This document analyzes the normal vibration modes of s-triazine through infrared and Raman spectral analysis and ab initio force field calculations. It finds that the 6-31G basis set provides the best results for frequency and intensity calculations for s-triazine. It assigns the observed IR and Raman active vibrations and identifies the inactive w4 and w5 modes based on gas phase IR and condensed phase Raman combination bands. It describes the vibration modes of s-triazine using a standing wave model to aid in visualizing the complex ring vibrations, finding coupling between some ring modes and motions of the triazine hydrogen atoms.

1. Spectrochimica Acta Part A 55 (1999) 1011–1020
The form of the normal modes of s-triazine: infrared and
Raman spectral analysis and ab initio force field
calculations
P.J. Larkin *, M.P. Makowski 1
, N.B. Colthup 2
CYTEC Industries, Stamford Research Labs, Stamford, CT, USA
Received 9 June 1998; received in revised form 4 August 1998; accepted 4 August 1998
Abstract
In this study, ab initio force field calculations with 6-31G basis sets are used in a comprehensive examination of the
Cartesian displacement vectors of the normal modes of s-triazine. Assignments are verified for the observed IR and
Raman active vibrations of s-triazine and the inactive triazine w4 and w5 modes are assigned based on analysis of gas
phase IR and condensed phase Raman combination bands. We use a standing wave description of the 12 elementary
vibrations of a six-membered ring to aid analysis of the complex ring vibrations of triazine and melamine. Vibrational
coupling of these ring modes with the rocking and bending vibrations involving the triazine hydrogen atoms are
discussed. Furthermore, we identify several ring modes where decreased vibrational coupling with the substituents
explains why certain bands make good group frequencies in related triazine derivatives. © 1999 Elsevier Science B.V.
All rights reserved.
Keywords: s-Triazine; Force field calculations; Vibrational coupling
1. Introduction
The compound, s-triazine, and related triazine
derivatives such as melamine represent an impor-
tant class of industrial chemicals. Melamine resins
are important synthetic thermosetting products
and are widely used in various industries as binder
components and crosslinkers [1]. Triazine deriva-
tives have also been used in recent investigations
of self-assembling nanostructures [2,3]. Typically,
IR [4,5], NMR [6,7], and mass spectroscopy [8,9]
are used for characterization of triazine
derivatives.
A better fundamental understanding of the
form of the vibrations of triazine derivatives is
needed to support efforts to synthesize new
melamine derivatives as well as in application of
MF resins in coating formulations. The molecular
structure and assignment of the fundamental
* Corresponding author. Tel.: +1-203-3212200; fax:
+1-203-3212298.
E-mail address: peter–larkin@st.cytec.com (P.J. Larkin)
1
Present address: PPG Industries, 4325 Rosanna Dr.,
Allison Park, PA 15101, USA.
2
Retired. Home address: 71 Strawberry Hill Ave. Apt 704,
Stamford, CT 06902, USA.
1386-1425/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.
PII: S1386-1425(98)00244-3

2. P.J. Larkin et al. / Spectrochimica Acta Part A 55 (1999) 1011–10201012
modes of s-triazine have been reported previously
[10–12]. The purpose of the earlier work on s-tri-
azine was to determine the structure, derive a set
of symmetry coordinate force constants, and as-
sign the fundamental vibrations [10–12]. The ac-
tual form of the normal modes of s-trazine was
not presented. In the present work we report a
comprehensive examination of the Cartesian dis-
placement vectors of the normal modes of s-tri-
azine using the 6-31G basis set to serve as a
foundation for further application to more com-
plex triazine derivatives. The Cartesian displace-
ments are very valuable when used to compare the
spectral features of related compounds and identi-
fying changes in bands due to vibrational interac-
tions [13].
