J. Phys. Chem. 1995,99, 9080-9086
9080
Theoretical Study of the Chemical Reactions of B2& with Lewis Bases (NH3, PH3, H20, and H2S) Shogo Sakai Department of Information Systems Engineering, Faculty of Engineering, Osaka Sangyo University, Daito, 574 Japan Received: May 20, 1994; In Final Form: October 28, 1994@
The potential energy surfaces for the reactions of diborane with four Lewis bases, XH, (NH3, HzO, PH3, and H2S), have been calculated at the MP4/6-3 1l+G(d,p)//MP2/6-31G(d,p) level with zero-point energy corrections. Two steps for the formation of HzB=XH,-I were studied. The first step is the formation pathway of a complex, H3BH3BXHn, or an adduct, H3B:XHn, and the second is 1,2- and 1,3-hydrogen elimination from the complex or the adduct. For the formation of the complex or the adduct, the reactions of diborane with NH3 and PH3 systems are more favorable than those with HzO and HzS systems. The energy barrier heights for this step are proportional to the values of the proton affinity of Lewis bases. The transition states of 1,Zhydrogen elimination from the adducts have high activation barriers (42-49 kcal/mol) for the above four systems. These energy barrier heights are proportional to the dissociation energies of the X-H bond in their adducts. The transition state of 1,2-hydrogen elimination for BH3PH3 system, which has a structure similar to those of the others, leads to a PH3 inversion complex (not the adduct) for the reactant side along the IRC pathway. On the other hand, 1,3-hydrogen elimination from the complexes have low-energy barriers except for the B2H6 PH3 system. For B2H6 PH3 system, the reaction through 1,Zhydrogen elimination of H,B(Hz)PH2BH3 is the lowest barrier pathway. At high temperatures, Gibbs free energy pathways for these systems were also discussed.
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Introduction Diborane, B2H6, has long been of interest to chemists as a consequence of its unusual structure and It reacts readily with a range of Lewis bases, in both solution and gas phase. Recently merged jet copyrolysis experiments show that B2H6 reacts with methanol: NH3J$6and HzS7 and leads to the formation of methoxyborane, aminoborane, and mercaptoborane, respectively. It was concluded from their results that these reactions produce aminoborane, methoxyborane, and mercaptoborane through a borane-Lewis base adduct. They proposed a two-step mechanism for it. The first step is the slow formation of a borane-Lewis base adduct, and the second is the rapid hydrogen elimination from the adduct. This conclusion comes from the fact that they did not observe evidence of the adduct as H3B:NH3 for the reaction of B2H6 with NH3: B,H6
+ NH, - H3B:NH3+ BH,
-.H2B=NH, + H,
H3B:NH3
(1) (2)
To clarify the mechanism for the reactions 1 and 2, Carpenter and Ault6 studied the pyrolysis of the adduct H3B:NH3, and observed evidence of H2B=NH2. They also studied the reaction of diborane with methylamine* (CH3NH2, (CH3)2NH, and (CH3)3N) by an infrared matrix isolation and observed evidence of the formation of HzB-NHCH3 , HzB=N(CH~)Z, and H3B: N(CH3)3, respectively. From these results, they concluded a mechanism for the reaction of B2H6 with Lewis base (XH,) in which the adduct H3B:XHfl is formed in the initial slow step and is followed by the rapid elimination of HZ to form H2B=XHfl- 1. In this mechanism estimated experimentally, the second step, 1,2-hydrogen elimination, is a 2s+2s reaction and is forbidden @Abstractpublished in Advance ACS Abstracts, May 1, 1995.
0022-365419512099-9080$09.00/0
thermally by the Woodward-Hoffmann rules. One can assume a vary high barrier for this reaction step. On the other hand, an ab initio MO study of the reaction mechanisms of Bz& with NH3 by McKeeg has provided a minimum-energy reaction path, which initiates with the formation of NH3(BH3)2, followed by 1,Zhydrogen elimination to give B2H5:NHZ HZand eventually leads to HzB=NHz BH3 HZwith very high barriers (42 and 48 kcdmol). Recently, Morokuma and co-workers'O calculated minimum-energy reaction paths for the formation of HS=BH2 through 1,Zhydrogen elimination from HzS:BH3 and SHz(BH3)z complex by ab initio MO methods. They provided the reaction paths for HzB=SH formation which are similar to those calculated by McKeeg for the reaction of Bz& and NH3. The calculated activation barriers for the formation of HzB-SH were 41 and 45 kcdmol. The reaction barriers calculated by these groups are very high because their paths are 1,Zhydrogen eliminations. Quite recently, for the reaction of diborane with ammonia, a new transition state (1,3-hydrogen elimination from H3BHBH2NH3 complex) of HzB=NH;? formation with a low-energy barrier (17 kcdmol) was reported in my previous paper" by ab initio MO methods. Morokuma and co-workersl*reinvestigated the reaction of Bz& with SH2 and found that my mechanism was operative at some temperatures in their system. I also calculatedI3 systematically the potential energy surfaces of the reactions of Bz& with N H 3 , which include the formations of H3BHBHzNH3 complex and H3B:NH3 adduct and three-type ( 1,1-, 1,2-, and 1,3-) hydrogen eliminations. For 1,l-hydrogen elimination from the adduct, the energy barriers are extremely high (over 100 kcdmol). In 1,Zhydrogen elimination from the adduct H3B:NH3, the transition state leads to HzB-NHz and H2 with a high-energy barrier (37.5 kcdmol). 1,2-Hydrogen elimination from the complex has a barrier of 39.0 kcallmol but does not lead to aminoborane. Two other 1,Zhydrogen elimination transition states were also calculated. However,
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0 1995 American Chemical Society
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Chemical Reactions of B2H6 with Lewis Bases
J. Phys. Chem., Vol. 99, No. 22, 1995 9081
H
\
XH"
Addition
Adduct 1
1,Bellmination
Complex 2
4
1,3slimination
z Figure 1. Geometrical shapes of stationary points for the treated reactions.
