Features of the lowest singlet and triplet potential energy surfaces of

Apr 28, 1993 - 02(32g)+ CO(* +), were investigated byab initio self-consistent-field methods with ...... (12) Breckenridge, W. H.; Taube, H. J. Chem. ...
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1484

J. Phys. Chem. 1993,97, 7484-7490

Features of the Lowest Singlet and Triplet Potential Energy Surfaces of COj Robert D. J. Froese and John D. Goddard' Guelph- Waterloo Centre for Graduate Work in Chemistry, Department of Chemistry and Biochemistry, University of Guelph, Guelph, Ontario, Canada NIG 2Wl Received: September 22, 1992; In Final Form: April 28, I993

Portions of the lowest singlet and triplet potential energy surfaces for the following reactions of oxygen atoms withcarbondioxide: O(lD) C02(1Zi)+O(3P) CO2('Z:),+O2('Ag) CO(1Z+),-02(3ZJ CO(lZ+) and O(3P) CO,('Zi) 0,(3Z;) CO(lZ+),were investigated by ab initio self-consistent-field methods with a split valence plus polarization basis set, 6-31G*, and with the inclusion of electron correlation by several methods. These ab initio results along with earlier experiments suggest that the predominant reaction pathway leads to a low-lying bound region of the singlet potential energy surface. This region involves two COS intermediates: a D3h structure and a C, isomer along with the transition state joining them. The highest levels of theory considered here support a C, ring structure for the COSintermediate which has been trapped in earlier experiments. The theoretical vibrational frequencies are analyzed and compared with experimental results. The bent triplet surface, involving cis and trans species, lies approximately 60 kcal/mol above the low-lying singlets. Diatomic products, CO(lZ+) and 0 2 (31;; or 'Ag) are disfavored by a high activation energy.

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Introduction The primary products formed in the reaction of excited state oxygen atoms with carbon dioxide are ground state oxygen atoms and carbon dioxide. This quenching mechanism predominates over the formation of diatomic products, CO(lZ+) and 0, (3Z; or lAg). The high efficiency of this spin-forbiddenprocess as compared to that of the spin-allowed reactions is somewhat unusual. If a bound COOcomplex was formed in a region of the singlet potential energy surface favorable for an intersystem crossing to the triplet surface, then the spin-forbidden process might become more important. Possible reaction pathways include

hE (kcal/mol)'

As mentioned above, quenching of the excited-state oxygen atom is the principal process observed. The CO and 02molecules were estimated to form very little of the total ~roduct.~.3A statistical model4 predicted that the branching ratio for the formationof CO and 02should be approximately30%. However, that analysis required a number of assumptions including that of low activation barriers for the reactions forming the diatomic products. Isotopic labeling e x p e r i m e n t ~ z .indicated ~~ that a scrambling mechanism must be operative in the quenching since l80was found with an equal statistical probability in any of the three possible positions. In the formation of the minor products, CO + 02, an initially isotopically labeled O(1D) atom was located only in the 0 2 molecule. This observation suggests a direct attack of the oxygen atom on COZ forming an lW-O-C-O minimum which then dissociates into l S O - 0 and C-0. The quenching process may involve some long-lived bound intermediate while the much less probable formation of the diatomic products, CO + 02, may proceed more directly but with a significant activation barrier. There is clear experimental evidence for a C 0 3 0022-3654/93/2097-7484So4.00/0

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intermediate. Excited-state oxygen atoms (O(lD)), from the photochemical decomposition of ozone by ultraviolet radiation, react with COz to generate a C 0 3 reactive intermediate first postulated to explain oxygen- 18 isotopic labeling experiments in 1962.8 This COP intermediate was later in solid matricesof C02 or Ar. A detailedinfrared study10of the products from the photolysis of solid C02 indicated that the CO3 structure possessed CZ,symmetry with a three-membered OCO ring and an exocyclic carbonyl group. There have been a number of studies on similar molecules. Modern research on S(lD) plus CS2('Z;) using laser induced fluorescence'' examined the CS3 potential energy surface and there were also earlier pioneering experiments12 on this system. The COS2 potential energy surface has been studied in great detail13 due to the importance of the secondary reaction (O(3P) CS(lZ+)) in one version of the carbon monoxide laser. There also has been some limited experimental work3J4on the C02S surface. Early theoretical studies on CO3 with semiempirical methodsl5J6 favored either the CZ,ring structure or the C, chain species depending upon the approximations used. A CNDO study16 of the D3hstructure suggested that a Jahn-Teller" distortionwould split the highest occupied degenerate molecular orbital of symmetry e' in the CNDO approximation into two orbitals with the system stabilized by the electrons in the lower energy a1 molecular orbital. Many other theoretical studieshaveconsidered the possibility of CZ,and/or C, structures for CO3. More recently, the C, structure was disregarded since it was predicted to be approximately 55 kcalfmol higher in energy than the CZ,form when electron correlation was considered.'* Many other theoretical studies10Jez3 have been performed, usually supporting the CZ,ring structure. In 1987, the first studyz4to predict that t h e & , structure might be the most stable species appeared. This ab initio study used configuration interaction (CI) and predicted that the 4 1 form was more stable than the CZ,species by 7.5 kcalfmol. Further studies using many-body perturbation theory also indicated that the D3h structure was more stable.zs.26 Since the D3h species has fewer infrared (IR) active bands than the Cb species and the matrix isolation experments observed the number of bands appropriate to a CZ,structure, it was suggested that somehow the carbon dioxide matrix may favour the formation of the CZ,ring structure. However, the CZ,form was also assigned to the species

