TOURNAL
J
O F THE A M E R I C A N C H E M I C A L S O C I E T Y Registered in U. S. Patent Ofice.
@ Cogyrirht, I 1970, b y the Amaricoa Chemical Socirty
VOLUME92, NUMBER 13
JULY1, 1970
Physical and Inorganic Chemistry Studies of Polyatomic Molecules Using Self-Consistent-Field Wave Functions. B,H,,, B,H,, and B,H,, Eugene Switkes, Irving R. Epstein, John A. Tossell, Richard M. Stevens, and William N. Lipscomb
Contribution from the Gibbs Chemical Laboratory, Harvard University, Cambridge, Massachusetts 02138. Received January 9, 1970 Abstract: SCF wave functions for B4H10,B5H9,and BSH1lshow (1) all atomic (Mulliken) charges are less than h O . 1 e, (2) apex borons are more negative than other borons, (3) borons in BH2groups are more positive than bo-
rons in BH groups, (4) no simple correlation exists between one-center diagonal F-matrix elements and charge, ( 5 ) all terminal hydrogens are negative and all bridge hydrogens are positive, (6) most properties of the unique hydrogen in the symmetry plane of B5Hll are intermediate between bridge and terminal hydrogens, (7) bridge hydrogens between BH and BH2groups are more strongly bonded toward the BH group, and (8) very low electron density directly between two B atoms exists if these borons are joined by a bridge hydrogen.
(1) K. Freudenberg, “Intramolekulare Umlagerung Optischaktiver Systeme,” from the Sitzungberichte der Heidelberger Akademie der Wissenschaften, Walter de Gruyter and Co., Berlin and Leipzig, 1927. (2) W. N. Lipscomb, “Boron Hydrides,” W. A. Benjamin, Inc., New York, N. Y. 1963. (3) (a) J. 0. Hirschfelder, H. Eyring, and N. Rosen, J . Chem. Phys., 4, 130 (1936); (b) J. 0. Hirschfelder, ibid., 6,795 (1938). (4) H. C. Longuet-Higgins, J . Chim. Phys., 46,269 (1949). ( 5 ) S. Winstein and H. J. Lucas, J . Amer. Chem. Soc., 60,836 (1938). (6) R. Hoffmann and W. N. Lipscomb, J. Chem. Phys., 36, 2179
boron hydrides. Owing to our desire for transferable parameters among atoms in molecules, as well as for extension of the SCF method to complex molecules, we employ Slater-type orbitals within a minimum basis set. An accurate SCF wave function and localized valence structure have been reported recently* for &He. Strong support for a localized bridge threecenter BHB bond was obtained, and boron hybrids of sp2.6were obtained from the optimized minimum basis set. In the present study we extend these SCF calculations and analysis of the wave functions to B4H10, BSH9,and BSHI1. In undertaking these SCF computations we have hoped to provide a quantitative basis for correlating some of the fascinating experimental observations on boron hydrides. Although our ab initio LCAO SCF calculations are among the most accurate which have been performed on larger molecules, we have tried to restrict our discussions only to those molecular properties where we can hope to obtain relatively unambiguous and physically relevant interpretations despite the limitations of the SCF approximations. The wave functions we present in this paper are the basis for
(1962). (7) F. P. Boer, M. D. Newton, and W. N. Lipscomb, J. Amer. Chem. Soc., 88,2361 (1966).
(8) E.Switkes, R. M. Stevens, W. N. Lipscomb, and M. J . Chem. Phys., 51,2085 (1969).
For
some 40 years the ideas underlying the chemistry of electron-deficient molecules have been a challenge to theoretical and experimental The boron hydrides, based upon polyhedra or their fragments, display an extensive chemistry. Both the geometrical and valence structures have correlated2 much of the chemistry, and have provided impetus for discoveries of new species and reactions. Wave functions based upon the extended Huckel (EH) method, which was developed, formalized, and programmed firsts for the boron hydrides, have been given a logical foundation and improvement by parametrization from self-consistent-field (SCF) model calc u l a t i o n ~ . ~A next more sophisticated step is the evaluation of accurate SCF wave functions for these
D.Newton,
3837
3838
4
/ \
Figure 1. B~HIo.
Figure 3. BSHI1.
Figure 2. B5Hg.
studies of three such properties which may be analyzed in terms of the one-electron charge distribution. A primary aim of our calculations has been to provide an ab initio analysis of bonding in the polyhedral boron hydrides. In this paper we discuss the interpretation of previously proposed bonding schemes in terms of the calculated electron densities, net atomic charges, and overlap populations. In the following paper9 we include a detailed analysis of bonding, preferred valence structures, and equivalent resonance structures in terms of localized orbital transformations on the SCF wave functions for B4H10,B6H9,and B5Hn. Another aim of these calculations has been to relate wave functions to magnetic properties and chemical reactivities of boron hydrides. We discuss below possible relations of the calculated ground-state charge densities to these properties. Presently one of the authors (J. A. T.) is applying the SCF wave functions to somewhat more detailed calculations of the ‘H and llB chemical shifts in these molecules. By utilizing the available wave functions for this series of four related molecules (B2He, B4HI0, B5Hg, and B6Hll), we may obtain interpretations of the trends in boron-1 1 chemical shifts among nuclei in different molecules as well as look at the relative shifts of boron nuclei in different geometric positions of the same molecule. This forthcoming analysis will be especially interesting because of the paramagnetic susceptibility predicted by a very complete coupled Hartree-Fock calculation lo for (91 E. Switkes. W. N. Lioscomb. and M. D. Newton. J . Amer. Chem. So>.: 92,3847 (1970). (10) (a) R. M. Stevens and W. N. Lipscomb, J . Chem. Phys., 42,3666 (1965); (b) R. A. Hegstrom and W. N. Lipscomb, ibid., 45, 2378 (1966).
