Heats of formation of some small molecules and radicals

Journal of Molecular Structure (Theochem), 151 (1987) 325-330 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

HEATS OF FORMATION OF SOME SMALL MOLECULES AND RADICALS

M. SANA,* G. LEROY,**

D. PEETERS and E. YOUNANG

Universitk Catholique de Louvain, Laboratoire de Chimie Quantique, Place L. Pasteur, 1, bte 35, B-1348 Louuain-la-Neuve (Belgium)

Bdtiment

Lauoisier,

(Received 14 November 1986)

ABSTRACT In this work, we determine the heat of formation of some small neutral molecules and radicals (NH,F, NHF, HOOH, HOO, NH,NH,, NH,OH, NH,O, NHOH, CH,NH,, CH,NH, CH,NH,, HNO, and CH,BH,). Atomization energies of these compounds are computed at the Mdller-Plesset level to full fourth order using a series of extended basis sets of 631G type. The results that we obtain confirm some experimental values (NH,, NH,, H,O,, . . . ); nevertheless, some other computed heats of formation call into question the experimental values of CH,NH, and HOO. We also predict Aags for CH,BH, (24.25 kcal mol-I), HNO, (-16.72), NHOH (25.25), NH,0 (-16.73) and NH,F (-9.64). INTRODUCTION

The knowledge of the energy contents of chemical species is of great interest for rationalizing many of their static and dynamic properties. In most cases, experimental heats of formation can be obtained with great accuracy. However, experimental techniques are generally less successful for transient species. So, each time experimental data are not available or subject to large imprecision, theory can be of some interest to estimate heats of formation. In a recent paper, Pople et al. [l] showed that the theoretical predictions of heats of formation for neutral AH, hydrides can be accurate within about 2 kcal mol-‘. A similar study on the silane compounds [ 21 leads to an overall accuracy of f 3 kcal mol-‘. In this paper, we consider a series of neutral molecules and parent radicals built with first and second row atoms. In part of the compounds that we consider, the reliability of the theory is tested by comparison with experimental values. COMPUTATIONAL

METHOD

The initial calculations have been carried out at the SCF level using the 6-31G basis set. Spin restricted Hartree-Fock (RHF) theory is used for *Senior Research Associate, National Foundation for Scientific Research, Belgium. **Author for reprint requests. 0166-1280/87/$03.50

o 1987 Elsevier Science

tibliiers B.V.

326

singlet state molecules and the unrestricted form (UHF) is employed for the doublet state radicals. For each species, harmonic vibrational frequencies were calculated analytically [ 31, using the fully optimized geometries. As shown in previous works, the theoretical frequencies of vibration calculated at this level are overestimated by lo-12% [4]. Nevertheless, one can adjust the theoretical values by applying some scaling procedure [5]. In the present work, we use a relation established for the 6-31G basis set [6] Q (adjusted) = -45.99

+ 0.92227 Q (theoretical), with 0 in cm-’

(1)

Thermal corrections are estimated in the classical framework of statistical thermodynamics, using the adjusted harmonic frequencies. Corrections take into account the eventual internal free rotators. For more precise energy calculations, the split-valence polarized 6-31G** basis set has been employed. MP4 calculations were carried out on the SCF 6-31G** optimized geometries. The principle of the method proposed by Pople et al. [7] as well as by other searchers [ 81 assumes that some basis set effects are purely additive: this seems to be a reasonably good approximation for the energy lowering due to the diffuse function (+), to the second d function (2d) or to the f atomic function (f). Then, we can write at the MP4 level (using all single, double, triple and quadruple excitations) E (6-31G””

(+, 2d, f)) 2 E (6-31G**)

+ E (6-31G** 2d) -E = E (Extrapolated) RESULTS

(6-31G”“)

+ E (6-31 + G**) -E + E (6-31G””

(6-31G**)

fl - E.(6-31G”“)

(2)

AND DISCUSSION

In Table 1, we report the total energies obtained at the MP4 level; we also give, in the same table, the extrapolated values of the total energy, obtained according to relation (2). Table 2 contains the thermodynamical properties of the compounds under consideration. The reported quantities refer to an ideal gas; it is usually found that the heat capacity and entropy are fairly accurate because those quantities depend only weakly on the normal modes of vibration. Finally, with the data of Tables 1 and 2, we can calculate the heats of reaction for the isogyric reactions listed in Table 3. We can then deduce the heats of formation for the compounds of interest if we know the heats of formation of the atoms [9]. The AT,,, results obtained for NH3 and NH2 confirm the accuracy of the theoretical method in use: our values (obtained in 6-31G basis sets) are very close to the theoretical predictions of Pople for the hydrides (obtained in 6311G basis sets). Let us comment briefly on the different heats of formation we report in Table 3. The A@(NH,F) we obtain enables us to predict a value for NHFz. So, more classically, using the following isodesmic reaction [lo]

327 TABLE

1

Total energies tions (a.u.)

at the MP4 level including

6-31** (a.u.)

