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On the barrier to internal rotation in phosphineborane
15 May 1973
CHEMICAL PHYSICS LETTERS
Volume 20, number 2
ON THE BARRiER
TO INTERNAL
ROTATION
IN PI-IOSPHINEBORANE
John R. SABIN Quantrtm Theory Proiecr and Deportment of Physics, Unhers~ty of Florida, GainesWe, Florida 32601, USA Received 30 hlarch I973
An ab initio STO-3G calcirlation is carried out on PH$H3. The electronic structure of the molecule is considered, and special attention is paid to the barrier to internaf rotation.
1. Introduction Recently, there has been increasing interest in the properties of the boron-p~losp~lorous dative sigma bonds formed between
the electron
deficient
boranes,
and the phosphines [l--3]. Both the electronic and physical properties of the bond have been discussed, and the relationship
between
the two has been con-
sidered f43. Very recently, the microwzive spectra of one ofthe simplest compounds containing a P-B dative bond, namely phosphineborane (PHJX$H1), have been studied, and accurate values for the structural param. eters for the molecule, and for the internal rotation potenria1 about the B-P bond have been measured I31In order to shed further fight on the nature of this interesting bond, an ab initio LCAO MO SCF calculation has been carried out on PH3131-13,as a function of P-B distance and rotational angle. The potentials, charge distribution, and molecular efectronic structure are thus reported.
2. Calculations Calculations were carried out using the IBMOL-5 [S] set of ab initio programs. The basis sets used were of the STO-3G type, contracted from (3s) for hydrogen, (6s; 3~) for boron, and (9s, 6p, 5d) for phosphor. ous. The orbital eqponents and contraction coeffi-
cients were prepared according to Stewart [6] from ST0 orbital exponents [7]. In all cases, the experimental values [3] for hydorgen bond lengths and angles wert: used (RBs = 1.2 12 8, +H = 1.399 A, 4BPH = 116.9°, &PM-i = 103.6”? WBH = 114.6” and WPH = 101.3’). Calculations were carried out for the eclipsed and staggered fgrms of PH3BH3 at a variety of P-B bond distances, both with and without inclusion of dorbi tals in the basis set.
3. R,zsults and discussion PhosFhineborane (see tig. I) has C,, symmetry in an6 has electron configuration
al1 rotamers,
‘AI: la:2a:3a:le~4a:5a:6af2e47a:3e4. .. Calculations were carried out at the experimental geometry for eclipsed and staggered conformations using basis sets with
and without
d-orbitais.
The ener-
then minimized with respect to the P-B bond in the staggered configuration using the d basis, and a mintinum was found at 2.080 A, compared to the experimental [3] value of 1.937 A. The calculated energies for these conformations are reported in table 1, along with the Fotational barriers. In alitcases, the staggered con~~ration.~vas found to be of lower energy than the eclipsed, in agreement with the microwave structure [3]. The value calculated at the experi. mental geometry using the d-orbital set agrees quite well 1;vit.hthe experimenta!ly determined [31 barrier gy was
Volume 20, number
2
15 hlay 1973
CHEMICAL PHYSICS LETTERS
barrier to any single cause, but an examination of the population analysis results does provide some clues. The overlap population between two juxtaposed protons in the eclipsed case changes very IittIe when the molecule is rotated to the staggered case. while the 2P,(B) - 3P,(P) (and equivalently for the J’ case) overlap population increases from 0.0078 to 0.01 I I on going from the eclipsed to the staggered case. Overlap populations involving d-orbitals change very little in this process. It thus appears that at least a si_tificant fraction of the barrier arises not f: :,n hydrogen non-bonded interaction, but from breaking P-B overlap of n-type. Alti~ough it is difficult to define a force constant
2 A
for a rotation, it is possible to obtain barrier in anotlzer way. In particular,
rotational
potential
I/= fV#-cos36) Fig. 1. Coordinate
system and conformation
of PHsBHs.
