far worse and is unlikely to give physically relevant information about these systems. Since accurate spectroscopic assignments of the primary stretching and bending modes of both VOCl3 and VOF3 have been made, it is a rather straightforward exercise to determine values for a generalized valence force field (GVFF) from the spectra.16 The force field, which consists of the two primary V
O and V
X stretches, F(V
O) and F(V-X), two interaction force constants between the V
O and V
X bonds, F(V
O,V
X) and F(V
X,V
X), and two bending force constants for the X
V
X and O
V
X angles, F( — X
V
X) and F( — X
V
O), was fit to the spectroscopic data using an iterative least-squares algorithm found in the Vibratz vibrational analysis software.17 The percentage of error between calculated and experimental frequencies was 3.04 and 2.08% for the Cl and F, respectively. The GVFF force constants are given in Table 1. Since we have a much larger force field, the values of the VdO force constants differ in value from those obtained from the diatomic approximation. Notably, however, the value for F(V
O) in the GVFF for VOCl3 is much closer to the diatomic approximation because it behaves as a pseudodiatomic oscillator. Consistent with this, the off-diagonal force constant, F(V
O,V
X), is extremely small, compared to that of VOF3. It is instructive to look at the highest-energy A1 normal mode in these small molecules, which is given in Table 1. This vibration is typically, and justifiably, referred to as the VdO stretch. In the derived GVFF, we find that the V
O force constant, F(V
O), accounts for 94% of the potential energy for VOF3 and 99% for VOCl3. Importantly, when the V
O
Si linkages are formed to attach the vanadyl group to the surface, three Si
O internal coordinates having force constants comparable to the V
O bonds are being coupled to the normal modes of vibration. This will profoundly change the nature of the vibration, and as such, the highest frequency mode will no longer be dominated by the VdO force constant. This can be seen quite simply by taking the force field for VOF3, changing the F atoms to O atoms, and adding three Si
O 10920

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COMMENT

Table 1 Cl3VO

F3VO

(Si
O)3VO

highest-energy A1

observed

1032

1057.8

-

mode (cm
1)

calculated

1034.7

1057.8

1067.6

F(V
O) F(X
O)

7.581 (99) 2.685 (1)

7.563 (94) 4.636 (2)

7.563 (54) 4.636 (22)

F(V
O,V
X)

0.003

0.197

0.197

F(V
X,X
X)

0.091

0.287 (4)

0.287

F( — X
V
O)

0.127

0.205

0.205

F( — X
V
X)

0.058

0.087

0.087

F(S
O)

-

-

4.48 (23)

force constant [mdyn/Å] (% contribution to the high energy A1 mode)

linkages with a force constant of 4.48 mdyn/Å. What we see (Table 1) is that the highest-energy A1 mode is now at 1067 cm
1 and, more significantly, that the contribution of the F(VdO) to that mode drops to 54%, with the Si
O
V bridge making the additional ∼45% of the mode. In short, the simple addition of three links to the surface decreases the contribution of the VdO stretch to the highest-energy, totally symmetric mode by 40%. If these force constants were refined to bring the calculated eigenvalues into agreement with the experimental frequencies for vanadia on silica, their values would change. In particular, the value of F(VdO) would drop significantly, as would its contribution to the 1032 cm
1 A1 normal mode. This is, in fact, exactly what we showed in our paper. The refined force field we arrived at yielded a VdO stretching force constant that contributed only about 3% to the total mode, while the F(V
O) and F(Si
O) contributed 47% and 45%, respectively. What is worth pointing out is that these results are physically very reasonable, and in fact, if additional Si
O internal coordinates coupling the vanadyl unit into the silica matrix were included to improve the model, we would expect a further decrease in the contribution of the VdO stretch to the highest-energy modes. Finally, it has been known since the very earliest studies of surface-bound vanadia that the position of the so-called VdO band changes with the substrate. In particular, Went, Oyama, and Bell reported VdO frequencies of 1042, 1030, and 1026 cm
1 for silica, titania, and alumina supports, respectively.3 While there have been many convoluted discussions of how these substrates “weaken” or “strengthen” the VdO bond through some postulated electronic interactions, the observed frequency change can be simply and correctly explained as arising from the contribution that the Si
O, Ti
O, and Si
O force constants make to the normal mode of vibration—in essence, direct proof that the band is not an isolated VdO stretch.

