2448
J. Phys. Chem. B 2000, 104, 2448-2459
FEATURE ARTICLE Vibrational Analysis of a Chemisorbed Polyatomic Molecule: Methoxy on Cu(100) Kanchana Mudalige, Samantha Warren,† and Michael Trenary* Department of Chemistry, UniVersity of Illinois at Chicago, 845 W. Taylor Street, Chicago, Illinois 60607-7061 ReceiVed: September 17, 1999; In Final Form: December 6, 1999
Infrared reflection absorption spectra were obtained from 900 to 3000 cm-1 for five C3V symmetry isotopomers of methoxy: H312C16O, H313C16O, H312C18O, D312C16O, D313C16O; and two Cs symmetry isotopomers: DH212C16O, and HD212C16O. Measured frequencies of the five C3V isotopomers were used to derive an empirical valence force field based on a C3V symmetry H3COCu3 model. Without further adjustment, this force field was used to calculate the harmonic frequencies of the two Cs symmetry isotopomers which were found to be in good agreement with the experimental frequencies. Comparison of a Cs symmetry H3COCu12 model with an adsorption site structure that accurately models the experimentally determined geometry, as well as with a C3V symmetry H3COCu model, shows that the internal vibrations of the methoxy unit are relatively insensitive to the adsorption site. Among other advantages, an accurate description of the normal modes of this molecule provides a quantitative understanding of the unusual intensity patterns in the CO stretch and CH3 symmetric deformation (δs(CH3)) region, which leads to an extremely low intensity for the δs(CH3) fundamental for the H312C16O isotopomer. In addition to the vibrational properties of methoxy that can be understood within the harmonic approximation, two manifestations of anharmonicty are observed: (1) the position of the overtone of the CO stretch; and (2) Fermi resonance in the CH stretch region between the symmetric CH stretch fundamental and the overtones of the symmetric and asymmetric CH3 bends. The normal coordinate analysis allows the position of the unperturbed vibrations in the CH stretch region to be more accurately estimated and helps to explain the weaker Fermi resonance in the CD stretch region of D3CO. Finally, the empirical valence force field is compared with the force field derived from an ab initio calculation of H3COCu.
I. Introduction Vibrational spectroscopy is currently one of the most powerful tools available for the study of molecular adsorbates on transition metal surfaces. Yet far more information can be extracted from the measured spectra if they are subjected to a normal-mode analysis. This is a procedure that has a long tradition in vibrational studies of polyatomic molecules in other environments, but has seldom been applied to molecules on surfaces. Here we report a normal-mode analysis of reflection absorption infrared spectroscopy (RAIRS) data obtained for various isotopomers of methoxy on the Cu(100) surface. The procedure that we used not only provides powerful new insights into this frequently studied adsorbate but also reveals some of the special features and limitations that pertain to applying such analyses to chemisorbed molecules. Although our primary focus is on the empirical force field derived by the GF matrix method, we have also performed ab initio calculations on the hypothetical CH3OCu molecule as an alternative method of obtaining the valence force field. In addition to properties that can be understood within the harmonic approximation, the spectra of methoxy on Cu(100) also display features due to anharmonicity that are commonly observed in the spectra of chemisorbed species. † Present address: Department of Physics, UMIST, PO Box 88, Manchester M60 1QD, U.K. * To whom correspondence should be sent.
The starting point for any interpretation of the vibrational spectra of polyatomic molecules, whether they are chemisorbed species or molecules in any other environment, is the harmonic approximation. Even a simple qualitative interpretation of a spectrum that involves assignment of the observed bands implicitly assumes the existence of normal modes, which in turn is based on the harmonic approximation. The most popular type of normal-mode analysis is based on the so-called Wilson GF matrix method1,2 in which the normal coordinates are expanded in a basis set consisting of internal coordinates, such as bond stretches and bond angle bends. The fact that an adsorbate molecule is attached to an extended surface containing a very large number of atoms necessarily means that the calculations cannot be made on the actual system. If vibrations involving metal atoms or vibrations of the whole adsorbate relative to the substrate are of interest, then a model that accurately represents the substrate structure should be used. On the other hand, if the focus is entirely on the internal vibrations of the adsorbate, as is the case here and in most other surface IR studies, the model needs to contain only a crude approximation of the substrate structure. The methoxy species has been studied on a large number of metal surfaces with part of the motivation being the use of Cu/ ZnO catalysts for the synthesis of methanol from CO and H2 and the use of other metals to oxidize methanol to formaldehyde. In a study on the Ag(111) surface, Sim et al.3 reviewed much
10.1021/jp9933121 CCC: $19.00 © 2000 American Chemical Society Published on Web 02/03/2000
Feature Article of the surface science literature pertaining to methoxy. Here we focus on studies most relevant to the vibrational spectrum of methoxy on Cu(100). Ryberg4 explored the methoxy overlayer structure with low-energy electron diffraction (LEED) and found that after reacting methanol with a c(2 × 2) O overlayer structure, a ∼0.5 ML (monolayer) c(2 × 2) methoxy structure could be formed in which it was assumed that methoxy was bound at the 4-fold hollow site. Theoretical studies indicate that methoxy adsorbs on the 4-fold hollow site on Cu(100).5,6 A photoelectron diffraction study found methoxy to occupy the 3-fold hollow site on Cu(111)7 but an asymmetric site midway between the 4-fold hollow and a bridge site on Cu(100).8 Of most relevance to the present study is the relationship between the site symmetry and the observed RAIRS spectrum. We calculate the spectrum using both C3V structural models as well as an asymmetric adsorption site model as proposed by Lindner et al.8 Sexton9 and Ellis and Wang10 obtained the vibrational spectrum of CH3O/Cu(100) with high-resolution electron energy loss spectroscopy (HREELS) and, in both cases, the following loss features were observed: νs(Cu-O) at 290 cm-1, ν(CO) near 1000 cm-1, and two bands in the C-H stretch region at 2830 and 2910 cm-1. Although Sexton detected the very weak δs(CH3) peak at 1450 cm-1, Ellis and Wang10 did not. Using RAIRS, Ryberg4 detected ν(CO) at 1013 cm-1 for the c(2 × 2) structure at a coverage of 0. 5 ML and multiple bands in the CH stretch region.11,12 Because a tilted methoxy would give two surface IR-allowed fundamentals in the CH stretch region, Ryberg concluded that the 3-fold axis was at a large angle from the surface normal. A tilted geometry was also assumed for methoxy on Ni(111)13 based on similar RAIRS data in the CH stretch region. However, Fermi resonances between the symmetric CH stretch and the overtones of δs(CH3), and δas(CH3) are well known. Two RAIRS peaks for ethylidyne (CCH3) on Pt(111) were observed and assigned to the δas(CH3) overtone (2790 cm-1) in Fermi resonance with the νs(CH3) fundamental (2885 cm-1).14 Chesters and McCash15 observed three CH stretch peaks for methoxy on Cu(111) which they assigned to the CH stretch fundamental in Fermi resonance with symmetric and asymmetric bending overtones. The Fermi resonance in the CH stretch region has been described in RAIRS studies of methoxy on Mo(110),16 Cu(100),17 Ni(100),18 and Ag(111).3 In all cases it was argued that the results are consistent with the CO axis being perpendicular to the surface. The Fermi resonance effects were also noted in a RAIRS study of methoxy on Ni(110),19 but the more complicated spectra were interpreted as indicating the presence of two tilted methoxy species. Uvdal and MacKerell20 considered the Fermi resonance effect for methoxy in detail and compared data and assignments for several surfaces. From the comparison they note that the methoxy spectrum is fairly insensitive to the substrate and site symmetry, a conclusion supported by our work. II. Experimental Section All experiments were performed in an ultrahigh vacuum (UHV) chamber coupled to a commercial FTIR (Mattson, RS1) spectrometer. The vacuum chamber, associated instrumentation, and IR optics were described in detail in an earlier publication,21 whereas a more recent publication describes some newer features of the system.22 The chamber is also equipped with LEED, Auger, and a quadrupole mass spectrometer. The base pressure was ∼5 × 10-11 Torr. The Cu(100) crystal (Monocrystals) was mechanically polished to within 0.5° to 1° of the (100) crystal face prior to mounting on a liquid-nitrogencooled manipulator. The crystal was heated resistively and was
