ARTICLE pubs.acs.org/JPCC
Theoretical Study of the Molecular and Electronic Structures of TiO4H4, Ti2O7H6, and Ti2O6H4 Takashi Tsuchiya* and Jerry L. Whitten Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695, United States ABSTRACT: State-of-the-art multistate configuration interaction (CI) calculations were performed for a series of titanium complexes, namely, TiO4H4, Ti2O7H6, and Ti2O6H4, which were chosen to identify features present in titanium oxide nanoclusters and titanium dioxide surfaces. All electrons were included in the calculations, and transformation methods were employed to achieve high accuracy for the excitations of interest. The electronic structures of the ground and excited states are discussed, and excitation energies are reported for different molecular conformations. Of particular interest is the extent of localization of the electron-hole pair formed upon excitation from the oxygen 2p molecular orbitals. Singlet and triplet excited states were resolved, and energies of electronic states are reported as a function of molecular geometry.
’ INTRODUCTION Titanium dioxide materials have been studied for a wide variety of applications, including use in photocatalysis and as a substrate for electron injection and transport from attached adsorbates.1,2 Such materials are complicated and are known to form surface and subsurface defects that have been implicated in many of the materials' chemical and physical properties.3-12 Titanium dioxides are known to be capable of photodissociating organic toxins into nontoxic substances, as well as photooxidizing water to produce oxygen and hydrogen.13-19 It is the latter process and the possibility of using solar photons to drive reactions on titanium oxide particles that encouraged the present study. In addition, since they were first synthesized more than a decade ago,20,21 titanium oxide nanoparticles have offered unique features because of their large surface area-to-volume ratio and because of the fact that their more widely spaced electronic states enable longer excited-state lifetimes. However, the large number of undercoordinated oxygen atoms on the surface of a small titanium dioxide particle give rise to unusual bonding situations not found in the interior of the solid. Excitation energies will be affected as a result, as will the electronic structure of surface and interior excitons. For bulk titanium dioxide in either rutile or anatase phases, the band gap of ∼3 eV would preclude using much of the solar spectrum. Finding ways to create lower-energy excitations in nanoparticles, perhaps by doping or atomic substitutions, is an additional important objective. In this article, we propose to address some of the basic electronic structure questions associated with titanium-oxygen bonding and the formation of low-lying electronic states. To achieve the accuracy required to resolve different spin states and to treat subtleties in the formation of excited electronic states, we employed r 2010 American Chemical Society
an ab initio many-electron theory based on configuration interaction expansion of the states of interest. Results for a series of titanium complexes, namely, TiO4H4, Ti2O7H6, and Ti2O6H4, are reported. The complexes were designed to model specific units of titanium oxide nanoparticles, particularly those associated with surface states. Two different kinds of oxygen were included in the model systems Ti2O7H6 and Ti2O6H4, namely, bridging oxygens and terminal oxygens; these are expected to play distinct roles in photochemical processes.
’ THEORETICAL METHOD Calculations were carried out for the full electrostatic Hamiltonian of the system " # N M N X X 1 2 X ZA 1 H ¼ - ri ð1Þ þ 2 r r i A iA i 10 - 4 au jEp - ERHF j r
ð5Þ
ijab
and
Then, the final CI wave function, Ψr, is determined as X X Ψr ¼ λ0 Ψintermediate þ λp ΦSD λq Φ q r p ¼
ð6Þ
Figure 1. Structures (a) of TiO4H4, (b) Ti2O7H6, and (c) Ti2O6H4. Refer to the text for detailed descriptions.
