Systematic ab initio calculations on the energetics and stability of covalent O 4

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1 JOURNAL OF CHEMICAL PHYSICS VOLUME 120, NUMBER 21 1 JUNE 2004 Systematic calculations on the energetics and stability of covalent O 4 Ramón Hernández-Lamoneda a) Centro de Investigación en Química, Universidad Autónoma del Estado de Morelos, Cuernavaca, Morelos 62210, México Alejandro Ramírez-Solís Departamento de Física, Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, Morelos 62210, México Received 26 November 2003; accepted 9 March 2004 Ab initio calculations with highly correlated methods together with extensive basis sets have been used to obtain the most accurate heat of formation and stability with respect to dissociation into molecular oxygen for the chemically bound tetraoxygen molecule. Our calculations show that the heat of formation is significantly smaller and that the barrier to dissociation is larger than previously assumed. In particular, we have shown that the previous theoretical estimate for the heat of formation of tetraoxygen was in error by a significant amount 18% 24% owing to lack of accuracy in the theoretical method then used. Our best estimates places that value in the range kcal/mol and this should be taken into consideration when discussing the possible relevance of tetraoxygen in a variety of experiments, as well as in the fundamental atmospheric chemical processes where oxygen species participate American Institute of Physics. DOI: / I. INTRODUCTION The search for a chemically bound form of tetraoxygen has been the subject of active and recent scientific scrutiny. 1 Initially the motivation was given by the analogy with the stable and well-known cyclic and chain forms of sulphur, the study of its fundamental properties and its possible use as a high energy-density material. 2 More recently it has been proposed as a possible intermediate in order to explain a variety of experimental findings 3 and has been detected by neutralization reionization NR mass spectrometry. 1 b Given the different experimental conditions for its preparation and identification, it is important to point out that several forms of tetraoxygen are most likely involved in the different experimental setups, which could include a variety of electronic states and isomers covering a wide range of intermolecular strengths. Thus, for example, in the photoionization spectra of the Suits group 3 b it has been shown 3 c,3 d that the O 4 metastable state corresponds to an excited complex between an O 2 molecule in its ground state and another in the excited c( 1 S u ) state. Furthermore, they provide convincing evidence that this same species could be involved in the electron transfer to O 4 experiments realized by Helm and Walter. 3 a As stated in their conclusions, although chemically bound tetraoxygen was not involved in their photoionization spectra, it cannot be ruled out as being present in the molecular beam and different probe techniques would have to be used to detect it. In the NR experimental detection of tetraoxygen, 1 b again, there is strong evidence that the species observed does not correspond to the two theoretically a Author to whom correspondence should be addressed. Electronic mail: ramon@servm.fc.uaem.mx predicted chemically bound forms (D 2d cyclic form and D 3h pinwheel form given the observed isotopic abundances of the diatomic fragments 1 and it remains an open question what is the nature of this novel species. Once more, the fact that the predicted chemically bound species were not observed may only be an indication that the method of preparation neutralization of O 4 ions formed from the association of O 2 and O 2 ) is not the most appropriate and, in fact, finding a better suited preparation method might be the main difficulty in the experimental search. Our interest in chemically bound tetraoxygen started when studying the relaxation properties of highly vibrationally excited O 2. 4 In that work we were able to theoretically reproduce the experimental measurements performed by the Wodtke group 5 for values of the vibrational quantum number v, uptov 25, but were unable to reproduce the sharp increase in depletion rates observed in the experiment. Based on energetic considerations, Wodtke proposed that the opening of the reactive channel leading to ozone formation could be the explanation for the observed dark channel, O 2 v O 2 v 0 O 3 O. Theoretical calculations by one of the present authors 6 and others 7 clearly showed that the above reaction proceeds at a rate which is too low to explain the observed jump in depletion rates. Although no calculations have been performed, chemically bound O 4 has been mentioned as a possible intermediate 4 a,7 c that could be responsible for the new relaxation mechanism observed for v 25 based, again, only on energetic considerations. For that reason we performed calculations on the reaction path for the reaction 8 O 2 O 2 O /2004/120(21)/10084/5/$ American Institute of Physics

