J . Phys. Chem. 1990, 94, 435-440
435
Estimation of Heats of Formation of Boron Hydrides from ab Initio Energies Michael L. McKee Department of Chemistry, Auburn University, Auburn, Alabama 36849 (Received: January 30, 1989; In Final Form: June 21, 1989)
-
Thermochemical reactions for boron hydrides can be constructed relative to BH, and H2 where x and y are varied in the reaction xBH3 boron hydride + yHz. From calculated relative energies (MP2/6-3 lG*//3-21G) and the experimental heat of formation of Hz and the adjusted heat of formation of BH,, heats of formation for several boron hydrides up to BI0Hl4 have been predicted. The average deviation from the known experimental values is 2-3 kcal/mol except for BIOHl4,which is predicted to be about 7 kcal/mol more stable then the current experimental value. Calculated geometries and vibrational frequencies (3-21G) are compared with experimental values, and dipole moments (6-31G*) are reported.
Introduction
Heats of formation are known for relatively few of the boron hydrides due in part to the difficulties encountered when working with these explosive compounds. The intent of this paper is to provide reasonable estimates of the heats of formation of several stable and unstable boron hydrides. All of the boron hydrides considered can be derived from eq 1 where x and y are integer values. For example, the boron xBH3
-
boron hydride
+ yH2
(1)
hydride B9H15can be written as 9BH3 - 6H2. Thus, exothermicities can be determined by ab initio calculations and combined with experimental heats of formation of H2 and BH, (adjusted) to estimate heats of formation of other boron hydrides. Computational Method
Geometries of the boron hydrides shown in Figure 1 were determined at the HF/3-21 G 1evel.l Vibrational frequencies were determined at that level and weighted by a 0.9 factor2 in order to make zero-point corrections. Relative energies were corrected to enthalpy changes at 298 K by calculating heat capacity corr e c t i o n ~ . ~The stabilities of the boron hydrides were calculated relative to BH, and H2 by using eq 1 with MP2/6-31G* energies (Table I) directly and also by combining relative energies from HF/6-31G, HF/6-31G*, and MP2/6-31G calculations (Le., additivity approximation3). The paper will be divided into three sections dealing, respectively, with (i) geometries, (ii) energetics, and (iii) vibrational frequencies of the boron hydrides. Boron Hydride Geometries
Since the predicted geometries of the smaller boron hydrides have been published previously:+ only the larger boron hydrides will be discussed here. (Additional geometry data on the boron ( I ) The GAUSSIAN86 program was used throughout. Frisch, M. J.; Binkley, J. S.;Schlegel, H. 8.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.; Pople, J. A. GAuSSIANB~; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984. (2) For a description of basis sets and use of the 0.9 weighing factor for vibrational freauencies see: Hehre. W. J.; Radom. L.; Schlever, P. v. R.; Pople, J. A. AbInilio Molecular Orbital Theory; Wiley: New York, 1986. (3) (a) McKee, M. L.; Lipscomb, W. N. J . Am. Chem. SOC.1981, 103, 4673. (b) Nobes, R. H.; Bouma, W. J.; Radom, L. Chem. Phys. Lett. 1982, 89, 497. (c) McKee, M. L.; Lipscomb, W. N. Inorg. Chem. 1985, 24, 762. (4) See: McKee, M. L.; Shevlin, P. B.;Rzepa, H. S. J . Am. Chem. SOC. 1986, 108, 5793. (5) B3H7, B,H*: McKee, M. L.; Lipscomb, W. N. Inorg. Chem. 1982,21, 2846. (6) B,H,, B4H12: McKee, M. L.; Lipscomb, W. N . Inorg. Chem. 1985, 24, 23 17. (7) B4HIO:McKee, M. L.; Lipscomb, W. N. Inorg. Chem. 1981,20,4452. (8) BSH9: McKee, M. L.; Lipscomb, W. N . Inorg. Chem. 1985, 24, 765. (9) BSHll,B6HIO: McKee, M. L. J . Phys. Chem. 1989, 93, 3426.