þ ΦDp
ð7Þ
λia Γi, a Φp
ð8Þ
closed-shell configuration and a set of the spin-adapted configurations X Φr0 ð12Þ Φr ¼
p
q
where ΦSD p ΦSp ¼
ΦSp
¼
X
r
ia
ΦDp
¼
X
λijab Γij, ab Φp
ð9Þ
ijab
and ÆΦq jHjΨintermediate æ2 r > 10 - 6 au jEq - Eintermediate j r
ð10Þ
Energy contributions from the remaining electronic configurations, which were not included in the above expansion, were estimated perturbatively.23,24 Through the above two-step procedure, important configurations of up to four-electron excitations were generated. Here, λ is the expansion coefficient; Φ is the configuration; E is the energy; and Γi,a and Γij,ab are the one-electron and two-electron excitation operators, respectively. {i, j, ...} denotes the occupied orbitals in the reference RHF ground state, whereas {a, b, ...} represents a functional space orthogonal to the occupied orbital space. A number of methods for selecting {a, b, ...} have been proposed for a shorter truncation of the full CI expansion.25-31 In the current study, {a, b, ...} was constructed by applying the projection operator X P ¼ jfu æÆfu j ð11Þ u
to a HF virtual orbital set, where the fu functions were chosen to be basis functions for 2p and 3d orbitals centered on oxygen and titanium atoms, respectively. In this way, the electron correlation within the valence region, oxygen 2p and titanium 3d orbitals and electrons, can be effectively calculated. In the state-specific CI calculations, ΦRHF in eq 3 was chosen r to be the RHF wave functions of the singlet and triplet states. In the multistate CI calculations, three-electron configurations were considered; that is, ΦRHF in equation eq 3 was replaced by a r
¼ Φclosed-shell singlet0 þ Φtriplet0 þ Φopen-shell singlet0
ð13Þ
All the Φ0r functions in eq 13 were expanded with the same oneelectron basis functions. To describe the open-shell singlet state with adequate accuracy, one-electron basis functions were constructed from the spatial part of the HF orbitals of the triplet state Φtriplet0 ¼ ΦRHF triplet
ð14Þ
and Φ0closed-shell singlet and Φ0open-shell singlet were also expanded using the spatial part of the RHF orbitals for the triplet state. Configurations were constructed to describe the ms = 0 component of the singlet and triplet states. The states generated were eigenfunctions of S2, that is, are triplet and singlet states.
’ COMPUTATIONAL DETAILS The basis set employed was of valence triple-ζ quality (doubleζ for hydrogen) and denoted as [14s13p6d]/(8s8p3d) for titanium, [11s6p]/(5s3p) for oxygen, and [5s]/(2s) for hydrogen. To maintain neutrality of the system and avoid artificial highspin states, the terminal oxygen atoms were bonded to hydrogen atoms. Although titanium oxide clusters can have from four to six oxygen-atom nearest neighbors to titanium, in this work, we selectively study complexes with a coordination number of four and assumed the local symmetry around a titaniun center to be tetrahedral. The titanium-oxygen and oxygen-hydrogen distances were optimized by means of the configuration interaction procedure described earlier, by minimizing the energy of tetrahedral TiO4H4 (Figure 1a). The resulting distances were 1.796 Å for Ti-O and 0.961 Å for O-H. These values are consistent with the MP2/6-311þþG(d,p) calculation for Ti(OH)4.32 In all remaining calculations, these values were fixed for both the singlet and triplet states, and the O-Ti-O angle of 109.5 was consistent with the intent of maintaining a tetrahedral local structure around the titanium center. Effects due to variations in molecular geometry are normally important, but the purpose of 1636
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Table 1. RHF and CI Energies (in Hartrees) of the Ground Singlet and Triplet States of TiO4H4, with Singlet-Triplet Excitation Energies (in eV) in Parentheses singlet ground state
triplet a
localizedb
delocalized
RHF
-1150.344127
-1150.135653 (5.67)
-1150.197578 (3.99)
CI
-1150.662559
-1150.470138 (5.24)
-1150.485051 (4.83)
a Electron-delocalized electronic structure. electronic structure.
b
Electron-hole-localized
the present work was to investigate simple, well-defined structures such as the tetrahedral structure that occurs in extended systems.20,21 Figure 1 depicts the structures of TiO4H4, Ti2O7H6, and Ti2O6H4, considered in the present study. TiO4H4 has a tetrahedral structure as described above. Two tetrahedra are connected with one bridging oxygen to form Ti2O7H6, and Ti2O6H4 is formed with two bridging oxygens. The structure of Ti2O7H6 (Figure 1b) can be classified as belonging to different conformational groups: In conformation I, two tetrahedrons are connected face-to-face (Ti-O-Ti angle is 180.0), and conformation II is its isomer. In the other systems, two tetrahedra are placed side-by-side at a Ti-O-Ti angle set to be 109.5. In conformations IV and V, one of three terminal hydroxyl groups on a titanium is tilting away from and toward the corresponding one on the other titanium, respectively, with conformation III being their isomer. The electronic structures were investigated for both the ground and excited states of titanium monocenter and two-center complexes. First, we report CI calculations for the ground singlet and excited triplet states separately and discuss the electronic structures of the respective states as well as the singlet (ground-state)triplet electronic excitations. Next, we show results of multistate CI calculations, in which three states, namely, the closed-shell singlet (ground) state, triplet state (ms = 0 component), and open-shell singlet (excited) state, were treated on an equal basis. Finally, we discuss in greater detail the spin-allowed singlet-singlet excitations. Because calclations were performed at fixed molecular structures, all of the excitations considered in the present study are vertical excitations.