these two transition states correlate to p-aminodiborane for the product side but not to the formation of aminoborane. Therefore, for 1,2-hydrogen elimination, only the transition state from the adduct relates directly to the formation of aminoborane. Consequently 1,2-hydrogen elimination from the adduct, 1,3hydrogen elimination from the complex, and 1,l-hydrogen elimination with extremely high barriers lead directly to aminoborane. However, for the reactions of B2H6 with other Lewis bases, neither the mechanism of these reactions nor the structure and stability of expected intermediates and products is not well understood. Molecular orbital calculations of potential energy surfaces of these reactions should be useful to that effect. To characterize the reaction mechanisms of the formation of H2B=XH,-l for a wide range of Lewis bases, I calculate the minimal energy pathways for the formation of H~B=XH,-I from diborane with four Lewis bases XH, (NH3, H20, PH3, and H2S) by ab initio MO methods. From the previous results, I study three types 1,Zhydrogen eliminations and 1,3-hydrogen elimination for hydrogen elimination step. Although the calculated results for B2H6 NH3 system were reported in the previous paper,I3these are presented in the present paper to be compared with other Lewis base systems.
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Computational Approach
The basis sets used were the split-valence plus polarization 6-3 1G(d,p)I4 and the split-valence plus polarization and diffuse function 6-31 l+G(d,p) sets.15 All molecular structures, including those for transition states, were obtained at the MP2/6-31G(d,p) level.I6 To verify the minima and transition states, it was
established that the matrixes of energy second derivativesI7have zero and one negative eigenvalue, respectively. The reaction energies were determined by using fourth-order Mdler-Plesset perturbation theory corrections with the 6-3 11+G(d,p) basis set. The intrinsic reaction coordinate (IRC)'* was followed from the transition state toward both reactants and products. All calculations were made by Gaussian92 program.I9 Results and Discussion
The structure shapes of stationary points for the treated reactions (B2H6 XH,: XH,=H20, NH3, HzS, and PH3) are shown in Figure 1. Their geometry parameters are listed in Table 1. Dissociationhtecombination Mechanism. The previous paperi3 showed that the adduct of borane and ammonia, H3B: NH3, is not produced in one step from B2H6 and NH3. The formation of the adduct occurs via two reaction pathways. One is through the complex (B& XH, H~BHBHzXH, H3B H3B:XH,) and the other is through the dissociation of diborane (BZH6 XH, 2BH3 XH, H3B H3B:XHn). The dissociationenergy of diborane is 34.4 kcal/mol at the MP4/ 6-31 l+G(d,p)//MP2/6-31G(d,p) ZPE level. The formation energies of the adducts 1 from BH3 and XH, are -25.6, -20.1, -10.8, and -9.6 kcal/mol for XH, = NH3, PH3, H2S, and H20, respectively. Consequently the adduct formations are endothermic reaction. These adduct formation energies (the binding energy of H3B and XH,) relate completely to the proton affinity of XH,; 219.9 kcal/mol for NH3, 197.7 kcaYmol for PH3, 179.7 kcal/mol for H20, and 176.6 kcal/mol for H2S at the MP2/631G(d,p) calculation. Because the B-X bond is formed by the
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Sakai
9082 J. Phys. Chem., Vol. 99, No. 22, 1995
Potentlal Energy Profile Potential Energy Proflle
....... E
*
55.3
Is1
.....
...... ....... .......... 12.0 I'
, . bs
I
q
B&*HrO
$5
....**. P.H....
,$'iB&+SH,
,+
7.2
's,,s*Ht
..-,....... .I
s,,
433
........
.*, .m.3 b
.7.9 ;L*BH,tH*
I+BH,&I,
Glbbs Free Energy Proflle
Figure 2. Potential energy and Gibbs free energy (400 "C) profiles along the minimal energy path for the reaction of BzH6 with HzO at the MP4/6-31 l+G(d,p) ZPE level. Potential energy and Gibbs free energy are shown as solid and dotted lines, respectively.
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Glbba Free Energy Profile
Figure 4. Potential energy and Gibbs free energy (400 "C) profiles along the minimal energy path for the reaction of B2H6 with H2S at the MP4/6-31 l+G(d,p) ZPE level. Potential energy and Gibbs free energy are shown as solid and dotted lines, respectively.
