Ellinger Y., Defranceschi M. (eds.) Strategies and applications in quantum chemistry (Kluwer, 200
.pdf416 |
F. PAUZAT AND D. TALBI |
The same conclusion, that MCSCF/SD expansions using orbitals optimized for the ion provide a better representation, is reached for the lowest states of symmetry which are also states of Rydberg type arising from an in-plane excitation from the carbene orbital.
4.2.2. Out-of-plane excited states
The lowest |
and |
excited states of |
correspond to valence excitations from the 1pc |
||
carbene lone pair to the |
and |
orbitals, the next states being Rydbergs. Because of this |
|||
mixing, the orbitals have been optimized in the configuration space of Table 11, hereafter referred to as MCSCF/{6422}. Here the orbitals are distributed in four different spaces according to their chemical nature and the electrons assigned so as to define a direct product of CAS subspaces. Because the second state is of Rydberg character, orbitals optimized for the ion in an equivalent expansion MCSCF/{6322} have been tested.
A PUZZLING INTERSTELLAR MOLECULE |
417 |
No significant improvement for the vertical excitation energy of the |
state was |
found. From these results we have decided to describe the lowest states of |
and |
symmetries with the same set of molecular orbitals, optimized for the neutral molecule within the MCSCF/{6422} expansion.
4.3. LOW ELECTRONIC EXCITED STATES OF
Our best estimation for the vertical excitation energies for states of |
symmetry are |
reported in Table 12. They correspond to a ground state calculated at |
level using |
orbitals optimized for the neutral molecule with the MCSCF/SD expansion, and excited
Rydberg states calculated at the |
level using orbitals optimized for the positive ion |
|||||
with the same expansion. The first excited |
state lies at 7.8 |
eV above the ground |
||||
|
state and the second excited |
state at 8.4 eV. They are all below the first |
||||
ionization potential which, in our best calculation |
is 8.98 eV. Transition moments |
|||||
have been evaluated in a first order treatment, |
The very weak value found between |
|||||
the |
and |
states leaves little hope for observation and the effort should be |
||||
concentrated on the |
to |
|
transition. |
|
|
|
The vertical excited states of |
symmetry, calculated at the |
level, are very high in |
||||
energy. The first one, |
|
is already at 8.60 eV above the ground state (Table 12) with |
||||
a transition moment of 0.16 a.u., probably too weak for the transition to be observed.
418 |
|
F. PAUZAT AND D. TALBI |
Vertical excitation energies to states of |
symmetry, calculated at the |
level using the |
orbitals optimized for the neutral molecule with the {MCSCF/6422} expansion, are
reported Table 12. The |
valence state and |
Rydberg state |
of |
are |
|
respectively 5.2 eV |
and 7.5 eV above the ground state with large transition moments of |
||||
0.60 and 0.50 a.u.respectively. |
|
|
|
||
Finaly, the lowest two |
states, calculated at the |
level using orbitals optimized for |
|||
the neutral molecule |
with the MCSCF/{6422} expansion are at 4.66 eV and 8.59 eV. |
||||
Transitions from the |
|
to these states are not symmetry-allowed and it is hardly probable |
|||
that vibronic coupling could make them observable in transient conditions. |
|
|
|||
The only state which could be seen in the 2000-6000 Å |
window is the |
valence state. |
|||
The fact that this state was not seen in spite of its strong transition moment may well be due to the experimental uncertainty of 10% at the limit of the window.
Concluding remarks
The present contribution illustrates the possible role of computational chemistry in supporting astrophysical studies aimed at the detection of new species from their radio, infra-red and electronic signatures. In the case of a very peculiar molecule such as
we have shown that theoretical approaches provide assistance at all levels of spectroscopy.
-The rotational constants, although difficult to establish with the accuracy needed for a direct search on the telescope, should be precise enough to identify the deuterated isomers in the laboratory.
-The IR spectrum of the deuterated isomers is different from what has been estimated by simple extrapolation of the hydrogenated species, which explains why several bands were not recognized in the experiments. In addition, the anharmonic progressions of the CH
stretching are found in agreement with the satellites of the |
band observed in space |
and support the "hot band hypothesis" for explaining part of their origin.
-The electronic spectrum reveals at least two states that should be observed, provided the experimental window is enlarged beyond the 2000-6000 Å region.
The results presented here show the adequation of Computational Chemistry to problems of astrophysical interest. They illustrate a promising partnership in a field largely promoted by G. Berthier in the late seventies.
