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Conformational studies by far infrared and Raman spectra of gases
Journal of
Molecular Structure, 80 (1982)447-466 Amsterdam-Printed
ElsevierScientific PublishingCompany,
447 inThe Netherlands
CONFORMATIONALSTDDIES BY FAR INFRARED AND RAMAN SPECTRA OF GASES
J. R. DIJRIGand J. F. SULLIVAN Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208 (U.S.A.)
ABSTRACT One of the major goals of conformational analysis is the calculation of the energy difference between two or more conformers, AE, as well as the energy necessary for interconversion. The calculation of these energy quantities is facilitated by using a potential function which describes the vibrational motion, or internal rotation (torsion), as a function of the dihedral angle, (Y. The potential function is called asymmetric because both the frame and top portions of the molecule have no symmetry element higher than a plane. The most common type of potential function where at least one of the minima coincides with the plane of symmetry is of the type: V(o) = mi(l
- cos irr). The
kinetic energy term, F(o), is extremely complicated. In general, if the only data being used to calculate the potential function are torsional transitions, and if one continues within the boundary conditions of a
one-dimensional
problem, then a cosine expansion of F(a) should be adequate: F(o) = F. + EFi cos ia.
For those systems where there is an equilibrium between a planar
form and two non-planar forms, Vs is usually the predominant term. because Va
represents a
three maxima/three minima potential per 2n
This is (360°)
internal rotation. In a similar fashion, Ve is found to be the predominant term in the potential function for a system consisting of two equivalent non-planar conformers. Several examples of our most recent studies are given where the potential function for interconversionof two conformershas been determined.
INTRODUCTION One of the major goals of conformational analysis is the calculation of the energy difference between the two
conformers, AE, as well as the energy
necessary for interconversion. Once these data are available, calculation of is possible. The calculation of the thermodynamic functions, G, H, S and C P' these energy quantities is facilitated by using a potential function which describes the vibrational motion, or internal rotation (torsion), as a function 0022-2860/82/0000-0000/$02.750 1982 Elsevier Scientific Publishing
Company
448 of
the
both
dihedral
the
higher tion
a plane.
the
molecule
of
order
to
to
the
difference
as
since
the
is
called
asymmetric
because
molecule
have
no symmetry
element
illustrated
by
1-butene
CeH5,
and
where
the
lighter
the
frame
por-
top
portion
is
the
potential
types
of
have
most
the
and
the
angle
is
this
re-
enthalpy
is
one of
in molecular
accurate
of
directly
relative
since change
(4)
the
the
the
case
the
kinetic
observation
band
least
Cs
of
fact
(gauche) hybrid
give
whereas the
is
contours
of
sometimes
out-ofone,
When
this
only
arise
for
contours
to A- or C-type
Q-branches,
con-
is
conformers,
location it
or
usually
band
rise
has at the
torsion
out-of-plane. since
be
calculate
For
in-plane
no such problems
which
the
symmetry.
either
A/B/C
strong
studied
asymmetric
non-planar to
to
being
are
axis
should
necessary
the
arise,
allow
of the overlapping
data
principal
bands
In
center.
at
properties
molecule
problems
of
exhibit only
of
which
rise
summary, they
observed
However,
giving
and thus
because
of
observed.
In
as
has
symmetry
vibrations
contour,
is
In
desirable
on the
normal
along
present,
have no Q-branches
band center
(3)
common type
vibrations,
contours.
at
levels
approximate
molecular
which
the
B-type
torsion.
frequency
a bearing
change a
of
The most
symmetry
usually
asymmetric
the
four
(torsional)
energy
conformers,
angle;
consequences
fundamental band
(2)
function,
dihedral
torsional
function;
torsional
out-of-plane
dipole
is
of
low energy
potential
of
potential
approximate
minima;
and
conformation,
to
asysanetric the
number
high
the
they
Cs
corresponds torsional
an
frequencies.
planar
The
C-type
function of
moiety,
(1)
function.
with
plane.
are
of
important
one
metry
he
ethyl
the
the
function
potential
have
the
because number
a
mentioned
former
can
required:
transition
Several
least
is
defining
torsional
the
portions
This
between
constraints energy
The potential top
characterize
are
conformer,
lated
o.
the
group.
information each
and
than
the vinyl In
angle,
frame
B-type
or
Ci
sym-
for
the
contours bands
fundamental difficult
the A-
may
torsional to
find
the
of the hot bands.
THEORY A molecule its
overall
manifested
cipal
energy in
The
energy. tion
undergoing
in
the
of
the
of
in the
motion,
necessary
requirement
molecular
dynamics
molecular
molecule which
calculation for involved
the in
rotation
angle,
vibrational
the
inertia
torsional
internal
torsional
torsional
change
geometry
moments
as
hindered
as
energy
as well
CYchanges,
are
dependent
of
the
energy which upon
understanding
of
internal
overall
arises
from
turn In
the
potential the
bond
energy
as the
in
o.
asymmetric
a single This
CI, changes.
rotational
hindered
about
energy
rotation.
changes
change
molecular the
alters
altera-
the
analysis function
prinof is
restrictions The
is
theoretical
the a and
449
treatment used most often is a rigorous numerical method involving the calculation of torsional eigenfunctions and corresponding eigenvalues which are then iterated, in a least-squares manner, to give the best possible fit to the experimentally observed torsional transition frequencies (ref. 1). If the molecule is totally asymmetric, with no plane or rotational axis present in any conformer, then the potential function must be expressed as a Fourier series in both sine and cosine terms. A potential of this type results in all the minima and all the barriers being nonequivalent. Simpler potential functions result when both the asyrmsetrictop and the molecular frame have planes of symmetry. In these types of systems at least one value of 01results in the entire molecule having a plane of symmetry. A much more insignificant consequence of symmetry in these systems is that a rotation of +CY or -o away from the planar. configuration results in energetically indistinguishableconformations since the potential function itself now has a plane of symmetry. A Fourier series expansion in one term is now adequate to describe the potential function. The most common type of potential function, where at least one of the minima coincideswith a plane of symmetry, is of the type
V(u) = #ZVi(l - COB i
icr).
In general it has been found that a six term expansion in Vi is sufficient to handle almost any molecular system (ref. 1). This is because Vr, Vg, and V3 are in general larger than V,, Vs, and Vs; thus, terms greater than Vs should be negligible. The kinetic energy term, T(o), is extremely complicated. Several different approaches have been made to solve this expression using either ab-initio or semi-empirical quantum mechanical methods. In general, if the only data being used to calculate the potential function are torsional transitions, and if one continues within the boundary conditions of a one-dimensionalproblem, then the following treatment is
adequate.
Calculation of the kinetic energy term
requires evaluation of the internal rotation constant, F, commonly called the "F number," which is related to the reduced moment of inertia of the top, Ir, by
F = h/8n2cIr.
(2)
In order to determine the angular dependence of F(o), F is calculated at various values of a, the results of which are then curve fitted to a Fourier expansion in o via a least-squaresmethod:
F(o) = Fo + D?. cos icu. 1 i
(3)
450 The kinetic term, T(a), can now be written as
T(o) = PoF(cr)Po
(4)
where Po is the conjugate momentum operator given by
Po = -(l/i)(a/&).
The two Fourier expansions, one in F(o) and one in V(o), are now substituted into the Schradingerequation for the general
torsional Hamiltonian,
H,Y = ErY
(6)
where
HT= PoF(o!)Po+ V(o).
The solution to the SchrGdinger equation is obtained by solving the secular equation for the Hamiltonian matrix, to give both the torsional eigenvalues and eigenfunctions. In order to symmetrize the Hamiltonian matrix, Eq. 7 is rewritten using the definition of Pa: Hr = +[P,*F(cr)+ F(or)P,*l+ f(o) + V(u),
(8)
where the new variable, f(n), is assumed to be negligible since the angular dependence of F is very small. Once
these
substitutions have
been
completed, every
element
in
the
Hamiltonianmatrix is then set up using a free-rotorbasis set,
y
=
m
(*n)-‘leimQ , where m
= 0, fl, +2...
In the case of the cosine-basedpotential function, each eigenfunction is either symmetric or asymmetric with respect to rotation about CI = 0.
These eigen-
functions are more cormsonlydenoted as even (+) or odd (-) for symmetric and asymmetric reflection about CY = 0, respectively. To preserve these synsaetry properties, a Wang transformation is applied to the free-rotor basis functions (Eq. 9) to express them as cosine or sine functions of even or odd syssaetry, respectively:
Y
even
n
=7l
-+
cos
nQ
n = 1, 2...
(10)
451
(11) Yn'dd = n-' sin II@
n = 1, 2...
(12)
The Hamiltonian matrix elements derived using the syrmnetrybasis set (Eqs. lo-12), are divided into two blocks, even and odd. These matrix elements can be used to calculate the infrared intensity of a band due to a transition from one eigenvalue,v”,
to a higher level, v'. The relative intensity of this band is
-E"/kT -E'/kT = (E' - R") < v' ~M/v">~ (g"e I - g'e I, v" , v'
(13)
where E' and E" are the energies of the v' and v" levels, respectively, < v'IMI v" > is the dipole transition matrix element, and g' and g" are the degeneracies of the v' and v" levels, respectively. It should be pointed out that those intensities are relative, and hold only for transitions of the same conformer. The selection rules for infrared and Raman activity are:
Infrared Raman
+ CJ -
+ c-,+, - *
-,
RESULTS
Although our laboratory has been involved in studies of asynvsetricpotential functions for many years, only recently have we begun to study molecules whose potential functions may be very difficult to calculate, due to the heavier masses of the rotors and, in general, more complex spectra to analyze. The results of our most recent studies will now be presented in which the utility of both the far infrared spectral region and the Raman effect will be stressed. For a more complete review of asyrmuetricpotential functions, the interested reader should consult an article which has recently appeared (ref. 2).
