Time-Resolved Dispersive IR Study on p-Nitroaniline
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(Figure 4a). First, the 1250–1370 cmꢀ1 region displays two,
well-separated strong bands with reversed relative intensi-
ties. In addition, the 1450–1650 cmꢀ1 region is distinct from
the experiment. These findings suggest that solvation of
PNA by CD3CN has substantial effects on the resulting IR
spectra and that one should not use a bare, gas-phase molec-
ular model for interpretation of the triplet-state IR spec-
trum. It is customary to account for the solvent effects by
using some implicitly solvated model, in which the solvent is
represented, for example, as a dielectric continuum with a
given dielectric constant (e=37.5 for CD3CN). The resulting
spectrum obtained with B3LYP combined with the polariza-
ble continuum model (PCM) does not show any considera-
ble improvement in comparison with the gas-phase spec-
trum. The main difference from experiment for the simulat-
ed B3LYP/PCM IR spectrum of PNA (Figure 4c) concerns
three details: 1) the doublet structure in the 1317 cmꢀ1 band
is missing, 2) the band around 1600 cmꢀ1 is split, and 3) the
band at 1636 cmꢀ1 is missing. The overall comparison of the
computed gas-phase and PCM spectra with experiment sug-
gest that none of these methods can be successfully used for
interpretation of the recorded triplet-state IR spectrum of
PNA.
can have substantial influence on the simulated IR spec-
tra.[28] It turned out that this effect is negligible,[4,16] but in
the course of this investigation, we have found that some
part of the spectrum changes quite dramatically with varia-
ꢀ
tion of the C NH2 distance. Slight elongation (0.012 ꢂ) of
ꢀ
the C NH2 bond from its equilibrium length (1.352 ꢂ) pro-
duces a hump on the single band at 1300 cmꢀ1, and gives
perfect agreement between the simulated spectra and the
experimental results in the whole spectral window studied
(Figures 3g and 4e). The energy of 0.07 kcalmolꢀ1 associat-
ed with such elongation is completely negligible on the mo-
lecular scale.
The origin of the doublet feature at around 1320 cmꢀ1 has
been a subject of debate.[13–15,17,19,21] Two possible mecha-
nisms for this doublet have been suggested: one is a Fermi
resonance[13,17] and the other is the existence of two distinct
solvated forms of PNA.[14,21] However, according to our cal-
culations, the higher- and lower-wavenumber components of
the doublet are attributed to the NO2 symmetric stretch cou-
ꢀ
pled with out-of-phase and in-phase combinations of the C
ꢀ
NH2 and C NO2 stretches, respectively (see Table 1). We
have found that their relative IR intensities are profoundly
affected by the geometry of PNA as well as by explicit sol-
vation.
Fortunately, the problems with the IR spectra obtained
with the gas-phase and PCM approaches can be almost com-
pletely resolved if one employs an explicitly solvated model
of PNA in which two CD3CN molecules are hydrogen-
bonded to the NH2 group (hereafter referred to as the
PNA+2ACN model; see Figure S3a in the Supporting In-
formation for its geometry). The resulting spectrum (Fig-
ure 4d) shows very good agreement with the experimental
data, except for the missing hump at 1332 cmꢀ1. We consid-
ered a multitude of various explicitly solvated models con-
taining one to six CD3CN molecules attached either to the
NH2 group or the NO2 group, or aligned along the ring (see
Figure 4 f for the calculated IR spectrum and Figure S3b in
the Supporting Information for the geometry of six solvent
molecules, i.e., PNA+6ACN). All of the resulting spectra
are quite similar in terms of a strong single band in the
1300–1400 cmꢀ1 region and reasonable agreement with ex-
periment in the 1600–1700 cmꢀ1 region. The main difference
lies in the region around 1500 cmꢀ1, for which the presence
of four or more solvent molecules results in two split bands.
This is an interesting finding, possibly suggesting that the
first solvation shell of PNA consists of maximally three sol-
vent molecules. One may argue that PNA is capable of
forming only two hydrogen bonds with the solvent mole-
cules through the NH2 group. However, we have found that
B3LYP predicts binding energies of CD3CN to the NH2 and
NO2 groups of similar order of magnitude: 5.5 and 3.5 kcal
molꢀ1, respectively.
One may argue that the bond elongation we have devised
is not justified. However, we would like to present a number
of justifications for such an action. First, we note that the
ꢀ
computed C NH2 bond length in the free and solvated PNA
models varies between 1.343 and 1.375 ꢂ depending on the
number and orientation of the explicitly attached solvent
molecules. The elongation we engineered to reproduce the
experimental spectrum yields a bond length of 1.364 ꢂ,
which falls in the above-mentioned interval. Note that the
engineered elongation is comparable in magnitude to a typi-
cal error (approximately 0.01 ꢂ) expected from DFT calcu-
lations of equilibrium bond lengths. The elongation may
give rise to a certain intensity redistribution in the simulated
IR spectrum, but it does not influence the positions of the
vibrational bands. If we reoptimize the molecular geometry
ꢀ
while keeping the new C NH2 bond length frozen and recal-
culate the spectrum, the largest frequency change is only
15 cmꢀ1. One may inquire whether the engineered elonga-
tion has some physical interpretation. This question is readi-
ly answered by taking into account the contrast between the
intrinsic static nature of the model used in our quantum
chemical calculations and the inherently dynamic behavior
of a real vibrating molecule. Quantum chemical methods
usually give us information about the (static) equilibrium
bond lengths re, but it would be more desirable to consider
the distances averaged over the ground vibrational wave
functions r0, which provide more physically meaningful in-
formation about the time-averaged interatomic distances in
a molecule. For a purely harmonic vibration, these two
The optimized structures of PNA with explicitly attached
solvent molecules display small variations in equilibrium ge-
ometry, which concern mainly the out-of-plane angles of the
ꢀ
quantities would be equal. However, the C NH2 bond
ꢀ
ꢀ
NH2 and NO2 groups and the C NH2 and C NO2 distances.
We have anticipated that the dependence of the out-of-
plane, low-frequency motions of the NH2 and NO2 groups
stretch, like nearly any other stretching vibration, has an an-
harmonic vibrational potential for which r0 is larger than re.
ꢀ
Additional support for the C NH2 bond elongation comes
Chem. Eur. J. 2012, 18, 2543 – 2550
ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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