’ RESULTS AND DISCUSSION Single-State CI Calculations. Calculations were first performed on TiO4H4 as the simplest model of hydrogen-terminated four-coordinate titanium oxide clusters. Table 1 compiles RHF and CI energies for the singlet and triplet states of TiO4H4. Two kinds of electronic structures were investigated for the triplet state: the electron-delocalized electronic structure and the electron-hole-localized electronic structure. As is well-known for oxides,33,34 the state having an electronhole-localized electronic structure tends to be considerably lower in energy than the state with the electrons in delocalized orbitals when calculated at the HF level. Table 1 shows that, by taking into account electron correlation effects, the difference in energy between the delocalized and electron-hole-localized descriptions of the triplet state energy is significantly reduced. The delocalized and localized energy difference is 1.68 and 0.41 eV for RHF and CI calculations, respectively. The significant reduction in energy difference for the CI calculations suggests possible equivalence of the two methods of expansion in the limit of an
exact correlation treatment, that is, convergence to the same triplet state. The same behavior has been reported for the unrestricted HF (UHF) wave function.35 At the level of theory employed in the present energy variational treatment, the electron-hole-localized description remains lower in energy than the delocalized description. In semiconductor systems, theoretical and experimental evidence supports the physical existence of electron-hole localization.36-44 In the following sections, we focus on the localized electron-hole description. The singlet- and triplet-state RHF and CI total energies, as well as the singlet-triplet excitation energies, are collected in Table 2 for TiO4H4, Ti2O7H6, and Ti2O6H4. Two distinct electron configurations were investigated for the triplet states. The localized hole is on the bridging oxygen in one configuration (denoted as bridge), whereas the localized hole is on one of the terminal oxygens in the other (denoted as terminal.) Note that the singlet-triplet excitation energy is larger in the CI calculation than in the HF calculation because the electron correlation energy is larger for the singlet ground state than for the triplet state because of the dominance of the closed-shell electron configuration in the ground state. The CI (RHF) triplet-singlet excitation energy for TiO4H4 was calculated to be 4.83 eV (3.99 eV). This corresponding excitation energy is almost the same for Ti2O7H6: 4.58 eV (4.04 eV), 4.56 eV (4.07 eV), 4.35 eV (3.89 eV), and 4.14 eV (3.91 eV) for structures I, II, III and IV, respectively, for the terminal electron configuration and 5.13 eV (4.46 eV), 5.09 eV (4.45 eV), 4.99 eV (4.25 eV), and 4.84 eV (4.28 eV), respectively, for the bridge configuration. However, a significant decrease occurs for Ti2O7H6 (V). The CI (RHF) values are 2.68 eV (2.33 eV) for the terminal excitation, the large reduction being due to the change in molecular conformation. Figure 2 shows the CI energies of the singlet and triplet states. It can be seen in Figure 2 that, throughout the series of Ti2O7H6, the tripet state energy is relatively invariant with respect to conformation change whereas the singlet groundstate energy increases significantly in conformation V. It is due to this relative destabilization of the singlet ground state that the singlet-triplet excitation energy decreases in conformation V. A further reduction also occurred in Ti2O6H4, where the CI (RHF) ground-state singlet-triplet excitation energy was found to be 2.65 eV (2.25 eV) for the terminal conformation and 2.09 eV (1.82 eV) for bridge conformation; thus, for these cases, the excitation