ARTICLE pubs.acs.org/JPCC
A Model DMMP/TiO2 (110) Intermolecular Potential Energy Function Developed from ab Initio Calculations Li Yang,† Ramona Taylor,‡ Wibe A. de Jong,§ and William L. Hase*,† †
Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States Spectral Sciences, Incorporated, 4 Fourth Avenue, Burlington, Massachusetts 01803-3304, United States § EMSL, Pacific Northwest National Laboratory, Richland, Washington 99352, United States ‡
ABSTRACT: A hierarchy of electronic structure calculations, scalings, and fittings were used to develop an analytic intermolecular potential for dimethyl methylphosphonate (DMMP) interacting with the TiO2 rutile (110) surface. The MP2/aug-cc-pVDZ (6-311þG** for Ti) level of theory, with basis set superposition error (BSSE) corrections, was used to calculate multiple intermolecular potential curves between TiO5H6 as a model for the Ti and O atoms of the TiO2 surface, and CH3OH and OdP(CH3)(OH)2 as models for different types of atoms comprising DMMP. Each intermolecular potential energy emphasized a particular atomatom interaction, and the curves were fit simultaneously by a sum of two-body potentials between the atoms of the two interacting molecules. The resulting analytic intermolecular potential gives DMMP/TiO5H6 potential curves in excellent agreement with those calculated using MP2/ aug-cc-pVDZ (6-311þG** for Ti) theory. MP2 theory with the smaller basis set, 6-31þþG** (6-31G** for Ti), gives DMMP/TiO5H6 potential energy curves similar to those found using MP2/aug-cc-pVDZ (6-311þG** for Ti), suggesting the smaller basis set may be used to describe DMMP interactions with larger cluster models of the TiO2 surface. The TiO5H6 cluster does not model either the 6-fold coordinated Ti atoms or the bridging O atoms of the TiO2 (110) surface, and to also model these atoms MP2/6-31þþG** (6-31G** for Ti) theory was used to calculate potential energy curves for DMMP interacting with the larger Ti3O13H14 cluster and much large cluster Ti11O40H36 cluster. The two-body potential energy curves for DMMP/TiO5H6 were scaled to fit both the DMMP/Ti3O13H14 and DMMP/Ti11O40H36 potential energy curves. The resulting parameters for the 5- and 6-fold coordinated Ti atoms and bridging and bulk O atoms were used to develop an analytic intermolecular potential for DMMP interacting with rutile TiO2 (110).
I. INTRODUCTION Understanding the destruction of organophosphorus compounds is of importance for devising new methods for the protection of persons exposed to chemical warfare agents (CWAs).17 Because of the highly toxic nature of nerve agents such as sarin and soman, research conducted at academic institutions has concentrated on benign analogues of these agents. Dimethyl methylphosphonate (DMMP)712 is widely used as a chemical warfare agent surrogate because it is much less toxic and possesses the necessary elemental composition to mimic nerve agents. The use of DMMP can provide a good measure for monitoring the effectiveness of methods to degrade CWAs. A recent study investigated pathways for DMMP decomposition in the gas phase.13 An important research area for CWA decomposition is catalytic oxidation using metals and metal oxides. Metal oxides such as MgO,14 Al2O3,1517 ZnO,18 CaO,19 TiO2,20 and RFe2O321 have been considered as destructive adsorbents for the decontamination of CWAs. Among these systems, titanium dioxides have been shown to be an effective catalyst for the degradation of a large number of organic and inorganic compounds in both aqueous solution and the gas phase. The TiO2 rutile surface, the most thermodynamically stable TiO2 surface, is particularly effective for this degradation. A number r 2011 American Chemical Society
of experimental studies have examined the reaction of gasphase DMMP with TiO2 and the DMMPTiO2 surface interaction.2225 The DMMP molecule interacts through the electron-rich phosphoryl oxygen with surface-bound hydroxyl groups and with Lewis acid sites of the TiO2 by donating a lone pair of electrons to the Tinþ (n = 3, 4).22 There have been a number of theoretical studies of molecular interactions on the surface of TiO2 such as O(3P)TiO2,26 O2TiO2,27 H2OTiO2,26,2833 CH3OHTiO2,28 NH3TiO2,34 pyridineTiO2,35 peptideTiO2,36 poly(ethylene oxide)TiO2,37 catecholTiO2,33,38 and lipidTiO2,39 which have provided detailed insight concerning the adsorption and decomposition processes. It is important to understand the influence of the TiO2 surface structure on DMMP structural and conformational properties and investigate different adsorption and decomposition mechanisms of DMMP on the TiO2 surface. To the best of our knowledge, there are no theoretical investigations of the interaction of DMMP on TiO2 (110). Because of the Received: November 24, 2010 Revised: May 10, 2011 Published: June 02, 2011 12403
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Figure 2. Chemical structure of the large cluster Ti11O40H36.
Figure 1. Chemical structure of DMMP, the molecules OdP(CH3)(OH)2 and CH3OH used to develop the potential, the small cluster model TiO5H6, and larger cluster model Ti3O13H14. P, O, C, H, and Ti are yellow, red, blue, white, and orange, respectively.
large dimensions of the DMMP/TiO2 surface system, fully ab initio and even semiempirical quantum mechanical modeling of such systems is very challenging. Therefore, other theoretical methods, such as the use of force fields which allow largescale simulations for the DMMP/TiO2 system, become important. An accurate prediction of the strength of the DMMPTiO2 interaction is important for a realistic representation of DMMP structural and dynamic properties in the proximity of TiO2 surface. The focus of the work presented here is to develop an analytical function which gives accurate potentials for DMMP interacting with the TiO2 rutile surface. As was done in previous studies,4042 ab initio calculations were performed for molecules, which represent atoms and functional groups of DMMP, interacting with the Ti(OH)4H2O cluster model for the TiO2 rutile surface. Ab initio intermolecular potentials, calculated for these molecules interacting with Ti(OH)4H2O, were fit with pairwise two-body interactions to derive potentials for the atoms of DMMP interacting with the atoms of the TiO2 surface. The accuracy of the derived potentials was tested by calculating ab initio potential energy curves for DMMP interacting with the larger Ti3O13H14 and Ti11O40H36 clusters. The resulting DMMP/ Ti3O13H14 and DMMP/Ti11O40H36 potentials were then used, in concert with the DMMP/Ti(OH)4H2O potentials, to develop a potential for DMMP interacting with the TiO2 (110) surface.