of 2.47 kcal/mole,
and although the barriers for other cases do not agree quite as well, they are certainly of the correct order of magnitude. As can be seen from table 1, the barriers calculated without d-orbit& are less than those calculated with d-orbitals, a.nd barriers at the minimum energy geometry are considerably lower than the corresponding barriers at the experimental geometry. The latter observation is not unexpected, as the increased P-B distance leads to increased H-H distances, and consequently a smaller interaction in the eclipsed case. It is difficult to assign the origin of the rotational Table 1 Calculated energies for PHsBHs Experimental geometry [ 31 RPB=1.937 A
hfinimum energy geometry R PB = 2.080 A
-364.78062 au -364.77788 1.7 2 kcal/mole
-364.78923 au -364.78764 1 .OOk&/mole
-364.85227 au -364.84880 2 18 kcal/mole
-364.85522 au -364.85324 1.25 kcal/mole
without d-orbit& staggered eclipsed barrier with d-orbitals staggered eclipsed barrier
the rotational one assumes the
to be of the form [3]: I
where VT is the barrier and V is the energy increment at tendant on rotating the molecule away from the minimum energy configuration by an angle 0. Such a calculation was done for 0 = j” for the case of the experimental P-B bond length, and an energy of -364.852208 au was obtained. This yields F;, = 2.208 kcal/mole, again in excellent agreement widl expet-iment. The gross atomic populations and overlap populations obtained from the MulEken population znnalysis are presented in table 2 for the staggered esperimental geometry, for the calculation using a d-orbital basis. The electron distribution shows both boron and phosphorous as well as the boron hydrogens to be slightly net negative. This charge difference is seen to be all at the expense of the phosphorous hydragens. Examination of the table shows a net migration of nearIy Table 2 Gross population analysis far PHsBH3 in the esperimentala) staggered conformation b) atom
HB
HP
B
P
HB HP B P
I.0722
0.0007 0.8787
0.7858 -0.0096 5.0766
-
0.0447 0.7522 0.3996 15.0603
a) See ref. [ 31.
b) Obtained from d-orbital basis. 213
Volume 20, number 2
CHEMICAL PHYSICS LE-lTERS
0.3Oe- from the PH, fragment to the BH, fragment. This is expected, since PH3 is forming a dative bond with the electron deficient BH, in PH,BH,, and one might consider this compound to be, in some sense, qf,the charge transfer type. The populations reported here are not in quantitative agreement with those previously reported [2], but the differences can probably be rationalized on the basis of different choices of the structural parameters [ 31. The question of the importance of d-orbital participation inevitably is raised when discussing compounds of this type [7,8], and a comment concerning this problem may be in order here. In this context. the difference between the qualitative importance of including such functions, i.e., when they span the ip reducible representation of an occupied molecular orbital which is not spanned by included s and p functions. and their quantitative importance. i.e., when they serve as polarization functions or simply to increase basis size, must be remembered [S]. In the first case, a consideration of the symmetry of the species will be sufficient to distingui.sh the importance of d functions, and when they are included, a d-orbital total population on the order of whole electrons may be expected. III the second case, consideration of energy differences with and without including d-orbit& is necessary, and populations of considerably less than one electron may be expected. In phosphineborane, the second case pertains, as the a1 and e cccupied irreducible representations are spanned by s and p functions. The inclusion of d.orbitals is obviously energetically important as can be seen in table 1, since the rotational barrier depends to within %5% on their inclusion. In addition, examination of the orbital population shows a total d-orbital popularion of 0.7&-, again indicating their quantitative importance. Finally from the P-B stretching potential obtained during the geometry search, a force constant can be obtained. In the harmonic approximation, the F-B stretching force constant is found to be 1.187 mdyn/ A, which indicates a relatively weak bond. This is consistent with! the small P-B overlap population (table 2;. Although no experimental force constants are
:214
I.5 May 1973
availeb!e for this system, the u4 vibration, which is assigned to the BLP stretch (aI symmetry), is found to occur at 563 cm-1 in the infrared [9]. An approximate vibrational frequency of 450 cm-l can be calculated from the force constant, assuming the harmonic approximation, and that the PH, and BH, fragments are point masses. This is considered to be in reasonable agreement with experiment.
