8260
J. Phys. Chem. 1996, 100, 8260-8267
Ab Initio Study of Diborane Hydrolysis Michael L. McKee Department of Chemistry, Auburn UniVersity, Auburn, Alabama 36849 ReceiVed: NoVember 20, 1995; In Final Form: February 25, 1996X
Ab initio calculations have been applied to the mechanism of diborane hydrolysis in the gas phase. In the first step, water adds to diborane to form a complex which eliminates H2 in a concerted step to form BH3, H2, and H2BOH. The subsequent steps to the formation of the ultimate product, B(OH)3, can take place via two alternative pathways. In the first pathway, H2BOH can form a complex with H2O which eliminates H2 to form HB(OH)2, followed by addition of another molecule of H2O and elimination of another H2. Alternatively, two molecules of H2BOH can associate to form a dimer which dissociates to form BH3 plus HB(OH)2. Likewise, the association/dissociation of H2BOH/HB(OH)2 to BH3/B(OH)3 completes the transformation. Thus, in the second pathway, H2BOH comes exclusively from the first step while the hydrolysis product is due to equilibrium steps driven by the greater thermodynamic stability of products.
Introduction The overall hydrolysis of diborane can be written as eq 1. In 1953 Weiss and Shapiro1 studied the vapor-phase hydrolysis of diborane. They found the reaction to be first order with
B2H6 + 6H2O f 2B(OH)3 + 6H2
(1)
respect to water concentration and half order with respect to diborane concentration and proposed the mechanism given in eqs 2-5.
B2H6 h 2BH3
(2)
BH3 + H2O f [BH3‚H2O] f H2BOH + H2
(3)
H2BOH + H2O f [H2BOH‚H2O] f HB(OH)2 + H2 (4) HB(OH)2 + H2O f [HB(OH)2‚H2O] f B(OH)3 + H2 (5) Evidence for their mechanism came from the reaction of diborane with ice at -80 °C,1 which produced 4 mol (rather than 6 mol) of H2 for every mole of B2H6 consumed. Presumably, attachment of the boron atom to two hydroxyl groups on the surface of the ice crystal prevents further hydrolysis. At -23 °C, the last hydrogen is replaced by OH and the ratio of hydrogen to diborane then approaches 6:1.1 Also, when diborane reacts with silica gel at -23 °C, the ratio of hydrogen to diborane is only 2:1, possibly due to the formation of a tethered BH2OSi- group.1 More recently, Pasternack et al.2 studied the kinetics of the reaction BH3 + H2O by monitoring, with a tunable diode laser, the disappearance of BH3 upon addition of H2O. Under their experimental conditions, they observed no reaction of BH3 with H2O and suggested that the mechanism proposed by Weiss and Shapiro1 for hydrolysis of diborane may need to be modified. Carpenter and Ault3 studied the reaction of B2H6 with CH3OH with the merged-jet copyrolysis of Ar/B2H6 and Ar/CH3X
Abstract published in AdVance ACS Abstracts, April 15, 1996.
S0022-3654(95)03406-X CCC: $12.00
OH followed by trapping on a low-temperature window. They isolated and characterized methoxyborane, H2BOCH3 and proposed the mechanism given in eq 6.
B2H6 + CH3OH f [BH3‚CH3OH] f H2BOCH3 + H2 (6) Two key intermediates in the hydrolysis mechanism, H2BOH and HB(OH)2, have been characterized by microwave spectroscopy by passing a mixture of B2H6 and H2O through a quartz tube heated to 900 °C and into a waveguide cell.4,5 In an effort to isolate H2BOH in a matrix, Carpenter and Ault6 used the merged-jet copyrolysis technique to direct B2H6 and H2O through a 400 °C pyrolysis zone onto a low-temperature matrix. However, rather than the expected H2BOH product, they observed only boroxin, B3O3H3. Their explanation was that H2BOH readily eliminates H2 to form HBdO which then rapidly trimerizes to form B3O3H3. They posited that the success of the microwave study relied on the greater sensitivity of microwave (relative to IR) which could detect H2BOH in much smaller amounts. The mechanism of hydrolysis of the boron halides may be similar to that of B2H6, where HX is eliminated rather than H2 in eqs 3-5. It is known that BX3 (X ) Cl, Br, I) undergo rapid hydrolysis to give first X2BOH, then XB(OH)2, and finally B(OH)3.7 While many computational studies have been carried out on the reactions of BH3 or B2H6 with Lewis bases, only those more relevant to this work will be cited. The complex, BH3‚H2O, which has been studied by several groups,8,9 has a calculated binding energy of about 10-12 kcal/mol. In a detailed study, Sana and Leroy9 calculated the activation barrier for the stepwise elimination of two molecules of H2 from the BH3‚H2O complex. Sakai,10 in a study that appeared during the course of this research, considered the reaction of B2H6 with H2O as well as with other Lewis bases. Finally, in a study of the mechanism of diborane oxidation, Mains11 considered complexes of H2BOH with BH3 and H2BOH. More detailed comparisons will be made below. Method All geometries were optimized at the MP2/6-31G(d) level.12,13 Vibrational frequencies were calculated at that level to determine © 1996 American Chemical Society
