Journal of Molecular Spectroscopy 193, 104 –117 (1999)
Article ID jmsp.1998.7709, available online at http://www.idealibrary.com on
The High-Resolution FTIR Far-Infrared Spectrum of Formamide
Don McNaughton,* Corey J. Evans,* Samantha Lane,† and Claus J. Nielsen‡
*Centre for High Resolution Spectroscopy and Optoelectronic Technology, Department of Chemistry, Monash University, Wellington Road, Clayton,
Victoria, 3168, Australia; †Motorola Australia Software Centre, 2 Second Avenue, Technology Park, Mawson Lakes, 5095, South Australia,
Australia; and ‡Chemistry Department, University of Oslo, PO Box 1033, Blindern, N-0315 Oslo, Norway
Received June 8, 1998; in revised form August 10, 1998
The far-infrared spectrum of formamide (HCONH2) has been recorded at high resolution and over 9000 vibration–rotation
lines assigned. Molecular parameters from the rovibrational analyses of the unperturbed 1210 out-of-plane vibration band have
been obtained for the ground state and the excited state. An analysis of the complicated resonance system between the 910, 1110,
and 1220 bands has also been carried out. The mid-infrared spectrum of formamide has been recorded at low resolution and
assignments for the fundamental, combination, and overtone bands in this region are given. The Large Amplitude Motion
(LAM) of the out-of-plane mode has been reanalyzed using the new parameter set. © 1999 Academic Press
INTRODUCTION
An understanding of the structure of formamide is of some
importance because formamide is the simplest amide containing an N–C–O configuration. The N–C–O (Peptide) linkage is
dependent on the structure and flexibility of the molecule
involved and is of importance in the synthesis of proteins (1).
The N–C bond distance in formamide is also of some interest
because of its partial double bond character. Consequently,
there has been considerable interest in the structure and spectroscopy of formamide over the last forty years.
Spectroscopic studies on formamide have been numerous
and the planarity of the molecule has been the subject of much
spectroscopic work. X-ray diffraction (2) and NMR studies (3)
favored a planar structure, while the first microwave study (4)
examined the isotopomers H2NCHO, cis/trans–HDNCHO, and
D2NCHO, and concluded from the small inertial defect that
formamide has a planar structure. Costain and Dowling (5)
investigated the microwave spectra of ten isotopic species of
formamide and found the observed inertial defects were only
explicable if formamide was nonplanar, with the NH2–C group
forming a shallow pyramid. A potential barrier of 370 6 50
cm21 was determined for the out-of-plane wagging motion of
the amino group. Hirota et al. (6) determined the complete r s
structure of formamide from the microwave spectra of 14
isotopically substituted formamide species and concluded that
formamide was planar.
Several ab initio calculations have been performed on formamide to determine its potential energy surface and structure.
The most recent was by Kwiatkowski and Leszcynski (7) who
performed calculations using the MP2/6-311G(3df,2p) level
of theory. They calculated a fully optimized geometry, dipole
moments, rotational constants, force constants, and the vibrational infrared spectrum of formamide and compared the results with the available experimental data. Formamide was
found to have a planar structure at this level of theory. However, similar calculations using the MP2/6-31G(d,p) level of
theory predicted a nonplanar structure with the difference in
energy for the planar to the nonplanar structure being only
0.003 kJ mol21. Wiberg and Breneman (8) investigated the
internal rotation about the CN bond using the MP2/6-31(d)
level of theory and calculated a barrier height of 16.7 kcal
mol21 which agreed well with the experimental value of
18 –19 kJ mol21 (9 –11).
Brown et al. (12) analyzed the rotational spectral data of
formamide using a semirigid bender technique and found that
formamide has a very shallow single minimum out-of-plane
potential. They also found that to account for the observed data
a strong parametric dependence on the torsion motion about the
C–N bond with the inversion coordinate (t) was required.
Their model indicated that as the amino group inverts, the
molecule twists about the C–N bond.
The infrared spectrum of formamide was first analyzed by
Evans (13). Subsequent studies have analyzed the liquid (14 –
17), matrix (18 –20), and vapor (18, 21–23) phases. In the
vapor-phase work, King (18) observed the out-of-plane motion
at 288 cm21, while Hansen et al. (21) assigned further transitions to the out-of-plane motion in the far-infrared spectrum.
Sugawara et al. (22) assigned the vibration–rotation structure
of a number of spectral bands recorded at 0.5 cm21, and
Brummel et al. (23) studied the high-resolution spectrum of the
symmetric N–H stretching region of formamide and deuterated
formamide in a molecular beam and found the mode to be
heavily coupled to other modes. The main uncertainty in characterizing the infrared spectrum of formamide has been in the
assignment of the bands in the far-infrared region (200 –700
cm21), which includes the out-of-plane, torsion, and the
N–C–O bending modes.
In this work, the high-resolution (0.0035 cm21) far-infrared
104
0022-2852/99 $30.00
Copyright © 1999 by Academic Press
All rights of reproduction in any form reserved.
105
FAR-INFRARED SPECTRUM OF FORMAMIDE
TABLE 1
Experimental Fundamental Wavenumber Values and ab initio Values (cm21) for Formamide
a
Ref. (23).