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0 1993 American Chemical Society

Potential Energy Surfaces of COS observed in the even less interacting argon matrix. Thus experiments favor the CZ, form. An isovalent system, CS3, has been studied by ab initio methods and the D3h structure was predicted to be 4.1 kcal/mol higher in energy than the CZ, species using perturbation theory (MP4/ 6-31G*//MP2/6-31GS with zero-point vibrational energy (ZPVE) corrections) or 9.7 kcal/mol using the quadratic configuration interaction method (QCISD(T)/6-3 lG*//MP2/ 6-31G" + AZPVE).2' The MP4/6-31G*//MP2/6-31G* notation implies a single-point energy prediction at the MP4 level employing the 6-3 1G* basis set and using the optimized geometry from an MP2/6-31G* calculation. It has been suggested that NO3+,which is isoelectronic with C03, also has a CZ,structure which is more stable than the D3h onesz8 Other ab initio studies including electron correlation effect~2~93~ on the lowest singlet and triplet potential energy surfaces of COS2 and C02S have indicated that the most stable intermediates are singlet ring compounds. This study uses ab initio methods with electron correlation included by Morller-Plesset perturbation theory (MPn), configuration interaction with single and double excitations (CISD), and coupled cluster methods (CCD, CCSD, QCISD(T)) to study portions of the lowest singlet and triplet potential energy surfaces of C03. Harmonicvibrationalfrequenciesarecomputed at several levels to verify the nature of the stationary points located. Theory sheds additional light on the quenching and on other reactive processes.

Computational Details Calculations were carried out with the GAUSSIAN 90 and GAUSSIAN 92 programs.31 The 6-31G* basis set32 was used for most computations. A few computations were carried out with the 6-31 lG* basis on particularly important structures to assessthe effects on energeticsof enlarging the basis set. Minima and transition states were found using energy gradient methods and the algorithms of Schlegel.33 These stationary points were characterizedby determiningthe harmonicvibrationalfrequencies using analytic second-deri~ative'~ methods at the SCF level. Many of the structures also were optimized at the simplest correlated level, namely, MP2. Harmonicvibrational frequencies were determined by finite differences of analytical gradients at suitably distorted geometries. The MP2 harmonic vibrational frequencies were scaled by a factor of 0.95 prior to comparison with experiment. Single point energies from full fourth-order Morller-Plesset perturbation theory (MP4SDTQ)35 were determined at these MP2 optimized structures. The notation MP4/ 6-31G*//MP2/6-3 1G* represents an MP4 single-point energy calculation with the 6-31G* basis set using the MP2/6-31G* optimized geometry. The geometries of the two lowest lying singlet minima also were optimized at the CAS-SCF, CISD, and CCD36 levels and CCD harmonic vibrational frequencies were computed. Singlepoint energies were predicted for selected structures at the CCSD or QCISD(T) levels.37 Hartree-Fock stability38.39checks of the SCF wave functionswere performed and any wavefunctionswhich showed a nonsinglet instability were reoptimized. The complete active space self-consistent-field(CAS-SCF) calculations using Pulay's scheme40 for active orbital selection were carried out in order to resolve certain difficulties in predicting the oxygen atom 3P to lD energy difference. With the unrestricted Hartree-Fock approach,UHF minima and transition states were found in certain regions of the singlet potential energy surface, and such discoveries were followed both by the reoptimization at the UMP2 level of these structures and by UMP4 single-point energy calculations. Intrinsic reaction coordinates (IRC) were followed at the SCF level in both the forward and reverse directions from the various transition states to ensure which minima each transition state was connecting.

The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7485

T1

T5

/?!1.406

OzzIC

Figure 1. Stationary points on the co3 chain triplet surface. 6-31G' SCFand MP2 structuresare shown. The truns (Tl) andcis (T2) minima are the lowest energy structures. These minima are linked to both reactants, O(3P) + CO,('Zi), through transition states (T5) and (T6) and to products, O,('Z;) + CO('Z+),through transition states (T3) and (T4). The two minima are connected by the internal rotation transition state, T7, which was located at the SCF level only. The transition state-s are labeled ($) and all other species are local minima.

SCF

T8

MP2

Figure 2. Optimizedgeometriesoftwo open triplet carbon trioxidespecies. The CZ,minimum (T8) and the asymmetrictransition state (T9, $)linking this minimum to the CO,('Z+) + O(3P) products areshown. Geometries were optimized at the 6-316' SCF and MP2 levels of theory.

