Abinitio SCF-MO calculations of features of the lowest ...

Ab initio SCF-MO calculations of features of the lowest triplet state potential surfaces of several tetraatomic carbonyl compounds

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A. KAPUR,'R. P. STEER,AND P. G. MEZEY Dc>partmcnt of Chetnistry and Chetnital Engineering, University of Saskatchewan, Saskatoorz, Sask., Cunuda S7N OW0 Received May 28, 1981 A . KAPUR,R. P. STEER,and P. G. MEZEY.Can. J. Chem. 60, 100 (1982). Non-empirical SCF-MO calculations have been carried out for a series of tetraatomic carbonyl compounds. Portions of the ground singlet and first triplet state potential energy surfaces, in particular those along the out-of-plane bending coordinates, have been determined. Estimates of the first triplet state out-of-plane vibrational frequencies have been calculated. A . KAPUR,R. P. STEERet P. G . MEZEY.Can. J . Chem. 60. 100 (1982). On a effectue des calculs de MO-SCF non empiriques sur une serie de composes carbonyles tetraatomiques. On a determine des portions des surfaces d'energie potentielle de I'etat fondamental singulet et du premier etat tiiplet. On a evalue les frequences de vibration hors du plan du premier etat triplet. [Traduit par le journal]

Introduction Tetraatomic carbonyl compounds in their ground and excited electronic states have been the subject of many experimental and theoretical investigations. Foremost among experimental work have been exhaustive studies of the electronic spectroscopy, the photochemistry, and the photophysics of formaldehyde (1-3). Despite these efforts, however, an unequivocal picture of the mechanism(s) of photodissociation of this molecule has yet to emerge, and recent calculations of features of potential energy surfaces relevant to its photofragmentations have proved to be very useful (4). B~ comparison, little experimental and less theoretical work has been reported on other similar tetraatomic carbonyls, such as the carbonyI halides, a notable exception is an SCF-CI study ( 5 ) on the vertical electronic spectrum of F2C0. Tetracarbonyl halides are the subject of the present study. Recently we reported the results of ab initio SCF-MO calculations on the ground and lowest triplet states of several thiocarbonyl compounds (6-8). It was shown that agreement between and ground and lowest triplet equilibrium geometries could be obtained for these even when an economical STO-3G basis set was used. In addition, good estimates of the triplet state inversion frequencies ""d be obtained by solving the vibrational eigenvalue problem after ab initio calculation of the triplet energies at severai points along the out-of-~'ane coordinates. A more thor"ugh ab initio study of the ground state structures IPresent address: Department of Chemistry, University of New Brunswick, Fredericton, N.B., Canada E3B 6E2.

of H2C0, HFCO, HCICO, F2C0, C12C0, ClFCO, HzCS, and FzCS has recently been reported by (9). In that work SCF-Mo Oberhammer and calculations were performed using the HartreeFock gradient Program of Pulay (10). when 4-21 basis sets were used for secoriJ row atoms and 3-3-21 basis sets supplemented with d orbitals were used for sulfur and chlorine, good agreement between calculated and experimental geometries was found. With the exception of studies of HFCO and F2CO ( 5 , 11-12), however, ab initio calculations have not been performed on excited states of the tetraatomic carbonyl halides, although several semi-~mpiricalstudies have been reported (13-16). In this Paper we present the results of calculations of the lowest triplet state structures and inversion vibrational frequencies of H,CO, HFCO, F2co, C12Coy and CIFCo. Ground state geometrlee" have also been calculated for comparison with previous work. Methods of calculation The initio calculations were carried out using a modified version of Gaussian-70 (17) adapted for a 36 bit word L>EC 2060 computer. The equilibrium of H,CO and HFCO in their lowest triplet states were obtained by sequential, cyclic of all geometric parameters using both the STO-3G and 4-31G basis sets. In addition, seven other points lying along the out-of-plane bending coordinate on one side of the double minimum potential were calculated for these two with both basis sets. For these latter points, geometric parameters except the out-of-plane angle, 8, were optimized. The equilibrium geometries and energies at various out-of-

0008-4042/82/020100-M$O1.OO/O 01982 National Research Council of Canada/Conseil national de recherches du Canada


KAPUR E T AL.