II. MOLECULAR MODELS AND ELECTRONIC STRUCTURE THEORY METHODS Since accurate ab initio calculations for DMMP interacting with a large atomistic model of the TiO2 (110) surface are prohibitively expensive, the DMMP/TiO2(s) intermolecular interactions were studied using smaller representative model systems. As was done in previous work,36,37 the TiO5H6 cluster (structure is given in Figure 1) was chosen to model the atoms of the TiO2 (110) surface. The relative positions between the Ti and O atoms were fixed to those for the rutile crystal.43 Hydrogen atoms were added to the TiO5 cluster along the directions of the OTi bonds in the rutile TiO2 crystal to fill the valency. The OH bond length was fixed to 0.97 Å.36 To develop an analytic potential energy function for DMMP interacting with TiO2 (110), it was assumed that DMMP (Figure 1) has six different types of atoms, i.e., C(P), C(O), H, O, =O, and P. Two molecules, CH3OH and OdP(CH3)(OH)2 (Figure 1), were used to model the interactions of these six atoms with the Ti and O atoms of TiO2 (110). The H, C(O), and O atoms were represented by CH3OH and the C(P), P, and =O atoms by OdP(CH3)(OH)2. MP2/aug-cc-pVDZ44,45 geometries were used for CH3OH and OdP(CH3)(OH)2. Potential energy curves for CH3OH and OdP(CH3)(OH)2 interacting with the TiO5H6 cluster were calculated using MP2 theory and a mixed basis set, i.e., 6-311þG**46 for the Ti atom and aug-cc-pVDZ for the P, C, O, and H atoms. The structures for CH3OH and OdP(CH3)(OH)2 were fixed for these calculations and set to their optimized MP2/ aug-cc-pVDZ geometries. As described in the next section, parameters for the analytic intermolecular potential energy function were determined by fitting these potential energy curves. To test the derived intermolecular potential energy function, the potential energies it gives for DMMP binding to the TiO5H6 cluster, to the Ti3O13H14 cluster (Figure 1), and to the much larger Ti11O40H36 cluster (Figure 2) were compared with those obtained from electronic structure theory calculations. The DMMP/ TiO5H6 binding potential energy was calculated with the same method as above, i.e., MP2/aug-cc-pVDZ (6-311þG** for Ti). The use of MP2 and the large basis set is prohibitively expensive for the very large DMMP/Ti11O40H36 system. Thus, MP2 calculations were performed for DMMP/TiO5H6 with the smaller basis set of 6-31G**47 for Ti and 6-31þþG**48 for P, C, O, and H to assess 12404
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Figure 3. Potential energy curves for the orientations AJ for CH3OH/TiO5H6. The lines are the fitted curves, and the points are the MP2/aug-ccpVDZ (6-311þG** for Ti) ab initio potential energies, with BSSE corrections. The potential energies are in kcal/mol, and the bond distance is in Å. 12405
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Table 1. Fitted Parameters for CH3OH/TiO5H6 Potential Energy Curvesa XYb
A
B
C
D
n
m
CTi
758 897
4.950 67
179.963
405.566
6
14
OTi H(C)Ti
619 910 565.289
4.932 73 5.499 63
2629.68 300.421
566.778 141.524
5 6
9 13
H(O)Ti
626 112
4.971 57
751.051
943.969
4
COs
147 941
3.947 32
223.945
OOs
649 227
4.395 21
281.188
206.696
V0
orientation
ab initio
fitted
ab initio
fitted
12
A
3.22
6
10
4
13
B C
3.40 3.49
3.15
20.35
20.01
3.30 3.79
1.18 0.92
1.26 0.80
D
5.06
4.98
0.58
0.84
15
E
3.83
3.83
1.37
1.26
CH3OH/TiO5H6
H(C)Os
7725.14
3.517 85
145.932
27934.2
5.430 67
246.648
883.013
181.172
752.608
4
12
F
4.35
4.44
0.82
0.57
73.8192 707.906
6 5
14 10
G
4.48
4.41
4.74
5.09
O Hs
518.003
5.444 14
H(C)Hs H(O)Hs
448.358 7209.31
5.497 20 3.743 61
84.3673 565.889
6
309.851
OO(H2)
b
R0
CHs
CO(H2)
a
1409.02
Table 2. Minima for the ab Initio and Fitted Potential Energy Curvesa
6
6
483.355
5
H(C)O(H2)
200.335
5
H(O)O(H2)
490.759
5
S1
0.634 28
S2
1.299 77 1
1
n
1
Units: A, kcal mol ; B, Å ; C, kcal Å mol ; D, kcal Å X is an atom of CH3OH and Y an atom of TiO5H6.
m
I
5.63
5.46
4.95
4.89
J
5.92
5.92
0.30
0.43
A B
3.64 3.20
3.64 3.20
2.38 1.87
3.09 1.56
C
4.77
4.72
19.99
19.73
D
4.01
4.09
1.10
0.85
E
4.23
4.16
4.21
4.51
F
6.67
6.67
0.33
0.35
OdP(CH3)(OH)2/TiO5H6
1
mol .