Results and Discussion

Triplet Potential Energy Surface. Optimized geometries for seven stationary points on the triplet chain potential energy surface are shown in Figure 1. All but one of these structures are planar and both cis and trans isomers have been located. Transition states T3 and T4 link the minima, T1 and T2, todiatomic products, CO(lZ+) and 02(3ZJ while T5 and T6 link the same minima to C02('Zl) and O(3P). The out-of-plane internal rotation transition state (T7) also is presented in this figure. Figure 2 shows two other triplet species, an open CZ, minimum (T8) and a transition state (T9) linking this species to the products. Table I contains data for all these triplet species at the MP2//MP2, MP4//MP2, and QCISD(T)//MP2 levels of theory. The zeropoint vibrational energy corrections calculated using the MP2 harmonic frequencies are reported along with the expectation value of 52 for the UHFprocedure. Only for the transition states do the 9 values differ from the ideal result of 2.00 by more than 5%. The two triplet minima (trans,T1 and cis, T2) shown in Figure 1 are predicted to be close in energy. Various levels of theory (MP2//MP2, MP4//MP2, and QCISD(T)//MP2, with MP2 ZPVE corrections) predict these two minima to be within 1 kcal/ mol of each other. Structural differences between the two minima at the MP2 level include an opening of the 04-0moiety from

Froese and Goddard

1486 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993

TABLE I: Ene etics of the Triplet Carbon Trioxide S iesG and the TransitiOa States Coapec ' I "to Reactants and products at the %2//MP2, MP4//MP2, and QCISDE//MP2 Levels of Theory Using the 63% W i Set MP2//MP2

E (4 -262.886 912 -262.885 624 -262.882 548 -262.881 186 -262.835 140 -262.861 350 -262.810 621 -262.956 084 -262.920 112

T1 T2 T3 T4

T5

T6 TP T8 T9

MP4//MP2

AE= 12.4 13.2 15.2 15.1 104.9 84.1 82.1 29.0 51.2

E (ad -262.918 299 -262.917 085 -262.911 881 -262.911 053 -262.812 906 -262.903 989 -262.900 826 -262.981 080 -262.956 185

QCISD(T)//MP2

AE 65.9 66.1 66.2 66.1 94.4 74.9 16.9 22.8 42.2

E (au) -262.918 581 -262.918 632 -262.921 504 -262.920 616 -262.887 369 -262.913 486 -262.903 519 -262.986 341 -262.965 314

AE 60.8 60.1 58.9 59.5 80.4 64.0 10.2 18.3 31.5

stationarypoint min min

TS TS TS TS

TS min TS

S2 2.02 2.03 2.06 2.01 2.34 2.12 2.04 2.04 2.12

ZPVEd 1.3 1.5 6.0 6.1 6.6 6.8 1.6 10.11 1.V

I, The cisjtrans chain structures all have stable Hartree-Fwk wave functions. Structures T8 and T9 have unstable Hartree-Fock wave functions. T8 (3A1),and T9 (3A'). e AE (kcal/mol) is the energy differencebetween the given structure and the singlet C%carbon trioxide ring compound. ZPVE: zero-point vibrational energy in kcal/mol calculated from the MP2 frequencies. No MP2 optimized structure was located, hence the energy evaluations were done at the SCF geometry, and the ZPVE correctionswere taken from the SCF frequencies. 1SCF convergence problems in calculating MP2 vibrational frequencies numerically were encountered. These ZPVE were calculated using SCF frequencies. b The electronicsymmetries of all these molecules are 3A'' except for T l

122.87O in the trans species to 129.57' in the cis isomer. This increased bond angle may serve to reduce nonbonded repulsions between the terminal oxygen atoms in the cis species. The bond lengths are very similar in these two triplet minima, with none of the three distances differing by more than 0.01 A at the MP2 level. These bond lengths and angles may be compared with those in triplet C02, which has a bond length of 1.235 A and a bond angle of 119.63O at the MP2/6-31G* level. These triplet cis and trans minima are metastable and lie considerably higher in energy than either the O(3P) CO,('Z;) reactants or the O,('Z-) CO(lZ+) products. For example, at the MP4//MP2 AZhVE level, the cis minimum lies 69.3 and 59.6 kcal/mol above the reactants and products, respectively. An internal rotation transition state, T7,between the cis and trans species was found at the SCF level, but could not be located using MP2 theory. At the Hartree-Fock level, the barrier to internal rotation from trans to cis is 7.1 kcal/mol (SCF//SCF AZPVE using SCF harmonicvibrational frequencies). A more reliable estimate of the barriers involves comparison of the QCISD(T) energies. At this level, the barrier to internal rotation is 8.7 kcal/mol. The precise value of the barrier is in question, but the surface is certainly flat. The geometry of this out-ofplane transition state should be noted. The central C-0 fragment has an SCF bond length of 1.406 A, which is significantly longer than in either the cis or trans minima, which have bond lengths of 1.340 and 1.362 A, respectively. Any extended electron conjugation in the C 0 3 species is lost in the twisted transition state. The small barrier to rotation may be the reason why this transition state was not located at the MP2 level. The "true" rotational barrier may be greater than that to dissociate the molecule into CO('Z+) 0,(3Z;). Thus, as the molecule rotates from cis to trans, it may be easier for it to dissociate into diatomic fragments than to continue along the internal rotation reaction path. The triplet oxygen atom and carbon dioxide reactants lead to the metastable cis and trans minima, which can dissociate to triplet diatomic oxygen and singlet carbon monoxide. The reactants, O(3P) and CO,(.'Z:), are very stable species and the activation barrier is quite high. On the cis surface, the transition state (T6)lies 76.8 kcal/mol (MP4//MP2 AZPVE) above these reactants. Another level of theory, QCISD(T), gave similar results with a barrier in kcal/mol (including AZPVE) of 66.1. Similarly, the barriers (in kcal/mol) to form the truns species through transition state (T5) are 96.1 for MP4 and 82.3 for QCISD(T). The 04-0 bond angles in these transition states have changed from linear ( 180') in the carbon dioxide reactant toapproximately 146' in thecis and 147O in the transstructures. At the SCF level, the forming 0-0 bond has a length of approximately 1.45 A in the cis but is much longer at 1.55 A in