Ref. (22).
c
Scaled by a factor of 0.97.
b
spectrum of formamide has been more completely analyzed.
Transitions involving five vibrational levels, the ground state,
121, 122, 111, and 91, have been assigned and fitted. A series of
fits to this data, taking account of some of the major perturbations between 1110, 910, and 1220, are also presented. The out-ofplane potential of formamide has also been reexamined using
the updated parameters and the semirigid bender method developed by Brown et al. (12).
EXPERIMENTAL
Spectrophotometric grade formamide (991%), was purchased
from Aldrich and used without further purification. All spectra
were recorded on a Bruker HR120 FTIR spectrometer. Infrared
spectra in the region of 100–650 cm21 were recorded using a
Cu/Ge helium-cooled bolometer with a 660-cm21 cold filter and
a 3.5-mm Mylar beamsplitter. The sample was contained in a
FIG. 1. Plots of the low-resolution (0.5 cm21) far-infrared (200 –700 cm21) spectrum of formamide.
Copyright © 1999 by Academic Press
106
MCNAUGHTON ET AL.
FIG. 2. (a) Low-resolution (0.1 cm21) mid-infrared spectrum of formamide between 650 –1800 cm21. (b) Low-resolution (0.1 cm21) mid-infrared spectrum
of formamide between 2500 –3650 cm21.
three-meter-long cell, fitted with polyethylene windows and
heated to approximately 400 K with the sample pressure maintained at 2.5 Pa. Spectra were recorded at 0.5 cm21 (40 scans) and
at 0.0035 cm21 (40 scans) unapodized resolution.
Infrared spectra in the region of 350 –750 cm21 were recorded using a KBr beamsplitter and a Si– helium-cooled bolometer detector equipped with a 750 cm21 cold filter. Spectra
were recorded at 0.5 cm21 (40 scans) and 0.0035 cm21 (60
scans) unapodized resolution with the vapor pressure of formamide maintained at 16 Pa.
To improve the signal to noise, an Infrared Inc. multitransversal cell with a 12-m pathlength was also used. Spectra were
taken at a resolution of 0.0035 cm21 in the 350 –750 cm21
region using a Si– helium-cooled bolometer detector. The cell
was fitted with KBr windows and was heated to a temperature
of approximately 370 K to maintain a pressure of 3.0 Pa. A
total of 50 scans were co-added.
Mid-infrared spectra were recorded using a liquid nitrogencooled MCT/InSb sandwich detector at 0.1 cm21 resolution,
over the range 650 – 4000 cm21, at pressures between 20 and
100 Pa. All high-resolution spectra were calibrated against
known lines of H2O (24).
RESULTS
Low-Resolution Analysis
Formamide is a near prolate asymmetric top molecule (k 5
20.95) and has C S symmetry. Hence, of the twelve fundamen-
tal modes, nine belong to the species a9 ( A/B-type bands) and
three belong to the species a0 (C-type bands). Table 1 shows
the predicted and observed wavenumber values of the twelve
fundamentals from this study together with previous assignments. The values in column one are the most up-to-date data
from the study of Brummel et al. (23), who obtained most
wavenumber values from a previous theoretical paper.
Low-resolution (0.5 cm21) spectra of the region 200–700
cm21 are shown in Fig. 1. The fundamental band 1210 can be seen
at 288 cm21, while the difference bands 1221 and 1232 can be seen
at 368.6 and 401 cm21, respectively. Hansen et al. (21) observed
a band at 415.7 cm21 that they attributed to the band 1243. On
investigation of this region in this study, no band was observed at
415 cm21. This may be a result of Hansen et al. using a higher cell
and sample temperature than in this work. The higher wavenumber portion (500–700 cm21) of the far-infrared spectrum is congested owing to four bands. These have been assigned to 910 (565
cm21), 1110 (602 cm21), and 1220 (657 cm21). A C-type band at
approximately 580 cm21 has yet to be firmly assigned and is
thought to be a hot band. Low-resolution (0.1 cm21) spectra of the
region 650–4000 cm21 are shown in Fig. 2. The assignment of
fundamentals is essentially the same as those of Sugawara et al.
(22) with the major difference being the band centers of 910 which
have been changed from 581 to 565 cm21 (see High-Resolution
Analysis, next section) and 1010, which has changed from 1021.2
to 1033.32 cm21. Although 1010 has not been rotationally analyzed
in this study, the high resolution of the current spectrum leads to
an accurate measurement of the band center due to the sharp and
Copyright © 1999 by Academic Press
FAR-INFRARED SPECTRUM OF FORMAMIDE
TABLE 2
Infrared Assignment of Formamide in Vapor Phase (cm21)
107
and combination differences were then transferred to the program RESONANCE (25) and were fitted to Watson’s A-reduced Hamiltonian (26). The results from the fit are shown in
Table 3. The low values for both the standard deviation and
rms error show a good fit to the data. The weights given to the
combination differences were assigned by multiplying the standard deviation of each transition (i.e., 0.0003 cm21 4 10% of
the linewidth) by =2. The fitted ground state parameters are
comparable to previous results.
The C-type out-of-plane mode 1210 was easily evaluated
using MacLoomis (27) and a total of 2686 transitions were
assigned. The transitions were transferred to the program RESONANCE and fitted to Watson’s A-reduced Hamiltonian.