energy is moving into a more accessible region of the spectrum. These large reductions of the excitation energies in Ti2O7H6 (V) and Ti2O6H4 stem from the electronic structures of the systems. Table 3 shows Mulliken populations of the singlet and triplet states of TiO4H4, Ti2O7H6 (I, V), and Ti2O6H4. The change in electron population due to the electron excitation is schematically shown in Figure 3. In the closed-shell singlet ground state, the electron population is totally symmetric in all cases, whereas in the triplet state, the electron-hole localization causes an asymmetric deviation. In TiO4H4, the excitation corresponds to a transfer of an electron from the p orbital of one of the oxygens to a 3d orbital of titanium. The resulting electron-hole pair on the oxygen and an electron in the d shell of titanium are highly localized. The electron distribution, then, shifts toward one side of the molecule, away from the electron-hole pair, as shown in Figure 3. In Ti2O7H6, the terminal excitation occurs by way of the electron transfer from the p orbital of one of the terminal oxygens 1637
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Table 2. RHF and CI Energies (in Hartrees) of the Singlet and Triplet States of TiO4H4, Ti2O7H6, and Ti2O6H4, as well as Singlet-Triplet Excitation Energiesa triplet terminalb
singlet
bridgec
total energy (hartree)
total energy (hartree)
ΔEd (eV)
-1150.344127 -1150.662559
-1150.197578 -1150.485051
3.99 4.83
total energy (hartree)
ΔEd (eV)
TiO4H4 RHF CI Ti2O7H6
n/a n/a
(I)
RHF
-2224.697088
-2224.548518
4.04
-2224.533300
4.46
CI
-2225.225229
-2225.053556
4.58
-2224.036587
5.13
(II) RHF
-2224.697229
-2224.547611
4.07
-2224.533627
4.45
CI
-2225.224617
-2225.057086
4.56
-2225.037665
5.09
(III) RHF
-2224.658730
-2224.515862
3.89
-2224.502591
4.25
CI
-2225.196282
-2225.036496
4.35
-2225.012929
4.99
(IV) RHF
-2224.650976
-2224.507410
3.91
-2224.493793
4.28
CI
-2225.181792
-2225.029567
4.14
-2225.003870
4.84
RHF
-2224.557932
-2224.472252
2.33
n/ce
CI Ti2O6H4
-2225.089214
-2224.990562
2.68
n/ce
(V)
RHF
-2148.400140
-2148.317380
2.25
-2148.333429
1.82
CI
-2148.893964
-2148.796625
2.65
-2148.817242
2.09
a Refer to Figure 1 for the molecular structures. b Hole localized on the terminal oxygen. c Hole localized on the bridging oxygen. d The singlet-triplet excitation energy. e Self-consistent-field (SCF) calculation did not converge.
Figure 2. CI energies (in eV) of the triplet state (top; blue) relative to the singlet ground state (bottom; red) of (a) TiO4H4, (b) Ti2O7H6, and (c) Ti2O6H4. In b, energies are relative to the singlet ground state of conformation I. Refer to Figure 1 for the molecular structures.
to a titanium 3d orbital. As observed in TiO4H4, the resulting electron distribution shifts away from the electron-hole pair. The electron flow from the titanium s and p orbitals to the p orbitals of the other adjacent terminal oxygens was observed in the tetrahedron in which the electron-hole pair was created. Furthermore, the increase in the electron population, although slight (∼0.1 electron), is observed in the other tetrahedron connected through the bridging oxygen. This partially compensates for a higher concentration of electrons on one of two titanium atoms, thus reducing the polarity of the electron distribution. This is the reason why the terminal excitation is
slightly more stable than the bridge excitation in all cases in Ti2O7H6. For the bridge excitation, the electron transfers from a p orbital of the bridge oxygen to a d orbital of one of the titaniums. Therefore, this side of the tetrahedron is highly populated by the electron, and slight electron flow (∼0.1 electron) from the other tetrahedron to the bridging oxygen occurs. Through a detailed analysis, it turns out that, in the tetrahedron into which the electron transfers upon excitation, the electron flows from the titanium s and p orbitals to the p orbitals of the adjacent terminal oxygens, whereas the excited electron is localized in the titanium d orbital. 1638