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the trans molecule. However, at the MP2 level, this difference decreases with the distance of the attacking oxygen atom to one of the oxygens in C02 in these two transition states being 1.49 A for cis and 1.52 A for trans. These minima dissociate to products CO(lX+) + 02(3Z;) through the transition states, T4 for cis and T3 for trans. The reaction barriers are predicted to be very low. The cis and trans species face barriers to dissociation (in kcal/mol) of only 1.1 and 1.5 kcal/mol at the most consistent level (MP2//MP2 including AZPVE). Higher level calculations, MP4 and QCISD(T) at the fixed MP2 geometries, actually predict that the transition state lies below the minima. The reaction barrier must be small. The transition state structures have a long internal C-O bond of 1.607 A in the cis and 1.599 A in the trans structure at the MP2 level. The external C-O and 0-0 bond lengths have shortened to approach those in the free diatomic molecules, CO and 0 2 . The C-O bond length has been reduced from 1.181 A in the cis minimum to 1.166 A in the transition state and these values may be compared with the 1.150 A bond length in CO at the same level of theory. Similarly, the C-O bond length on the trans pathway has changed from 1.183 A in the minimum to 1.167 A in the transition state before proceeding to products. The bond length of the 0 2 moiety in both the cis and trans structures has decreased from approximately 1.34 A in the minimum to 1.28 A in the transition state. The ground state oxygen molecule is predicted to have a bond length of 1.246 A, which compares with the experimental value41 of 1.208 A. Since both of these transition states are severely bent, some rotational excitation of the products would be expected. In addition, the transition-state bond lengths differ significantly from the products which should lead to some vibrational excitation of the product. Overall, the triplet chain surface itself is very flat with low barriers. The significant barriers are those to proceed from reactants, O(3P) + CO,('Z;), to the chain surface as barriers of 76.8 and 96.1 kcal/mol exist for cis and trans (MP4//MP4 AZPVE). If the chain triplet surface can be accessed, the products should be formed quite rapidly because the surface is extremely flat and the products (as with the reactants) lie much lower in energy. The overall reaction

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o()P)

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+ co2(lz;)

0 , ( ~ 2 ;+ ) CO('Z+)

is endothermic by 7.8 kcal/mol,l and our ab initio results (MP4// MP2 + AZPVE) reliably predict a value of 9.7 kcal/mol. Unlike the CS3 potential energy s u r f a d 7 which has distinct trans and cis reaction pathways because the internal rotation transition state has a significantly higher barrier than the other transition states, the C 0 3triplet chain potential energy surface is extremely flat and distinct cis and trans reaction mechanisms would not be expected.

