CHAPTER II
The Reaction Path of PH5-----► PH3 + H2 Using an SCF
Study
Page No.
2.1
Introduction
39
2.2
Methods of Computation
41
2.3
The 'Hypothetical' Molecule PH5
41
2.4
The Possible H2 Abstraction
43
2.5
The Source Molecule PH3
45
2.6
The Present Work Supports 'WH Allowed Abstration'
46
2.7
Density Functional Theory Considerations
48
2.8
The Geometry of PH3 Molecule
50
2.9
The Geometry of PH5 Molecule
51
2.10
The Effect of Polarization Functions
52
2.11
Molecular Orbital Energies
53
2.12
Atomic Populations and Dipolemoment
54
2.13
The Harmonic Force Field of PH3 and PH5
54
2.14
Conclusion
56
References
57
CHAPTER II
The Reaction Path of PH5----- > PH3 + H2 Using an SCF Study
2.1 Introduction
Molecules with pentacoordinated phosphorous are very interesting from the point
of view of valence theory and have been the subject of several quantum chemical
studies in the past few years.
The molecule PH5 is the prototype of the phosphoranes
PR5 and has the special feature in its binding and it is characterized by the possible
description via a three center, four electron bond and the importance of d atomic
orbital contributions [1,2], PH5 is one of the simplest of all electron-rich ‘nonrigid’
molecules.
Its isomerization barrier from the D3h ground state configuration via a
C4v structure is only ~ 2kcal/mol [3,4],
This is an obvious contrast to the rigidity
of PH3, which has an inversion barrier of ~ 38 kcal/mol [5],
Phosphine (PH3) is the simplest compound of C3v symmetry in PHn group. It
is of pyramidal structure and the experimental bond length and bong angle are 1,419
+0.3
A
and 93.55 +0.25° [6] respectively.
molecule is predominantly of s character.
The unshared pair of electrons in the
Several theoretical studies have been
performed for the PH3 [1,7-9] and PH5 [10-15] molecules and a few experimental
results [16,17] have also been reported for the PH3 molecule.
The molecule PH5 has not yet been observed experimentally and why this is
so is a challenging problem.
It is evident that the trigonal-bipyramidal D3h structure
represents a local minimum of the potential energy surface.
A theoretical study [18]
on the reaction mechanism has also been reported in the literature.
Still there is a
controversy about why the molecule PH5 is in the metastable state or unobservable
It is of thought that the high H-H bond energy, coupled with the low electronegativity
[19] of H precludes its formation.
Apart from the semi empirical calculations, the
first non empirical LCAO-MO-SCF (Hartree Fock) calculations were performed by
Rauk et al., [7],
To explore the nature of the polytopal rearrangement, the electronic
structure of phosphorous with an ‘expanded valence shell’ and a minimal amount of
experimental input, calculations were carried out on PH5 and model systems were also
derived from PH5.
On the basis of these calculations, it was suggested that the lowest
frequency fundamental of trigonal - bipyramidal phosphoranes corresponds to the
equatorial in-plane bending motion.
Most of the theoretical investigations were
performed by using standard geometrical parameters and it has also been observed
that there is inconsistency among the geometrical parameters for both the molecules,
available from the different theoretical sources.
Since the source molecule of PH5 is PH3, on studying the reaction path of
PH5----- > PH3 + H2 the present work is focussed on the transition state of the PH3
molecule.
The PH3 molecule is studied by assuming the C2v, D3h and C3v symmetries
and the molecule PH5 is studied by assuming the D3h and C4v symmetries.
These
studies were undertaken on the basis of density functional theory and molecular orbital
theory to explore more informations about the instability of the PH5 molecule.
40
In the present investigation, geometrical optimization, force fields, chemical
hardness, chemical potential and mean amplitude of vibration for the PH3 molecule
have been studied, and a similar parallel study has also been performed on the PH5
molecule.
2.2 Methods of Computation
The geometries were optimized at the HF-SCF level of theory employing split
valence basis sets, HF/3-21G, HF/3-21G* and HF/6-31G for the C3v, C2v and D3h
symmetry structures of the PH3 molecule and for the D3h symmetry structure of the
PH5 molecule. The C4v structure of the PH5 molecule has also been optimized using
6-31G basis set.
