131
J. Phys. Chem. 1992, 96, 131-135
We can speculate on what may be the most important dipole transition moments contributing to nonlinear optical susceptibility in T i 0 6 and related species. The first point to note is that the lowest virtual orbitals are dominated by titanium d orbitals, which might figure prominently in low-lying excited states. If so, then the hyperpolarizability would be enhanced both by strong transition moments and by small energy denominators in the sum over states. Another observation is that the A state, with its large dipole moment, may contribute significantly to a nearby excited state. The difference between excited-state and ground-state dipole moments has a strong influence on the hyperpolarizability, and in consequence the u charge-transfer mechanism of the A state may play a role in the nonlinear optical susceptibility of the species. Titanium, possessing partially occupied d orbitals, is especially well suited to support this charge-transfer pathway in the distorted octahedron. Conclusions
The quasi-octahedral species Ti(OH)402z-, formed by positioning 0-ions above and below a planar Ti(OH)4 group, has been used to model electronic structure in potassium titanyl phosphate. This subunit is intended to capture the principal geometric and electronic features of the distorted T i 0 6 octahedra that are characteristic of the KTP structure. When abstracted from the unit cell, the doubly charged anion is stable relative to the isolated atoms once hydrogens are attached to the four oxygens normally coordinated to phosphorus.
Our analysis has emphasized the role played by the two axial oxygens in determining the state of the system and has identified, in particular, states of A and B symmetry under the point group C4. Various possibilities arise according to the initial p(u) and p(a) configurations of the axial oxygens. The A state develops when the oxygens approach with filled p(a) orbitals but only partially filled p(u) orbitals. In axially distorted octahedra, a marked transfer of charge from the distant oxygen to the near oxygen then takes place through the u system. This movement is facilitated by the available d orbitals on the transition metal, through which electrons apparently flow without permanently altering the indigenous population. We have suggested that this mechanism of charge transfer may contribute to the nonlinear optical properties of KTP, primarily through enhanced axial dipole moments in low-lying excited states. The B state, which is lower in energy than the A, is complementary in many ways. Here it is the p(u) system that is filled at the outset, and communication between the axial oxygens thus proceeds through the d ( r ) orbitals on the metal. The transfer of electrons between oxygen p ( r ) orbitals appears to be less effective than the corresponding pathway in the A state, however, and is less sensitive to axial distortions. Moreover, the more distant oxygen in the B state retains a slight excess of charge over the near oxygen, presumably owing to the former's weaker bonding with the titanium and the attendant inability of its electrons to delocalize efficiently throughout the entire system. Registry No. KTiOP04, 12690-20-9.
Theoretical Studies on the Chemical Reaction Mechanisms of an AI Atom with the COz Molecule Shogo Sakai Department of Computer Science, Faculty of Engineering, Osaka Sangyo University, Daito 574, Japan (Received: May 14, 1991)
The potential energy surfaces for the reaction of an AI atom with a COz molecule are studied by ab initio molecular orbital methods. The reaction takes two steps: the initial formation of the MC02 complex and the subsequent dissociation of A10 from CO. With trans- and Cz,-type AlC02 complexes, the reaction is a typical charge-transfer-reaction mechanism. The two transition states of the AICOz dissociation, to AIO(AZII) + CO and to AIO(XZZ+)+ CO, are close to each other in energy. Accordingly, a surface crossing possibly occurs between the reaction paths to the A10(A211)and A10(X2Z+)products.
Introduction
AI
+ Cop
e
AICOp'
-
AI0
+ CO
(1)
Investigations of chemical reaction mechanisms of atoms with small molecules are very active in both the experimental and theoretical areas. The reactions of main metal atoms with small molecules are particularly important because they may be a key to elucidating the crossing point between organic and inorganic chemistry. Fontijn and Felderl studied the reactions of an A1 atom with a COz molecule over a wide temperature range in a fast-flow reaction. They showed that the reaction exhibited non-Anhenius behavior, interpreting the results on the basis of the second reaction channel to A10(A211)and preferential Al-COz reaction in bending modes. Recently, Parnis and his co-workers2 studied the pressure dependency for the A1-COz reaction in the gas phase by laser-induced fluorescence monitoring of A1 and A10. They proposed reaction mechanisms, including a complex formation channel that would yield a stable AICOz adduct as shown below.