J. Phys. Chem. B, Vol. 104, No. 11, 2000 2449 cleaned by the usual sputter and anneal cycles. The sample temperature was measured with a K-type thermocouple held between the crystal and mounting plate. Attainment of a clean and well-ordered Cu(100) surface was verified with LEED and Auger electron spectroscopy. The RAIR spectra were recorded using an MCT detector, with 1024 scans, and a resolution of 4 cm-1. The sample was dosed by back-filling the chamber with the appropriate gas, and reported exposures are based on uncorrected ion gauge readings. The mass spectrometer was used to check the purity of the gas during dosing. Oxygen (16O2 99.998% from Matheson) was used as supplied. The methanol isotopomers 12CH3OH (99.95%), 13CH3OH (99%), CD3OD (98%), CHD2OH (98%), CH318OH (95%), and 13CD3OD (99%), all from Cambridge Isotope Laboratories, were each subjected to a freeze-pump-thaw treatment before use. The Cu(100) crystal was cleaned at the start of each experiment, followed by exposure of 300 L of O2 at 300 K. This high dosage of oxygen was found to give a sharper LEED pattern. The crystal was then annealed to 425 K for 5 min, and then cooled to 300 K where the LEED pattern was observed. Wuttig et al.23 carefully examined the LEED patterns formed by O on Cu(100) and concluded that a saturation coverage of O on Cu(100) yields a (2x2 × x2)R45° pattern. They note that the extra spots that distinguish a c(2 × 2) ) (x2 × x2)R45° from a (2x2 × x2)R45° pattern are difficult to observe. We did not examine this issue in detail but we assume that the LEED pattern we observed corresponds to the (2x2 × x2)R45° structure discussed by Wuttig et al.23 The sample was cooled to 200 K where a background IR spectrum was obtained. The crystal was then exposed to 2.0 L of the appropriate methanol isotopomer, heated to 300 K for 30 s to desorb the water byproduct, and then cooled back to 200 K, where the sample IR spectrum was obtained. This procedure also yielded a sharp LEED pattern for the methoxy layer. III. Theoretical Background In this section we briefly review the theoretical aspects most relevant to the interpretation of our experimental data. The basic theory of molecular vibrations is contained in the classic book by Wilson, Decius, and Cross1, whereas a less detailed yet excellent summary is given by Nakamoto.2 The theory of vibrations in crystalline solids is given by Decius and Hexter24 and by Maradudin et al.25 The harmonic approximation, in which the potential energy for vibrational motion is assumed to depend only on quadratic terms in the displacement coordinates, is the starting point for any treatment of vibrational spectra. Within this approximation normal coordinates can be found in which the potential energy depends on a sum of squares of the normal coordinates without any cross terms. Each normal coordinate obeys the equation of an independent harmonic oscillator. The same frequencies and normal coordinates are predicted whether the problem is treated classically or quantum mechanically, with the classical equations being particularly simple. As Nakamoto2 points out, the phrase normal coordinate analysis is essentially synonymous with the GF matrix method, which is the method that we use here. In this method the normal coordinates are expressed as linear combinations of internal coordinates. The potential and kinetic energies are expressed in the set of internal coordinates through the F and G matrixes, respectively. The classical equations of motion lead to a set of linear equations which have a solution when the following equation is satisfied:
|GF - Eλ| ) 0
(1)
2450 J. Phys. Chem. B, Vol. 104, No. 11, 2000 where F is the force constant matrix defined in terms of internal coordinates and is the same for all isotopomers of a given molecule, G is a mass- and structure-dependent matrix that relates the kinetic energy to the internal coordinates, and E is the identity matrix. For a nonlinear molecule of N atoms, there are 3N - 6 nonzero roots, λ, to this equation. Corresponding to each root is a normal coordinate. Because the G matrix is fixed by the structure and atomic masses, the chosen force constants determine the harmonic frequencies. A normal coordinate analysis then consists of adjusting the force constants (the force field) until the calculated frequencies agree with the experimental ones. Although the GF method has been and is still being widely used, it has some inherent limitations. First, experimental spectra are affected by anharmonicity, so that one does not directly measure harmonic frequencies. An experimental spectrum consists of fundamentals (the v ) 0 f v ) 1 transitions of a given normal mode), overtones, combinations, and hotbands, with the fundamentals usually, but certainly not always, more intense than the other transitions. Even when the fundamentals are correctly identified, their observed positions are slightly shifted from where they would be in the absence of anharmonicity. However, if enough combinations and overtones are observed, then an experimental value for the harmonic frequency can be established. Because in practice this is difficult to do, the force field is adjusted to give the best agreement possible between the calculated harmonic frequencies and the measured fundamental frequencies. The second major limitation with the method is the large number of force constants needed to completely define a harmonic force field. The complete force field in an internal coordinate basis consists of the diagonal force constants plus all off-diagonal interaction force constants. Even for small molecules of high symmetry, there are generally more force constants than measurable fundamentals. This is true even when extensive isotopic substitution is employed to generate more independent experimental frequencies. Consequently, it is generally not possible to derive a unique harmonic force field from experimental spectra. The only practical way to proceed, then, is to make some assumptions about the force field. A third minor problem is that there can be some ambiguities and other problems in the definition of internal coordinates, the use of which is not strictly necessary. In fact, the problem is in many ways easier to formulate in a Cartesian basis set. One of the original motivations for the use of internal coordinates was to make the secular determinant smaller by eliminating the translational and rotational degrees of freedom, an important consideration when doing the problem “by hand”, but irrelevant with today’s computers. However, a key advantage of still formulating the problem in an internal coordinate basis set is that the force constants have clearer physical meaning. For example, a bond stretching force constant is directly related to the bond strength. Similarly, a comparison of the force constants of two molecules provides more insight into their internal bonding than does a comparison of frequencies alone. This advantage of the method is clearly demonstrated by the results described below. Establishing a harmonic force field for a molecule on a surface involves some special considerations. Whereas for an isolated molecule the exact structure can be used, the essentially infinite number of atoms of the substrate to which the adsorbate is attached makes a calculation for the exact structure impossible. The vibrations of a periodic crystal can be solved in the harmonic approximation by methods somewhat analogous to the GF matrix method using so-called slab models.24,25 Hence,
Feature Article for problems where the adsorbates are arranged with twodimensional periodicity on a surface, the methods used to calculate surface phonon dispersion curves can also be used to calculate adsorbate vibrations. The adsorbate-adsorbate interactions can then be represented by suitable force constants. Such methods would allow one to calculate the two-dimensional dispersion of the adsorbate vibrational modes. This approach does not seem to have been employed so far, possibly because the magnitudes of the frequency shifts for polyatomic adsorbates are small relative to the possible shifts due to anharmonicity, and because it would introduce even more force constant parameters to be fit to an already limited set of experimental frequencies. For this reason, and because the focus is mainly on the internal bonding of an adsorbate, the information of most interest is obtained by representing the surface by a cluster of atoms including the simplest possible cluster, a single atom. Models to treat coverage-dependent frequency shifts due to the specific case of an adsorbate-adsorbate interaction that is dominated by dipole-dipole coupling have been developed.26 As shown below, for the most part a structural model that accurately represents the surface is only essential if the focus is on low-frequency modes involving substantial displacements of the substrate atoms. Another significant aspect of normal coordinate analyses of adsorbate vibrations is the surface selection rule, which further restricts the number of observable frequencies. Despite all of these potential difficulties, our results demonstrate that by making a few reasonable assumptions about the force field of an adsorbate, a great deal of information beyond that of a qualitative description can be obtained from a normal coordinate analysis. An increasingly attractive alternative to the empirical determination of harmonic force fields is to obtain them through ab initio electronic structure calculations. Pulay and co-workers27,28 considered in detail the problem of obtaining harmonic force fields for small isolated molecules from ab initio calculations. They note that interaction force constants can be more accurately determined by ab initio calculations, whereas the diagonal force constants are probably still more accurately obtained by empirical methods. Whitten and Yang reviewed the status of electronic structure calculations for studying chemisorption and reactions at surfaces.29 They note that for some problems representing the surface by a cluster of atoms consisting of 1-100 atoms is adequate. Uvdal and co-workers used ab initio calculations of small molecules, including methoxy, attached to a single metal atom to analyze surface vibrational spectra.20,30 We used the same method to calculate the harmonic frequencies for a methoxy fragment attached to a single Cu atom for comparison with the results obtained by the GF matrix method. Regardless of whether the harmonic force field is obtained empirically by the GF matrix method or through first principles electronic structure calculations of a small adsorbate-cluster model, the advantages and limitations of interpreting experimental spectra within the harmonic approximation will remain the same. IV. Results and Discussion A. Experimental Spectra. Figure 1 shows two examples of the full spectrum of the H312C16O isotopomer of methoxy obtained under slightly different conditions. In both cases there are strong bands for the CO stretch (1014 and 1020 cm-1) and three bands in the CH stretch region: 2799-2800, 2876, and 2911-2912 cm-1. These features have been observed in virtually all previous RAIRS studies of methoxy. In addition, two very weak features are also present. In (a) there is a band
Feature Article
J. Phys. Chem. B, Vol. 104, No. 11, 2000 2451
Figure 1. Spectra of methoxy on Cu(100) at 200 K for the c(2 × 2) structure. The two spectra were obtained under slightly different conditions that led to a higher frequency CO stretch peak in the lower spectrum compared with the upper spectrum. In the upper spectrum the CO stretch overtone is clearly seen at 1946 cm-1, whereas the lower spectrum shows the very weak δs(CH3) peak at 1433 cm-1.
