To assess the validity of using two-dimensional approach, we compare the 2D
calculations using B3LYP/6-311+G(d,p) and MP2/aug-cc-pVTZ with the 4D and
6D calculations by Yang [19]. In Table 2, it is clear that our results using B3LYP/6311+G(d,p) does not differ significantly with MP2/aug-cc-pVTZ. This in turn
justifies the use of B3LYP in this study. Moreover, vibrational variational calculations in this study will be limited to two degrees of freedom, z and R. The
researchers feel that two-dimensional treatment is sufficient for our purposes due to
the fact that: (1) An assignment of the peak is not a major concern in this study.
Instead, only a qualitative picture is sough which demonstrates quantum confinement. (2) Based from Yang’s dissertation [19], two-dimensional treatment gives
frequencies close within 250 cm
−1 .
3 Results and Discussion
Standard static quantum chemistry calculations yield an intuitive hypsochromic
shift as the degree of methylation is enhanced. Given the delocalization of the
shared proton due to its quantum nature, we carried out vibrational variational
calculations and our results show a counter intuitive bathochromic shift. The
physical origin of this counter intuitive picture is analyzed and possible experimental observables were proposed.
3.1 An Intuitive Trend Based on a Static Picture
Key structural parameters for the other amines calculated by B3LYP/6-311+G(d,p)
are tabulated in Table 3. The results show consistency with usual chemical wisdom.
Across the series, N–N distance increases due to steric strain from ammonia to
trimethylamine. On the other hand, the N–H distance decreases across the series
Table 2 Vibrational transition energies in cm
−1 for (NH 3 ) 2 H
+ ; results were from a |z, R, ф 1 , ф 2 >
(4D) and |z, R, ф 1 , ф 2 , x, y> (6D)
B3LYP
MP2
MP2
MP2
Experiment
|z, R, ф 1 , ф 2 , x, y>
2D
2D
4D
6D
Full-dimension
|0, 1, 0, 0, 0, 0>
462.98
469
421
403
–
|1, 0, 0, 0, 0, 0>
613.49
594
460
409
374
|0, 2, 0, 0, 0, 0>
888.20
893
729
701
–
|1, 1, 0, 0, 0, 0>
1,016.45
997
760
713
743
The experimental values are also tabulated for reference
All of the coordinates mentioned are the same as were defined in Fig. 1
84
J.A. Tan et al.
calculations using B3LYP/6-311+G(d,p) and MP2/aug-cc-pVTZ with the 4D and
6D calculations by Yang [19]. In Table 2, it is clear that our results using B3LYP/6311+G(d,p) does not differ significantly with MP2/aug-cc-pVTZ. This in turn
justifies the use of B3LYP in this study. Moreover, vibrational variational calculations in this study will be limited to two degrees of freedom, z and R. The
researchers feel that two-dimensional treatment is sufficient for our purposes due to
the fact that: (1) An assignment of the peak is not a major concern in this study.
Instead, only a qualitative picture is sough which demonstrates quantum confinement. (2) Based from Yang’s dissertation [19], two-dimensional treatment gives
frequencies close within 250 cm
−1 .
3 Results and Discussion
Standard static quantum chemistry calculations yield an intuitive hypsochromic
shift as the degree of methylation is enhanced. Given the delocalization of the
shared proton due to its quantum nature, we carried out vibrational variational
calculations and our results show a counter intuitive bathochromic shift. The
physical origin of this counter intuitive picture is analyzed and possible experimental observables were proposed.
3.1 An Intuitive Trend Based on a Static Picture
Key structural parameters for the other amines calculated by B3LYP/6-311+G(d,p)
are tabulated in Table 3. The results show consistency with usual chemical wisdom.
Across the series, N–N distance increases due to steric strain from ammonia to
trimethylamine. On the other hand, the N–H distance decreases across the series
Table 2 Vibrational transition energies in cm
−1 for (NH 3 ) 2 H
+ ; results were from a |z, R, ф 1 , ф 2 >
(4D) and |z, R, ф 1 , ф 2 , x, y> (6D)
B3LYP
MP2
MP2
MP2
Experiment
|z, R, ф 1 , ф 2 , x, y>
2D
2D
4D
6D
Full-dimension
|0, 1, 0, 0, 0, 0>
462.98
469
421
403
–
|1, 0, 0, 0, 0, 0>
613.49
594
460
409
374
|0, 2, 0, 0, 0, 0>
888.20
893
729
701
–
|1, 1, 0, 0, 0, 0>
1,016.45
997
760
713
743
The experimental values are also tabulated for reference
All of the coordinates mentioned are the same as were defined in Fig. 1
84
J.A. Tan et al.