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153 19.0
Potentlal Energy Proflle
Polenllal Energy Profile n3
n3
m
I
BWTS
66.1
Is5
61.6
4m*
Glbbs Free Energy Proflle
Figure 3. Potential energy and Gibbs free energy (400
Glbbs F r N Energy Proflle
Figure 5. Potential energy and Gibbs free energy (400 "C) profiles
"C) profiles along the minimal energy path for the reaction of B2H6 with NH3 at the MP4/6-31 l+G(d,p) ZPE level. Potential energy and Gibbs free energy are shown as solid and dotted lines, respectively.
along the minimal energy path for the reaction of B2H6 with PH3 at the MP4/6-31 l+G(d,p) ZPE level. Potential energy and Gibbs free energy are shown as solid and dotted lines, respectively.
interaction between the vacant orbital of BH3 and the lone-pair orbital of XH,. Mechanism of the BzhXH, Complex Formation. The complexation energies between the adduct H3B:XHn and BH3 parts in the complex 2 are almost similar values for four Lewis bases; 15.8 kcaUmol for NH3, 14.5 kcal/mol for H20, 11.2 kcaY mol for PH3, and 10.9 kcal/mol for H2S at the MP4/6-311+G(d,p) ZPE level. The complexation energies are essentially one B-H-B bridged bond energy as shown in the previous paper.I3 The differences (maximum 4.9 kcaYmo1) for these
energies arise from the perturbational substitution effects for the B-H-B bond. The activation energy barriers at the transition states TS1 for the formation of the complex 2 are 5.4,20 11.9, 15.2, and 23.4 kcaYmol above the reactants of B2H6 with NH3, PH3, H2S, and H20, respectively. The order of these barrier heights is almost the same as that of the proton affinity of XH,. For the steps of the adducts 1 ~d the complex 2 formations, the reactions for B2H6 with NH3 and PH3 are more favorable in energy than those for B2H6 with H20 and H2S.
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Chemical Reactions of B2H6 with Lewis Bases
J. Phys. Chem., Vol. 99, No. 22, 1995 9083
TABLE 1: Some Geometry Parameters of Stationary Points from the Treated Reactions
TABLE 2: Total Energies (hartree) and Zero-Point Energies (kcaYmol) for Various Species ~
stationary points adduct 1 complex 2
Lewis bases H2O
NH3
H2S
PH3
B -X B*-X B*-B B*-H* B-H**
bond
1.730 1.601 2.303 1.272 1.334
1.657 1.605 2.287 1.262 1.337
2.036 1.962 2.310 1.246 1.367
1.949 1.933 2.253 1.253 1.361
B-X B-B B-H* B-X B-B B-H* B*-H* B*-X B*-X B-X B-X B*-X B*-B B*-H* B-H* B*-H** B-H** B -X Ha-Hh B-Hh B-Ha X-Ha B*-X B*-B B*-Hh B * -Ha X-Ha Ha-Hh B*-H* B-H* B*-X B-X B*-Hb B*-Ha X-Ha Ha-Hh B*-X Ha-Hh B*-B X-Ha B-Hh B*-H* B-H*
1.359 1.906 1.326 1.543 1.774 1.272 1.361 1.381 1.377 1.762 1.890 1.834 1.925 1.334 1.260 1.773 1.207 1.593 0.993 1.330 1.376 1.273 1.548 2.106 1.337 1.399 1.262 1.001 1.240 1.374 1.672 1.759 1.295 1.424 1.211 1.039 1.484 0.893 2.338 1.316 1.382 1.443 1.254
1.391 1.903 1.329 1.560 1.786 1.262 1.384 1.414 1.456 1.746
1.771 1.946 1.310 1.923 1.760 1.290 1.329 1.829 1.796 2.159 2.029 2.163 2.068 2.048 1.200 1.253 1.342 2.051 1.129 1.258 1.376 1.563 2.003 2.286 1.254 1.345 1.616 1.081 1.221 1.435 2.186 2.094 1.228 1.409 1.484 1.267 1.919 0.940 2.277 1.703 1.301 1.349 1.275
1.864 2.028 1.325 1.920 1.759 1.304 1.313 1.932 1.906 1.999
HzB=XH,-]
3 4 5
6 7
TS1
1,2-TS TS2
1,2-TS TS3
1,2-TS TS4
1,3-TS TS5
2.067 1.859 1.594 1.223 1.308 1.284 1.582 0.964 1.354 1.370 1.376 1.545 2.159 1.368 1.382 1.398 0.955 1.245 1.370 1.808 1.735 1.250 1.347 1.230 1.116 1.485 0.875 2.531 1.537 1.331 1.644 1.231