101

plane angles in the lowest triplet states of F 2 C 0 , been described (21) and was used in the present ClFCO, and C1,CO were calculated similarly, ex- work. Q, and 8 are related via cept that only the more economical STO-3G basis set was employed. For purposes of comparison with previous work, the equilibrium geometries of all five ground state molecules were calculated using the STO-3G basis set and those of H,CO, and three approximate methods of carrying out this Q6-8 transformation have been outlined and comHFCO, and F,CO using the 4-31G basis set. The calculated SCF energies along the out-of- pared previously (21). The model involves the plane bending coordinates of the lowest triplet "best" energy values obtained along the optimized states of all five molecules were used to find (using "relaxed" inversion path (corresponding to a nona non-linear least-squares fitting program) best rigid bender model), combined with the application values of the parameters, h, A , and a 2 ,defining the of a vibrational Hamiltonian preserving some feashape of the double minimum potential function tures of a rigid bender. That is, the resuits refer to a rigid bender model where the energy values along (18, 191, the bending coordinate are replaced by those of the non-rigid molecule. The most general and most accurate of these three methods, involving truncation of the series solution lo [3] only after the fourth Here (2, is the mass-weighted out-of-plane bending term, has been used in the present work. coordinate whose values must be calculated from the corresponding out-of-plane angles, 8. The eigenResults and discussion values and eigenvectors for the inversion vibraThe calculated and experimental ground state tion were obtained as previously described (6, 7). geometries for the tetraatomic carbonyls consiThe vibrational eigenvalues, in multiples of hcvo, dered in this study are given in Table 1. The data of measured relative to the potential minima, can be Oberhammer and Boggs (99 are included for comobtained in the form (18) parison. As expected, calculations with the 4-31G basis set reproduce the measured ground state geometries better than those with the STO-3G basis set. It has been noted previously (9, 12) that where B = blv, is a dimensionless parameter the use of the latter basis set results in a systematic proportional to the barrier height, b; p is a shape underestimation of the C=O bond shortening factor defined by a 2 = ePh/2A, and vo is the effects of electron-withdrawing substituents. Morewavenumber (in cm-l) of the harmonic oscillator over, the C-Cl bond lengths are systematically appropriate to the parabolic part of the potential overestimated, by as much as 5% in the case of CIFCO. On the other hand, calculations with the and is given by v, = hIi2/2nc. Past experience (6, 7) has shown that the eigen- 4-3 1G basis give quite satisfactory agreement with values are very sensitive to the number of harmonic experiment when the differences between the defioscillator basis functions taken and that the number nitions of the calculated and the experimentally of basis functions required for convergence may be measured bond lengths are accounted for (for a strongly dependent on p. In the present work, the discussion of this point see ref. 28). number of vibrational basis functions has arbiDespite the fact that either the 4-3 1G basis set or trarily been set to 100. Increasing this number led those used by Oberhammer and Boggs (9) give to no significant numerical change in any of the better ground state geometries, general trends in calculated eigenvalues. the predicted geometries are correctly reproduced A general method of transforming the out-of- with the STO-3G basis. Since we were primarily plane angle, 8, to the corresponding mass-weighted interested in obtaining estimates of the lowest coordinate, Q,, involves the use of the appropriate triplet inversion barriers and out-of-plane bending matrix element, G,, (ref. 20. For molecules of C, mode frequencies, and since a large number of symmetry the matrix element is G,, but is G,, for points along the double minimum paths had to be C,, molecules. Here G,, is used throughout for calculated to do so, only the STO-3G basis set was convenience). An analytic expression for the G6, used for the F,CO, ClFCO, and C1,CO triplets. Table 2 shows the predicted equilibrium geommatrix element of tetraatomic molecules having either C,, or C, equilibrium symmetry has recently etries and inversion barrier heights for the lowest

102

CAN. J. CHEM. VOL. 60, 1982

TABLE1. Calculated and experimental ground state geometries of some tetraatomic carbonyls, XYCOu r(C=O) X,Y