In this study, the form of the normal modes of
s-triazine are discussed using a standing wave
description for easier visualization of the form of
the ring vibrations. Assignments are verified for
the observed IR and Raman active vibrations of
s-triazine and the inactive triazine w4 and w5
modes are assigned based on analysis of measured
gas phase IR and condensed phase Raman combi-
nation bands. The form of the 12 elementary
vibrations for a six-membered ring with equal
bond lengths, masses, and no substituents is pre-
sented to aid analysis of the triazine and
melamine ring vibrations. We describe vibrational
coupling of specific triazine ring modes with the
rocking and bending vibrations involving the tri-
azine C–H bonds. The nature of this vibrational
coupling and the band intensity determines what
ring modes are likely to result in good group
frequencies for triazine derivatives.
2. Experimental
2.1. Computational details
All computations were carried out using soft-
ware programs from Biosym/MSI of San Diego,
CA, using a Silicon Graphics Power Indigo2 XZ
workstation employing a 175 MHz MIPS R8000
processor and 256 MB of main memory. The
molecular model for s-triazine was constructed
using the Insight®
II Builder Module ver. 3.0. To
obtain a reasonable geometry and Hessian matrix
as input for the ab initio calculation, the structure
was first optimized for the minimum energy struc-
ture using the Discover®
ver. 95 molecular me-
chanics package. The Biosym CFF91 force field
and VA09A optimization algorithm were used
with electrostatic potentials included. The MM
optimized structures were then submitted directly
as input to the Turbomole ab initio package for
further HF/SCF optimization and force field
calculations.
2.2. Basis set selection
Once a suitable, optimized structure was avail-
able as input for Turbomole, we proceeded to
investigate which basis set would best suit our
needs for this study. A series of HF/SCF opti-
mizations and force calculations were carried out
on s-triazine at the STO-3G, 3-21G, 6-31G, and
6-31G* levels of theory and the findings were
compared to IR and Raman spectral data for
s-triazine. The IR data included the s-triazine gas
phase spectrum and the Raman data included the
solid-state s-triazine spectrum and liquid Raman
spectrum by Lancaster et al. [10]. The 6-31G basis
set used in this study was found to yield the best
results for both frequency and intensity for s-tri-
azine [13], however, the 3-21G basis set was found
to represent a good compromise between compu-
tation time and accuracy of the calculated fre-
quencies and intensities for a series of larger
triazine derivatives [13]. The use of 6-31G and
3-21G basis sets results in slightly different force
fields for the normal modes but with no major
differences in the combination of internal coordi-
nates contributing to their forms, which were
nearly identical for both basis sets. The Cartesian
coordinate force field using Turbomole was found
to yield legitimate but slightly skewed forms for
the degenerate ring modes which we discuss be-
low. Rather than using the graphical output from
Insight®
II, which reflects the skewed normal mode
vectors, we present the preferred, unskewed illus-
tration of the forms of the degenerate normal
modes which were derived directly from the dis-
placement vector data contained in the output
files.

3. P.J. Larkin et al. / Spectrochimica Acta Part A 55 (1999) 1011–1020 1013
Fig. 1. The 12 elementary ring vibrations for a six-membered ring with equal bond lengths, masses and no substituents illustrated
with vibrational standing waves. The elementary stretching vibrations are shown in the top row and the in-plane and out-of-plane
bending vibrations are shown in the second row. Abbreviations used include: s, stretch; c, contract; b, bend; o, open; plus and minus
indicate out-of-plane motion, and vectors indicate in-plane motion. The magnitude of the movement of the atoms in the vibrations
is indicated by the size of both the vectors and the plus and minus signs.
2.3. Infrared and Raman measurements
The 1,3,5-triazine used for the gas-phase FT-IR
and FT-Raman measurement was purchased from
Aldrich. The structure of s-triazine is shown
below.