Journal of the American Chemical Society 1 92:13
1 July
I , 1970
the closed-shell ‘2 state of diatomic BH. We also present a very qualitative discussion of reactivities in these boron hydrides. More quantitative calculations, now in progress, will be the topic of a subsequent publication. The level of reliability of these SCF wave functions for a series of related molecules may permit correlation of the relative reactivities for borons in different hydrides as well as explain the differences in reactivity for borons at nonequivalent sites in the same molecule, in those reactions in which the transition state retains some features of the initial charge distribution. As large polyatomic calculations using Slater-type orbitals become feasible one may compare the results with those of other ab initio and empirical methods and reevaluate the strengths and limitations of the SCF approximation. For this purpose we report the SCF energies, dipole moments, Koopmans ionization potentials, atomic populations, and atomization energies calculated from our wave functions. Using an approximate, but nonempirical, method, Boer, Newton, and Lipscomb7?l1have studied these boron hydrides. We discuss their predictions on the transferability of diagonal SCF one-electron Hamiltonian elements and their other approximations. We compare our results with those obtained by their method as well as with those from semiempirical calculations.
Calculations Our LCAO SCF calculations were performed on an IBM 7094, Model I, computer using a modified version of the program described by Stevens.12 The geometries of the boron frameworks have been taken from X-ray diffraction ~ t u d i e s l a - and ~ ~ the hydrogen coordinates have been idealized using suggested angles and distances. The assumed symmetries were CZv, C4”, and C, for B4H10,B6H9,and B6Hll, respectively. The coordinates of the unique atoms are given in Table I. Our labeling of the atoms is shown in Figures 1-3. Our basis consisted of a minimum set of Slater-type orbitals with exponents taken from an optimized calculation for diborane.* These exponents are 1.147 (11) F. P. Boer, “Molecular and Valence Structures of Boron Compounds,” Ph.D. Thesis, Harvard University, 1965. (12) R. M. Stevens, J. Chem. Phys., 52, 1397 (1970). (13) C. E. Nordman and W. N. Lipscomb, ibid., 21, 1856 (1953), BIHNstructure. (14) W. 3. Dulmage and W. N. Lipscomb, Acta Crystallogr., 5, 260 (1952), BsHs structure. (15) L. R. Lavine and W. N. Lipscomb, J . Chem. Phys., 22, 614 (1954), BsHll structure.
3839 Table I. Unique Coordinates for Boron Hydrides (au)
Energetics The total energies and virial ratios from our wave functions are given in Tables 11, 111, and IV. Deviations of the virial ratio from unity are small and comparable in magnitude to that for BzH6.* Slightly larger deviations in the higher hydrides are expected because of the greater uncertainties in the molecular geometry and lack of reoptimization of exponents. In Table V we compare the atomization energies calculated from our wave functions with values from more approximate calculations and from experiment. The accurate estimation of reaction energies from Hartree-Fock wave functions requires either a consistent cancellation of correlation energies or an appropriate estimate of these quantities. We suggest that minimum basis set calculations such as ours do not treat molecules with an accuracy comparable to an optimized single-{ atomic c a l ~ u l a t i o n ,and ~ ~ thus we present both the usual atomization energies utilizing Clementi's atomic energies" and atomization energies utilizing SCF calculations for boron and hydrogen,
-
Y
X
2.71313
0.0 0.0 2 57295 1.65354 0.0 0.0 4.42977 1.84496 0.0 2.36580 0.0 0.0 2.78980 4.70746 2.48090 0.0 2.72120 0.0 1.67240 2 . 9 1140 I
~~
a
Z
- 1.98557
0.0 2.67363 4.42724 1.81222 0.0 2.63244 0.0 0.0 1.84496 0.0 0.0 1.99750 4.19050 - 1.64580 3.28840 4.68300 -0.30120 1.35970 2.16740 0.0 3.0063
3.82733 0.22396 1.47906 0.0 1.57889 4.30542 0.91555 - 1.68509 2.05662 0.0 3.99470 0.77060 1.04810 1.3345 - 1,50250 - 1.87730 - 1.86100 1.75240 0.0 0.0
~
xz and y z are symmetry planes.
b
z is a symmetry axis.
c
y z is
the symmetry plane.