Ground state values were held constant at those given in Table
3. The resulting parameters derived for 1210 are given in Table
3. The fit was performed on transitions from the R R K 5 1–18,
R
Q K 5 5–13, P P K 5 2–18, and P Q K 5 8–13 subbands and
the resulting standard deviation and rms error indicate a very
good fit to the data and a band free from perturbations.
Interaction between 910, 1110, and 1220
Initial Assignments
The next band higher in wavenumber from the out-of-plane
mode (1210) is the difference band 1221 centered at 370 cm21.
TABLE 3
Fitted Molecular Parameters (cm21) of the Ground State and
the Out-of-Plane Mode n12 of Formamidea
a
Tentative assignments.
prominent Q-branch head. The A-type band at 769.52 cm21 has
been assigned to the 1231 band making the C-type band at 1054.93
cm21 most likely, due to 1230. A weak band was observed centered
at 816 cm21; in the proposed assignment by Hansen et al., this
band was attributed to the 1242 band, thus requiring 1240 to be at
approximately 1474 cm21. On analysis of this region, however,
no band was observed. Proposed assignments of all the observed
bands are given in Table 2.
High-Resolution Analysis
Ground State and Out-of-Plane Mode 1210
Accurate ground state parameters were found by using 41
( J # 29, K # 6) microwave transitions from Ref. (6), 975
( J # 50, K # 16) A-type combination differences (from the
1220 band), and 756 ( J # 44, K # 18) C-type combination
differences (from the 1210 band). The microwave transitions
a
The numbers in parentheses are 1 standard deviation (expressed in the last
two digits) from the least squares fit.
Copyright © 1999 by Academic Press
108
MCNAUGHTON ET AL.
FIG. 3. MacLoomis plot of 1220 formamide band. The black peaks (K9a 5 10) in the center of the plot show a distinct perturbation around J9 5 15 due
to an avoided crossing.
The 1221 band is a C-type band and was easily assigned using
MacLoomis. Confirmation of the assignment was found by
calculating excited state combination differences (ESCD) using the constants derived from the 1210 band and comparing
them with the lower state combination differences calculated
from transitions of the 1221 band. A total of 1006 transitions
from R R K 5 3–12 and P P K 5 5–14 subbands were assigned
to the 1221 band. The transitions were transferred to the program
RESONANCE and fitted to Watson’s A-reduced Hamiltonian.
The initial results of the fit indicated that the band was severely
perturbed.
To help in the investigation of these perturbations, the 1220
A/B-type band, centered around 657 cm21, was assigned. This
band has the same upper state as 1221 and thus is effected by the
same perturbations as those observed in 1221. Using MacLoomis and ground state combination differences, a total of 2861
A-type transitions were assigned to the Q R K 5 0–16, Q P K 5
0–16, and Q Q K 5 4–14 subbands. The MacLoomis plot (Fig.
3) clearly shows a typical perturbation occurring in the K a 5
10 series (black peaks in the center of the plot) at around J9 5
15. This type of perturbation results from an avoided crossing
of energy levels.
The many perturbations can be attributed to the energy
levels associated with the bands 910 and 1110 interacting with
those from 1220. Nielsen and Sørensen (28) previously investigated the microwave spectrum of formamide and assigned
lines to the v9 5 1 and v11 5 1 excited states. They successfully fitted the lines from both the states by including two
resonance terms (a- and b-type Coriolis) coupling the states
together.
The 910 and 1110 bands are centered at around 565 and 602
cm21, respectively. The spectrum in this region is heavily
congested with lines from these two bands and the 1220 band,
making assignment of these two bands difficult, especially
where the overlying 1220 structure is very intense. The torsion
mode (1110) is a C-type band and is easily assigned using
MacLoomis. A total of 1661 transitions were assigned to the
R
R K 5 1–11, P P K 5 1–13, P Q K 5 6–11, and R Q K 5 4–9
subbands of this mode.
The O–C–N bend (910) is a A/B-type band. Using MacLoomis, the series previously assigned to 1110 were removed from
the plot and the remaining peaks were thoroughly investigated.
Several series from an A-type band were found centered at 565
cm21 and the initial assignment was subsequently confirmed
using ground state combination differences. A total of 1475
A-type transitions were assigned to the Q R K 5 0–12, Q P K 5
0–12, and Q Q K 5 4–12 subbands of 910. Initial fits of 910 and
1110 both showed effects from strong perturbations.
Copyright © 1999 by Academic Press
FAR-INFRARED SPECTRUM OF FORMAMIDE
109
Perturbation Analysis
Molecules of C S symmetry can have two types of rotation–
vibration perturbations (a- and b-axis Coriolis or c- axis Coriolis and Fermi resonance) occurring simultaneously and affecting a single infrared band. Coriolis interaction is possible
between rotational levels of vibrational states, v9 and v0, which
obey Jahn’s rule:
G~ c v9! 3 G~ c v0! . G~R x! and/or G~R y! and/or G~R z!.