TABLE 1: The CO Stretch Overtone Position and Shift from Twice the Fundamental for the Methoxy Isotopomers isotopomer
νf(CO)
νo(CO)
[2νf(CO)-νo(CO)]
12CH 16O 3 13CH 16O 3 12CH 18O 3 12CD 16O 3 13CD 16O 3 12CDH 16O 2 12CHD 16O 2
1012 995 979 980 971 1015 1017
1949 1913 1897 1907 1887 1955 1929
75 77 61 53 55 75 105
at 1433 cm-1, due to δs(CH3), which has not been reported in the previously published RAIRS spectra of methoxy on copper surfaces.4,11,12,15,17 As discussed more fully below, all of the observed bands are associated with what would be the totally symmetric, or A1, vibrations of the C3V point group and these are the only surface-IR-allowed vibrations for a geometry with the CO axis perpendicular to the surface. For a tilted geometry, vibrations associated with the CH3 rock and the asymmetric CH3 deformation modes would also be allowed. Careful examination of the 1000-1900 cm-1 region shows that if any other peaks are present, they must have intensities less than about 25% of the 1433 cm-1 band. Thus there is nothing in our spectra to contradict the generally held conclusion that the CO axis is perpendicular to the surface. In (b) the peak at 1946 cm-1 is assigned to the overtone of the CO stretch vibration. The overtone was reported for the CH3O/Ni(111)13 system at 2017 cm-1 and at 1960 cm-1 in Sexton’s HREELS study of CH3O/Cu(100).9 Because these features are so weak, they are difficult to reproduce under all conditions; spectrum (a) provides the clearest example of the δs(CH3) band, whereas spectrum (b) contains the best example of the CO overtone. The latter peak is frequently obscured by miscancellation of sharp features present in both the background and sample spectra. Nevertheless, this overtone has been reproducibly observed for all isotopomers, the values of which are given in Table 1. Table 1 also lists a value of the overtone shift from twice the fundamental frequency, [2νf(CO) - νo(CO)]. This quantity would represent the anharmonicity of the CO bond for an isolated system. However, due to lateral interactions, the CO stretch fundamental is properly described as a two-dimensional
phonon with a certain dispersion. The band position will shift with coverage due to a combination of both dipole-dipole coupling and a chemical shift. In general, these two types of shifts can be distinguished through isotopic dilution experiments combined with coverage-dependent studies.31 For the CH3O/ Ni(111) system the dipole coupling shift was found to be 6.5 cm-1,13 while for CH3O/Mo(110) it was found to be 18 cm-1 at 0.25 ML,32 where the fundamental and overtone are observed at 1043 and 2011 cm-1, respectively. For a small dispersion for the fundamental and a large intramolecular anharmonicity, the overtone state is described as a two-phonon bound state that is localized on the adsorbate. For methoxy on Mo(110), it was found that [2νfs(CO) - νo(CO)] ) 39 cm-1, where νfs(CO) is the singleton frequency defined as the observed position minus the dipole-dipole coupling shift.32 At the lowest coverages we have studied, corresponding to a 0.1 L methanol exposure, the CO stretch is observed at 994 cm-1. Ryberg4 reported a shift of 37 cm-1 from 976 cm-1 at the lowest coverages to 1013 cm-1 at the highest coverage. He estimated that almost all of this shift was due to dipole-dipole coupling. The strong dependence of the CO stretch frequency on coverage is evidently responsible for variations in the reported values. For example, Camplin and McCash17 report the ν(CO) band at 984 cm-1. The exact value of the CO stretch frequency will depend not only on the exact coverage but also on how much oxygen is coadsorbed with the methoxy. Differences in methoxy and/or oxygen coverage are the likely reason for the differences in ν(CO) for the two spectra shown in Figure 1. The much stronger coverage dependence of the CO stretch fundamental for methoxy on Cu(100), compared with Mo(110), makes it doubtful that the overtone can be described as a two-phonon bound state. Uvdal and MacKerell note20 that in order to compare the observed CO stretch with that calculated in an ab initio study of an isolated CH3O-M unit, it is important to subtract the coupling shift from the experimental frequency. However, in our case it is less important because the effect of the dipoledipole coupling shift will be incorporated into the CO stretch force constant. Such a force constant will give an internally consistent description of the harmonic force field for all of the isotopomers studied, provided each isotopomer is at the same coverage and has the same coverage of coadsorbed oxygen, as is the case here. Recently, another group33 obtained RAIRS spectra of methoxy on Cu(100) with even better signal-to-noise ratios than obtained here. At the methoxy saturation coverage on an oxygen-free surface, they observe δs(CH3) at 1433 cm-1, ν(CO) at 1021 cm-1, and 2ν(CO) at 1956 cm-1. They also made a detailed study of the dependence of ν(CO) and 2ν(CO) on methoxy and oxygen coverage and found that both bands are sensitive to not only the methoxy coverage but also to the amount of oxygen coadsorbed with the methoxy. Figure 2 shows spectra for six different isotopomers of methoxy/Cu(100). Although not shown, spectra for the CH318O isotopomer were obtained and the CO stretch frequency was included in the force constant fits. For the CH3O isotopomers there are three bands in the CH stretch region and an intense CO stretch band. The CD3O isotopomers show two bands in the CD stretch region, with the relatively sharp lower frequency band associated with the CD stretch fundamental. The higher frequency band is broader and appears to consist of two components due to the overtones of both the asymmetric and symmetric bends. The normal-mode calculations show that the fundamentals of these two modes are nearly equal. This near equality for the CD3 isotopomers, but not for the CH3 isoto-
2452 J. Phys. Chem. B, Vol. 104, No. 11, 2000
Feature Article the rest of the molecule. McKean34 showed that λs and λas, the roots for the symmetric and asymmetric vibrations, are given accurately by the product of a single G matrix element with a single F matrix element
λas ) [µH + µC(1 - cos R)][fd - fdd]
(2)
λs ) [µH + µC(1 + 2 cos R)][fd + 2fdd]
(3)
where the µ values are the inverse masses in amu-1, R is the HCH angle, fd and fdd are the CH stretch and CH stretch-CH stretch interaction constants, respectively, in mdyne Å-1, and the λ values are related to the frequency, ν, in cm-1, by λ ) 4π2c2ν2. The CH stretch in the CD2H isotopomer is given by
λ ) [µH + µC][fd]
Figure 2. Spectra of six different isotopomers of methoxy on Cu(100) at 200 K for the c(2 × 2) structure. All spectra were obtained following exposure of an oxygen overlayer to 2.0 L of methanol at 200 K, annealing to 300 K for 30 s to desorb water, and cooling back to 200 K were the spectra were obtained.
pomers, stems from the different composition of the normal modes. For CD3O the bend of A1 symmetry consists of large amounts of both CO stretch and CD3 bend, while the degenerate E bending mode cannot have a contribution from the CO stretch. In CH3O, the A1 bending mode has much less contribution from the CO stretch internal coordinate. The bending modes for the HD2CO isotopomer are sufficiently reduced in frequency to remove the Fermi resonance in the CH stretch region so that only a single band is seen there, although two bands are seen in the CD stretch region due to a Fermi resonance between the CD2 bend overtone and the CD stretch fundamental. The analogous behavior is seen for the CH and CD stretch regions of DH2CO. In the 1200-900 cm-1 region, two bands are observed for DH2CO whereas three are observed for HD2CO. As described below, this experimental fact is predicted from the normal modes calculated for these two Cs symmetry isotopomers using a force field that was determined using input only from the five C3V isotopomers. All of the measured fundamental frequencies are given in Tables 4 and 6 along with the calculated values. B. Force Constants for the CH (CD) Stretch Region. To be complete, the valence force field for CH3O/Cu(100) should include the relevant force constants for the CH stretch region. These force constants should be based on the position that the CH stretch vibrations would have in the absence of the Fermi resonance, something that is not directly obtainable from the spectra. Because the CH stretch normal modes consist almost entirely of the CH stretch internal coordinates, the stretching vibrations of the CH3 group can be considered separately from
(4)