Table 11. BIHlo Occupied (and Lowest Unoccupied) Molecular Orbitals and Energies in1 IS zn7 I S 3*1
IS
-1.61lk
-1.611k
0.000
0.000 0.000
0.000 0.004
*nr I S 5 H l 1s
-0.004
by1
IS
-0.003
1s 2 H B IS 3nn 1 s 4HI I S 10 IS
0.002
1*8
2s 2P1 2Pl 2PY
28
1s
38
2s 2PI 2P I 2PY 1s 2s 2P1 2PX 2PY
k8
IS 2s 2PL 2PX 2PY
0.003 0.002 -0.002
-0.002
0.000 0.000 0.000 0.000 0.Y03
0.000 0.000
0.000 0.000 0.003 -0.103 -0.020 0.001
0.000 0.002 0.103
0.020 -0.001 0.000 0.002
-1.5979
-1.5916
-0.9155
-0.1121
-0.lkkL
-0.6291
-0.5519
-0.553k
0.003
0.003 -0.003 0.000 0.000 0.000 0.000 0.003
0.014 0.05k 0.058
0.000 0.000 0.139
-0.121 0.121
0.225
0.000 0.000
-0.252 -0.252
0.000
-0.111 -0.111 -0.027 -0.021 -0.363
-0.003 -0.003 0.003 -0.103
-0.067 -0.061 -0.039 -0.039 -0.039 -0.039 -0.090 0.260 -0.151 -0.037 0.000
0.000 0.000 0.000 0.000 0.000
0.004
0.003 0.000
0.004
0.001)
0.00k 0.001
0.000 0.000 0.003 0.003
0.002 0.002 0.002 0.002 -0.005
-a.io>
0.003
-0.011
0.001 -0.002 0.000 -0.005 0 -003 0 .OO I
-0.002 -0.001 0.000 -0.103
0.002 0.000 -0,103 -0.020 0.001 0,000 0.002 -0.103 -0,020
0.001
0,OOI
o*ooo
-0.002
-
0.003
0.003
-0.023 -0.001
0.003 0.000 0.103
0.058 0.048
-0.139
0.048 0.12k
-0.145
0.000
0.157
0.126
0.151 -0.151
-0.226 0.226 0.226 -0.226 0.116
0. L2k 0.12k -0.122
0.251 0.011 -0.017 0.000 -0.122
-0.018
0.023
0.251
-0.002
C.0OL 0.003
0.077
0.000 0.005 O.CO4
-0.002 0.000
-0.003
0.000 0.000 0.000 0 .ooo 0.001
-0.002
0.000 0.000 0.000 0.000
0.000
0.001
0.003
0.000
0.005 0.00k
Electronic energy -208.1403 au Nuclear repulsion- 1 0 3 . W au Total energy. -1W. 2559au
O.Ul7 0.000 -0.100 0.201 -0.021 0A00 -0.0111 -0.100 0.201 -0.021 0.000 0.018
0.Lk5
-0.151 0.000 0.000 0.000 0.000 0.152
0.000 0.000 0.000 0.000 0.152
-0.139 0.350 -0.011 0.000 -0.022 0.139 -0.350
0.011 0.000
-3.022
-0.307 -0.076 -0.091
0.000 -0.116 0.301 0.016 -0.09 1 0.000 0.000 0.000 0.000 -0.146 0.000 0.000 0.000 0.000 -0.1k6 0.000
0.225
-0.090
0.260 -0.151
0.031 0.000 0.013 -0.205 -0.161
0.000 -0.042
0.013 -0,205
-0.161 0.000 0.042
0.000
0.238 0.000 0 .no0 0.000 -0.256 0.000 0.000 0.000 0.000
-0.363
-0.4898
-0.4544
-0.k312
0.281 0.281
0.121 -0.k2l 0.000
0.000 0.000
0.081 0.081
-0.136 0.136
0.267
0.000 0.31k
-0.374 -0.216 01216
0 .O4O 0.040 0 .O 10 0.040 -0.023
-0.013 -0.013 0.013 0.013
0.013 0.165 -0.091
0.00lJ
3.000 -0.023 0.073
-0.U97
0.165 0.091
5.000 0.000 -0.097
0.000 0.058 -0.112 0.114
0.000 -0.268
0.256
0.058 -0.112 0.114 0.000
0.000
0.2b8
--
-0.5033
0.000
0.000 0.300 U.000
0.215 0.215
-0.151 -0.157 0.013 0.013
0.013 0.013 -0.012 0 .o 3 5 -0.151 C.281 0 .no0
0.ooc
-c.c\z
3.000
0.035 -0.151
-0.Glb 0.Okl
0.352 0.000 -0.012 0.016 -0.067 -0.352 0.000
-0.072
-0.281 0.000 0.021 -0.Cb2 0.239 0.CX 0.010 0.121 -0.062 0.239
0.000 -0.010
0.000 0.000
0.000 -0.135
0.135 0.135 -0.135 -0.05u
0.140 -0.302 0.104 0.ildL
0.050 -0.140 3.3U2 0.124
u.wo 0.u3: 0.900 3.00"
-c. 1 2 1 o.nco 0.'?0:
c.:u1 1.oco
-G.L21 3.COO
-0.353 0.353 0.188 0.188
-0.188 -0.188 C.000 C.OOO 0.000 0.000
0.231 0 .OD0 C.000 0.000
c .OOC 0.231 C.C29 -0.081
0.261 -0.042
-0.0k2 -3.256 -0.256 -0.256 -0.156
-0.015 0.066 -0.195 -0.33C 0.oco
-0.015 OaC46 -U.IF5 0.33k
0.COO -0.031 0.102
-0.028
0.136
0.000 -0.311 -G.O29 0.001
0.000 -0.060
0.028
u.000 -0.317
-0.0>2 0.102 0.13b
0.2k35
0.000 'O.O*O 0.257 -0.251
0.021 -0.021 -0.5k8 -0.540 0.548 0.548
0.000 0.000
c.c00 0.000 0.221 C.CC0 0.000 0.000
0.c00 0.221 -0.051 0.2b2 -0.221 0.000 -0.361
0.051 -0.2bZ
0.221
O.COO
C.OOO
0.068
-0.3bL
Two-electron energy 134. O W au Kinetic energy 1W. 2516 au - U T ' 1.00004
for terminal hydrogens, 1.209 for bridge hydrogens, 4.680 for boron Is, 1.443 for boron 2s, and 1.477 for boron 2p. Each unique integral over atomic orbitals was calculated t o at least five decimal place accuracy, and full advantage was taken of molecular symmetry. Approximate computation times were 116, 140, and 320 min for B4HI0,B5H9,and B5Hl1, respectively. The wave functions and SCF energies are listed in Tables IT, 111, and IV. Although our calculations employ minimum basis sets, their quality is enhanced by the favorable ratio of basis functions to electron pairs in minimum basis sets for neutral boron hydride molecules. This 2 : l ratio provides a freedom not available in minimum basis set calculations involving heavier atoms of the first row in the periodic table, and is shown in BzHB by the relatively small energy improvement found by extending the basis set.*f16 However, extension of the basis set may allow for adequate polarization at the H atom positions. J.