Calcd-xpt

H.H

1.227 1.206 1.208

1.2078

1.211 1.179 1.181

1.181

CI, C1

1.195 1.180

1.180

CI, F

1.201 1.175

1.173

F,F

1.209 1.170 1.171

1.170

H, F


r(C-X) Calcd

r(C-Y) Expt

Calcd

IX-C-0 Expt

Calcd

LY-C-0 Expt

Calcd

Expt

Ref

=Bond lengths in A. bond angles in deg. b F o r each calculated quantity the value obtained using the STO-3G basis set isgiven first. followed by that o b t a ~ n e dusing the 4-31G basis. followed by the value of Oberhammer and Boggs (9).

TABLE2. Calculated geometries and inversion barrier heights for the lowest triplet states of several tetraatomic carbonyls, XYCOa X, Y

r(C-O)b

r(C-X)

r(C-Y)

i X-C-0

L Y-C-0

0 (deg)

b(cm-')

H, H

1.3936 1.3690

1.0888 1.0726

1.0888 1.0726

114.2 114.4

114.2 114.4

38.1 33.0

700 287

H, F

1.412 1.374

1.102 1.072

1.355 1.365

112.7 113.5

112.7 112.0

44.1 44.7

2194 2503

CI, C1

1.400

1.793

1.793

112.1

112.1

44.4

2981

CI, F

1.414

1.815

1.343

112.5

110.7

47.6

4552

Energy .. (au) - 112.327673

- 113.636103 - 209.788096 -212.357135 - 1020.331235 - 663.797903

"Bond lengths in A , bond angles in deg. T o r each calculated quantity, the value obtained using the STO-3G basis set is given first and is followed by that o b t a ~ n e dusing the 4-3 1G basis for and HFCO.

triplet states of this series of five tetraatomic carbonyls. Experimental data for 0 and b are available only for H2C0(3A'?,although crude estimates of these quantities may be obtained for triplet HFCO, F,CO, and C12C0 from measurements on the corresponding '(n,n *) states. Thus, there is only limited opportunity to judge the accuracy of the calculated results. Nevertheless, qualitatively the results appear to be reasonable. The C-0 bond length generally increases with increasing electronegativity of the substitutent groups (H,CO FZ C1,CO c HFCO % ClFCO < F2CO),and the predicted extent of non-planarity of these triplets is generally in accord with the Walsh postulates (29). As previously noted from CND012 calculations on n,n* states of several carbonyls (131, the change in p , electron density on the central carbon atom in proceeding from the planar to the equilibrium non-planar conformation, Ap(p,),

may be correlated with the magnitude of the equilibrium out-of-plane angle and the inversion barrier height. The data for the five molecules chosen for the present study is given in Table 3. In fact, over the range of out-of-plane angles encountered in these five molecules, a linear relationship exists between Ap(p,) and 8, as shown in Fig. 1. Such a relationship was also observed for a similar series of thiocarbonyl triplets (6, 7) and lends quantitative support to Walsh's Rule. Figure 2 shows the variation of potential energy along the out-of-plane bending coordinate for all five molecules, calculated with the STO-36 basis set. Only small differences between the parabolic parts of these double minimum curves and those calculated with the 4-3 1 6 basis set were noted for HFCO, as illustrated in Fig. 3 . The calculated barrier heights were particularly sensitive to choice of basis set for H,CO, however, and, perhaps

KAPUR ET AL.

TABLE3. Carbon 2p orbital electron densities for planar and equilibrium non-planar triplet tetraatomic carbonyls


Carbonyl H,CO HFCO F,CO ClFCO ClzCO

2p,

2p,

2p,

0.5086 0.5093 0.5077 0.5091 0.5169

0.6113 0.5343 0.4804 0.4791 0.4802

1.1021 1.1422 1.1755 1.1671 1.1557

H FCO 4-31G I.\

I

I

r"

\

\ \

4

OUT-OF-PLANE ANGLE @(DEGREES

FIG. 1 . Correlation between the decrease of electron density on the p , orbital of carbon atom and the calculated equilibrium out-of-plane angle for a series of tetraatomic carbonyls.

