J. Phys. Chem. C 2007, 111, 11039-11044
11039
Adsorption of CH2CHF on the Anatase (101) Surface: A Quantum-Mechanical Study Jessica Scaranto* and Santi Giorgianni Dipartimento di Chimica Fisica, UniVersita` Ca’ Foscari di Venezia, Dorsoduro 2137, I-30123 Venezia, Italy ReceiVed: March 30, 2007; In Final Form: May 16, 2007
The adsorption of CH2CHF on the anatase (101) surface has been studied by a periodic approach using hybrid-exchange density functional theory. The simulation was performed on the basis of a recently proposed experimental model for vinyl fluoride and chloride describing the adsorption of CH2CHX through the halogen atom rather than the CdC double bond according to the infrared spectra. The adsorption has been investigated using different surface coverages and periodicities, and the energetics have been considered in terms of interaction, distortion, and binding energies. A simple model of nearest and next-nearest neighbors has been adopted to obtain the energies in the limit of an isolated adsorbed molecule and to quantify the lateral effects. The adsorbate-substrate interaction for the anatase surface resulted weaker than that for the rutile (110) one. The vibrational frequencies of the adsorbed molecule have been computed and found in agreement with the experimental ones thus supporting previous infrared interpretations.
Introduction
Computational Details
Vinyl halides, widely employed in the industry as chemical reagents, cause serious problems concerning the impact on the human health.1-3 Heterogeneous photocatalysis on TiO2 represents a promising approach for removing these contaminants from the air; the complete photocatalytic mineralization results in the formation of simple molecules, such as H2O, CO2, and mineral acids.4,5 Since the decomposition of the pollutants occurs after their adsorption on the photocatalyst surface, the study of the nature of the adsorbate-substrate interaction can provide useful information for a better understanding of the reaction mechanisms involved in the degradation. In a previous work, Fourier transform infrared (FTIR) spectroscopy was used to investigate the adsorption of vinyl fluoride and chloride on powdered TiO2 (mixture of rutile and anatase) at room temperature.6 The infrared spectra of adsorbed vinyl halides were compared with those of the compounds in the gas phase, and the observed differences led to the formulation of an adsorption model consisting in an acid-base interaction between the halogen and the surface Lewis acid site (Ti4+) and an H-bond between one hydrogen of the CH2 group and a surface Lewis basic site. According to this model, a quantum-mechanical study on the adsorption of vinyl fluoride on the rutile (110) surface has been performed.7 The aim of this work is to study the adsorption of vinyl fluoride on the anatase (101) surface at DFT/B3LYP level to obtain a more complete understanding of the experimental vibrational frequencies of the adsorbed molecule.6 The adsorption has been considered using different surface coverages and periodicities; the energetics have been investigated in terms of interaction, distortion and binding energies according to a recent scheme8 in which a simple model of nearest and next-nearest neighboring molecules has been used.
The calculations have been performed at DFT level using the CRYSTAL03 and CRYSTAL06 software packages.9,10 The titanium and oxygen atoms have been described by a double valence all-electron basis set (an 86-51G* contraction: one s, three sp, and one d shell) and a triple valence (an 8-411G contraction: one s and three sp shells), respectively;11 the most diffuse sp exponents are RTi ) 0.598 and RO ) 0.184 bohr-2. The vinyl fluoride molecule has been described using the standard 6-31G** contraction (one s, two sp, and one d shell for carbon and fluorine and two s and one p shell for hydrogen).12 The B3LYP hybrid functional13 has been adopted. The exchange-correlation functional has been integrated numerically on a grid of points; integration over radial and angular coordinates has been performed using Gauss-Legendre and Leebedev schemes, respectively. A pruned grid consisting of 75 radial points and 5 sub-intervals with (50,146,194,434,194) angular points has been used for all calculations (see option LGRID in the CRYSTAL manual9). The default truncation thresholds of 10-6, 10-6, 10-6, 10-6, and 10-12 for the Coulomb and exchange series9,14 have been adopted along with a Monkhorst-Pack shrinking factor equal to 4 (corresponding to 13 symmetry unique k points in the bulk structure). The selfconsistent field procedure has been converged to a tolerance in the total energy of 1 × 10-8 Hartree per unit cell. The internal coordinates have been determined by minimizing the total energy within an iterative procedure on the basis of the total energy gradient calculated analytically with respect to the nuclear coordinates. Convergence has been determined from the root-mean-square (rms) and the absolute value of the largest component of both gradients and nuclear displacements. The thresholds for the maximum and the rms forces (the maximum and the rms atomic displacements) have been set to 0.00045 and 0.00030 (0.00180 and 0.00120) in atomic units. Geometry optimization has been terminated when all four conditions were simultaneously satisfied.15,16 The vibrational frequencies have been calculated by using the CRYSTAL06 package.10 They have been evaluated from
* Corresponding author. Phone: +39 041 2348598. Fax: +39 041 2348594. E-mail:
[email protected].