0 .PO0 -0.306 0.306 -0.306 0.306 0 .EO0 0.000 0.000 0.000 -0.238 0.000 0.000 0.000
-0.5141
(16) R. T. Buenker, S.D. Peyerimhoff, L. C. Allen, and J. L. Whitten, Chem. Phys., 45, 2835 (1966).
which use our optimized molecular exponents from diborane. The surprising degree of cancellation of energy errors arising from correlation, atomic orbital contraction,'* and our limited basis sets, evidenced in the latter method for calculating the atomization energies of boron hydrides, is also found in calculations on hydrocarbons. l9 Here atomic energies calculated using optimized molecular exponents were subtracted from the molecular energies. We emphasize the fortuitous, if consistent, nature of such an approximation or "prescription" for atomization energies and refer to more complete discussions which make the correct alterations on experimental enthalpies before comparison with calculated electronic energies.2o Table V also contains the ratios of these atomization energies to the corresponding energies of BzH6. As may be E. Clementi and D. L. Raimondi, ibid., 38,2686 (1963). K. Ruedenberg, Rev. Mod. Phys., 34,326 (1962). E. Switkes and J. Tossell, unpublished results. (a) L. C. Snyder, J . Chem. Phys., 46, 3602 (1967); (b) L. C. Snyder and H. Basch, J . Amer. Chem. Soc., 91,2189 (1969). (17) (18) (19) (20)
Switkes, Epstein, Tossell, Stevens, Lipscomb
/ SCF Studies of BaHio, BSH9, BsHii
3840 Table 111. BsHs Occupied (and Lowest Unoccupied) Molecular Orbitals and Energies -c.aoa
imr zmr
II SS 3wr I S w r IS 5Wl I S
IS 2s
a.000
0.000
-a.rqT
0.001
0.000
-0.101
a m 0
o.oi8
0.001
0.001 0.000 O.C0O 0.060 0.000 0.002 0 .GO"
-0.012
2P1
0.001
2PI
c.000 0.000 -0.657 -0.012
2 P I
a.mi
0.021 -0.001
a.ooi -o.aoa
2P1 1P"
0.0a1 0.000 0.000
a.ooo
2PV
IS
-0.497 -0.012
21 2P1
0.001 0.000 -0.000
2." 2PI
-
a.000 0.000 0.002 0.000
o.ona
o.aoo
0..91
a.ooo
-0.000
0.002
'0.001 0.000
o.aoo
-O.WI
-0.497
'0.021
-0.c18
c.aoo
a.ooi 0.000 0.003
0.000
0.000 0.010
0.001
o.ow .oa 2
-0.121
0.000
0.000 0.000 0.000 0.000
-0.101 -0.107 -0.101
0.000
-0.107
0.000
-0.001 -0.OC5 -0.003
0.021
-0.018 a.000 0.000 -0.ao4
0.192 0.192
a.ow
O.Ol0
0.002
0.116
0.000
0.0GO 0.105 -0.191
"1.001
0.010 0.000 O.l1+ U.105
-0.193
u.010
-a.ooz
-0.II.
-0.003 -0.005
0.140 -0.155 U.039 0.011 0.000 0.000 0.000 a.000 -0.158 0.000 -0. I10 J. 1 5 5 -C.019 0.015
0.000
u.000 0.000
-a.isd 0.110 -0.155 O.01P
o.000 0.000
-0.160 0.355 -0.019
-a.
114
--
0 . m
0.000
a m 0
o.ma
0.102
0.000
0.048
0.000 0 * 260 0.000
-0.235
-0.001 O.CL6
-0.030
o.wo 0.102
a.000
-0. I 9 2 0.000
0.015
-0.063
o.mu
4.10.
-0.01,
-0.213
-0.lb5
-0.247 J.WO o.003
0.217 0.035
0.600 0.16,
0.000 0.000 0.000 0.000 -0.260 0.OOU 0.000
".OW 9.YOO 0.100
-G.ZILI
3.001
-0.2,1
o.oao o.aoa o.ooa o.ow
0.000
0.000
0.100 -0.016
O.OCO
O.lOb 0.022 0.000 -0.021
0.06s
0.106
o.aao
-0.u30 0.104 0.218 '0.241
-0.165
0.000 -C.l68 0.1b5
0.019
0.000 0.000 0.IOC 0.036 -C.lOI
0.080 4.217 -0.035 0.165 -0.080 0.231 0.035
-0.260 0.000
-0.215
-3.237
-0.097 0.000 0.000
0.000
0.000 0.022 -0.021
0.065 0.106 '0.022
0.000 -0.021 O.Cb5 O.l0b
o.ia+
0.000
o.aoa a. 190
0.219
o.om
0.000 -0.022
-0.2.7
c.000
c.000
a.w
-0.1b8
-a.ioq
o.ooa
0 . m
0.lb8 0.000
0.120 0.120 -0.10s
-0.109 0.073 -0.212 - 0 . ~ 1 0.000 0.000 -0.027
0.000
C.003
0.000
0.120
-o.ia?