Ab Initio Study of Diborane Hydrolysis
J. Phys. Chem., Vol. 100, No. 20, 1996 8261
TABLE 1: Absolute Energies (hartrees) of Relevant Speciesa H2 H2O BH3 B2H6 HBdO H2BOH (1) HB(OH)2 (2) B(OH)3 (3) B2H5OH (4a) 4b 4c 4d(TS) B2H4(OH)2 (5a) 5b 5c 5d B2H3(OH)3 (6a) 6b B2H2(OH)4 (7) B2(OH)6 (8a) 8b 8c BH3‚H2O TS1 TS2 1‚H2O TS3 2‚H2O TS4 TS5 B2H6‚H2O (open) TS6 TS7 TS8 a
sym
MP2/a
MP2/b
QCI/a
ZPEb
Cp (298 K)
S
D∞h C2V D3h D2h C∞V Cs Cs C3h Cs Cs Cs C1 C2h Cs C1 C2h Cs Cs C2h C2h Ci C2h Cs C1 Cs C1 C1 C1 C1 Cs C1 C1 C1 C1
-1.144 14 -76.196 85 -26.464 24 -52.992 82 -100.424 48 -101.577 69 -176.687 15 -251.789 73 -128.079 70 -128.079 21 -128.059 97 -128.054 93 -203.174 74 -203.171 71 -203.168 68 -203.154 50 -278.279 38 -278.269 01 -353.394 98 -503.602 35 -503.588 47 -503.551 22 -102.689 66 -102.645 59 -101.476 91 -177.783 62 -177.735 96 -252.892 56 -252.831 60 -129.171 52 -129.177 89 -129.163 24 -204.255 16 -204.243 76
-1.160 27 -76.308 96 -26.504 80 -53.079 82 -100.529 40 -101.706 72 -176.905 48 -252.097 59 -128.256 38 -128.251 02 -128.229 78 -128.224 82 -203.430 03 -203.430 20 -203.429 50 -203.421 63 -278.627 07 -278.614 23
-1.151 64 -76.207 89 -26.484 65 -53.033 51 -100.440 13 -101.602 01 -176.714 57 -251.820 45 -128.123 98 -128.122 81 -128.104 31 -128.099 24 -203.221 31 -203.219 18 -203.215 62 -203.202 23 -278.330 16 -278.319 08
-102.838 64 -102.801 45 -101.613 37 -178.021 63 -177.981 16 -253.219 52 -253.166 19 -129.365 36 -129.372 83 -129.363 67 -204.537 92 -204.534 06
-102.720 47 -102.674 33 -101.498 02 -177.818 49 -177.767 90 -252.930 76 -252.866 90 -129.223 10 -129.229 34 -129.212 88 -204.311 60 -204.296 88
6.48(0) 13.48(0) 17.06(0) 41.02(0) 9.07(0) 22.72(0) 27.03(0) 30.84(0) 44.96(0) 45.56(0) 43.31(0) 43.13(1) 49.38(0) 47.38(0) 48.76(0) 48.73(0) 51.25(1) 52.53(0) 55.74(0) 63.20(0) 62.08(1) 61.01(1) 35.53(0) 33.02(1) 18.04(1) 38.45(0) 36.53(1) 42.24(0) 39.62(1) 56.08(1) 57.05(0) 54.33(1) 58.08(1) 58.17(1)
2.08 2.37 2.40 2.81 2.18 2.48 2.82 3.30 3.21 3.01 3.95 3.42 3.51 4.51 3.71 3.88 4.36 4.12 5.64 6.80 6.68 6.36 3.13 2.64 2.52 4.26 3.20 5.00 3.85 4.31 4.15 3.58 5.63 4.12
31.10 45.14 44.98 55.26 48.49 55.05 61.03 64.51 63.84 62.30 69.64 65.51 67.08 77.43 69.03 69.37 76.26 73.40 87.36 98.99 97.37 89.86 60.47 57.33 55.29 72.80 64.15 82.15 70.71 73.06 71.20 66.97 86.26 72.93
Basis set “a” is 6-31G(d); basis set “b” is 6-311+G(2df,p). b Zero-point energy in kcal/mol with number of imaginary frequencies in parentheses.
the nature of the potential energy surface and to make zeropoint corrections (frequencies weighted by a 0.95 factor). For all species except (HB(OH)2)2 and (B(OH)3)2, single-point calculations were made at the QCISD(T)/6-31G(d) and MP2/ 6-311+G(2df,p) levels and combined14 to estimate relative energies at the [QCISD(T)/6-311+G(2df,p)] level, which, when zero-point corrections have been added, will constitute the “standard” level. All MP2 and QCISD(T) calculations were made with the “frozen-core” approximation. Corrections have not been made for basis set superposition error (BSSE) which may lead to a small (1-2 kcal/mol) overestimation of complexation energies.15 Heat capacities and entropy corrections were made using unscaled frequencies and standard statistical procedures16 to determine relative enthalpies and free energies at 298 K. Free energies at 698 K were estimated from eq 7.
∆G(698 K) ≈ ∆H(298 K) - 698∆S(298 K)
(7)
Molecular plots of all structures are given in Figure 1. A boldface notation system is used for the species in the figures, tables, and text to aid in identification. In addition, transition state structures (except for 4d(TS)) are given successive bold numbers TS1 through TS8. Relative energies (kcal/mol) are presented in Table 1 with respect to the top entry in each section of structures. In Table 2, enthalpies at 298 K and free energies at 298 and 698 K are tabulated relative to B2H6 + H2O, 4a + H2O, or 5a + H2O, respectively, which is given a value of zero. Potential energy diagrams of enthalpies at 298 K are given for the reaction path from B2H6 + H2O (Figure 2), 4a + H2O (Figure 3), and 5a + H2O (Figure 4) to products.