References
1.P.Thaddeus, J.M. Vritilek and C.A. Gottlieb, Astrophys J. Lett.. 299, L63 (1985).
2.D. J. DeFrees and A.D. McLean, Astrophys. J. Lett.. 308 L31 (1986).
3.M. Vrtilek, C.A. Gottelib and P. Thaddeus, Astroph. J. 314, 716 (1987).
4.M. Bogey, C. Demuynck, J.L. Destombes and H. Dubus J. Mol. Spectr. 122, 313 (1987).
5.P. Cox, C.M. Walmsley and R. Gusten Astron. Astrophys. 209, 382 (1989).
6.P. Cox, R. Gusten and C. Henkel, Astron. Astrophys. 206, 108 (1988).
7.N. Brouillet, A. Baudry and G. Daigne Astron. Astrophys. 199, 312 (1988).
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422 |
Y. TAO |
2. Method and Results
The different structures and transitions states of interest in the neutral and negative ion reactions are represented in Fig. 2. A first approach was done at the SCF level, using the split-valence 4-31G basis set. In order to provide a better estimation of the energy differences implied in this reaction schemes, extensive calculations have been performed at the MP2 level of theory using the 6-311++G** basis set which contains the diffuse orbitals necessary to quantitatively describe the negative ions.
The optimized geometries are reported in Table 1. The total and relative energies of all species illustrated in Figure are presented in Table 2. All calculations have been carried out with the 82 and 90 versions of the GAUSSIAN program system [4].
3.Discussion
3.1.GEOMETRIES
For nitromethane and aci-nitromethane, the optimized structures of the present calculations with the small basis set (4-31G) are very similar to the 3-21G and 6-31G * McKee's optimized structures [1]; the variation of bond lengths and bond angles with the level of theory follows the expected trends with an increase in the bond lengths when correlation effects are taken into account. The results of the present calculations for nitromethane are also in better agreement with the cristal structure [5|.
The geometry of nitromethane (1) is characterized by the equivalence of the two NO bonds, the single bond character of the CN bond, the coplanarity of the four nonhydrogen atoms, and a value of the angle larger than 120°. The geometry of aci-nitromethane (4) is characterized by the nonequivalence of two NO bonds, the double bond character of the
AN AB INITIO STUDY OF THE INTRAMOLECULAR HYDROGEN SHIFT IN NITROMETHANE |
423 |
424 |
Y. TAO |
bond, the coplanarity of all atoms, and the retention of the ethylene-type double bond character for the CN bond.
Nitromethylene anion (5) and aci-nitromethylene anion (7) are planar molecules. In the nitromethylene anion, there is an equivalence of the two NO bonds and a clear trend of the various bond angles toward the trigonal value of 120°. By contrast, the aci-nitromethylene anion shows the nonequivalence of the two NO bonds, a typical double bond character for the CN bond, and a larger deviation of all bond angles from 120°.
Comparing with the neutral molecules, it can be seen that the presence of the negative charge makes all bond lengths in the anion increase, particulary the bond connected to the
atom bearing the negative charge. This suggests that the |
conjugation in the anionic |
systems is reduced, and the trend toward a single bond increased. In addition, the angle variation in the anions shows a smaller steric repulsion and a greater electrostatic attraction between atoms.
The transition state for the 1,3-hydrogen shift of the neutral molecule (2) involves a planar
four-membered ring. The requirement for cyclization brings the |
bond distance to a |
||||
value intermediate between the |
bond lengths of the two tautomers; there is an increase |
||||
in the CN bond, a shortening of the |
bond, and a closing of the |
angle. The |
|||
fact that the |
bond (1.123/1.065 Å |
)is less than the |
bond (1.624/1.725 Å ) in |
||
the (SCF/MP2) transition structure shows that the shifted hydrogen atom is closer to the oxygen with the larger electronegativity, namely the transition structure resembles acinitromethane with an higher energy.
The 1,3-hydrogen shift transition state of the anion (6) is a planar molecule. Similarly, due to the requirement for cyclization, the bond distances between the ring-forming atoms show a tendency to averaged values relative to those of the anions in their equilibrium states,
while the |
angle becomes smaller. In the same way, the transition structure in the |
negative ion is more similar to aci-nitromethylene though of higher energy because of the shifted hydrogen atom being closer to the negatively charged oxygen.
3.2.RELATIVE ENERGIES
It can be seen from Table 2 that the order of the relative energies is identical for the calculations at the SCF/4-31G and MP2/6311++G** levels of theory.