Rotation about C-C (sp3 - sp3) bonds Theoretically, n-butane is an interesting compound because it is the simplest alkane with a possible equilibrium between low and high energy conformers. The conformations to be expected are s-trans and gauche, and in previous studies (refs. 3-6) it was concluded that the s-trans conformer is the predominant form near room temperature. Durig and Compton (ref. 7) recorded the far infrared and Raman spectrum of gaseous n-butane. They observed two strongly polarized lines at 116 and 107 cm-l in the Raman spectrum which could only be assigned to the asymmetric torsion of the gauche conformer (C, sysxaetry). The s-trans torsion
452 was expected to show sharp Q-branches in the infrared spectrum; however, only a broad, ill-defined band centered at 121 cm-l was observed. By using these three transitions and an assumed value of AR, they calculated the following potential coefficients: V, = 418 * 6, V, = 639 f 67 and Vs = 136 f 23 cm-l, and a value of 310 cm-l for AR.
Subsequent to this study, Compton et al. (ref. 8) re-
recorded the low frequency Raman spectrum with higher sensitivity. They were able to resolve four bands due to the gauche conformer and, additionally, they observed several bands between 260 and 210 cm-' of which four bands were assigned to the overtones of the asymmetric torsion of the s-trans conformer. From these data, potential coefficients of VI = 395 f 2, Vs = 1166 2 5, Vs = 26 + 1 and Vs = -34 f 2 cm-' were found. The resulting potential function has an enthalpy difference of 311 ? 10 cm-l and a gauche dihedral angle of 118 f 1". The main difference between these two most recent studies is in the value of Vs, which is not surprising since this coefficient is determined by the spacing of the gauche transitions.
Rotation about C-C (sp3 - sp*) bonds 1-Butene is the simplest alkene which exists as an equilibrium mixture of high and low energy conformers. Prior to our study of 1-butene (ref. 9), it had been established (ref. 10) that the stable conformers are s-cis and gauche, where the methyl group lies, respectively, eclipsing the double bond or skewed from this position by 120°, but the relative stabilities of these conformers was in doubt. Therefore we recorded (ref. 9) the low frequency Raman and far infrared spectra of gaseous 1-butene and observed a number of sharp bands below 200 cm-l. The series of bands observed in the Raman spectrum between 110 and 80 cm-' could only be assigned to the gauche conformer (C, symmetry) because these bands are polarized. Similarly, the s-cis asymmetric torsion should give rise to sharp Q-branches in the infrared spectrum because it is an out-of-plane vibration.
Therefore the series of six bands beginning at 154 cm-' were
assigned to the s-cis asymmetric torsion. Additionally, based on a variable temperature study of the Raman spectrum of the liquid, evidence was obtained that the s-cis conformer is more stable than the gauche, even though the latter predominates in concentration in all three phases (ref. 9). A total of twelve transitions arising from both the gauche and s-cis asymmetric torsions and an estimated value of 50 cm-' for AR were then used to calculate the potential coefficientslisted in Table 1. Similar to l-butene, the relative stability of the stable conformers of 2-methyl-1-butene (s-trans and gauche) had been in question (refs. 11-13). Therefore, we recorded (ref. 14) the low frequency vibrational spectrum of gaseous 2-methyl-1-butene. The far infrared spectrum was very rich with several
453 TABLE 1 Potential function coefficients (cm-l) for rotation about C-C (sp3 - sp2) bonds
no1.ecule
1-buteae 2-methyl-1-buteae 3-methyl-1-buteae propaaal 3-bromopropene 3-chloropropeae
Conformers Present Low High "1 Energy Energy C
g
-243
t t
g g
-129
C
g
g
C
C
g
292 -98
"2
"3
"4
185 921 165 79 1484 108 361 627 559 651 -105 -581 577 73 743 237
"5
"6
AR
-36 -76 26 -95 -29 61 30 145 -46 241 -69 272 -93 32
series of transitions occurring near 260, 230, 170, and 115 cm-l which could be assigned to both the asymmetric torsions of the two conformers and/or the methyl torsions. The Ramaa spectrum was far less complex with only two very weak lines observed near 115 cm-l and assigned to the single quantum transitions of the gauche asymmetric torsion based on the fact that the depolarized torsion of the traas conformer should not be observable. The two series of transitions near 260 and 170 cm-l were confidently assigned to the methyl torsions and thus only the series near 230 cm-' remained to be assigned. The two-quantum transitions of the gauche asymmetric torsion would be expected to begin near 234 cm-l or higher and therefore the transitions beginning at 231 cm-l and falling to successively lower frequencies were assigned to the two-quantum transitions of the s-traas asymmetric torsion. The results of the potential function calculation based on the more detailed assignment given in Ref. 14 are summarized in Table 1. A study of 3-methyl-l-butenehas also recently been completed by Durig and Gerson (ref. 15) in which transitions due to the high energy gauche asymmetric torsion were observed in the Ramaa spectrum, and Q-branches arising from a combination of a skeletal bend at 293 cm-l and the s-traaa asymmetric torsion at -100 cm-l were observed in the far infrared spectrum. Examination of the potential coefficients, listed in Table 1, shows that the values of VI through V3 are significant,as is Vs, and the Vs is approximatelytwice Vz. Contrary to the molecules previously discussed, all of the asymmetric torsional data for gaseous propanal (ref. 16) arose only from the far infrared spectrum which is shown in Fig. 1. The strong band at 271.5 cm-l had previously been assigned (refs. 17,18) to the s-cis in-plane bending mode ~15 whereas the s-cis asymmetric torsion ve4 was assigned (ref. 17) to an infrared absorption at 133 cm-l. These two bands were found to remain in the spectrum of the annealed solid phase (ref. 16). From Fig. 1, one can see that the asymmetric torsional mode at 133 cm-l is not one Q-branch, but a
series of Q-branches. The
appearance of these bands has a striking resemblance to those of the correspoad-
I
I
I
250 Fig. 1. 16).
(cm-‘)
I
100
Far infrared spectrum of gaseous propanal, used by permission (ref.
ing mode in s-cis 1-butene (ref. 9), although the presence of the carbonyl group in propanal enhances the intensity of these torsional bands markedly. As in the case of 1-butene, the observed bands do not follow the normal trend for the relative intensities expected from normal Boltzmann statistics, and very careful analysis was necessary in order to assign these bands to the correct torsional transitions. The observation of a number of weak, sharp bands, similar in frequency to the skeletal bending modes, enabled a definitive assignment to be made, since these bands turned out to be the two-quantum transitions (double jumps) of the asymmetric torsion. The complete assignment of the observed far infrared bands, excluding those bands which were assigned to the methyl torsional modes, is presented in Table 2.
The potential function coefficients
calculated from these observed transitions are listed in Table 1 and the potential function is shown in Fig. 2.
The poor fit of the s-cis 8 + 7 transition
results from the proximity of the eighth level to the barrier, being the last transition observed below the barrier.
Because of this, the level is very
sensitive to small changes in the potential function. A variety of structural and vibrational studies had previously been carried out for the identification of the rotational isomers of 3-bromopropene,but no attempt had been made to apply gas-phase Raman spectroscopy to locate the torsional transitions in order to determine the potential function governing the
455 motion between the cis and gauche conformers. Durig and Jalilian (ref. 19) recorded the Raman spectrum of gaseous 3-bromopropene and observed five polarized bands near 100 cm-l which arise from the gauche conformer (Ci symmetry). Additionally, a broad, depolarized band observed at 61 cm-' was assigned to the 1 + 0 asmetric
torsional transition of the cis conformer. These six known
frequencies were used to calculate the potential constants V, through Va, and with these data it was possible to fit two additional potential constants, V, and Vs, all of which are given in Table 1. TABLE 2 Observed far infrargd bands and proposed assignment for the asymmetric torsions of gaseous propanal
u(cm-l) 271.5 269.3 264.0 262.5 250.6 244.4 238.0 232.0 135.1 133.8 128.3 124.3 121.0 116.5 113.1 110.7 108.1 102.2 101.5
Rel Int.b
Assignment
vs S S S
m vw W
ObsCalc
skeletal bend, vi5 2+0 skeletal bend, vi5 3+1 4~2 5+3 6~4
-2.0c -7.1C -3.5c 3.6'
I+0 2+1 3+2 4-3 5+4 6+5 lfif oi 7+6 2f + li: 3- f 2+ 8~7
1.2 0.3 -2.6 -2.6 -0.1 3.2 -2.6 0.1 2.1 o.sc 6.8c
2.0c
VW vs
C
vs
C
VW
C
W
C
m
C
S
C
W
g
m
C
W
8
VW
g
VW
C
:Data taken from Ref. 16 Abbreviations used: v, very; s, strong; q, medium; w, weak 'Not used in the final fit
We are currently investigating the infrared and Raman spectra of gaseous 3-chloropropene and our preliminary findings indicate that the cis conformer is more stable than the gauche conformer. Four Q-branches in the 147 to 128 cm-l region of the far infrared spectrum have been assigned to the cis asymmetric torsion, and a band at 91 cm-l with two accompanying Q-branches in the Raman spectrum has been assigned to the gauche asysxaetrictorsion, based on the polarized nature of these lines. A potential function has been calculated, the results of which are presented in Table 1, but further studies are necessary in order to make definite conclusions about the most stable conformer of 3-chloropropene.