Discussion Several steps of the diborane hydrolysis reaction have been previously studied.9,10 There is good agreement in relative energies in three studies (Table 3) which have been carried out at similar levels of theory. The [QCISD(T)/6-311+G(2df,p)] method used in this study is probably on par with the MP4/6311++G(3df,2p) level used by Sana and Leroy9 and slightly more accurate than the MP4/6-311+G(d,p) level used by Sakai.10 Indeed, the average difference of relative energies in Table 3 between this work and that of Sana and Leroy9 is only 0.5 kcal/mol. A comparison of the MP2/6-31G(d) geometries of H2BOH and HB(OH)2 and the microwave structures4,5 shows that the two are in good agreement. At the HF/6-311+G(2df,p) level the dipole moments of H2BOH and HB(OH)2 are 1.63 and 1.68 D, respectively, compared to microwave values of 1.506 and 1.47 D.4,5 The MP2/6-31G(d) vibrational frequencies of H2BOH, HB(OH)2, B(OH)3, and (B(OH)3)2 are given in Table 4. The calculated values are in good agreement with experiment for B(OH)3 in the vapor phase.17 Vibrational shifts due to formation of the B(OH)3 dimer are also given in Table 4 in the hopes that the dimer might be identified in the vapor phase. The reaction of diborane with water is known to take place in solution (at room temperature) as well as in the vapor phase (at elevated temperature).1 While the present calculations are of direct relevance to the gas-phase mechanism, they may be of indirect relevance to the aqueous-phase mechanism. In solution, the intermediate complexes will be longer lived since entropy will not be as unfavorable as in the gas phase. Thus, in solution, enthalpies of activation and reaction will play the guiding role while in the gas phase, free energies will be more decisive.
8262 J. Phys. Chem., Vol. 100, No. 20, 1996
McKee
Figure 1. Molecular plots of relevant species with geometric parameters given at the MP2/6-31G(d) level. Values in parentheses for H2BOH and HB(OH)2 are microwave values.4,5
Ab Initio Study of Diborane Hydrolysis
J. Phys. Chem., Vol. 100, No. 20, 1996 8263
TABLE 2: Relative Energies (kcal/mol) of Various Species MP2/a
MP2/b
QCI/a
[QCI/b]
+ZPCb
∆H (298 K)
∆G (298 K)
∆G (698 K)
B2H6 + H2O 2BH3 + H2O BH3 + BH3‚H2O BH3 + TS1 BH3 + H2BOH + H2 BH3 + TS2 + H2 BH3 + HBdO + 2H2 TS5 B2H6‚H2O TS6 4a + H2 4b + H2 4d(TS) + H2 4c + H2
0.0 40.4 22.4 50.1 2.3 65.5 8.0 11.4 7.4 16.6 -21.4 -21.1 -5.9 -9.1
0.0 44.1 28.4 51.8 10.7 69.2 21.4 14.7 10.0 15.8 -17.5 -14.1 2.3 -0.8
0.0 40.3 22.8 51.7 2.0 67.2 8.4 11.5 7.6 17.9 -21.5 -20.7 -5.9 -9.1
0.0 44.0 28.8 53.4 10.3 70.9 21.8 14.8 10.2 17.1 -17.5 -13.7 2.2 -0.9
0.0 37.4 27.0 49.2 2.5 58.7 7.1 16.3 12.6 16.9 -20.4 -16.1 -2.4 -5.3
0.0 39.4 27.3 49.1 4.3 60.5 10.7 15.4 11.6 15.3 -20.3 -16.2 -2.1 -4.5
0.0 29.1 25.8 48.5 -4.8 51.3 -5.7 23.6 20.3 25.2 -18.7 -14.1 -0.9 -4.6
0.0 15.3 23.7 47.7 -17.0 38.1 -29.2 35.3 32.8 39.4 -16.4 -11.1 0.8 -4.7
4a + H2O 4b + H2O BH3 + H2BOH + H2O BH3 + H2BOH‚H2O BH3 + TS3 BH3 + HB(OH)2 + H2 TS7 BH3‚H2O + H2BOH TS1 + H2BOH TS8 2H2BOH + H2 5a + H2 5b + H2 5c + H2 5d + H2
0.0 0.3 23.7 18.0 47.9 -11.9 13.4 5.8 33.4 20.6 -14.4 -26.6 -24.7 -22.8 -13.9
0.0 3.4 28.1 24.4 49.8 -3.3 17.2 12.5 35.9 19.6 -5.2 -15.7 -15.8 -15.3 -10.4
0.0 0.7 23.4 18.0 49.8 -11.9 12.7 5.9 34.8 22.0 -14.9 -25.8 -24.4 -22.2 -13.8
0.0 3.8 27.9 24.4 51.7 -3.3 16.5 12.6 37.3 21.0 -5.8 -14.9 -15.5 -14.8 -10.3
0.0 4.4 22.9 21.6 47.1 -10.8 16.2 12.5 34.7 20.8 -12.0 -17.3 -19.9 -17.8 -13.4
0.0 4.2 24.6 22.7 47.1 -9.0 16.2 12.5 33.7 19.3 -10.5 -17.3 -18.9 -17.6 -13.0
0.0 4.6 13.8 20.1 47.0 -17.4 23.0 10.6 32.6 30.0 -20.1 -14.1 -18.8 -15.0 -10.5
0.0 5.2 -1.7 16.4 47.0 -29.4 32.7 7.9 31.0 45.3 -33.8 -9.5 -18.7 -11.3 -6.9
5a + H2O 5b + H2O 2H2BOH + H2O BH3 + HB(OH)2 + H2O BH3 + HB(OH)2‚H2O BH3 + TS4 BH3 + B(OH)3 + H2 6a + H2 6b + H2 H2BOH + H2BOH‚H2O H2BOH + TS3 H2BOH + HB(OH)2 + H2 BH3‚H2O + HB(OH)2 TS1 + HB(OH)2
0.0 3.8 12.1 14.6 9.3 47.5 -16.6 -32.6 -26.1 6.4 36.4 -23.5 -3.3 24.4
0.0 0.3 10.4 12.4 9.2 42.7 -14.8 -30.3 -22.3 6.7 32.1 -21.0 -3.2 20.1
0.0 3.6 10.8 13.9 8.6 48.7 -17.3 -33.0 -26.0 5.5 37.2 -24.5 -3.7 25.3
0.0 0.1 9.1 11.6 8.6 43.9 -15.5 -30.8 -22.2 5.7 32.9 -22.0 -3.6 21.0
0.0 -0.5 5.4 6.6 5.2 38.0 -23.5 -35.6 -25.9 4.1 29.5 -28.3 -3.9 18.4
0.0 -0.3 6.8 8.3 6.7 38.4 -21.6 -35.1 -25.9 4.9 29.3 -26.8 -3.8 17.9
0.0 -0.9 -6.0 -3.3 2.3 37.3 -30.1 -33.6 -23.6 0.3 27.2 -37.2 -6.6 16.1
0.0 -1.7 -24.3 -19.9 -4.0 35.7 -42.3 -31.5 -20.3 -6.3 24.4 -52.1 -10.6 13.5
a
Basis set “a” is 6-31G(d); basis set “b” is 6-311+G(2df,p). b Zero-point correction (with 0.95 factor) added to [QCI/b] relative energy.