The computations were carried out, employing MICROMOL MARK
V [20] computer program. Force constants were obtained by
using the Wilson’s FG
matrix method [21] for the ab initio and experimental frequencies.
for the molecules were calculated by using the Cyvin’s method
Mean amplitudes
[22],
2.3 The ‘Hypothetical’ Molecule PH5
Several theoretical investigations of PH5 molecule have been published
[1,7-9,23], but this molecule served mainly as a model compound for the known
substituted species and the prediction of the properties of the molecule have only
played a minor role.
The calculations on PH5 molecule published so far have
indicated [1,7-9] that the energy of the most stable structure of PH5 lies 40 to 50
41
kcal/mol above the sum of the energies of the separated PH3 and H2 molecules.
disintegration processes, like PH5---- 4
Other
PH4 + H, which is also possibly followed
by PH4 + H----- > PH3 + H2 are hardly competitive [24], The binding energy of PH4
with respect to PH3 + H reaction is found to be 10 kcal/mol.
Howell and Olsen
[24] have calculated that PH4 is 13 kcal/mol higher in energy than PH3 + H
4-31G SCF study and
functions.
using
the result is not changed significantly due to inclusion of d
Kutzelnigg et al., [3] have performed an SCF calculation of PH4 molecule
by using the polarization functions to the basis sets with Howell’s geometry mid found
its energy to be 11 kcal/mol above the sum of energies of PH3 and H.
Electron
correlation effects stablize the PH5 molecule with respect to PH3 + H2 by about 10
kcal/mol and from the above results, it has been concluded that PH4 + H lies at least
50 - 60 kcal/mol above PH5 molecule. Keil et al., [1] have studied the reactions of
PH5 ----- > PH3 + 2H and PH5----- > PH3 + H2 and reported that PH5 is bound by
64 kcal/mol with respect to PH3 + 2H but it is unstable with respect to PH3 (planar)
+ H2 by 38 kcal/mol.
Electron correlation effects stabilizes the PH5 molecule
compared to PH3 + 2H by 25 kcal/mol.
From the above discussions it is evident that the most possible disintegration
path of PH5 can be considered to be the concerted H2 abstraction. The reaction of
PR5 ----- j- PR3 + R2, most commonly known with R as Cl has a venerable history
dating from the middle of the 19th century to every contemporary freshman textbook
of general chemistry.
Given a trigonal-bipyramid geometry of PR5, it is to be
reinvestigated with modern kinetics to find whether the components of R come at
42
random from axial and equatorial positions or is one of the specific mechanism in
which figure 12, 13 or 14 is operative (Fig 2.1). The ‘conservation of orbital
symmetry’ yields a simple and surprising answer.
2.4 The Possible H2 Abstraction
The occupied molecular orbitals of PH5 in D3h symmetry structure are shown
in the Fig.2.2.
The evolution of the orbitals in the course of reaction and the least
motion process of 12 in which an axial and equatorial hydrogen atoms depart, where
R = H can be considered as follows.
As the motion 12 begins, the D3h structure is
initially distorted to a Cs symmetry structure. The la', 2a' and la" orbitals of that Cs
form have the proper shape for becoming the PH a bonds, of the PH3 pyramid.
The
PH3 orbitals in question are la3 and le; the 3a' orbital becomes the PH3’s lone pair.
Thus the H2 crg orbital must be derived from 4a', and has a node between the
departing hydrogens.
No continuous evolution of orbitals is possible in this mode
such that the PH5 orbitals yield a ground state configuration of PH3 and simultaneously
one of H2.
Hence this reaction is to be considered as a forbidden reaction.
The next possible reaction is the equatorial departure 13.
diagram for this reaction is given in the Fig.2.3.
The correlation
The orbitals at left are those of
D3h symmetry structure of PH5 molecule, reclassified in symmetry according to the
two mirror planes maintained.
PH3 and
At right are the orbitals of the product - a T shaped
H2.
43
Fig. 2.1 Operative mechanisms of
abstraction of H2 from PH 5
2a i
11.17
-
17.66
18.06
-
O
4—o
O
Fig. 2.2 The occupied molecular orbitals of
PH^ in
symmetry [8].
22.26
-
la',
------
ss
SA
SS
SS
Fig. 2.3 Correlation diagram for the departure of two equatorial
hydrogens from PH^ (left) to yield PH3 + H2 (right).
The transformation of T -shaped PH3 into the equilibrium C3v structure does
not change the nodal patterns, and hence this is an allowed reaction.
The PH3
fragment in this allowed fragmentation would begin distorting toward a pyramid even
in the early stages of the reaction.