0022-3654/90/2094-0435$02.50/0
hydride discussed here are given in tables of computer-generated coordinates (Z-matrix) as supplementary material.) B6HI2.A very recent microwave structure by Greatrex et a1.I' has appeared for B6H12that establishes that the molecule has C2 symmetry. Earlier work'' could not definitively distinguish between a C2symmetry structure or a structure of Ci symmetry. In agreement with the microwave results, the lowest energy calculated structure of B6HI2is predicted to have C, symmetry. In comparison, the Ci structure is calculated to have one imaginary frequency and to be 29.0 kcal/mol higher in energy than the C2 structure at the MP2/6-31G*+ZPC//3-21G level. Greatrex et a1.I0 discuss a structural relationship in the series B4HIo,B5Hll, and B6H12where the structures of B!HII (in CI symmetry) and B6Hl, (in C, symmetry) can be built up from B4Hloby replacing a bridging hydrogen with a BH2 group and converting a terminal hydrogen to a bridging hydrogen. Ab initio calculations (3-21G) predict that the central B-B distance in B4HI0 increases in the order 1.733, 1.759, 1.792 A, as one replaces bridging hydrogens in B4Hlowith BH2 groups, which is in good agreement with the experimental trend (1.705, 1.742, 1.821 A). Similarly, the B-B edge distance in B4Hlo is predicted to decrease in the order 1.902, 1.835, 1.741 A, also in agreement with experiment (1.856, 1.812, 1.777 A). The largest deviations between predicted and experimental B-B distances are between BIB2(predicted to be too long by 0.16 A) and BIB6(predicted to be too short by 0.15 A). While errors of this magnitude would indicate a serious discrepancy in a molecule with all two-center two-electron bonding, in the boron hydrides such errors may indicate a difference in the degree of participation of the borons (in this case BI, B2, B6) in a three-center tweelectron bond. To determine whether improvement in the basis set would improve the predicted geometry, the Czstructure was reoptimized at the 6-31G* level. The geometry changed very little, and the energy lowering on going from the 6-31G*//3-21G level to the 6-31G*//6-31G* level was only 0.3 kcal/mol. It is not likely that further improvement in the basis set would significantly alter the geometry. A single calculation was made on the experimental geometry1° to determine the energetic consequence of the disagreement. At the MP2/6-31G* level, the energy at the experimental geometry was 56.1 kcal/mol higher than the energy at the 3-21G geometry and 56.4 kcal/mol higher than the same calculation a t the 6-31G* geometry. Since it was necessary to make a number of assumptions about hydrogen positions in the (10) Greatrex, R.; Greenwood, N. N.; Millikan, M. B.; Rankin, D. W. H.; Robertson, H. E. J. Chem. SOC.,Dalton Trans. 1988, 2335. (1 1) (a) Gaines, D. F.; Schaeffer, R. Proc. Chem. Soc., London 1963,267. (b) Gaines, D. F.; Schaeffer, R. Inorg. Chem. 1964,3,438. (c) Lutz, C. A.; Philips, D. A.; Ritter, D. M. Inorg. Chem. 1964, 3, 1191. (d) Collins, A. L.; Schaeffer, R. Inorg. Chem. 1970, 9, 2153. (e) Leach, J. B.; Onak, T.; Spielman, J.; Rietz, R. R.; Schaeffer, R.; Sneddon, L. G.Inorg. Chem. 1970, 9, 2170. (f) Clouse, A. 0.; Moody, D. C.; Rietz, R. R.; Roseberry, T.; Schaeffer, R. J . Am. Chem. SOC.1973, 95, 2496. (g) Lipscomb, W. N. J. Phys. Chem. 1961, 65, 1064.
0 1990 American Chemical Society
436
The Journal of Physical Chemistry, Vol. 94, No. I , 1990
1 762 1829 1.291
B6H12
13%
1.387 1273
1913 1.699 1308 1 M8 1.416 1200
McKee
4320
5210 1.763 1818 1.746
3-21G 185.3 179,
1816 1926 t 848 2 087 1558 1 956 1.395 1232 1614
1.812 1.732
1.663 1831 1.356 1.3a 1.313 1345
1.314
x.ny 1707 1806 7.120 1 830 1 808 1.792 1.710 1.674 1.822 1282 1.496 1.287 1.327
B10H14
3.21G Heulron Dlfl 1 8 ~ 1.778 1770 1742 1756 1.715
1808 1.811
2.011 1.322 1326
1.786 1.775 1.973 1298 1347
B7H11 2502
B3H15
Figure 1. Geometric parameters for selected boron hydrides at the 3-21G level. The microwave structure for B6H12is from ref I O all other experimental values were obtained from ref 16. TABLE I: Total Energies (hartrees),Zero-Point Energies (kcal/mol), and Heat Capacities (cal/(mol.°C)) for Various Boron Hydrides mol svm 3-21G 6-31G 6-31G* MP2l6-3 1G MP2l6-3 IG* ZPE' C.. H,
D-h
BH,
D3h
B2H6
DZh
B3H7 B3H9 B4H8
cs
B4H12
C3L C2" C2L C2'