The gas-phase IR spectrum of s-triazine was
measured using a Digilab FTS-60A spectrometer
with an MCT detector at 1 cm−1
resolution with
1028 scans. For this study a small amount of
s-triazine was introduced into a 10 cm length gas
cell (Barnes) and the IR spectrum of the vapor
measured at room temperature (26°C). The FT-
Raman spectrum was measured using a BioRad
FT Raman accessory, attached to a Digilab FTS-
6000 spectrometer with 1064 nm Nd:YAG excita-
tion. The FT-Raman spectrum was collected at 4
cm−1
resolution with 100 scans. Solid-state 1,3,5-
triazine (Aldrich) was used as supplied for the
FT-Raman measurements.
3. Results and discussion
3.1. Standing wa6e description of ring 6ibrations
The s-triazine molecule has a total of 21 modes
of vibration. Many of these modes of vibration
involve the more complex vibrational modes of
the triazine ring. The apparent complexity of
many of these ring vibrations can be greatly re-
duced by using the standing wave description
introduced by Colthup for benzene rings [5]. This
technique allows easy visualization of the form of
the ring vibrations and aids identification of me-
chanical interaction with ring substituents.
Fig. 1 shows the form of the 12 elementary
vibrations for a six-membered ring with equal
masses, bond strengths, and no substituents. The
vibrational standing waves for these vibrations
are also shown. The top row illustrates the six
ring stretching vibrations and the bottom row the
six bending vibrations for this simple six-mem-
bered ring. The dashed lines show the nodal lines
used to define the sextant, quadrant, semicircle or
whole ring vibrations (see below). These lines
separate molecular segments which vibrate out-of-
phase with each other. The doubly degenerate
ring modes are labeled with subscripts ‘a’ and ‘b’.
The sextant ring stretching vibration is depicted
in Fig. 1 by mode number 4. This vibration
involves alternating stretching and contracting of

4. P.J. Larkin et al. / Spectrochimica Acta Part A 55 (1999) 1011–10201014
the ring bonds, where three nodal lines separate
the ring into sextants. The two vibrations labeled
3a and 3b, are the doubly degenerate quadrant
stretches. Here, two nodal lines separate the ring
into quadrants where ring bonds which are pre-
dominantly in one quadrant, stretch, while ring
bonds predominantly in an adjacent quadrant,
contract. Ring bonds that are bisected by a nodal
line do not change in length. The doubly degener-
ate semicircle stretches are shown in Fig. 1 by the
modes labeled 2a and 2b. In this case only one
nodal line separates the ring into semicircles
which vibrate out-of-phase with each other. The
whole ring in-phase stretching vibration shown in
mode 1 has no nodes.
The in-plane ring bending modes shown in the
bottom row consist of a sextant in-plane bending
vibration (mode 6) and the doubly degenerate
quadrant in-plane bending vibrations (modes 5a
and 5b). The sextant in-plane bending vibration
(mode 6) involves alternating bending and open-
ing of the ring angles, where three nodal lines
separate the ring into sextants. Both quadrant
in-plane bending vibrations, labeled 5a and 5b,
have two nodal lines that separate the ring into
quadrants where bond angles bend in one quad-
rant and open in an adjacent quadrant. Bond
angles which are bisected by a nodal line do not
change during the vibration. The out-of-plane
ring bending modes can be similarly described in
terms of the sextant (mode 8) and quadrant
(modes 7a and 7b) out-of-plane bending
vibrations.
3.2. Vibrational modes of s-triazine
The liquid state Raman spectrum and the gas,
liquid and solid state IR spectra of s-triazine have
been measured previously [10–12]. Early work by
Lancaster et al. [10] used a simple valence force
field normal coordinate analysis to assign the
fundamental vibrations for this heteroaromatic
species. Many of the remaining bands were as-
signed to combination and overtone bands. More
recent work by Pyckhout et al. [11] used ab intio
force field calculations with a 4-21G basis set to
determine the frequencies of the normal modes
and the molecular structure of the gas phase
s-triazine. However, the actual form of the nor-
mal modes was not presented in either work.