10.1021/jp072513z CCC: $37.00 © 2007 American Chemical Society Published on Web 07/04/2007
11040 J. Phys. Chem. C, Vol. 111, No. 29, 2007
Figure 1. (a) Model of the anatase (101) surface: O(2f) and O(3f) indicate twofold and threefold coordinated oxygen ions while Ti(5f) and Ti(6f) correspond to fivefold and sixfold coordinated titanium ions. (b) The CH2CHF molecule and the half of the slab used to simulate the anatase (101) surface. Parts a and b have been obtained by using the XCRYSDEN program.25
the dynamical matrix, obtained by numerical differentiation of the analytical gradient of the energy with respect to the atomic positions using a displacement of 0.001 bohr in a two-point sampling.17,18 Results and Discussion Geometry and Energetics. The anatase (101) surface has been cut from the bulk whose parameters have been previously optimized.8 As it can be seen from Figure 1a, the surface consists of threefold and twofold coordinated oxygen ions, labeled as O(3f) and O(2f), and sixfold and fivefold coordinated titanium ions, labeled Ti(6f) and Ti(5f). The surface Lewis acid and basic site is represented by the Ti(5f) and O(2f), respectively. The surface adopted for the calculations has been simulated by a 30-atomic layers slab (see Figure 1b). This thickness has been chosen as it converges with respect both the structural relaxation and the surface formation energy.8 Before considering the adsorption of the molecule in agreement with the model formulated on the basis of the experimental data, a preliminary investigation on all the possible adsorbatesubstrate structures have been done.19 The obtained results indicate that the molecule can interact with the surface Lewis acid site by the halogen atom or the double CdC bond; in the
Scaranto and Giorgianni former case, an H-bond between the CH2 group and the surface Lewis basic site can also be present. This interaction corresponds to the model previously formulated,6 and then, it has been used for the current work. The adsorption of vinyl fluoride has been considered by placing the molecule on the surface in an initial geometry with its symmetry plane perpendicular to the plane of the surface, with the fluorine atom above the fivefold coordinated titanium ion and one hydrogen above the twofold coordinated oxygen ion (see Figure 1b). The adsorption has been investigated by considering a range of surface coverage (θ) in commensurate periodic arrays defined by surface unit cells of dimension na and mb, where a and b represent the lattice vectors of the primitive surface and are equal to 3.741 and 5.322 Å, respectively. The angle γ between these two vectors is equal to 109.4°. Before considering the adsorbed molecular structure, the lateral effects due to the direct repulsion between the molecules have been evaluated by taking into account the optimization of the structure of the molecule arranged in a monolayer of CH2CHF molecules having the same periodicity used to simulate the surface. Table 1 summarizes the geometrical parameters of the molecule isolated and arranged in the considered monolayers. The biggest distortions are observed for the (1 × 1) monolayer while no variations are present in the case of the (2 × 2) monolayer. The structural parameters of the adsorbed vinyl fluoride are reported in Table 2. The changes occurring upon the adsorption can be summarized as follows: (1) The C1sF, C2sH2, and C2sH3 bond lengths as well as the H1sC1sC2 and H2-C2-H3 bond angles increase. (2) The C1sH1 and C1dC2 bond length and the FsC1sC2 and H2sC2sC1 bond angles decrease. The variation of the molecular structural parameters is associated to a charge redistribution as it is reported in Table 3, which summarizes the results obtained from the Mulliken population analysis on the molecule isolated and adsorbed on the (2 × 2) surface. As it can be seen, the adsorption gives rise to a decrease of the charge of the CH2 group and of the H1 