o.aao
-0.081
o.oao -o.ceo
0.000
0.000
0.000
O.Ulb
O.2W
-L'.192 -0)rObl 0.000
-0.i86 -0.186
O.*OO
a.om a.mo
o.am
0.235
-0.186 0.186
O.COO
0.068
a .om
0.186 0.I8b
0.180
0.215 0. o m
-0.010 0.102 0.019
0.186
-0. I I b
0.0(10
o.ooa
0.120
.a00 0.110 0
0.000
o.oa
-0.55b
o .ana -0.110
0.000 0.000
o.ooa
-0.OM
0.000 O.Ob3
0.000 -0.l58
0.000 0.000
0.000
0.000 -0.310 0.000 0.370 0 .a00
0.000 o m 0 0.000 O.OO0
0.000
0.102
-0.001 0.016
0.010 0.000
-a.zw
-a .030
0.000 0.015
o.aw
0.295 -0.295 0.295
0.000 0.000
0.000 0.000 0.000
0.000 -0.296 0.286 -0.m 0.2a~
0.000 a m 0
a.iii
-0.001 -0. 0.Olb IP2
-0.IPl
0.105
0.000 -0.002
0.000 -0.IPb o m 0
-0.158
-0,001
0.205 0.205 0.205 0.205 0.159 -0.181 0.010 0.000 0.000 -0.003 a.aib -0.1q2 0.0b1 0.000
o.oao
a.oao
a.ooa
0.000
-0.003
0.000
a.ooo 0.000 a.ooo
0.125
0.211 0.217 0.231 0.217 0.021 0.021 0.021 a.021 O.0OL 0.12b
-0.003
0.000
-L.I06 0.000
0.105
-0.172 - o m 3
-0.003
-2.112 0.192 O.lP2
-Q.L92 0.000 0.000
- 0 . I13
-0.003 -0.005 O.OC0 u.002 -0.00)
0.103
Electronic energy -265.8357 au Nuclear repulsion- U7.5292 au Total energy = -128.3065 au
o.wo
-0.005 -0.Y03
-0 .00 I
3
U.105 -Q.lbl V.12, 0 . m a.000
0.018 -0.000
0.000 -0.+91
o.ooa
0.99,
0.000 0.000 -0.117 0.000 O.l27 -0.192
0.121 0.000 -0.192
-a.o15
0.013 -0.007
0.001 c.+91
0.00b
0
a .on
-a.oas
-0.035 -0.035
o.ow
0.000
-a.o21
-0.014
0.000
o .ow
0.000
0.004
o .ow
-0.004 0.000
a m 6
0.000
o.om
I S 2s
0.000 -0.002 0.002 -0.002 0.002
0.000 -0.001 0.003 0.003 -0.003 -0.003 C.CC0 0.000
0.000 0.000 0.000 0.000 0.000
-0..g7
2s
5b
0.000 0.001 -0.003
0.000
o m 0 0.003
-0.00b 0.001 -0.002
-0.012 0.001 0.000
2P1 2PI 2P. IS
m o o
-0.001 0.003 0.000 0.000 0.000
o.ow
2PI 2D.
*I)
-0.001
0.00b 0.00b 0.001
2s 2P1
31
0.000 0.003
0.002
h e IS
2 ~ IS 8 awe I S bM8 I S I B I S
29
(1.002
0.002 0.002
omc
0.145
-a.i,s
O.IbS -0.1.5 -0.I.5
-0.145 0.145 0.000
a.000
o.mc
a . m
0.000
C.OOO
.0.'21 0.000
C.CCO -n.G21 0.COi:
0.02b -0.oq0 -@.)ab 0.323 1.000 C.OOO 0 ,000 0.000 -0.128
c.onn P .ooc P.CL0
-0.120 0.02'
-0.~90 -0.101
C.COO
0.000 -0.Lbl 0.161 -0.161 0.161
a .a00
o.aoo
0.000 0.00c 0.000 0.000 0.u00
0.c00
o .ma
-0.050 0.311 "1.510 d.034
b.0c0 1."5b -c.313 0.510
0.000
o.uo0
0.321
-0.02.