The Journal of Physical Chemistry, Vol. 97, NO. 29, 1993 7487

Potential Energy Surfaces of COS

minimum (SI) was found at the MP2 level. Once the D3h minimum (Sl) is formed, the transition state leading to the CZ, ring minimum can be reached. This region with CZ, and D3h minima as well as the transition state for their interconversion is the most likely candidate for the bound area on the singlet surface where an exchange of the oxygens occurs. Another transition state linking the reactants to the intermediate region of the potential energy surface was found leading to the CZ, minimum. This transition state (S5) leads to the open CZ, minimum (see the UMPZ geometry of S2 in Figure 3). The UMP4//UMP2 AZPVE barrier leading from O(1D) and CO,('Z;) through this transition state (S5) is 7.7 kcal/mol. However, the value of this barrier is somewhat uncertain as will be discussed further below. The transition state (S4) linking the D3h and CZ, structures represents a barrier of 8.6 kcal/mol (CZ,to D3h) at the QCISD(T) AZPVE level. The 0-0 bond length in the three-membered ring of the CZ,structure is predicted to be 1.629 A. This value is increased to 1.996 8, in the transition state and the fully symmetric D3h structure has a distance between oxygens of 2.226 A. It is interesting that the two C-O bond lengths in the transition state of 1.286 A are almost identical to those in the D3h structure, whichare 1.285A. Hencetheprimarycomponentsofthereaction coordinate after the transition state (CZ,to D3h) are the changing of the 0-C-O bond angle and the carbonyl C=O bond length. The barrier to traversing transition state S3 from reactants directly to the D3h minimum is extremely high (>35 kcal/mol), and thus this transition state is probably experimentally unimportant. Comparison of the L& and C, Structures. A detailed comparison of two low-lying singlet structures has been carried out with complete geometry optimizations at the RHF, UHF, MP2, UMP2, CAS(2,2), CISD, and CCD levels of theory. In addition, single-point energy calculations were carried out at the MP4//MP2, UMP4//UMP2, CAS(4,4)//SCF, and QCISD(T)//CISD levels. Figure 3 shows the optimized geometries and Table I11 collects selected energetic data. Unrestricted methods were employed because the HartreeFock wave functions for both the CZ,and the D3h structures were found to be singlet unstable. These instabilities lead to lower energy solutions with expectation values of Sz which deviate significantly from the ideal value of zero for a closed shell singlet. TheUHFdescriptionofthe Cbring structureleads toanoptimized 0-0 distance which is increased from 1.512 (RHF) to 2.137 A (UHF) with = 0.98. The molecule is no longer a ring since the 0-0 distance is too long to allow for significant overlap. This UHF singlet species has diradical character as indicated by the occupation numbers of the natural orbitals.43 As mentioned previously, an open C, triplet structure (T8) was optimized at the SCF and MP2 levels of theory and that species has some similarity to the UHF singlet. The 0-0distances in the triplet are SCF and MP2 2.072 and 2.105 A, while for the UHF singlet, these values are 2.137 and 2.158 A. Similarly, the 0-C-Obond angles in the triplet species of 114.6O and 113.4' are comparable to the angles of 107.6O and 107.3' in the UHF singlet molecule. The C-O bond lengths differ considerably as the singlet still possesses a normal carbonyl group while the triplet species has two shorter and one longer C - O bond. The D3h structure was examined for Hartree-Fock instabilities. UHF and UMPZ optimized structures were located which possessed D3h geometries, but the wave function no longer treated all three oxygens equivalently as indicated by the atomic charges. An unphysical closed shelldescription of such a D3h speciesrequires double occupancy of only one of two degenerate orbitals. In addition, there is a very low-lying virtual orbital of symmetry a2'. Instabilities and unrestricted singlet solutions were examined initially as much lower SCF energies could be located if unrestricted methods were used. However, once electron corD3h

RHF

UHF Mpz

UMPZ CISD

CCD

c2v

e :107.6 71.0

s2

m

s3 + s5

1.339 1.321 1.334

0

,1.J I 1 / O-!k?!-C . ]1521.2 1.220\ 157.80 1.204 n

74.5 107.3 72.4 73.4

lLll

CZv

'6

Figure 3. Optimized geometries for four singlet species on the carbon trioxidepotential energy surface. The D3h (Sl) and the CZ,(S2) minima were optimized at the RHF, UHF, MP2, UMP2, CISD, and CCD levels of theory using the 6-31G' basis set. The transition state joining the reactants to the D3h minima (S3)was optimized at the MP2 level, while the transition state linking the Ca and D3h minima (S4) was optimized at the MP2 and CCD levels. The two transition states are labelled ($) and the other species are local minima.

An open CZ,symmetric COS triplet species (T8) was found which was considerably lower in energy than the chain triplets discussed previously. This triplet speciesdoes not possess a carbon oxygen double bond as the one C-O bond length is 1.313 A, while the pair of symmetry equivalent oxygens have bond lengths of 1.259 A. The exocyclic CO bond length is comparable to that in the 3n7r* state of a molecule such as f ~ r m a l d e h y d e .The ~~ 042-0bond angle is 113.4O in this open triplet species. A transition state (T9) was located which links this structure to the reactants. In the transition state, one of the carbon-oxygen distances increases to 1.573 from 1.259 A in the minimum and the 0-C-0 bond angle of 123.3O in the minimum has increased to 150.4O in the transition state, thus approaching the linear bond angle in carbon dioxide. The other two C-0 bond lengths have shortened from 1.259 to 1.238 A and 1.335 to 1.191 A. The barrier (in kcal/mol) to forming O(3P)+ COZ(l2+)through this transition state is 7.2 for SCF, 19.3 for MP2, 16.f for MP4, and 10.3 for QCISD(T). The probable value of the barrier is =lo kcal/mol. It is unlikely that T8 would dissociate into 0, (32,) CO(lZ+). An asymmetric distortion of T8 could lead to O(3P) CO,('Z:) through T7 as discussed earlier, or it could lead to the minimum T1, which then would have to traverse a high energy transition state since T1 lies 39.7 kcal/mol above T8. To symmetrically remove both oxygens from T8 to form 0, ('2;) CO('Z+) probably would require a large amount of energy to surmount a barrier caused by the great change in 0-0 bond length from 2.105 A in T8 to 1.246 A in 0,(32;). Singlet Potential Energy Surface. There have been many previous studies which have investigated the two lowest energy singlet structures. Figure 3 showsthegeometriesof thelow energy CZ,(s2) and D3h (SI) minima, the transition state (s4) joining these two, the transition state (S3) connecting the D3h minimum with the reactants, O(1D) C02('2:),.and the transition state (S5) connecting the CZ, minimum with the reactants. The energetic data for these singlet stationary points are collected in Table 11. An open Cb transition state (S3) joining the reactants to the