B5H9
c4,
B5H I I B6H10 B6H12
Cl
B6H I 4
c2 h
B7Hlla B7Hllb BEHI2
cs c,
c,
B9H15
cs
B10H14
C2"
B4H10
c, c 2
-1.12296 -26.237 30 -52.497 81 -77.58501 -78.71778 -102.668 11 -103.843 90 -104.95397 -127.821 96 -128.94960 -152.939 I O -154.06351 -155.20769 -177.95996 -178.010 I O -203.17239 -229.426 33 -253.44727
-1.126 81 -26.376 78 -52.77539 -77.99706 -79.13240 -103.21221 -104.39007 -105.50053 -128.49302 -129.62955 -153.74474 -154.87564 -156.02463 -178.89340 -178.95054 -204.240 17 -230.616 75 -245.776 53
-1 .I26 81 -26.39001 -52.81237 -77.04734 -79.18208 -103.27972 -104.456 76 -105.558 13 -128.57807 -129.710 16 -153.83762 -154.971 97 -156.12486 -178.99806 -179.03668 -204.36050 -230.749 25 -254.921 74
-1.144 14 -26.431 68 -52.91037 -78.19500 -79.34289 -103.48435 -104.675 22 -105.77373 -128.83420 -129.98064 -154.15257 -155.29472 -156.41646 -179.377 16 -179.37529 -204.79230 -231.252 66 -255.474 I5
-1.144 14 -26.464 22 -52.99241 -78.31355 -79.45889 -103.64930 -104.84052 -105.91855 -129.04858 -130.18378 -154.39702 -155.53791 -156.65608 -179.66238 -179.63016 -205.1 1681
5.99 ( 0 ) 15.56 (0) 37.59 (0) 44.51 (0) 56.20 (0) 49.82 (3) 65.55 (0) 73.99 (0) 62.55 (0) 73.24 (0) 71.39 (0) 82.47 (0) 93.76 (0) 75.70 (2) 76.79 (0) 87.67 (0) 108.49 (0) 118.38 (0)
4.97 6.46 10.48 15.48 19.28 16.25 21.56 28.46 20.27 25.93 24.45 28.72 32.18 29.73 33.78 32.90 39.61 39.17
Zero-point energy (kcal/mol) weighted by a factor of 0.9. I n parentheses is given the number of imaginary frequencies. electron diffraction study,I0 a 3-21G optimization of the hydrogens was made with the positions of the boron atoms fixed at the experimental geometry. A single MP2/6-31G* calculation at this geometry gave an energy 18.8 kcal/mol higher than the MP2/ 6-31G* energy at the fully optimized 3-21G geometry. Hence, allowing the position of the hydrogens to vary decreased the energy by 37.3 kcal/mol (56.1-18.8) and probably indicates that some of the assumptions made about the hydrogen positions are overly restrictive. &HI+ Experimental evidence has been reported12that supports the existence of a hydrogen-bridged B6HI4species. The "B-NMR spectrum consists of two signals in a 2: 1 ratio that would indicate a hydrogen-bridged B,H, dimer with two sets of magnetically
equivalent borons on the NMR time scale. High-level calculations on this system soon f ~ l l o w e dwhere '~ five alternative structures were considered. The most stable was tris(diborane) (1) followed by the other four structures including 2 and 3; all lie within 8.3 kcal/mol. In the study, a DZP quality basis (double-{ plus d functions on borons and p functions on hydrogens) was used to optimize geometries and electron correlation was estimated within a slightly smaller basis (excluding p functions on hydrogen). The final calculated relative energies for 1-3 (not including zero-point corrections) were 0.0, 4.4, and 7.6 kcal/mol, respectively. In the present study at the MP2/6-31G*//3-21G level, the three structures (1-3) are within 5.5 kcal/mol (0.0 kcal/mol, 1; 3.0 kcal/mol, 2; 5 . 5 kcal/mol, 3). When zero-point corrections are
(12) Brellochs, B.; Binder, H. Angew. Chem., In?. Ed. Engl. 1988, 27, 262.
( 1 3) Horn, H.; Ahlrichs, R.; Kolmel, C . Chem. f h y s . Le??.1988, f50,263.
Estimation of Heats of Formation of Boron Hydrides H
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 431
H
TABLE II: Calculated Dissociation Energies (kcal/mol) of B2H, at Various Levels AH,," method ref 43.1 (37.0) MP4/6-31 lG++(3d,f;3p,d) b ~
42.6 (36.2) 41.8 (35.3) 41.0 (33.9) (36.2) 40.2 (36.8) 36.0 (32.6) 34.3-39.1
G1
c
CCSD+T(CCSD)/6-311G**(6d) d MP4/6-31G** BACMP4 MP2/6-31G* [MP2/6-31G*] exptl
e
f
this work this work
-
g
"Heat of reaction for B2H6 2BH3. Values in parentheses have been corrected for differences in zero-point energies. Several values also include heat capacity corrections. bPage, M.; Adams, G. F.; Binkley, J. S.;Melius, C. F. J . Phys. Chem. 1987, 91, 2675. cCurtiss, L. A.; Pople, J. A. J . Chem. Phys. 1988, 89, 4875. dStanton, J. F.; Bartlett, R. J.; Lipscomb, W. N. Chem. Phys. Lett. 1987, 138, 525. CDefrees, D. J.; Raghavachari, K.; Schlegel, H. B.; Pople, J. A.; Schleyer, P. v. R. J. Phys. Chem. 1987, 91, 1857. fMelius, C. F. Private communication. ZRuscic, B.; Mayhew, C. A.; Berkowitz, J. J. Chem. Phys. 1988, 88, 5580.