456
+I80 DIHEDRAL ANGLE Fig. 2. Torsional potential function, including observed energy levels, for the asymmetric torsion of propanal. The dihedral angle of zero corresponds to the s-cis conformer. The gauche levels shown are doubly degenerate, with the splittings between these levels too small to be apparent on the scale used. Used by permission (ref. 16).
Rotation about C-C (sp2 - sp*) bonds It has been known for a number of years that the halides of propenoic (acrylic) acid are anomalous among the substituted butadienes in that they possess only a small enthalpy difference between the high and low energy conformers, and therefore they have substantial concentrations of the high energy conformer present at normal temperatures. We studied the low frequency vibrational spectra of gaseous propenoyl fluoride and propenoyl chloride (ref. 20) in order to resolve the discrepancies among the reported values of the s-cis asymmetric torsions in these two compounds. A series of strong, sharp Q-branches was observed in the infrared spectrum of gaseous propenoyl fluoride beginning at 116.7 cm-l with successive transitions falling at lower frequencies. A much weaker series of bands starting at 101.5 cm-' with a smaller spacing was found upon closer examination of the spectra. In the Raman spectrum there appeared to be one band at 107 cm-' with two weaker wings at 120.5 and 88.5 cm-'; however, this observation did not coincide with the band centers found in the infrared spectrum. The Raman spectrum was hand-resolved into two overlapping bands, one
457 of which is similar in appearance to the one observed for 2-chlorobuta-1,3-diene (ref. 20). The minima of these Raman bands then approximately correspondedwith the torsional transitions observed in the infrared spectrum. The projected minimum of the torsion for the s-trans conformer is at 115 cm-l and corresponds with the second transition of the infrared series. The minimum of the Raman band for the torsion of the s-cis conformer is at 99 cm-l and in this case corresponds best to the third transition in the s-cis torsional series in the infrared spectrum. The apparent difference in the position of the Raman minima with respect to the infrared transitions is presumably due to the close spacing in the infrared series. The infrared spectrum of gaseous propenoyl chloride has a weak series of sharp transitions starting at 108.5 cm-l and progressing to lower frequency, with the second transition in the series being the most intense. In the Raman spectrum is a band that appears very much like the torsional mode observed in the spectrum of propenoyl fluoride. Treatment of this Raman band of propenoyl chloride also produced two "resolved" lines. The minimum of the first band at 106.5 cm-l corresponds to the second transition in the infrared spectrum, and is analogous to the case encountered with propenoyl fluoride. On the basis of this band resolution, a value of 80.5 cm-l was determined for the Raman line resulting from the torsional mode of the other conformer. This frequency was assigned to the third torsional transition of the s-cis conformer and is in agreement with the corresponding assignment for propenoyl fluoride. The asymmetric potential functions were then calculated for both propenoyl fluoride and propenoyl chloride, the results of which are presented in Table 3. The torsional potential functions of these two molecules are qualitatively similar in that the barriers to internal rotation of the s-trans conformers of the fluoride and chloride are 1925 and 1840 cm-l, respectively, which is only a small difference. The main difference between the two potential functions is that the calculated value of AH for the chloride, 615 f 60 cal/mol, is larger than the value of 99 f 15 cal/mol calculated for the fluoride. However, these two values are in good agreement with the respective values of -600 (ref. 21) and 90 f 100 cal/mol (ref. 22) calculated previously from data obtained by other techniques. Different structural and vibrational studies (refs. 23-25) including infrared, Raman and microwave spectroscopy have previously been carried out for the identification of the rotational isomers of methyl vinyl ketone, and a previous attempt to apply gas-phase infrared spectroscopy (ref. 26) to locate the torsional transitions, in order to determine the torsional potential function governing the
internal rotation between the conformers, was unsuccessful.
Therefore we undertook a careful examination of the far infrared spectrum of gaseous methyl vinyl ketone (ref. 27) in the region of 450 to 50 cm-' as shown
458 TABLE 3 Potential function coefficients (cm-l) for rotation about C-C (sp2 - sp2) bonds
Molecule
Conformers Present Low High Vl Energy Energy
propenoyl fluoride propenoyl chloride methyl vinyl ketone methacryloyl fluoride
t t
C
t
C
t
C
C
I
I
I
I
400
-108 96 180 257
300 WAVENUMBER
V2
V3
1859 168 1734 134 827 113 1582 173
V4
V5
-80 -16 -123 150 -
I I
200
V6
3 -
AB
36 215 280 430
I I
100
Cari’)
Fig. 3. Far infrared spectrum of gaseous methyl vinyl ketone, used by permission (ref. 27).
in Fig. 3.
Both the s-cis and s-trans conformers are of Cs symmetry and thus
the out-of-plane modes should give rise to C-type infrared band contours. Therefore the Q-branches observed at 116, 109 and 104 cm-l were assigned to the first three asymmetric torsional transitions of the s-trans conformer. The two remaining Q-branches at 87 and 84 cm-' were assigned to the 1 + 0 and 2 + 1 torsional transitions, respectively,of the s-cis conformer. The results of the asymmetricpotential function calculationare listed in Table 3.
459
The halides of acrylic and methacrylic acid are anomalous among the substituted butadienes in that they possess a relatively small enthalpy difference between the high and low energy conformers. Relatively few investigations of the rotational isomerism of methacryloyl fluoride, CH&(CHa)COF,
have been
reported; however, from a microwave study (ref. 28), evidence was presented that the molecule exists as a mixture of the two planar conformers, s-trans and s-cis, and the relatively high stability of the s-trans isomer was qualitatively established. Glebova and co-workers investigated the W
absorption spectrum
(ref. 29) and assigned a frequency of -80 cm-' to the s-trans asymmetric torsion and 59.3 cm-' to the torsion of the s-cis conformer. Additionally, from an infrared study of the gas (ref. 30), they determined AH to be 320 f 30 cm-'. We recorded the far infrared spectrum of gaseous methacryloyl fluoride (ref. 31), and a series of sharp Q-branches, indicative of C-type bands, beginning at 73.2 cm-' were attributed to the asynxaetrictorsions. The six Q-branches between 73.2 and 67.8 cm-l
were
assigned to the low energy conformer, s-trans, as
determined from the microwave investigation (ref. 28). The high energy, s-cis, asymmetric torsional series was then assigned to the three bands beginning at 55.6 cm-l and falling to successively lower frequencies. The potential function for the asymmetric torsion was calculated (see Fig. 4) using these eleven observed transitions. Our results (see Table 3) differ significantly from the results reported previously (refs. 29,30), particularly in the barrier to internal rotation of the s-trans conformer and the value of AH.
However we
believe our values are relatively accurate since eleven transitions were fit within 20.6 cm-'. The methacryloyl chloride molecule, CHx=C(CHa)COCl, has not been studied by rotational or vibrational methods; however, we are currently investigating the microwave and vibrational spectra of this molecule. From the microwave study, it is clear that the s-trans conformer predominates, but there are numerous additional lines which could not be fit to the s-tie conformer. Therefore, we believe that the gauche conformer, in which the COCl moiety is skewed out-ofplane, may be present at ambient temperature. We have also recorded the far infrared spectrum of gaseous methacryloyl chloride and have observed a series of transitions near 55 cm-' and another series near 45 cm-l. The calculation of the asyassetricpotential function is in progress, and it appears that the potential function will be based on the low energy trans form and two equivalent gauche forms. The presence of the gauche conformer is not surprising if one considers the steric hindrance present if a large chlorine atom lies cis to the methyl group.
460
1000
0 -180
+180 DIHEDRAL ANGLE
Fig. 4. Torsional potential function, including observed transitions, for the asymmetric torsion of methacryloyl fluoride. The dihedral angle of zero corresponds to the s-trans conformer.
Rotation about C-O, C-S, and C-R bonds Although from a microwave study (ref. 32) a complete structural determination was carried out for the s-trans conformer of ethylmethylether,no experimental evidence for the assumed high energy gauche conformer was found, and hence its structure was not determined. We therefore investigated the far infrared and Raman spectra of both gaseous ethylmethylether-doand ethylmethyl-da-ether(ref. 33).
In the Raman spectrum of the -do molecule, only a very weak, broad band
centered at -95 cm-l was observed. However, a series of Q-branches, starting at 115.4 cm-l in the -do molecule and 106.1 cm-i in the -da compound and moving to lower frequency, were observed in the far infrared spectra. The regularity of these series indicated that this asymmetric torsional mode acts as a reasonably harmonic oscillator and is not significantly coupled with other low frequency vibrations in.either isotope. Closer examination of the spectra revealed weak bands which did not fit these relatively "harmonic" series, and they were thus assigned as transitions in the gauche potential well. The more detailed assign-
461 ment is given in Ref. 33; the coefficients resulting from the calculated potential function are listed in Table 4. From the potential function shown in Fig. 5, minima are found at o = O" and +116“ representing the s-trans and gauche wells, respectively.
TABLE 4 Potential function coefficients (cm-') for rotation about C-O, C-S, and C-N bonds Conformers Present Low High Energy Energy
Molecule
ethylmethylether ethylmethyl-da-ether methylvinylether methyl-da-vinylether ethylmethylsulfide isopropylamine isopropylamine-de
t t
g g
C
g
c g t t
g t g g
"1
"2
"3
562 -26 897 535 887 -222 1073 1058 -413 1434 1177 -45 24 1230 65 30 979 31 188 863
"4 228 85
"5
"6
-25 -43
-5 -21 -91 -96 -125 -143 -27
AR 390 390 402 402 16 156 183
1500
-1
10
0
DIHEDRAL ANGLE
+180
Fig. 5. Torsional potential function, including observed energy levels, for the asynsaetrictorsion of ethylmethyl-ds-ether. The dihedral angle of zero corresponds to the s-trans conformer. Used by permission (ref. 33).