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Table 3. Mulliken Electron Populations of the Singlet and Triplet States of TiO4H4, Ti2O7H6 (I, V), and Ti2O6H4 Ti
OH1a
singlet
19.55
9.62
triplet
19.75
8.92
conf I
(a) TiO4H4 OH2
OH3
OH4
total
9.61
9.62
9.62
58.0
9.78
9.78
9.78
58.0
(b) Ti2O7H6 Obb Ti1 OH11c OH12 OH13 Ti2 OH21 OH22 OH23 total
singlet 8.60 19.71 9.67 triplet (t)d 8.76 19.93 8.94
9.67 9.67 19.71 9.67 9.67 9.67 106.0 9.79 9.79 19.69 9.69 9.69 9.70 106.0
triplet (b)e 8.25 19.70 9.83
9.80 9.80 19.91 9.57 9.56 9.56 106.0
conf V singlet
Ob Ti1 OH11c OH12 OH13 Ti2 OH21 OH22 OH23 total 8.46 19.92 9.49
9.68 9.68 19.92 9.49 9.68 9.68 106.0
triplet (t) d 8.53 20.04 8.99
9.82 9.82 19.93 9.61 9.69 9.69 106.1
Ob1f Ob2 singlet
Ti1
(c) Ti2O6H4 OH11g OH12
Ti2
OH21 OH22 total
8.48 8.48 20.29
9.62
9.62
20.29 9.62
9.62
96.0
triplet (t)d 8.60 8.60 20.63
8.85
9.74
20.19 9.70
9.68
96.0
triplet (b)e 8.14 8.52 20.41
9.63
9.63
20.41 9.63
9.63
96.0
a
Hole localized on this O (terminal oxygen) upon electron transfer to Ti. b Hole localized on this O (bridging oxygen) upon electron transfer to Ti1. c Hole localized on this O (terminal oxygen) upon electron transfer to Ti1. d Hole localized on the terminal oxygen. e Hole localized on the bridging oxygen. f Hole localized on this O (bridging oxygen) upon electron transfer to Ti1 and Ti2. g Hole localized on this O (terminal oxygen) upon electron transfer to Ti1 and Ti2.
In the other tetrahedron, the electron flow from terminal oxygens to titanium s and p orbitals occurs because of Coulombic attraction because of the localized hole on the bridging oxygen. The consequence of these two directions of electron flow is that the net electron population of the titanium on which the excited electron is localized remains unchanged on electron excitation, whereas the net electron population of the other titanium increases after the excitation, corresponding to a reduction in the electron population of its adjacent terminal oxygens. The positively charged oxygens (relative to the ground state) are created on the production of the electron-hole pair. However, they are not in the direct vicinity of the titanium atom participating in the electron excitation but are around a different titanium atom connected with the oxygen atom on which the hole is localized. The bridge excitation is more likely to occur in nanoparticles and surfaces. Therefore, it is expected that these surrounding oxygens play an important role in photoinduced reactions on titanium oxide nanoparticles and titanium dioxide surfaces. In Ti2O6H4, on the other hand, the bridge excitation is more stable than the terminal excitation. A single electron, transferred from one of two bridging oxygens, is shared with two titaniums. Conceptually, it might be helpful to imagine a series of steps: First, an electron transfers from one of the bridging oxygens to a single titanium atom; then, an electron flows to the second titanium atom through the other bridging oxygen. However, because the second titanium atom is bonded to the first bridging oxygen from which the electron excitation occurred, electron density can shift back to the origin of the excitation. In this way, virtually all the electron population changes are absorbed into the central
Figure 3. Schematic representations of electron density shifts (calculated from Mulliken population changes relative to the ground singlet state) in the triplet states of (a) TiO4H4, (b) Ti2O7H6 (I, V), and (c) Ti2O6H4. The transfers of the excited electrons are indicated by arrows.