-o.ce+
0.Oi)C O.CO0 c.oc0 0.000
4.054
o.aqo 0.W' 0.321
C.000 0.000 1.000
-0.128 -0.026 O.OPO
0 .OOO -0.128
0.000
o.ia6 0.000 0.323
0.111 -C.510 -0.011. O.OCO 0.058 -0.913
o.sia
o .aao 0.096
Two-electron energy 175.5347 au Kinetic energy 128.6543 au -EIT * 0.99730
Table IV. B5Hll Occupied (and Lowest Unoccupied) Molecular Orbitals and Energies -1.b185
-1.6383
-I.Ul2
-1.Ml2
-7.5445
-I.OOlb
-0.8165
0.000 0.000
0.000
0.000
-0.000 0.003
0.005 0.005
-0.035
a.ooa
-a.ooi
-0.001 0.000 - 00.000 .000 -0.000
-o.oab
0.wo
-0.001 0.001 -0.000 0.000 0.000
-0.000
o.aoo
-0 .OO I -0.00)
-0.001 0.001
0.001
0.000
-0.005 0.002
0.000 0.000
0.000
0.002
0.001 0.103 -0.001 0.019
0.oo.a -0.7c3
C.000
o.cai 0.101 0.019 -0.000 -0.0oL c.003 0.003 -0.002 -0.000 0.001 0.002
- 0.001 o m 2
-0.023
a.aaJ a.oco
0.000 '0.JOd 0.090
-0.003 0.001
-a.ooo
-0.000 0.001 0.013 0.003
-P.OOI a.00) 0.000
-0.001 0.001 0 ..a00 000 0.000 -0.001 u.000
0.003
-0.000
- 00.00. .001
0.005 0.000 o.oao
0.003 0.003 0.000
0.703
-0.002 0.001
0.021 -0.000
0.000 0.002
0.002 0.001 C.COI 0.000 -0.031
0.00, 0.002 O.YOO -0.001 -0.002
o.aa6
-0.002
-0.000 -0.001
-0.001 -0.000
0.002
0.002
-0.001 0.002
(1.00)
0.701
-0.703
0.020 "1.00 I
-0.020
0.001 0.002
-0.c02 -0.oOl -0.703 -0.020 O.Wl
-0.001 0.002
Electronic energy -275.5MO au Nuclear repulsion- 146. 1359 au Total energy. - 1 2 9 . 4 2 8 1 1 ~
-0.032
Oc.000 .OOL
-0.001 -0.002 -0.000
-0.103 0.002
-0.020 0.001 -0.002 0.002
-00.151 -0.118 -0.118 0.107 -0.190 u.1~12 00.000 .OII
--0.000 0.99,
-0.001
o.oai
- 00.002 .001
-0.000 -0.000
-0.oao
-0.001
-0.002
-o.aoo
-0.000 0.003 (1.001
-0. -0.0.5 LO3 -0.015 -0.026 -0.026 -0.036 -0.036
-0.oao -0.000
0.00, 0.002
0.118
0.002
- 00.027 .238
-0.001
0.073 -0.ca9
0.002 0.002
-0.238 0.1II
0.06.
0.021
0.001 0.002
0.000
0.0I+ -0.136 O.011
o.wi
0.002
-o.ooo -0.002
0.055 0.051
0.000
a.074
0.001
-0.IIA
0.002
O.0Il -0.055
0.002 -0.000
0.051
Two.eleclron energy Kinetic energy
-
-0.b8bb
-0.LIl8
-0.070
-0.168
-4.017
-0.081
0.185 --0.22b 0.226
-0.28b 0.011
o.au
a.on
-0.066
a.on
-0.064 -0.06.
a .ooo
-0. LOO 0.300
-0.019 0.089 -0.08~
-0.100
0.237 -0.237 0.000 0.000
0.251
-0.063
0.093
c.128 -0.11+
-0.015 0.029
0.000 o.ow
-0.110 0.000
n.221
- 00.199 .017
-0.015 U.099 0.06)
-0.011
-0.072 -00.086
0.091 -0.223
-0.071 0.199
0 . 00 63 55
-0.081
-0.09q -0.116
0.086 -0.072
0.26,
-0.11. 0.071
-0.031
-0.019
4.011 '0.078 0.116
-0.0.
-0.26. U.039
-0.041 0.078
o.aiz
0.136
0.051
a.cn
-0.1,.
-a.oiq
-0.1502
-0.5+10
-0.5040
o.aoo
o.aw o.wa
a . m
0.117
-0.22b -0.18' -0.18, -1.017 -0.067
-0.221 -0.221 0.120
- 00..223355
0.000
0.050 -0.050 0.000 0.000 00.000 .005
- 00.116 .lll 0.286 -0.296
-0.036 0.036 0.000 -0.253 0.253 0.000
o.ow c.aoo
-0.162 -0.093
-0.101
'0.092 D.27*
0.12,
-0.134 -0.201
0.011 -0.ow P.101
a.tii 1.000 -0.111 0.0.0 0.16. -0.109 0.n29
0.092 -0.27.
-0.0.0
Y.Cb5 0.01'
0.019 c.034
0.091
0.015
-a.iai
-0.162 -aO.Ovl
- 00.018 .121 -0.066 - 00.Ibb .121 0.011 -0.06, -0.001 O.lbb
-0.055
-0,127 -0.ObI
-0.064
-0.001
0.000
0.035 Li.092
-0.13. 0.085 0 .201 0.050 -0.057 *.I+.
- 00.107 .033 0.079 O.OP0
-0.232
0.033
-0.l.2 a.060
--0.149 0.018
0.050
'0.019
-0.1.. -0.057 0. 142
0.232
-0.011 -0.018 O.Lb9
0.0t.O
0.01, -0.16.
0.029 0.109 '0.0.0 0,123
0.222 0.13,
0.051 O.0bO -0.12, -0.222 0.133 -0.051
-0.215 -a.231 0.152 0.10
-0.03s - 00..0I2I ,'
- 0c.000 .l.b
-J.O3u 0.OOP a.018 0.041
0.009 0 .2w -0.010 O.Jl8 3.290 -0.011 0.0011 -0.010 0.022 '0.022 -3.226
a.oo8
-0.010 0.022
4 0.022 .226
-0.ll2
-0.4738 -0.521 -0.043 0.025 0.025
o.m(
- 00.320 .023
0.105 0.005 0.005
-0.021 0.252 -0.101 -0.101
-a.i%
-0.009 0.02. 0 . w
0.000 -0.OLI
0.021 -a.adb -0.082 -0.19s 0.05. 0.021 -o.aLb
-0.157 -0.157 0.055 -a.ibo -0..29 0.000 -0.11, -0.025 0.073 0.1.6
-a.ow
0.06g
0.05.