-

-60 -40 -20

0

BUT- OF- PLANE ANGLE

20

40

60

8 (DEGREES)

FIG.2. Calculated out-of-plane bending potentials for the first triplet states of a series of tetraatomic carbonyls (using 3G basis sets).

OUT-OF- PLANE ANGLE 8 (DEGREES) F I G . 3. Comparison of STO-36 and STO-4-31'3 double minimum out-of-plane bending potentials of triplet states of H,CO and HFCO.

fortuitously, better agreement with experiment (19) (8 = 37.9", b = 775.6 cm-') was found when the §TO-3G basis was employed. Nevertheless, with either basis set the expected trend in variation of barrier height with electron-withdrawing power of the substituent atoms is predicted. If the order of increasing barrier heights is the same for the 3A" states as for the 'A" states, then the predicted trend is confirmed by experimental data. For the 'A"


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CAN. J. CHEM. VOL. 60, 1982

states of H 2 C 0 , HFCO, C12C0, and F,CO barrier heights of 356.2, 2550, 2170, and >4000 cm-I, respectively, have been measured (19, 30-32). The only direct, quantitative comparison that can be made between experimental and the present calculated lowest triplet state geometries is for formaldehyde. For this molecule agreement between the calculated and the measured equilibrium geometry is relatively poor when either basis set is used, compared with the ground state. Similar difficulties in calculating "good" equilibrium geometries and, in particular, inversion barrier heights for the lowest excited states of formaldehyde have been encountered even when more extensive basis sets and CI methods have been used (1 1, 33, 34). The fact that there is relatively close agreement between the STO-36 calculated inversion barrier (700 cm-') and the experimental barrier (775.6 cm-') deduced from out-of-plane bending frequencies observed in the 'A" t 'A ' absorption spectrum of H,CO (19) must therefore be regarded as fortuitous. Nevertheless, on the basis of comparisons with the triplet thiocarbonyl halides (6, 7, 3 3 , for which more extensive experimental data are available, the worst agreement between experiment and calculation might be expected for the molecules with the lowest barriers; H,CZ (Z = 0 , S). Recent results on H,CS have indicated that in our earlier study, the UHF method produced convergence to a solution dominated by a higher triplet state, possibly due to an erratic convergence of density matrices (36), and the poor agreement with experiment is likely to stem from this, as well as from the approximation used to calculate bond angles, valid only in the case of small amplitudes and small out-of-plane angles (37). We have assumed that the relative potential energies along the out-of-plane bending coordinates, calculated in the present study with a minimal basis set, can be used to give reasonable first estimates of the lowest triplet inversion frequencies in the carbonyl halides. These data are not readily obtainable from spectral measurements. Table 4 presents the predicted eigenvalues of the out-of-plane bending vibrations of the carbonyl halide triplets, relative to the zero point levels which are assigned energies of zero. Also shown are the values of p, b , and vo which provide the best fit of the potential function, eq. [I], to the potentials calculated with the STO-36 basis set, and values of G(Of), the estimated zero-point energies. Four and five significant figures are quoted in this table only to provide estimates of the resolving power which might be required to observe inversion splittings in

TABLE4. Triplet inversion vibrational eigenvalues for several tetraatomic carbonyl halides G (ern-') Level