The conformational analysis of methylvinylether had been the subject of considerable controversy. Prior to our study of the low frequency vibrational
462 spectra been
of
gaseous
established
s-cis
conformation,
doubt.
The
owing 235
to
cm-r
series
small
isotopic
bands
analysis
transitions higher
the
227
series
at
doublets
starting
from
452
This
which
singly
Therefore
predicted.
the
the
exists
the
high
the
-do
of
as
of
the
36)
assigned
the
cm-l
and
falling
to
other cm-’
analysis
multiplets
we concluded
and,
variance
transitions that
additionally,
to
with
are
the the two
the
the
splitting
of
our
4 f
jump 2 and
potential
present,
well one
1
1 I
400
L I
300
1
200
100
WAVENUMBER Ccni’l) Fig. 6. vinylether
Far infrared spectra of gaseous methylvinylether (bottom), used by permission (ref. 34).
(top)
a
torsional
potential
series
of
a series
double
the
torsional s-cis
the
two tor-
However, of
in
compounds,
torsion
splitting
in
basis
and “heavy”
frequency.
in
there
the
On the
asymmetric lower
had
complicated
torsions
moiety, 6.
it
the planar remained
was very
“light”
significant
was at
34), in
conformer
methyl Fig.
indicated
showed
degenerate
in
the
(ref.
resolution
energy
and asysraetric
shown
spectra
(ref.
predominantly
molecule
methyl
deuteration
high
or
at
of
of
separated,
between
at
of
spectrum
upon
and co-workers
into
structure
well
shift
transitions.
function were
became
this
the molecule
frequencies
However,
starting
and methyl-ds-vinylether
that
the
of
similar
of
vibrations
but
region.
Shimanouchi
35)
analysis
the
sional
of
methylvinylether (ref.
and methyl-da-
463 of which is the basic torsional fundamental and the other being a "hot band" series of
this
fundamental with another fundamental, probably the methyl
torsion. The Raman spectra of gaseous methylvinylether -do and -dg were also recorded (Fig. 7) and polarized lines were observed at 144 and 138 cm-l,
Fig. 7. Raman spectra of gaseous methylvinylether (top) and methyl-ds-vinylether (bottom),used by permission (ref. 34).
respectively. This shift is too small to assign to the methyl torsion, and thus they were assigned to the asymmetric torsion of the high energy conformer, which must be the gauche conformer because of the polarized nature of the Raman lines. The asymmetric potential functions for both the -do and -d3 compounds were calculated, the results of which are presented in Table 4.
Minima in the cal-
culated potential function were found at a =O and 144O representing the s-cis and gauche torsional potential wells, respectively. The conformationalanalysis of
qethylvinyletherwas very complicated and therefore the reader should consult
Ref. 34 for a more complete explanation of the assignmentsand calculations. Similar to ethylmethylether, an equilibrium between s-trans and gauche conformers also exists for ethylmethylsulfide. We recorded the far infrared and Raman spectra of gaseous ethylmethylsulfideand observed a polarized Raman line at 92 cm-l and several strong Q-branches in the same region of the infrared spectrum (ref. 37).
This observation indicated that both conformers have
similar frequencies and is in agreement with normal coordinate calculations
464 (ref. 38) from which it was concluded that the torsions of the two conformers have nearly the same frequency. In the calculations of the asyaxaetric potential function, the three strongest bands at 90.8, 92.5 and 93.4 cm-l were assigned to the gauche conformer on the basis that this conformer should be present in a ratio of about 3:l. The remaining three bands at 91.3, 92.2 and 93.1 cm-l were then assigned to the s-trans conformer. The results of the calculation are given in Table 4.
Minima in the potential function were found at 0 and 2121"
representing the s-trans and gauche potential wells, respectively. It should be pointed out that a potential function was also calculated in which the reversed assignment was used, i.e., the s-trans torsional series beginning at 90.8 cm-l instead of 91.3 cm-l, but this calculation resulted in higher dispersions and a poorer fit of the data. A study of the low frequency vibrational spectrum of methylvinylsulfideis currently being conducted in our laboratory. We have recorded the far infrared spectrum of the vapor and observed several series of strong Q-branches. However, the spectrum is difficult to analyze due to the overlap of the cis methyl torsion and the cis asymmetric torsion in both the fundamental (-165 cm-r) and overtone (-335 cm-l) regions. We are currently preparing the deuterated analog, methyl-da-vinylether,in order to simplify the analysis of the conformational equilibrium in qethylvinylsulfide. We have recently reported (ref. 39) the complete vibrational spectra of isopropylamine-do and -dx. Gaseous phase band contour and depolarization data taken together showed that the s-trans conformer is the more stable. The far infrared spectra of both isotopic species were very rich, and torsional bands due to the asymmetric torsion were observed in both cases. The deuterium shift allowed the methyl and asyanaetrictorsions to be accurately assigned, and twoquantum transitions of the asymmetric torsions of both conformers were observed in the spectrum of the -dx compound. The s-trans asymmetric torsion of the -dp compound was assumed to be in Fermi resonance with a bending vibration because the observed series of transitions were somewhat irregular, but the torsions of the -do compound did not appear to be perturbed in the same manner. The large number of transitions observed in both the gauche and s-trans wells of the two compounds, as well as the observed -dp double jumps, allowed a high confidence in the potential functions. The results of these calculations are presented in Table 4.
The calculated value of AH (156 cm-') for isopropylamine-dowas found
to be substantially larger than that found experimentally (ref. 40) for the solution phase. Hydrogen bonding present in the solution was invoked to explain this result. Additionally, the two sets of potential coefficients as well as the values of All do differ between the -do and -da molecules, and is assumed to arise from a different amount of coupling between the asymmetric torsion and other vibrationalmodes.
465 CONCLUSIONS It is clear from the numerous studies discussed that the moat effective means of collecting and analyzing torsional data is the complementaryuse of infrared and Raman spectroscopy. When two or more conformers are present in appreciable quantities, it may be difficult to distinguish which Q-branch series should be assigned to which conformer. In many cases the Raman spectrum of the vapor can provide the depolarization data necessary for making the correct assignment. Additionally, for some molecules the asymmetric torsional overtones are observed in the Raman spectrum and from these data a check of the assignments made on the basis of infrared data can be made.
However, we have found that the far
infrared spectrum usually contains many more
transitions than the Raman
spectrum. In all of the studies discussed, little was mentioned about the coupling of the asynssetrictorsions with the methyl torsions or other low frequency modes. This effect is especially prevalent when the two torsional modes have similar vibrational frequencies, and deuteration of one top has the effect of altering the amount of coupling as well as the vibrational frequency. The selective deuteration of one part of the molecule often substantiallyalters the potential distribution of mixed modes, and thus results in different contributions from the asysssetrictorsion.
If torsional data can be obtained for a number of
isotopic species where such mixing occurs, it may be possible to estimate the effect on the asymnetricpotential function.
ACKNOWLEDGEMENT The authors gratefully acknowledge the financial support of these studies by the National Science Foundation through Grant CHE-79-20763.
RlmmiNCES
lJ.D. Lewis, T.B. Malloy, Jr., T.H. Chao and J. Laane, J. Mol. Struct., 12 (1972)427. 2 D.A.C. Compton, in J.R. Durig (Ed.), Vibrational Spectra and Structure,Vol. 9, Elsevier, Amsterdam, 1981, p.255. 3 G.J. Sxasx, N. Sheppard and D.H. Rank, J. Chem. Phys., 16(1948)704. 4 R.A. Bonham and L.S. Bartell, J. Am. Chem. Sot., 81(1959)3491. 5 K. Kuchitsu, Bull. Chem. Sot. Jpn., 39(1959)748. 6 W.F. Bradford, S. Fitzwater and L.S. Bartell, J. Mol. Struct., 38(1977)185. 7 J.R. Durig and D.A.C. Compton, J. Phys. Chem., 83(1979)265. 8 D.A.C. Compton, S. Montero and W.F. Murphy, J. Phys. Chem., 84(1980)3587. 9 J.R. Durig and D.A.C. Compton, J. Phys. Chem., 84(1980)773. 10 S. Kondo, E. Hirota and Y. Morino, J. Mol. Spectrosc.,28(1968)471. 11 T. Shimanouchi,Y. Abe and M. Mikami, Spectrochim.Acta, 24A(1968)1037. 12 J.W. deHaan, L.J.M. van de Van, A.R.N. Wilson, A.E. van der Hout-Ludder,C. Altona and D.H. Faber, Org. Magn. Reson., 8(1976)477. 13 T. Shimanouchi,Y. Abe and K. Kuchitsu, J. Mol. Struct., 2(1968)82. 14 J.R. Durig, D.J. Gerson and D.A.C. Compton, J. Phys. Chem., 84(1980)3554. 15 J.R. Durig and D.J. Gerson, J. Phys. Chem., 85(1981)426.