-0.025 0.071 0.0C9 O.Llb 0.0b9
0.1.9 0.110
-0.026 0.079
- 00.199 .082
-0.a1~ 0.201
0.059 -0.017
o.iia
-0.201 0.1,s 0.059
0.070 0.011 0.001 -0.02b
o.m +.ai1 o.wo
0.001
-0.6736
-0.blbb
-0.6011
a.aoa
-0.153 0.141 0.051
0.000
0.000 -0.2b8 0.268 0.012 -0.012 -0.320 0.120
a m 0 0.025 -0.025
(1.000 0.000
0.000 0.111 C.000
o.aii
-C.O30 -0.42-0.m 0.256
-3.011 O c.030 .02P --0.056 0.2%
-0.002
a.001 a.191 -0.006 -0.22. 0.002 -O.oY, -0.191 -0.OOb 0.224
0.000
0.051
0.025 -0.025
0.101 0.101
- 0O. 2. 2 67 Il
-0.311 -0.131 0.158 0.026
0.1% -0.150
0.026
0.210 0.000
o .ow
-0.210
0.001 -0.OII
0.000 0.000
-a.m
c.ma
0.3b8 0.004
-0.151 -0.a11 ' 00.151 .066
0.00.
0.17P U.000 -0.018 0.062 0.197 -0.072 0. I O 5 0.018
-0.ab2
0.17)o
0.000 -0.054 0.000
o.a%
a.ou
-0.012 4.079
0.019 0.000
U.OO -0.08b 0.000
o.aoo a.ooo
0.152
0.000 -0.OI3 -0.527 0.2b0
-0.0e2 -0.220 0.041
-0.O 1 3I l1 -0.151 -0.Obb 0.01b -0.0.9
-0.021
0.213 0.020 -0.121
-a.310 o.a.7
- 00.01b .0b9
-0 0.021 .01,
-0.012
0.213
-0.021
-a. u)s
-0.330 4.d.l
-0.2.9
-0.010 -0.125
183.7597 au 129.7291 au -EIT 0.99768
-0.191
-".IO5 -0.OIZ 0.086 0.021
~
.
-J.260 0.521 -0.082 0.220 -0.059 0.012 -0.2.9 0.105
a.m 0.059
_..
d _ > e O
* *
Table V. Atomization Energies (au)
.
A BzHs B4HlO BsH9 B5Hll
-0.5WI
0.000 0.268 -C.268 -0.153 0.155
--0.187 0.1e1
0.116 0.ObO 00 . 0 2 53 .1
0.000 -a.iii
-0.OPI
0.010
0.0Ib '0.226 0.010
o.aoc
-0.075 -0.075
0.0l2 0.229 -0.061
0.04.
0.000 0.107
--0.073 0.008
0.002 0.000
-0alb97
-A/ABBs
SCP
SCFb
ExptlC
NEMOa
SCP
SCFb
ExptlC
NEMOa
-0.721 -1.262 -1.315 -1.436
-0.917 -1.659 -1.762 -1.894
-0.917 -1.670 -1.800 -1.954
-1.022 -1 .758d 1.896d -1.91oe
1.0 1.748 1.827 1.989
1.o 1.782 1.893 2.034
1 .o 1.821 1.963 2.131
1 .o 1.719 1.852 1.868
-
The reference atoms employ Clementi's best single-t exponents: E(B), - 24.4984; E(H), -0.500.17 The reference atoms employ optimized diborane exponents: E(Bt), -24.4372; E(H3, -0.4892; E(HBJ, -0.4781. c S. R. Gunn and L. G. Green, J. Phys. Chem., 65,2173 (1961). d Reference 7 (Slater exponents with H 1s = 1.20). Reference 11 (partially optimized BH8exponents). @
Tabel VI.
Ionization Potentials SCF
B4HlO BsHs
B5Hll
0.431 0.379 0.401
Exptla
NEMO
0.382 0.386 0.379
0.415b 0. 387b 0.403O
a T. P. Fehlner and W. S. Koski, J. Amer. Chem. Soc., 86, 581 Reference (1964). Reference 7 (Slater exponents, H Is = 1.2). l l (partially optimized BHs exponents).