2 J. Chem. Phys., Vol. 120, No. 21, 1 June 2004 Energetics and stability of O TABLE I. Number of uncontracted CSF in the multireference correlated methods, using different basis set size. The dimension of the ACPF diagonalizations are given in parentheses, which correspond to the number of contracted CSF considered in each case. Basis set type AVDZ 92 MO AVTZ 184 MO AVQZ 320 MO CASSCF-RS CASSCF-ACPF which showed that the C 2 symmetry is conserved, implying that both molecules have to be vibrationally excited in order to form O 4 and, on this basis, we considered unlikely that tetraoxygen could be of relevance in Wodtke s experiments. Similarly, we believe that any preparative method aimed at forming chemically bound O 4 must start from oxygen molecules in highly vibrationally excited states. Two quantities which are of great interest in order to characterize this system are its relative energy with respect to two oxygen molecules and the barrier for this unimolecular decomposition. Many of the experiments that postulate tetraoxygen as an intermediate do so on the basis of the relative energies sampled in the experiment and use the estimate given by Schaeffer s group. 2 b,2 c Analogously, the most recent NR experiments use the complex stability towards unimolecular decomposition to judge the feasibility of detecting tetraoxygen and use the based value obtained by the present authors. 8 The primary goal of this paper is to revise these two quantities and calculate them by performing large scale benchmark quantum chemical calculations in order to provide the most reliable estimates, given their obvious importance in the tetraoxygen debate. II. METHOD AND COMPUTATIONAL DETAILS A proper and well balanced description of the electronic structure of the O 4,O 3 O, and O 2 O 2 systems is still a challenging task for quantum chemistry. The openshell nature of the diatomic, the description of bond breaking/making processes, and the complicated spin recouplings necessary to describe the transition from open-shell to closed-shell species can only be properly dealt with large multiconfigurational wave functions. Therefore, in order to properly include all the nondynamic correlation effects at the zeroth order, we have used reference wave functions of complete-active-space SCF CASSCF type keeping the 1s and 2s orbitals doubly occupied in all configurations and explicitly correlating the remaining 16 valence electrons in the full valence space of 12 orbitals the 2p shell of each oxygen atom leading, in the C 2v point group, to CASSCF 16,12 wave functions containing configuration state functions CSF. In order to accurately include the dynamic electronic correlation effects, we have used three different approaches, performing second order multireference Rayleigh Schrödinger perturbational calculations RS2, the single-reference coupled cluster with single and double excitations including a perturbative triples estimation which shall as usual be denoted as CCSD T, and the averaged coupled pair functional or ACPF. For the RS2 and ACPF methods we have used as multiconfigurational references the CASSCF 16,12 wave functions previously mentioned. Geometry optimizations were performed at the RS2 and CCSD T levels where analytical gradients are available. For the ACPF calculations the optimized geometries were taken from the previous calculations RS2 or CCSD T, depending on whether the minimum or saddle point structures were being calculated. More details are given in the next section. In order to probe the quality of our results as a function of the basis set size, we have used three increasingly large basis sets: the aug-cc-pvdz AVDZ, aug-cc-pvtz AVTZ, and aug-cc-pvqz AVQZ basis sets. 9 This means O 4 basis sets composed of 92, 184, and 320 molecular orbitals, respectively. The inclusion of the dynamical correlation effects using such large basis sets and with such sophisticated methods is a must for the purpose of this work since, as presented in the introduction, we are looking for extremely accurate relative energy differences. This means that considering the largest basis set, we have truly performed benchmark variational calculations that must be considered as such for future investigations concerning the thermochemistry of these species. See Table I where the number of uncontracted contracted CSF appearing in each of the methods used is considered. The internally contracted scheme as programmed in the MOL- PRO code 10 was used. The largest ACPF calculation with uncontracted CSF took more than 16 CPU