The axial-axial elimination 14, at first sight appears sterically unlikely, but it
is a continuation of the Berry pseudorotation.
Hence this reaction is also allowed in
view of symmetry. The axial - axial (aa) and equatorial - equatorial (ee) abstraction
need not be regarded as independent processes.
In the (aa) abstraction one must bring
the two axial atoms closer together, and this is easily achieved by a pseudorotation.
The (aa) abstraction is then supposed to follow the same way as the (ee) abstraction.
The (ee) abstraction is WH (Woodward Hoffmann) allowed [8], In this
abstraction, the PH3 fragment is left in T - shape with the lone pair in a n orbital,
antisymmetric to the plane with respect to which the MO of the removed H2 is
symmetric.
In this process, C2v symmetry is conserved (Fig.2.4) and under this
symmetry constraint a smooth transition from the initial to final configuration is
possible.
It has been confirmed that [18] the T-shaped PH3 has in fact a ground
state with a rc-type lone pair. The state with a a type lone pair and empty n MO
lies ~ 100 kcal/mol higher.
While with no symmetry constraint at all the number of degrees of freedom
for PH5 is 12 and it is reduced to 5 in C2v symmetry.
One finds that the PH
distances in the remaining PH3 fragment are not very relevant and that one introduces
44
H
H
4
3
Fig. 2.4 Equatorial - equatorial abstraction of H2 from PH^
errors smaller than ~ 1 kcal/mol if one keeps these PH distances constant, and takes
the same value in the equilibrium structures of PH5 and PH3 molecules.
If PH3 fragment is to be left in T-shaped form, in an over simplified way,
one can say that first H]PH2 angle is closed until the distance between H1 and H2
is nearly equal to that of in isolated H2 and then the H2 moves away.
of the saddle point is
and
r
= 0.74
A
R=l,588
A,
R = 0.9
A
The geometry
to be compared with R = 1.421
A
in H2.
2.5 The Source Molecule PH3
In the present work, PH3 molecule is optimized in its T shaped form and the
energy minimum was found to be at R = 1.405
PH distance is 1.466
A
in the HF/6-31G basis set.
The
(HF/6-31G) in PH5 molecule and shortened in its T shaped
form after the abstraction of concerted H2 atoms.
to relax, it takes on
A
When the PH3 molecule is allowed
t v ->■ D3h structure in all the HF/3-21G, HF/3-21G* and HF/
6-31G basis sets and the bond length is further shortened to 1.386
A
(6-31G). As
the structure changes to C3v symmetry, the PH bond length is once again Iengethened
to 1.424
A
(6-31G). The energy of the PH3 molecule in the T shaped form is 40
kcal/mol above the D3h structure and the ground state configuration of C3v symmetry
is less by 29 kcal/mol than the D3h structure.
The geometrical parameters and total
energies of PH3 molecule in T shaped form, D3h and C3v symmetries and of PH5
molecule in D3h and C4v symmetries in HF/3-21G, HF/3-21G* and HF/6-31G basis
sets are presented in Table 2.1.
45
Table 2.1
Optimized geomentries ( r in angstroms, a in degrees) and total energy (hartees) of
PH, and PH5 molecules.
Molecule
Parameter
3-21G
3-21G*
6-31G
PH3
(T shaped)
r
Total
Energy
1.401
1.391
1.405
PH,
(°3h)
PH,a
(c3v)
ph5
(DJh)
ph5
(CJ
r
Total
Energy
r
a
Total
Energy
rax
r
Total
Energy
CCj
r
ap
* bas
Total
Energy
-340.5926
1.380
-340.6559
1.423
95.98
-340.7045
1.541
1.425
-341.6983
-340.6955
1.375
-340.7633
1.409
95,21
-340.8234
1.470
1.411
-341.8784
-342.2899
1.386
-342.3538
1.424
93.8
-342.4007
1.466
1411
-343.501
1.409
1.487
-343.3944
The experimental values for PH3 are r = 1.424 A and a = 93.8 degrees |6|
2.6 The Present Work Supports ‘WH Allowed Abstraction’
Dixon et al., [25] and Minyaev [26], have shown with the help of ab initio
calculations that the pyramidal C3v symmetry molecules do indeed invert through a T
shaped C2v genuine transition state.
It can be explained by the fact that electrostatic
repulsion between the lone pair of the central atom and the ligands is considerably
less in a T shaped form than in a
form.