Figure 2. Potential energy diagram (enthalpies at 298 K) for the reaction of B2H6 with H2O.
Two general mechanistic schemes were considered. In the first (Scheme 1), H2 is eliminated successively from B2H6 +
SCHEME 2 B2H6 9 8 BH3 + H2BOH -H
+H2O
B2H6 9 8 BH3 + H2BOH 9 8 -H -H 2
H2O, H2BOH + H2O, and HB(OH)2 + H2O to form B(OH)3. In the second (Scheme 2), H2 is eliminated only from B2H6 + +H2O
SCHEME 1 +H2O
Figure 3. Potential energy diagram (enthalpies at 298 K) for the reaction of B2H5OH with H2O to form B2H4(OH)2 plus H2 (BH3/HB(OH)2/H2).
2
2
+H2O
BH3 + HB(OH)2 9 8 BH3 + B(OH)3 -H 2
4 + H2BOH f 5 + BH3 5 + H2BOH f 6 + BH3
8264 J. Phys. Chem., Vol. 100, No. 20, 1996
McKee
TABLE 3: Comparison of Relative Energies (kcal/mol) between Several Methods MP4/6-311+G(d,p)// MP2/6-31G(d,p)a
MP4/6-311++G(2df,2p)// MP2/6-31G(d,p)b
[QCISD(T)/6-311+G(2df,p)]// MP2/6-31G(d)c
14.5 0.0 26.1 -16.0
14.7 0.0 24.3 -17.2 41.6 -6.4
15.2 0.0 24.6 -18.5 42.1 -7.0
BH3 + H2O BH3‚H2O TS1 H2BOH + H2 TS2 + H2 HBdO + 2H2 a
Reference 10. b Reference 9. c This work.
TABLE 5: Association Energies and Thermodynamic Properties for the HB(OH)2 and B(OH)3 Dimers
Figure 4. Potential energy diagram (enthalpies at 298 K) for the reaction of B2H4(OH)2 with H2O to form B2H3(OH)3 plus H2 (BH3/ B(OH)3/H2).
TABLE 4: Calculated Vibrational Frequencies (cm-1) and Intensities (km) for H2BOH, HB(OH)2, and B(OH)3 calc
B(OH)3
H2BOH
HB(OH)2
calc
obsa
a′ 3795(70) a′ 2766(176) a′ 2657(96) a′ 1412(143) a′ 1218(71) a′ 1214(63) a′′ 1095(69) a′ 919(62) a′′ 814(110)
a′ 3835(85) a′ 3774(57) a′ 2730(144) a′ 1485(381) a′ 1268(186) a′ 1151(28) a′ 1034(78) a′ 998(83) a′′ 960(44) a′′ 659(91) a′′ 541(211) a′ 475(42)
a′ 3823(0) e′ 3823(230) e′ 1494(860) a′ 1056(0) e′ 1052(386) a′ 880(0) a′′ 675(120) e′′ 551(0) a′′ 445(380) e′ 425(66)
3673 3668 1426 1020 1010 (880) 675 578 514 448
calcb (B(OH)3)2 ag/bu 3821/3821(151) ag/bu 3809/3809(165) ag/bu 3608/3641(1431) ag/bu 1534/1539(821) ag/bu 1436/1472(990) ag/bu 1234/1173(216) ag/bu 1072/1074(173) ag/bu 1055/1052(315) ag/bu 878/878(5) au/bg 774/728(280) au/bg 671/668(149) au/bg 546/549(23) ag/bu 456/492(18) au/bg 474/457(503) ag/bu 434/453(30) ag 158(0) bu 155(14) ag 132(0) bg 83(0) au 54(0) au 20(0)
a Reference 17. b The frequencies are listed in pairs (ag/bu or au/bg) for the modes associated with the B(OH)3 units. The intensity is given for the IR active mode in each pair (bu and au). The hydrogen-bonded stretches (3608 and 3641) are about 200 cm-1 lower than in free B(OH)3 with a very intense band (1431 km) predicted for the bu mode at 3641 cm-1.
