To further check if the same trend is observed in higher dimension, twodimensional calculations were performed. The chosen internal coordinates are z and
R. A two dimensional potential energy surface was calculated and its corresponding
vibrational Schrödinger equation was numerically solved using eleven-point finite
difference. The results are shown in Table 4. Based from the results, the same trend
was found to that of the one-dimensional treatment.
3.3 Possible Experimental Observables
To link this counter intuitive bathochromic shift to possible experimental observables. We compute IR spectra associated from transition from ground vibrational
state from the two-dimensional PES. The integrated absorption coefficient is calculated by integrating over the dipole surface computed by the same level of DFT
method. In Fig. 6, the stick spectra are shown, note that the most intense transitions
(|0, 0> to |1, 0>) associated with ν sp can be found within 300–650 cm
−1 . From
ammonia to trimethylamine these intense peaks show a low-frequency shift—a
clear demonstration of the bathochromic shift we proposed.
Vibrational signature of ν NN is normally forbidden in IR, but in these systems we
can observe strong combination bands due to the strong coupling between z- and
R-motion. ν NN can be found within 200–500 cm
−1 and the decrease of the gaps
associated with ν NN is mainly due to the increase of mass from ammonia to
trimethylamine.
So far experimental vibrational spectra for proton bound dimers of methylamine,
dimethylamine and trimethylamine are not yet available in the literature. We hope
that our calculated IR spectra can stimulate further experimental work along this
direction.
Table 4 Transition wavenumbers (ν) relative to the ground state for protonated symmetric dimers
of ammonia and amines under two-dimensional (z and R) treatment
(NH 3 ) 2 H
+
(MeNH 2 ) 2 H
+
(Me 2 NH) 2 H
+
(Me 3 N) 2 H
+
|z, R>
ν (cm
−1
)
ν (cm
−1
)
ν (cm
−1
)
ν (cm
−1
)
|0, 0>
0.00
0.00
0.00
0.00
|0, 1>
462.98
334.91
266.02
213.98
|1, 0>
613.49
546.32
462.54
345.65
|0, 2>
888.20
647.23
512.94
410.75
|1, 1>
1,016.45
837.22
694.62
536.95
Proton Quantum Confinement on Symmetric …
87
R. A two dimensional potential energy surface was calculated and its corresponding
vibrational Schrödinger equation was numerically solved using eleven-point finite
difference. The results are shown in Table 4. Based from the results, the same trend
was found to that of the one-dimensional treatment.
3.3 Possible Experimental Observables
To link this counter intuitive bathochromic shift to possible experimental observables. We compute IR spectra associated from transition from ground vibrational
state from the two-dimensional PES. The integrated absorption coefficient is calculated by integrating over the dipole surface computed by the same level of DFT
method. In Fig. 6, the stick spectra are shown, note that the most intense transitions
(|0, 0> to |1, 0>) associated with ν sp can be found within 300–650 cm
−1 . From
ammonia to trimethylamine these intense peaks show a low-frequency shift—a
clear demonstration of the bathochromic shift we proposed.
Vibrational signature of ν NN is normally forbidden in IR, but in these systems we
can observe strong combination bands due to the strong coupling between z- and
R-motion. ν NN can be found within 200–500 cm
−1 and the decrease of the gaps
associated with ν NN is mainly due to the increase of mass from ammonia to
trimethylamine.
So far experimental vibrational spectra for proton bound dimers of methylamine,
dimethylamine and trimethylamine are not yet available in the literature. We hope
that our calculated IR spectra can stimulate further experimental work along this
direction.
Table 4 Transition wavenumbers (ν) relative to the ground state for protonated symmetric dimers
of ammonia and amines under two-dimensional (z and R) treatment
(NH 3 ) 2 H
+
(MeNH 2 ) 2 H
+
(Me 2 NH) 2 H
+
(Me 3 N) 2 H
+
|z, R>
ν (cm
−1
)
ν (cm
−1
)
ν (cm
−1
)
ν (cm
−1
)
|0, 0>
0.00
0.00
0.00
0.00
|0, 1>
462.98
334.91
266.02
213.98
|1, 0>
613.49
546.32
462.54
345.65
|0, 2>
888.20
647.23
512.94
410.75
|1, 1>
1,016.45
837.22
694.62
536.95
Proton Quantum Confinement on Symmetric …
87