its accuracy. The DMMP/Ti3O13H14 and DMMP/Ti11O40H36 binding potential energies were calculated using MP2/631þþG** (6-31G** for Ti). As for the TiO5H6 cluster, the relative positions between the Ti and O atoms of the Ti3O13H14 and Ti11O40H36 clusters were fixed to those for the rutile crystal. For the Ti3O13H14 cluster the H atoms were added along the directions of the OTi bonds in the rutile crystal, as described above for the TiO5H6 cluster. Given the complexity of the Ti11O40H36 cluster, the positions of the H atoms were optimized with the positions of the Ti and O atoms fixed. The structure for DMMP was fixed at its MP2/ aug-cc-pVDZ geometry. Calculations were performed that did and did not include a correction for the basis set superposition error (BSSE), using the counterpoise (CP) method.49,50 Including the BSSE correction decreases the depths of the potential minima and shifts them to greater atomatom separations. The largest shift in atomatom separation is only 0.28 Å. However, the differences in the potential energy minima with and without BSSE correction vary from 0.31 to 4.45 kcal/mol, which illustrate the importance of including the BSSE correction in calculating the potential energy curves. The BSSE correction was included in all the electronic structure theory calculations reported here. The calculations for the TiO5H6 and Ti3O13H14 cluster systems were carried out with the Gaussian 03 package.51 The calculations for the DMMP/Ti11O40H36 system were particularly computationally demanding and were performed with the highly parallel NWChem 6.0 software package.52 The structures of the TiO5H6, Ti3O13H14, and Ti11O40H36 clusters were fixed as described above, and the structures of CH3OH, OdP(CH3)(OH)2, and DMMP were fixed at their MP2/aug-cc-pVDZ geometries.
III. RESULTS OF THE ELECTRONIC STRUCTURE CALCULATIONS AND FITTING THE POTENTIAL ENERGY FUNCTION The procedure used here to develop the analytic intermolecular potential for DMMP interacting with TiO2 (110) is the
a
R0 is in units of Å and V0 in kcal/mol.
same as that used previously to develop potentials for projectile peptide ions colliding with organic surfaces.4042 Model molecules are used to represent atoms of the surface, and similarly, different molecules are used as models for the different types of atoms and functional groups comprising the projectile. Intermolecular potential energy curves are calculated for different relative orientations of the surface and projectile model molecules, which emphasize the different atomatom interactions between the surface and projectile. As described in the following, the curves for the different orientations of a particular system are fit simultaneously to determine potential parameters. A. CH3OH þ TiO5H6 System. 1. Electronic Structure Calculations. For the CH3OHTiO5H6 system, 10 orientations focusing on different atomatom interactions were considered as shown in Figure 3. The different orientations are identified as AJ. Potential energy curves were calculated for each atom of CH3OH approaching the Ti atom of TiO5H6 along the TiO(H2) bond axis in four different orientations: A, the O atom approaches Ti along a line bisecting the COH(O) angle; B, the C atom of CH3OH approaches Ti with collinear OC and TiO axes; and C and D, the orientations are similar to B except a H(C) or a H(O) of CH3OH approaches Ti. For the interactions between the atoms of CH3OH and one of the four surface oxygen atoms (Os) of TiO5H6, similar respective orientations E, F, G, and H were considered as AD above. For the pseudohydrogens (Hs) of the surface, two orientations focusing on O(H)Hs, I, and H(C)Hs, J, were considered. Interaction terms for the Hs atoms are unnecessary to model DMMP binding with TiO2 (110), but they must be included to derive accurate atomatom potential terms for CH3OH/ TiO5H6. The structures of CH3OH and TiO5H6 were held fixed as described in section II for the calculating the potential energy curves. 12406
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Figure 4. Potential energy curves for the orientations AF for OdP(CH3)(OH)2/TiO5H6. The lines are the fitted curves, and the points are the MP2/ aug-cc-pVDZ (6-311þG** for Ti) ab initio potential energies, with BSSE corrections. The potential energies are in kcal/mol, and the bond distance is in Å.
2. Potential Fitting. The 10 potential energy curves in Figure 3 were fit simultaneously with a sum of two-body interactions between the atoms of CH3OH and TiO5H6. The H2O group, attached to the Ti atom from “below”, was treated as a united atom. The interactions between the C, O, H(C), and H(O) atoms of CH3OH and the surface Ti, O atoms (Os), and pseudohydrogens (Hs) are represented by Vxy ¼ Axy expðBxy rÞ þ Cxy =r n þ Dxy =r m
ð1Þ
where the Dxy/rm term is added to the Buckingham potential to provide additional flexibility in the fitting. The single term Vxy ¼ Cxy =r n
ð2Þ
was used to describe the interactions of each atom of CH3OH with the H2O united atom. The fitting was done by a genetic algorithm that performs a global search within the feasible region. For the fitting, the parameters were restricted to physically meaningful values. 12407
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Table 3. Fitted Parameters for OdP(CH3)(OH)2 Potential Energy Curvesa XYb
a
A
B
PTi
529 710
3.277 54
O(P)Ti C(P) Ti
697 502 312 809
4.866 86 4.845 05
C
D
n
m
11782.6
1352.58
6
8
5972.95 2024.88
1498.74 1387.47
6 6
7 12
POs
31108.9
5.411 58
4124.90
O(P)Os
110 841
4.026 55
1477.84
842.053 1202.72
5
13
6
12
C(P) Os
365 601
5.378 13
1298.70
6
10
PHs
209 868
5.384 07
199.118
1476.40
6
7
O(P)Hs
214 163
4.363 06
127.397
1475.80
6
8
C(P) Hs
838 120
5.248 30
446.398
6
7
720.460
629.648
PO(H2) O(P)O(H2)
299.733 170.458
5 6
C(P)O(H2)
293.162
5
Units: A, kcal mol1; B, Å1; C, kcal Ån mol1; D, kcal Åm mol1. b X is an atom of OdP(CH3)(OH)2 and Y an atom of TiO5H6.