2.312 1.937 1.795 1.210 1.275 1.320 2.165 1.139 1.246 1.257 1.727 2.138 2.311 1.247 1.249 1.737 1.139 1.215 1.457 2.154 1.944 1.227 1.265 1.652 1.245 1.950 0.91 1 2.266 1.819 1.317 1.354 1.266
sym H2 BH3 HzO NH3 H2S PH3 B2H6 H3B:OHz 1 H3B:NH3 1 H3B:SH2 1 H3B:PH3 1 H3BHBH20H2 2 H3BHBH2NH3 2 H~BHBH~SHZ 2 H3BHBH2PH3 2 H2B=OH 3 H2B=NH2 3 H2B=SH 3 H2B=PH2 3 H2BHBHzNH2 4 HzBHBHzPH2 4 HzBHiBHOH 5 H2BHzBHNH2 5 H2BH2BHSH 5 H2BH2BHPH2 5 H2BOHBH3 6 H2BSHBH3 6 H2BPH2BH3 6 H3BOHzBH3 7 H Z B H ~ B H ~ OTS1 H~ H ~ B H Z B H ~ NTS1 H~ H2BH2BH2SH2 TS1 H2BH2BHzPH3 TSl H2B(H2)0H TS2 H2B(Hz)NH2 TS2 HzB(H2)SH TS2 HzB(H2)PHz TS2 H3BHBH(H2)0H TS3 H3BHBH(H2)NH2 TS3 H3BHBH(H2)SH TS3 H3BHBH(H2)PHz TS3 H2B(H2)0 HBH3 TS4 H2B(H2)N H2BH3 TS4 H2B(H2)S HBH3 TS4 HzB(Hz)PHzBH3TS4 H3B(H)BH2OH(H2) TS5 H~B(H)BHzNH~(H~) TS5 H3B(H)BHzSH(H2) TS5 H3B(H)BH2PH2(H2) TS5 a
In comparison with Gibbs free energies at 400 "C for these species, the barrier heights at the addition transition states TS1 for these four systems increase with about 20 kcdmol from those at 0 K, respectively. The dissociation energy of BH3 from B2H6 decreases with 22.4 kcdmol. Gibbs free energies at TSl become equal to that of the dissociation state at -103 "C for H20 system, 174 "C for NH3 system, 30 "C for HzS system, and 85 "C for PH3 system. At 400 "C, the energies of the addition transition states TS1 for all systems are 15-33 k c d mol higher than those of the dissociation states (2BH3 iXH,). Therefore, the formations of the complexes 2 and the adducts 1 occur through the dissociation state of B2H6 at high temperatures. The relative energies of the complex 2 for all systems increase with the increasing of a temperature. The energies of adduct system (1 f BH3) do not much change for the variation of a temperature. The energies of the complex 2 becomes equal to those of the adduct system at 139 "C for H20 system, 237 "C for NH3 system, 44 "C for H2S system, and 69 "C for PH3
D-h D3h C2" C3" C2" C3" D2h CI C3" C, C3" CI CI CI CI C, C2" C, C, Czy C2" CI C, CI CI CI CI C, C2v CI C, C, C, CI C, Ci CI Ci CI CI CI CI C, CI CI CI CI CI CI
MP2/ 6-31G(d,p) -1.15766 -26.486 16 -76.219 79 -56.383 22 -398.810 10 -342.578 58 -53.038 51 -102.734 27 -82.932 29 -425.316 70 -369.101 45 -129.251 03 -109.44095 -451.824 54 -395.609 44 -101.604 28 -81.774 37 -424.175 32 -367.914 41 -108.309 90 -394.461 30 -128.129 88 -108.284 07 -450.704 31 -394.455 83 -128.108 74 -450.670 76 -394.430 25 -129.231 40 -129.226 88 -109.419 13 -451.820 25 -395.594 83 -102.694 15 -82.855 81 -425.286 50 -369.044 62 -129.193 00 -109.358 93 -451.781 27 -395.539 08 -129.20039 -109.371 59 -451.786 13 -395.567 76 -129.231 99 -109.393 77 -451.805 24 -395.555 28
MP4/ 6-31 l+G(d,p) ZPE' -1.167 69 -26.518 28 -76.287 03 -56.434 26 -398.871 99 -342.642 04 -53.102 20 -102.828 43 -83.002 75 -425.414 49 -369.199 35 - 129.377 56 -109.552 89 -45 1.956 80 -395.740 96 -101.686 23 -81.834 57 -424.258 03 -367.999 31 -108.407 20 -394.577 62 - 128.244 82 -108.385 77 -450.818 55 -394.572 48 -128.220 66 -450.787 91 -394.549 13 - 129.356 68 -129.354 51 -109.530 92 -451.951 50 -395.725 64 - 102.786 80 -82.936 61 -425.382 24 -369.142 25 -129.319 11 -109.472 58 -451.910 97 -395.670 99 -129.324 71 -109.482 95 -451.918 03 -395.698 97 -129.359 19 -109.508 45 -45 1.936 27 -395.687 37
6.6 17.2 13.7 22.3 10.0 15.8 41.2 35.9 45.4 31.6 37.4 57.6 66.8 52.9 59.0 23.0 31.1 19.9 24.8 54.6 47.4 45.3 52.7 42.3 47.6 43.7 40.0 45.4 55.9 56.6 65.4 52.2 57.7 33.5 41.4 30.1 35.9 54.3 62.4 50.9 56.4 54.0 62.9 50.5 56.7 55.0 62.6 51.3 56.6
Zero-point correction in kcal/mol.