For a molecule with C S symmetry, such as formamide, this
relation is true for any two vibrations. Unlike in higher symmetry cases, the Hamiltonian for molecules with C S symmetry
is unable to be factored into four Wang submatrices but can be
factored into only two submatrices a9 and a0. Programs (CS
and CS3) for simultaneously fitting two types of resonance
terms in molecules of C S symmetry have recently been developed by Joo et al. (29) and we have adapted these programs to
the current problem. The adapted programs are referred to in
this paper as CSMOD and CS3MOD.
It was found that six different types of interactions could
occur simultaneously among the three sets of energy levels.
Rovibrational constants from the initial fits of the data, where
the major perturbations were weighted out of the fit, were used
to construct a energy level diagram. This diagram is shown in
Fig. 4, and each avoided crossing is outlined with a rectangle.
The diagram clearly shows the main interactions occurring
among the three bands. Nielsen and Sørensen fitted a long
range a-type Coriolis (DK 5 0) and a b-type Coriolis (DK 5
61) interaction between 910 and 1110. Other possible perturbations involving these two levels are a b-type Coriolis DK 5
63 and a-type Coriolis DK 5 62 interactions. Possible
perturbations between 1110 and 1220 are a-type Coriolis, DK 5
0 and DK 5 62, and b-type Coriolis, DK 5 61 and DK 5
63. Interactions between 910 and 1220 are c-type Coriolis DK 5
63 and a long-range first-order Fermi (DK 5 0) interaction.
To account for the major resonances, the program CS3MOD
was modified to include a- and b-axis Coriolis coupling between 910 and 1110 and a- and b-Coriolis coupling between 1110
and 1220. These interactions were thought to be the cause of
major resonances in the perturbed system. Inclusion of more
interaction parameters would have resulted in strong correlation effects between the different interaction parameters when
varied. To minimize these correlation effects, it was thought
best not to include the interactions between 910 and 1220. The
Coriolis matrix elements included are shown in Table 4.
Least-Squares Fits
Fits were obtained for low J and K a transitions of the
combined microwave and infrared data using the results from
Nielsen and Sørensen with j a9,11 5 1.701 (30) and j b9,11 5
0.3250 (28) as starting values. The microwave transitions
were given a standard deviation of 0.01 MHz, while transitions
FIG. 4. Energy level diagram of the 91 (squares), 111 (circles), and 122
(triangles) states of formamide. Rectangles show the avoided crossings between the states.
with a residual over 0.1 MHz were given a standard deviation
of 0.1 MHz. Infrared transitions were given a standard deviation of 0.0003 cm21. Infrared transitions with residuals between 0.001 and 0.0025 cm21 were given a standard deviation
of 0.003 cm21 while those with residuals above 0.003 cm21
were not included in the fit.
Higher J and K a transitions were slowly incorporated into
the fit with the Coriolis parameter j b11,12 for the 1110–1220
interaction between K9a 5 11 and K9a 5 10. It was found that
the sextic distortion parameter F K for 1110 and 1220 was required
to be varied in achieving a good fit. Three other Coriolis
parameters were included after successive fits to account for
noticeable resonances: a-type (DK 5 62) and b-type (DK 5
63) between 910 and 1110 and a-type DK 5 62 between 1110
and 1220.
It was found that energy levels belonging to K9a 5 12 of 1110
were being incorrectly assigned within the program as K9a 5
13 of 910 for J , 24, which was probably due to the heavy
mixing of the wavefunctions in this region. Figure 5 shows a
plot of the eigenvector coefficients of 910 (K9a 5 13) and 11 10
Copyright © 1999 by Academic Press
110
MCNAUGHTON ET AL.
TABLE 4
Included Coriolis Matrix Elements
(K9a 5 12) for J9 5 12–30. The plot clearly shows the extent
of the mixing. It can be seen that at J9 5 21, the eigenvector
coefficients of the two states are nearly equal. The CS3MOD
program was unable to correctly assign the eigenvalues of the
two states with mixing of this severity. Transitions from these
levels were subsequently not included in the least-squares fit.
The results of the final fit, which included 4764 transitions,
are shown in Table 5. In comparing the calculated rotational
constants against those evaluated by Nielsen and Sørensen it is
apparent the value of A of 910 and 1110 has been transposed. This
is probably due to the small number of transitions Nielsen and
Sørensen used in the fit and the high weighting that was given
to the microwave transition. The inclusion of the infrared data
and the lowering of the microwave transitions weighting have
allowed more accurate and reliable constants to be obtained.
The residuals of the fit indicated some strong perturbations
effecting J . 25 for K9a 5 0 and 1 of 910. Due to strong
correlations with other fitted parameters, the parameter j a9,11
was kept constant during the last series of fits. The standard
deviation of the final fit (1.28) shows some unaccounted perturbations still affect the system.
A reliable indicator of how well the included Coriolis parameters have fitted the perturbations is to examine the centrifugal distortion parameters and compare them with the
ground state values. The parameters d K , F JK , F KJ , and F K all
have values considerably different to those of the ground state.
The main two discrepancies are F JK , which is up to 100 times
larger than the ground state values, and F K , which is up to 10
times as large the ground state value. In both cases, the sign of
these parameters has been transposed for the 1110 state. This
difference from the ground state shows that the Coriolis parameters included in the fit are not taking account of all the
perturbations present. This may be due to strong correlation
between the centrifugal distortion parameters and the resonance parameters or an unaccounted K a -dependent interaction.