466 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
3.R. Durig, D.A.C. Compton and A.Q. McArver, J. Chem. Phys., 73(1980)719. S.G. Frankiss and W. Kynaston, Spectrochim.Acta, 28A(1972)2149. A. Chapput, B. Roussel and G. Fleury, J. Raman Spectrosc.,2(1974)117. J.R. Durig and M.R. Jalilian, .I.Phys. Chem., 84(1980)3543. J.R. Durig, J.S. Church and D.A.C. Compton, J. Chem. Phys., 71(1979)1175. J.E. Katon and W.R. Feairheller,J. Chem. Phys., 47(1967)1248. J.J. Keirns and R.F. Curl, Jr., J. Chem. Phys., 48(1968)3773. K. Noack and R.N. Jones, Can. J. Chem., 39(1961)2225. A. Krantz, T.D. Goldfarb and C.Y. Lin, J. Am. Chem. Sot., 94(1972)4022. P.D. Foster, V.M. Rao and R.F. Curl, Jr., J. Chem. Phys., 43(1965)1064. W.G. Fateley, R.K. Harris, F.A. Miller and R.E. Witkowshi, Spectrochim.Acta 214\(1965)231. J.R. Durig and T.S. Little, J. Chem. Phys., 75(1981)0000. R.G. Latypova, A.Kh. Mamleev, L.N. Gunderova and N-M. Posdeev, Zh. Strukt. Khim., 17(1976)849. L.A. Glebova, Yu.A. Peotin and V.I. Tyulin, Vestn. Mosk. Univ., Ser. 2: Khim., 34(1979)23. L.A. Glebova, A.V. Abramenkov,L.N. Margolin, A.A. Zenkin, Yu.A. Pentin and V.I. Tyulin, Zh. Strukt. Khim., 20(1979)1030. J.R. Durig, P.A. Brletic and J.S. Church, J. Chem. Phys., 76(1982)000. M. Hayashi and K. Kuwada, J. Mol. Struct., 28(1975)147. J.R. Durig and D.A.C. Compton, J. Chem. Phys., 69(1978)4713. J-R. Durig and D.A.C. Compton, J. Chem. Phys., 69(1978)2028. N.L. Gwen and N. Sheppard, Trans. Faraday Sot., 60(1964)634. M. Sakakibara,F. Inagaki, I. Harada and T. Shimanouchi,Bull. Chem. Sot. Jpn., 49(1976)46. J.R. Durig, D.A.C. Compton and M.R. Jalilian, J. Phys. Chem., 83(1979)511. M. Ohsaku, Y. Shiro and II.Murata, Bull. Chem. Sot. Jpn., 46(1973)1399. J.R. Durig, G.A. Guirgis and D.A.C. Compton, J. Phys. Chem., 83(1979)1313. P.J. Krueger and J. Jan, Can. J. Chem., 48(1970)3229.
Molecular Structure, 80 (1982)447-466 Amsterdam-Printed
ElsevierScientific PublishingCompany,
447 inThe Netherlands
CONFORMATIONALSTDDIES BY FAR INFRARED AND RAMAN SPECTRA OF GASES
J. R. DIJRIGand J. F. SULLIVAN Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208 (U.S.A.)
ABSTRACT One of the major goals of conformational analysis is the calculation of the energy difference between two or more conformers, AE, as well as the energy necessary for interconversion. The calculation of these energy quantities is facilitated by using a potential function which describes the vibrational motion, or internal rotation (torsion), as a function of the dihedral angle, (Y. The potential function is called asymmetric because both the frame and top portions of the molecule have no symmetry element higher than a plane. The most common type of potential function where at least one of the minima coincides with the plane of symmetry is of the type: V(o) = mi(l
- cos irr). The
kinetic energy term, F(o), is extremely complicated. In general, if the only data being used to calculate the potential function are torsional transitions, and if one continues within the boundary conditions of a
one-dimensional
problem, then a cosine expansion of F(a) should be adequate: F(o) = F. + EFi cos ia.
For those systems where there is an equilibrium between a planar
form and two non-planar forms, Vs is usually the predominant term. because Va
represents a
three maxima/three minima potential per 2n
This is (360°)
internal rotation. In a similar fashion, Ve is found to be the predominant term in the potential function for a system consisting of two equivalent non-planar conformers. Several examples of our most recent studies are given where the potential function for interconversionof two conformershas been determined.
INTRODUCTION One of the major goals of conformational analysis is the calculation of the energy difference between the two
conformers, AE, as well as the energy
necessary for interconversion. Once these data are available, calculation of is possible. The calculation of the thermodynamic functions, G, H, S and C P' these energy quantities is facilitated by using a potential function which describes the vibrational motion, or internal rotation (torsion), as a function 0022-2860/82/0000-0000/$02.750 1982 Elsevier Scientific Publishing
Company
448 of
the
both
dihedral
the
higher tion
a plane.
the
molecule
of
order
to
to
the
difference
as
since
the
is
called
asymmetric
because
molecule
have
no symmetry
element
illustrated
by
1-butene
CeH5,
and
where
the
lighter
the
frame
por-
top
portion
is
the
potential
types
of
have
most
the
and
the
angle
is
this
re-
enthalpy
is
one of
in molecular
accurate
of
directly
relative
since change
(4)
the
the
the
case
the
kinetic
observation
band
least
Cs
of
fact
(gauche) hybrid
give
whereas the
is
contours
of
sometimes
out-ofone,
When
this
only
arise
for
contours
to A- or C-type
Q-branches,
con-
is
conformers,
location it
or
usually
band
rise
has at the
torsion
out-of-plane. since
be
calculate
For
in-plane
no such problems
which
the
symmetry.
either
A/B/C
strong
studied
asymmetric
non-planar to
to
being
are
axis
should
necessary
the
arise,
allow
of the overlapping
data
principal
bands
In
center.
at
properties
molecule
problems
of
exhibit only
of
which
rise
summary, they
observed
However,
giving
and thus
because
of
observed.
In
as
has
symmetry
vibrations
contour,
is
In
desirable
on the
normal
along
present,
have no Q-branches
band center
(3)
common type
vibrations,
contours.
at
levels
approximate
molecular
which
the
B-type
torsion.
frequency
a bearing
change a
of
The most
symmetry
usually
asymmetric
the
four
(torsional)
energy
conformers,
angle;
consequences
fundamental band
(2)
function,
dihedral
torsional
function;
torsional
out-of-plane
dipole
is
of
low energy
potential
of
potential
approximate
minima;
and
conformation,
to
asysanetric the
number
high
the
they
Cs
corresponds torsional
an
frequencies.
planar
The
C-type
function of
moiety,
(1)
function.
with
plane.
are
of
important
one
metry
he
ethyl
the
the
function
potential
have
the
because number
a
mentioned
former
can
required:
transition
Several
least
is
defining
torsional
the
portions
This
between
constraints energy
The potential top
characterize
are
conformer,
lated
o.
the
group.
information each
and
than
the vinyl In
angle,
frame
B-type
or
Ci
sym-
for
the
contours bands
fundamental difficult
the A-
may
torsional to
find
the
of the hot bands.
THEORY A molecule its
overall
manifested
cipal
energy in
The
energy. tion
undergoing
in
the
of
the
of
in the
motion,
necessary
requirement
molecular
dynamics
molecular
molecule which
calculation for involved
the in
rotation
angle,
vibrational
the
inertia
torsional
internal
torsional
torsional
change
geometry
moments
as
hindered
as
energy
as well
CYchanges,
are
dependent
of
the
energy which upon
understanding
of
internal
overall
arises
from
turn In
the
potential the
bond
energy
as the
in
o.
asymmetric
a single This
CI, changes.
rotational
hindered
about
energy
rotation.
changes
change
molecular the
alters
altera-
the
analysis function
prinof is
restrictions The
is
theoretical
the a and
449
treatment used most often is a rigorous numerical method involving the calculation of torsional eigenfunctions and corresponding eigenvalues which are then iterated, in a least-squares manner, to give the best possible fit to the experimentally observed torsional transition frequencies (ref. 1). If the molecule is totally asymmetric, with no plane or rotational axis present in any conformer, then the potential function must be expressed as a Fourier series in both sine and cosine terms. A potential of this type results in all the minima and all the barriers being nonequivalent. Simpler potential functions result when both the asyrmsetrictop and the molecular frame have planes of symmetry. In these types of systems at least one value of 01results in the entire molecule having a plane of symmetry. A much more insignificant consequence of symmetry in these systems is that a rotation of +CY or -o away from the planar. configuration results in energetically indistinguishableconformations since the potential function itself now has a plane of symmetry. A Fourier series expansion in one term is now adequate to describe the potential function. The most common type of potential function, where at least one of the minima coincideswith a plane of symmetry, is of the type
V(u) = #ZVi(l - COB i
icr).
In general it has been found that a six term expansion in Vi is sufficient to handle almost any molecular system (ref. 1). This is because Vr, Vg, and V3 are in general larger than V,, Vs, and Vs; thus, terms greater than Vs should be negligible. The kinetic energy term, T(o), is extremely complicated. Several different approaches have been made to solve this expression using either ab-initio or semi-empirical quantum mechanical methods. In general, if the only data being used to calculate the potential function are torsional transitions, and if one continues within the boundary conditions of a one-dimensionalproblem, then the following treatment is
adequate.
Calculation of the kinetic energy term
requires evaluation of the internal rotation constant, F, commonly called the "F number," which is related to the reduced moment of inertia of the top, Ir, by
F = h/8n2cIr.
(2)
In order to determine the angular dependence of F(o), F is calculated at various values of a, the results of which are then curve fitted to a Fourier expansion in o via a least-squaresmethod:
F(o) = Fo + D?. cos icu. 1 i
(3)
450 The kinetic term, T(a), can now be written as
T(o) = PoF(cr)Po
(4)
where Po is the conjugate momentum operator given by
Po = -(l/i)(a/&).
The two Fourier expansions, one in F(o) and one in V(o), are now substituted into the Schradingerequation for the general
torsional Hamiltonian,
H,Y = ErY
(6)
where
HT= PoF(o!)Po+ V(o).