They revealed the complexation and abstraction channels in the A1-COz reactions. Parnis, Kanigan, et al. suggested the formation of the AICOz complex, in another study of the Al-COz reactions in the gas phase by laser-induced fl~orescence.~ More recently, Le Quere and Manceron4 studied the reactions of an A1 atom with a C 0 2 molecule in the gas phase, and two forms of the A1CO2 complex were isolated in the IR spectrum. In all of the abovementioned studies, as well as those of others, the potential energy surfaces of the A1-CO2 reactions have not been theoretically treated. To study the exact reaction mechanisms of the system, we calculated the stationary-point geometries and energies for the reactions of an A1 atom with a COz molecule by a b initio M O methods.
(1) Fontijn, A,; Felder, W. J . Chem. Phys. 1977, 67, 1561. (2) Parnis, J. M.; Mitchell, S. A.; Hackett, P. A. Chem. Phys. Lett. 1988, 151, 485.
(3) Parnis, J. M.; Mitchell, S. A.; Kanigan, T. S.;Hacket, P. A. J . Phys. Chem. 1989, 93, 8045. (4) Le Quere, A. M.; Manceron, L. J . Phys. Chem. 1991, 95, 3031.
AC02
0022-365419212096-13 1$03.00/0 0 1992 American Chemical Society
132 The Journal of Physical Chemistry, Vol. 96, No. 1 , 1992
Sakai TABLE I: Total Energies (trartrees) and Relative Energies ( k a l / a d , in Parentheses) for tbe AlC02 Systems from the AI Atom and CO, Molecule Including Zero-Point Correction (HF/C31G(d))
..
MP4( SDTQ) / MP4(SDTQ) / 6-31G(d)// 6-31G(d)// HF/6-3 lG(d) MP2/6-3 1G(d)
HF/6-31G(d)// HF/6-3 1G(d)
.
Figure 1. Stationary point geometries of the A1C02 complex by HF/6-
AI -429.491 15 (0.0)
31G(d) and MP2/6-31G(d) methods. MP2 results in parentheses. All bond distances are in angstroms.
Theoretical Approach The basis sets used here were the split-valence 3-21G sets and the split-valence plus polarization 6-31G(d) set: All equilibriumand transition-state geometries were determined with analytically calculated energy gradients' at the Hartree-Fock (HF) level, using unrestricted Hartree-Fock (UHF) wave functions. The force constant matrix and thereby the vibrational frequencies were calculated with analytically calculated energy second derivatives.8 Additional calculations were performed to obtain improved energy comparisons-the calculations with the HF-optimized structures with electron correlation (excluding inner shells) incorporated through the second-, third-, and fourth-order Mdler-Plesset perturbation theories [MP2, MP3, and MP4(SDTQ)I .9 To study the potential energy surface for the dissociation of the AICOz complex into A10 and CO, we calculated the transition states and the products by the multiconfigurational (MC) selfconsistent field (SCF) method with the 3-21G basis set. The MC-SCF and the intrinsic reaction coordinatelo (IRC) calculations were performed with the GAMESS program." The other calculations were carried out with the GAUSSIAN~~ pr0gram.l'
-429.50093 (-6.9) -429.50316 (-8.6) -429.50390 (-8.8) -429.50310 (-8.6) -429.46785 (13.5)
type 1 (C,) type I11 (trans) type IV (cis)
TS (cis-trans)
TS
+
A1 C02 --c type 111
+ C02 -430.02390 (0.0)
Complex -430.04219 (-12.3) -430.03757 (-9.6) -430.03749 (-9.4) -430.03682 (-9.2) -430.01838 (2.3)
-430.03081 (0.0) -430.04675 (- 10.8) -430.04228 (-8.2) collapses"
" Collapses to Type I at this level of theory. TABLE II: Theoretical Harmonic Vibrational Frequencies"for AICO, Complexes by HF/C31G(d) freq symm exptl resultsb approx description I (C2") 1715 Bz 1443.5 C-O stretch
111 (trans)
Results and Discussion AK02Complex. The structures of the complexes of alkali-metal atoms (Li and Na) with COz were studied by Jordan and his ~0-worker.I~They proposed two stable structures [type I and 111 for both the Li-C02 and Na-C02 complexes by ab initio MO
1535 907 419 342 130 2063 1345 849 508 66 51
A, A, A, B,
1265.5 796.5 428 213.5
B2
A' A' A' A' A" A'
1780 1146.5 773 468.5
" Harmonic frequencies in cm-I.