H
included, 2 is significantly stabilized with respect to 1 (0.0 kcal/mol, 1; 0.1 kcal/mol, 2; 5.8 kcal/mol, 3). Further theoretical and experimental work will be needed to clarify the potential energy surface of B6HI4. B7Hll. The only heptaborane that has been detected is B7Hll for which there exists mass spectrometry evidence.14 The boron hydride has not been isolated either as the free boron hydride or as an adduct, which probably indicates that it has little thermodynamic stability. Two structures of C, symmetry (see Figure 1) with styx notation of 4320 (denoted B7Hlla in Tables I and 111) and 2502 (denoted B,Hllb in Tables I and 111) were optimized. The 4320 geometry was based on B6HI0,a capped pentagon, where a bridging BH group is added and four hydrogens are allowed to bridge around the open face. The 2502 geometry was based on an open B5H9 structure that has been shown8 to be reasonably close in energy to the C, symmetry structure. At the HF/6-31G level, the more open 2502 structure is 35.8 kcal/mol more stable than the compact 4320 structure. Polarization functions and electron correlation favor the 4320 structure, and at the MP2/6-31G* level, the 4320 structure is 20.2 kcal/mol (21.3 kcal/mol including ZPC) more stable than the 2502 structure. Clearly, two structures do not constitute a thorough search of the potential energy surface; however, the high calculated heat of formation is reasonable since the boron hydride has not been is01ated.I~ BaHl2. The optimized structure of BsH12is compared to the X-ray structureI6 in Figure 1. The hydrogen bridge between B B5 and BsB7 is predicted to be nearly symmetrical (1.348, 1.313 which disagrees with the X-ray structure that reveals an unsymmetrical bridge (1.496, 1.287 A). Perhaps most noteworthy are the predicted short B3B8bond (1.663 A) and the long B3B4bond ( 1 3 3 4 A) that agree with X-ray results (1.674, 1.822 A) but
A),
oppose intuition, since the unbridged boron positions would be expected to be shorter than bridged borons (Le., a single-bonded B-B distance as in B6Hlo would be shorter than a BB distance connected by a BHB bond). B9H15. The 3-21G geometry of is in good agreement with the X-ray structure16 for the reported boron-boron distances. Both methods, ab initio and X-ray, indicate that the B4B5/B9B8 distance is exceptionally long (1.973 A, 3-21G; 1.95 A, X-ray). The experimental locations of bridging hydrogens between B3B9 and B3B4were not reported; however, the 3-21G geometry is in agreement with an earlier M N D O calculation17 that predicts considerable asymmetry (B3H3,4/B9H3,4:1.463/1.241 A, 3-21G; 1.635/1.232 A, MNDO). B I d l 4 . The structure of B10H14 has been solved by both X-ray diffraction and neutron diffraction.I6 The 3-21'3 geometry is compared with the neutron diffraction structure in Figure 1. While the trend in the boron-boron distances is reproduced at the 3-21G level, the bond lengths are predicted to be too long by about 0.02 A. The asymmetry of the brid ing hydrogen is underestimated at the 3-21G level (1.322p.326 !,3-21G; 1.298/1.347 A, neutron diffraction). Boron Hydride Energetics
A comparison of the calculated dissociation energy of B2H6is made with high-level calculations in Table 11. It appears that the method used presently (MP2/6-31G*+ZPC//3-21G) underestimates the stability of B2H6by about 0-2 kcal/mol. If the trend for higher boron hydrides is consistent (i.e., underestimation of the boron hydride with respect to BH3 of about 0-1 kcal/mol per boron), we can compensate for it in eq 2 by reducing the heat
+
AHf(boron hydride) = AH,,, X [ A H ? ~ ~ ( B H ~ ) (2) ] of formation of BH3 by 0-2 kcal/mol. The adjusted value would be in the range 23.5-25.5 kcal/mol, a reduction of 0-2 kcal/mol from the experimental value of 25.5 f 2 kcal/mol.l8 Any error in the heat of formation of BH3 is magnified in the estimated heat of formation of the boron hydride due to the multiplicative factor in eq 2. For that reason, the value of AHLBH,) used in eq 2 was fit for B5HI1,a medium-sized boron hydride. A value of 23.34 kcal/mol was chosen, which yields the experimental heat of formation of B5HII and is in the expected range. When the additivity approximation is used, there is about a 3 kcal/mol underestimation of the stability of boron hydrides compared to ~~
(17) Dewar, M. J. S.; McKee, M. L. Inorg. Chem. 1978, 17, 1569.
(14) McLaughlin, E.; Rozett, R. W. Inorg. Chem. 1972, 11, 2567. (15) The 2502 geometry proposed by Lipscomb for B,H,, rearranges without activation to the structure calculated here. Lipscomb, W. N. Inorg. Chem. 1964, 3, 1683. (16) Beaudet, R. A. In Molecular Structures and Energetics. Advances in Boron and the Boranes; Liebman, J. F.,Greenburg, A,, Eds.; VCH: New York, 1988; Vol. 5.
(18) Heats of formation are taken from: Chase, M. W., Jr.; Davies, C. A,; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A,; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed. J . Phys. Chem. Re$ Data Suppl. 1985, 14 (1).
(19) Bauer, S. H. In Molecular Structures and Energetics. Advances in Boron and the Boranes; Liebman, J. F., Greenburg, A,, Eds.; VCH: New York, 1988; Vol. 5. (20) Greenwood, N. N.; Greatrex, R. Pure Appl. Chem. 1987, 59, 857.