The solution to the SchrGdinger equation is obtained by solving the secular equation for the Hamiltonian matrix, to give both the torsional eigenvalues and eigenfunctions. In order to symmetrize the Hamiltonian matrix, Eq. 7 is rewritten using the definition of Pa: Hr = +[P,*F(cr)+ F(or)P,*l+ f(o) + V(u),
(8)
where the new variable, f(n), is assumed to be negligible since the angular dependence of F is very small. Once
these
substitutions have
been
completed, every
element
in
the
Hamiltonianmatrix is then set up using a free-rotorbasis set,
y
=
m
(*n)-‘leimQ , where m
= 0, fl, +2...
In the case of the cosine-basedpotential function, each eigenfunction is either symmetric or asymmetric with respect to rotation about CI = 0.
These eigen-
functions are more cormsonlydenoted as even (+) or odd (-) for symmetric and asymmetric reflection about CY = 0, respectively. To preserve these synsaetry properties, a Wang transformation is applied to the free-rotor basis functions (Eq. 9) to express them as cosine or sine functions of even or odd syssaetry, respectively:
Y
even
n
=7l
-+
cos
nQ
n = 1, 2...
(10)
451
(11) Yn'dd = n-' sin II@
n = 1, 2...
(12)
The Hamiltonian matrix elements derived using the syrmnetrybasis set (Eqs. lo-12), are divided into two blocks, even and odd. These matrix elements can be used to calculate the infrared intensity of a band due to a transition from one eigenvalue,v”,
to a higher level, v'. The relative intensity of this band is
-E"/kT -E'/kT = (E' - R") < v' ~M/v">~ (g"e I - g'e I, v" , v'
(13)
where E' and E" are the energies of the v' and v" levels, respectively, < v'IMI v" > is the dipole transition matrix element, and g' and g" are the degeneracies of the v' and v" levels, respectively. It should be pointed out that those intensities are relative, and hold only for transitions of the same conformer. The selection rules for infrared and Raman activity are:
Infrared Raman
+ CJ -
+ c-,+, - *
-,
RESULTS
Although our laboratory has been involved in studies of asynvsetricpotential functions for many years, only recently have we begun to study molecules whose potential functions may be very difficult to calculate, due to the heavier masses of the rotors and, in general, more complex spectra to analyze. The results of our most recent studies will now be presented in which the utility of both the far infrared spectral region and the Raman effect will be stressed. For a more complete review of asyrmuetricpotential functions, the interested reader should consult an article which has recently appeared (ref. 2).
Rotation about C-C (sp3 - sp3) bonds Theoretically, n-butane is an interesting compound because it is the simplest alkane with a possible equilibrium between low and high energy conformers. The conformations to be expected are s-trans and gauche, and in previous studies (refs. 3-6) it was concluded that the s-trans conformer is the predominant form near room temperature. Durig and Compton (ref. 7) recorded the far infrared and Raman spectrum of gaseous n-butane. They observed two strongly polarized lines at 116 and 107 cm-l in the Raman spectrum which could only be assigned to the asymmetric torsion of the gauche conformer (C, sysxaetry). The s-trans torsion
452 was expected to show sharp Q-branches in the infrared spectrum; however, only a broad, ill-defined band centered at 121 cm-l was observed. By using these three transitions and an assumed value of AR, they calculated the following potential coefficients: V, = 418 * 6, V, = 639 f 67 and Vs = 136 f 23 cm-l, and a value of 310 cm-l for AR.
Subsequent to this study, Compton et al. (ref. 8) re-
recorded the low frequency Raman spectrum with higher sensitivity. They were able to resolve four bands due to the gauche conformer and, additionally, they observed several bands between 260 and 210 cm-' of which four bands were assigned to the overtones of the asymmetric torsion of the s-trans conformer. From these data, potential coefficients of VI = 395 f 2, Vs = 1166 2 5, Vs = 26 + 1 and Vs = -34 f 2 cm-' were found. The resulting potential function has an enthalpy difference of 311 ? 10 cm-l and a gauche dihedral angle of 118 f 1". The main difference between these two most recent studies is in the value of Vs, which is not surprising since this coefficient is determined by the spacing of the gauche transitions.
Rotation about C-C (sp3 - sp*) bonds 1-Butene is the simplest alkene which exists as an equilibrium mixture of high and low energy conformers. Prior to our study of 1-butene (ref. 9), it had been established (ref. 10) that the stable conformers are s-cis and gauche, where the methyl group lies, respectively, eclipsing the double bond or skewed from this position by 120°, but the relative stabilities of these conformers was in doubt. Therefore we recorded (ref. 9) the low frequency Raman and far infrared spectra of gaseous 1-butene and observed a number of sharp bands below 200 cm-l. The series of bands observed in the Raman spectrum between 110 and 80 cm-' could only be assigned to the gauche conformer (C, symmetry) because these bands are polarized. Similarly, the s-cis asymmetric torsion should give rise to sharp Q-branches in the infrared spectrum because it is an out-of-plane vibration.
Therefore the series of six bands beginning at 154 cm-' were
assigned to the s-cis asymmetric torsion. Additionally, based on a variable temperature study of the Raman spectrum of the liquid, evidence was obtained that the s-cis conformer is more stable than the gauche, even though the latter predominates in concentration in all three phases (ref. 9). A total of twelve transitions arising from both the gauche and s-cis asymmetric torsions and an estimated value of 50 cm-' for AR were then used to calculate the potential coefficientslisted in Table 1. Similar to l-butene, the relative stability of the stable conformers of 2-methyl-1-butene (s-trans and gauche) had been in question (refs. 11-13). Therefore, we recorded (ref. 14) the low frequency vibrational spectrum of gaseous 2-methyl-1-butene. The far infrared spectrum was very rich with several
453 TABLE 1 Potential function coefficients (cm-l) for rotation about C-C (sp3 - sp2) bonds
no1.ecule
1-buteae 2-methyl-1-buteae 3-methyl-1-buteae propaaal 3-bromopropene 3-chloropropeae
Conformers Present Low High "1 Energy Energy C
g
-243
t t
g g
-129
C
g
g
C
C
g
292 -98
"2
"3
"4
185 921 165 79 1484 108 361 627 559 651 -105 -581 577 73 743 237
"5
"6
AR
-36 -76 26 -95 -29 61 30 145 -46 241 -69 272 -93 32
series of transitions occurring near 260, 230, 170, and 115 cm-l which could be assigned to both the asymmetric torsions of the two conformers and/or the methyl torsions. The Ramaa spectrum was far less complex with only two very weak lines observed near 115 cm-l and assigned to the single quantum transitions of the gauche asymmetric torsion based on the fact that the depolarized torsion of the traas conformer should not be observable. The two series of transitions near 260 and 170 cm-l were confidently assigned to the methyl torsions and thus only the series near 230 cm-' remained to be assigned. The two-quantum transitions of the gauche asymmetric torsion would be expected to begin near 234 cm-l or higher and therefore the transitions beginning at 231 cm-l and falling to successively lower frequencies were assigned to the two-quantum transitions of the s-traas asymmetric torsion. The results of the potential function calculation based on the more detailed assignment given in Ref. 14 are summarized in Table 1. A study of 3-methyl-l-butenehas also recently been completed by Durig and Gerson (ref. 15) in which transitions due to the high energy gauche asymmetric torsion were observed in the Ramaa spectrum, and Q-branches arising from a combination of a skeletal bend at 293 cm-l and the s-traaa asymmetric torsion at -100 cm-l were observed in the far infrared spectrum. Examination of the potential coefficients, listed in Table 1, shows that the values of VI through V3 are significant,as is Vs, and the Vs is approximatelytwice Vz. Contrary to the molecules previously discussed, all of the asymmetric torsional data for gaseous propanal (ref. 16) arose only from the far infrared spectrum which is shown in Fig. 1. The strong band at 271.5 cm-l had previously been assigned (refs. 17,18) to the s-cis in-plane bending mode ~15 whereas the s-cis asymmetric torsion ve4 was assigned (ref. 17) to an infrared absorption at 133 cm-l. These two bands were found to remain in the spectrum of the annealed solid phase (ref. 16). From Fig. 1, one can see that the asymmetric torsional mode at 133 cm-l is not one Q-branch, but a
series of Q-branches. The
appearance of these bands has a striking resemblance to those of the correspoad-
I
I
I
250 Fig. 1. 16).
(cm-‘)
I
100
Far infrared spectrum of gaseous propanal, used by permission (ref.
ing mode in s-cis 1-butene (ref. 9), although the presence of the carbonyl group in propanal enhances the intensity of these torsional bands markedly. As in the case of 1-butene, the observed bands do not follow the normal trend for the relative intensities expected from normal Boltzmann statistics, and very careful analysis was necessary in order to assign these bands to the correct torsional transitions. The observation of a number of weak, sharp bands, similar in frequency to the skeletal bending modes, enabled a definitive assignment to be made, since these bands turned out to be the two-quantum transitions (double jumps) of the asymmetric torsion. The complete assignment of the observed far infrared bands, excluding those bands which were assigned to the methyl torsional modes, is presented in Table 2.
The potential function coefficients
calculated from these observed transitions are listed in Table 1 and the potential function is shown in Fig. 2.
The poor fit of the s-cis 8 + 7 transition
results from the proximity of the eighth level to the barrier, being the last transition observed below the barrier.