In fitting the parameters, it was found that the H atoms for the four TiOH units do not have the same interaction potentials, which arises from a greater Mulliken charge of 0.29 |e| for two of the Hs atoms as compared to the value of 0.17 |e| for the other two. The two H atoms with the large charge are those directed closely toward the O atom of the adjacent TiOH unit (see Figure 1). The OTiO valence angles are 81.2° for these two H atoms, while 98.8° for the other two H atoms. Both pairs of Hs atoms were fit with the same two-body potential for interaction with an atom of CH3OH. However, the potential for the two atoms with the smaller charge was multiplied by a scale factor S1 in the fitting. The same scale factor was used for the interactions of these two Hs atoms with all four atom types in CH3OH. The Mulliken charges are very similar for the Os atoms of the four TiOH units. A similar approach was used to represent differences in the O-H interactions, which arise from a 1.0 charge for the O atoms of the TiOH units and a 0.5 charge for the O atom of CH3OH. Thus, the (O)H--Os interaction is not the same as that for O--Hs. Both of these interactions were fit by the same twobody function, but the O--Hs potential for the pair of Hs atoms with the larger Mulliken charge was scaled by the factor S2 to give the (O)H--Os potential. The fits to the ab initio potential energy curves are shown in Figure 3, with the fitted parameters listed in Table 1. The parameter m was required to be larger than n, and the values for n range from 4 to 6, as found in previous work.4345 The parameter n was allowed to assume any value and could have become ∼1, with m ∼ 6, which is the form of the standard Buckingham potential with an electrostatic term included. However, the fitting did not converge to such a form and instead converged to n = 46 with a larger value for m to more accurately describe the repulsive region of the potential. It is of interest that the S1 and S2 scale factors have fitted values consistent with the different interactions identified by the Mulliken charges. The value for S1 = 0.63 is very similar to the ratio of charges 0.17/0.29 = 0.59 for the two different Hs atoms. For the (O)H--Os interaction the product of charges is 0.19 (1.0), and for the O atom of CH3OH interacting with the most charged Hs-atom the product of charges is 0.29 (0.5). The ratio 0.19 (1.0)/[ 0.29 (0.5)]
Figure 5. Comparison of the analytic function and (]) MP2/aug-ccpVDZ (6-311þG** for Ti) ab initio potential energy curves for two orientations of DMMP/TiO5H6.
equals 1.31 and is very similar to the fitting term S2 = 1.30. The fitting was not forced to fit these charge ratios, and though the fitting does not converge to electrostatic potentials, it is of interest that the charges describe relative interaction strengths. R0 and V0 values, where R0 and V0 stand for the equilibrium distance and its corresponding potential energy, were calculated for both the fitted and ab initio potential energy curves and are compared in Table 2. The fitted values of R0 values are less than 0.1 Å different from the ab initio values for most of the curves, except for orientations C and I, with differences of 0.30 and 0.17 Å, respectively. The V0 values are in overall very good agreement with the ab initio values, differing by less than 0.35 kcal/mol. B. OdP(CH3)(OH)2 þ TiO5H6 System. 1. Electronic Structure Calculations. Six different orientations for the OdP(CH3)(OH)2/TiO5H6 system were considered as shown in Figure 4. OdP(CH3)(OH)2 was fixed in its optimized geometry, and TiO5H6 was fixed in a geometry representative of the TiO2 (110) surface structure as described above. Three orientations A, B, and C were considered which emphasize respectively the PTi, CTi, and O(P)Ti interactions between OdP(CH3)(OH)2 and TiO5H6. Similarly, the three D, E, and F orientations were considered to emphasize the respective interactions between the phosphoryl oxygen, phosphorus, and carbon atoms of Od P(CH3)(OH)2 and the Os atom of the surface. The potential energy curves were calculated using MP2 theory, with the 6-311þG** basis set for Ti and the aug-cc-pVDZ basis set for P, C, O, and H, and are shown in Figure 4. The structures of OdP(CH3)(OH)2 and TiO5H6 were held fixed, as described in section II, for calculating the potential energy curves. 2. Potential Fitting. In order to retain consistency with the potential parameters obtained from the above fitting for the CH3OH þ TiO5H6 system, the interaction potentials between the H(C), O(H), and H(O) atoms of OdP(CH3)(OH)2 and the atoms of TiO5H6 were assumed to be the same as those 12408
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Figure 6. Optimized ab initio geometries for DMMP-TiO5H6, MP2/ aug-cc-pVDZ (6-311þG** for Ti), and DMMP-Ti3O13H14, MP2/631þþG** (6-31G** for Ti), with the structures of DMMP and the clusters fixed as described in section II.
Figure 8. Two orientations used to calculate the DMMP/Ti11O40H36 and DMMP/TiO2 potential energies and the comparison of analytic function energy curves with the MP2/6-31þþG** (6-31G** for Ti) ab initio potential energy points (]) for two orientations of DMMPTi11O40H36.