438
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
McKee
TABLE 111: Relative Energies (kcal/mol) for Various Boron Hydrides HF/6-31G X
Y
AHnn
H2
0
1
BH3
1 2 3 3 4 4
0 0
0 0 -13.7 4.1 -1.3 25.9 -6.1 4. I 6.6 0.4 5.5 2.9 -1 1.0 69.0 33.2 8.3 8.4 -14.6
B2H6
B,H,
B3H9 B4H5 B4Hlo
-1
0 -2 -1
B4H12
B5H9
B5HIl
B6Hlo B6H12 B6H14
B7Hl,a B7Hllb
BEHI2 B9Hl5
BioHI4
5 5 6 6 6 7 7 8 9 IO
-3 -2 -4 -3 -2 -5 -5 -6 -6 -8
HF/6-31G* AH,, 0 0 -20.2 -2.6 -7.6 16.8 -14.8 1.2 -5.3 -8.6 -3.0 -7.7 -24.1 61.5 37.2 -0.8 0.0 -22.7
MP2/6-31G AHmn
0 0 -29.5 -27.7 -30.6 -28.8 -58.2 -29.5 -67.9 -69.4 -87.3 -86.0 -72.0 -47.8 -46.6 -127.9 -145.9 -194.9
MP2/6-31GIaqb AH,,, 0 (0) 0 (0) -36.0 (-32.6) -34.4 (-33.4) -36.9 (-32.1) -37.9 (-41.2) -66.9 (-62.8) -32.4 (-26.9) -79.8 (-80.8) -78.4 (-76.1) -95.8 (-97.4) -96.6 (-92.9) -85.1 (-80.2) -55.3 (-61.8) -42.6 (-46.8) -137.0 (-141.4) -154.3 (-154.2) -203.0 (-196.2)
estmdC
MP2/6-31G** AHmn 0 (0) 0 (0) -40.2 (-36.8) -40.8 (-39.8) -41.6 (-36.8) -50.6 (-53.9) -80.2 (-76.1) -38.7 (-33.2) -100.4 (-101.4) -94.7 (-92.4) -1 18.2 (-1 19.8) -1 16.1 (-1 12.4) -99.8 (-94.9) -83.8 (-90.3) -63.6 (-67.8) -168.1 (-172.5)
AHi 0 20.0ge 7.6 26.8 28.1 39.1 17.5 53.4 19.6 24.3 23.1 27.6 40.3 78.8 93.8 19.2 26.5 4.6
estmdc
exptld
AHi 0 23.34' 9.9 30.2 33.2 39.5 17.3 60.2 15.3 24.3 20.2 27.6 45.1 73.1 95.6 14.2
AHi 0 25.5 f 2, 23.8' 9.8 f 4, 8 . d
I5.q 17.5 f 2, 17.5' 24.3f 22.2f
(22.2)g 11.3 f 4.5, 7.1f
"Heat of reaction is determined by using the additivity approximation (ref 3). *Values in parentheses include zero-pint and heat capacity corrections. CEstimatedheat of formation obtained from eq 2. dHeat of formation at 298 K. Unless otherwise indicated, values are from ref 18. CThevalue for AHI(BH3)is set to the value that yields the experimental heat of formation of BSH,, from eq 2. fGuest, M. F.; Pedley, J. B.; Horn, M. J. Chcm. Thermodyn. 1969, I, 345. ZEstimated: Laurie, D.; Perkins, P. G. Inorg. Chim. Acta 1982, 63, 53. TABLE I V BH3 Affinities (kcal/mol) and Hz Affinities (kcal/mol) of Boron Hydrides Calculated from Predicted AHI Values in Table
TABLE V Calculated Dipole Moments (debye) at the HF/6-31G* Level for Several Boron Hydrides
111"
BHI affinity* -36.8 (-32.6) 0.0 (0.4) -36.2 (-29.4) 3.7 (5.2) -38.5 (-34.9) -11.0 (-12.1) -2.5 (-4.1) (-12.8)
dipole moment, D
H, affinity' B3H7 B4Hs B4Hlo B5H9 B6Hlo B6Hl2
3.0 -22.2 42.9 9.0 7.4 17.5
0.89 0.50 0.01 0.58 0.43 2.19 1.60 2.61
(1.3) (-21.6) (35.9) (4.7) (4.5) (12.7)
"The values in parentheses are computed by using the additivity approximation. *Calculated heat of reaction for the addition of BH3to the indicated boron hydride to form the next higher boron hydride. 'Calculated heat of reaction for the addition of H2 to the indicated boron hydride. the MP2/6-3 IC* values. The value of AHLBH), that yields the experimental heat of formation for B5Hll when the additivity approximation is used is 20.08 kcal/mol. The foregoing implies not that the experimental heat of formation of BH3 is in error but rather that the calculated exothermicities of reaction given by eq 1 are in error by a predictable amount and that the error can be compensated for by a fairly small adjustment of the heat of formation of BH, (Le., a one-parameter fit). Table 111 gives the computed reaction exothermicities from eq 1 and the estimated heats of formation from eq 2. The largest error is about 3 kcal/mol except for BI0Hl4,which is predicted to be about 7 kcal/mol more stable than the experimental value (AHf(B,,HI4): 4.6 kcal/mol, estimated; 11.3 f 4.5 kcal/mol, experimental). Although too much emphasis should not be made of this disagreement since it involves a calculation where an error in the heat of formation of BH, would be magnified in the product, it can be said that the calculations favor the lower end of the experimental range (6.8-15.8 kcal/mol). It should be noted that the heat of formation obtained by Pedley (7.1 kcal/mol, Table 111) is in good agreement with the theoretical estimate. It is also worthwhije to point out the importance of electron correlation in determining heats of reaction. For the larger boron hydrides, heats of reaction in Table 111 are in error by over 100 kcal/mol at the HF/6-31G or HF/6-31G* levels. From the values tabulated in Table 111, BH, and H2 affinities (Table IV) can be derived. Large BH3 affinities are predicted for BH,, B3H7, and B4H8,which are proposed intermediates in the pyrolysis of d i b ~ r a n e . ' ~The * ~ three ~ boron hydrides, BsH9, B S H l l ,and BEHI,are predicted to add BH3 with the release of energy to form B,H12, B,H14, and B9H15,respectively. For all