Hence it follows that after the abstraction
of H2 from PH5 molecule, the remaining PH3 fragment attains a T shaped form and
relaxes into D3h structure which is also the transition state of PH3 during the inversion
process.
For the same reaction, Howell [23] has stated that the system prefers the
distorted WH forbidden path in which there is equatorial-axial abstraction
But
Howell’s results are conceptually an artifact of the reduction of the process to a two
dimensional hypersurface, while a three dimensional one would be required, and
numerically its artifact of using a basis without polarisation functions is unable to
describe the bonding situation in PH5 appropriately.
Kutzelnigg and Wasilewski [18]
have studied the potential energy surface (PES) for the reaction PH5----- > PH3 -f H2
in terms of ab initio calculations and the results were found to be very sensitive to
the level of computational sophistication.
On an intermediate level of SCF with
polarisation functions, they have found two saddle points one of which corresponds
to a WH allowed concerted reaction and the other to a nonleast motion variant of a
WH forbidden process that is better described as a Zwitterionic reaction going via
PH4+ + H'.
The barrier for the concerted process is slightly smaller than that for
46
the zwitterionic one, but the region of the PES between the two saddle points is
extremely flat.
There is no clear distinction between the two reaction channels.
On
a higher level of calculations with inclusion of electron correlation only the ‘concerted’
saddle point ‘survives’, but the saddle point region remains flat.
On the basis of variations in bondlengths and total energies and through the
results of density functional theory and force constants of PH3 and PH5 molecules,
the present work also obtains results that are more favourable for the (ee) abstraction,
which is WH allowed.
The length of the equatorial bond of PH5 (1.411
r(PH) of PH3 (1.424
bonding.
A
A
in HF/6-31G) is close to
in HF/6-31G) in which p atomic orbitals are involved in
PH4+, with an sp3-hybrid on P has a shorter r(PH) of 1.39
PH3 with an sp2 hybrid on P,
r(PH) is still shorter (1.37
A).
A
and in planar
The presence of the
axial bonds in PH5 obviously weakens the equatorial bonds. The axial bond
1.466
A
length
(HF/6-31G) is the weakest bond. The calculated force constants also confirm
the same trends. The large value of fae in Table 2.6 reveals the existence of strong
coupling between axial and equatorial bonds, which confirms that either bond would
be different without the presence of the other.
for PH3 is 3.635 mdyn
constant is 3.656 mdyn
A'1
The symmetric stretch force constant
(SCF) and for PH5 the equatorial symmetrical stretch force
A'1,
whereas the axial symmetrical stretch force constant in
the case of PH5 is 2.724 mdyn
A'1.
47
The axial bonds of PH5 are lengthy compared with all other PH distances of
PH3 and PH5 and stretching force constants are at a minimum for these bonds that
makes the molecule to be less stable.
2.7 Density Functional Theory Considerations
The above problem can be analysed from a different point of view using
density functional theory [27] (DFT) which has many important application to chemistry.
Recently the density functional theory
of many electron systems has been found to
be useful in providing quantitative definitions for several qualitative chemical concepts.
Accordingly, there has been upsurge of interest in understanding structure, properties,
reactivity and dynamics of atoms and molecules using DFT.
Two important properties
of this theory are the electronic chemical potential p and the chemical hardness q.
The electronegativity of Pauling and Mulliken, which is the average of the
ionization potential I and electron affinity A has long been known to be of great use
in chemistry.
In general the quantity % = 1/2 (I + A)
tendency of electrons from a species.
= -p measures the escaping
Here % is the absolute electronegativity and
its negative p is the chemical potential; it has the same significance as the chemical
potential in the classical thermodynamics of macroscopic systems.
is defined as
of electrons.
q
=1/2 ( I - A ) and it refers resistance to
The hardness q
change in the number
According to Koopmans’ theorem, the ionization potential is simply the
orbital energy of the HOMO (Highest Occupied Molecular Orbital) with change in
sign.
For spin paired molecules, the electron affinity is the negative of the orbital
48
energy of the LUMO (Lowest Unoccupied Molecular Orbital); therefore on an orbital
basis, we can write
l1 = (
and
ehomo
rj = ( ELUMO
+
elumo
) 1 2
- EHOMO ) / 2
The gap between the HOMO and LUMO is simply equal to 2r| (both p and
r|
are measured in electron volts).