The extent of the shifts in the rotational levels of the 1220 band
is shown in Fig. 6. This diagram was generated by including
the two main resonance terms j a9,11 and j b9,11 and setting the
other resonance terms to zero. The avoided crossings between
1220 (K9a 5 10) and 1110 is easily seen.
After the initial assignments, the MacLoomis plot contained
several unassigned series. Since bands with a9 symmetry are
able to have both A- and B-type transitions, it was thought
these series should be B-type transitions belonging to 910 or 1220.
Using the parameters in Table 5, B-type transitions of 910 were
predicted and matched that of the observed series. A total of
FIG. 5. Plot of eigenvector coefficients of 91 (K9a 5 13) and 111 (K9a 5 12) states of formamide for J9 5 12–30.
Copyright © 1999 by Academic Press
FAR-INFRARED SPECTRUM OF FORMAMIDE
TABLE 5
Formamide 3-Way Interactiona
Note. Results (in cm21) from least-squares fit using A- and C-type infrared
and microwave transitions, K a # 14 and J # 30.
a
The numbers in parentheses are 1 standard deviation (expressed in the last
two digits) from the least-squares fit.
b
Constrained to ground state values.
c
Kept constant during last series of fits. Estimated uncertainty 61.0E-04
cm21.
d
Constrained to zero.
732 B-type transitions were assigned to the R R K 5 2,11 and
R
Q K 5 4,11 subbands of 910. No transitions from the P P K
subbands of 910 were observed.
The results of the fit, including these B-type transitions with
J , 61 and K a # 14 (5850 transitions), are shown in Table
6, conclude with similar parameters, and are of similar quality
to the previous fit with J # 30. From the residuals, it was
found that K9a 5 8, 9, 10, 11 levels for J . 35 of 1220 were
affected by a strong perturbation.
A first-order K-dependent interaction between 1110 and 1220 is
considered to be a likely cause of the anomalies in the centrifugal distortion parameters in the previous fits. Starting with
111
parameters given in Table 6, a first-order a-type Coriolis
parameter j a11,12 was included in the fit. By slowly varying the
value of j a11,12 and checking the values of the centrifugal
distortion parameters, a value of 20.6 was found to produce a
value of F K close to that of the ground state. It was also found
that transitions up to K a # 15 for 1220 could be fitted. As
before, the number of transitions in the fit were increased with
the number of varied parameters. It was found that only transitions up to J # 40 could be fitted satisfactorily with the
j a11,12 parameter incorporated in the fit. The resulting parameters can be seen in Table 7. As can be seen from the results,
the F K parameter is close to that of the ground state; however,
the parameters d K , F JK , and F KJ are still significantly different from the parameters of the ground state. As before, due to
their strong correlation with other parameters, some of the
resonance parameters were held constant during the final set of
fits. The resulting standard deviation of 1.18 is better than the
previous fit obtained without the inclusion of j a11,12 . The
resulting residuals show that the K9a 5 0 and 1 series of 910 with
inclusion of j a11,12 were able to be satisfactorily fitted. However, most of the residuals around J $ 40 increased significantly, perhaps the result of strong mixing of the wavefunctions.
The standard deviation and rms error from each fit indicated
that the data was fitted satisfactorily using a number of rovibrational and resonance terms. However, the rovibrational and
Coriolis constants found are not necessarily the true values for
those particular states. The complexity and number of possible
interactions in this three-band system result in strong correlation effects between resonance terms and other rovibrational
terms. These strong correlations make accurate determination
of parameters difficult. To overcome these correlation effects,
more data are required, especially where the perturbations are
severe. Interactions between 910 and 1220 bands that were not
included in this work may also affect the system considerably.
However, the inclusion of these interactions without sufficient
data would only increase the correlation problems. Reanalysis
of these bands at higher resolution and with better signal-tonoise may improve knowledge of the interactions occurring,
thereby allowing a better determination of rovibrational and
resonance constants.
The problem of how to determine highly correlated constants may be also be solved by using a combination of theory
and experiment to derive sets of molecular parameters. Using
high-level ab initio molecular orbital calculations, quadratic,
cubic, and quartic force fields for linear molecules such as
FCCF (30) and FCCC1 (31) can be found. The rovibrational
parameters derived from these force fields can be used to guide
analysis of high-resolution FTIR data. Similar work by East et
al. (32) on ketene and Robertson (33) on thioketene have
helped analyze the spectra of complicated resonance systems in
these molecules.
Copyright © 1999 by Academic Press
112
MCNAUGHTON ET AL.
FIG. 6.
Shifts (residuals from the least-squares fits) in the K a 5 9–12 rotational levels of 1220.
Large Amplitude Motion
Previous Studies
Several attempts have been made to analyze the out-of-plane
potential of formamide. King (18) analyzed the far-infrared
spectrum of formamide and assigned bands to the 1210 and 1221
out-of-plane modes. King (18) calculated the energy levels
(using different barrier heights) of the out-of-plane mode by
assuming formamide had a double minimum potential. However, the results failed to explain the observed far-infrared
spectrum adequately. Hirota et al. (6) observed a set of strong
satellites around the ground state transitions and also obtained
the far-IR spectrum of D2NCHO. The most intense satellite
lines were assigned to the out-of-plane mode v12 5 1, and other
lines were assigned to v9 5 1, v11 5 1, and v12 5 2 vibrational
states. Combining their own data with the data from King (18),
Hirota et al. (6) recalculated the out-of-plane potential. The
energy levels of the out-of-plane were calculated assuming the
potential function:
V~ t ! 5 V 2t 2 1 V 4t 4 1 V 6t 6.