Figure 7. Comparison of analytic function potential energy curves with the MP2/6-31þþG** (6-31G** for Ti) ab initio potential energy curves (]) for two orientations of DMMPTi3O13H14. The red dashed line is for the analytic function derived from the ab initio calculations for the DMMPTiO5H6 system. The black solid line is for the scaled analytic function.
determined for the CH3OH þ TiO5H6 system. The Mulliken charges of the H(C), O(H), and H(O) atoms are very similar for CH3OH [0.31, 0.50, 0.19, respectively] and OdP(CH3)(OH)2 [0.31, 0.55, 0.17, respectively], supporting the use of this fitting procedure. With this model for the fitting, only the interactions between the P, C(P), and O(P) atoms of OdP(CH3)(OH)2 and the atoms of TiO5H6 needed to be fit, which reduced the number of fitting parameters. In fitting the interactions with the Hs atoms of TiO5H6, the same scale factor as above, S1 = 0.63, was used to represent the interactions with the two different types of Hs atoms. The ab initio potential energy curves for the six orientations were fit simultaneously, and the resulting fits are shown in Figure 4. The fitted parameters are listed in Table 3. The values of R0 and V0 for the six potential energy curves, determined from these fits, are listed in Table 2 where they are compared with the
ab initio values. Their potential minima are in good agreement with the differences for V0, ranging from 0.02 to 0.71 kcal/mol. The R0 values differ by less than 0.08 Å. C. Analysis of the Analytic Intermolecular Potential Function. The intermolecular potential energy function developed above was tested by using it to calculate potential energy curves for DMMP interacting with the TiO5H6 and Ti3O13H14 clusters and with the much larger Ti11O40H36 cluster and comparing these curves with those determined from ab initio calculations. These analyses are given in the following. 1. DMMP þ TiO5H6. Two potential energy curves were analyzed for DMMP interacting with TiO5H6. The structures of both DMMP and TiO5H6 were fixed as described in section II. Both potential curves were calculated versus the separation between the P atom of DMMP and the Ti atom of TiO5H6. One curve emphasizes the strongest interaction between DMMP and TiO5H6 and is along the collinear PdO and TiO(H2) axis. A less attractive interaction is considered for the second potential energy curve. The orientations of DMMP with respect to TiO5H6 for the two potential energy curves are illustrated in Figure 5. Ab initio potential curves were calculated using MP2/ aug-cc-pVDZ (6-311þG** for Ti) and shown in Figure 5, where they are compared with the curves determined from the fitted analytic potential energy function; R is the TiP distance. For each orientation the ab initio and analytic potential energy curves are in very good agreement with similar V0 and R0 values. For the most attractive orientation V0 and R0 are 21.8 kcal/mol and 3.59 Å for the ab initio curve and 23.1 kcal/mol and 3.57 Å for the analytic potential energy curve. For the other orientation the ab initio V0 and R0 are 2.21 kcal/mol and 5.75 Å, and the analytic function’s values are 1.47 kcal/mol and 5.56 Å. For an additional comparison between the ab initio and fitted energies, the ab initio DMMP/TiO5H6 geometry was optimized with the structures of DMMP and TiO5H6 fixed. The resulting optimized structure, shown in Figure 6, has V0 and R0 values 12409
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Table 4. Two-Body Potential Energy Parameters for DMMP/TiO2 (110)a DMMP atoms
A
B
C
D
n
m
Parameters for 5-fold Ti P
730 999
3.277 54
16259.9
1866.56
6
8
O(P) O(C)
830 027 737 693
4.866 86 4.932 73
7107.81 3129.32
1783.50 674.466
6 5
7 9
C(P)
372 242
4.845 05
2409.61
1651.09
6
12
C(O)
903 087
4.950 67
214.156
482.623
6
14
H(C)
780.099
5.499 63
414.581
195.303
6
13
Parameters for 6-fold Ti P
599 419
3.277 54
13333.2
1530.58
6
8
O(P)
680 622
4.866 86
5828.40
1462.47
6
7
O(C)
604 908
4.932 73
2566.04
553.062
5
9
C(P) C(O)
305 239 740 531
4.845 05 4.950 67
1975.88 175.608
1353.89 395.751
6 6
12 14
H(C)
639.681
5.499 63
339.956
160.149
6
13
Parameters for Bridging O P
54418.8
5.411 58
7215.69
1473.00
5
13
O(P)
224 852
4.026 55
2997.95
2439.84
6
12
O(C)
1 317 022
4.395 21
C(P)
741 658
5.378 13
2634.54
C(O) H(C)
258 793 13513.6
3.947 32 3.517 85
2464.80 255.279
P
37019.6
5.411 58
4908.63
1002.04
5
13
O(P)
152 961
4.026 55
2039.42
1659.75
6
12
O(C)
895 933
4.395 21
285.240
4
13
C(P)
504 529
5.378 13
1792.21
994.235
6
10
C(O)
176 049
3.947 32
1676.73
266.495
6
10
H(C)
9192.92
3.517 85
570.418
419.304 1461.53 391.747
4
13
6
10
6 6
10
Parameters for Bulk O
a
388.039
173.659
6
Units: A, kcal mol1; B, Å1; C, kcal Ån mol1; D, kcal Åm mol1.