Acknowledgement Thanks are due to Dr. Lionel A. Carreira for discussicjn of this problem. Acknowledgement is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work, and to the University of Florida Conipu ter Center for a grant of computer time.
References [ 1) R.L. Kuczowski and D.R. Lide. J. Chem. Phys. 46 (1967) 337; J.P. Pasinski and R.L. Kuczotvski, J. Chem. Pflys. 54 (1971) 1903; P.S. Bryan ilnd R.L. Kunowski, Inorg. Chem. 11 (I 972) 553. 121 J. Demuynck nnd A. Veillard, Chcm. Commun. (1970) 873. [ 31 J.R. Durig, Y.S. Li, L.A. Carrcim and J.D. Odom, 1. Chcm. Phys., to be published. [4] A.B. Burg, Rec. Chem. Prog. 15 (1954) 159; R.W. RudoIph and R.W. Parry, J. Am. Chem. Sot. 89 (1367) 1621. [5] E. Clemcnti and J. hiehl, IBNOL-5 Program Users Guide, IBM publication RJ 889. [6] R.F. Stewart, J. Chem. Phys. 52 (1970) 431. J .A_.Pople, Accounts Chem. Res. 3 (1970) 2 i 7 ; E. Switkes, R.M. Stevens and W.N. Lipscomb, 1. Chcm. Phys. 5 1 (1969) 5229; D.B. Boyd nnd W.N. Lipscomb, J. Chem. Phys. 46 (1967) 910. M./I. Ratner and J.R. Sabin, J. Am. Chcm. Sot. 93 (1571) 3542. R.Vi. Rudolph, R.W. P;!rry and C.F. Farran, Inorg. Chem. 5 (1966) 723.
CHEMICAL PHYSICS LETTERS
Volume 20, number 2
ON THE BARRiER
TO INTERNAL
ROTATION
IN PI-IOSPHINEBORANE
John R. SABIN Quantrtm Theory Proiecr and Deportment of Physics, Unhers~ty of Florida, GainesWe, Florida 32601, USA Received 30 hlarch I973
An ab initio STO-3G calcirlation is carried out on PH$H3. The electronic structure of the molecule is considered, and special attention is paid to the barrier to internaf rotation.
1. Introduction Recently, there has been increasing interest in the properties of the boron-p~losp~lorous dative sigma bonds formed between
the electron
deficient
boranes,
and the phosphines [l--3]. Both the electronic and physical properties of the bond have been discussed, and the relationship
between
the two has been con-
sidered f43. Very recently, the microwzive spectra of one ofthe simplest compounds containing a P-B dative bond, namely phosphineborane (PHJX$H1), have been studied, and accurate values for the structural param. eters for the molecule, and for the internal rotation potenria1 about the B-P bond have been measured I31In order to shed further fight on the nature of this interesting bond, an ab initio LCAO MO SCF calculation has been carried out on PH3131-13,as a function of P-B distance and rotational angle. The potentials, charge distribution, and molecular efectronic structure are thus reported.
2. Calculations Calculations were carried out using the IBMOL-5 [S] set of ab initio programs. The basis sets used were of the STO-3G type, contracted from (3s) for hydrogen, (6s; 3~) for boron, and (9s, 6p, 5d) for phosphor. ous. The orbital eqponents and contraction coeffi-
cients were prepared according to Stewart [6] from ST0 orbital exponents [7]. In all cases, the experimental values [3] for hydorgen bond lengths and angles wert: used (RBs = 1.2 12 8, +H = 1.399 A, 4BPH = 116.9°, &PM-i = 103.6”? WBH = 114.6” and WPH = 101.3’). Calculations were carried out for the eclipsed and staggered fgrms of PH3BH3 at a variety of P-B bond distances, both with and without inclusion of dorbi tals in the basis set.