’ BOND ENERGY ARGUMENTS Continuing the diatomic approximation, the authors perform a Birge
Spooner plot from which they extract a purported VdO bond dissociation energy of ∼698 kJ/mol for the VdO bond. This analysis has no physical significance for several reasons. First, a Birge
Spooner plot only has meaning when applied to a diatomic or demonstrably pseudodiatomic oscillator, a fact that is

well-known in the literature.18 When used for a polyatomic molecule with complex normal modes, the value obtained has no obvious physical meaning since it cannot be directly associated with any single bond. In fact, all that has been calculated is the dissociation energy of a fictitious diatomic molecule with a reduced mass of 12.17 amu and a vibrational frequency of 1041 cm
1. If we carry the logic of the bond energy analysis further, it becomes even more problematic. Since the authors assign the spectral band to a VdO stretch, implicit in this assignment is the presumption that, at the dissociation limit, the terminal oxygen would cleave off, leaving a pyramidal (Si
O
)3V group on the surface. This is nonphysical since the V
O and Si
O bonds are, individually, weaker than the VdO bond, so the calculated dissociation limit is unlikely to be reached before other catastrophic structural changes occur. To support their treatment of the 1032 cm
1 vibration as diatomic, the authors compare their dissociation energy to that of the known diatomic VO. Unfortunately, apart from containing both vanadium and oxygen, this species has little in common with the surface-bound vanadyl group. Specifically, neutral VO is a diatomic containing a V2þ (d3) ion and an oxygen atom. It is known that it has an X4Σ
ground state, which corresponds to a triple bond of a (σδ2) configuration.19 This is, of course, completely different from the d0 (VdO) system of the surfacebound vanadyl, which would be much better approximated as a (þ3) VdO ion. The vibrational frequency of neutral VdO in the ground state is 1012 cm
1, which yields a force constant of 7.35 mdyn/Å, significantly lower than the diatomic estimates for the surface-bound vanadyl group.20 If we continue with the diatomic approximation, the lower force constant suggests a much lower dissociation energy than that of the surface vanadyl group in the same approximation. As such, the fact that the calculated bond dissociation energy is in “nice agreement” when it should not have been should have served as a clear indicator to the authors that something was amiss. In their conclusion, Wu et al. state that “the symmetry, dissociation energy, and force constant associated with the νc mode strongly suggest that it can only be due to the VdO stretching”. As can clearly be seen in our analysis, absolutely none of these parameters, as determined by these authors, has any physical meaning whatsoever with respect to the normal mode that is responsible for the 1032 cm
1 band, and no such conclusion can be drawn from it. In an even more problematic analysis, Wu et al. assign the 920 cm
1 band in the spectrum to a Si
O
V triatomic oscillator, which they then elect to treat as a diatomic oscillator. While it is one thing to assume that a mode is a diatomic oscillator and treat it accordingly, it is entirely another to assume that a mode is a bent triatomic oscillator and then to proceed to treat it as a diatomic. This is particularly pointless since the analytical expression for bent triatomic oscillators can be trivially derived. Using the diatomic oscillator function, they calculate a force constant of 4.57 mdyn/Å, from the 920 cm
1 band using a reduced mass that appears to be simply the mass of an oxygen atom. What is being done here is that the mode is being approximated as an oxygen atom vibrating against a surface of infinite mass. While there are times when such an approximation may be appropriate in analyzing the vibrations of species at surfaces, this is not one of them, because both the Si
O and V
O force constants are of similar magnitude and are, in turn, each close in 10921

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The Journal of Physical Chemistry C value to the single force constant calculated by the authors. In short, Wu et al. appear to be trying to argue that a triatomic oscillator with two force constants of almost equal magnitude can somehow meaningfully be approximated by a single vibrating atom with a force constant of approximately the same magnitude—an argument with no physical relevance whatsoever. They use the value they obtain to make a spectroscopic assignment by claiming that “the value of the calculated force constant (4.58 mdyn/Å) indicates that the vanadium oxo is not double bonded as in VdO whose force constant is much higher (>7 mdyn/Å)”. No such conclusion can be drawn from this argument. 18 O Labeling Studies. The authors carry out an 18O labeling study in which they observe that the 1032 cm
1 band undergoes an isotopic shift to ∼986 cm
1, while the 920 cm
1 band shifts to 885 cm
1. In their effort to reinforce the isolated VdO and V
O
Si assignments, they point out that these shifts are consistent with what would be expected for a Vd16O converting to a Vd18O and a V
16O
Si converting to a V
18O
Si. It is important to note that we also performed a thorough labeling study in which identical results were observed. More importantly, we were able to fully account for all of the observed isotopic shifts through the effect of isotopic substitution of the coordination sphere around V on the normal modes that we derived. Both the experimental results and the analysis provided by Wu et al. have been published previously; as such, no new information is provided in their report. A key flaw in their analysis of the 1032 cm
1 band as an isolated VdO stretch is that they do not explain the spectral intensity that appears in the spectrum, which can be seen clearly in Figure 3a of their paper, between the 1032 and 986 cm
1 peaks as a function of the degree of isotopic substitution. This spectroscopic behavior cannot be explained by oxygen exchange from a single isolated diatomic oscillator. Specifically, if the mode did behave as a diatomic oscillator, the band at 1032 cm
1 would cleanly disappear, and there would be a concomitant increase in the 989 cm
1 band. If the authors had performed a more careful analysis, properly deconvoluting the spectral region between the 1032 and 986 cm
1 peaks, what they would have observed is that those two resolved peaks cannot account for the spectral intensity between them without postulating nonphysical band widths and shapes. Furthermore, using properly integrated peak areas, it is unlikely that the decrease in the 1032 cm
1 band is quantitatively accounted for by the appearance of the 989 cm
1 band. The relatively continuous build-up of intensity in the region between the 1032 and 989 cm
1 band as a function of 18O substitution was comprehensively and quantitatively explained by us as an effect of the sequential and partial 18O substitution of the entire O3VO coordination sphere on the normal modes. Moreover, in our experiments, we used a less efficient method for incorporating 18O into the system (reduction and reoxidation using 18O2), which allowed the intermediate stages of substitution to be observed more closely. Wu et al. either do not understand the significance of this result in accounting for the isotopic exchange or choose to ignore it. What they perform is, in fact, a much poorer experiment, which contributes nothing new to the understanding of the nature of the mode. In particular, they use H2O18 to insert the labeled oxygen. This approach is extremely facile, and nearly complete labeling occurs after several cycles. Scrutiny of their data shows that isotopic exchange is complete in 2
3 cycles,