C-O stretch C 0 2 bending 0-A1 stretch flapping C02-A1 rock C - O stretch C-0 stretch C 0 2 bending AI-O stretch AI-O-C bending A1-0-C bending
Experimental frequencies from ref
4.
and cis) were known as the intermediate compo~nds'~ of reaction 2. These four types of structures were used as the provisional I C2"
II linear
I11 trans
rv
HO
+ CO
+
HOC0
+
H
+ COS
(2)
CIS
methods. Type I is C, symmetrical, and the C U M bond angle in type I1 is almost linear. The structures of type I11 and IV (trans (5) Binkley, J. S.;Pople, J. A.; Hehre, W. J. J . Am. Chem. Soc. 1980,102, 1980. Gordon, M. S.;Binkley, J. S.;Pople, J. A,; Pietro, W. J.; Hehre, W. J. J. Am. Chem. SOC.1982, 104, 2997. (6) Hariharan. P. C.: PoDle. J. A. Mol. Phvs. 1974. 27. 209. Francl, M. M.'Pietro, W. J.: Hehre, W. J.; Binkley, J. SI;Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (7) Komomicki, A.; Ishida, K.; Morokuma, K.; Ditchfield, R.; Conrad, M. Chem. Phys. Lett. 1977,45, 595. (8) Pople, J. A.; Binkley, J. S.;Seeger, R. Int. J . Quantum Chem. 1975, 9, 229. Pople, J. A.; Krishnan, R.; Schegel, H. B.; Binkley, J. S. Int. J . Quantum Chem. 1979,513, 225. (9) Mdler, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618. Binkley, J. S.; Pople, J. A. Int. J . Quantum Chem. 1975, 9, 229. Pople, J. A.; Binkley, J. S.; Seeger, R.Inr. J . Quantum Chem. 1976, S10, 1. Krishnan, R.; Pople, J. A. Int. J . Quantum Chem. 1978, 14, 91. Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72,4244. (10) Fukui, K. J . Phys. Chem. 1970,74,4161. Ishida, K.; Morokuma, K.; Komornicki, A. J . Chem. Phys. 1977, 66, 2153. Schmidt, M. W.; Gordon, M. S.; Dupuis, M. J. Am. Chem. SOC.1985, 107, 2585. (1 1) Dupuis, M.; Spangler, D.; Wendoloski, J. J. NRCCSofware Catalog 1980; 1 (Program QGOI). Schmidt, M. W.; Boatz, J. A.; Buldridge, K. K.; Koseki, S.; Gordon, M. S.; Elbert, S. T.; Lam, B. T. QCPE 1987, 1, 115. (12) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Ragavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Ruder, E. M.; Pople, J. A. GAUSSIAN8Z; Carnegie-Mellon University: Pittsburgh, PA, 1983. (13) Yoshioka, Y.; Jordan, K. D. Chem. Phys. Lett. 1981,84, 370. Jordan, K. D. J. Phys. Chem. 1984, 88, 2459.