E (MP4) molecules F 0 N C B H

-99.49865 -7 4.89597 -54.47326 -37.75043 -24.57594 -0.49823 -1.16453 -56.40004 -55.72949 -155.33339 -154.69004 -151.16950 -150.53233 -111.56582 -110.92970 -131.37805 -130.74287 -130.75023 -95.58510 -94.92919 -94.92399 -65.72306 -205.18623

H* NH, NH, NH,F NHF H,C, OOH NH,NH, NHNH, NH,OH NHOH NH,0 CH,NH, CH, NH, CH,NH CH,BH, HNO,

all single,

6-31+** (a.u.)

6-31** (a.u.)

-99.51087 -74.90173 -54.47570 -37.75426 -24.57988 -0.49823 -1.16453 -56.40828 -55.73558 -155.35349 -154.70653 -151.18564 -150.54475 -111.57975 -110.94234 -131.39395 -130.75595 -130.76481 -95.59411 -94.94001 -94.93100 -65.72590 -205.20526

-99.53086 -74.91794 -54.48305 -37.75987 -24.58309 -0.49823 -1.16453 -56.41791 -55.74537 -155.38385 -154.73834 -151.22341 -150.58356 -111.59618 -110.95822 -131.41968 -130.78257 -130.79003 -95.60957 -94.95283 -94.94689 -65.69933 -205.25564

double,

(2d)

triple

6-31** (a.u.)

and quadruple

(f)

-99.51715 -74.91158 -54.48004 -37.75534 -24.57799 -0.49823 -1.16453 -56.41793 -55.74497 -155.37390 -154.72888 -151.21268 -150.57424 -111.60443 -110.96672 -131.41906 -130.78219 -130.79021 -95.61860 -94.96183 -94.95520 -65.74628 -205.25127

Correction (a.u.) -0.06292 -0.04332 -0.01902 -0.01817 -0.01313 0.00000 0.00000 -0.04399 -0.03744 -0.11106 -0.10362 -0.11323 -0.10556 -0.08290 -0.07820 -0.09855 -0.09210 -0.09436 - 0.06698 -0.06710 -0.06112 -0.00233 -0.15347

excita-

Extrapolatio (a.u.) -99.56158 -74.93930 -54.49227 -37.76861 -24.58907 -0.49823 - 1.16453 -56.44403 -55.76694 -155.44446 -154.79366 -151.28273 -150.63789 -111.64872 -111.00789 -131.47660 -130.83497 -130.84459 -95.65208 -94.99629 -94.98511 -65.72539 -205.33791

2 NHFz + NFJ + NHzF and the following data E (NH2F) = -,154.90951

a.u. (6-31G)

E (NHF2) = -253.66311

a.u. (6-31G)

E (NF,) = -352.31625 and

As2s8

a.u. (6-31G)

(NF3) = -31.57

kcal mol-’ [ll]

we obtain AgZ9s (NHFJ = -20.10 kcal mol-‘. The theoretical heat of atomization of NHzF correlates quite nicely with the experimental heats of atomization of NH3 and NFJ. We find indeed A%M

(NH3--nF,) 7 276.53 - 26.01 II (kcal mol-‘) (p = 0.99)

(3)

Similar-y, the results we have obtained for NHF correlate with the experimental values of NH2 and NF2 (AHZss (NF,) = 8.3 kcal mol-‘) Ae

298(NH,,F,)

= 170.96 - 14.64 n (kcal mol-‘) (p = 0.99)

(4)

328 TABLE

2

ZPE and thermodynamical

properties

ZPE kcal mol-’ F 0 N C B H

Akt(O

H,O, OOH NH,NH, NHNH, NH,OH NHOH NH,0 CH,NH, CH,NH, CH,NH CH,BH, HNO,

-+ T)

kcal mol-’ 1.481 1.481 1.481 1.481 1.481 1.481 8.131 23.182 13.885 19.282 10.220 18.148 10.612 35.093 26.478 27.170 18.496 19.016 41.511 32.908 32.492 36.566 15.946