expected, this ratio is always smaller than the ex-
Journal of the American Chemical Society
92:13
1 July I , I970
hydrides. First ionization potentials calculated from the orbital eigenvalues are compared in Table VI with those from NEMO calculations and with the experimental values. The inconsistent agreement of these energy-related quantities with experiment emphasizes the care which must be exercised when using minimum basis set SCF wave functions in interpretations of energetics. However, schemes which allow some estimation of the correlation en erg^^+^^ have been used to obtain
3841
reaction energies of chemical accuracy from HartreeFock SCF wave functions. The Koopmans ionization potentials seem especially sensitive to changes in orbital exponents. NEMO calculations" using partially optimized BHa orbital exponents (B 1s = 4.68, B 2s = 1.38, B 2p = 1.35, H 1s = 1.20) give ionization potentials similar to those obtained from our SCF calculations, while Table VI indicates that the use of Slater exponents in NEMO calculations7 yields markedly different ionization potentials. This sensitivity is also evident in &He, where both SlaterZ4and optimized8 basis sets have been used in SCF computations. The accurate SCF wave functions also enable us to check some of the approximations of the NEMO theory. In Table VI1 we list the relevant SCF HamilTable VII. Comparison of Diagonal SCF Hamiltonian Matrix Elements and NEMO a's (au)
BzHs BrHio .~ 1B 2B
FBzs
FBzpav
-1.133
-0.318
-1.177 -1.156
-0.275 -0.247
B5Hg 1B 2B
-1.175 -1.201
-0.277 -0.297
B5Hii 1B 2B 4B
-1.192 -1.225 -1.153
-0.295 -0.319 -0.242
NEMOo
-1.081
-0.337
a
FH is Ht Hh 1HI 3Ht 5Ht 1Hb 1Ht 2Ht 1Hb 1Ht 2Ht 3Ht 5Ht 7Ht 1Hb 2Hb Ht Hb
-0.473 -0.566 -0.465 -0.491 -0.477 -0.527 -0.418 -0.464 -0.576 -0.439 -0.605 -0.483 -0.461 -0.478 -0.619 -0.599 -0.464 -0.593
Lipscomb suggested that unreasonable charge distributions in their NEMO calculations might be due to overestimation of the boron 2s, 2p zero-overlap Hamiltonian matrix elements. The B 2s, B 2p, matrix element for 1B in B5H8 in our calculation is 0.2137, somewhat smaller than the NEMO value (0.250). Also, B 2s, B 2p elements for boron atoms bonded to two terminal hydrogens are approximately 0.06 to 0.08, slightly smaller than the 0.10 for the B 2s, B 2p, element in the &He calculation which Newton, Boer, and Lipscomb used for calibration of their zero-overlap approximation factor.
Population Analysis The Mulliken charges and significant overlap populations25 for B4H10, B5HB, and B5Hll are given in Tables VI11 and IX. We omit an atom-by-atom Table VIII. Charge Distributions -B$IloAtom 1B 3B 1Ht 3Ht 5Ht 1Hb
B4HlO
(23) (a) P. E. Cade and W. M. Huo, J . Chem. Phys., 47, 614 (1967); (b) ibid., 47, 649 (1967). (24) W. E. Palke and W. N. Lipscomb, J . Amer. Chem. SOC.,88,2384 (1966).
-0.02
7B5H9Atom Charge
-B5H11Atom
Charge
0.00 +0.06 -0.09 -0.04 +0.01
1B 2B 4B 1Ht 2Ht 3Ht 5Ht 7Ht 1Hb 2Hb
-0.08 +0.05 +0.09 -0.07 +0.06 -0.03 -0.06 -0.07 +0.03 $0.06
1B 2B 1Ht 2Ht 1Hb
+0.08 -0.05 -0.07 -0.07 $0.06
Table IX. Bond Overlap Populations
Reference 7.
tonian matrix elements and the diagonal Hamiltonian elements (a's) used by Boer, Newton, and Lipsc ~ m b . ~These , ~ ~comparisons show that the use of single values of a for all terminal or bridge hydrogens or for all borons produces serious errors in charge distributions and eigenvalues. We observe in Table VI1 that the BH2 borons (B4H10, 2B; B5Hl1, 2B) have a's which are higher than those for any of the other borons. We also find that apical terminal hydrogens (BSHg, lHt; B6H11, l H t ; aav = 0.428) may be distinguished from other terminal hydrogen (aav = -0.473) by their higher values of a. Bridge hydrogen a's are always more negative than terminal hydrogen a's except for 2Ht in B6Hll. This unique hydrogen assumes a value for a characteristic of a bridge hydrogen. Although this atom is designated as a normal terminal hydrogen in formal valence structures, its geometric position and participation in multicenter localized bondingg make such distinctions ambiguous. Unfortunately, even within the groups of chemically similar atoms noted above there are still significant variations in a. The applicability of such a grouping is further reduced by its failure to take into account the anisotropy of the boron 2p a's. Newton, Boer, and
Charge
B5HO
B5Hll
Bond
Distance, A
Overlap populations
1B-2B 1B-3B 1B-lHt 3B-3Ht 3B-5Ht 1B-lHb 3B-1Hb 1B-2B 2B-3B 1B-1Ht 2B-2Ht 2B-1Hb 1B-2B 1B-4B 2B-3B 2B-4B lB-lHt 1B-2Ht 2B-3Ht 4B-5Ht 4B-7Ht 2B-1Hb 2B-2Hb 4B-2Hb 4B2Ht
1.75 1.84 1.19 1.19 1.19 1.33 1.43 1.66 1.77 1.19 1.19 1.35 1.72 1.85 1.77 1.72 1.19 1.19 1.19 1.19 1.19 1.34 1.34 1.32 1.71
0.534 0.299 0.825 0.819 0.830 0.479 0.285 0.531 0.347 0.832 0.821 0.388 0.476 0.324 0.337 0.414 0.833 0.613 0.840 0.821 0.801 0.381 0.418 0.330 0.093
comparison of these results with those obtained from nonempirical molecular orbital (NEMO)', l l and extended Hiickel (EH)26 calculations on these molecules because of the difference in basis sets employed, since (25) R. S.Mulliken,J. Chem. Phys., 23,1833 (1955). (26) R. Hoffmann and W. N. Lipscomb, ibid., 37,2872 (1962).
Switkes, Epstein, Tossell, Stevens, Lipscomb
SCF Studies of BaH1o,B6H9, BSHH
3842
some wave functions which give nearly identical total electron densities give quite different Mulliken populations when decomposed in terms of different basis set^.^^^^ However, some of the more interesting trends are noted below. Our atomic charges, as expected, are all smaller in magnitude than those calculated by the non-selfconsistent m e t h o d ~ . ~ > ~We ~ * *find 6 that for all three molecules terminal hydrogens are slightly (