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(a2)

7488 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993

Froese and Goddard

TABLE II: Energetics of the Singlet Carbon Trioxide Species’ MP2//MP2

stationary point ZPVEc min 9.2 min 8.8 s2 TS 8.4 s3 TS 8.4 s4 TS 7.7 s5 The D3h minimum (Sl), the CZ,minimum (S2), the transition state (s4) joining these two minima, the transition state connectingthe D3h minimum to reactants (S3), and the UMP2 transition state (S5) joining the CZ,minimum to reactants are tabulated. Structures were optimized at the SCF and MP2 levels. Energies are given at the MP2//MP2, MP4//MP2, and QCISD(T)//MP2 levels of theory all using the 6-31G* basis set. b AE (kcal/mol) is the difference between the energy of the given structure and a low-energypoint on the singlet surface, the CZ,carbon trioxide ring compound (S2). ZPVE zero-point vibrational energy calculated from the MP2 harmonic vibrational frequencies except for the D3h structure (Sl) which used the CISD vibrational frequencies.

s1

E (au) -263.028 977 -263.002 345 -262.855 451 -262.976 160 -262.913 161

QCISD(T)//MP2 E (au) AE

MP4//MP2 AEb

-16.7 0.0 92.2 16.4 56.0

E (au) -263.042 931 -263.023 393 -262.898 028 -263.008 174 -262.947 001

AE

-12.3 0.0 78.7 9.6 47.9

TABLE III: Com rison of the a b and CZ,Structures at Various Levels of fieory Using Both the 6-31C* and 6-3116* Basis Sets’ level of theory

RHF/RHF

DJhenergy

-262.220 -262.344 -263.042 -262.991 CAW,2)//CAWJ) -262.355 CISD+SCC//CISD -262.983 QCISD(T)//CISD -263.006 -263.009 QCISD(T)//CCD -262.941 CCD//CCD -262.954 CCSD//CCD -263.074 CCSD//CCDd -263.080 QCISD//CCW -263.137 QCISD(T)//CCD UHF//UHF MP4//MP2 UMP4//UMP2

693 771 931 273 012 624 291 175 421 565 613 334 031

Cb energy -262.317 571 -262.379 739 -263.023 393 -262.988 388 -262.386 228 -263.003 644 -263.01 1 609 -263.014 312 -262.974 789 -262.985 459 -263.104 114 -263.108 421 -263.139 774

AI? -60.8 -21.9 12.3 1.8 -19.6 -12.6 -3.3 -3.2 -20.9 -19.4 -18.5 -17.6 -1.7

AI% (+AZPVE)C -61.2 -22.3 11.9 1.4 -20.0 -13.0 -3.7 -3.6 -21.3 -19.8 -18.9 -18.0 -2.1

‘Structures were optimized at the RHF, UHF, MP2, UMP2, CAS(2,2), CISD, and CCD levels of theory using the 6-31G* basis set. Additional single-point energy calculations using the 6-3 lG* basis sets were made at the levels of MP4//MP2, UMP4//UMP2, QCISD(T)/

/CISD, QCISD(T)//CCD, and CCSD//CCD. Single-point energy predictions using a larger basis set (6-311G*) at the CCD/6-31G* optimized geometry were made at the CCSD, QCISD, and QCISD(T) levels. AE represents the energy difference (kcal/mol) between the D3h and CZ,structures, E(Ca) Energy difference including the zero-point vibrational energies computed as 9.2 kcal/mol for the D3h structure (CISD) and 8.8 kcal/mol for the CZ,isomer (MP2). Larger basis set prediction as the single-point energies were determined using the 6-311G’ basis set at the CCD/6-31GS geometry.

relation was included, the MP2 energies based on a closed shell singlet starting point were lower. Predictions of the geometries a t the closed shell SCF (RHF), closed shell MP2 (MP2), configuration interaction with single anddouble substitutions (CISD), and coupled cluster with double excitations (CCD) levels have been made using the 6-31G* basis set. In addition, single-point energy calculations at many other levels of theory have been carried out. From the energetic data presented in Table 111, all levels of theory except perturbation theory support the CZ,structure as the lowest energy species. The MP2 and MP4 approaches indicate that the D3h species is the ground state. There are some significant changes in the energy differences in Table I11 with methodology. As indicated by this table, the energy difference (including ZPVE) between the CZ, and D3h structures using the QCISD(T)//CISD was 3.7 kcal/ mol and that for QCISD(T)//CCD was 3.6 kcal/mol, indicating that the choice of optimized geometries at which to carry out higher levelsingle-point energy calculations was not a determining factor. The extension of the basis set had only a minor effect as theenergydifferenceat theCCSD/6-3 1G*//CCD/6-31G1 level was 19.8 kcal/mol, while the energy difference at the CCSD/ 6-31 lG*//CCD/6-31G* level was 18.9 kcal/mol. The last two entries (QCISD versus QCISD(T)) in Table I11 do indicate that the effect of triple substitutions plays an enormous role in the energy differences between the two species. The poor R H F starting point for the D3h species as shown by the 61.2 kcal/mol