3. R,zsults and discussion PhosFhineborane (see tig. I) has C,, symmetry in an6 has electron configuration
al1 rotamers,
‘AI: la:2a:3a:le~4a:5a:6af2e47a:3e4. .. Calculations were carried out at the experimental geometry for eclipsed and staggered conformations using basis sets with
and without
d-orbitais.
The ener-
then minimized with respect to the P-B bond in the staggered configuration using the d basis, and a mintinum was found at 2.080 A, compared to the experimental [3] value of 1.937 A. The calculated energies for these conformations are reported in table 1, along with the Fotational barriers. In alitcases, the staggered con~~ration.~vas found to be of lower energy than the eclipsed, in agreement with the microwave structure [3]. The value calculated at the experi. mental geometry using the d-orbital set agrees quite well 1;vit.hthe experimenta!ly determined [31 barrier gy was
Volume 20, number
2
15 hlay 1973
CHEMICAL PHYSICS LETTERS
barrier to any single cause, but an examination of the population analysis results does provide some clues. The overlap population between two juxtaposed protons in the eclipsed case changes very IittIe when the molecule is rotated to the staggered case. while the 2P,(B) - 3P,(P) (and equivalently for the J’ case) overlap population increases from 0.0078 to 0.01 I I on going from the eclipsed to the staggered case. Overlap populations involving d-orbitals change very little in this process. It thus appears that at least a si_tificant fraction of the barrier arises not f: :,n hydrogen non-bonded interaction, but from breaking P-B overlap of n-type. Alti~ough it is difficult to define a force constant
2 A
for a rotation, it is possible to obtain barrier in anotlzer way. In particular,
rotational
potential
I/= fV#-cos36) Fig. 1. Coordinate
system and conformation
of PHsBHs.
of 2.47 kcal/mole,
and although the barriers for other cases do not agree quite as well, they are certainly of the correct order of magnitude. As can be seen from table 1, the barriers calculated without d-orbit& are less than those calculated with d-orbitals, a.nd barriers at the minimum energy geometry are considerably lower than the corresponding barriers at the experimental geometry. The latter observation is not unexpected, as the increased P-B distance leads to increased H-H distances, and consequently a smaller interaction in the eclipsed case. It is difficult to assign the origin of the rotational Table 1 Calculated energies for PHsBHs Experimental geometry [ 31 RPB=1.937 A
hfinimum energy geometry R PB = 2.080 A
-364.78062 au -364.77788 1.7 2 kcal/mole
-364.78923 au -364.78764 1 .OOk&/mole
-364.85227 au -364.84880 2 18 kcal/mole
-364.85522 au -364.85324 1.25 kcal/mole
without d-orbit& staggered eclipsed barrier with d-orbitals staggered eclipsed barrier
the rotational one assumes the
to be of the form [3]: I
where VT is the barrier and V is the energy increment at tendant on rotating the molecule away from the minimum energy configuration by an angle 0. Such a calculation was done for 0 = j” for the case of the experimental P-B bond length, and an energy of -364.852208 au was obtained. This yields F;, = 2.208 kcal/mole, again in excellent agreement widl expet-iment. The gross atomic populations and overlap populations obtained from the MulEken population znnalysis are presented in table 2 for the staggered esperimental geometry, for the calculation using a d-orbital basis. The electron distribution shows both boron and phosphorous as well as the boron hydrogens to be slightly net negative. This charge difference is seen to be all at the expense of the phosphorous hydragens. Examination of the table shows a net migration of nearIy Table 2 Gross population analysis far PHsBH3 in the esperimentala) staggered conformation b) atom
HB
HP
B
P
HB HP B P
I.0722
0.0007 0.8787
0.7858 -0.0096 5.0766
-
0.0447 0.7522 0.3996 15.0603
a) See ref. [ 31.