Fig. 2 shows the gas-phase IR and solid-state
Raman spectra of s-triazine. Table 1 lists the
observed frequencies as well as the symmetry for
the 14 normal modes of s-triazine where each
degenerate pair is counted as one mode with only
one frequency. The observed frequencies from the
solid-state and liquid Raman spectra are from our
FT-Raman measurements and previously re-
ported work [10], respectively. The measured gas-
phase frequencies are consistent with those
reported previously [10]. The calculated frequen-
cies in Table 1 have been multiplied by 0.9 which
is an average scaling factor, i.e. the ratio of the
observed to calculated frequencies. The use of
scaling factors is well known for these types of
calculations [11]. In the last column of Table 1 we
list the exact ratio of the calculated to observed
frequencies for each of the s-triazine fundamen-
tals. Fig. 3 illustrates the calculated forms of all
21 of the vibrations for s-triazine. The form of the
ring vibrations are discussed using the standing
wave description presented above for the 12 ele-
mentary vibrations of a six-membered ring.
3.3. A%1 6ibrational modes
The three vibrational modes of s-triazine with
A%1 symmetry are numbered 1–3 in Fig. 3. The
in-phase CH stretch, or w1 mode, is assigned to
the 3042 cm−1
band and does not involve any
significant ring stretching. The w2 and w3 modes
observed at 1132 and 992 cm−1
are described as
the in-phase carbon radial and in-phase nitrogen
radial ring vibrations, respectively. In the in-phase
C-radial ring vibration, the attached hydrogen
atom moves with the carbon atom, in such a way
that the CH bond does not change appreciably in
length. In the in-phase N-radial ring vibration,
there is very little motion of the rest of the
molecule, which is a characteristic of a good
group frequency, seen in the Raman spectra of
related derivatives at 1000–970 cm−1
[13,14]. The
form of the s-triazine w2 and w3 modes result from
mechanical coupling of the whole ring in-phase
stretch mode vibrating in- and out-of-phase with
the sextant in-plane bending mode. The elemen-

5. P.J.Larkinetal./SpectrochimicaActaPartA55(1999)1011–10201015
Table 1
Observed and calculated frequencies for the vibrational spectrum of s-triazine a
Sym type Activity Description of vibration Calcb
cm−1
×0.9Mode (w) IR (gas) cm−1
Raman (liquid) Ratiob
obs/calcRaman (solid)
cm−1
cm−1
E% IR, Rdw6 CH str, out-of-phase 3109 3057 – – 0.883
A%1 Rp CH str, in-phase 3117 – 3042w1 3043 0.880
E% IR, Rd Quadrant str, ring+CH rk 1567w7 1557 1555 1548 0.893
w8 E% IR, Rd CH rk+ring semi-circle str 1401 1409 1410 1404 0.906
w4 A%2 Inactive CH rk, in-phase 1356 1367c
– 1358 (0.905)
E% IR, Rd Semi-circle str, ring+CH rk 1145w9 1172 1176 1171 0.921
A%1 Rpw2 C radial, in-phase 1129 – 1132 1123 0.902
E%% Rd CH wag, out-of-phase 1047w13 – 1031d
1031 (0.887)
w3 A%1 Rp N radial, in-phase 978 – 992 991 0.912
w5 A%2 Inactive Sextant stretch, ring 956 938c
– – (0.882)
A%%2 IR Sextant out-of-plane bend+ 0.867w11 962 927 – –
CH wag
w12 A%%2 IR Sextant out-of-plane bend, 0.888748 737 – –
ring
E% IR, Rd Quadrant in-plane bend, ring 675 676 676 675 0.900w10
E%% Rd Quadrant out-of-plane bend,w14 406 0.754– 340 338
ring
a
The assignments use the standing wave description of ring vibrations. The vibrational descriptions in the table list the largest component vibrations first and lesser
components after. All fundamental frequencies are from the gas phase IR and the solid-state FT-Raman spectrum of s-triazine. The assignments for the inactive w4
and w5 modes are from this work. Bands from the liquid phase Raman are from [10] and are included for comparison.
b
The resultant scaling factor (avg 0.9) obtained from the ratio of the observed relative to the calculated frequency for each of these 14 modes indicates that the
present study is comparable to previous work [12].
c
Calculated from MO results and observed combination bands. See text.
d
From [10], calculated from the product rule.