-263.009 -263.015 -262.895 -263.001 -262.956

765 440 709 077 093

3.6 0.0 75.1 9.0 37.2

TABLE Iv: Comparison of Scaled Theoretical Vibrational Frequencies with Experiment.. Scaled Vibrational Frequencies and the Indicated Infrared Intensitiesb at the MP2 and CCD Levels of Theory for the Singlet Cz, Carbon Trioxide (COB)Ring Structure and at the CISD and CCD Level for the Symmetric a b Species MP2 CCD Ca ring (0.95 scaled) (0.95 scaled) mode VI a] 1967 (457.0) 2041 (538.6) CO stretch vz bl 1036 (164.3) 1026 (103.7) COz asymmetricstretch 1098 (12.1) COzsymmctricstretch v3 a1 1051 (12.1) COzscissor 637 (18.7) 670 (14.8) v4 a1 635 (38.8) out-of-planewag bl 624 (164.3) 558 (1 1.5) CO bend and COz rock V6 bz 532 (8.0) D3h VI

e’

CISD

CCD

(0.95 scaled) 1642 (118.3) 1169 (0.0) 761 (42.9) 466 (15.3)

(0.95 scaled) 1840 (152.7) 1 1 16 (0.0) 729 (35.0) 667 (152.8)

mode

totally symmetricstretch out-of-plane wag az” e’ Experimental frequenciesg(cm-I): uI(a1) = 198 1, uz(b1) = 972, us(a1) = 1073, ~q(a1)= 593, Vg(bZ) = 568. Infrared intensities are given in brackets in km/mol. vz v3 v4

81’

energy difference a t that level explains why the 0 3 6 isomer is lowered more in energy than the CZ,species when higher order correlation corrections such as the approximate inclusion of triple substitutions in QCISD(T) are computed. It is interesting to compare three frequently used electron correlation methods (MP2, CISD, and CCD) for these two species. As Figure 3 indicates, the bond lengths (A) for the D3h structure at the three levels of theory (MP2/CISD/CCD) are 1.285,1.239, and 1.253. The values for the C, ring structure are as follows: carbonyl C = O 1.187, 1.169, and 1.178; ring C-0 1.346, 1.321, and 1.334; ring 0-0 1.629,l S60, and 1.594;and LO-C-O 74.5O, 72.4’, and 73.4O. As thesenumbers indicate, therearesignificant structural differences a t the three levels of theory, especially for the D3h C-0 and CZ,0-0bonds. Harmonic Vibrational Frequencies. The predicted harmonic and scaled vibrational frequencies of the CZ,and D3h species are collected in Table IV. A comparison of the frequencies for the CZ,species at the SCF, MP2, and CCD levels with the matrix isolation experiments gives reasonable agreement. The MP2 and CCD values (both scaled by 0.95) are in reasonable accord with experiment for the Cb molecule. There are complications in comparing the D3h structure with experiment. Determination of the SCF frequencies yielded an imaginary frequency of symmetry e’. This difficulty was anticipated as a similar problem had occurred for the symmetric D3h singlet CS3molecule.27 The MP2 results were expected to rectify the problem as they had with the CS3 molecule, but did not. The C-0 stretch was predicted to occur at 3524 cm-1 with an intensity of 48624 km/mol, both of which are unphysical. Merller-Plesset perturbation theory based on a wave function that is Hartree-Fock unstable is giving erroneous results. The