dipole moment, D 0.81 0.00 2.1 1 1.35 2.48 2.81 3.25
B6H12
B6H14 B7Hlla B7Hllb
BBH12 B9H15 B10H14
TABLE VI Calculated Heats of Reaction for Several Borane Pyrolytic Reactions w a n
reaction B2H6 + BH, B3H7 + H2 B3H7 + B2H6 BSHII + H2 B3H7 + B4H10 BSHll + B2H6
-
+
+
B3H7
+ B5HII
B6H12
+ B2H6
B3H7 + B5H9 -* B ~ H I+o BzH6 B3H7 + B6H10 B9H15 + H2 B4H8 + BzH6 BSHII + BH, B4H8 + B 5 H l l B5H9 + B4H10 B4H8 + B6Hlo B9H15 + BH, -+
+
B4H8
B4H8
+ B6H12
+ B8H12
B9Hls + BH,
-+
4
B5H9 BIOH14
+ B5Hll
+ B2H6
BloHI4 + 2H2
V B S-R" 12.8 -31.6 -40.0 -68.1 -51.7 -55.5 10.4 -21.9 1.o 4.2 -63.0 -36.8
b -3.0 -15.8 -13.3 -17.0 -15.4
(-0.9) (-10.1) (-12.4) (-15.9) (-15.7) (-23.0) -1.4 (-2.3) -30.8 (-26.3) (-1 5.6) -27.5 (-22.8) (-46.1) (-42.0)
" Heats of reaction are estimated by using valence bond structureresonance theory (ref 21). bThis work. Heats of reaction are calculated from estimated heats of formation in Table 111. Values in parentheses were determined by using the additivity approximation to determine relative energies of the boron hydrides. boron hydrides studied, adding H2 results in a less table compound except in B4Hs, which forms B,H,, with a calculated release of 22.2 kcal/mol. For reference, the dipole moments of the boron hydrides calculated at the HF/6-31G* level are tabulated in Table V. Calculated heats of reaction of several reactions thought to be involved in diborane pyrolysis are presented in Table VI and compared with recent values that have been estimated from a valence bond structure-resonance approach.21 Errors of up to (21) Herndon, W. C.; Ellzey, M. L.; Armstrong, R. L.; Millet, 1. S.In Mathematics and Computational Concepts in Chemistry; TrinajstiE, N., Ed.; Wiley: New York, 1986; pp 98-109.
Estimation of Heats of Formation of Boron Hydrides
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 439
TABLE VII: Calculated Vibrational Frequencies (cm-’) for BH3, B2H, B4Hlo, and B5H9at the HF/3-21C Level” sym calc exDtl % diff sym calc exDtl % diff 2683 1210
2623b 1125 B2H6
2761 2259 1287 814 926 1915 885 2861 1136
253P 2088 1183 790 833 1760 860 2609 949
2853 2836 2748 2370 161 1 1268 1 I42 898 828 746 537 263 2361 1514 1222 1125 929 602
2576 2570 2475 2095 1444 1255 1 I45 965 908 827 785 559 2150 1308 1117 1023 868 737
2 8
BH3
e’ e‘
0 3
2808 1256c
~ ( - L ~ ~ ~ =~ 0, . ~9 1/1 ~D ~ ~ ~ ) 9 8 9 3 11 9 3 IO 20
bzu big bl, bl,
bl,
bo8 b3,, b3, b3,
439 2847 968 1966 1074 1234 2746 1821 1280
B4H10 [ ( ~ D e a p d ~ U c a ~ = c ) 0.94Id
11 10
a2
11
b1
13 12 1 0 -7 -9 -10 -32 -53
bl bl
IO 16 9 IO 7 -18
bl
bl
bl bl bl b2 b2 b2 b2 b2 b2 b2 b2
b2
B 4 9 [ ( E u c x p d C ~ c a d=
2884 2862 2007 1308 1081 829 762 1444 779 1929 1 I48 760 666 2860
2807 1293
26289 2610 1844 1126 985 799 702
741 241 2610
IO
IO 9 16 10 4 8
2 176 IO
b2 b2 b2 b2
e e e e e e e e e
430 2829 2349 1584 1250 1126 993 829 558 2849 2744 2362 1378 1242 1012 860 438 261
0.94Id 1791 873 750 460 2869 1950 1627 1204 1020 980 829 672 560
19 10 6 1 10 21 9 14 9
662 2570 2150 1324 1196 966 846
-35 10 9 20 4 16 17
1036 785 599 2610 1800 1634 1410 1035 890 711 618 569
1 -
BiHia
369 2596 915 1940 972 1020 2520 1603 1172
2570 2475 2150 1388 1140 1064 898 472 236
.20.0
11 11 10 -1 9
-5 -4 -7
IO
-16 -4 -23 10 8 0 -15 -1 10 16 9 2
OVibrational frequencies are for the IlB isotope. bKaldor, A,; Porter, R. F. J . Am. Chem. SOC.1971, 93,2140. ‘The theoretical value at the MP2/6-31G* level is used due to the probable error in the experimental assignment of the e’ mode. See: Hout, R. F.; Levi, B. A.; Hehre, W. J. J . Comput. Chem. 1982, 3, 234. dRatio of the sum of experimental vibrational frequencies to the sum of calculated vibrational frequencies. eDuncan,J. L.; McKean, D. C.; Torto, I.; Nivellini, G . D. J . Mol. Spectrosc. 1981, 85, 16. fDahl, A. J.; Taylor, R. C. Inorg. Chem. 1971, 10, 2508. EKalasinsky, V. F. J . Phys. Chem. 1979, 83, 3239.