0.000 0.000 0.000 0.000 0.000 0.000

H* NH, NH, NH,F NHF

at 298.15K

6.057 20.670 11.512 16.852 7.807 15.429 8.184 32.323 23.534 24.543 15.985 16.301 38.588 29.900 29.581 33.533 13.478

C, (T) cal mole1 K-l 4.968

4.968 4.968 4.968 4.968 4.968 6.955 9.284 8.030 8.944 8.604 9.790 8.752 12.092 11.586 10.604 9.712 10.189 12.472 13.289 11.582 13.452 9.358

S, (T) cal mol-’

K-l

36.144 36.437 36.612 36.596 35.840 27.391 31.063 46.393 46.384 54.947 55.251 60.075 54.958 56.834 59.482 56.048 56.021 55.796 58.507 59.392 60.040 59.228 56.987

If we now consider the series XNHz (with X = CH3, NH2, OH and F) and the parent radicals XNH, we find a regular evolution of the heats of atomization with respect to the atomic number of the heavy atom lying in the X group Ax

298 (NH2X) = 1135.43

AH”, 298

(NHX) = 1021.02

- 99.57 2x (kcal mol-‘) (p = 0.99) - 96.56 2x (kcal mol-‘) (p = 1.00)

(5) (6)

It is interesting to quote that in the NHzX series the theoretical heats of formation are 3 kcal mol-’ lower than the experimental range, but the HO0 radical is the only one whose value seems to be at the limit of the experimental range (for the most recent experimental values we have 2.5-3.5 kcal mol-’ against 5.75 in the present work). It remains that, in this last case, our results are on the same correlation line as the NHzOH and CHJO radicals Ax

29s

(X0) = 1026.10

- 108.15 2x (kcal mol-‘) (p = 1.00)

Finally, Table 3 contains some new values of the heats of formation radicals (NH20, NHOH) and molecules (HN02, CHJBH2).

(7) for

329 TABLE

3

Heats of reaction

(HR) and heats of formation

Reactions

(Hf) A&

(kcal mol-‘) AHf (Th.)

NH,

NH,+3H+N+3H,

-31.33

NH,

NH,+2H+N+2H,

-35.45

44.45

NH,F NHF HOOH HO0

NH,F+4H-*N+F+3H, NHF+3H+N+F+2H, O,H, + 4H + 20 + 3H, O,H+3H+20+2H,

-66.90 -54.76 -57.27 -42.93

-9.64 30.32 -32.01 5.75

NH,NH, NH,NH

N,H, N,H,

-105.87 -88.19

19.84 54.00

NH,OH

NOH,+5H+N+0+4H,

-75.10

NHOH NH,0 CH,NH, CH,NH,

NHOH+4H+N+O+3H, NH,O+4H+N+O+3H, CNH,+5H+C+N+5H, CH,NH,+4H+C+N+4H,

-58.09 -52.57 32.50 41.10

22.25 16.73 -8.75 34.80

CH,NH

CH,NH+4H-C+N+4H,

34.41

41.40

CH,BH, HNO,

BCH,+3H+B+C+4Hz HNO,+7H-+N+20+4H,

122.95 -115.86

24.58 -16.72

+ 6H -+ 2N + 5H, + 5H + 2N + 4H,

-11.97

-12.36

AHf(Exp.) -10.97 -10.8 44 45.5 45.8

Ref. 11 7 12 11 7

-a -32.5 5 2.5 3.5 22.8 46.80 53.72 -10.2 -9.74

-5.5 37 36 31.1,30.3 39.3 43.6 42.4

13 14 15 16 13 17 18 8:

(OK)

13 21b 22 23 24 25 26

sThe following isodesmic reaction [27] : 2 NHF -+ NH, + NF, gives in 4-31G AHf= 28.54 b37 becomes 34.2 if one introduces the most recent heat of formation of kcal mol-‘. C,H,CH, ( AHf = 47 kcal mol-’ ) [ 28 ] in the Benson’s discussion.