For the CD2H isotopomer there are no bending mode overtones near the CH stretch fundamental, so that a measurement of the CH stretch position for the CD2H isotopomer directly yields the diagonal force constant, fd. For a molecule not adsorbed on a surface, it is usually possible to also measure the asymmetric CH stretch, which is generally not perturbed by Fermi resonance. Thus in the general nonsurface case, measurements of unperturbed frequencies combined with eqs 2 and 4 yields both fd and fdd. The position of the unperturbed symmetric CH stretch can then be calculated via eq 3. Here and throughout our calculations we used the exact masses for H, D, 12C, 13C, 16O, and 18O to six decimal places. This is important in terms of reproducibility of calculated frequencies for a given set of force constants. From our measurement of 2899 cm-1 for the CH stretch of CD2HO/Cu(100), we obtain fd ) 4.604 mdyne Å-1, which we round to 4.60 in the full calculation. Because the surface dipole selection rule does not allow us to measure the asymmetric CH stretch, we cannot use eq 2 to determine fdd. However, McKean tabulated a large number of fdd values for molecules containing the CH3 group and they are generally in the range of 0.021-0.046 mdyne Å-1. If we use 0.04 for fdd, then we calculate a value of 2851 cm-1 for the unperturbed CH stretch, whereas the value used for methanol of 0.019 mdyne Å-1 gives an unperturbed CH stretch frequency for CH3O/Cu(100) of 2838 cm-1, suggesting that we can be reasonably confident that the frequency lies in the range of 2838-2851 cm-1. Although it is somewhat arbitrary, we use a value of 0.019 mdyne Å-1 for fdd, along with the more rigorously determined value of fd ) 4.60 mdyne Å-1 in the final force field. In the full calculation these force constant values result in a calculated frequency for the unperturbed CH stretch frequency of 2841 cm-1, only 3 cm-1 higher than that calculated from eq 3. The same force constant that allows us to calculate the CH stretch vibrations can be used to understand the Fermi resonance in the CD stretch region. Using our measured CD stretch frequency of 2141 cm-1 for DH2CO in eq 4 (with µH replaced by µD) we obtain fd ) 4.658, compared with 4.604 based on the CH stretch of H2DCO. Although in the harmonic approximation fd should be the same for the two cases, McKean34 notes that because of different degrees of anharmonicity, CD stretch force constants are larger than CH stretch force constants calculated from observed fundamentals. If we assume fdd ) 0.019 for both CD3 and CH3, we obtain a value of 2049 cm-1 for the value of the symmetric CD3 stretch in the absence of Fermi resonance. If we use fd ) 4.604 and fdd ) 0.019 for the CD and CH stretches of all isotopomers, we obtain νs(CD3) ) 2037 cm-1 via eq 3 and 2050 cm-1 via the full calculation in
Feature Article which there is some contribution from other internal coordinates. It is clearly coincidental that the experimental value is also 2050 cm-1 because if we had used fd ) 4.658 in the full calculation we would expect to obtain a value around 2060 cm-1. These estimates of νs(CD3) in the absence of Fermi resonance do suggest that the Fermi resonance is weaker for CD3O than for CH3O, as is also suggested by the weakness of the bend overtones relative to the CD stretch fundamental. For the CH3 and CD3 cases, our calculated values of the fundamentals of the bending modes provides one way to estimate the position of the overtones, which would be at exactly twice the fundamental frequency in the absence of anharmonicity. For CH3O, 2δs(CH3) ) 2864 cm-1, 2δas(CH3) ) 3068 cm-1 compared with the perturbed experimental values of 2876 and 2912 cm-1. For CD3O, the calculated values are 2δs(CD3) ) 2190 cm-1, 2δas(CD3) ) 2192 cm-1 compared with a single broad band observed at 2172 cm-1. The Fermi resonance should blue-shift the overtones relative to their unperturbed values, whereas the anharmonicity of the modes will red-shift the overtones relative to twice the fundamentals. Depending on which perturbation is stronger, the observed overtones can be at either a higher or lower frequency than twice the corresponding fundamentals. Because of this ambiguity, it is not possible to know how much the bands are shifted by the Fermi resonance. Recently, A Ä smundsson and Uvdal35 reported a new set of RAIRS spectra in the CH stretch region for methoxy on Cu(100) and made a detailed analysis of the Fermi resonance. They argued that the anharmonicity associated with the CH3 bending modes should be small and that the unperturbed positions of the overtones can be taken as twice the fundamental frequencies. This has allowed them to obtain the Fermi resonance coupling constants from which they were able to calculate frequency shifts and intensity redistributions that were in qualitative agreement with their measured spectra. C. Force Field for the H3COCu3 Model. We performed the normal-mode calculations using a standard set of programs.36 Most of our analysis is based on a H3COCu3 model. The use of a model with the highest symmetry possible for the adsorbate, C3V in this case, greatly facilitates the interpretation of the results. Because many of the geometric parameters specific to surface methoxy are unknown, we need to use assumed values. For the CH3O unit, we used parameters from methanol:37 rCO ) 1.42 Å, rCH ) 1.093 Å, and θHCH ) 108.63°. The Cu-O distance of 1.97 Å is taken from a theoretical study of methoxy on Cu(100)5 and the Cu-Cu distance of 2.553 Å is that of the Cu(100) surface.38 The initial force constants are listed in Table 2 and are based largely on those determined for methanol. Table 2 also lists the values of the final force constants adjusted to fit the experimental frequencies. The H3COCu3 cluster will give rise to 18 normal modes; 5 belong to the totally symmetric A1 representation, 6 are doubly degenerate E vibrations, and the torsion is of A2 symmetry. A basis set of 20 internal coordinates was used: three CH stretches, three HCH bends, the CO stretch, three HCO bends, three CuO stretches, three CuOC bends, three CuCu stretches, and the torsion. The fact that there are two more internal coordinates than normal modes means that some of these internal coordinates are redundant. For example, the HCH and HCO bends are linearly dependent. The existence of redundant coordinates is not a problem; it simply means that of the 20 modes calculated, two will have zero frequency and will correspond to translation or rotation of the entire cluster. The 20 internal coordinates are combined into 20 symmetry coordinates. This allows the 20 × 20 F matrix to be block diagonalized into a 7 × 7 A1 block, two 6 × 6 E blocks, and
J. Phys. Chem. B, Vol. 104, No. 11, 2000 2453 TABLE 2: Initial and Final Force Constantsa for Methoxy on Cu(100) force constants
initial values
final values
% change
C-H stretch C-O stretch H-C-H bend H-C-O bend Cu-O stretch Cu-Cu stretch Cu-O-C bend Torsion C-H/C-H H-C-H/H-C-H H-C-O/H-C-O H-C-O/C-O Cu-O/Cu-O
4.67b 5.10b 0.515b 0.853b 1.93c 2.30d 0.054c 0.026f 0.019b -0.04e -0.02b 0.437b 0.024c
4.60 4.52 0.549 0.853 0.715 0.78 0.054 0.026f 0.019 -0.04 -0.02 0.437 0.024
-1.5 -11.4 +6.6 not varied -63.0 -66.1 not varied not varied not varied not varied not varied not varied not varied
a The units are mdyne Å-1 for bond stretches and interactions between bond stretches; mdyne Å-1 radian-2 for valence angle bends and the torsion and interactions between bends; mdyne radian-1 for interactions between stretches and bends. b Ref 39. c Ref 43. d Ref 41. e Ref 40. f Value was chosen to yield 270 cm-1 for the torsion fundamental in methanol. It differs from the values used in refs 37 and 39 presumably because of differences in how the normalization constant for the torsional coordinates is defined.
TABLE 3: Comparison of Calculated and Experimental Frequencies for Methoxy and Methanol Using the Initial Force Constants of Table 2 CH3O/Cu(100)a band assignment
calcd
asym CH3 str., E sym CH3 str., A1 asym CH3 def., E sym. CH3 def., A1 asym OCH3 def., E C-O str., A1 asym Cu-O str., E sym Cu-O str., A1 sym Cu-Cu str., A1 asym Cu-Cu str., E Torsion, A2 asym Cu-O-C def., E
2957 2863 1496 1417 1148 1124 469 430 225 171 118 75
exptl 2798
1012
methanolb calcd
exptl
2959, 2957 2863 1500,1496 1416 1143, 1067 1034
2972 2837 1477 1463 1160, 1120 1037
290 270
290
a The calculated values are from this study for the CH OCu cluster 3 3 and the experimental values are from the RAIRS data of this study, with the exception of the band at 290 cm-1 which is from ref 9. b Ref 39.
a 1 × 1 A2 block. The symmetry greatly reduces the number of independent force constants needed. In principle, with 20 distinct internal coordinates, 210 distinct force constants would be needed. With the C3V model, this reduces to 51. Furthermore, because only the A1 vibrations are observable, we are only concerned with the A1 block, which has a maximum of 15 independent force constants, 5 diagonal constants, and 10 interaction constants. However, it is quite reasonable to assume that many of the interaction constants can be neglected. To take an extreme example, the 15 independent force constants include an interaction between the CuCu and CH stretch A1 symmetry coordinates, which is surely insignificant. Before considering the optimization of the force constants, it is instructive to consider how close the calculated frequencies are to the experimental frequencies using the initial set of force constants, based primarily on those of methanol, without any optimization. Table 3 shows the results of such a calculation, along with the calculated and experimental results for methanol. Because the internal coordinates, their force constants, and the geometric parameters associated with the OCH3 portion of each molecule are essentially the same, the differences in the calculated frequencies are due largely to the structural effect of
2454 J. Phys. Chem. B, Vol. 104, No. 11, 2000
Feature Article
TABLE 4: Comparison of Experimental Frequencies for Five Methoxy Isotopomers on Cu(100) and Calculated Frequencies for the C3W Symmetry Methoxy Cu3 Cluster Using the Final Force Constants of Table 2 12CH 16O 3
fundamental
calc
ν1 (E) ν2 (A1) ν3 (E) ν4 (A1) ν5 (E) ν6 (A1) ν7 (A1) ν8 (E) ν9 (A1) ν10 (E) ν11 (A2) ν12 (E)
2936 2841 1534 1436 1150 1014 306 293 205 169 118 73
a
exp 2798 1433 1012 290a
13CH 16O 3
calc 2923 2838 1533 1430 1142 997 305 293 203 169 118 72
12CH 18O 3
exp 2795
995
calc 2935 2841 1533 1435 1147 983 304 282 202 168 118 72
12CD 16O 3
exp 2797
979
calc 2191 2050 1096 1092 895 974 301 288 200 168 84 66
13CD 16O 3
exp 2050 1095 980
calc 2173 2043 1094 1076 887 968 300 288 198 169 84 66
exp 2046 1080 971
From ref 9.