[1]
The observed frequencies of the “inversion” could be explained using only V 2 and V 4 , and hence a planar structure,
where V 2 5 156 6 35 cm21 and V 4 5 398 6 29 cm21.
Calculations of the inertial defect did not correspond well with
the observed values and the discrepancies were thought to be
due to the inadequate treatment of the intramolecular vibrations
and a possible coupling of the out-of-plane and internal rotation motions.
Hansen et al. (21) investigated the far-infrared spectrum of
formamide in the vapor phase. They observed and assigned
several bands relating to the out-of-plane mode. A potential
function for the amino- out-of-plane mode was calculated
assuming all other deformations were frozen. The out-of-plane
motion was described as an internal rotation about the NCO
plane through the nitrogen and perpendicular to the CN bond.
The potential function was defined as:
V~ g ! 5 12 V 1~1 2 cos g ! 1 12 V 2~1 2 cos 2 g ! 1 · · · ,
[2]
where g is the angle between the HNH plane and the NCO
plane. The resulting parameters were found to be V 1 5 11 241
Copyright © 1999 by Academic Press
113
FAR-INFRARED SPECTRUM OF FORMAMIDE
TABLE 6
Formamide 3-Way Interactiona
amide has a very shallow minimum out-of-plane potential and
that during the out-of-plane motion the amino group rotates
around the CN bond. The analysis was able to account for all
the experimental data relating to the planarity of formamide
and its out-of-plane vibration. Nine parameters were used to
completely describe the planar geometry of formamide and
three dihedral angles included for out-of-plane coordinates
during the out-of-plane vibration. The potential had the functional form:
V~ t ! 5 a t 2 1 b t 4.
[3]
We have undertaken a reanalysis including the new spectral
TABLE 7
Formamide 3-Way Interactiona
Note. Results (in cm21) from least-squares fit using A/B- and C-type
infrared and microwave transitions, K a # 14 and J # 60.
a
The numbers in parentheses are 1 standard deviation (expressed in the last
two digits) from the least squares fit.
b
Constrained to ground state values.
c
Kept constant during last series of fits. Estimated uncertainty 61.0E-04
cm21.
d
Estimated uncertainty 61.0E-05 cm21.
e
Constrained to zero.
cm21 and V 2 5 22769 cm21. They concluded that the
equilibrium configuration for formamide is planar and the
vibrational mode is best described as an out-of-plane vibration
rather than a classical inversion (i.e., ammonia).
The investigation by Hirota et al. (6) could not explain the
positions of the strong vibrational satellites relative to the
ground state using their structure and out-of-plane potential. To
explain the vibrational satellite spectra, strongly anharmonic
vibrational effects must be considered. Brown et al. (12) reanalyzed the vibration–rotation spectral data of formamide using
a semirigid bender technique adapted for unsymmetrical large
amplitude motions (LAM). Their results showed that form-
Note. Results (in cm21) from least-squares fit using A/B- and C-type
infrared and microwave transitions, K a # 15 and J # 40.
a
The numbers in parentheses are 1 standard deviation (expressed in the last
two digits) from the least squares fit.
b
Constrained to ground state values.
c
Estimated uncertainty 61.0E-04 cm21.
d
Estimated uncertainty 61.0E-05 cm21.
Copyright © 1999 by Academic Press
114
MCNAUGHTON ET AL.
TABLE 8
Optimized Structural and Energy (Hartrees) Data
for Formamidea
TABLE 9
Internal Coordinates of Formamide
in the LAM Rotation Model, Calculated
Using the MP2/6-311G(d,p) Level Theorya
t 5 Out of plane angle. Initial values: rCN 5
1.3635, XCN 5 0.02314, NCO 5 124.98, CNHa
5 118.9, CNHb 5 121.48, XCNHb 5 20.1627,
and t5 5 0.441. Bond lengths in Angstroms.
Bond angles in degrees. Expansion coefficients
for bond lengths, angles and dihedral angles are
in Å cm21 and dimensionless, respectively. Refer to Figure 7 for numbering.
a
a
b
All bond lengths in Angstroms; all bond angles in degrees.