system. Consequently, the experimental detection of the adducts 1 and/or the complexes 2 may depended on thermal condition. Hydrogen Eliminations. 1,2-Hydrogen Elimination. The transition states TS2 of 1,Zhydrogen elimination lead to the adducts 1 for the reactant side and to H2B=XHn-, 3 H2 for the product side along the IRC paths, except for TS2 of X = P. For the system of X = P, TS2 leads to a PH3-inversion complex as follows:
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Symmetry
Sakai
9084 J. Phys. Chem., Vol. 99, No. 22, 1995 TABLE 3: Relative Energies and Gibbs Free Energies at 400 "C (kcdmol) for Various Stationary Points on the Potential Energy Surface B2H6 +H20 H2BH2BH20H2 TS1 H3BHBHzOH2 2 H3B:OHz 1 BH3 H2B(H2)0H TS2 BH3 H3BHBH(Hz)OH TS3 HzBHzBHOH 5 + H2 H3BOH2BH3 7 HzB(H2)OHBH3TS4 H2BOHBH3 6 H2 H,B(H)BHzOH(Hz) TS5 H2B=OH 3 BH3 H2
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B2H6 1 NH3 H ~ B H z B H ~ NTS1 H~ H3BHBH2NH3 2 H3B:NH3 1 BH3 H2B(H2)NH2 TS2 BH3 H,BHBH(Hz)NH2 TS3 H2BH2BHNH2 5 + H2 H z B ( H ~ ) N H ~ BTS4 H~ H2BHBH2NH2 4 H2 H3B(H)BH?NHz(Hz)TS5 HzB=NH2 3 BH3 H2
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BzHs + H2S H ~ B H ~ B H z STS1 H~ H3BHBH2SH2 2 H3B:SHz 1 BH3 HzB(H2)SH TS2 BH3 H~BHBH(HI)SHTS3 HzBH2BHSH 5 H2 HzB(Hz)SHBH3TS4 H2BSHBH3 6 H2 H3B(H)BH>SH(H2)TS5 HzB=SH 3 BH3 H2
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B2H6 1 PH3 H ~ B H ~ B H z PTS1 H~ H3BHBH2PH3 2 H3B:PH3 1 BH3 PH3-invTS BH3 PH3-inv complex BH3 H2B(H2)PH2 TS2 BH3 H3BHBH(H2)PH2 TS3 HzBHzBHPH2 5 H2 H z B ( H ~ ) P H ~ BTS4 H~ H2BPH2BH3 6 H2 H3B(H)BH2PH2(H2) TS5 H?B=PH2 3 BH3 H2 P - H ~ B H B H ~ P H4~ H2
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MP4/6-311+G(d,p) 0.0 21.8 7.3 26.7 52.8 44.0 - 14.6 20.4 40.5 0.6 18.9 10.7
+ZPE 0.0 23.4 10.3 24.8 48.6 43.3 -17.6 21.4 39.6 -4.1 18.9 -0.5
0.0 3.5 -10.3 9.7 51.2 40.1 -10.7 33.6 -24.1 17.6 10.0 0.0 14.2 10.9 26.0 46.2 39.7 -7.6 35.2 11.7 23.8 19.0 0.0 11.7 2.1 16.7 60.5 39.3 52.5 46.0 2.6 28.4 17.2 35.7 37.0 -0.7
0.0 5.4 -7.0 8.8 46.3 39.0 - 14.8 33.0 -26.4 16.7 1.5 0.0 15.2 12.7 23.6 42.4 39.4 -9.9 34.6 7.1 23.9 11.5 0.0 11.9 3.6 14.8 56.1 33.8 48.6 45.4 -0.3 28.1 12.2 37.0 28.2 -3.7
AG 0.0 44.5 31.3 22.2 48.2 64.8 -13.3 38.3 60.1 -3.5 42.2 -20.3 0.0 26.6 14.2 9.1 45.7 61.6 -11.3 53.0 -19.3 39.8 -17.4 0.0 35.4 34.1 21.9 42.2 60.3 -5.4 55.3 7.2 48.0 -7.9 0.0 31.8 25.8 15.0 53.4 22.1 47.4 66.1 3.7 49.8 13.9 60.8 8.1 2.9
The PH3 inversion complex is a very weak complex between BH3 and PH3, which has the complexation energy of - 1.9 k c d mol at the MP4/6-31 l+G(d,p) level. The B-P distance in the PH3 inversion complex is 3.408 A. The transition state of PH3 inversion between the PH3 inversion complex and adduct 1 has a high energy barrier (41.3 kcal/mol from adduct 1). Accordingly the formation of PH3 inversion complex occurs through the dissociation (BH3 and PH3) of the adduct 1. The transition state of 1,2-hydrogen elimination from the adduct 1 could not be found for the reaction system of X = P. The reason arises from the difference of the electron negativity of hydrogen and X atoms. The electron distribution of the P-H bond dissociating from 1 is P+- - -H-, and for the other systems (X = N, 0, and S) is X-- - -H+: the natural charge of H atom in XH, is +0.487e for H20, f0.378e for NH3, f0.136e for H2S, and -0.041e for PH3. On the other hand, the product side of TS2 for X = P relates to a weak complex between 3 and H2. This weak complex is 10.0 kcaymol below TS2 in energy and 5.6 kcal/mol above 3 H2 at the MP4/6-3 11+G(d,p) calculation.