CONCLUSION

This work confirms that theoretical calculations lead to quite nice thermochemical values and can be of some interest each time the experimental data are unknown or difficult to be measured. Using the heats of formation listed in Table 3, one observes that the bond dissociation energies (BDE) are very sensitive to the chemical environment BDE(HNH-H) = 108.32 kcal mol-’ BDE(CHJNH-H) = 102.25 kcal mol-’ BDE(NH,NH-H) = 86.26 kcal mol-’ BDE(HONH-H) = 86.71 kcal mol-’ BDE(FNH-H) = 92.06 kcal mol-’

330

It appears that this effect is more important like OH or NH2 than with CH3.

with electronegative

groups

ACKNOWLEDGEMENTS

We thank the National Foundation for Scientific Research (Belgium) for its financial support which allowed us access to large computers. We also thank Dr. Cl. Wilante for documentation of this work. REFERENCES 1 J. A. Pople, B. T. Luke, M. J. Frischand J. S. Binkley, J. Phys. Chem., 89 (1985) 2198. 2 P. Ho, M. E. Coltrin, J. S. Binkley and C. F. Melius, J. Phys. Chem., 89 (1985) 4647. 3 J. A. Pople, R. Krishnan, H. B. Schlegel and J. S. Binkley, Int. J. Quantum Chem., Quantum Chem. Symp., No 13 (1979) 225. 4 J. A. Pople, H. B. Schlegel, R. Krishnan, D. J. De Frees, J. S. Binkley, M. J. Friach and R. A. Whiteside, Int. J. Quantum Chem., Quantum Chem. Symp., No 15 (1981) 269; M. M. Franci, W. J. Pietro, W. J. Here, J. S. Binkley, M. S. Gordon, D. J. De Frees and J. A. Pople, J. Chem. Phys., 77 (1982) 3654. 5 G. Fogarasi and P. Pulay, Ann. Rev. Phys. Chem., 35 (1984) 191. 6M. Sana in I. G. Csizmadia and R. Daudel (Eds.), Computational Theoretical Organic Chemistry, Reidel, Dordrecht, NL, 1981 p. 183. 7 J. A. Pople, B. T. Luke,M. J. Frischand J. S. Binkley, J. Phys. Chem., 89 (1985) 2198. 8 M. L. McKee and W. N. Lipscomb, Inorg. Chem., 24 (1985) 762. 9 The heats of formation of the atoms (in standard state) are the following: H = 52.1 kcal mol-‘, B = 132.6 kcal mol-I. C = 170.9 kcal mol-I, N = 113 kcai mol”, 0 = 59.56 kcal mol-‘, and F = 18.86 kcal mol-I. 10 Unpublished results. 11 M. W. Chase, J. L. Curnutt, J. R. Downey, R. A. McDonald, A. N. Syverud and E. A. Valenzuela, JANAF Thermochemical Tables, Supplement, J. Phys. Ref. Data, 11 (1982) 695. 12 W. Tsang, Int. J. Chem. Kinet., 10 (1978) 41. 13 S. W. Benson, Thermochemical Kinetics, J. Wiley, New York, 1976. 14 S. N. Foner and R. L. Hudson, J. Chem. Phys., 36 (1962) 2681. 15C. J. Howard, J. Am. Chem. Sot., 102 (1980) 6937. 16L. G. S. Schum, J. Phys. Chem., 87 (1983) 3479. 17 S. N. Foner and R. L. Hudson, J. Chem. Phys., 29 (1958) 442. 18 V. H. Dibeler, V. H. Franklin and R. M. Reex, J. Am. Chem. Sot., 81 (1959) 68. 19 J. Betts, Can. J. Chem., 43 (1982) 2157. 20R. E. Kutina, G. L. Goodman and J. Berkowitz, J. Chem. Phys., 77 (1982) 1664. 21 A. J. Colussi and S. W. Benson, Int. J. Chem. Kinet, 9 (1977) 30. 22 D. Griller and F. P. Lossing, J. Am. Chem. Sot., 103 (1981) 1586; T. J. Burkey, A. L. Castelhano, D. Griller and F. P. Los&g, J. Am. Chem. Sot., 104 (1983) 4701. 23M. A. Grela and A. Colussi, J. Phys. Chem., 88 (1984) 5995; Int. J. Chem. Kinet., 17 (1985) 257. 24D. M. Golden, R. K. Solly, N. A. Gac and S. W. Benson, 94 (1972) 363. 25 J. L. Franklin and D. K. Sen Sharma, Adv. Mass Spectrom., 6 (1974) 947. 26 D. F. McMillen and D. M. Golden, Ann. Rev. Phys. Chem., 33 (1982) 493. 27 J. Berkowitz, J. P. Greene, J. Foropoulos and 0. M. Neskovic, J. Chem. Phys., 81 (1984) 6166.