H2O, while HB(OH)2 and B(OH)3 are formed by equilibration through association/dissociation reactions. B2H6 + H2O (Figure 2). The mechanism for reaction of B2H6 with H2O is similar to the reaction of B2H6 with NH310,18,19 and H2S.20,21 Rather than undergo initial dissociation into two BH3 units, B2H6 reacts directly with the Lewis base (H2O, NH3, or H2S) to form a BHbB bridged intermediate isostructural with B2H7-. This intermediate can then eliminate H2 through a “tight” transition state which has a low enthalpic barrier but unfavorable entropy. The alternative process (B2H6 f 2BH3; BH3 + H2O f H2BOH + H2) has a higher activation barrier
MP2/a
+ZPC
∆H (298 K)
∆G (298 K)
∆G (698 K)
2 HB(OH)2 (2) 7
0.0 -13.0
0.0 -11.4
0.0 -11.4
0.0 -1.0
0.0 13.0
2 B(OH)3 (3) 8a 8b 8c
0.0 -14.4 -5.6 17.7
0.0 -12.9 -5.3 17.1
0.0 -12.7 -5.2 16.8
0.0 -3.8 4.2 28.5
0.0 8.1 16.8 44.2
but more favorable entropy change. At 298 K, the free energy difference between the transition state for H2 elimination directly from the B2H6‚H2O complex (“direct” mode) and the transition state for H2 elimination from the BH3‚H2O complex plus BH3 (“indirect” mode) is 23.3 kcal/mol (Table 2, 48.5-25.2) and is reduced to only 8.3 kcal/mol at 698 K (Table 2, 47.7-39.4). The product from “direct” H2 elimination is actually BH5 rather than BH3 plus H2, i.e., the H2 fragment forms a complex with the BH3 empty p orbital. Indeed, the incipient BH5 formation is anticipated by the short B-H distances of the forming H2 in the “direct” transition state (TS6, 1.303, 1.614 Å, Figure 1). However, since higher-level calculations22 show that the H2BH3 binding energy is much less than 1 kcal/mol, the complex was not explicitly considered in the hydrolysis mechanism. The potential energy surface calculated by Sakai10 for B2H6 plus H2O is similar to that depicted in Figure 2 with one important difference. The activation barrier calculated by Sakai10 for forming the single hydrogen-bridged intermediate is 8.5 kcal/mol higher than the present calculations (24.8 kcal/ mol, Sakai; 16.3 kcal/mol, Table 2). The reason is that Sakai has located a higher-energy transition state for addition of H2O to B2H6. As shown in Figure 1, the incoming H2O displaces the bridging hydrogen on the opposite side of the boron atom (B-Hb 2.101 Å). In contrast, in the transition state calculated by Sakai,10 the adjacent bridging hydrogen is displaced. As a consequence, the B2H6‚H2O open complex is predicted by the present study to be in a much shallower potential energy well (3.7 kcal/mol, 298 K) than predicted by Sakai (8.6 kcal/mol, 0 K). The elimination of H2 from H2BOH was not considered by Sakai. However, at elevated temperatures, this reaction becomes very competitive. Relative to B2H6 + H2O, the enthalpy of the transition state for loss of H2 from H2BOH is (TS2) 45.2 kcal/mol higher than for loss of H2 from B2H6‚H2O (TS5, Table 2). However, at 698 K, the free energies of the two transition states are separated by only 1.3 kcal/mol (Table 3). Since HBdO rapidly trimerizes to form boroxin, B3O3H3, this result may explain why boroxin is isolated rather than H2BOH in the merged-jet copyrolysis of Ar/B2H6 and Ar/H2O.6 As pointed out by Carpenter and Ault,6 in the analogous reaction of B2H6 with H2S, H2BSH is the initial product which is followed by the formation of HBS. From the product monomers, BH3 and H2BOH, three complexes were considered (4a-c). The most stable complex (4a), which is bound by 24.6 kcal/mol23 (20.3 + 4.3, Table 2),
Ab Initio Study of Diborane Hydrolysis has the diborane structure with a terminal OH group. Only 4.1 kcal/mol less stable than 4a is the complex 4b with a bridging OH group. The third complex, 4c, is 11.7 kcal/mol less stable than 4b and separated from 4b by a 2.4 kcal/mol barrier (4d(TS)). This complex (4c) is a Lewis acid/Lewis base adduct which involves no bridging hydrogens. While BH3‚H2BOH is bound by only 8.8 kcal/mol, this mode of stabilization becomes more pronounced in BH3‚HB(OH)2 and BH3‚B(OH)3, which parallels the increasing strength of the Lewis base, H2BOH < HB(OH)2 < B(OH)3. H2B(H2)BHOH (4a) + H2O (Figure 3). The next stage considered in the diborane hydrolysis mechanism is the reaction of the most stable BH3/H2BOH complex, 4a, with water. The reader is reminded that at elevated temperature in the gas phase the reactive species is most certainly H2BOH rather than the complex, but at lower temperatures or in solution, the complex may prevail. The complex 4a can react with water to form a transition state very similar to that for addition of H2O to B2H6. However, rather than form a BHbB-bridged intermediate, two products are formed, BH3‚H2O and H2BOH. Evidently, a single hydrogen bridge is not sufficient to hold the complex together. The probable reason is that the terminal OH group donates electron density into the empty p-orbital on the adjacent boron atom, thereby reducing the acceptor strength of the H2BOH moiety.24,25 As discussed above, the B2H6‚H2O intermediate undergoes elimination of H2 in a unimolecular step (via TS6). A very similar transition state (TS8) for H2 elimination was found for the bimolecular step, BH3‚H2O + H2BOH. The transition state for H2 elimination from B2H6‚H2O (TS6) is 15.3 kcal/mol higher than B2H6 + H2O (Figure 2) compared to 19.3 kcal/mol for the difference between the analogous transition state (TS8) and 4a + H2O (Figure 3). In an alternative to the bimolecular step, BH3‚H2O (product from the reaction of 4a + H2O) can undergo H2 elimination in a unimolecular step. The enthalpy (298 K) is 15.0 kcal/mol higher than the bimolecular step (i.e., BH3‚H2O f TS1 versus BH3‚H2O + H2BOH f TS8) but the free energy is only 3.3 kcal/mol higher (298 K). At 698 K, the free energy order changes and the unimolecular step is preferred by 13.4 kcal/ mol. The complex 4b can dissociate into BH3 + H2BOH, whereupon either product can complex with H2O. Since the BH3‚H2O complex has already been discussed, attention is focused on the H2BOH‚H2O complex. Two interactions are possible in the H2BOH‚H2O complex, formation of a hydrogen bond or formation of a dative bond between boron and oxygen. The actual complex appears to partake of both. The oxygen of the water molecule is positioned above the boron (2.312 Å) while a water hydrogen is directed toward the oxygen of the hydroxyl group (2.481 Å). Both interactions are weak and the complex is only bound by 1.9 kcal/mol (298 K). The transition-state geometry for H2 elimination from H2BOH‚H2O (TS3) is very similar to the geometry for H2 elimination from BH3‚H2O (TS1). The activation barriers are similar as well; 24.4 kcal/mol, H2BOH‚H2O f TS3; 21.8 kcal/ mol, BH3‚H2O f TS1. Four product complexes are considered 5a-d which are bound in the range 2.5-8.4 kcal/mol with respect to two H2BOH molecules. The most stable complex (5b) is a donor/ acceptor complex between HB(OH)2 and BH3. The complex 5a, which is more stable at the MP2/6-31G(d) level, has two bridging hydroxy groups in a diborane-like structure while the least stable complex (5d) has two terminal hydroxyl groups. Complex 5c, bound by 7.1 kcal/mol and characterized by one
J. Phys. Chem., Vol. 100, No. 20, 1996 8265
Figure 5. Illustration showing the formation of a double OH-bridged complex (5a) from two H2BOH units. An equilibrium between 5a and a OH/H-bridged species (5c), in effect, converts H2B(OH) to HB(OH)2. In the analogous equilibrium between H2BOH/HB(OH)2 and BH3/ B(OH)3, the OH/H-bridged species may be a transition state since the double OH-bridged complex (6b) is calculated to be unbound with respect to monomers.
bridging and one terminal hydroxyl group, is relevant in the association/dissociation mechanism for converting two H2BOH molecules into BH3 and HB(OH)2 (Figure 5). When 5c dissociates, products form if the bridging hydroxyl group moves toward the B(H)OH side while reactants are re-formed if the OH moves toward the BH2 side. Mains11 has previously studied 4a,b and 5a,b, while Sakai10,23 has reported calculations on 4a. At comparable levels of theory, there is agreement for the complexation energies of 4a and 4b. However, Mains11 reports that 5a and 5b are unbound with respect to H2BOH monomers at the MP4/6-31G(d)//6-31G(d) level, while present calculations at the [QCISD(T)/6-311+G(2df,p)]//MP2/6-31G(d) level give complexation energies of 9.1 and 9.7 kcal/mol for 5a and 5b, respectively. H2B(OH)2BH2 (5a) + H2O (Figure 4). The third stage of diborane hydrolysis involves the reaction of 5a with water. If 5a dissociates into two H2BOH molecules, one monomer can complex with H2O forming H2BOH‚H2O and then undergo elimination of H2 in a reaction discussed in the second stage of hydrolysis. If 5b dissociates into BH3 plus HB(OH)2, then H2O can form a complex with either molecule and undergo subsequent H2 elimination. Since H2 elimination from BH3‚H2O has already been considered in the first stage of hydrolysis, attention is focused on the HB(OH)2‚H2O complex. The two hydroxyl groups in HB(OH)2 make boron a poor electron acceptor,24,25 and there is no tendency to form a dative B-O bond with water. Instead, a hydrogen bond is formed which is stable by 1.6 kcal/ mol. The transition-state geometry for H2 elimination in HB(OH)2‚H2O is again very similar to the geometries for H2 elimination in H2BOH‚H2O and BH3‚H2O (Figure 1). Indeed, the geometric parameters form a smooth trend for the three transition states (TS1, TS3, and TS4) as the number of hydroxyl groups on boron increases. For example, the forming H-H distance increases (1.015, 1.032, 1.049 Å) and the breaking O-H distance decreases (1.278, 1.244, 1.224 Å) along the trend. There is also a trend of increasing activation barriers (15.3, 22.5, 30.1 kcal/mol, Table 6) perhaps due to the reduced participation of boron (due to decrease of Lewis acidity as the number of OH groups increases) in stabilizing the forming H2. Two product complexes were considered 6a,b. Complex 6a is a dative complex between BH3 and B(OH)3 which is bound by 13.5 kcal/mol.26 The corresponding complexes of BH3 with H2BOH (4c) and HB(OH)2 (5b) are bound by smaller amounts,
8266 J. Phys. Chem., Vol. 100, No. 20, 1996
McKee
TABLE 6: Activation Parameters for the Elimination of H2 B2H6 + H2O f TS6 H2BOH + H2O f TS3 HB(OH)2 + H2O f TS4
MP2/a
MP2/b
QCI/a
[QCI/b]
+ZPC
∆Hq (298 K)