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However, the energy barrier from this weak complex to 3 H2 along the IRC pathway is only 3.3 kcdmol at the MP2/63 lG(d,p) calculation. At the MP4/6-3 11+G(d,p) level, this transition state is 0.1 kcdmol lower in energy than the weak complex. The energy barriers at TS2 are 41.5, 35.8, 26.1, and 20.2 kcdmol above the adducts, H3B:XH, for X = N, P, 0, and S at the MP4/6-311+G(d,p) level, respectively. These baniers for the systems of H3B:NH3 and H3B:PH3 are extremely high. From the transition-state geometry parameters, the first process of 1,Zhydrogen elimination is the breaking of the X-H bond, and the second is the breaking of the B-H bond. The transition state is close to the first process. Consequently, the order of energy barriers for these reactions corresponds to that of the X-H bond energies (dissociation energy: H~B:X-H,-I H+). The X-H bond energies of H3B:XH, (X = N, P, 0, and S ) are 367.2, 346.9, 340.7, and 329.9 kcal/mol at the MP4l 6-3 11+G(d,p) calculation, respectively. However, overall potential energies for these reactions from the reactant (B2H6 XH,) are almost equal each other. The difference of the largest energy barrier (49.1 kcaymol for H3B:PH3) and the smallest one (42.4 kcdmol for H3B:SHz) is only 7.3 kcdmol. For other 1,Zhydrogen elimination, we also calculated the transition state of TS3 type, which has a B-H-B bond as the complex 2 or diborane. The transition states TS3 lead to the complex 2 for the reactant side and to XH,-]-substituted diborane 5 H2 for the product side along the IRC pathway, except for TS3 of X = P. The transition state TS3 of X = P leads to B2H6 PH3 for the reactant side and to 5 and H2 for the product side. The mechanism for the reactant side of X = P system is similar to that of TS2. That is, the electron distribution of the active P-H bond is different from those of the X-H bonds for other systems. From the reaction pathway for the product side, the reaction via TS3 does not yield directly H2B=XH,- 1 . The transition states TS4, which have the interaction between BH3 and X, are examined for these systems. In the previous paper treated B2H6 NH3, two transition states (side-on and back-donation types) were found for TS4 type. The transition state of the back-donation type for B&+NH3 system is
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Side-on type
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Back donation type
6.5 kcdmol lower in energy than that of the side-on type at the MP4/6-3 11+G(d,p) calculation. In this paper, the transition state of the back-donation type was shown. The transition state TS4 of X = 0 leads to a hypervalent compound 7 (H3B:OH2: BH3) for the reactant side and to a weak complex between 6 and H2 for the product side along the IRC pathway. The complexation energy for the weak complex is only 0.7 kcal/ mol at the MP4/6-31l+G(d,p) calculation. Two transition states of TS4 type for the reaction system of X = S were found; one has the conformation of the back-donation type and the other has that of the side-on type. The geometry parameters of the side-on type are very similar to those of the transition state previously proposed by Morokuma and co-workers.lo The transition state of the back-donation type is 3.5 kcal/mol lower than that of the side-on type. The transition state TS4 of the back-donation type leads to the adduct 1 BH3 for the reactant
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Chemical Reactions of B2H6 with Lewis Bases
J. Phys. Chem., Vol. 99, No. 22, 1995 9085
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side and to 6 H2 for the product side along the IRC pathway. This reaction mechanism is the same to that of X = N. For the reaction system of X = P, TS4 leads to a weak complex between 1 and BH3 for the reactant side and to a weak complex between 6 and H2 for the product side along the IRC pathway. The complexation energies for these weak complexes are 0.6 kcaYmol for 1 and BH3 and 4.9 kcdmol for 6 and H2. In 1,2hydrogen eliminations of three types (TS2, TS3, and TS4), the reactions through TS4 have the lowest energy barrier for all systems (X = 0, N, S, and P). 