HFCO

C12C0

ClFCO

F2C0

the 3A"t ' A ' near uv absorption spectra of these compounds. Acknowledgements The authors wish to thank the Natural Sciences and Engineering Research Council of Canada for its continuing financial support. The authors are grateful to Drs. J. D. Goddard and D. Cluthier for their thorough checking of our earlier numerical data and for pointing out an error in the assumed geometry of thiocarbonyls used in the calculation of vibrational frequencies. 1. D. C. MOULEand A. D. WALSH.Chem. Rev. 75,67 (1975). 2. J . C. WEISSHAAR and C. B. MOORE.J. Chem. Phys. 70, 5135 (1979) and references therein. 3. K. Y. TANG,P. W. FAIRCHILD, and E. K. C. LEE.J. Phys. Chem. 83, 569 (1979) and references therein. 4. J . D. GODDARD and H. F . SCHAEFER. J. Chem. Phys. 70. 5117 (1979) and references therein. 5. K. VASUDEVAN and F. GREIN.Int. J. Quant. Chem. 14,717 (1978). 6. A. KAPUR,R. P. STEER,and P. G. MEZEY.J. Chem. Phys. 69, 968 (1978). 7. A. KAPUR,R. P. STEER,and P. G. MEZEY.J. Chem. Phys. 70, 745 (1979). 8. A. KAPUR,R. P. STEER,and P. G. MEZEY.J . Chem. Phys. 71, 5022 (1979). and J . E. BOGGS.J . Mo1. Stmct. 55. 283 9. H. OBERHAMMER (1979). 10. P. PULAY.Theor. Chim. Acta, Berlin, 50, 299 (1979). J . E. DEL BENE,and J. A. POPLE.J . Am. 11. R. DITCHFIELD, Chem. Soc. 94, 4806 (1972). 12. J . E. DELBENE,G. T. WORTH,F. T. MARCHESE, and M. E. CONRAD.Theor. Chim. Acta, Berlin, 36, 195 (1975). and D. C. MOULE.Theor. Chim. Acta, 13. D. A. CONDIRSTON Berlin, 29, 133 (1973). 14. E. R. FARNWORTH, G. W. KING,and D. C. MOULE.Chem. Phys. 1, 82 (1973). 15. Y . Y O N E Z A W A T. ~FUENO. ~~ Bull. Chem. Soc. Jpn. & , 2 2 (1975). 16. R. ZAHRADNIKand J. LESKA Collect. Czech. Chem. Commun, 42, 2060 (1977).


KAPUR ET .4L.

26. 17. W . J . HEHRE, W. A. LATHAN,R. DITCHFIELD,J . A. 27. POPLE,and M. D. NEWTON.Quantum Chemistry Program 28. Exchange, Program 236. Indianauniversity, Bloomington, IN. 18. J . B. COON,N. W. NAUGLE.and R. D. MCKENZIE.J. Mol. 29. 30. Spectrosc. 20, 107 (1966). 19. V. T. JONESand J. B. COON.J. MoI. Spectrosc. 31, 137 31. (1969). 20. E. B. WILSON,JR., J. C. DECIUS, and P. C . CROSS. 32. Molecular vibrations. McGraw-Hill, New York. 1955. 21. A . KAPUR,P. G. MEZEY,and R. P. STEER.Chem. Phys. 33. Lett. 78, 81 (1981). 34. 22. K. TAKAGIand T. OKA.J . Phys. Soc. Jpn. 18, 1174 (1963). 23. J. L . DUNCAN.Mol. P h y s 28, 1177 (1974). 24. R. F. MILLERand R. F. CURL.J . Chem. Phys. 34, 1847 35. 36. (1961). 25. K . KUCHITSU.Seventh Austin Symposium on Molecular 37. Structure, Austin, TX. 1978.

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H. OBERHAMMER. J. Chem. Phys. 73,4310 (1980). J . H . CARPENTER. J. Mo1. Spectrosc. 50, 182 (1974). K . KUCHITSU.Molecular structure and vibrations. Edited by S. J . Cyvin. Elsevier, Amsterdam. 1972. A. D. WALSH.J . Chem. Soc. 858 (1956). G. FISCHERand Y. SOREK.J. MoI. Spectrosc. 74, 136 (1979). D. C. MOULE and P. D. F o o . J . Chem. Phys. 55, 1262 (1971). G. L . WORKMAN and A. B. F . DUNCAN. J . Chem. Phys. 52, 3204 (1970). S. BELL. Mol. Phys. 37. 255 (1979). W. MEYERand P. PULAY.Theor. Chim. Acta, Berlin, 32. 253 (1974). R. P. STEER.Rev. Chem. Intermed. 4, 1 (1981). P. G . MEZEY. 0. P. STRAUSZ,and R. K. GOSAVI.J. Comput. Chem. 1, 178 (1980). J . D. GODDARD. Private communication.