replacing the hydroxyl H atom with three Cu atoms to give an overall symmetry of C3V. The higher symmetry makes the OCH3 deformation mode (the methyl rock) doubly degenerate and of E symmetry, and as such the mode cannot contain any contribution from the CO stretch internal coordinate, which is of A1 symmetry. For methanol, the degeneracy of the OCH3 deformation is split into A′ and A′′ components. Furthermore, the OH bend (calculated to be at 1345 cm-1 but not included in Table 3) has A′ symmetry. Thus the A′ normal modes, with calculated fundamentals at 1345, 1067, and 1034 cm-1, have substantial contributions from the OH bend, CO stretch, and OCH3 bend internal coordinates of A′ symmetry. In contrast, for H3COCu3 the A1 mode with a calculated fundamental at 1124 cm-1 is well-separated from the other A1 modes and therefore consists almost entirely of CO stretch. Thus even though exactly the same CO stretch force constant is used for H3COCu3 and H3COH, the calculated CO stretch fundamentals differ by 90 cm-1. This illustrates a very important point. If one tried to infer something about the strength of the CO bond in methoxy on Cu(100) relative to the CO bond in methanol from frequencies alone, one might erroneously conclude if the two measured frequencies were equal that the CO bond was equally “stiff” in the two cases. However, the normal-mode analysis shows that the CO stretch force constant would have to be considerably smaller for methoxy in order to obtain the same frequency. The frequencies that we calculated for methanol differ from those calculated by Furic´ et al.39 for two primary reasons. First, we include a HCH-HCH interaction constant of -0.04 as was used in a normal mode calculation of H3CC-Ni3, a model for ethylidyne on the Ni(111) surface.40 The fact that we include this interaction constant, whereas Furic´ et al.39 did not, accounts for the much larger separation between the calculated pair of CH3 bending modes at 1500 and 1496 cm-1 and the one at 1416 cm-1. However, if we had not included this interaction constant the calculated degenerate CH3 bend would be lower than the symmetric bend, a result that is generally at odds with results for adsorbed H3CX species. Second, we used the precise masses for the H, C, and O atoms to six decimal places, whereas Furic´ et al.39 appear to have used masses rounded to the nearest amu. For the same OH stretch force constant, the use of the more precise H atom mass lowers the OH stretch frequency by 14 cm-1. These two factors account for most of the differences between our calculated methanol frequencies and those of Furic´ et al.39 However, using even exactly the same force constants and presumed masses employed by Furic´ et al.,39 there remained a root mean square difference between our calculated frequencies and theirs of 9 cm-1. In contrast, we could reproduce the
calculated frequencies of Serrallach et al.37 to a root mean square difference of only 0.54 cm-1. However, the latter set of force constants was less convenient for applying to a C3V symmetry model. For the sake of reproducibility, it is important to note that the force constants listed in Table 2 are the exact ones used, as opposed to listing a set that is rounded to the indicated significant figures from the constants actually used. The issue of reproducibility is, of course, quite distinct from the issue of the accuracy of normal mode calculations, which certainly would not justify such careful attention to the precision of the input parameters. Several criteria were used to obtain the final force constants listed in Table 2. Because relatively few of the fundamentals of methoxy on Cu(100) are observable, unless the number of force constant parameters is greatly restricted, the number of fitting parameters will greatly exceed the number of observed bands, despite the extensive number of isotopomers used. Therefore, we chose to hold all interaction force constants at their initial values. Also, the CH stretch region was not included in the fitting process because the Fermi resonance effects that dominate this region are outside the normal mode approximation. Instead, the final CH stretch force constant was obtained as described earlier and was held fixed at the value of 4.60 while the other parameters were adjusted. The initial value of the CuCu stretch force constant was set equal to that of the Cu(100) surface,41 where the degree of coordination to other copper atoms is much higher than in the H3COCu3 model. Therefore, it is not surprising that this value would need to be drastically reduced. The Cu-Cu force constant was adjusted so that the highest frequency mode, primarily due to CuCu stretch motion, was approximately at the top of the Cu phonon band at around 240 cm-1.42 The same CuCu force constant was used in the Cu12 cluster, which gave (without methoxy attached) a highest Cu-Cu stretch frequency of 251 cm-1. Thus the CuCu force constant was not used as a variable to fit the methoxy frequencies. This left three force constants as adjustable parameters to fit the nine experimental frequencies that occur below 1500 cm-1 (i.e., exclusive of the CH stretch region) for the five isotopomers listed in Table 4. Except for the CuO stretch at 290 cm-1, all of the experimental frequencies come from the present study. The initial value of the CuO stretch force constant is from a compound with a Cu-O coordination quite different43 from that of methoxy on Cu(100), so it is also not surprising that it is substantially reduced in order to get a CuO stretch at 290 cm-1. One feature that emerges from the calculations is that the normal modes with calculated fundamentals at 306 and 293 cm-1 have large contributions from both the CuCu and CuO symmetry coordinates. This feature is
Feature Article
J. Phys. Chem. B, Vol. 104, No. 11, 2000 2455
TABLE 5: Comparisons of the Highest Frequencies Calculated for the CuOCH3 and Cu12OCH3 Models Using Force Constants Optimized for the Cu3OCH3 Model mode
Cu3OCH3, C3V
Cu12OCH3, Cs
CuOCH3, C3V
1 2 3 4 5 6 7 8 9
2936 2841 1534 1436 1150 1014 306 293 205
2935 2841 1534 1436 1154, 1151 1008 299 297 258
2935 2841 1533 1436 1152 1005 237 122
retained in the results of the Cu12OCH3 cluster. A lattice dynamics calculation of O on Cu(100) gave dipole active modes at 441 and 277 cm-1, with the latter one being more intense.42 It is likely that the 290 cm-1 HREELS peak for CH3O/Cu(100) was simply the most intense of two and possibly more modes consisting of substantial amounts of CuCu and CuO stretching. A more detailed experimental study of the low-frequency region combined with a proper model of the substrate vibrations would be needed to properly address this issue. Our calculated potential energy distribution (PED) for the C-O stretch mode shows that it consists of 91% CO stretch with a 5% contribution from the CuO stretch. A good description of the low-frequency modes is of minor relevance to the internal vibrations of methoxy, which are our primary focus. The frequencies calculated from the final set of force constants for the five C3V isotopomers of methoxy are given in Table 4. With the small adjustments in the HCH bend and CO stretch force constants indicated in Table 2, we find that the calculated frequencies (outside of the CH/CD stretch region) agree with the measured values to within 6 cm-1. This indicates that the internal bonding of the OCH3 unit of methoxy is quite similar to that in methanol. Because only the A1 symmetry fundamentals are observable for the C3V isotopomers, only the symmetrized force constants of the A1 block are obtained from the optimization process. Therefore, in principle, it should not be possible to determine how the E symmetry vibrations for methoxy differ from those of methanol. However, by assuming that the values of the interaction constants in Table 2 are the same as those of methanol, it is possible to calculate the unsymmetrized force constants, shown in Table 2, the linear combinations of which give the E block of the symmetrized force constant matrix. In this way we were able to calculate frequencies of the E modes using the optimized force constants. To test the importance of the number of Cu atoms used to represent the surface, we repeated the calculations using a C3V symmetry CuOCH3 model and a Cs symmetry Cu12OCH3 model where the Cu atoms occupy points of a square two-dimensional lattice. In the latter model there is an inner square consisting of four Cu atoms with each of these atoms bound to two outer Cu atoms. The inner atoms are given a mass of 63 amu while the outer atoms are given infinite mass. The same CuCu stretch force constant of 0.78 mdyne Å-1 was used for the bonds between inner and outer atoms and between two inner atoms, while no force constant is used between the outer atoms. A CuCuCu bend force constant of 0.08 mdyne Å-1 radian-2 was also used. These force constants gave a highest frequency of 260 cm-1 for the Cu12 layer when the CuO force constant was set to zero. In the Cu12OCH3 model the methoxy is placed in an asymmetric site between the 4-fold hollow and the 2-fold bridge site as determined in a photoelectron diffraction study.8 Table 5 compares frequencies calculated for the three models where all of the force constants are the same as the final force