atom and to an increase of the charge of the F and C1 atoms. These variations can be explained by a strong electronwithdrawing effect of the fluorine atom through which a charge transfer of about 0.050 |e| occurs from the molecule toward the surface. As a consequence of the adsorption, the surface ions relax in both the y- and z-directions; the biggest displacement consists in a movement upward of about 0.1 Å of the fivefold coordinated titanium ion. This relaxation occurs to favor the interaction between the surface Lewis acid site and the fluorine atom. The adsorption energetics have been studied following a scheme elsewhere reported.8 In synthesis, the formation of the adsorbate-substrate system has been investigated by considering not only the binding energy, BE, but also the real strength of the final adsorbate-substrate system (interaction energy Eint) and the changes of the geometry associated to the electronic redistribution occurring inside the molecule and the surface as a consequence of the adsorption process (distortion energy Edis). The relashionship between these three energies is
BE ) Eint + Edis
(1)
As the calculations are periodic, the calculated energies refer to the adsorption of a monolayer of molecules interacting with each other. For this reason they are called periodic and indicated by the superscript P. In brief, the periodic interaction
CH2CHF Adsorption on the Anatase (101) Surface
J. Phys. Chem. C, Vol. 111, No. 29, 2007 11041
TABLE 1: Optimized Structural Parameters for the Isolated CH2CHF Molecule and for the Molecule Arranged in (n × m) Monolayersa monolayerb C1sF C1dC2 C1sH1 C2sH2 C2sH3 H1sC1sC2 H2sC2sC1 FsC1sH1 H2sC2sH3
(1 × 1)
%
1.346 1.324 1.087 1.084 1.083 125.0 118.8 111.7 118.4
-0.1 -0.1 0.0 0.1 -0.1 -0.4 -0.8 -0.3 -0.3
(1 × 2)
(1 × 3)
%
moleculec
(2 × 1)
%
1.345 -0.1 1.345 -0.1 1.347 1.324 -0.1 1.324 -0.1 1.325 1.087 0.0 1.087 0.0 1.087 1.083 0.0 1.083 0.0 1.084 1.084 0.0 1.084 0.0 1.084 125.4 -0.1 125.4 -0.1 125.2 119.9 0.1 119.9 0.1 119.3 112.0 0.0 112.0 0.0 111.9 118.8 0.0 118.8 0.0 118.6
%
(3 × 1)
%
(2 × 2)
%
Opt
exptl20
%exptl
0.0 0.0 0.0 0.1 0.0 -0.2 -0.4 -0.1 -0.2
1.347 1.325 1.087 1.084 1.084 125.3 119.3 111.9 118.6
0.0 0.0 0.0 0.1 0.0 -0.2 -0.4 -0.1 -0.2
1.347 1.325 1.087 1.083 1.084 125.5 119.8 112.0 118.8
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1.347 1.325 1.087 1.083 1.084 125.5 119.8 112.0 118.8
1.347 1.329 1.082 1.077 1.087 129.2 119.0 110.0 120.1
0.0 -0.3 0.5 0.6 -0.3 -2.9 0.7 1.8 -1.1
a Lengths and angles are reported in angstroms and degrees, respectively. b The percentage deviation (%) refers to the isolated optimized molecule (Opt). c %exptl represents the difference in the isolated molecule between computed and experimental structure (exptl).
TABLE 2: Optimized Structural Parameters for the Isolated CH2CHF Molecule Adsorbed at Various Surface Periodicities (n × m)a C1sF C1dC2 C1sH1 C2sH2 C2sH3 H1sC1sC2 H2sC2sC1 FsC1sH1 H2sC2sH3 FsTi(s) H3sO(s) C1sFsTi(s) C2sH3sO(s)
(1 × 1)
%
(1 × 2)
%
(1 × 3)
%
(2 × 1)
%
(3 × 1)
%
(2 × 2)
%
1.376 1.320 1.084 1.085 1.088 128.6 118.1 109.3 121.6 2.340 2.082 136.7 138.9
2.2 -0.4 -0.3 0.2 0.4 2.5 -1.4 -2.4 2.4
1.383 1.319 1.082 1.084 1.086 129.5 118.6 109.1 120.8 2.259 2.210 140.4 136.8
2.7 -0.5 -0.5 0.1 0.2 3.2 -1.0 -2.6 1.7
1.386 1.318 1.082 1.084 1.086 129.8 118.6 108.9 120.7 2.241 2.231 140.9 136.4
2.9 -0.5 -0.5 0.1 0.2 3.4 -1.0 -2.8 1.6
1.385 1.319 1.082 1.085 1.087 129.3 118.2 109.0 121.2 2.264 2.145 138.8 137.4
2.8 -0.5 -0.5 0.2 0.3 3.0 -1.3 -2.7 2.0
1.391 1.319 1.082 1.085 1.086 129.4 118.1 108.9 121.1 2.250 2.117 138.9 136.4
3.3 -0.5 -0.5 0.2 0.2 3.1 -1.4 -2.8 1.9
1.392 1.318 1.082 1.084 1.085 130.0 118.4 108.8 120.7 2.219 2.218 141.1 135.9
3.3 -0.5 -0.5 0.1 0.1 3.6 -1.2 -2.9 1.6
a Lengths and angles are reported in angstroms and degrees, respectively. For each periodicity, the percentage deviation (%) with respect to the isolated optimized molecule is reported.