Because of this, the level is very
sensitive to small changes in the potential function. A variety of structural and vibrational studies had previously been carried out for the identification of the rotational isomers of 3-bromopropene,but no attempt had been made to apply gas-phase Raman spectroscopy to locate the torsional transitions in order to determine the potential function governing the
455 motion between the cis and gauche conformers. Durig and Jalilian (ref. 19) recorded the Raman spectrum of gaseous 3-bromopropene and observed five polarized bands near 100 cm-l which arise from the gauche conformer (Ci symmetry). Additionally, a broad, depolarized band observed at 61 cm-' was assigned to the 1 + 0 asmetric
torsional transition of the cis conformer. These six known
frequencies were used to calculate the potential constants V, through Va, and with these data it was possible to fit two additional potential constants, V, and Vs, all of which are given in Table 1. TABLE 2 Observed far infrargd bands and proposed assignment for the asymmetric torsions of gaseous propanal
u(cm-l) 271.5 269.3 264.0 262.5 250.6 244.4 238.0 232.0 135.1 133.8 128.3 124.3 121.0 116.5 113.1 110.7 108.1 102.2 101.5
Rel Int.b
Assignment
vs S S S
m vw W
ObsCalc
skeletal bend, vi5 2+0 skeletal bend, vi5 3+1 4~2 5+3 6~4
-2.0c -7.1C -3.5c 3.6'
I+0 2+1 3+2 4-3 5+4 6+5 lfif oi 7+6 2f + li: 3- f 2+ 8~7
1.2 0.3 -2.6 -2.6 -0.1 3.2 -2.6 0.1 2.1 o.sc 6.8c
2.0c
VW vs
C
vs
C
VW
C
W
C
m
C
S
C
W
g
m
C
W
8
VW
g
VW
C
:Data taken from Ref. 16 Abbreviations used: v, very; s, strong; q, medium; w, weak 'Not used in the final fit
We are currently investigating the infrared and Raman spectra of gaseous 3-chloropropene and our preliminary findings indicate that the cis conformer is more stable than the gauche conformer. Four Q-branches in the 147 to 128 cm-l region of the far infrared spectrum have been assigned to the cis asymmetric torsion, and a band at 91 cm-l with two accompanying Q-branches in the Raman spectrum has been assigned to the gauche asysxaetrictorsion, based on the polarized nature of these lines. A potential function has been calculated, the results of which are presented in Table 1, but further studies are necessary in order to make definite conclusions about the most stable conformer of 3-chloropropene.
456
+I80 DIHEDRAL ANGLE Fig. 2. Torsional potential function, including observed energy levels, for the asymmetric torsion of propanal. The dihedral angle of zero corresponds to the s-cis conformer. The gauche levels shown are doubly degenerate, with the splittings between these levels too small to be apparent on the scale used. Used by permission (ref. 16).
Rotation about C-C (sp2 - sp*) bonds It has been known for a number of years that the halides of propenoic (acrylic) acid are anomalous among the substituted butadienes in that they possess only a small enthalpy difference between the high and low energy conformers, and therefore they have substantial concentrations of the high energy conformer present at normal temperatures. We studied the low frequency vibrational spectra of gaseous propenoyl fluoride and propenoyl chloride (ref. 20) in order to resolve the discrepancies among the reported values of the s-cis asymmetric torsions in these two compounds. A series of strong, sharp Q-branches was observed in the infrared spectrum of gaseous propenoyl fluoride beginning at 116.7 cm-l with successive transitions falling at lower frequencies. A much weaker series of bands starting at 101.5 cm-' with a smaller spacing was found upon closer examination of the spectra. In the Raman spectrum there appeared to be one band at 107 cm-' with two weaker wings at 120.5 and 88.5 cm-'; however, this observation did not coincide with the band centers found in the infrared spectrum. The Raman spectrum was hand-resolved into two overlapping bands, one
457 of which is similar in appearance to the one observed for 2-chlorobuta-1,3-diene (ref. 20). The minima of these Raman bands then approximately correspondedwith the torsional transitions observed in the infrared spectrum. The projected minimum of the torsion for the s-trans conformer is at 115 cm-l and corresponds with the second transition of the infrared series. The minimum of the Raman band for the torsion of the s-cis conformer is at 99 cm-l and in this case corresponds best to the third transition in the s-cis torsional series in the infrared spectrum. The apparent difference in the position of the Raman minima with respect to the infrared transitions is presumably due to the close spacing in the infrared series. The infrared spectrum of gaseous propenoyl chloride has a weak series of sharp transitions starting at 108.5 cm-l and progressing to lower frequency, with the second transition in the series being the most intense. In the Raman spectrum is a band that appears very much like the torsional mode observed in the spectrum of propenoyl fluoride. Treatment of this Raman band of propenoyl chloride also produced two "resolved" lines. The minimum of the first band at 106.5 cm-l corresponds to the second transition in the infrared spectrum, and is analogous to the case encountered with propenoyl fluoride. On the basis of this band resolution, a value of 80.5 cm-l was determined for the Raman line resulting from the torsional mode of the other conformer. This frequency was assigned to the third torsional transition of the s-cis conformer and is in agreement with the corresponding assignment for propenoyl fluoride. The asymmetric potential functions were then calculated for both propenoyl fluoride and propenoyl chloride, the results of which are presented in Table 3. The torsional potential functions of these two molecules are qualitatively similar in that the barriers to internal rotation of the s-trans conformers of the fluoride and chloride are 1925 and 1840 cm-l, respectively, which is only a small difference. The main difference between the two potential functions is that the calculated value of AH for the chloride, 615 f 60 cal/mol, is larger than the value of 99 f 15 cal/mol calculated for the fluoride. However, these two values are in good agreement with the respective values of -600 (ref. 21) and 90 f 100 cal/mol (ref. 22) calculated previously from data obtained by other techniques. Different structural and vibrational studies (refs. 23-25) including infrared, Raman and microwave spectroscopy have previously been carried out for the identification of the rotational isomers of methyl vinyl ketone, and a previous attempt to apply gas-phase infrared spectroscopy (ref. 26) to locate the torsional transitions, in order to determine the torsional potential function governing the
internal rotation between the conformers, was unsuccessful.
Therefore we undertook a careful examination of the far infrared spectrum of gaseous methyl vinyl ketone (ref. 27) in the region of 450 to 50 cm-' as shown
458 TABLE 3 Potential function coefficients (cm-l) for rotation about C-C (sp2 - sp2) bonds
Molecule
Conformers Present Low High Vl Energy Energy
propenoyl fluoride propenoyl chloride methyl vinyl ketone methacryloyl fluoride
t t
C
t
C
t
C
C
I
I
I
I
400
-108 96 180 257
300 WAVENUMBER
V2
V3
1859 168 1734 134 827 113 1582 173
V4
V5
-80 -16 -123 150 -
I I
200
V6
3 -
AB
36 215 280 430
I I
100
Cari’)
Fig. 3. Far infrared spectrum of gaseous methyl vinyl ketone, used by permission (ref. 27).
in Fig. 3.
Both the s-cis and s-trans conformers are of Cs symmetry and thus
the out-of-plane modes should give rise to C-type infrared band contours. Therefore the Q-branches observed at 116, 109 and 104 cm-l were assigned to the first three asymmetric torsional transitions of the s-trans conformer. The two remaining Q-branches at 87 and 84 cm-' were assigned to the 1 + 0 and 2 + 1 torsional transitions, respectively,of the s-cis conformer. The results of the asymmetricpotential function calculationare listed in Table 3.
459
The halides of acrylic and methacrylic acid are anomalous among the substituted butadienes in that they possess a relatively small enthalpy difference between the high and low energy conformers. Relatively few investigations of the rotational isomerism of methacryloyl fluoride, CH&(CHa)COF,
have been
reported; however, from a microwave study (ref. 28), evidence was presented that the molecule exists as a mixture of the two planar conformers, s-trans and s-cis, and the relatively high stability of the s-trans isomer was qualitatively established. Glebova and co-workers investigated the W
absorption spectrum
(ref. 29) and assigned a frequency of -80 cm-' to the s-trans asymmetric torsion and 59.3 cm-' to the torsion of the s-cis conformer. Additionally, from an infrared study of the gas (ref. 30), they determined AH to be 320 f 30 cm-'. We recorded the far infrared spectrum of gaseous methacryloyl fluoride (ref. 31), and a series of sharp Q-branches, indicative of C-type bands, beginning at 73.2 cm-' were attributed to the asynxaetrictorsions. The six Q-branches between 73.2 and 67.8 cm-l
were
assigned to the low energy conformer, s-trans, as
determined from the microwave investigation (ref. 28). The high energy, s-cis, asymmetric torsional series was then assigned to the three bands beginning at 55.6 cm-l and falling to successively lower frequencies. The potential function for the asymmetric torsion was calculated (see Fig. 4) using these eleven observed transitions. Our results (see Table 3) differ significantly from the results reported previously (refs. 29,30), particularly in the barrier to internal rotation of the s-trans conformer and the value of AH.
However we
believe our values are relatively accurate since eleven transitions were fit within 20.6 cm-'. The methacryloyl chloride molecule, CHx=C(CHa)COCl, has not been studied by rotational or vibrational methods; however, we are currently investigating the microwave and vibrational spectra of this molecule. From the microwave study, it is clear that the s-trans conformer predominates, but there are numerous additional lines which could not be fit to the s-tie conformer. Therefore, we believe that the gauche conformer, in which the COCl moiety is skewed out-ofplane, may be present at ambient temperature. We have also recorded the far infrared spectrum of gaseous methacryloyl chloride and have observed a series of transitions near 55 cm-' and another series near 45 cm-l. The calculation of the asyassetricpotential function is in progress, and it appears that the potential function will be based on the low energy trans form and two equivalent gauche forms. The presence of the gauche conformer is not surprising if one considers the steric hindrance present if a large chlorine atom lies cis to the methyl group.