Ti-O-Ti-O ring; the electron population changes in the terminal oxygens were found to be negligible (Table 3c). Furthermore, in Ti2O6H4, the electron distribution in the triplet state is close to symmetric; the net electron population change on the excitation is small. This leads to a small energy difference between the singlet (ground) state and the triplet (excited) state. The small polarity of the electron population distribution in the triplet state of Ti2O6H4 (bridge) implies a low activation barrier for electron-hole hopping because only a small electron redistribution needs to occur. Therefore, high mobility of the electronhole pair or, in other words, high conductivity can be expected. In the case of bridge excitation, the electron distribution in the resulting triplet state relaxes to become nearly symmetric, whereas for the terminal excitation, the electron distribution is shifted on one side, as is the case in TiO4H4. This large asymmetric shift of the electron distribution makes a terminal excitation less stable. Table 4 shows contributions from constituent atoms to two singly occupied orbitals of TiO4 H4 , Ti2O7H6 (I, V), and Ti2O6H4, for both the terminal and bridge electron configurations. It is clearly seen that, in all of the cases investigated, the first singly occupied orbital, which is lower in orbital energy, consists almost entirely of a localized oxygen 2p component, whereas the second orbital is the titanium 3d component. Because of the ring structure in Ti2O6H4, both titanium atoms are equally populated in the bridge excitation, whereas, in the other case, only one titanium orbital is populated by the excited electron. In both cases, the localized electron-hole description is valid. Singlet-triplet excitation energies (from the ground state to the first excited state) were found to be small in both Ti2O7H6 (V) and Ti2O6H4. However, it should be noted that the mechanisms for achieving the small excitation energies are different. In the case of 1639
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Ti2O7H6 (V), the Coulombic repulsion between the electrons of the two terminal oxygens, which is reduced in the triplet state because of the electron-hole pair on one of the two oxygens, increases the energy of the singlet state; that is, the relative instability of the singlet state is the cause of the small singlet-triplet excitation energy. On the other hand, in Ti2O6H4, the relative stability of the triplet state originates in the lower polarity of the electron distribution in the triplet state. Multistate CI Calculations. The singlet-triplet electron excitation is spin-forbidden, and because spin-orbit coupling is small for titanium, the transition probability would be very low. Table 4. Contributions of Constituent Atoms to Singly Occupied Orbitals in the Triplet States of TiO4H4, Ti2O7H6 (I, V), and Ti2O6H4a,b (a) TiO4H4 O1
Ti triplet
O2
O3
O4
S2
0.90
0.05
-
-
-
S1
0.05
0.94
-
-
-
conf I
Ob
Ti1
(b) Ti2O7H6 O11 O12 O13 Ti2 O21 O22 O23
triplet (t)c
S2
-
0.91 0.05
-
-
-
-
-
-
triplet (b)d
S1 S2
-
0.05 0.95 0.95 -
-
-
-
-
-
-
S 1 0.95 conf V
Ob
triplet (t) c
triplet (t)
triplet (b)d
-
-
-
-
-
-
-
Ti1
O11
O12
O13
Ti2
O21
O22
O23
S2
-
0.88
0.06
-
-
-
-
-
-
S1
-
0.06
0.82
-
-
-
0.11
-
-
O22
Ob1 c
-
(c) Ti2O6H4 Ob2 Ti1 O11
O12
Ti2
O21
S2
-
-
0.76
0.07
-
0.12
-
-
S1
-
-
0.07
0.93
-
-
-
-
S2
-
-
0.46
-
-
0.42
-
-
S1
0.91
-
-
-
-
-
-
-
a
Values larger than 0.05 are listed. b S 1 and S 2 denote the second highest and the highest singly occupied orbitals, respectively. c Hole localized on the terminal oxygen. d Hole localized on the bridging oxygen.
However, essentially all of the preceding discussion concerning the triplet state also applies to the corresponding open-shell singlet state, because the electronic structures of these two states are nearly equivalent. The terminology for ground-state singlettriplet excitation used in the earlier sections can be applied without modification to describe the ground-singlet to excited-singlet excitation. Table 5 reports CI total energies of the closed-shell singlet ground state, as well as excitation energies of the triplet and openshell singlet excited states for both the terminal and bridge electron configurations of TiO4H4, Ti2O7H6, and Ti2O6H4. The open-shell singlet state consists predominantly of the same electron configurations as the ms = 0 component of the triplet state. In the multistate CI calculation, the RHF molecular orbitals of the triplet state are used to define multiple reference