constants listed in Table 2. The results show that the calculated frequencies for the methoxy internal vibrations are largely unaffected by how the adsorption site is represented. Although the reduction in site symmetry in the Cu12OCH3 model does lift the degeneracy of the E modes of the C3V model, it is a very small effect that is unlikely to be observable in a RAIRS experiment. This is at first a surprising conclusion since the internal vibrations of small molecules such as CO and NO (i.e., the CO and NO stretch vibrations) are quite sensitive to the adsorption site. However, it should be emphasized that the results in Table 5 merely show that for a given set of force constants, the internal vibrations are relatively insensitive to the adsorption site. However, it is far more likely that the internal bonding within the adsorbate, and hence the force constants, will be different at different sites. This is surely the case for CO and NO and it would likely be the case for methoxy as well. The only A2 symmetry normal mode of the Cu3OCH3 model, the torsion (or hindered rotation about the CO bond), is calculated to be at 118 cm-1 for the three CH3O isotopomers and at 84 cm-1 for the two CD3O isotopomers. Under C3V symmetry, the torsion mode consists entirely of the torsion internal coordinate and its frequency is completely determined by the torsion force constant. As expected, the frequency of this mode depends only on the masses of atoms that are not on the 3-fold axis. Because the same force constant gave a torsional frequency of 270 cm-1 for methanol, the substantially lower frequency of this mode in methoxy is due mainly to the fact that the CH3O unit is attached to the three relatively heavy copper atoms instead of to a single H atom. When the symmetry is reduced to Cs in the Cu12OCH3 model, this A′′ mode is one of several A′′ modes of similar frequency. It might therefore be expected that the A′′ normal modes would contain substantial contributions from several of the A′′ symmetry coordinates. However, the mode of Cu12OCH3 with a calculated frequency of 118 cm-1 has a PED that is 92% torsion. This lack of mixing, although allowed by symmetry and expected by the relatively high density of A′′ states below 300 cm-1, is another indication of the special character of such modes. Although our experiment provides no information about the torsion mode of methoxy on Cu(100), some indirect information on such modes is available from other techniques. The technique of ESDIAD (Electron Stimulated Desorption Ion Angular Distribution) has been used to infer the frequency of the torsional mode of PF3 on the Ni(111) surface.44 We discussed the possibilities of indirect manifestations of such modes in the context of an IR study of ethylidyne on Pt(111).14 The value we predict of 118 cm-1 for this mode for methoxy on Cu(100) will provide an initial estimate for any future study that seeks to measure it. An independent test of the force field obtained by fitting the force constants to the frequencies of the C3V isotopomers is provided by using the unsymmetrized force field, without further adjustment, to calculate the frequencies for the two Cs isotopomers, CH2DOCu3 and CD2HOCu3. The results are shown in Table 6 along with a description of the modes in terms of the symmetry coordinates that make the largest contributions to the PED for the mode. These results clearly validate the final force field as well as the normal mode calculations. For CD2HO, three bands of A′′ symmetry in the 900-1100 cm-1 region are predicted and three are observed at approximately the right values. For CDH2O only two A′ bands are predicted in this region and only two are observed. The agreement between the observed and calculated frequencies is fair and is about as good as can be expected for a purely harmonic description. The modes
2456 J. Phys. Chem. B, Vol. 104, No. 11, 2000
Feature Article
TABLE 6: Comparison of Experimental Frequencies for CDH2O and CHD2O on Cu(100) and Calculated Frequencies for the Cs Symmetry Methoxy Cu3 Cluster Using the Final Force Constants of Table 2 12CDH 16O 2
mode
calc
1, A′′ 2, A′ 3, A′ 4, A′ 5, A′′ 6, A′ 7, A′′ 8, A′ 9, A′ 10, A′ 11, A′′ 12, A′ 13, A′ 14, A′′ 15, A′ 16, A′′ 17, A′′ 18, A′
2935 2876 2143 1503 1377 1326 1082 1020 933 305 293 290 204 170 169 104 70 70
12CHD 16O 2
exp 2912 2141
1015 921
PED
mode
calc
exp
PED
0.99CH 0.99CH 0.97CD 0.73HCH + 0.21HCO 0.59DCH + 0.41HCO 0.48DCD + 0.44HCO 0.58HCO + 0.40DCH 0.77CO + 0.15DCO 0.71DCO + 0.11CO 0.31CuCu + 0.28CuO 0.88CuO + 0.07CuOC 0.87CuO + 0.06CuCu 0.40CuCu + 0.27CuO 0.94CuCu 0.94CuCu 0.98torsion 0.89CuOC 0.91CuOC
1, A′ 2, A′′ 3, A′ 4, A′ 5, A′′ 6, A′ 7, A′ 8, A′ 9, A′′ 10, A′ 11, A′′ 12, A′′ 13, A′ 14, A′ 15, A′′ 16, A′′ 17, A′ 18, A′′
2907 2192 2095 1362 1334 1094 1012 944 907 303 291 288 202 169 169 93 68 67
2899
0.99CH 0.97CD 0.97CD 0.61HCO + 0.35HCD 0.97HCD 0.55DCD + 0.29DCO 0.64CO + 0.10HCD 0.38DCO + 0.22CO 0.96DCO 0.46CuO + 0.27CuCu 0.86CuO + 0.06CuCu 0.87CuO + 0.06CuCu 0.54CuCu + 0.39CuO 0.94CuCu 0.98CuCu 0.98torsion 0.90CuOC 0.90CuOC
corresponding to the most intense band observed for both isotopomers has its biggest contribution from the CO stretch coordinate. In fact, if we assume that the intensity of all of the bands comes mainly from the CO stretch, then the PED implies that the 1015 cm-1 band for CDH2O should be more intense than the 1017 cm-1 band of CD2HO, as is observed. A more quantitative treatment of relative intensities is possible from the description of the normal modes and is presented in the next section for the C3V isotopomers. D. The Relative Intensities of the CO Stretching and CH3 Bending Modes. One of the remarkable features of the spectra of Figures 1 and 2 is the extreme weakness of the δs(CH3) band compared with the very high intensity of the CO stretch for the CH3O isotopomers. In contrast, for CD3O the intensity of the δs(CD3) band is about half of that of the ν(CO) band. Qualitatively, the reason for this strong change in relative intensity upon deuterium substitution is that the composition of the modes in terms of internal coordinates is quite different in the two cases. For CD3O, the PED shows a 23% contribution by the CO stretch to the δs(CD3) mode, whereas for CH3O there is only a 1.7% contribution of CO stretch to the δs(CH3) mode. A large relative intensity change upon deuterium substitution is also observed for ethylidyne, where for the CCH3 isotopomer the δs(CH3) band is the most intense band in the spectrum with a somewhat weaker CC stretch. However, for CCD3, the CC stretch band gains in intensity relative to the CC stretch of CCH3, while the δs(CD3) band is quite weak and was unobservable in a RAIRS study of ethylidyne on Pt(111), an observation that was qualitatively explained by the very different composition of the normal modes for the two isotopomers.45 Recently, a normal-mode analysis for ethylidyne on Ni(111) was carried out by Bu¨rgi et al.40 and was used to quantitatively explain the intensity changes observed between the CCH3 and CCD3 isotopomers. The same method can be used to quantitatively analyze the intensities in methoxy. The measured intensity, Ii, of a given IR band, i, is related to ∂µ/∂Qi, which can be expressed as a linear combination of ∂µ/ ∂Sn by
∂µ ∂Qi
)
( ) ∂µ
∑n Lin ∂S
(5)
n
where the Sn are the symmetrized internal coordinates and the Lin are the elements of the L matrix. The L matrix defines the
2143 1068 1017 950
normal coordinates in terms of symmetrized internal coordinates and is the main result of a normal coordinate analysis. Whereas there is a different L matrix for each isotopomer, the ∂µ/∂Sn are the same for all isotopomers and so once a set of ∂µ/∂Sn are determined for one isotopomer, the relative intensities of the IR bands for different isotopomers can be predicted. We find that although the modes we label “CO stretch” and “HCH bend” consist predominantly of these two internal coordinates, the CuO stretch also makes a significant contribution to the CO stretch mode and cannot be ignored. We thus need three terms in the sum over internal coordinates. For this analysis we use the L matrixes obtained from the CH3OCu model in order to avoid any contribution from CuCu stretches. From the L matrixes we can therefore write for CH3OCu
∂µ ∂µ ∂µ ∂µ ) -1.99 - 0.071 - 0.023 ∂Q4 ∂S1 ∂S2 ∂S3 ∂µ ∂µ ∂µ ∂µ ) -0.248 - 0.370 + 0.183 ∂Q6 ∂S1 ∂S2 ∂S3 ∂µ ∂µ ∂µ ∂µ ) +0.006 + 0.018 + 0.211 ∂Q7 ∂S1 ∂S2 ∂S3 and for CD3OCu
∂µ ∂µ ∂µ ∂µ ) +1.48 - 0.217 - 0.041 ∂Q4 ∂S1 ∂S2 ∂S3 ∂µ ∂µ ∂µ ∂µ ) -0.336 - 0.300 + 0.189 ∂Q6 ∂S1 ∂S2 ∂S3 ∂µ ∂µ ∂µ ∂µ ) -0.004 - 0.018 + 0.203 ∂Q7 ∂S1 ∂S2 ∂S3 We label the A1 combination of HCH bends as S1, the CO stretch as S2, and the CuO stretch as S3. Although the original set of internal coordinates included HCO bends, these are redundant coordinates, with the A1 HCO combination equal to -0.971 of the HCH combination, so that the HCO and HCH contributions to each Q can be combined. The normal coordinates are numbered as in Table 4. For each isotopomer we have three equations in three unknowns that can be solved for the ∂µ/∂Si from the experimentally determined ∂µ/∂Qi, which in turn are related to the experimental intensity by ∂µ/∂Qi ∝ ( Ii1/2.