and I/O days on a single Power4@1.3 GHz processor of the UAEM IBM p690 supercomputer, allocating up to 21Gb of SMP RAM. In the ACPF cases, the CASSCF reference had a weight close to 0.91, and for the RS2 cases, the perturbational norms were around 0.05 within the intermediate normalization. It should be pointed out that in the ACPF wave function of O 4 the largest coefficient was 0.84 and that up to 16 CSF had coefficients larger than This is again a confirmation of the clear multiconfigurational nature of the wave function and highlights the need to use such type of zeroth-order reference for this complex problem. III. RESULTS AND DISCUSSION In Table II we present the results of our geometry optimizations and compare them with previous calculations. Figure 1 shows the minimum and transition state structures. First we note that the RS2 and CCSD T optimized geometries are very similar for a given basis set, indicating that this structure can be reliably obtained via either method. Regarding basis set effects we see that the equilibrium distance

3 10086 J. Chem. Phys., Vol. 120, No. 21, 1 June 2004 R. Hernández-Lamoneda and A. Ramírez-Solís TABLE II. a Optimized geometries of O 4, in angstroms and degrees. b Optimized geometry of the saddle point in angstroms and degrees. Method/basis set RS2 CCSD T Previous AVDZ AVTZ AVQZ AVDZ AVTZ AVQZ geometry a O 1 O O 1 O 2 O 3 angle O 1 O 2 O 3 O 4 angle Geometrical parameter VDZ RS2 VTZ Previous geometry a O 1 O O 2 O O 1 O O 1 O 2 O 3 angle O 1 O 2 O 3 O 4 angle a CCSD T values with DZP basis from Ref. 2 b. changes the least while the dihedral angle changes the most and is the most difficult parameter to converge. Comparison with the previous results of the Schaeffer group 2 c are consistent with the fact that a much smaller double-zeta plus polarization-dzp basis and the CCSD T method were used then and their own speculation concerning the effect of increasing the basis size a shortening of the bond by Å is confirmed by our calculations. For the transition state the use of a single-configuration based method such as CCSD T can be seriously questioned, as has been discussed in previous works. 2 c,8 For this reason we have optimized the geometry using only the RS2 method. Again, the basis set dependence is relatively weak for the O O distances and, when compared with the behavior observed for the minimum, the angular coordinates are less sensitive. Comparison with previous theoretical estimates indicates that the CCSD T method is able to recover a large fraction of the correlation energy, even though the single reference starting point is poor. The previous CCSD T short and long bond distances are in excellent agreement with ours, but the medium bond distance shows a significant difference between the two methods, which shows again the limitations of the single reference method for this structure. In this regard it is worth pointing out that the CASSCF value 8 for this parameter 1.48 Å is much closer to the RS2 value, giving us confidence about this result. We can point out that, regarding the geometrical properties of the minimum and transition state, the previous theoretical estimates 2 c,8 were already of good quality although FIG. 1. a Geometry of the optimized O 4 molecule. D 2d symmetry. b Geometry of the optimized saddle point. C 2 symmetry. non-negligible quantitative differences exist with our improved calculations particularly for the saddle point geometry. We now turn our attention to the thermochemical properties of the system, where a large discrepancy with previous theoretical estimates has been found. In order to pinpoint where the problem with previous calculations appears, we consider the following reactions: 4O 3 3O 4, 3 2 O 2 O 3. 2 In order to estimate the formation energy for chemically bound tetraoxygen, i.e., the heat of the reaction: 2O 2 O 4 3 the Schaeffer group estimated the heat of reaction 1 using a DZP basis and the CCSD method 2 c note that no connected triple excitations were considered and used the experimental value for the heat of reaction 2 which, when properly combined, yield the heat of reaction 3. An experimental value was used for reaction 2 because large basis sets and highly correlated methods are required to obtain a reliable estimate. Unfortunately, we have found that these requirements are even harder to meet for reaction 1 and this was the main problem with the previous estimate for the heat of reaction 3. In Table III we show the results of our calculations for reactions 1, 2, and 3 and compare these with previous estimates. For reaction 2 the highly accurate CCSD T and ACPF methods with the largest AVQZ basis set yield results that are within 2 kcal/mol and 1 kcal/mol of the experimental value, respectively. The RS2 method provides a good estimate of this quantity but it does not reach chemical accuracy. The accurate estimate of the heat of reaction 1 is definitely a challenging task for quantum chemistry. As seen from Table III, there are significant variations between the three methods and, at the highest levels of theory, the CCSD T and ACPF methods show a discrepancy of roughly 11 kcal/mol. Since the heat of reaction depends on the choice 1