TABLE 3: Mulliken Population Analysis of the CH2CHF Molecule (Charges in |e|)a isolated
adsorbed
atom
q
q
∆q
%
C1 C2 H1 H2 H3 F
5.750 6.282 0.903 0.889 0.883 9.294
5.771 6.260 0.866 0.881 0.801 9.367
0.021 -0.022 -0.037 -0.008 -0.082 0.073
0.37 -0.35 -4.10 -0.90 -9.29 0.79
a ∆q and % represent the charge difference and the percentage deviation relative to the isolated molecule.
EPint, distortion EPdis, and binding energies BEP are the following:
EPint
) Esys - (Emon|sys + Esur|sys)
(3)
) Emon|sys - Emon; EP,sur where EP,mon dis dis ) Esur|sys - Esur; and Emon and Esur mean the optimized energies of the monolayer and the surface, respectively.
BEP ) EPint + EPdis ) Esys - (Emon + Esur)
ELint ) Emon|sys - Emol|sys
(5)
where Emol|sys is the energy of the molecule calculated at the geometry of the system.
ELdis ) (Emol|sys - Emol) - (Emon|sys - Emon)
(6)
(2)
where Esys is the optimized energy of the adsorbate-substrate system while Emon|sys and Esur|sys are the energies of the monolayer and the surface, respectively, both calculated at the geometry of the system. A negative (positive) value of EPint means attraction (repulsion) between the adsorbate and the substrate.
+ EP,sur EPdis ) EP,mon dis dis
A negative (positive) value of BEP means that the adsorption is a favorable (unfavorable) process. To take into account the lateral effects due to the direct interactions between the molecules constituting the monolayer, also the lateral energies, indicated with the superscript L, have been considered. The lateral interaction ELint, distortion ELdis, and binding energies BEL are then
(4)
where Emol is the optimized energy of the molecule.
BEL ) ELint + ELdis ) Emon - Emol
(7)
Finally, the sum of the periodic and the lateral energies giving the net energies, indicated with the superscript N, have been considered. The net interaction ENint, distortion ENdis, and binding energies BEN are therefore
ENint ) EPint + ELint ) Esys - (Emol|sys + Esur|sys) ENdis ) EPdis + ELdis ) (Emol|sys - Emol) + (Esur|sys - Esur)
(8) (9)
11042 J. Phys. Chem. C, Vol. 111, No. 29, 2007
BEN ) BEP + BEL ) ENint + ENdis ) Esys - (Emol + Esur) (10) All the obtained energies are summarized in Table 4; the interaction and binding energies have been corrected for the basis set superposition error (BSSE) by using the counterpoise (CP) method.21 The table points out that the formation of the adsorbate-substrate system is a favorable process in all six of the considered cases. It is interesting to notice that the interaction and the binding energies associated to the adsorption through the double CdC bond are about half of those concerning the adsorption through the fluorine atom.19 A simple model of nearest and next-nearest neighboring molecules has been adopted to quantify the lateral effects and to extrapolate the energies in the limit of an isolated adsorbed molecule, that is, when the lateral effects are negligible (see Appendix A). To develop the model, it has been assumed that the constants along na and mb can be neglected in the case of the (3 × 1) and (1 × 3) systems, respectively. In addition, the constants along (na, mb) have been considered only for the (1 × 1) cell. All the constants are summarized in Table 5. It is interesting to note the large value of the interaction constant ji1a which in turns gives rise to a big value for the corresponding binding constant jb1a. The large value of ji1a is attributable to the strong repulsion of the π electrons of the CdC double bond, and the quantity (8.47 kJ‚mol-1) is smaller than that concerning the adsorption on the rutile