1,3-Hydrogen Elimination. The transition states TS5 of 1,3hydrogen elimination for all systems lead to the complexes 2 for the reactant side along the IRC pathways. For the product side, the transition states TS5 lead to 3 BH3 H2, except for the X = P system. The transition state TS5 for X = P relates to p-phosphidediborane 4 HZthrough a weak complex with the similar structure to TS5. The distance between H2BHBHzPH2 and H2 in this weak complex is longer than that in TS5; the distance between the middle point of H2 and B* in H2BHB*H2PH2 is 2.919 8, length for the weak complex and 2.594 A length for TS5. The energy barrier height between the weak complex and p-phosphidediborane 4 H2 is 0.1 k c d mol from the weak complex at the MP4/6-3 11+G(d,p) level. Therefore, phosphideborane, HzB=PH2, does not form directly through 1,3-hydrogen elimination from complex 2. The formation of H2B=PH2 from 4 occurs through BH3 elimination. In 1,3-hydrogen elimination, the energy barrier heights for B2H.5NH3 and B2H6PH3 systems are 27.9 and 33.6 kcaYmol from their complexes with 2, respectively. However, for B2H6NH3 system, complex 2 is extremely stable. Hence, the energy barrier height of 1,3-hydrogen elimination for B2H6NH3 system is only 16.7 kcaYmol from the isolated B2H6 and NH3 and for B2H6PH3 system is 37.0 kcdmol from the isolated B2H6 and PH3. On the other hand, the energy barrier heights for B2H6' OH2 and B2H6SH2 systems are 11.5 and 12.9 kcdmol from their complexes 2 at the MP4/6-31 l+G(d,p) calculation, respectively. The complexes 2 for B2H60H2 and B2H6SH2 systems are about 17-20 kcaYmo1 higher in relative energy than that of B2H6NH3 system. As a result, the transition states TS5 for B2H6 H20 and H2S systems have small energy barriers, 18.9 and 23.9 kcaYmo1 from the isolated B2H6 H20 and the isolated BzH6 4-H2S, respectively. The heats of reaction from the reactants XH,) to the products (H?B=XH,-l BH3 H2) are almost 0 kcaumol for the X = N and 0 systems. For the B2H6 H2S system, the energy barrier of 1,3-hydrogen elimination is about 5 kcaYmo1 higher than that for B2H6 H20 system, and the heat of reaction is also about 12 kcaYmo1 higher than that for B2H6 -t H20 system. For the X = P system, the heat of reaction from the reactant (B2& PH3) to the products (3 BH3 H2) is about 28 kcaYmol, and it is a high endothermic reaction. The minimal energy path from the reactant (B2H6 XH,) to the product (3 BH3 H2) is the reactant TS1 2 TS5 the product for the systems of X = 0, N, and S, and for the system of X = P the minimal energy path is the reactant TS1- 2 TS4 -the product. The highest energy barrier on the minimal energy pathway for the X = 0 system is 23.4 kcaYmol at TS1. For the X = N and S systems, the highest energy barriers are 16.7 and 23.9 kcaYmol at TS5, respectively. For the X = P system, the highest energy on the minimal energy pathway is 28.2 kcaYmo1 at the product. Changes in Gibbs Free Energy along the Minimal Energy Paths. In Gibbs free energy calculations, the energy baniers at TS2 for all systems change little with increasing temperature. The largest difference in the energy barriers at the temperatures
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of 0 K and 400 "C is only 1.2 kcdmol (for the system of X = P). The energy barriers at TS3 and TS4 increase with increasing temperature. The barriers of TS3 at 400 "C are 20.7-22.6 kcaY mol higher in energy than those at 0 K. The energy barriers of TS4 at 400 "C are 20.0-21.7 kcaYmo1 higher than those at 0 K. The energy barrier at TS5 also increase with increasing temperature. The barriers of TS5 at 400 "C rise in the range of energies 23.1-24.1 kcdmol from those at 0 K. At 400 "C, the minimal Gibbs free energy path from the reactant (B2H6 XH,) to the product (3 BH3 H2) is the reactant the dissociation state (2BH3+XHn) 1 2 TS5 the product for the systems of X = 0 and N. The largest energy barriers on these paths of X = 0 and N are 42.2 and 39.8 kcal/mol at TS5, respectively. Accordingly, the formation of H2B=XHn.l (X = 0 and N) occurs through 1,3-hydrogen elimination of TS5 in the range of the experimental temperatures 180-360 0C.3-8 The minimal Gibbs free energy path at 400 "C for the system of X = S is the reactant the dissociation state 1 TS2 the product. The largest energy barrier on the pathway at 400 "C is 42.2 kcdmol at TS2. Since the difference of the energy barriers at TS2 and TS5 for the system of X = S is only 5.8 kcdmol at 400 "C, the reaction occurs through 1,Zhydrogen elimination of TS2 and/or 1,3-hydrogen elimination of TS5 in the range of the experimental temperatures 180360 OC. For the system of X = P, the minimal Gibbs free energy path at 400 "C is the reactant the dissociation state PH3 inversion complex TS2 the product. The largest energy barrier height on the pathway is 47.4 kcdmol at TS2. The energy barrier at TS4 is only 2.4 kcaYmo1 higher than that at TS2. The reaction system of X = P has the highest energy barrier in four systems (X = 0,N, S, and P). Also the formation of H2B=PH2 is a highly endothermic reaction during the experimental temperatures 180-360 "C. These results for the system of X = P corresponds to that of a recent experimental matrix isolation study2I for the reaction of B2H6 PH3, which did not show the detection of H2B=PH2 as a product. As a result, at high temperature the reaction pathways for the formation of H~B=XH,-I are different for these reaction systems; the reactions for B2H6 NH3 and H20 occur through 1,3-hydrogen elimination and for B2H6 H2S may occur through 1,2-hydrogen elimination of TS2 and/or 1,3hydrogen elimination.