4 J. Chem. Phys., Vol. 120, No. 21, 1 June 2004 Energetics and stability of O TABLE III. Electronic energy difference for the relevant reactions in kcal/ mol with the various methods and basis sets used. Previous theoretical values in parentheses. Reaction Basis set RS2 CCSD T ACPF Expt. 4O 3 3O 4 AVDZ AVTZ AVQZ b 3/2 O 2 O 3 AVDZ a AVTZ AVQZ O 2 O 4 AVDZ AVTZ AVQZ b a In order to provide a comparison with our present results, the experimental value has been modified to account for the ZPE correction. b CCSD/DZP values from Ref. 2 c. of the stoichiometric coefficients chosen, it is perhaps better to report the difference as a percent of the total value; in this case it represents 7% 8% of the total value, which should be taken as an acceptable difference given the great difficulty involved in calculating accurate energies for both, tetraoxygen, and ozone. On the other hand, comparing with the previous theoretical estimate, a very large difference is observed: 18% 24%. Finally, looking at the heat of reaction 3 we notice a very good agreement between the CCSD T and ACPF predictions, 2 kcal/mol, and a large disagreement, 11% 13%, with the previous theoretical estimate using a limited DZP basis set. The performance of the RS2 method for reactions 1 and 3 is good but not highly accurate. Clearly, the main problem with the previous estimate was the use of the single reference CCSD/DZP method to predict the heat of reaction 1. The observed large difference then appears again, in a diminished form, for the estimate of the heat of reaction 3. Estimating this quantity was not the main objective of that previous work and, for this reason, it is understandable that no special attention was given to this issue. On the other hand, all of the recent experimental and many theoretical papers continue to quote their estimate as a reference for the relative energy of tetraoxygen and, on this basis, suggest its possible relevance in a variety of processes as summarized in the introduction. In particular, we would like to point out that our revised estimate of the heat of reaction 3 becomes very close to that of the ozone forming reaction, 2O 2 O 3 O, H 94.4 kcal/mol, so that both channels become open at roughly the same energy. This point is of relevance for the proposed 7 c four center reaction leading to O 4, as a possible explanation of the dark channel observed in Wodtke s experiments. The other quantity which is of relevance in discussing the stability of tetraoxygen is the energy barrier to dissociation into oxygen molecules, i.e., the reverse of reaction 3. In Table IV we show estimates of this barrier and compare them with the previous theoretical figure. Two points are worth noticing. First, the highly accurate ACPF method predicts values that are significantly larger than those coming TABLE IV. Electronic energy barrier for O 4 2O 2. Energies in kcal/mol. Method Basis set AVDZ AVTZ AVQZ Previous value a RS ACPF b 7.9 a CCSD T values with DZP basis from Ref. 2 b. b Estimation using basis set extrapolation, see discussion in Sec. III. from RS2 calculations and both methods indicate that the barrier should increase as basis set convergence is approached. Second, judging from the similar basis set convergence of both methods, the ACPF/AVTZ estimate could be within 0.5 kcal/mol of the converged value. Even though the multireference ACPF calculation with the largest basis set is still beyond our current computational capabilities because the saddle point has less spatial symmetry than reactants and products, we have been able to make a reasonable estimation of the value at the ACPF/AVQZ level. This was done by using the ratios of the O 4 2O 2 energy barriers at the RS2 and ACPF levels when going from the AVDZ to the AVTZ basis 46%/38%, and then applying a linear scaling to the AVTZ to AVQZ energy change at the RS2 level we obtain a 9.27 kcal/mol estimate at the ACPF/AVQZ level, which is within less than 0.2 kcal/mol of the ACPF/AVTZ value see Table IV. Thus, we have shown that the energy barrier is higher than previously estimated and this is of relevance for the recent experimental work of Cacace et al., 1 b and in general, for other preparative methods, since the neutralization method they use to obtain tetraoxygen requires barrier heights relative to dissociation on the order of 10 kcal/ mol, so that the previous estimates were clearly