Hard molecules have a large HOMO-LUMO gap
and soft molecules have a small HOMO-LUMO gap.
Soft molecules are more
polarizable and are more reactive, in general than the hard molecules.
Table 2.2 shows the results of density functional theory calculations for the
PH3 and PH5 molecules under various symmetries obtained through HF/6-31G basis
set.
The largest HOMO-LUMO energy gap (2r|) of PH3, which is
14.846 eV in
the C3v symmetry, shows the highest stability of the molecule in that symmetry.
In
the reaction, PH5----- > PH3 + H2, after the H, abstraction, PH3 at a bondlength of
1.405
eV.
A
in which the energy is minimum in the T shape, has an energy gap of 9.257
During the relaxation process, the T shaped structure reaches
symmetry with a bondlength of ! .386
A
’
D3h
and the HOMO-LUMO energy gap is widened
tiirther to 12.375 eV.
The low ionization potential of 7.905 eV, given as the negative of the energy
of the highest occupied molecular orbital, contributes to the instability of PH5 by
rendering it susceptible to attack by Lewis acids [8].
The HUMO-LUMO energy gap
is more widened in the case of D3h symmetry than in the case of C4v symmetry by
49
Table 2.2
Density functional theory calculation of PH, and PH5 molecules (all values are in eV)
E
'"HOMO
EL.UMO
*2p
2r\
PH3
(T shaped)
8.264
0.993
7.271
9.257
PH3
(D,h)
8.264
4.190
4.073
12.375
PH3
(C3V)
10.245
4.601
5.643
14.846
7.905
4.348
3.556
12.253
8.081
2.852
5.230
10.933
ph5
(D3h)
ph5
(CJ
1.32 eV.
These results of DFT theory confirm that the most stable state of PH5 is
the D3h structure.
2.8 The Geometry of PH3 Molecule
The optimized geometrical parameters of PH3 molecule in HF/3-21G, HF/321G* and HF/6-31G basis sets are given in Table 2.1 along with experimental values.
Deviations from experiment in calculated bondlengths for the HF/3-21G and HF/3-21G*
basis sets are 0.001
A
and 0.015
A
respectively and the value of HF/6-31G basis
sets obtained is same as obtained by Nielson [6] through experiment.
Inclusion of d
functions in HF/3-21G basis set shortens the bondlength and leads to more deviation
from the experimental bondlength. It is observed that the deviations from experimental
values are more higher in HF/STO-3G, HF/44-31G and HF/STO-3G* basis sets [28]
(shorter by 0.041
A
in STO-3G*).
1.403
A
A
in STO-3G, longer by 0.019
A
in 44-31G and shorter by 0.042
For the same bond Reed et al., [29] have obtained a value
through the HF/6-3IG* basis set.
of
From these observations, it has been
noticed that the inclusion of polarization functions in 3-21G and 6-31G basis sets did
not improve the geometrical parameters of the PH3 moiecuie.
Kutzelnigg et al., [3] have computed the bondlength of PH3 as 1.409
1.413
A
(Cl) and 1.417
A
A
(SCF),
(CEPA) and bond angle as 94.6° (SCF), 92.9° (Cl) and
92.5° (CEPA). Ewig et al., [30] have studied the energies and stabilities of PHn, SHn
and CIHjj compounds and they have optimized the geometries and obtained the energies
at MP2/6-31G* and MP4
levels
of theory.
50
For the PH3 molecule, the obtained
bondlength and bond angle are
A
1.405
and 94.5° respectively.
The CEPA
geometrical parameters with double - zeta - plus polarization type basis set are
accurate to within 0.003
A
with the experimental values.
2.9 The Geometry of PHS Molecule
An experimental geometry of PH5 is not known and there is no good agreement
between the different available theoretical values.
rax is obtained as 1.541
A,
1.470
A
and 1.466
In the present work the value of
A
in
HF/3-21G, HF/3-21G* and
HF/6-31G basis sets respectively and the value of req is obtained as 1.425
A
and 1.411
[29],
A
in 3-21G, 3-21G* and 6-31G
have obtained rax as 1.464
A
basis
and Req as 1.407
1.468
A
Kutzelnigg et al., [3]
(Cl)
and 1.471
(Cl) and 1.419
A
A
(CEPA).
parameters of PH5 as 1.463
approximations.
A
1.411
Reed et al.,
in D3h symmetry
using
and r^ as 1.440
A
in C4v
have computed rax bondlengths as 1.471
A
(SCF),
HF/6-31G* basis set. They have obtained rax as 1.388
symmetry.
sets respectively.