electron configurations to describe the open-shell singlet state with the same accuracy as the triplet-state description. This could, in principle, sacrifice the accurate description of the closed-shell singlet state, whose dominant electron configurations are considerably different from those in the open-shell states. However, in the present CI calculations, the closed-shell singlet state was also described with equivalent accuracy. For example, for TiO4H4, the multistate CI total energy for the closed-shell singlet state is 1150.666 hartree, to be compared with the state-specific CI energy, -1150.663 hartree, and the excitation energies of the triplet state are 4.84 and 4.83 eV for the multistate CI and the state-specific CI calculations, respectively (Tables 2 and 5.) The agreement between the multistate calculations and the statespecific calculations is quite good for both the closed-shell singlet and triplet states. Table 5 also includes the triplet-singlet (open-shell) separation. In all cases investigated, open-shell singlet states were found close to the triplet states. Almost all of the open-shell singlet states lie within 0.8 eV above the corresponding triplet states. The only exception is Ti2O7H6 (V), for which the triplet-singlet separation is 1.21 eV. This large value is due to strong mixing between the closed-shell and open-shell electron configurations in the singlet states; by mixing with the open-shell configuration, Coulombic repulsion between closely spaced terminal oxygens in the closed-shell electron configuration is reduced, and the ground state is stabilized while the singlet excited state is destabilized to the same degree. Table 6 reports contributions of the closedshell and open-shell reference electron configurations to the ground and excited singlet states. It can be seen that, in Ti2O7H6 (V), both the open-shell and closed-shell configurations contribute
Table 5. CI Total Energies (in Hartrees) of the Closed-Shell Singlet Ground State and Excitation Energies (in eV) of the Triplet and Open-Shell Singlet Excited States of TiO4H4, Ti2O7H6, and Ti2O6H4 terminala
Ti2O6H4
closed-shell singlet
triplet
open-shell singlet
ΔEtsc
closed-shell singlet
triplet
open-shell singlet
ΔEtsc
-1150.666144
4.84
5.18
0.34
(I)
-2225.234670
4.34
4.87
0.53
-2225.234974
5.24
5.28
0.04
(II)
-2225.238098
4.29
4.55
0.26
-2225.225301
5.03
5.07
0.04
TiO4H4 Ti2O7H6
bridgeb
n/a
(III)
-2225.229143
4.18
4.79
0.61
-2225.208189
4.92
5.46
0.54
(IV) (V)
-2225.223906 -2225.111417
4.33 2.63
4.74 3.84
0.41 1.21
-2225.193410 n/cd
4.78
5.51
0.73
-2148.890102
2.23
3.01
0.78
-2148.897631
1.78
1.84
0.06
a
Localized hole on the terminal oxygen in the reference RHF wave function. b Localized hole on the bridging oxygen in the reference RHF wave function. c Energy difference (in eV) between the triplet and open-shell singlet states. d Self-consistent-field (SCF) calculation did not converge. 1640
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Table 6. Contributions of the Closed-Shell and Open-Shell Electron Configurations to the Ground and Excited Singlet States of TiO4H4, Ti2O7H6, and Ti2O6H4 ground state
TiO4H4 Ti2O7H6
Ti2O6H4
excited state
closed-shell
open-shell
closed-shell
open-shell
photoinduced reaction, but also the nearby oxygens would seem likely to play a role. Many of the electronic effects found for the model systems should carry over to nanoparticles or TiO2 surfaces because of the presence of undercoordinated oxygen sites. Likewise, one can infer for these larger systems that electron-hole pairs formed from interior and surface oxygens will differ significantly in excitation energy and that further variations will occur with conformational changes.
0.64
0.08
0.01
0.62
(I)
0.56
0.18
0.10
0.61
(II)
0.55
0.20
0.12
0.61
(III)
0.54
0.23
0.15
0.60
’ AUTHOR INFORMATION
(IV) (V)
0.53 0.39
0.24 0.39
0.14 0.28
0.57 0.40
Corresponding Author
0.49
0.25
0.19
0.54
significantly to both the ground and excited singlet states, whereas in the other cases, the closed-shell and the open-shell configurations are dominant in the ground and excited singlet states, respectively. However, a characteristic of the singlet excited state is still the dominance of the open-shell electron configuration, just as in the triplet state. Therefore, with the open-shell singlet state consisting of the same dominant electronic configurations as the triplet state, the analyses made in the previous section still apply to open-shell singlet states and singlet-singlet electronic excitations.