structures for the geometry optimization of the complexes by the HF/6-31G(d) and the MP2/6-31G(d) calculations. The calculated stationary-point geometries are shown in Figure 1. In the type I structure, we calculated three states: 'A,, *B2,and 'BI. The A1 atom was not bound with COz for either the 2B2or the 2B1states. The ground state of type I is the 'AI state and is the charge-transfer-like complex from the charge density (12.447e) on the A1 atom by the HF/6-31G(d) method. An unpaired electron localizes upon the a l or a' orbital of the carbon atom in each of three complexes in the figure. The A1-O-C angle in the trans-type complex showed the largest difference between the two different optimized geometry parameters calculated by the HF/6-31G(d) and by the MP2/6-31G(d) methods. The difference in the relative energies for both trans-type optimized structures, however, is weak (1.4 kcal/mol at the MP4 calculation level). An attempt to optimize the cis-type structure by the MP2 method showed the structure collapsing to a type I. In the HF/3-21G calculation level, there was no stationary point for the cis or trans type I11 and IV structures, but for type I and type 11, stationary points were found (not shown here). The type I1 structure is not at the stationary point at the HF/6-3 1G(d) and MP2/6-31G(d) calculation levels but is in the transition state of the isomerization into trans and cis (or type I) structures. The energy value of the calculated barrier of the isomerization of trans (14) Aoyagi, M.; Kato, S. J . Chem. Phys. 1988, 88, 6409.
The Journal of Physical Chemistry, Vol. 96, No. 1 , 1992 133
Theoretical Studies on the Reaction of A1 with C 0 2
Addition
1
f/
87.8
Abstraction
^i'
,767
2.291
,n i------IbO
1.147
1.18 7
&$'O
123.1,-A.&E'
\.,
AI
0-c 1.124
Figure 3. Transition-state geometries by HF/6-31G(d).
-
12.0
J
1
I
1.6
3.0
TABLE 111: Dissociation Energies of the A I 4 and O C O Bonds (kcalh") D(C-O) D(AI-0)'II D(AI-0)22 HF/6-31G(d)// HF/6-31G(d) MP2/6-31G(d)// HF/6-31G(d) MP3/6-31G(d)// HF/6-31G(d) MP4(SDTQ)/ 6-31G(d)// HF/6-31G(d) MP4(SDTQ) / 6-3 lG(d)// MP2/6-3 1G(d) exP
1
I
3'5
100
AI-C
dlatanec
IA)
Figure 2. Electron density (- -) and 0-C-0 angle (- - -) vs the AI-C distance in the AIC02 (C2"symmetry) complex.
and cis structures with the HF/6-31G(d) optimized structure is small (0.4 kcal/mol above that of the trans structure at the MP4 level). Total energies and the relative energies of the stationary-point geometries are listed in Table I. The type I structure is the most stable, being 2-3 kcal/mol more stable than the other structures at the MP4 calculation level. These calculated binding energies of the complexes are consistent with the experimental estimation2 (>9 kcal/mol). Calculated frequencies for the type I and I11 structures are listed in Table 11. Considering the deviations of calculated frequencies by the HF/6-31G(d) method are about +lo%, our calculated frequencies correspond well with the experimental v a l ~ e s . ~ AI C 0 2 AlCO2 Complex. The calculated geometry parameters of the transition state on the least motion path (C2" s mmetry) to the most stable complex, type I, were AI-C = 2.945 and 0-C-0 = 146.5' a t the HF/6-31G(d) level. This force constant matrix has two imaginary frequencies (98i and 1759i cm-I). One (17591' cm-') corresponds to the reaction coordinate, while the other (98i cm-l) has b2 symmetry. Therefore, this C2,-type transition state is unreal, (pseudotransition state). The value of the energy barrier of the pseudotransition state is 32.0 kcal/mol from the isolated atom and molecule (A1 + C 0 2 ) at the HF/6-3 1G(d) level (including the zero-point correction). To help understand the feature of the pseudopathway reaction mechanism, the variations of the 04-0 angle and the electron density on the A1 atom versus the AI-C distance (corresponding well to the reaction coordinate) are shown in Figure 2. The dotted line shows the electron density on the A1 atom; and the dash-dotted line the 