A,
A
(CEPA) and req bondlengths as 1.416
A
(SCF), 1.416
A
Ewig and Wazer [30] have obtained the structural
A
for rax and 1.414
A
for req using MP2 and MP4
The difference between the present HF/3-21G structural parameters
and the other theoretical values are higher.
But at the same time, the HF/6-31G values
of the present work closely agrees with the other theoretical values, in both, axial
and equatorial bondlengths, and the differences are very small.
51
2.10 The Effect of Polarization Functions
Kutzelnigg et al., [3] have reported that electron correlation lengthens the axial
and equatorial bondlengths by 0.01
A,
as expected, because the effect of electron
correlation on ordinary bonds is always lengthening and this is related to the incorrect
dissociation behaviour of covalent bonds in the SCF approximation.
The axial bonds
are less affected by the correlation, since the bonds are ionic to a large extent and
suffer less due to the effect of SCF approach.
The axial bonds are lengthening more
if d functions are removed from the phosphorous atom.
By comparing HF/3-21G*
basis set values, it can be seen that, in the present 3-21G values, in which d orbitals
are removed, axial bond is lengthening by 0.071
found in the case of 4-31G basis set [28].
A
A
[29].
A
is
In the case of 6-31G basis set, removal
of d functions lengthen the axial bond by 0.002
lengthened by 0.004
and a difference of 0.014
A
and the equatorial bond is
Table 1 shows that in general, the apical bonds are
shortened more than the equatorial bonds due to the inclusion of polarization functions.
The total energy of PH3 and PH5 molecules are computed in 3-21G, 3-21G*
and 6-31G basis sets and are presented in the Table 2.1.
The total energy of PH5
molecule is calculated as -343.501 hartree in the 6-31G basis set and it is less by
1.8 hartree and 1.6 hartree from 3-21G and 3-21G* basis set values respectively.
It
can also been observed from the Table 2.1 that the total energy of PH5 is less by
67 kcal/mol for the D3h structure than the C4v structure.
52
2.11 Molecular Orbital Energies
The molecular orbital energies for the molecules PH3 and PH5 have been
calculated in 3-21G and 6-31G basis sets and are given in the Table 2.3.
Rauk et
al., [7] have tabulated the orbital energies for PH3 and PH5 and ordering of the
valence orbitals is identical with the present work.
Although the d-type functions make
a significant contribution to the total energies of both the molecules, they influence
the orbital energies of PH5 more, than of PH3.
However, the computed results for
each molecule are qualitatively unaffected by the presence of the d-type functions.
The
ordering of the orbital enemies are not altered due to the inclusion of d-type functions.
The nodal structure of the highest occupied molecular orbital of the D3h geometry
precludes appreciable contribution to this orbital from s type functions of phosphorous.
The symmetry of this orbital (a'j) excludes contributions from p-type functions on
phosphorous.
As a consequence of nodal and symmetry restrictions, the d-type
functions of phosphorous are the only functions on this center that contribute to these
molecular orbitals.
It is important to realize, however, that the presence or absence
of the d-type functions in the basis set plays no part in determining the symmetry or
nodal structure of the highest occupied molecular orbitals of the D,h symmetry.
The innermost molecular orbitals of PH3 and PH5 are localized to phosphorous
and may be considered to be the Is, 2s and 2p atomic orbitals of the heavy atom
The molecular orbitals
may be characterized simply as s-like (nodeless), p-like
(having a single node) and d-like (having two nodal sufaces).
The highest occupied
molecular orbital of PH5, which is d-like, is non bonding if d type functions are
omitted from the basis set but is bonding if d-type functions are included, since only
53
CL
X
<N
i
cc"
<6
<N
cT
-0.569
-0.324
-0.571
-0.292
-0.578
-0.593
fN
<N
-0.381
-0.593
cT
-0.382
-0.904
-0.933
3a,
<N
-0.380
-5.415
-5.432
r<
-0.578
-5.418
-5.434
ci~
-0.528
-0.528
-5.418
-5.434
cT
-0.527
-0.527
-0.859
-5.379
-5.381
-5.381
-79.550
-79.481
n
-0.527
-0.527
-0.857
-0.875
a
2e
-5.357
O
-5.358
-5.432
fN
-5.345
-5.358
<N
rr
CN
ri
-7.547
3-2 1G*
3-21G
6 -3 1G
-0.324
-0.517
-0.579
-0.579
-0.907
-5.436
-5.439
-5.439
tJ*
V!
ri
•5.345
-7.487
-79.933
6 -3 1G
and PH 5 molecules (Hartress)
55
i
-7.469
-79.475
*
D
-7.461
PHL,
CL
-79.386
of
»Ti
3-2 1G
Molecular Orbital Energies
Table 2.3
X
<N
cT
CO
(N
ctT
these functions on phosphorous are of the required symmetry for effective overlap.