of 22.4 kcal/mol and 3.53 Å. The fitted analytic potential gives V0 = 24.4 kcal/mol for this structure, which is in good agreement with the ab initio value. The analytic potential energy function correctly represents the ab initio potential energy between DMMP and TiO5H6. The 6-311þG** for Ti, aug-cc-pVDZ for P, C, O, H basis set is prohibitively expensive for studying the interaction between DMMP and a much larger cluster model for the TiO2 (110) surface. To investigate the accuracy of using a smaller basis set, the above potential energy curve for the most attractive orientation was also calculated using the 6-31G** for Ti and 6-31þþG** for P, C, O, H basis set with the MP2 theory. A complete potential energy curve was not calculated with the small basis set, and only several points were calculated near the potential energy minimum to establish values for V0 and R0. With the smaller basis set the V0 and R0 values found are 19.9 kcal/mol and 3.63 Å. The MP2 value for V0 with the small basis set is only 2 kcal/mol different than V0 = 21.8 kcal/mol for the large basis set, and R0 is similar to the large basis set value of 3.59 Å, suggesting that the small basis set may be used to study DMMP interactions with much larger cluster models of TiO2 (110). 2. DMMP þ Ti3O13H14. The TiO5H6 cluster model represents the 5-fold coordinated Ti atoms and surface O atoms for the
TiO2 (110) surface. The above analysis shows that the analytic function, whose development is based on this cluster model, provides a good representation of the intermolecular potential between DMMP and TiO5H6. However, the TiO2 (110) surface also has 6-fold coordinated Ti atoms and bridging O atoms, and the analytic potential must also describe DMMP interacting with these atoms. This was tested by calculating ab initio potential energy curves for DMMP interacting with the Ti3O13H14 and Ti11O40H36 clusters. The results for the latter cluster are given in the next section. Potential energy curves were calculated for the DMMP/ Ti3O13H14 system, at the MP2/6-31þþG** (6-31G** for Ti) level of theory, for the two orientations shown in Figure 7. Orientations I and II were chosen to emphasize attractive and repulsive interactions, respectively, between DMMP and the cluster. The structures of DMMP and Ti3O13H14 were fixed, as described in section II, for calculating the potential energy curves. For orientation I, the double bond O atom of DMMP approaches the 5-coordinated Ti-atom, with collinear PO and TiO axes to enhance the O(P)Ti interaction. For orientation II, the P atom approaches above one of the 6-coordinated Ti atoms, with O(P) approaching above the middle bridging O atom and a methoxy O atom approaching above a side bridging O atom. The MP2/6-31þþG** (6-31G** for Ti) potential energy curves for these two orientations are shown in Figure 7. Orientation I has a well depth of 34.2 kcal/mol at a TiO(P) distance of 3.59 Å. For orientation II the potential curve is purely repulsive. Potential energy curves were determined using the analytic intermolecular potential energy function for these two orientations (see Figure 7). The resulting values of V0 and R0 for orientation I are 34.6 kcal/mol and 3.51 Å, which are in excellent agreement with the above MP2 values. However, the analytic potential energy for orientation II is not purely repulsive and, instead, has a potential minimum of 5.06 kcal/mol at TiP of 6.46 Å. Thus, the analytic potential energy function does not represent the ab initio potential energy curve for orientation II. Different approaches were used to scale the analytic potential energy function so that it would fit the MP2 potential energy curve for orientation II, while retaining the excellent fit for orientation I. A successful scaling approach was to retain the two-body potential energy terms developed for the Ti and O atoms of TiO5H6 as representations for the five-coordinated Ti atoms and surface O atoms of Ti3O13H14 but to scale these terms by STi6 and SOb, respectively, to obtain different potential energy terms for the 6-fold coordinated Ti atoms and bridging O atoms. In addition, it was necessary to scale all the two-body interactions for the H atoms of TiO5H6 by the scale factor SH to represent the interactions for the H atoms of Ti3O13H14 interacting with DMMP. Also, all the repulsive and attractive terms in the twobody interactions for DMMP/TiO5H6 were scaled by Srep and Satt, respectively, to establish these terms for DMMP/Ti3O13H14. The resulting fitted scale factors are STi6 = 0.817, SOb =1.469, SH = 0.502, Satt = 1.194, and Srep = 1.383. Figure 7 shows that with this scaled potential the excellent fit to the MP2 potential curve for orientation I is retained and the fit to the MP2 curve for orientation II is much improved. It should be noted that the above value for SH is similar to the S1 scale factor determined for the DMMP (see section III.A.2). For orientation I the scaled analytic potential’s values of V0 and R0 are 32.0 kcal/mol and 3.57 Å, in comparison to the ab initio values of 34.2 kcal/mol and 3.59 Å. For an additional comparison of the ab initio and fitted potentials, the DMMP/Ti3O13H14 12410
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Figure 9. Potential energy curves for DMMP interacting with the TiO2(110) surface for orientations I and II (see Figure 8). The curves are for the analytic intermolecular potential, with parameters in Table 4. The form of the atomistic model for the TiO2(110) surface is also depicted. The actual model used for the surface is twice as wide, with respect to the rows of Ti atoms, and 1.6 times longer. A surface of this size was needed to converge the calculated DMMP/TiO2 (110) potential energy.