6. P.J. Larkin et al. / Spectrochimica Acta Part A 55 (1999) 1011–10201016
Fig. 2. The gas-phase FT-IR and the solid-state FT-Raman spectra of s-triazine. The gas-phase IR spectrum of s-triazine was
measured at 1 cm−1
resolution using a 10 cm gas cell at room temperature. The FT-Raman spectrum was measured at 4 cm−1
resolution.
tary ring vibrations which mechanically couple
resulting in the s-triazine w2 and w3 modes are
labeled 1 and 6, respectively, in Fig. 1. These two
fundamental ring modes are of the same symme-
try species in s-triazine and can therefore mix. In
ring systems such as benzene (with 6-fold symme-
try) these two modes are of different symmetry
and cannot mix.
3.4. A%2 6ibrational modes
The two vibrational modes of s-triazine with A%2
symmetry are IR and Raman inactive and are
numbered 4 and 5 in Fig. 3. Analysis of the
combination bands (see below) indicates that the
w4 and w5 modes occur at ca. 1367 and 938 cm−1
,
respectively, in the gas-phase. Furthermore, we

7. P.J. Larkin et al. / Spectrochimica Acta Part A 55 (1999) 1011–1020 1017
Fig. 3. The form of the 14 normal modes of s-triazine. The seven doubly degenerate modes are labeled with subscripts a and b. The
calculated and observed frequencies and the description of the modes are summarized in Table 1.
observed a very weak Raman band in solid-state
s-triazine at 1358 cm−1
that we assign to the w4
mode. The w4 mode involves the all-clockwise CH
rock and the w5 mode involves the ring sextant
stretch. The s-triazine w5 ring sextant stretch also
has a small amount of CH rock involved in the
vibration, however, the s-triazine w5 mode is quite
similar to the elementary ring sextant stretch vi-
bration shown in Fig. 1 (mode 4).
Previous work by Pyckhout et al. [11], calcu-
lated the inactive w4 and w5 modes with scaled
wavenumbers at ca. 1359 and 939 cm−1
, respec-
tively. Using a scaling factor of 0.9 we calculate
these two modes at 1356 and 956 cm−1
. Experi-
mental evidence for these calculated values has
not been previously reported, but they are verified
here by our assignments to previously measured
and unassigned s-triazine combination bands [10].
Below we show our calculations and assign-
ments for the gas phase IR and condensed phase
Raman active combination bands (E%) involving
the w4 and w5 modes. The calculations for the w4
mode involve the weak and unassigned [10] 2921
(IR, gas-phase) and 2771 cm−1
(Raman, solid-
state) bands and are shown below.
2921 cm−1
=w7 +w4
w4 =2921−1557 (w7)=1364 cm−1
2771 cm−1
=w8 +w4
w4 =2771−1409 (w8)=1362 cm−1
As a further check we have subtracted the previ-
ously assigned (w7 +w8) 2962 cm−1
(IR) combina-
tion band [10] from the 2921 cm−1
band assigned
above.
2921 cm−1
=w7 +w4
−(2962 cm−1
=w7 +w8)
−41 cm−1=w4 −w8

8. P.J. Larkin et al. / Spectrochimica Acta Part A 55 (1999) 1011–10201018
Then substituting the known frequency for the 68
mode, we arrive at a calculated value of 1368
cm−1
for the 64 mode.
w4 =1409 (w8)−41=1368 cm−1
We were able to identify only one combination
band involving the w5 mode. We assign a weak,
solid-state Raman band at 1286 cm−1
to the
w14 +w5 combination band which will be Raman
active (E%%).
1286 cm−1
=w14 +w5
w5 =1286−338(w14)=948 cm−1
Using a similar calculation on the liquid-state
Raman data [10] we calculate the w5 frequency to
be 938 cm−1
.