COMMENT

effectively bypassing the important intermediate stages of 18O insertion and obscuring the intermediate bands in many of their spectra. Arguments Based on Resonance Raman Behavior. Our paper provided one of the first systematic resonance Raman studies of the silica-bound vanadium oxide. Among the results contained in that report were polarization studies in which we noted that virtually all spectroscopic bands, even those formally assigned as E symmetry, were strongly polarized. This was attributed to the expected loss of symmetry as the vanadyl group was bonded to the amorphous silica surface. This observation in conjunction with our previously published assignments of the electronic transitions of the vanadia
silica system led us to conclude that all of the resonant enhancement occurred through the A-term of the Kramers
Heisenberg dispersion relationship. Wu et al. also note that the resonant enhancement arises from the A-term and assert that this fact indicates that the 1032 cm
1 band is “a totally symmetric mode with a large displacement of the vanadium oxo bond length in the excited state”. However, in no way does the observation of either overtones or the assignment of A-term enhancement support the assignment of the 1032 cm
1 mode to an isolated VdO stretch or in any way specifically implicate the VdO oscillator. The fact that the resonant enhancement of a mode occurs through the A-term simply means that the normal mode and the electronic transition being excited are totally symmetric—nothing more. In the A-term, the normal modes of vibration appear functionally as the Frank
Condon factors for the vibrational modes that are coupled to the electronic absorption. The magnitude of the Frank
Condon factor is governed, in part, by the normal coordinate change between the ground and the excited state.18 For the normal coordinates of the supported vanadyl system, given in eqs 2
4, the normal coordinate change will be given by ΔQ = (q1A1)ground
(q1A1)excited, which will include the changes in all of the internal coordinates that make up the mode in going from the ground to the excited state. As such, the totally symmetric normal mode that we derived in our analysis is completely consistent with the observed resonant enhancement. In fact, it could reasonably be argued that a pseudodiatomic oscillator will provide a much smaller normal coordinate change and hence will exhibit substantially less resonant enhancement than a physically realistic normal mode in which all of the internal coordinates contribute to the net normal coordinate change. Temperature Arguments. Wu et al. argue in their paper that the disappearance of the shoulder band at 1060 cm
1 at high temperature is an indication the V
O associated with this band is weaker than the one associated with band at 1032 cm
1. This argument is based on a prior literature study, which purportedly showed that more severe temperature effects on the intensity of Raman bands will be found on metal oxide with a weaker metal
oxygen bond. This assertion has no physical basis whatsoever. In fact, the temperature dependence of Raman bands responsible for single phonon transitions (i.e., excitation of a single fundamental) is extremely well understood.21 The intensity of a Raman absorption in the Stokes regime will be proportional to the population of the ground state phonons as given by the Boltzmann distribution (eq 7; ν0 is the incident laser frequency, ν is the vibrational frequency, and the symbols have their customary meaning). The opposite is observed on the anti-Stokes side, 10922

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where the intensity of the anti-Stokes regime will increase with temperature. I Stokes 