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Conclusions The reaction mechanisms of B2H6 with four Lewis Bases (NH3, H20, PH3, and H2S) were studied by ab initio MO methods. The reaction pathways for the adduct 1 and the complex 2 formations and hydrogen eliminations were calculated. The X-B bond formation energies in the adducts 1 from BH3 and XH, are proportional to the values of the proton affinity of XH,. The energy barrier heights at TS1 for the formation of the complex 2 are also proportional to the values of the proton affinity of Lewis bases. In comparison with Gibbs free energies, it is considered that the formations of the adducts 1 and the complexes 2 occur through the transition state TS1 and/or the dissociation state of B2H6 at high temperatures. For the hydrogen elimination step, the transition states TS2 of 1,Zhydrogen elimination lead to the adducts 1 for the reactant side and to 3 H2 for the product side, except for TS2 of B2H6 PH3 system. The transition state TS2 for B2H6 PH3 system relates to the PH3 inversion complex and to 3 and H2. The energy barriers for 1,Zhydrogen eliminations from the adducts 1 are proportional to the X-H bond energies. The transition states TS3 lead to the complex 2 for the reactant side and to 5 H2 for the product side, except for the system of X = P. The
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Sakai
9086 J. Phys. Chem., Vol. 99, No. 22, 1995
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transition state TS3 for X = P relates to B2H6 PH3 and to 5 Hz. The mechanism for the reactant side of X = P is similar to that of TS2 for X = P. The transition states TS4 for the systems of X = N, S, and P lead to the adduct 1 BH3 for the reactant side, and for X = 0 leads to 7. The transition states TS4 lead to 6 Hz for the product side, except for the system of X = N. The transition states TS5 for 1,3-hydrogen elimination lead to the complex 2 for the reactant side in all systems. For the product side, TS5 lead to 3 BH3 Hz, except for the system of X = P. The transition state TS5 for BzH6 PH3 system relates to P-HZBHBH~PHZ Hz. The energy barrier heights of 1,3-hydrogen elimination are lowest in those of four hydrogen eliminations (through TS2, TS3, T U , and TS5) from the isolated B2& and XH,, except for the system of X = P. The reaction with the lowest energy barrier for the system of X = P occurs through TS4. From Gibbs free energies at high temperatures the formations of H2B=XHn-l occur through 1,3-hydrogen elimination for N H 3 and H20 systems and for H2S system may occur through the pathway of TS2 and/or TS5.
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Acknowledgment. The present research is supported in part by a Grant-in-Aid for Scientific Research on Priority Area “Theory of Chemical Reactions” from the Ministry of Education, Science and Culture. This work is also supported in part by a Grant-in-Aid for Special Research from the Sangyo Institute of Osaka Sangyo University. The computer time was made available by the Computer Center of the Institute for Molecular Science and by the Information Systems Engineering Department of Osaka Sangyo University with its CONVEX C240 minisupercomputer.
References and Notes (1) Stock, A.; Massenez, C. Chem. Ber. 1912, 45, 3539. (2) Muetterties, E. Boron Hydride Chemistry, Academic Press: New York, 1975. (3) Lane, C. F. Chem. Rev. 1976, 76, 773. (4) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1992, 96, 4288. (5) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1991, 95, 3502. (6) Carpenter, J. D.; Ault, B. S. Chem. Phys. Lerr. 1992, 197, 171. (7) Carpenter, J. D.; Auk, B. S. J. Phys. Chem. 1992, 96, 7913. (8) Carpenter, J. D.; Auk, B. S. J. Phys. Chem. 1991, 95, 3507. (9) McKee, M. L. J. Phys. Chem. 1992, 96, 5380. (10) Mebel, A. M.; Musaev, D. G.; Morokuma, K. J. Phys. Chem. 1993, 97, 7543. (11) Sakai, S. Chem. Phys. Lett. 1994, 217, 288. (12) Mebel, A. M.; Musaev, D. G.; Morokuma, K. Chem. Phys. Lett. 1993, 216, 313. (13) Sakai, S. J. Phys. Chem., in press. (14) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. Gordon, M. S. Chem. Phys. Lett. 1980, 76, 163. (15) McLean, A. D.; Chandler, G. S. J. Chem Phys. 1980, 72, 5639. Frisch, M. J.; Pople, J. A,; Binkley, J. S. J. Chem. Phys. 1984, 80, 3261. (16) Pople, J. A.; Seeger, R.; Krishnan, R. Inr. J. Quantum Chem 1979, S l l , 149. (17) Pople, J. A.; Binkley, J. S.; Seeger, R. Inr. J. Quantum Chem. 1975, 9. 229. Poole. J. A,: Krishnan. R.: Scheeel. H. B.: Binklev, J. S. In?. J. Quanrum them. 1979, S13, 225. (18) Fukui, K. J. Phvs. Chem. 1970, 74, 4161. Ishida, K.; Morokuma, K; Komomicki, A. J. Chem Phys. 1977, 66, 2153. (19) Frisch, K. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Comperts, E.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, L. R.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J.A. GAUSSIAN92, Gaussian, Inc.: Pittsburgh, PA, 1992. (20) I found two types of transition states (ionic and covalent) for B2& NH3 system. I chose here the lower one (covalent type). (21) Carpenter and Auk, private communications to the reviewer. I
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