phase (i.e., 39.87 kJ‚mol-1).7 Such difference is due to the fact that the a vector of the anatase surface (3.741 Å) is bigger than that of the rutile one (2.995 Å), and then, the distance between two molecules increases for the adsorption on the anatase (101) surface. Considering all the 1a and 1b constants, it is interesting to notice that the direct lateral effects behave differently from the surface-mediated ones. In fact, the direct interaction and binding constants are stronger along the a direction than along the b one while the opposite occurs for the surface-mediated constants. The surface-mediated distortion constant is approximately equal for both the two directions. However, the constants referring to the molecule and the surface show a different behavior. In fact, the absolute value d,m d,s d,s of Jd,m 1a is bigger than that of J1b while J1a is smaller than J1b . This indicates that the relaxation of the molecule (surface) is obstructed more along the a (b) direction than along the b (a) one. The energies in the limit of an isolated adsorbed molecule are summarized in Table 6 and for completeness are compared with those concerning the rutile (110) surface.7,8 As it can be observed, the value associated to the adsorbate-substrate interaction is smaller than that referenced to the rutile one. This means that the adsorption on the anatase phase is weaker than that referenced to the rutile one. Vibrational Frequencies. The (2 × 2) system represents a good approximation for a model of low coverage, and hence it was used for the determination of the vibrational frequencies. Vinyl fluoride is a planar molecule with nine vibrations of A′ symmetry and three of A′′ symmetry. In Table 7 the calculated and experimental frequencies are reported along with an approximate description of the corresponding eigenvectors. The calculated frequencies have been scaled with the scaling factor equal to 0.9611 as determined for the adsorption on the rutile surface.7 Considering the isolated molecule as a reference, the influence of the direct lateral effects between the neighboring molecules can be isolated through the comparison with the frequencies obtained for the vinyl fluoride arranged in the free monolayer; the interaction between the molecule and the surface
Scaranto and Giorgianni TABLE 4: Interaction, Distortion, and Binding Energies (kJ‚mol-1) as a Function of the Periodicity (n × m)a θ EPint EP,mon dis EP,sur dis EPdis BEP ELint ELdis BEL ENint ENdis BEN
(1 × 1)
(1 × 2)
(1 × 3)
(2 × 1)
(3 × 1)
(2 × 2)
1 -19.37 4.35 3.77 8.12 -11.25 10.46 -1.85 8.61 -8.91 6.27 -2.64
1/2 -27.16 3.96 7.61 11.57 -15.59 8.70 -0.78 7.92 -18.46 10.79 -7.67
1/3 -29.95 4.25 8.51 12.76 -17.19 8.47 -0.62 7.85 -21.48 12.14 -9.34
1/2 -24.38 4.43 5.99 10.42 -13.96 2.51 -0.99 1.52 -21.87 9.43 -12.44
1/3 -27.65 5.00 7.36 12.36 -15.29 1.64 -0.79 0.85 -26.01 11.57 -14.44
1/4 -31.24 4.79 8.74 13.53 -17.71 1.09 -0.32 0.77 -30.15 13.21 -16.94
a The interaction and binding energies are corrected for the BSSE (see text). The superscripts P, L, and N mean periodic, lateral, and net, respectively. EP,mon (EP,sur dis dis ) is the distortion energy of the monolayer (surface).
TABLE 5: Direct and Surface-Mediated Constants (kJ‚mol-1)a ji jd jb Ji Jd,m Jd,s Jd Jb
1a
2a
1b
2b
1a,1b
8.47 -0.62 7.85 7.36 -1.41 -2.49 -3.90 3.46
0.86 -0.20 0.66 3.27 -0.57 -1.37 -1.94 1.33
1.64 -0.79 0.85 9.66 -0.65 -3.64 -4.29 5.37
0.23 -0.16 0.07 2.80 -0.29 -0.90 -1.19 1.61
0.17 -0.22 -0.05 0.46 0.38 -0.55 -0.17 0.29
a The superscripts i, d, and b mean interaction, distortion, and binding, respectively.