∆Gq (298 K)
∆Gq (698 K)
16.6 24.2 32.9
15.8 21.7 30.3
17.9 26.4 34.8
17.1 23.8 32.3
16.9 24.1 31.4
15.3 22.5 30.1
25.2 33.2 40.6
39.4 48.5 55.6
TABLE 7: Change in Structural Type of the Most Stable B2H6-n(OH)n Complex as a Function of Number of OH Groups n complex 0 1 2 3 4 6
B2H6 4a 5b 6a 7 8a
product
complex structural type
binding energy ∆H (0 K)
2BH3 BH3/H2BOH BH3/HB(OH)2 BH3/B(OH)3 2HB(OH)2 2B(OH)3
diborane-like diborane-like donor/acceptor donor/acceptor complementary H-bond complementary H-bond
38.8 22.9 30.7 12.1 8.7 9.2
8.8 and 9.9 kcal/mol, respectively. Complex 6b is a diboranelike structure with one terminal and two bridging hydroxyl groups. Relative to H2BOH + HB(OH)2, 6b is unbound by 0.9 kcal/mol (but bound by 2.6 kcal/mol at the level of theory used for geometry optimization). This result is in keeping with the general decrease in stability of the diborane-like structure which is observed as the degree of OH substitution increases in the monomers. Thus, the association/dissociation mechanism for conversion of H2BOH + HB(OH)2 to BH3 + B(OH)3 (Figure 5) may go through a double-bridged transition state rather than through a bound intermediate. HB(OH)2 and B(OH)3 Dimers. To the author’s knowledge, an experimental determination of the structure of (B(OH)3)2 has not been made. While the dimer of BF3 has been studied in inert matrices at low temperature by several groups,27 no definitive structure could be assigned. The diborane structure, though initially suggested, appears to be unlikely due to its computed high relative energy compared to other possibilities.27 At the HF/6-31G(d) level (no zero-point correction), the lowestenergy structure of B2F6 (C2h) was bound by 2.9 kcal/mol, while the D2h diborane-like structure was unbound by 15.1 kcal/mol.27 In the present work at the MP2/6-31G(d)//MP2/6-31G(d) level, the corresponding values for (B(OH)3)2 are very similar (-5.6 (8b) and 17.7 kcal/mol (8c), Table 5). The diborane-like structure was optimized in C2h symmetry (8c) rather than D2h symmetry to allow relaxation of the OH groups. While unbound, the diborane-like structure may serve as an intermediate/transition state for hydroxyl ligand exchange. Such ligand exchange is known to occur between borate esters, B(OR)3 and B(OR′)3, as well as between haloboranes, BX3 and BX3′.7,27,28 The lowest-energy structure for (HB(OH)2)2 and (B(OH)3)2 involve complementary hydrogen bonds. At the MP2/6-31G(d)//MP2/6-31G(d)+ZPC level, the HB(OH)2 dimer (7) is bound by 11.4 kcal/mol, while the B(OH)3 dimer (8a) is bound by 12.9 kcal/mol (Table 5). Gajhede29 has reported the optimized geometry (DZ basis set) of 8a in a study of the electric field gradient tensor but did not report the binding energy.
General Comments A series of borane complexes B2H6-n(OH)n with n in the range 0-6 is now available for comparison. As the Lewis acid strength of the borane units decrease, there is a change in the nature of the most stable complex: from diborane-like (n ) 0,1), to donor-acceptor (n ) 2,3), to complementary hydrogen bonds (n ) 4, 6; Table 7). As the number of OH groups attached to boron increases, the activation barrier for elimination of molecular H2 increases (Table 6). As a consequence, in the aqueous phase, the expected hydrolysis mechanism is likely to be loss of H2 only through the first reaction in Table 6. The formation of HB(OH)2 and B(OH)3 can take place through association/dissociation reactions. The overall driving force of the hydrolysis reaction is the greater thermodynamic stability of products as shown in the first equilibrium in Table 8. The stepwise progress of the reaction through association/dissociation equilibria are also thermodynamically driven through greater stability of products (second and third equilibria in Table 8). Conclusion The reaction of H2O with B2H6 to form B(OH)3 has been studied at a consistent level of theory. In the vapor phase, the predicted mechanism follows the elimination of H2 from B2H6 + H2O (TS6, ∆Ha ) 15.3 kcal/mol), elimination of H2 from H2BOH + H2O (TS3, ∆Ha ) 22.5 kcal/mol), and elimination of H2 from HB(OH)2 + H2O (TS4, ∆Ha ) 30.1 kcal/mol). The elimination of H2 from H2BOH to form HBdO (TS2, ∆Ha ) 56.1 kcal/mol) is predicted to be competitive (in free energy at 698 K) with the other H2-elimination steps and would lead to the HBdO trimer, B3O3H3. An alternative mechanism for the formation of B(OH)3 may be more reasonable in condensed phase. In this mechanism, H2 elimination occurs only in the first step, while HB(OH)2 and B(OH)3 are formed in association/ dissociation equilibria. An interesting change in the mode of complexation occurs in the series B2H6-n(OH)n as n increases from 0 to 6. The lowest energy complex changes from diborane-like to donor/ acceptor to complementary H-bonded as the number of OH groups increases, reflecting changes in the acidity/basicity for the monomer components. Acknowledgment. Computer time for this study was made available by the Alabama Supercomputer Network and the NSFsupported Pittsburgh Supercomputer Center. I would like to thank Brian J. Duke from Northern Territory University for helpful discussions.