3.5. E% 6ibrational modes
The vibrational modes of E% symmetry are all
doubly degenerate and are numbered 6–10 in Fig.
3. All doubly degenerate ring modes are labeled
with subscripts ‘a’ and ‘b’, where analogous ele-
mentary ring modes (compare Fig. 1) of the same
phase share the same subscript. The doubly de-
generate out-of-phase CH stretches, or w6a and w6b
modes, are assigned to the 3057 cm−1
band and
do not involve any appreciable ring stretching or
bending. The w7a and w7b modes involve the dou-
bly degenerate quadrant ring stretches with some
in-plane CH bend, and are assigned to the 1557
cm−1
band. Despite this mechanical coupling, the
w7a and w7b modes are quite similar to the elemen-
tary quadrant ring stretches shown in Fig. 1
(modes 3a and 3b). Tangentially moving carbon
and hydrogen atoms move in more or less oppo-
site directions. These are good group frequencies
for triazine derivatives including normal
melamines, which have strong IR bands at
1600−1500 cm−1
[5,13,14].
The w8a, w8b, w9a, and w9b modes shown in Fig. 3,
all involve the semicircle ring stretch coupled with
the in-plane CH bend. The mechanical coupling
of the in-plane CH bend with the semicircle
stretch results in two sets of degenerate modes.
The w9a and w9b modes are assigned to the 1172
cm−1
band and involve the tangentially moving
hydrogen atoms and the attached carbon atoms
moving approximately in the same direction. The
w8a and w8b modes are assigned to the 1409 cm−1
band and involve the opposite phases of the semi-
circle stretch and the in-plane CH bend. Compari-
son of the w8a, w8b, w9a, and w9b modes to the
elementary semicircle stretches shown in Fig. 1
(modes 2a and 2b) illustrates how mechanical
coupling has changed these ring modes.
The doubly degenerate quadrant in-plane ring
bending, or w10a and w10b modes are assigned to
the 676 cm−1
band. Only slight mechanical cou-
pling of the in-plane CH bend with the quadrant
in-plane ring bending occurs in the w10a and w10b
modes, which are very similar to the elementary
quadrant in-plane ring bend modes shown in Fig.
1 (modes 5a and 5b).
3.6. A%%2 and E%% 6ibrational modes
The vibrational modes of A%%2 and E%% symmetry
all involve out-of-plane vibrations and are num-
bered 11–14 in Fig. 3. The w11 and w12 modes of
A%%2 symmetry are assigned to the 925 and 737
cm−1
bands, respectively. The w11 mode involves
the ring sextant out-of-plane bend coupled with
the out-of-plane CH wag, where the carbon and
attached hydrogen atoms move in opposite direc-
tions. When the hydrogen atoms are substituted
for nitrogen atoms in normal melamine, the w11
mode becomes a good, medium intensity IR
group frequency, near 812 cm− 1
[5,13,14]. Simi-
larly, the w12 mode also involves the sextant out-
of-plane bend coupled with the out-of-plane CH
wag, but where the carbon and attached hydrogen
atoms move in the same direction. Although the
hydrogen atoms move considerably in the w12
mode, the HCN2 group rotates as a whole but
becomes only slightly non-planar, indicating only
a slight CH wag interaction. The doubly degener-
ate out-of-phase CH wag, or w13a and w13b modes
of E%% symmetry are assigned to the 1031 cm−1
band in the Raman spectrum. The doubly degen-
erate w14a and w14b modes of E%% symmetry are
assigned to the 340 cm−1
band. These modes
involve mainly the ring quadrant out-of-plane
bend interacting slightly with the out-of-plane CH
wag, as observed in w12.

9. P.J. Larkin et al. / Spectrochimica Acta Part A 55 (1999) 1011–1020 1019
Fig. 4. Comparison of skewed and corrected forms of the
normal coordinate components Q10a and Q10b for s-triazine.