460
1000
0 -180
+180 DIHEDRAL ANGLE
Fig. 4. Torsional potential function, including observed transitions, for the asymmetric torsion of methacryloyl fluoride. The dihedral angle of zero corresponds to the s-trans conformer.
Rotation about C-O, C-S, and C-R bonds Although from a microwave study (ref. 32) a complete structural determination was carried out for the s-trans conformer of ethylmethylether,no experimental evidence for the assumed high energy gauche conformer was found, and hence its structure was not determined. We therefore investigated the far infrared and Raman spectra of both gaseous ethylmethylether-doand ethylmethyl-da-ether(ref. 33).
In the Raman spectrum of the -do molecule, only a very weak, broad band
centered at -95 cm-l was observed. However, a series of Q-branches, starting at 115.4 cm-l in the -do molecule and 106.1 cm-i in the -da compound and moving to lower frequency, were observed in the far infrared spectra. The regularity of these series indicated that this asymmetric torsional mode acts as a reasonably harmonic oscillator and is not significantly coupled with other low frequency vibrations in.either isotope. Closer examination of the spectra revealed weak bands which did not fit these relatively "harmonic" series, and they were thus assigned as transitions in the gauche potential well. The more detailed assign-
461 ment is given in Ref. 33; the coefficients resulting from the calculated potential function are listed in Table 4. From the potential function shown in Fig. 5, minima are found at o = O" and +116“ representing the s-trans and gauche wells, respectively.
TABLE 4 Potential function coefficients (cm-') for rotation about C-O, C-S, and C-N bonds Conformers Present Low High Energy Energy
Molecule
ethylmethylether ethylmethyl-da-ether methylvinylether methyl-da-vinylether ethylmethylsulfide isopropylamine isopropylamine-de
t t
g g
C
g
c g t t
g t g g
"1
"2
"3
562 -26 897 535 887 -222 1073 1058 -413 1434 1177 -45 24 1230 65 30 979 31 188 863
"4 228 85
"5
"6
-25 -43
-5 -21 -91 -96 -125 -143 -27
AR 390 390 402 402 16 156 183
1500
-1
10
0
DIHEDRAL ANGLE
+180
Fig. 5. Torsional potential function, including observed energy levels, for the asynsaetrictorsion of ethylmethyl-ds-ether. The dihedral angle of zero corresponds to the s-trans conformer. Used by permission (ref. 33).
The conformational analysis of methylvinylether had been the subject of considerable controversy. Prior to our study of the low frequency vibrational
462 spectra been
of
gaseous
established
s-cis
conformation,
doubt.
The
owing 235
to
cm-r
series
small
isotopic
bands
analysis
transitions higher
the
227
series
at
doublets
starting
from
452
This
which
singly
Therefore
predicted.
the
the
exists
the
high
the
-do
of
as
of
the
36)
assigned
the
cm-l
and
falling
to
other cm-’
analysis
multiplets
we concluded
and,
variance
transitions that
additionally,
to
with
are
the the two
the
the
splitting
of
our
4 f
jump 2 and
potential
present,
well one
1
1 I
400
L I
300
1
200
100
WAVENUMBER Ccni’l) Fig. 6. vinylether
Far infrared spectra of gaseous methylvinylether (bottom), used by permission (ref. 34).
(top)
a
torsional
potential
series
of
a series
double
the
torsional s-cis
the
two tor-
However, of
in
compounds,
torsion
splitting
in
basis
and “heavy”
frequency.
in
there
the
On the
asymmetric lower
had
complicated
torsions
moiety, 6.
it
the planar remained
was very
“light”
significant
was at
34), in
conformer
methyl Fig.
indicated
showed
degenerate
in
the
(ref.
resolution
energy
and asysraetric
shown
spectra
(ref.
predominantly
molecule
methyl
deuteration
high
or
at
of
of
separated,
between
at
of
spectrum
upon
and co-workers
into
structure
well
shift
transitions.
function were
became
this
the molecule
frequencies
However,
starting
and methyl-ds-vinylether
that
the
of
similar
of
vibrations
but
region.
Shimanouchi
35)
analysis
the
sional
of
methylvinylether (ref.
and methyl-da-
463 of which is the basic torsional fundamental and the other being a "hot band" series of
this
fundamental with another fundamental, probably the methyl
torsion. The Raman spectra of gaseous methylvinylether -do and -dg were also recorded (Fig. 7) and polarized lines were observed at 144 and 138 cm-l,
Fig. 7. Raman spectra of gaseous methylvinylether (top) and methyl-ds-vinylether (bottom),used by permission (ref. 34).
respectively. This shift is too small to assign to the methyl torsion, and thus they were assigned to the asymmetric torsion of the high energy conformer, which must be the gauche conformer because of the polarized nature of the Raman lines. The asymmetric potential functions for both the -do and -d3 compounds were calculated, the results of which are presented in Table 4.
Minima in the cal-
culated potential function were found at a =O and 144O representing the s-cis and gauche torsional potential wells, respectively. The conformationalanalysis of
qethylvinyletherwas very complicated and therefore the reader should consult
Ref. 34 for a more complete explanation of the assignmentsand calculations. Similar to ethylmethylether, an equilibrium between s-trans and gauche conformers also exists for ethylmethylsulfide. We recorded the far infrared and Raman spectra of gaseous ethylmethylsulfideand observed a polarized Raman line at 92 cm-l and several strong Q-branches in the same region of the infrared spectrum (ref. 37).
This observation indicated that both conformers have
similar frequencies and is in agreement with normal coordinate calculations
464 (ref. 38) from which it was concluded that the torsions of the two conformers have nearly the same frequency. In the calculations of the asyaxaetric potential function, the three strongest bands at 90.8, 92.5 and 93.4 cm-l were assigned to the gauche conformer on the basis that this conformer should be present in a ratio of about 3:l. The remaining three bands at 91.3, 92.2 and 93.1 cm-l were then assigned to the s-trans conformer. The results of the calculation are given in Table 4.
Minima in the potential function were found at 0 and 2121"
representing the s-trans and gauche potential wells, respectively. It should be pointed out that a potential function was also calculated in which the reversed assignment was used, i.e., the s-trans torsional series beginning at 90.8 cm-l instead of 91.3 cm-l, but this calculation resulted in higher dispersions and a poorer fit of the data. A study of the low frequency vibrational spectrum of methylvinylsulfideis currently being conducted in our laboratory. We have recorded the far infrared spectrum of the vapor and observed several series of strong Q-branches. However, the spectrum is difficult to analyze due to the overlap of the cis methyl torsion and the cis asymmetric torsion in both the fundamental (-165 cm-r) and overtone (-335 cm-l) regions. We are currently preparing the deuterated analog, methyl-da-vinylether,in order to simplify the analysis of the conformational equilibrium in qethylvinylsulfide. We have recently reported (ref. 39) the complete vibrational spectra of isopropylamine-do and -dx. Gaseous phase band contour and depolarization data taken together showed that the s-trans conformer is the more stable. The far infrared spectra of both isotopic species were very rich, and torsional bands due to the asymmetric torsion were observed in both cases. The deuterium shift allowed the methyl and asyanaetrictorsions to be accurately assigned, and twoquantum transitions of the asymmetric torsions of both conformers were observed in the spectrum of the -dx compound. The s-trans asymmetric torsion of the -dp compound was assumed to be in Fermi resonance with a bending vibration because the observed series of transitions were somewhat irregular, but the torsions of the -do compound did not appear to be perturbed in the same manner. The large number of transitions observed in both the gauche and s-trans wells of the two compounds, as well as the observed -dp double jumps, allowed a high confidence in the potential functions. The results of these calculations are presented in Table 4.
The calculated value of AH (156 cm-') for isopropylamine-dowas found
to be substantially larger than that found experimentally (ref. 40) for the solution phase. Hydrogen bonding present in the solution was invoked to explain this result. Additionally, the two sets of potential coefficients as well as the values of All do differ between the -do and -da molecules, and is assumed to arise from a different amount of coupling between the asymmetric torsion and other vibrationalmodes.
465 CONCLUSIONS It is clear from the numerous studies discussed that the moat effective means of collecting and analyzing torsional data is the complementaryuse of infrared and Raman spectroscopy. When two or more conformers are present in appreciable quantities, it may be difficult to distinguish which Q-branch series should be assigned to which conformer. In many cases the Raman spectrum of the vapor can provide the depolarization data necessary for making the correct assignment. Additionally, for some molecules the asymmetric torsional overtones are observed in the Raman spectrum and from these data a check of the assignments made on the basis of infrared data can be made.
However, we have found that the far
infrared spectrum usually contains many more
transitions than the Raman
spectrum. In all of the studies discussed, little was mentioned about the coupling of the asynssetrictorsions with the methyl torsions or other low frequency modes. This effect is especially prevalent when the two torsional modes have similar vibrational frequencies, and deuteration of one top has the effect of altering the amount of coupling as well as the vibrational frequency. The selective deuteration of one part of the molecule often substantiallyalters the potential distribution of mixed modes, and thus results in different contributions from the asysssetrictorsion.
If torsional data can be obtained for a number of
isotopic species where such mixing occurs, it may be possible to estimate the effect on the asymnetricpotential function.
ACKNOWLEDGEMENT The authors gratefully acknowledge the financial support of these studies by the National Science Foundation through Grant CHE-79-20763.
RlmmiNCES
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