Feature Article
J. Phys. Chem. B, Vol. 104, No. 11, 2000 2457
TABLE 7: Relative Values for the Dipole Moment Derivatives with Respect to Symmetrized Internal Coordinates: S1-HCH or DCD Bend; S2-CO Stretch; S3-CuO Stretch 12CH O 3 12CD O 3 13CD O 3
∂µ/∂Q4
∂µ/∂Q6
∂µ/∂Q7
∂µ/∂S1
∂µ/∂S2
∂µ/∂S3
positive negative positive
positive negative positive
positive positive positive
+0.56 -0.86 -0.71
-32 -34 +30
+7.5 +8.5 +8.2
The intensities of the ν(CO), δs(CH3), and δs(CD3) bands were obtained from the areas of Lorentzian functions fitted to our spectra using absorbance (not ∆R/R as in Figures 1 and 2) as the ordinate. Although we have not measured the CuO stretch frequency, it was measured with HREELS by Sexton for both CD3O and CH3O. Taking into account that HREELS intensities are attenuated by a factor of 1/ν3 relative to RAIRS intensities,46 we obtain a value for the relative CuO stretch intensity. The sign ambiguity in the relationship between measured intensity and the ∂µ/∂Qi can be resolved by performing the calculations for each possible relative sign combination and finding the combination that gives the same set of ∂µ/∂Sn for each isotopomer.47 The results are shown in Table 7. The agreement among the three isotopomers is good for the given sign combination while other sign combinations gave distinctly poorer agreement. The results show that the change in dipole moment associated with stretching the CO bond is greater by a factor of 46 ( 8 than the change due to bending the HCH angle. Furthermore, the ∂µ/∂S1 and ∂µ/∂S2 are of opposite signs leading to a partial cancellation of terms in the sums for ∂µ/∂Q4, further weakening the intensity of the bending fundamental. For CD3O the relatively large contribution from the CO stretch overwhelms the opposite but much smaller contribution from the CD3 bend. Table 7 also shows results for the 13CD3O isotopomer. Alternatively, we can use the average values of ∂µ/∂S1 and ∂µ/∂S2 for the CD3O and CH3O isotopomers to predict the ν(CO) band to δs(CD3) band intensity ratio for 13CD3O; the calculated ratio is 5.2 compared with the experimental ratio of 5.6. The corresponding experimental ratio for 12CD3O is 3.6. Thus, the normal coordinate analysis not only allows us to understand quantitatively the frequency shifts upon isotopic substitution, but also provides a quantitative understanding of the observed intensity variations among the isotopomers. E. Vibrational Frequencies from Ab Initio Electronic Structure Calculations. Following the example of Uvdal and co-workers,20,30 we used Gaussian 9848 at the Hartree-Fock level with the LANL2DZ basis set to calculate the vibrational frequencies of a CH3OCu model. The frequencies were calculated after geometry optimization with the model constrained to C3V symmetry. Without this constraint, optimization yields a slightly nonlinear Cu-O-C unit. The only significant effect of calculating the frequencies with a C3V symmetry model was that the lowest frequency modes, the degenerate Cu-O-C bends, could not be calculated correctly because the potential energy with respect to the Cu-O-C angle is not at a minimum at 180°. The optimized C3V geometric parameters are Cu-O ) 1.82 Å, O-C ) 1.40 Å, C-H ) 1.09 Å, and HCH ) 107.3 °. A comparison of the calculated and experimental frequencies is presented in Table 8, where the fundamentals are numbered in the same way as in Table 4. With this numbering scheme, the modes are listed from highest to lowest frequency for the three CH3 isotopomers but not for the CD3 isotopomers. However, each row corresponds to the same type of mode for all five isotopomers. For example, all frequencies for the ν6(A1) row correspond to a mode where the CO stretch internal coordinate makes the largest contribution. Associating frequen-
cies with the correct mode was based on Cartesian atomic displacement coordinates. As usual for ab initio frequencies, the values reported in Table 8 were obtained by multiplying the directly calculated frequencies by a scale factor. At the Hartree-Fock level, a scale factor of 0.90 appears to be generally appropriate49 and is the value we used for the frequencies reported in Table 8. In comparing the calculated and experimental results, it is clear that the ab initio calculation fails to adequately describe the ν4 and ν6 modes. The fact that the scaled ν6(A1) frequency is 137 cm-1 higher than the experimental value for the CO stretch indicates that the model with one Cu atom does not accurately represent methoxy on the Cu(100) surface. In the normal-mode calculations we also found that the CO stretch force constant from methanol was too large and had to be reduced by 11.4% to agree with experiment. The overestimation of the CO stretch force constant not only results in a CO stretch frequency that is too high for the OCH3 isotopomer, but also leads to an incorrect ordering for the OCD3 isotopomers. Because of this incorrect ordering, the CO stretch,ν6, for the OCD3 isotopomers was calculated to be at a higher frequency than that for the OCH3 isotopomers. This occurs because in combining the CD3 bend and CO stretch internal coordinates to form the ν6 and ν4 normal modes, the lower frequency of the bend pushes up the ν6 frequency and at the same time the ν4 frequency is pushed down by the higher CO stretch frequency. This is not an unphysical result and for ethylidyne on Pt(111) the CC stretch fundamental for CCD3 is observed at a higher value than that for CCH3.45 However, for methoxy on Cu(100) the calculated result is contrary to observation. In comparing the scaled calculated frequencies with the experimental frequencies in Table 8 it is important to realize that the calculation is still based on the harmonic approximation and all of the limitations of this approximation still pertain. For example, as also noted by Uvdal and MacKerell,20 the Fermi resonance effects in the CH stretch region cannot be understood with such calculations. However, unlike the empirical force field, the ab initio calculation yields the full harmonic force field, i.e., the diagonal force constants plus all of the interaction force constants. This, in principle, allows us to evaluate whether some of the interaction force constants are in fact negligible, as assumed in the normal coordinate analysis. However, a comparison can only be made if the internal coordinates are defined in exactly the same way, which is not the case here. In contrast to our ab initio results, Uvdal and MacKerell20 report much better agreement with experiment for methoxy on Mo(110) using a CH3OMo model with an overall charge of +1 and essentially the same method of calculation. One minor source of the difference is that we used a single standard literature scale factor, whereas they used two different scale factors of 0.86 for the 1900-3000 cm-1 region and 0.88 for the 900-1500 cm-1 region, with the latter chosen to bring the calculated and experimental CO stretch into agreement. When multiple scale factors are used as fitting parameters, it is no longer strictly an ab initio calculation. To better understand the source of the difference, we also carried out the calculation for CH3OMo+ using both the LANL2DZ and LANL1DZ basis sets. Although we obtain exact agreement with ref 20 using the LANL1DZ basis set including a calculated value of 1002 cm-1 for ν(CO), with the larger and presumably better LANL2DZ basis set, we obtained a CO stretch for the CH3OMo+ model at 1053 cm-1 using a scale factor of 0.88. This compares with the experimental value at a saturation coverage of 0.25 ML of 1043 cm-1 32 from which the dipole-dipole coupling shift has not been subtracted.
2458 J. Phys. Chem. B, Vol. 104, No. 11, 2000
Feature Article
TABLE 8: Comparison of Experimental Frequencies for Five Methoxy Isotopomers on Cu(100) and Frequencies for the C3W Symmetry Methoxy-Cu Cluster Obtained from an Ab Initio Calculation; the Listed Calculated Frequencies Were Obtained by Multiplying the Ab Initio Frequencies by a Scale Factor of 0.90 12CH 16O 3
fundamental
calc
ν1 (E) ν2 (A1) ν3 (E) ν4 (A1) ν5 (E) ν6 (A1) ν7 (A1)
2851 2805 1485 1458 1131 1149 420
a
exp 2798 1433 1012 290a
13CH 16O 3
calc 2841 2803 1482 1452 1124 1132 414
12CH 18O 3
exp 2795
995
calc 2851 2805 1485 1457 1128 1111 414
12CD 16O 3
exp 2797
979
calc 2113 2008 1080 1072 866 1159 402
13CD 16O 3
exp 2050 1095 980
calc 2098 2004 1075 1072 860 1136 397
exp 2046 1080 971
From ref 9.