0-C-O angle. The X in the figure is the location of the pseudotransition state. Both the 0-C-0 angle and the electron density change drastically in the vicinity of the transition state. Namely, the N 0 angle becomes the reaction coordinate in this region. This pseudotransition state is an earlier transition state in reference to the AI-C distance. Consequently, this reaction shows the charge-transfer reaction mechanism. The 0-C-0 angle is indicated to be >180° for the region where the A1-C distance is longer than that of the transition state. Therefore, the real transition state is possibly present. in the trans-type reaction path. The transition-state geometry for trans-type addition a t the HF/6-31G(d) level is shown in Figure 3, and the force constant matrix has one imaginary frequency (7361 cm-') corresponding to the reaction coordinate. The Al-0 distance, the 0-C-O angle, and the electron density on the A1 atom along the IRC path are shown in Figure 4. The solid line indicates the A1-0 distance; the dotted line the electron density on the A1 atom; and the dash-dotted line the 0-C-0 angle. While the A1-0 distance varies gradually in the region neighboring the transition state, between about 1.0 and 1.0 (amu)'I2 bohr of IRC, the electron density on the A1 atom and the 0-C-O angle change drastically
+
K
-
70.5
64.1
51.0
128.1
97.6
95.9
112.4
93.6
88.1
118.7
95.4
94.7
120.5
95.5
95.1
126.0'
15.456 kcal/mol above D ( 2 2 )
121.5 & l C 123.1 & Id 132 & 6d
"Reference 14. bReference 17. cReference 15. dReference 16.
in the same region. Accordingly, this reaction is the same charge-transfer reaction mechanism as seen for the C2, pathway. The activation energy at this transition state is 2.3 kcal/mol a t the MP4(SDTQ)/6-31G(d)//HF/6-31G(d) level, which corresponds with the experimental estimation (>1.0 and 2.6 f 1.3 kcal/mol'). Therefore, the A1 + C02 reaction produces a trans-type AlOCO complex with a 2.3 kcal/mol energy barrier. On the other hand, the energy barrier of the t r a n s 4 isomerization of the AlOCO complex is weak enough (0.4 kcal/mol above that of the trans-type complex) to be ignored. AlC02Complex AlO + CO. The reaction Al + C 0 2 AlO C O gives the heat of reaction, which is the difference between the 0--CO dissociation energy and the Al- -0formation energy. To check the accuracy of the heat of reaction by the Hartree-Fock and M P calculation levels, the dissociation energy values of the 0--CO and Al- -0dissociations by various methods are listed in Table 111. The 0--CO dissociation energy by the MP calculation is in agreement with the experimental value within 10% error. On the other hand, though the Al- -0dissociation energy has not been fully determined experimentally, the 2Z state of the A10 is knownI8 to be lower in energy by about 15 kcal/mol than the 211 state. From Table 111, every calculated energy of the 211 state of A10 is lower than that of each corresponding 2Z state. The calculated dissociation energy of the 211state by the HF/6-31G(d) level is lower by about 13 kcal/mol than that of the 2Z state, and the 211state by the MP4 calculation level is lower by 0.4 kcal/mol than that of the 2Z state. Because of the inaccurate energy estimation of A10 (2Z and 211) by the HF calculation, only the transition state leading to A10(A211) + C O (trans type is shown in Figure 3) was found, but one that leads to A10(X2Z) + CO was not found. Therefore, the MC-SCF calculations with the 3-21G basis set for the transition state and the products calculations in this reaction were performed (Table IV). Eleven active spaces corresponding
+
-
-
(1 5) JANAF Thermochemical Tables; National Standard Reference Data Service; US.GPO: Washington, DC, 1971. (16) Dagdigian, P. J.; Cruse, H. W.; Zare, R. N. J. Chem. Phys. 1975, 62, 1824. (17) Schamps, J. Chem. Phys. 1973, 2, 352. (18) McDonald, J. K.; Innes, K. K. J. Mol. Specfrosc. 1969, 32, 501.
134 The Journal of Physical Chemistry, Vol. 96, No. 1, 1992
Sakai 180
2.5
D
0 0
s *
* ?!
w
-7
2.4