Potential Energy Surfaces of CO3

TABLE V: Energetics of the S i l e t and Triplet Oxygen Atom at RHF, UHF, MP4, UMP4, MPS, CAS(4,4), CISD, CCD, QCISD(T), and QCISD(TQ) Levels Using the 6-316+ Basis Set' singlet tridet oxygen atom AE -14.656 604 19.9 RHF -14.146 216 UHF -74.183 934 23.6 MP4 -74.793 141 64.5 -14.895 913 UMP4 -14.858 809 23.3 -14.195 132 -14.896 521 MP5 63.2 -74.719 512 -74.188 194 CAS(4,4) 43.1 -14.191 149 -14.894 011 CISD 60.4 -14.895 314 -14.805 001 56.1 CCD -14.812 818 52.6 -14.896 631 CCSD(T) -74.896 682 -14.812 150 QCISD(T) 52.1 -14.814 645 -14.896 803 51.6 QCISDVQ) experimental' 45.4 a The singlet-triplet energy splitting for the oxygen atom is given in kcal/mol at the various levels of theory and the experimentalresult is also provided. CISD and CCD methods gave the vibrational frequencies listed in Table IV for the D3h isomer. These values are certainly far more reasonable than the MP2 ones. These predicted frequencies for the CZ, species are in better agreement with the findings of the matrix isolation experiments. It should be noted that the quoted frequency of 1981 cm-i is not truly an observed value. It has been suggestedgthat the observed value of 2045 cm-l is lowered to the quoted value by Fermi resonance with the overtone of the 972 cm-' band. The CZ,geometry is predicted to be the ground state of C 0 3 by the most reliable calculations performed in this study and the vibrational frequencies are in good agreement with experiment. Reaction Pathways. Experimental evidence suggests that the bound region of the C 0 3 singlet surface must be reached for the reaction of excited oxygen atoms and carbon dioxide. Thus it is anticipated that the C, and D3h minima must be accessed. A low or possibly even no barrier through S5 leads to the CZ,minimum. Since the singlet oxygen atom reactant is not well described, our best estimate is that there is essentially no activation energy. Table V presents energy calculations at several levels of theory for the oxygen atom. If it is assumed that the ground-state triplet of these species is described relatively well, then the substantial differences at the various levels of theory are due to variations in the description of the singlet species. The R H F description leads to a splitting which is far too large. However, the U H F description with one electron in each of the two degenerate orbitals leads to a singlet diradical which too closely resembles the triplet, leading to a singlet-triplet splitting which is too small. A multiconfigurational SCF approach is required to be even semiquantitatively correct. The CAS(4,4) method uses a four orbital, four electron active space and this method gives the singlettriplet splitting result which agrees best with experiment. Thus, for the O(lD) and CO,('Z;) endpoint, the CAS(4,4) singlettriplet energy splitting was used to correct the QCISD(T)// UMP2 energy for the O(3P) and CO,('Z:) limit. If this estimated value for the O(lD) and C02('Z;) endpoint is used (see Figure 4), then the transition state (S5) lies just below the reactants (by -3 kcal/mol) and no barrier to the reaction exists. In an earlier study, the CS3 triplet chain potential energy surface27 was shown to be more accessible than the C03 chain triplets. In fact, the CS3 triplet trans minimum is only 0.9 kcal/ mol above the reactants and only 34.1 kcal/mol above the lowest lying singlet, the C , ring structure. In contrast, the C03chain triplet minimum lies 20.3 kcal/mol above the reactants and 59.3 kcal/mol above the CZ, singlet. The differences in the heights of the two chain triplet surfaces relative to the low-lying singlets suggest that the C03 triplet surface is much less likely to be accessed experimentally than in the CS3 case. As alluded to in the introduction on C 0 3 and from experimental work on CS3, it

The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7489

A

59.9..

kAo s2

. d +coz

/

/O

3 0

o=c ' 0I

c 2" QCISD(T)/MF2

0-c '0 D3h

TRIPLET SINGLET Figure 4. Schematic representation of the energetics for some singlet and triplet carbon trioxide species. All energy differences are in kcal/ mol relative to the Ca singlet minimum, S2, and are from the QCISD(T)/MP2 method except for the O(*D)+ CO,('Z:) endpoint which corrects the reliable OcP) + CO,('Zl) energy with the CAS(4,4) splitting of the oxygen atom. Transition states, S3 and S5, lead from O(lD) + COZ('2+)to the D3h and CZ, minima, respectively, with the barrier through S! being lower. Transition state S4 links the two lowlying singlet minima. The O(3P) + CO,('Zi) products can be formed from the open CZ, minimum (T8) through the asymmetric transition state (T9). The transition states in this figure are clearly labeled ($)and all other species are local minima. would seem that the low-lying bound singlet regions (containing the CZ,and D3h species) of both surfaces are reached. The large difference in energy of the singlet and triplet surfaces can rationalize the formation of products, CS(lZ+) + S,('Z;), as observed on the CS3 potential energy surface while the quenching process forming the ground state C02 and 0 dominates for the C 0 3 reaction. The most likely mechanism proceeds from O(lD) C02 ('E;) through transition state (S5) to the open diradical minimum (S2). This path allows for the low-lying bound region to be reached (S1 and S2). The CZ, or D3h bound region of the singlet potential energy surface if reached can explain the scrambling results from experiments. In or near this region, an intersystem crossing to the triplet surface may occur possibly near the CZ,open triplet minimum (T8). Therelatively low barrier through T9 to form O(3P) C02('Z:) can then be surmounted easily. No experimental information was located on the addition of O(3P) to C02. Due to the high stability of the reacting species and large activation barriers, it must be difficult for that reaction to proceed. The relative energies of the key singlet and triplet species are shown schematically in Figure 4.

+

+

Conclusions The following conclusions can be drawn from this ab initio study of the lowest singlet and triplet potential energy surfaces of C03: (1) A low-lying bound region of the singlet potential energy surface is predicted which can account for the observed equivalence of all oxygens in isotopic labeling experiments. The ground state isomer of C 0 3 is predicted to possess CZ, geometry. (2) A considerably larger activation barrier than that required to reach the complex singlet region exists for the addition of oxygen onto an oxygen of carbon dioxide to form triplet intermediates. Formation of the CO + 0 2 products is less likely. (3) The minor products, CO('Z+) + O2('Z;), are formed by a direct mechanism on the high energy triplet surface without scrambling of the isotopically labeled oxygens.

7490 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993

Acknowledgment. This research was supportedby the Natural Sciences and Engineering Research Council of Canada through an operating grant to J.D.G. Referencea and Notes (1) Chase, Jr., M. W.; Davies, C. A.; Downey, Jr., J. R.; Frurip, D. J.;

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