Although differences in basis set accounts for some of the differences in the calculations for the CuOCH3 and CH3OMo+ models, it still appears that the ab initio calculation based on the CuOCH3 model is less effective at predicting the frequencies for methoxy on Cu(100) than the CH3OMo+ model is for methoxy on Mo(110). The ab initio calculations also yield values for the IR intensities for each mode. The results for 12CH316OCu agree with experiment in that the CO stretch is the most intense, followed by the CH stretch and with the CH3 bending mode being much weaker than the other two. However, the calculated intensities do not show nearly as much change upon deuterium substitution as is observed. This is due at least in part to the fact that the calculations do not give a very good description of the normal modes. Even if this were not the case, ab initio calculations generally do a poor job in quantitatively predicting the relative intensities in an IR spectrum. V. Summary and Conclusions A harmonic force field for methoxy on Cu(100) was obtained both through a standard normal-mode analysis and through ab initio calculations. The normal-mode analysis yields force constants that are only slightly different from those of an isolated methanol molecule. The diagonal force constant of methanol that has to be modified the most is that of the CO stretch, which is 11.4% smaller for methoxy on Cu(100). This indicates that the CO bond of methoxy/Cu(100) is substantially perturbed relative to that of methanol. This conclusion pertains regardless of whether the analysis is based on a model containing 1, 3, or 12 Cu atoms. An accurate description of the normal modes provides a quantitative explanation of the dramatic change in relative intensity of the ν(CO) and δs(CH3) fundamentals upon deuterium substitution. As in the general case, there are more force constants than measured frequencies so that a unique harmonic force field cannot be obtained. The problem is compounded for an adsorbate molecule because the number of fundamentals observed is further restricted by experimental limitations on the spectral range and/or sensitivity and by the more restrictive surface IR selection rule. Even with these restrictions, the combined use of extensive isotopic substitution with a normal-mode analysis can greatly enhance the value of surface vibrational spectroscopy as a probe of adsorbate structure. Although an ab initio calculation can in principle be used to determine the full anharmonic potential that determines the vibrational spectrum, such methods are still mainly used to merely determine the harmonic force field. Thus although all of the advantages described for a normal-mode analysis are retained, the calculated spectra can be only as good as the harmonic approximation. Nevertheless, vibrational analysis using ab initio calculations offers two big advantages. First, the
full harmonic force field, i.e., the diagonal and all interaction force constants, is readily determined. Second, it is not necessary to obtain spectra of numerous isotopomers. As Fogarasi and Pulay28 note, the accuracy of diagonal force constants determined by ab initio methods is generally lower than those determined empirically, whereas the opposite is true for the interaction force constants. Because a good description of the normal modes depends most critically on the diagonal force constants, an empirical force field often leads to a better description of the normal modes. This is clearly seen here where the inaccurate ab initio CO force constant led to an incorrect ordering for the ν(CO) and δs(CD3) fundamentals of the OCD3 isotopomers. As Fogarasi and Pulay note,28 the best way to obtain a harmonic force field is to combine the features of both methods by selective adjustment of the ab initio force constants in order to match the experimental and calculated frequencies. Acknowledgment. This work was supported by a grant from the National Science Foundation (CHE-9616402). We thank Dr. Patrick Mills for valuable discussions and a careful reading of the manuscript, Dr. Hugo Celio for providing unpublished spectra of methoxy on Cu(100), Dr. Per Uvdal for providing a preprint of ref 35, and the referee who provided us with the results of an independent ab initio and normal-mode calculation of CH3OCu. References and Notes (1) Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations, The Theory of Infrared and Raman Vibrational Spectra; Dover Publications: New York, 1980. (2) Nakamoto, K. Infrared and Raman Spectra of Inorganic and Coordination Compounds 5th Ed.; Wiley: New York, 1997. (3) Sim, W. S.; Gardner, P.; King, D. A. J. Phys. Chem. 1995, 99, 16002. (4) Ryberg, R. J. Chem. Phys. 1985, 82, 567. (5) Zeroka, D.; Hoffmann, R. Langmuir 1986, 2, 553. (6) Wander, A.; Holland, B. W. Surf. Sci. 1988, 203, L637. (7) Hofmann, Ph.; Schindler, K.-M.; Bao, S.; Fritzsche, V.; Ricken, D. E.; Bradshaw, A. M.; Woodruff, D. P. Surf. Sci. 1994, 304, 74. (8) Lindner, Th.; Somers, J.; Bradshaw, A. M.; Kilcoyne, A. L. D.; Woodruff, D. P. Surf. Sci. 1988, 203, 333. (9) Sexton, B. A. Surf. Sci. 1979, 88, 299. (10) Ellis, T. H.; Wang, H. Langmuir 1994, 10, 4083. (11) Ryberg, R. Phys. ReV. B. 1985, 31, 2545. (12) Ryberg, R. Chem. Phys. Letts. 1981, 83, 423. (13) Zenobi, R.; Xu, J.; Yates, J. T.; Persson, B. N. J.; Volokitin, A. I. Chem. Phys. Lett. 1993, 208, 414. (14) Malik, I. J.; Brubaker, M. E.; Mohsin, S. B.; Trenary, M. J. Chem. Phys. 1987, 87, 5554. (15) Chesters, M. A.; McCash, E. M. Spectrochim. Acta 1987, 43A, 12, 1625. (16) (a)Weldon, M. K.; Uvdal, P.; Friend, C. M.; Serafin, J. G. J. Chem. Phys. 1995, 103, 5075. Uvdal, P.; Weldon, M. K.; Friend, C. M. Phys. ReV. B 1994, 50, 12258. (17) Camplin, J. P.; McCash, E. M. Surf. Sci. 1996, 360, 229. (18) Huberty, J. S.; Madix, R. J. Surf. Sci. 1996, 360, 144.
Feature Article (19) Dastoor, H. E.; Gardner, P.; King, D. A. Chem. Phys. Lett. 1993, 209, 493. (20) Uvdal, P.; MacKerell, A. D., Jr. Surf. Sci. 1997, 393, 141. (21) Brubaker, M. E.; Trenary, M. J. Chem. Phys. 1986, 85, 6100. (22) Celio H.; Trenary, M. AIP Conference Proceedings; American Institute of Physics: Woodbury, New York, 1998; Vol. 430, p 17. (23) Wuttig, M.; Franchy, R.; Ibach, H. Surf. Sci. 1989, 213, 103. (24) Decius, J. C.; Hexter, R. M. Molecular Vibrations in Crystals; McGraw-Hill: New York, 1977. (25) Maradudin, A. A.; Montroll, E. W.; Weiss, G. H. Theory of Lattice Vibrations in the Harmonic Approximation; Academic Press: New York, 1963. (26) (a) Persson, B. N. J.; Ryberg, R. Phys. ReV. B 1981, 24, 6954. (b) Ibach, I.; Mills, D. L. Electron Energy Loss Spectroscopy and Surface Vibrations; Academic Press: New York, 1982. (27) (a) Pulay, P. J. Mol. Struc. 1995, 347, 293. (b) Pulay, P.; Fogarasi, G.; Boggs, J. E. J. Chem. Phys. 1981, 74, 3999. (c) Rauhut, G.; Pulay, P. J. Phys. Chem. 1995, 99, 3093. (28) Fogarasi, G.; Pulay, P. In Vibrational Spectra and Structure; Durig, J. R. Ed.; Elsevier: Amsterdam, 1985; Vol. 14, p 125. (29) Whitten, J. L.; Yang, H. Surf. Sci. Rep. 1996, 24, 55. (30) (a) Uvdal, P.; A Ä smundsson, R.; MacKerell, A. D., Jr. Phys. ReV. Lett. 1999, 82, 125. (b) Uvdal, P.; MacKerell, A. D., Jr.; Wiegand, B. C. J. Electron Spectrosc. Relat. Phenom. 1993, 84/85, 193. (c) Uvdal, P.; MacKerell, A. D., Jr.; Wiegand, B. C.; Friend, C. M. Phys. ReV. B 1995, 51, 7844. (31) Brubaker, M. E.; Trenary, M. J. Chem. Phys. 1989, 90, 4651. (32) Uvdal, P.; Weldon, M. K.; Friend, C. M. Phys. ReV. B 1996, 53, 5007. (33) Ihm, H.; Smith, K. C.; Celio, H.; White, J. M. To be submitted for publication. (34) McKean, D. C. Spectrochim. Acta, Part A, 1973, 29, 1559. (35) A Ä smundsson, R.; Uvdal, P. J. Chem. Phys. 2000, 112, 366. (36) QCPE Program No. QCMP 067: McIntosh, D. F.; Peterson, M. R. Quantum Chemistry Program Exchange, Indiana University, Department of Chemistry, 1988. (37) Serrallach, A.; Meyer, R.; Gunthard, H. H. J. Mol. Spectrosc. 1974, 52, 94.
J. Phys. Chem. B, Vol. 104, No. 11, 2000 2459 (38) Watson, P. R.; Van Hove, M. A.; Hermann, K. Atlas of Surface Structures, Vol. 1A; Journal of Physical and Chemical Reference Data, Monograph 5; National Institute of Standards and Technology: Washington, DC, 1994. (39) Furic´, K.; Mohacˇek, V.; Mamic´, M. Spectrochim. Acta A 1993, 49A, 2081. (40) Bu¨rgi, T.; Trautman, T. R.; Haug, K. L.; Utz, A. L.; Ceyer, S. T. J. Phys. Chem. B. 1998, 102, 4952. (41) Hall, B. M.; Mills, D. L.; Mohamed, M. H.; Kemodel, L. L. Phys. ReV. B 1988, 38, 5856. (42) Oshima, C.; Umeuchi, M.; Nagao, T. Surf. Sci. 1993, 298, 450. (43) Giricheva, N. I.; Belova, N. V.; Girichev, G. V.; Shlykov, S. A. J. Mol. Struct. 1995, 352-353, 167. (44) Alvey, M. D.; Yates, J. T., Jr.; Uram, K. J. J. Chem. Phys. 1987, 87, 7221. (45) Malik, I. J.; Agrawal, V. K.; Trenary, M. J. Chem. Phys. 1988, 89, 3861. (46) Hoge, D.; Tu¨shaus, M.; Schweizer, E.; Bradshaw, A. M. Chem. Phys. Lett. 1988, 151, 230. (47) Dickson, A. D.; Mills, I. M.; Crawford, B. J. Chem. Phys. 1957, 27, 445. (48) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A.; GAUSSIAN 98 (Revision A.2); Gaussian, Inc.: Pittsburgh, PA, 1998. (49) Scott, A. P.; Radom, L. J. Chem. Phys. 1996, 100, 16502.