The
inclusion of d-type functions in the 6-31G basis set increases the electron density in
the apical bonding, indicating bondlength shortening.
2.12 Atomic Populations and Dipolemoment
The atomic populations, dipolemoment, quadrupolemoment, and moment of
inertia values for PH3 and PH5 molecules are presented in the Table 2.4.
The total
atomic population on phosphorous in PH3 is 15.25 and for hydrogen it is 0.92 in the
HF/6-31G basis set.
For the PH5 molecule the atomic population of phosphorous is
14.63 and it is more in the axial hydrogen atom by 0.16 than the equatorial hydrogen
atom.
The total atomic population values for PH3 and PH5 molecules in HF/6-31G
basis set are in agreement with the values of Rauk et al., [7],
The dipolemoment of
the molecule depends upon the co-ordinates of the phosphorous and hydrogen atoms
and in the D3h symmetry, the dipolemoment is zero.
2.13 The Harmonic Force Field of PH3 and PH5
The force field of PH3 molecule has been extensively studied, using
experimental vibrational frequencies and structural parameters and given in the Table
2.5. Several authors have attempted to extract the harmonic force field and Kutzelnigg
et al., [3] have obtained harmonic force field for PH3 and PH5 molecules using
different theoretical and experimental frequencies.
In the present investigation, the force
constants of PH3 molecule have been determined, using different theoretical and
54
Table 2.4
Atomic Populations, Dipolemoment, Quadrupolemoment and moment of inertia for PH, and PH;
molecules (dipolement in debyes, quadrupolemoments in atomic units and moment of intertia in
MHz).
PH,
Atomic
Population
P
H
ph5
3-21G
6-31G
14.911
1.029
15.248
0.917
6-31G
P
^axial
^equatorial
Dipolemoment
1.23
0.88
0.58 (Expt. value)
Quadrupolemoment
1.095
1.095
-2.191
1.028
1.028
-2.056
13.559D+04
13.559D+04
11.206D+04
13.835D+04
13.835D+04
11.572D+04
Qyy
Moment of Inertia
I
k
k
14.631
1.165
1.012
9yj.
1.931
1.931
-3.862
k
83.937D+03
68.798D+03
68.799D+03
i
Table 2.5
Force constants of PH., molecule (mdyn/A)
SCF“
CEPAh
Experiment
f
r
3.6347
3.555
3.4677
f.
rr
0.0597
0.00433
0.004667
L
0.0663
0.04206
0.02153
L-
0.0183
0.00686
0.03993
f .
aa
-0.0303
-0.0236
-0.034
f
a
0.8487
0.7582
0.7270
Experimental geometrical parameters r = 1.424 A and a = 93.8° are used. [6],
a SCF frequencies [3]; 2547, 1136. 2501. 1241 cnr1
b CEPA frequencies (3): 2482, 1081, 2487, 1170 cnr1
c Experimental frequencies (10). 2452. 1041. 2457. 1154 cnr1
experimental frequencies, experimental structural parameters and HF/6-31G structural
parameters of the present work.
For the PH5, molecule, other theoretical frequencies
and the HF/6-31G structural parameters of the present work have been used to
determine the force constants.
The computed values are given in the Table 2.6 and
they closely agree with the values of Kutzelnigg et al., [3],
It has been noticed that
the stretching force constants for the bond P-H in PH3 molecule is slightly higher for
the theoretical frequencies.
Usually the theoretical ab initio frequencies are always
higher then the experimental frequencies, even after scaling.
The force constant
calculations of theoretical parameters do not differ much from the force constant
calculations of experimental parameters.
Mean amplitudes were calculated from these
force constants and are presented in Table 2.7.
The experimental root mean amplitude
A
[10] and this value closely agrees with
of the P-H stretching vibration is ± 0.085
the theoretically calculated values. Kutzelnigg et al., [3] have reported that the diagonal
force constants are much depending on the different basis sets used at the SCF level.