TABLE 8: Equilibrium Energies and Thermodynamic Properties of Association and Dissocation Reactions 6 4a h 5B2H6 + 2B(OH)3 2 4a h B2H6 + 5a 4a + 5a h B2H6 + 6 assoc/dissoc 2H2BOH h 5a 5a h 5c 5c h BH3 + HB(OH)2
MP2/a
MP2/b
QCI/a
[QCI/b]
+ZPC
∆H (298 K)
∆G (298 K)
∆G (698 K)
-42.9 -5.7 -11.4
-55.3 -4.9 -16.2
-44.9 -5.8 -12.3
-57.4 -4.9 -17.0
-63.6 -5.6 -19.6
-61.0 -5.3 -18.9
-70.4 -4.6 -19.6
-83.9 -3.6 -20.6
-12.1 1.9 12.8
-10.4 -0.1 12.5
-10.8 1.3 12.5
-9.1 -0.7 12.3
-5.4 -2.6 9.1
-6.8 -1.6 9.9
6.0 -4.6 1.4
24.3 -8.9 -10.8
Ab Initio Study of Diborane Hydrolysis References and Notes (1) (a) Weiss, H. G.; Shapiro, I. J. Am. Chem. Soc. 1953, 75, 1221. (b) Shapiro, I.; Weiss, H. G. J. Phys. Chem. 1953, 57, 219. (2) Pasternack, L.; Balla, R. J.; Nelson, H. H. J. Phys. Chem. 1988, 92, 1200. (3) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1992, 96, 4288. (4) Kawashima, Y.; Takeo, H.; Matsumura, C. J. Chem. Phys. 1981, 74, 5430. (5) Kawashima, Y.; Takeo, H.; Matsumura, C. Chem. Phys. Lett. 1978, 57, 145. (6) Carpenter, J. D.; Ault, B. S. J. Mol. Struct. 1994, 319, 139. (7) Purcell, K. F.; Kotz, J. C. Inorganic Chemistry, Saunders: Philadelphia, 1977; pp 386-392. (8) For an early calculated binding energy of BH3‚H2O (6 kcal/mol) see: Dill, J.; Schleyer, P. v. R.; Pople, J. A. J. Am. Chem. Soc. 1975, 97, 3402. (9) Sana, M.; Leroy, G. Int. J. Quantum Chem. 1993, 48, 89. (10) Sakai, S. J. J. Phys. Chem. 1995, 99, 9080. (11) Mains, G. M. J. Phys. Chem. 1991, 95, 5089. (12) (a) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian92/DFT (Rev. G.2); Gaussian, Inc.: Pittsburgh, PA, 1993. (b) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian94 (Rev. B.1), Gaussian, Inc.: Pittsburgh PA, 1995. (13) For a general description see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (14) (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,
J. Phys. Chem., Vol. 100, No. 20, 1996 8267 89, 497. (c) McKee, M. L.; Lipscomb, W. N. Inorg. Chem. 1985, 24, 762. (15) van Duijneveldt, F. B.; van Duijneveldt-van de Rijdt, J. G. C. M.; van Lenthe, J. H. Chem. ReV. 1994, 94, 1873. (16) McQuarrie, D. A. Statistical Thermodynamics, Harper & Row: New York, 1973. (17) Gmelin Handbook of Organic and Inorganic Chemistry (Boron Compounds); Springer-Verlag: New York, 1993; 4th Supp., Vol. 2,pp 157188. (18) McKee, M. L. J. Phys. Chem. 1992, 96, 5380. (19) Sakai, S. Chem. Phys. Lett. 1994, 217, 288. (20) Mebel, A. M.; Musaev, D. G.; Morokuma, K. J. Phys. Chem. 1993, 97, 7543. (21) Mebel, A. M.; Musaev, D. G.; Morokuma, K. Chem. Phys. Lett. 1993, 216, 313. (22) (a) Stanton, J. F.; Lipscomb, W. N.; Bartlett, R. J. J. Am. Chem. Soc. 1989, 111, 5173. (b) Schreiner, P. R.; Schaefer, H. F.; Schaefer, P. v. R. J. Chem. Phys. 1994, 101, 7625. (c) Watts, J. D.; Bartlett, R. J. J. Am. Chem. Soc. 1995, 117, 825. (23) Sakai predicts 4a to be bound by 17.1 kcal/mol relative to monomers at the MP4/6-311+G(d,p)//MP2/6-31G(d)+ZPC level. In comparison, Mains predicts 4a to be bound by 23.6 kcal/mol at the MP4/6-31G(d)//6-31G(d) level. (24) Budzelaar, P. H. M.; Kos, A. J.; Clark, T.; Schleyer, P. v. R. Organometallics 1985, 4, 429. (25) Sana, M.; Leroy, G.; Wilante, C. Organometallics 1991, 10, 264. (26) One imaginary frequency is calculated for 6a which corresponds to rotation of the BH3 group. Rotating the BH3 group by 30° and reoptimizing in Cs symmetry produced another stationary point slightly higher in energy. A reoptimization of 6a in C1 symmetry was not carried out. (27) (a) Nxumalo, L. M.; Ford, T. A. J. Mol. Struct. 1993, 300, 325 and references therein. (b) Nxumalo, L. M.; Ford, T. A. J. Mol. Struct. 1995, 357, 59. (28) Burg, A. G.; Schlesinger, H. I. J. Am. Chem. Soc. 1933, 55, 4020. (29) Gajhede, M. Chem. Phys. Lett. 1985, 120, 266.
JP953406K