TABLE 6: Interaction, Distortion, and Binding Energies (kJ‚mol-1) in the Limit of an Isolated Adsorbed Moleculea Elim int lim Edis,m Elim dis,s Elim dis BElim
anatase (101)
rutile (110)8
-37.32 5.65 11.00 16.65 -20.67
-43.65b 7.30 14.51 21.81 -21.84
lim Edis,m (Elim dis,s) is the distortion energy associated to the molecule b (surface). Also from ref 7. a
can be evaluated by analyzing the shifts in the frequencies obtained for the adsorbed molecule. The symmetry classification of the vibrational modes was considered the same in both the interacting and non-interacting molecule as the molecular symmetry plane has been maintained during the optimization of the adsorbate-substrate system. The frequencies of the adsorbed CH2CHF molecule have been placed in correspondence of those of the isolated molecule on the basis of the eigenvectors of the normal modes. As it can be seen from Table 7, there is not too much difference between the frequencies referenced to the isolated molecule and those belonging to the free monolayer. Therefore, the shifts upon the adsorption can be mainly considered as due to the interaction of the molecule with the surface. The frequencies of the adsorbed molecule show that the modes above 1000 cm-1 shift toward lower wavenumbers, except for the ν2, and the largest differences correspond to the C-F and C-H stretchings. For the modes below 1000 cm-1 (νi, i ) 8-12) the most significant shifts concern the CH2 inplane and out-of-plane deformation consisting of a large redshift of the ν8 and a blue-shift of the ν11 vibrations, respectively.
CH2CHF Adsorption on the Anatase (101) Surface
J. Phys. Chem. C, Vol. 111, No. 29, 2007 11043
TABLE 7: Vibrational Frequencies (cm-1) of the CH2CHF Molecule Isolated and Adsorbed on the Anatase (101) Surfacea isolated
monolayer
adsorbed
band
symetry species
approximated description
exptlb
calcd
%
calcd
exptlc
calcd
%
ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12
A′ A′ A′ A′ A′ A′ A′ A′ A′ A′′ A′′ A′′
CH2 asymmetric stretch C-H stretch CH2 symmetric stretch CdC stretch CH2 deformation CdC-H planar deformation CsF stretch CH2 rock CdCsF planar deformation twist CH2 wag torsion
3140 3094 3049d 1655 1380 1305 1155 93223 48324 93023 862 711
3157 3082 3063 1670 1373 1289 1143 909 463 939 841 704
0.54 -0.39 0.46 0.91 -0.51 -1.23 -1.04 -2.47 -4.14 0.94 -2.44 -0.98
3158 3078 3060 1669 1372 1290 1143 908 463 939 841 704
3043 3125 2980 1642 1361 1297 1074; 1092e
3143 3155 3047 1656 1345 1284 1080 855 469 885 943 693
3.28 0.97 2.24 0.85 -1.21 -1.00 0.58;-1.07
a exptl and calcd indicate the experimental and calculated frequencies, respectively; the calculated frequencies have been scaled using a scaling factor equal to 0.9611. b Data from ref 22 when not otherwise specified. c Data from ref 6 referring to low coverage. d From a crystalline film.e The two experimental values refer to the adsorption on the two observed surface Lewis acid sites.
In particular, the attention has been focused on the modes above 1000 cm-1 as they give rise to absorptions which can be compared with the experimental spectra.6 As it can be seen, the adsorption affects the vibrational modes involving the CHF and the CH2 groups and the most significant aspects concern (1) the weakening of the C-F bond as a consequence of the interaction of the halogen atom with the surface Ti(5f), evident from the large red-shift of the C-F stretching (ν7); (2) the strengthening of the C-H bond in the CHF group which is apparent from the shift toward higher wavenumbers of the vibration related to the C-H stretch (ν2); and (3) the decrease of the strength of the C-H bonds in the CH2 group, originated by the formation of the H-bond with the surface O(2f) atom, which is deducible from the red-shift of the two vibrations (ν1 and ν3) attributed to the CH2 group. The reported shifts are generally in agreement with the variations of the structural parameters (see Table 2). Concerning the ν4, assigned to the CdC stretching, the small red-shift of this vibrational mode has not been attributed to a slight weakening of the corresponding bond length upon the adsorption. In fact, as it is known, the eigenvectors associated with the vibrations of the CH2CHF molecule are only approximatively described by the used annotations. The small shift of the CdC stretching toward lower wavenumbers was explained by considering that the related vibration is not a pure motion but a mixed one involving, to some extent, the vibrational mode corresponding to the C-F stretching. By the way, it is interesting to notice that the model with CH2CHF interacting with the surface Lewis acid site through the CdC double bond leads to a red-shift of about 35 cm-1 and a blue-shift of about 10 cm-1 for the ν4 and ν7 modes, respectively. From the comparison