b) Obtained from d-orbital basis. 213
Volume 20, number 2
CHEMICAL PHYSICS LE-lTERS
0.3Oe- from the PH, fragment to the BH, fragment. This is expected, since PH3 is forming a dative bond with the electron deficient BH, in PH,BH,, and one might consider this compound to be, in some sense, qf,the charge transfer type. The populations reported here are not in quantitative agreement with those previously reported [2], but the differences can probably be rationalized on the basis of different choices of the structural parameters [ 31. The question of the importance of d-orbital participation inevitably is raised when discussing compounds of this type [7,8], and a comment concerning this problem may be in order here. In this context. the difference between the qualitative importance of including such functions, i.e., when they span the ip reducible representation of an occupied molecular orbital which is not spanned by included s and p functions. and their quantitative importance. i.e., when they serve as polarization functions or simply to increase basis size, must be remembered [S]. In the first case, a consideration of the symmetry of the species will be sufficient to distingui.sh the importance of d functions, and when they are included, a d-orbital total population on the order of whole electrons may be expected. III the second case, consideration of energy differences with and without including d-orbit& is necessary, and populations of considerably less than one electron may be expected. In phosphineborane, the second case pertains, as the a1 and e cccupied irreducible representations are spanned by s and p functions. The inclusion of d.orbitals is obviously energetically important as can be seen in table 1, since the rotational barrier depends to within %5% on their inclusion. In addition, examination of the orbital population shows a total d-orbital popularion of 0.7&-, again indicating their quantitative importance. Finally from the P-B stretching potential obtained during the geometry search, a force constant can be obtained. In the harmonic approximation, the F-B stretching force constant is found to be 1.187 mdyn/ A, which indicates a relatively weak bond. This is consistent with! the small P-B overlap population (table 2;. Although no experimental force constants are
:214
I.5 May 1973
availeb!e for this system, the u4 vibration, which is assigned to the BLP stretch (aI symmetry), is found to occur at 563 cm-1 in the infrared [9]. An approximate vibrational frequency of 450 cm-l can be calculated from the force constant, assuming the harmonic approximation, and that the PH, and BH, fragments are point masses. This is considered to be in reasonable agreement with experiment.
Acknowledgement Thanks are due to Dr. Lionel A. Carreira for discussicjn of this problem. Acknowledgement is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work, and to the University of Florida Conipu ter Center for a grant of computer time.
References [ 1) R.L. Kuczowski and D.R. Lide. J. Chem. Phys. 46 (1967) 337; J.P. Pasinski and R.L. Kuczotvski, J. Chem. Pflys. 54 (1971) 1903; P.S. Bryan ilnd R.L. Kunowski, Inorg. Chem. 11 (I 972) 553. 121 J. Demuynck nnd A. Veillard, Chcm. Commun. (1970) 873. [ 31 J.R. Durig, Y.S. Li, L.A. Carrcim and J.D. Odom, 1. Chcm. Phys., to be published. [4] A.B. Burg, Rec. Chem. Prog. 15 (1954) 159; R.W. RudoIph and R.W. Parry, J. Am. Chem. Sot. 89 (1367) 1621. [5] E. Clemcnti and J. hiehl, IBNOL-5 Program Users Guide, IBM publication RJ 889. [6] R.F. Stewart, J. Chem. Phys. 52 (1970) 431. J .A_.Pople, Accounts Chem. Res. 3 (1970) 2 i 7 ; E. Switkes, R.M. Stevens and W.N. Lipscomb, 1. Chcm. Phys. 5 1 (1969) 5229; D.B. Boyd nnd W.N. Lipscomb, J. Chem. Phys. 46 (1967) 910. M./I. Ratner and J.R. Sabin, J. Am. Chcm. Sot. 93 (1571) 3542. R.Vi. Rudolph, R.W. P;!rry and C.F. Farran, Inorg. Chem. 5 (1966) 723.