geometry was optimized with the structures of DMMP and Ti3O13H14 fixed as described in section II. The resulting optimized structure is shown in Figure 6. Its R0, TiP, and V0 values are 3.48 Å and 39.7 kcal/mol. For comparison, the fitted analytic potential gives a similar V0 value of 34.3 kcal/mol for the ab initio optimized geometry. It is of interest that this optimized potential energy minimum for DMMP/Ti3O13H14 is substantially deeper than the value of 22.4 kcal/mol found for DMMP/TiO5H6 (section III.C.1). The scaled analytic potential energy function provides a good representation of the ab initio potential energy between DMMP and Ti3O13H14. 3. DMMP þ Ti11O40H36. The above analysis shows that the scaled analytic potential energy function fits MP2 potential energy curves for the DMMP/Ti3O13H14 system. It is of both interest and importance to determine whether the scaled potential also fits MP2 potential energies for the much larger DMMP/ Ti11O40H36 system. Two orientations were considered as shown in Figure 8. For orientation I, the double bond O atom of DMMP approaches the middle Ti atom along the TiO axis, and at the same time, one of the methoxy O atoms of DMMP approaches another Ti atom. Thus, both the O(P)Ti and O(C)Ti interactions are emphasized. For orientation II, the double bond
O atom of DMMP approaches the middle Ti atom with collinear PO and TiO axes and only the O(P)Ti interaction is emphasized. Using MP2/6-31þþG** (6-31G** for Ti) for such a big system is very computationally expensive, and thus, for these two orientations the complete MP2 potential energy curves were not calculated. Instead, only points near R0 were determined as shown in Figure 8. The MP2 potential minima for orientations I and II have similar TiO(P) distances of 2.39 and 2.44 Å, respectively. Orientation I has a well depth of 29.4 kcal/mol, which is deeper than that of orientation II, whose well depth is 19.5 kcal/mol. Potential energy curves were determined using the scaled analytic intermolecular potential energy function for these two orientations as shown in Figure 8. The resulting values of R0 and V0 are 2.42 Å and 31.3 kcal/mol for orientation I and 2.60 Å and 18.7 kcal/mol for orientation II. Thus, the scaled analytic potential function gives a very good representation of the MP2 potential for both orientations I and II of the DMMP/ Ti11O40H36 system. It is of interest to identify the role of the two-body potential terms for the H atoms of Ti11O40H36 on the DMMP interaction energy. Thus, a model calculation was performed, with the 12411
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The Journal of Physical Chemistry C analytic potential energy function, to determine potential curves for orientations I and II, but for the DMMP/Ti11O40 system without the cluster’s H atoms. For orientation I the resulting R0 and V0 are 2.41 Å and 30.0 kcal/mol, and for orientation II R0 and V0 are 2.59 Å and 17.9 kcal/mol. These values are very similar to those given above for DMMP/Ti11O40H36 with the cluster’s H atoms present in the analytic potential, which illustrates the H atoms have only a minor effect on the DMMP/Ti11O40H36 potential energy calculated with the analytic function. D. DMMP þ TiO2 (110) Potential. The above analyses show that the same scaling of the analytic potential energy function, derived for the DMMP/TiO5H6 system, provides very good fits to potential energies for both the DMMP/Ti3O13H14 and DMMP/Ti11O40H36 systems. This is an important finding, since these latter two larger Ti clusters contain the four types of atoms present for the TiO2 (110) surface, i.e., 5- and 6- coordinated Ti atoms and bridging and surface O atoms. Thus, these two clusters are models for the TiO2 (110) surface, and since their potential energies for interactions with DMMP are fit by the same analytic potential energy function, this function is expected to be a good representation of the DMMP/TiO2 (110) potential. Two-body parameters for DMMP interacting with the TiO2 (110) surface are listed in Table 4. They are the scaled parameters described in section III.C.2. Potential energy curves are given in Figure 9 where the distance is TiO(P) for DMMP interacting with the TiO2 (110) surface. The two orientations I and II are depicted in Figure 8. The atomistic model for the TiO2 (110) surface is given in Figure 9. The size of the surface model was varied and increased until the DMMP/TiO2 (110) interaction converged (see caption to Figure 9). The V0 and R0 values for orientation I are 44.2 kcal/mol, 2.30 Å and are 35.3 kcal/mol, 2.17 Å for orientation II. The well depths for DMMP/TiO2 (110) are 14 and 18 kcal/mol deeper respectively for orientations I and II as compared with the values for the DMMP/Ti11O40H36 cluster with the H atoms removed. The respective R0 values are shifted by 0.1 and 0.4 Å.
IV. SUMMARY In the research presented here ab initio calculations were performed to develop an analytic intermolecular potential energy function for the interaction of DMMP with the rutile TiO2 (110) surface. This potential function may be used in chemical dynamics simulations of energy transfer and adsorption for collisions of DMMP with TiO2 (110). The ab initio calculations were performed at the MP2/aug-cc-pVDZ (6-311þG** for Ti) level with BSSE correction and involved the use of CH3OH and OdP(CH3)(OH)2 to represent the atoms and functional groups of DMMP and the TiO5H6 cluster model to represent the TiO2 (110) surface. Potential energy curves were calculated for CH3OH and OdP(CH3)(OH)2 interacting with TiO5H6 for a range of orientations, and the potential energy function was constructed by fitting these curves with a sum of generalized Buckingham two-body potential energy terms. The resulting DMMP/TiO5H6 potential energy curve is in very good agreement with one determined using MP2/aug-cc-pVDZ (6-311þG** for Ti) theory. The TiO5H6 cluster models the 5-coordinated Ti atoms and surface O atoms of the TiO2 (110) surface, but not the 6-coordinated Ti atoms and bridging O atoms. To also model these latter two atom types the Ti3O13H14 and Ti11O40H36 clusters were used. The use of the MP2/aug-cc-pVDZ