with the experimental frequencies (see Table 7), the vibrational frequencies of the simulated CH2CHFanatase (101) system well reproduce the behavior of the modes referring to the real system; that is, they shift toward lower or higher frequency at the same manner of the experimental data. As it is well-known, the magnitude of these shifts is affected by several conditions, for example, the method, the basis set, and the exchange-correlation functional, and then it is difficult to obtain the calculated values very close to the experimental ones. In particular, this can be seen for the C-H stretching referring to the presence of an H-bond. In fact, the largest percentage error, equal to about 3%, corresponds to the CH2 asymmetric stretch. However, it is interesting to notice that the simulated system reproduces quite well the large the red-shift observed for the ν7, the small one for the ν4 mode, and the influence on the C-H stretching vibrations. These characteristics
represent the main reasons for which the model describing the adsorption of CH2CHX through the halogen atom rather than the double CdC bond and the formation of an H-bond between the surface and one hydrogen of the CH2 group of the adsorbate has been formulated. It is then clear that the model formulated on the basis of the experimental data provides a good description for the adsorption of CH2CHX on the anatase (101) surface. Conclusions The adsorption of vinyl fluoride on the anatase (101) surface has been studied by periodic hybrid-exchange density functional theory. The surface has been modeled using a 30-atomic layers slab, and the adsorbate-substrate system has been simulated by considering an acid-base interaction between the fluorine atom and the surface Lewis acid site and an H-bond between the CH2 group and the surface Lewis basic site according to the infrared spectra.6 The computation has been performed by employing different surface coverages and periodicities, and the energetics have been investigated in terms of interaction, distortion, and binding energies. The formation of the adsorbate-substrate system is always a favorable process. The energies in the limit of an isolated adsorbed molecule have been evaluated by using a simple model of nearest and next-nearest neighbors. The obtained energies are smaller than those obtained for the adsorption on the rutile (110) surface. The adsorption causes significant shifts for most of the vibrational modes, in particular for the C-F stretching one. In general, the computed vibrational frequencies have been found in good agreement with the available experimental results, and therefore the model employed provides a good description for the adsorption of vinyl fluoride on the anatase (101) surface. Acknowledgment. Financial support by PRIN 2005 funds (project: “Trasferimenti di energia e carica a livello molecolare”) is gratefully acknowledged. Appendix A: Nearest and Next-Nearest Neighboring Molecules Model By using this model it is possible to subdivide the lateral effects in direct and surface-mediated interaction, distortion, and binding constants as follows. The direct (ji) and surface-mediated (Ji) interaction constants are given respectively by i ELint ) jina + jimb + 2jna,mb
(A.1)
11044 J. Phys. Chem. C, Vol. 111, No. 29, 2007
Scaranto and Giorgianni
and i i i EPint ) Elim int + (Jna + Jmb + 2Jna,mb)
(A.2)
where Elim int is the interaction energy in the limit of an isolated adsorbed molecule. The interaction constants are labeled such that jina (Jina) and jimb (Jimb) are the interaction energies between a molecule and another molecule which is placed in a site separated from the previous one solely by na and mb, i i (Jna,mb ) denotes the diagonal constant, that respectively; jna,mb is, the interaction energy between two molecules separated by the vector (na, mb). A positive (negative) value of ji and Ji means that there is repulsion (attraction) between the two molecules. In analogy with the interaction constants, the direct distortion, jd, and binding, jb, constants are respectively d ELdis ) jdna + jdmb + 2jna,mb
(A.3)
b BEL ) jbna + jbmb + 2jna,mb
(A.4)
Finally, the surface-mediated distortion, Jd, and binding, Jb, constants are respectively d d d EPdis ) Elim dis + (Jna + Jmb + 2Jna,mb)
(A.5)
b ) BEP ) BElim + (Jbna + Jbmb + 2Jna,mb
(A.6)
lim are the distortion and binding energies in where Elim dis and BE the limit of an isolated adsorbed molecule, respectively. Elim dis can be subdivided into the contribution due to the lim distortion of the molecule, Elim dis,m, and of the surface, Edis,s, as follows:
d,m d,m d,m ) Elim EP,mon dis dis,m + (Jna + Jmb + 2Jna,mb)
and lim d,s d,s d,s EP,sur dis ) Edis,s + (Jna + Jmb + 2Jna,mb)
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