Ref. (6).
data. Brown et al. (12) used ab initio calculations to assess the
amount of coupling between the out-of-plane vibration and
torsion and the effect on the geometry during the out-of-plane
motion. In this work, the geometry was optimized using the
planar configuration with the HF/6-311G(d,p) and MP2/6311G(d,p) levels of theory. The results from these optimizations are given in Table 8. The internal coordinates chosen for
the description of the large amplitude motion were the same as
those used by Brown et al. (12), who used the HF/6-31(d,p)
level of theory. Calculations were carried out using the MP2/
6-311G(d,p) level of theory and are shown in Table 9. The
out-of-plane motion coordinate t is defined as the dihedral
angle between CNH planes and is zero for the planar molecule
(Fig. 7). The torsion is described by the dihedral angle d 5 that
the NHa bond makes with the CCN plane. Spectroscopic
constants for v12 5 2 were taken from the results listed in Table
6. These constants were thought to be more reliable than the
those listed in Table 7 because of smaller correlation effects.
parameters varied in the fit are well determined and uncorrelated. As in the previous LAM analysis, the a and b terms of
the potential function were correlated. Consequently, a was
RESULTS
The weighted least-squares program SEMIRIGID was employed in fitting the spectral data. The program was written by
Kleibömer (34) and used successfully in modeling molecules
with large amplitude motions (LAM) such as formamide, cyanamide, fluoroketene, and ketenimine. The final fitted parameters are listed in Table 10, with spectroscopic constants and
vibrational wavenumber values listed in Tables 11 and 12. The
FIG. 7. Formamide structure. Definition of LAM parameters.
Copyright © 1999 by Academic Press
FAR-INFRARED SPECTRUM OF FORMAMIDE
115
TABLE 10
Fitted Parameters in the 1-LAM Rotation Model of Formamidea
a
The numbers in parentheses are 1 standard deviation (expressed in last two digits) from the
least squares fit. All bond lengths in Angstroms. All angles in degrees. Units of X CN, X CNHb are
Å rad22, d 5 is dimensionless, and b is cm21 rad24.
b
Taken from Ref. (12).
kept fixed to the value of 100 cm21 rad22 (12) because the final
results of the LAM calculation were found by Brown et al. to
be insensitive to the value of a chosen.
Table 10 shows two fits produced in this work. LAM Model
(1) used the same weighting system as Brown et al. (12). LAM
Model (2) gave lower weights to the rotational constants and
vibrational wavenumber values from the 1220 band. From the
results it can be seen that the CN bond length from either fit is
larger than that of the r s structure and the previous LAM
analysis (12). Another significant difference relates to the bond
angles between CNHa and CNHb . The previous LAM analysis
predicted a HNH angle of 119.85° which is close to the 120°
which one may expect for an amino group lying opposite to a
CN bond of partial double character. However, with LAM
Model (1), the HNH angle decreased to 117.94°, 2° smaller
than previously calculated, while the HNH angle decreased to
119.15° with LAM Model (2). The results of X CNHb and d 5 also
differ considerably from the previous LAM analysis. This
difference suggests that the results of the LAM Model (1),
when using the same weighting system as Brown et al. (12),
are biased towards the normal species and do not give an
accurate representation of the equilibrium geometry. For more
accurate results on the structure, additional data on the higher
vibrational states of the mono- and dideuterated species would
be required.
The values given in Tables 11 and 12 are from the results of
LAM Model (2). The predicted ground state constant results
are similar to those calculated previously, with the prediction
of the B rotational constant improved slightly for most isotopic
species. The variations of the rotational constants with the
out-of-plane motion quantum number are in good agreement
with that observed. The predicted vibrational wavenumber
values compare well with the observed values and are more
accurate than the previous fit. The band at 814 cm21 assigned
by Hansen et al. (21) as 1242 was not included in the final fit.
The predicted wavenumber value of this band is 832 cm21, a
difference of 18 cm21 from the observed value. The other
out-of-plane vibrations are predicted with some degree of
accuracy (within 5 cm21) making the assignment of this band
as 1242 a little doubtful. There is little chance that this band
TABLE 11
Observed and Predicted Out-of-Plane Vibration Wavenumbers
of Formamide (cm21)
a
b
Taken from Ref. (12).
Not included in fit.
Copyright © 1999 by Academic Press
116
MCNAUGHTON ET AL.
could belong to an impurity because it is observed both by us
and Hansen et al. (21) and its band shape and distribution is
consistent with that expected. If this band is due to the hot band
1242, the disagreement between predicted and observed values
may be due to the upper state v12 5 4 being severely perturbed.
A strong perturbation may shift the center wavenumber value
of the band a considerable distance, a shift which the LAM
model is unable to take into account (i.e., outside the assumed
parameters of the LAM model).
A plot of the out-of-plane potential can be seen in Fig. 8.
This reanalysis of the out-of-plane potential of formamide
substantiates the results of Brown et al. (12) showing that
formamide has a very shallow minimum out-of-plane potential.
The potential function derived by Hansen et al. (21) is also
similar, showing the same shallow potential with no barrier at
zero degrees. The inclusion of the spectral data on 1220 has
improved the accuracy of some of the LAM parameters used in
modeling the out-of-plane motion.
CONCLUSION
The infrared spectrum of formamide has been reinvestigated
and the vibrational assignments reassessed. The far-infrared
spectrum of formamide has been investigated at high resolution. Improved rotational constants for the ground and the 1210
states have been calculated using a weighted least-squares
TABLE 12
Variation of Rotational Constants (MHz) and Inertial Defect
FIG. 8. Out-of-plane potential of formamide calculated using the function
V( t ) 5 a t 2 1 b t 4 , where a 5 100 cm21 rad22 and b 5 699.825 cm21
rad24. t is the out-of-plane coordinate.
program. The three-way interaction between 910, 1110, and 1220
has been analyzed and a series of fits completed. It was found
that strong interactions exist between 910 and 1110 and 1110 and
1220. A program was modified to take account of these perturbations and rovibrational and Coriolis (a- and b-type) parameters fitted. Two different fits were obtained, with one fit
including a first-order a-type Coriolis term between 1110 and
1220. The results of the fits show that other perturbations affect
these bands and a more complete analysis at higher resolution
would be required to obtain more information on the perturbed
levels. With the improved spectral data from this work, an
analysis of the out-of-plane motion potential of formamide was
performed using a semirigid bender technique. The results of
this analysis are similar to those of a previous study performed
by Brown et al. (12) but give better determined parameters.