They have reported that the electron correlation is not at all affecting force constants
much.
The force constants for the present work are slightly longer than the other
theoretical values.
The axial stretching force constant is found to be smaller than
the equatorial stretching force constant.
The root mean amplitudes of vibration for
the PH5 molecules is not compared due to the non availability of experimental values.
The P-H stretching force constant is 3.4677 mdyn/A for the PH3 molecule.
For the
PH5 molecule, axial bond stretching force constant is 2.492 mdyn/A and equatorial
bond stretching force constant is 3.462 mdyn/A.
The force constants of PH5 molecule
are calculated by using HF/ 6-31G** basis set parameters, rax = 1.4626
A
and r
1.4137 A of Ewig et al., [30] and also by using rax = 1.466 A and req = 1.411
of the present ab initio geometry.
55
=
A
Table 2.6
Force constants of PH5 molecule (mdyn/A)
SCFd
SCFe
CEPAf
CEPA8
fa
2.724
2.725
2.493
2.492
faa .
0.0328
0.0318
-0.121
-0.1197
fe
3.656
3.656
3.4601
3.462
fee-
0.00623
0.00657
-0.1419
-0.1429
fP
0.4646
0.3362
0.4401
0.0966
f
0.2142
0.1518
0.02123
-0.0829
-0.1119
-0.0484
-0.1045
0.06706
0.2078
0.2078
0.0988
0.0988
-0.07073
-0.06986
-0.0675
-0.0681
fa
0.05957
0.05957
0.0643
0.06407
L
-0.00078
0.02893
0.0639
0.02827
f„
e|l
-0.172
-0.172
-0.384
-0.166
f«P
-0.00726
0.06747
0.1389
0.0612
w
fxpp"
fae
fa = f (axial); f = f (equatorial); fp = f (angle between axial and equatorial bonds);
f0 ” f (angle between equatorial bonds).
d SCF frequencies [3]; 2561, 2064. 2261, 1284, 2571, 1365, 612 and 1585 cm'1.
Geometrical parameters [30]; rM = 1.4626
A
and r
= 1.4137
A.
e Calculations were made using the same SCF [3] frequencies with the geometrical
parameters of the present work, riX = 1.466 A and re(j = 1.411 A.
f CEPA frequencies [3]; 2337, 1970, 2227, 1260. 2554. 1328, 648 and 1534 cnv1.
Geometrical parameters [30]; rM = 1.4626
A
and r
= 1.4137
A.
g Calculations were made using the same CEPA [3] frequencies with the geometrical
parameters of the present work, rM = 1.466 A and r^ = 1.411
A.
u
0.1229
to
U
C/3
0.1194
m
00
SC P
0.0849
0.1554
0.2487
0.2488
o“
b
tf
b
a
a
see Foot note o f the Table 2.5
d.e.f.g see p o o t n o te 0 p t [ie ja jjje 2.6
O'
0.1554
(0
0.0858
b
0.1243
Parameter
•**
00
o
©
ahc
Experiment1
and PH, molecules (A)
a.
a<
ct
m
0.0834
of PH,
<*)
0.0829
Parameter
Mean Amplitudes
X
6on
8S800
T ab le.2.7
1
0.2399
0.1573
0.0867
0.0871
CEPA
0.24
0.1573
0.0867
0.0871
u
U
X
vn
a,
b
to.
2.14 Conclusion
The geometries of the PH3 and PH5 molecules are optimized at the SCF level
employing HF/3-21G, HF/3-21G* and HF/6-31G basis sets.
For both the molecules
inclusion of polarization functions shortens all the PH bonds and in the case of PH5,
the efect is well pronounced in apical bonds.
The apical bonds of PH5 are the
weakest bonds and in the reaction PH5 ----- » PH3 + H2 the (ee) abstraction of
concerted H2 which is WH allowed is much favoured [31].
In this reaction path,
detached PH3 becomes T-shaped and relaxes to a transition state of D3h structure.
From density functional theory, it was found that the hardness of the PH3 molecule
increases from the abstraction state to the D3h transition state.
Increasing hardness
accompanies the approach of a chemical system to equilibrium.
The PH3 molecule
has a maximum hardness of C3v symmetry which happens to be its state of equilibrium,
and for the PH5 molecule hardness is greater in the D3h structure than in the C4v
structure.
56
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58