The skewed forms of the degenerate modes are labeled a and
b and the preferred forms of the degenerate modes are labeled
a% and b%, which are symmetric and antisymmetric to a vertical
plane of symmetry. Details of this transformation are dis-
cussed in the text. The vector addition is shown only for the
top hydrogen atoms.
axis of the input file does not coincide with suit-
able symmetry elements of the molecule. In this
case, the forms of the Cartesian displacement
vectors will not be symmetric or antisymmetric to
any of the three planes of symmetry of s-triazine.
We found the forms of the degenerate modes for
s-triazine (and benzene) obtained using the force
subroutine in Turbomole were skewed in this way.
It is well known that the forms of doubly
degenerate vibrations are not uniquely defined
[15]. Linear combinations of any degenerate pair
(say Qa and Qb), can be used to generate new
degenerate pairs (say Q%a and Q%b), which have the
same vibrational frequency and energy as the
original pair. The appropriate equations for these
transformations are [16]:
Q%a =Qa cos ƒ−Qb sin ƒ
Q%b =Qa sin ƒ+Qb cos ƒ
where the common factor, ƒ, can be any angle
and the above two equations are for the rotation
of vectors. For example, the Qa cos ƒ term re-
quires all the Cartesian displacement vectors for
the Qa mode be multiplied by cos ƒ. Some angle
ƒ can always be chosen which will transform
skewed forms of degenerate modes into symmetric
and anti-symmetric forms. Fig. 4a and b show the
skewed degenerate normal coordinate compo-
nents Q10a and Q10b for triazine along with pre-
ferred symmetric and antisymmetric forms (4a%
and b%). All of the illustrations of the degenerate
modes of s-triazine presented in this work are
unskewed.
4. Conclusions
This study presents a comprehensive examina-
tion of the form of the normal modes of s-triazine
using ab initio force field calculations. We assign
the observed IR and Raman active bands of
s-triazine as well as the inactive triazine w4 and w5
modes. The descriptions of the complex ring vi-
brations are aided by use of a standing wave
description of the 12 elementary vibrations of a
six-membered ring. The vibrational coupling be-
tween the ring modes and the C–H bonds of
3.7. Orientation adjustment of skewed degenerate
modes
For a molecule with D3h symmetry such as
s-triazine, the forms of doubly degenerate modes
are usually illustrated so that one component is
symmetric and the other component is antisym-
metric relative to one of the three planes of sym-
metry perpendicular to the molecular plane [15].
This occurs automatically when the calculations
are done using symmetry coordinates. In the case
of a D3h six-membered ring, the preferred repre-
sentation of the doubly degenerate normal modes
has a plane of symmetry defined by bisecting the
ring through opposing vertices, as shown in Fig.
4a% and b%. These preferred modal orientations are
not unique, however, and other viable degenerate
component pairs exist which will be skewed rela-
tive to the symmetry planes [15]. When a Carte-
sian coordinate force field is used, the cartesian
displacement vectors calculated for degenerate vi-
brations will be skewed (although valid) if the xyz

10. P.J. Larkin et al. / Spectrochimica Acta Part A 55 (1999) 1011–10201020
s-triazine is also discussed and helps explain why
certain bands make good group frequencies in
related triazine derivatives [5,13,14]. For both the
IR and Raman spectra of s-triazine and related
melamines, these include the quadrant ring stretch
in the 1580−1550 cm−1
region, and the semicircle
ring stretch in the 1467−1410 cm−1
region. A
particularly useful Raman band is the ring nitrogen
in-phase radial mode found in the 992−981 cm−1
region. The skewed calculated forms for the degen-
erate vibrations have been converted to the usual
symmetric and antisymmetric forms.
Acknowledgements
The authors gratefully acknowledge Dr Prashant
S. Bhandare of Bio-Rad, Digilab Division for his
help with the FT-Raman measurement of s-tri-
azine. We also acknowledge CYTEC Industries for
support and permission to publish this work.
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