Supplementary data in the form of assigned lines and leastsquares fits have been lodged with the publisher.
ACKNOWLEDGMENTS
a
Taken from Ref. (12).
This work was supported by the Australian Research Council. We thank
Professor D. J. Clouthier and Professor A. Merer for kindly supplying the
original fitting program that we modified for this work. Corey Evans was the
recipient of a Monash University Postgraduate writing-up award.
Copyright © 1999 by Academic Press
FAR-INFRARED SPECTRUM OF FORMAMIDE
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
M. Teeter and D. A. Case, J. Phys. Chem. 94, 8091– 8097 (1990).
B. Post and J. Ladell, Acta Crystallogr. 7, 559 –564 (1954).
R. A. Kromhout and G. W. Moulton, J. Chem. Phys. 25, 34 –37 (1956).
R. J. Kurland and E. B. Wilson, J. Chem. Phys. 27, 585–590 (1957).
C. C. Costain and J. M. Dowling, J. Chem. Phys. 32, 158 –165 (1960).
E. Hirota, R. Sugisaki, C. J. Nielsen, and G. O. Sørensen, J. Mol.
Spectrosc. 49, 251–267 (1974).
J. S. Kwiatkowski and J. Leszczynski, J. Mol. Struct. 297, 277–284 (1993).
K. B. Wiberg and C. M. Breneman, J. Am. Chem. Soc. 114, 831– 840
(1992).
B. Sunner, L. H. Piette, and W. G. Schneider, Can. J. Chem. 38, 681– 688
(1960).
H. Kamei, Bull. Chem. Soc. Jpn. 41, 2269 –2273 (1968).
T. Drakenberg and S. Forsen, J. Phys. Chem. 74, 1–7 (1970).
R. D. Brown, P. D. Godfrey, and B. Kleibömer, J. Mol. Spectrosc. 124,
34 – 45 (1987).
J. C. Evans, J. Chem. Phys. 22, 1228 –1234 (1954).
I. Suzuki, Bull. Chem. Soc. Jpn. 33, 1359 –1365 (1976).
Y. Tanaka and K. Machida, J. Mol. Spectrosc., 63, 306 –316 (1976).
J. Bukowska, Spectrochim. Acta Part A 35, 985–988 (1979).
J. Bukowska and K. Miaskiewicz, J. Mol. Struct. 74, 1–10 (1981).
S. T. King, J. Phys. Chem. 75, 405– 410 (1971).
K. Itoh and T. Shimanouchi, J. Mol. Spectrosc. 41, 86 –99 (1972).
M. Räsänen, J. Mol. Struct. 101, 275–286 (1983).
117
21. E. L. Hansen, N. W. Larsen, and F. M. Nicalaisen, Chem. Phys. Lett. 69,
327–331 (1980).
22. Y. Sugawara, Y. Hamada, and M. Tsuboi, Bull. Chem. Soc. Jpn. 56,
1045–1050 (1983).
23. C. L. Brummel, M. Shen, K. B. Hewett, and L. A. Philips, J. Opt. Soc. Am.
B 11, 176 –183 (1994).
24. G. Guelachvili and K. Narahari Rao, “Handbook of Infrared Standards,”
Academic Press, Orlando, 1986.
25. E. G. Robertson, Ph.D. thesis, Monash University, 1996.
26. J. K. G. Watson, in “Vibrational Spectra and Structure” (J. R. Durig, Ed.),
Vol. 6, p. 1, Elsevier, Amsterdam, 1977.
27. D. McNaughton, D. McGilvery, and F. Shanks, J. Mol. Spectrosc. 149,
458 – 473 (1991).
28. C. J. Nielsen and G. O. Sørensen, “7th Colloquium on High Resolution
Molecular Spectroscopy,” Reading, UK, B9, 1981.
29. D. L. Joo, D. J. Clouthier, and A. J. Merer, J. Chem. Phys. 101, 31–38
(1994).
30. H. Bürger, W. Schneider, S. Sommer, and W. Thiel, J. Chem. Phys. 95,
5660 –5669 (1991).
31. J. Breidung, H. Bürger, M. Senzlober, and W. Thiel, Ber. Bunsenges.
Phys. Chem. 99, 282–288 (1995).
32. A. L. L. East, D. A. Allen, and S. J. Klippenstein, J. Chem. Phys. 102,
8506 – 8532 (1995).
33. D. McNaughton, E. G. Robertson, and L. D. Hatherley, J. Mol. Spectrosc.
175, 377–385 (1996).
34. B. Kleibömer, Ph.D. thesis, Monash University, 1986.
Copyright © 1999 by Academic Press