50 kcal/mol indicate that this approach does not yield qualitative agreement. A plot of the exothermicities of reactions involving the addition of BH, or elimination of H 2 from certain boron hydrides is presented in Figure 2. It is clear that if BH3 is present, the formation of larger boron hydrides is thermodynamically favorable. Vibrational Frequencies
Calculated vibrational frequencies of BH,, B2Ha, B4Hlo,and B5H9are compared with experimental frequencies in Table VII. The higher frequency BH, terminal stretches are predicted to be (22) Hanousek, F.; Stibr, B.; Heimhek, S.; PleSek, J. Collect. Czech. Chem. Commun. 1973, 38, 13 12.
.4o.c-
.60.0-
Figure 2. Plot of exothermicities of reactions involving the addition of BH3 or elimination of H2 from boron hydrides. The vertical scale is in
kilocalories per mole. TABLE VIII: Calculated Vibrational Frequencies for BIHlb B&, and
a’
. ..
2879 2872 2839 2830 2819 2064 2016 1960 1617 1237 1202 1169 1129 1069 1043 1019 962 928 880 829 795 777 754 729 693 658 605 576 458 28 1
,/t
2868 2860 2831 203 1 1681 1578 1499 1162 1062 1033 1011 959 934 906 794 767 758 728 693 610 546 454 359 321
.
a, 2875 2855 2839 2837 2827 2820 2698 2387 2089 2012 1735 1362 1272 1256 1209 1120 1073 1062 1049 959 944 909 869 852 78 1 770 738 728 688 671 661 599 554 484 386 312 220
._ ..
..
,/r
2865 2851 2824 2402 2074 1808 1619 1430 1233 1180 1114 1056 1043 1010 975 96 1 945 908 826 767 754 739 695 605 568 501 462 389 208
al 2871 (10) 2854 (10) 2836 (10) 2821 (10) 2060 ( 5 ) 1838 (-1) 1288b (17) 1062 1054 1023 904 898 804 780 720 682 665 577 44 1 356
a, 2847 1977 1657 1192 1057 1000 990 908 804 761 708
605 533 244
bi 2853 (10) 2818 (10) 2004 (6) 1727b (10) 1237 1107 1024 983 843 787 764 738 642 633 358
b, 2866 (IO) 2846 (10) 2833 (10) 2036 (5) 1726 (14) 1213 1118 1052 980 956 872 816 750 713 662 556 47 1
‘The values in parentheses are the percent differences from the reported infrared bands in ref 21. Assignments are tentative. ”he calculated splitting between the BHb out-of-plane and BH, bend is 394 cm-I (scaling factor, 0.9), which compares to an experimental splitting of 412 cm-’ (1100-1512 cm-’, ref 21).
between 9-1 1% too high, which is typicaL2 For the lower frequency modes, there is a larger nonsystematic deviation from experiment. The ratio of the sum of experimental vibrational frequencies to calculated vibrational frequencies varied from 0.91 to 0.94 (Table VII). These values are slightly larger than the typical weighting factor of 0.9 used to estimate zero-point corrections and may reflect the underestimation of the stability of nonclassical structures relative to classical ones. If the potential well is predicted to be too shallow, then distortions will be predicted to be too “soft” and hence the typical overestimation will be smaller.
J . Phys. Chem. 1990, 94, 440-442
440
Vibrational frequencies at the HF/3-21G level are reported for the remaining stable boron hydrides, B8HIZ, and BIoH14, except for B5H,, and B6HI0,which have been reported previously? An infrared studyz2of BI0Hl4and its deuterio derivatives has allowed a partial comparison with experiment (Table VIII). The BH, stretching modes are systematically predicted to be 10% too large while the BHb distortions indicate larger deviations. Conclusions
The boron hydrides have been studied at a uniform level of theory. Geometry optimizations at the ab initio level are reported for the first time for B6H12,B7Hll,BBHIZ,B9HIs,and BIOHl4. Heats of formation are calculated with an estimated accuracy of f2-3 kcal/mol. Calculated vibrational frequencies are reported for the first time for the larger boron hydrides. Note Added in Proof. Sana, Leroy, and Henriet2j have estimated the heats of formation of BH3 and BzH, as 25.9 and 8.5 kcal/mol, respectively, by calculating total energies at the MP4/6-3 1 +G**(2d,f) and including zero-point and heat capacity corrections. Recent ~ o r k has ~ shown ~ - ~that ~ electron correlation (23) Sana, M.; Leroy, G.; Henriet, Ch. THEOCHEM 1989, 187, 233. (24) Stanton, J. F.; Lipscomb, W. N.; Bartlett, R. J.; McKee, M. L. Inorg. Chem. 1989, 28, 109.