ðν0
νÞ4 νð1
e
hv=kT Þ

ð7Þ

What this means is that as the sample is heated up the ground state will be depopulated, causing the intensity to decrease in the Stokes region as a function of temperature, with lower frequency modes decreasing more rapidly than higher frequency modes. There will be a concomitant increase in the band intensities in the antiStokes regime. While the frequency that appears in eq 5 will be related indirectly to the various bond strengths of the internal coordinates that comprise the normal mode, apart from that there is absolutely no direct relationship that can be drawn between a specific bond strength and the observed temperature effect. If the temperature dependence data published by Wu et al. had been analyzed correctly using eq 7, it is likely that they would have seen that it conforms to the expected Boltzmann distribution. Notably, deviations from the Boltzmann distribution, which are often observed, are explained by the fact that highly coupled modes (e.g., combination bands and Fermi resonances) will deviate from the Boltzmann distribution.22 Furthermore, while correlations of vibrational frequencies with bond strength are obvious, there is no theoretical basis anywhere in the literature, of which we are aware, that correlates the Raman band intensities to bond strength. Other Conclusions. While the principal focus of this Comment is to correct the inaccuracies and misconceptions contained in the report of Wu et al. with respect to the assignment of the vibrational spectra in a supported metal oxide catalyst, there are other erroneous conclusions that warrant comment as well. One hypothesis put forward in this study is that by using different excitation wavelengths new vanadia species can be observed on the silica surface. The spectroscopic principle that guides this assertion is that two different species will have two different absorption spectra, and therefore different excitation frequencies should selectively enhance bands from different species. While this sounds good in principle, in reality conditions will almost never exist in a supported catalyst in which a new species can be unambiguously identified by this approach. This is because of two factors. The first is that a single well-defined and isolated species will, in and of itself, show different resonant enhancement at different frequencies as dictated by the Kramers
Heisenberg relationship. As such, there will always be uncertainty as to whether one is observing a new species or just the resonant enhancement of a new mode of a single species, especially considering that resonant enhancement can make bands that are completely unobservable under nonresonant conditions suddenly appear. The other problem is that the electronic absorption spectra of different monodispersed, high-valent (d0) species derived from the same compounds (i.e., different vanadium oxo species) will have electronic absorption bands in the same energy regime (e.g., all oxo-to-vanadium charge transfer) and, in fact, are likely to have very similar spectral features on a given substrate. As such, if two species are present, excitation at a specific frequency will almost certainly excite both species, yielding a set of enhanced bands that cannot be unambiguously separated into two species. While this problem might be less severe in the low-energy region of the spectrum, where some separation in the absorbance bands is likely to be present, as the excitation is moved to higher energy (e.g., 244 nm), high-energy states of all the species will likely be

pumped, making identification of individual species unlikely. For lower valent metals where there are d
d transitions, the technique may be more successful; however, for those types of ions, other techniques are available that are more definitive. Wu et al. observe that the high-energy A1 mode occurs at 1041 cm
1 in nonresonant Raman and at 1032 cm
1 under resonant enhancement, causing them to proclaim the observation of a new species. This is a dubious claim. The 1041 and 1032 cm
1 bands are one and the same; a 9 cm
1 shift in going from the visible region to near-UV excitation is unremarkable and arises from the fact that when enhanced the spectral congestion of nearby bands (in this case, the E modes at 1060 cm
1), whose overlap will distort the apparent peak position, will have less of an effect. Moreover, as the excitation is moved to higher energy, the accuracy to which the peak positions of the Raman bands is known becomes lower (i.e., the assignments of the peak positions are less accurate), which exacerbates comparing peak positions acquired from different excitation wavelengths. In our view, the tendency of workers in the field of heterogeneous catalysis to automatically assign any previously unobserved vibrational band to a new species, even though there is likely a good spectroscopic assignment consistent with the already established structure of the site, causes undue obfuscation of the sites that are actually present on the surface, generating as it does a menagerie of fanciful catalytic sites. From the standpoint of basic inorganic chemistry, there is no reason to believe that simple, monomeric transition metal oxides supported on an anhydrous oxide surface will form a wide range of coordinately different species. It is likely that for all the commonly studied oxide sites (e.g., V, Cr, Ti, Mo, W) each exhibits a single basic geometry that is present at low loadings (i.e., isolated sites) in the solid state, the immediate symmetry of which is broken by bonding to the irregular surface. To summarize, for the reasons outlined, we believe that the study by Wu et al. fails to support their assignment of specific spectroscopic bands observed in the Raman spectra of silica-supported vanadium oxide to VdO and Si
O
V “modes”. This comes about for two reasons. The primary one is that VdO and Si
O
V simply do not describe normal modes for the supported vanadyl site, and therefore, there is no basis for attempting to make such an assignment. The second is that the spectroscopic arguments put forth to assign normal modes are simply not valid. Interestingly, the authors also seem to believe that because the conclusions they draw from their spectroscopic arguments appear to agree with those from density functional calculations they are in some way vindicated. However, since, as we have shown, their conclusions are not supported in any way by their analysis of the spectroscopic data, such a comparison has no meaning.

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