below the threshold, whereas our most recent and accurate estimates are just below it, thus allowing the possibility of detection through this method. In this regard the role of zero-point energy zpe effects becomes of relevance since they will lower the above classical barrier. Comparison between previous theoretical estimates of zero-point energy effects 2 b,2 c,8 show differences on the order of tenths of kcal/mol. We consider that the most reliable estimate comes from CCSD T /DZP calculations 2 b,2 c which predict a lowering of 1.7 kcal/mol and, as explained in that work, this result can only change by a small percent 10% when going to higher levels of calculation. As a last comment, we would like to point out that the importance of the scalar relativistic the Darwin and the mass-velocity corrections and spin orbit effects on the energies here calculated are actually negligible for two basic reasons: first, because of the very low 8 Z value and because these effects will almost be cancelled out in the energy differences we have obtained; for instance, the spin orbit splitting for the J 2, 1, and 0 components of the 3 P state oxygen are only 158 and 257 cm 1, respectively. Even more, these effects will actually be much smaller since they will be quenched by the presence of covalent bonds in the molecular environment. In any case the values here presented for the energy difference and energy barrier from O 4 to dissociation into two oxygen molecules, represent the best and most ac-

5 10088 J. Chem. Phys., Vol. 120, No. 21, 1 June 2004 R. Hernández-Lamoneda and A. Ramírez-Solís curate estimations thus given at the purely electronic Hamiltonian approximation. IV. CONCLUSIONS The chemically bound form of tetraoxygen and the transition state leading to its dissociation into molecular oxygen has been studied through benchmark calculations, using state-of-the-art multireference perturbational and variational methods together with extensive basis sets. The optimized geometry of the minimum at the highest level of theory differs from previous estimates mainly in the dihedral angle, whereas for the transition state the largest difference is obtained for the medium bond distance. We have shown that the previous estimate for the heat of formation of tetraoxygen was in error by a significant amount owing to lack of accuracy in the theoretical method then used CCSD/DZP. Our best estimates places that value in the range kcal/mol and this should be taken into consideration when discussing the possible relevance of tetraoxygen in a variety of experiments, as well as in the fundamental atmospheric chemical processes where oxygen species participate. Furthermore, we have shown that, at the highest level of theory, the barrier to dissociation is higher than previously estimated such that once formed, it is likely that the complex could be observed experimentally, for example, as it has been done recently 1 b for a different species using NR mass spectrometry. ACKNOWLEDGMENTS We are thankful for support from CONACYT Projects No E and E as well as from SESIC-SEP FO- MES2000 project Cómputo científico for unlimited CPU time on the 32-processor IBM p690 supercomputer at UAEM. 1 a D. Schröder, Angew. Chem., Int. Ed. Engl. 41, ; b F. Cacace, G. de Petris, and A. Troiani, ibid. 40, , and references therein. 2 a V. Adamantides, D. Neisius, and G. Verhaegen, Chem. Phys. 48, ; b E. T. Seidl and H. F. Schaeffer, J. Chem. Phys. 96, ; c K. Dunn, G. E. Scuseria, and H. F. Schaeffer, ibid. 92, a H. Helm and C. W. Walter, J. Chem. Phys. 98, ; b H. Bevsek, M. Ahmed, D. S. Peterka, F. C. Sailes, and A. G. Suits, Faraday Discuss. 108, ; c D. S. Peterka, M. Ahmed, A. G. Suits, K. J. Wilson, A. Korkin, M. Nooijen, and R. J. Bartlett, J. Chem. Phys. 110, ; d 111, 5279 E 1999 ; e F. A. Gorelli, L. Ulivi, M. Santoro, and R. Bini, Phys. Rev. Lett. 83, ; f Phys. Rev. B 63, R. Hernández, R. Toumi, and D. C. Clary, J. Chem. Phys. 102, a J. M. Price, J. A. Mack, C. A. Rogaski, and A. M. Wodtke, Chem. Phys. 175, ; b C. A. Rogaski, J. A. Mack, and A. M. Wodtke, Faraday Discuss. 100, R. Hernández-Lamoneda, M. I. Hernández, E. Carmona-Novillo, J. Campos-Martinez, J. Echave, and D. C. Clary, Chem. Phys. Lett. 276, a N. Balakrishnan and G. D. Billing, Chem. Phys. Lett. 242, ; b A. J. C. Varandas and W. Wang, Chem. Phys. 215, ; c D. M. Lauvergnat and D. C. Clary, J. Chem. Phys. 108, R. Hernández-Lamoneda and A. Ramírez-Solís, J. Chem. Phys. 113, K. A. Peterson, A. K. Wilson, D. E. Woon, and Th. H. Dunning, Theor. Chem. Acc. 97, MOLPRO is a package of programs written by H. J. Werner and P. J. Knowles with contributions from R. D. Amos, A. Bernhardsson, A. Berning et al. CASSCF geometry optimization algorithm from Roland Lindh. CCSD T geometry optimization algorithm by F. Eckert.