has a significant effect on the geometry of B3H9. In light of this work, a better estimate for the heat of formation of B3H9 would be about I O kcal/mol lower than the value calculated here.
Acknowledgment. We thank the donors of the Petroleum Research Fund, administered by the American Chemical Society, for financial support. Computer time for this study was also donated by the Auburn University Computer Center and the Alabama Supercomputer Network. Registry No. H2, 1333-74-0; BH,, 13283-31-3; BzH,, 19287-45-7; B3H7, 12429-70-8; B,Hg, 36350-66-0; B4Hg, 66455-86-5; B4H,o, 1828393-7; BdHI2, 60349-62-4; B5H9, 19624-22-7; BsHII, 18433-84-6; B6HI0, 23777-80-2; B6HI2, 12008-19-4; B6HI4, 12008-20-7; B7Hllsr 12430-08-9; B7HIlb, 12430-08-9; BgHl2, 19469-16-0; B9HI5, 19465-30-6; BloHI4, 17702-41-9.
Supplementary Material Available: Tables of computergenerated coordinates (Z-matrix) of boron hydrides optimized at the 3-21G level (6 pages). Ordering information is given on any current masthead page. (25) Stanton, J. F.; Lipscomb, W. N.; Bartlett, R. J. J . Am. Chem. SOC. 1989, 111, 5165. ( 2 6 ) McKee, M. L., submitted for publication.
Thin-Film Infrared Spectroscopic Method for Low-Temperature Vapor Pressure Measurements R. K. Khanna,* J. E. Allen, Jr.,+ C. M. Masterson, and G. Zhao Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742 (Receiued: March 2, 1989; In Final Form: April 24, 1989)
A new thin-film infrared (TFIR) technique is presented for measuring the vapor pressures of organics at low temperatures. It is based on the measurement of the loss rate of the sample at a particular temperature. This loss rate is measured by monitoring a characteristic infrared absorption feature for the compound. The method was calibrated by using solid C 0 2 for which previous low-temperature vapor pressure data are available in the literature. The vapor pressures of solid C4H2 and C4N2 were also determined. Results differ from extrapolated values of high-temperature measurements by as much as a factor of 2 5 .
Introduction
The Voyager 1 and 2 flybys as well as ground-based observations have revealed that the atmospheres of several planetary systems contain complex H-, C-, and N-bearing compounds. In these low-temperature environments, some of these species may condense. For example, diacetylene (C4H2), which is photochemically produced from CH4, is likely to condense out on Uranus, Neptune, and possibly Saturn,l while dicyanoacetylene (C4N2)has been identified in the solid phase in the upper atmosphere of Titan where temperatures in the 140-160 K range are encountered.2 To obtain internally consistent models of the concentration profiles in planetary atmospheres, a knowledge of the temperature dependence of vapor pressures for the identified species is essential. Laboratory data on vapor pressures of organics at low temperatures are extremely scarce. Typically, vapor pressure measurements at ambient temperatures are extrapolated by using the Clausius-Clapeyron equation
I n P2 - = - AH PI
1 R (TI
i2)
'Code 691, N A S A Goddard Space Flight Center, Greenbelt, MD 20771.
0022-3654/90/2094-0440$02.50/0
to obtain values at lower temperatures. In the absence of any knowledge of its temperature dependence, the enthalpy of vaporization (or sublimation) is generally assumed to be temperature independent. However, this can lead to significant errors if the temperature interval over which the vapor pressure is extrapolated is large. Possible structural phase transitions in the temperature range of interest can add to these errors. It is, therefore, desirable to obtain laboratory measurements of the vapor pressures of condensed hydrocarbons in the appropriate temperature ranges. There are several techniques currently in use for vapor pressure measurements. Thermocouples and diaphragm gauges, including the capacitance manometer, are suitable for measurements down Torr. These, however, are not species-specific; therefore, to high sample purity is desirable. Ionization gauges measure pressures as low as IOd Torr; however, their main utility is in checking leaks in a system. They cannot provide reliable data for organics which can exhibit complex cracking patterns on ionization. The spinning rotor is an important new development in pressure measurement and technology.' It measures pressures
-
(1) Kunde, V.
-
G.; Aikin, A. C.; Hanel, R. A,; Jennings, D. E.; Maguire,
W. E.; Samuelson, R. E. Nature 1987, 292, 686. (2) Khanna, R. K.; Perera-Jarmer, M . A,; Ospina, M. J. Spectrochim. Acta 1987, 4 3 A ( 3 ) , 421
0 1990 American Chemical Society