’ CONCLUSIONS A series of configuration interaction (CI) calculations were performed for the titanium oxide complexes TiO4H4, Ti2O7H6, and Ti2O6H4, which model specific local structures in titanium oxide nanoparticles and titanium dioxide surfaces. The electronic structures were investigated for the ground and excited states by means of both state-specific and multistate CI calculations. All electrons were explicitly treated in the calculations, and a transformation technique of the virtual orbital spaces was used to achieve an accurate description of both the ground and excited states. In all systems studied, the most important conclusion is that the lowest-energy excited state is excitonic in nature, with a hole localized on oxygen and an electron localized in the 3d shell of neighboring titanium ions. This description emerges even though, by symmetry, there is an opportunity in both the calculations and in principle to form more delocalized electronic states. One would expect similar electron-hole pairs to form in the interior and on the surface of nanoparticles and TiO2 surfaces on electronic excitation. The fact that the excitation creates unpaired d electrons on titanium would affect the conductivity of a titanium dioxide system in much the same way as the formation of oxygen defects. Studies of the model systems also show that conformational changes can significantly reduce the excitation energy, and the introduction of a ring structure, as in Ti2O6H4, further reduces the excitation energy. Different mechanisms dominate the reduction of excitation energies of Ti2O7H6 and Ti2O6H4. In the former case, it is due to the relative destabilization of the ground state by a strong Coulombic repulsion between two closely spaced terminal oxygens, whereas in the latter case, it is due to a stabilization of the excited state stemming from the nearly nonpolar nature of the charge distribution. The localized electron-hole pair significantly alters its surrounding environment, and nearby oxygens become more reactive. Therefore, not only the electron-hole pair would contribute to a
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[email protected].
’ ACKNOWLEDGMENT This work was supported as part of the UNC EFRC: Solar Fuels and Next Generation Photovoltaics, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. Computer support and summer support for J.L.W., a total of 50% of the project cost, was provided by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Award DEFG0297ER45624. ’ REFERENCES (1) Kalyanasundaram, K.; Gr€atzel, M. Coord. Chem. Rev. 1998, 77, 347–414. (2) Carp, O.; Huisman, C. L.; Reller, A. Prog. Solid State Chem. 2004, 32, 33–177. (3) Gr€atzel, M. Nature 2001, 414, 338–344. (4) Frank, A. J.; Kopidakis, N.; van de Lagemaat, J. Coord. Chem. Rev. 2004, 248, 1165–1179. (5) Cronemeyer, D. C. Phys. Rev. 1952, 87, 876–886. (6) Breckenridge, R. G.; Hosler, W. R. Phys. Rev. 1953, 91, 793–802. (7) Poumellec, B.; Durham, P. J.; Guo, G. Y. J. Phys.: Condens. Matter 1991, 3, 8195–8204. (8) Linsebigler, A. L.; Lu, G.; Yates, J. T., Jr. Chem. Rev. 1995, 95, 735–758. (9) Yagi, E.; Hasiguti, R. R.; Aono, M. Phys. Rev. B 1996, 54, 7945–7956. (10) Nowotny, J.; Radecka, M.; Rekas, M. J. Phys. Chem. Solids 1997, 58, 927–937. (11) Gonzalez, R. J.; Zallen, R.; Berger, H. Phys. Rev. B 1997, 55, 7014–7017. (12) Ohno, T.; Sarukawa, K.; Matsumura, M. New J. Chem. 2002, 26, 1167–1170. (13) Fujishima, A.; Honda, K. Nature 1972, 238, 37–38. (14) Maruska, H. P.; Ghosh, A. K. Solar Energy 1978, 20, 443–458. (15) Sato, S.; White, J. M. Chem. Phys. Lett. 1980, 72, 83–86. (16) Munuera, G.; Gonzalez-Elipe, A. R.; Fernandez, A.; Malet, P.; Espinos, J. P. J. Chem. Soc., Faraday Trans. 1 1989, 85, 1279–1290. (17) Munuera, G.; Espinos, J. P.; Fernandez, A.; Malet, P.; Gonzalez-Elipe, A. R. J. Chem. Soc., Faraday Trans. 1990, 86, 3441– 3445. (18) Sayama, K.; Arakawa, H. J. Chem. Soc., Chem. Commun. 1992, 150–152. (19) Sayama, K.; Arakawa, H. J. Chem. Soc., Faraday Trans. 1997, 93, 1647–1654. (20) Campana, C. F.; Chen, Y.; Day, V. W.; Klemperer, W. G.; Sparks, R. A. J. Chem. Soc., Dalton Trans. 1996, 691–702. (21) Steunou, N.; Kickelbick, G.; Boubekeur, K.; Sanchez, C. J. Chem. Soc., Dalton Trans. 1999, 3653–3655. (22) Whitten, J. L.; Hackmeyer, M. J. Chem. Phys. 1969, 51, 5584– 5596. 1641
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