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(6-311þG** for Ti) level of theory is impractical for studying the interaction of DMMP with the large Ti11O40H36 cluster, and MP2 theory with a smaller basis set is required. The MP2/631þþG** (6-31G** for Ti) theory was found to give a DMMP/ TiO5H6 interaction potential in very good agreement with the one determined with MP2/aug-cc-pVDZ (6-311þG** for Ti) theory, and this former MP2 method was used to calculate potential energy curves for DMMP interacting with the Ti3O13H14 and Ti11O40H36 cluster models. The DMMP/TiO2 analytic potential function developed using the TiO5H6 cluster was tested by comparing with MP2/ 6-31þþG** (6-31G** for Ti) calculations for DMMP interacting with the Ti3O13H14 and Ti11O40H36 clusters. Two orientations were considered for both the DMMP/Ti3O13H14 and DMMP/Ti11O40H36 calculations. It was possible to scale the analytic potential developed using TiO5H6 so that it accurately represents the MP2 potential energy curves for both DMMP/ Ti3O13H14 and DMMP/Ti11O40H36. As discussed above, both the Ti3O13H14 and Ti11O40H36 clusters model the TiO2 (110) surface, and since their potential energies for interactions with DMMP are well represented by the same analytic potential energy function, the parameters for the scaled function are expected to provide a good model for the DMMP/TiO2 (110) potential. This analytic intermolecular potential energy function will be used in future chemical dynamics simulations of DMMP collisions with the rutile TiO2 (110) surface. Though the analytic intermolecular potential presented here was developed specifically for DMMP interacting with the rutile TiO2 (110) surface, it is of interest to consider its possible applicability to other rutile faces and other phases of TiO2. The rutile (110) surface and face contains four types of atoms, i.e., 5- and 6-fold coordinated Ti atoms, 3-fold coordinated bulk O atoms, and 2-fold coordinated bridging O atoms. As described above, and shown in Table 4, different potential parameters were derived for the two types of Ti atoms as well as for the two types of O atoms. Thus, the bonding motifs for the Ti and O atoms of the surface appear to be important in establishing their twobody intermolecular potential energy parameters. The rutile (100)53 surface has similar four types of atoms, and the DMMP/ rutile TiO2 (110) potential may be applicable to this surface. The uncertainty arises from the nature of the TiO bonding which is planar for the (110) surface but nonplanar for the (100) surface. The atoms for the (101) and (001) surfaces of rutile53 are different than those for the (110) face, and the potential developed here is not expected to be applicable to these two surfaces. Of the other phases of TiO2 (i.e., anatase and brookite), the potential developed here may be applicable to the anatase (101) surface54,55 which has the same four types of atoms as the rutile (110) surface. However, as for the rutile (100) surface, the TiO bonding for the anatase (101) surface is nonplanar. Clearly, tests are needed to verify the applicability of the DMMP/rutile (110) intermolecular potential developed here to other TiO2 surfaces. Finally, a more expansive application of the model developed here is to assume the two-body potentials for atoms of DMMP interacting with atoms of rutile (110) are transferable to atoms of other adsorbent molecules. This is an intriguing possibility and needs future testing.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. 12412
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’ ACKNOWLEDGMENT This material is based upon work supported by the Army Research Office under Contract HDTRA1-07-C-0098 and the Robert A. Welch Foundation under Grant D-0005. Support was also provided by the High-Performance Computing Center (HPCC) at Texas Tech University, under the direction of Dr. Philip W. Smith. The research was also performed using EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. The authors acknowledge important conversations with Hans Lischka and Adelia Aquino. ’ REFERENCES (1) Mitchell, M. B.; Sheinker, V. N.; Tesfamichael, A. B.; Gatimu, E. N.; Nunley, M. J. Phys. Chem. B 2003, 107, 580. (2) Segal, S. R.; Suib, S. L.; Tang, X.; Satyapal, S. Chem. Mater. 1999, 11, 1687. (3) Henderson, M. A.; White, J. M. J. Am. Chem. Soc. 1988, 110, 6939. (4) Nassar, A. F.; Lucas, S. V.; Jones, W. R.; Hoffland, L. D. Anal. Chem. 1998, 70, 1085. (5) Knagge, K.; Johnson, M.; Grassian, V. H.; Larsen, S. C. Langmuir 2006, 22, 11077. (6) Panayotov, D. A.; Morris, J. R. J. Phys. Chem. C 2008, 112, 7496. (7) Smentkowski, V. S.; Hagans, P.; Yates, J. T., Jr. J. Phys. Chem. 1988, 92, 6351. (8) Cuisset, A.; Mouret, G.; Pirali, O.; Roy, P.; Cazier, F.; Nouali, H.; Demaison, J. J. Phys. Chem. B 2008, 112, 12516. (9) Tzou, T. Z.; Weller, S. W. J. Catal. 1994, 146, 370. (10) Ferguson-McPherson, M. K.; Low, E. R.; Esker, A. R.; Morris, J. R. Langmuir 2005, 21, 11226. (11) Henderson, M. A.; Jin, T.; White, J. M. J. Phys. Chem. 1986, 90, 4607. (12) Hedge, R. M.; White, J. M. Appl. Surf. Sci. 1987, 28, 1. (13) Yang, L.; Shroll, R. M.; Zhang, J. X.; Lourderaj, U.; Hase, W. L. J. Phys. Chem. A 2009, 113, 13762. (14) Li, Y.; Schlup, J. R.; Klabunde, K. J. Langmuir 1991, 7, 1394. (15) Templeton, M. K.; Weinberg, W. H. J. Am. Chem. Soc. 1985, 107, 97. (16) Templeton, M. K.; Weinberg, W. H. J. Am. Chem. Soc. 1985, 107, 774. (17) Sheinker, V. N.; Mitchell, M. B. Chem. Mater. 2002, 14, 1257. (18) Blajeni-Aurian, B.; Boucher, M. M. Langmuir 1989, 5, 170. (19) Wagner, G. W.; Koper, O. B.; Lucas, E.; Decker, S.; Klabunde, K. J. J. Phys. Chem. B 2000, 104, 5118. (20) Ma, S.; Zhou, J.; Kang, Y. C.; Reddic, J. E.; Chen, D. A. Langmuir 2004, 20, 6986. (21) Lin, S. T.; Klabunde, K. J. Langmuir 1985, 1, 600. (22) Rusu, C. N.; Yates, J. T. J. Phys. Chem. B 2000, 104, 12292. (23) Rusu, C. N.; Yates, J. T. J. Phys. Chem. B 2000, 104, 12299. (24) Trubitsyn, D. A.; Vorontsov, A. V. J. Phys. Chem. B 2005, 109, 21884. (25) Zhou, J.; Varazo, K.; Reddic, J. E.; Myrick, M. L.; Chen, D. A. Anal. Chim. Acta 2003, 496, 289. (26) Qu, Z. W.; Kroes, G. J. J. Phys. Chem. B 2006, 110, 23306. (27) Rasmussen, M. D.; Molina, L. M.; Hammer, B. J. Chem. Phys. 2004, 120, 988. ngel San Miguel, M.; Sanz, (28) Oviedo, J.; Sanchez-de-Armas, R.; A J. F. J. Phys. Chem. C 2008, 112, 17737. (29) Bandura, A. V.; Sykes, D. G.; Shapovalov, V.; Troung, T. N.; Kubicki, J. D.; Evarestov, R. A. J. Phys. Chem. B 2004, 108, 7844. (30) Bandura, A. V.; Kubicki, J. D. J. Phys. Chem. B 2003, 107, 11072. (31) Mattioli, G.; Flilippone, F.; Caminiti, R.; Amore Bonapasta, A. J. Phys. Chem. C 2008, 112, 13579.
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