interactions
Similar attention has been paid to the interactions containing the ethylene -orbitals.
Intramolecular – interactions in diethanodihydronaphthalene (3-1a)8 and diethenodihydro- naphthalene (4-1b) must provide a fundamentally important starting point for the intramolecular –
interactions between ethylene moieties. Chart 3-1 illustrates the structures of 3-1a and 4-1b, of which intramolecular – interactions are to be clarified. The intramolecular – interactions in the derivatives of 3-1a and 4-1b must also be the typical candidates to be elucidated. The intramolecular – interactions in 3-1a, 4-1b, and the derivatives are substantially controlled by the
distances would be shorter or longer, especially for those in the rigid structures, than those expected for the minima in the intrinsic energy surfaces of the intermolecular – interactions.
It must be desirable to employ such basis set system (BSS) that reproduces well the observed distances in question, since the predicted interaction distances will affect (much) on the behavior of the – interactions. Namely, it is inevitable to examine the predicted distances, in relation to the observed ones, if the theoretically predicted behavior of the interactions is discussed in relation to the observed distances. In this case, it is necessary for the target molecule of which structure being suitably determined. The structure of 3-1a has been reported, determined by the X-ray crystallographic analysis,8 together with some derivatives,6,8 whereas that of 4-1b seems not yet, to the best of his research group knowledge. 3-1a is chosen as the first candidate to clarify the intramolecular – interaction, together with the derivatives, therefore. Chart 3-1 illustrates the structures of 3-1a and the derivatives (3-2a–3-12a), together with the molecular graphs for 3-1a–
3-12a evaluated with MP2/6-311+G(d). Numbers are given for some carbon atoms to specify the interactions.
The quantum theory of atoms-in-molecules (QTAIM) approach, introduced by Bader,15–17 enables us to analyze the nature of chemical bonds and interactions.18–23 Recently, his research group proposed QTAIM dual functional analysis (QTAIM-DFA),24–26 for experimental chemists to analyze their own results, concerning chemical bonds and interactions, by their own image.
QTAIM-DFA provides an excellent possibility for evaluating, understanding, and classifying weak to strong interactions in a unified form.24–27 Hb(rc) are plotted versus Hb(rc) – Vb(rc)/2 in QTAIM-DFA, where Hb(rc) and Vb(rc) are the total electron energy densities and potential energy densities, respectively, at bond critical points (BCPs). In his research group treatment, data for perturbed structures around fully optimized ones are employed for the plots, in addition to those of the fully optimized structures.24–28
correspond to the static nature of interactions. QTAIM-DFA is applied to typical chemical bonds and interactions, and rough criteria have been established, which can distinguish the chemical bonds and interactions in question from others. QTAIM-DFA and the criteria are explained in Chapter 2, employing Schemes 2-1–2-3, Figure 2-1 and eqs (2-8)–(2-12). The basic concept of the QTAIM approach is also surveyed in Chapter 2.
QTAIM-DFA is now applied to elucidate the dynamic and static behavior of the intramolecular
– interactions in 3-1a–3-12a, for the better understanding of the chemistry derived from the –
interactions. Herein, he presents the results of the investigations on the nature of the intramolecular
– interactions in question, as the first step to clarify the various types – interactions. The interactions are classified and characterized by employing the criteria, as a reference.
Methodological Details in Calculations
The structures were optimized employing the Gaussian 09 programs.29 Several types of basis sets were examined to search the suitable methods for the purpose. The Møller-Plesset second order energy correlation (MP2) level is applied to the calculations.30 The DFT level of M06-2X31 is also employed to examine the methods. The optimized structures were confirmed by the frequency analysis. QTAIM functions were calculated using the Gaussian 09 program package29 with the same method of the optimizations and the data were analyzed with the AIM2000 program.32
Normal coordinates of internal vibrations (NIV) obtained by the frequency analysis were employed to generate the perturbed structures.33 The method is explained in Chapter 2.
Results and Discussion
Optimizations of 3-1a and Derivatives
How can the intramolecular --- interactions in 3-1a–3-12a be suitably evaluated? Table 3-1 shows the structural parameters for 3-1a optimized with the 6-311G(d), 6-311G(3d), and
parameters are defined in Scheme 3-1. The averaged values are shown in Table 3-1 as the observed ones, since 3-1a is optimized retaining the C2v symmetry, whereas the observed structure has the C1
symmetry.
The magnitudes in the differences between predicted and observed (averaged) values in R1 are less than 0.01 Å if evaluated with MP2/6-311+G(3d), MP2/6-311G(3d), and MP2/6-311G(d).
Therefore, MP2/6-311G(d) is mainly employed for the structural optimizations of 3-1a–3-12a and the whole picture of the intramolecular – interactions between ethylene moieties is drawn with the method. (See Table 3-A3 of the Appendix and the footnote for the C---C distances.)
The substantial distortions between ethylene moieties are predicted for 3-2a–3-4a, if optimized with MP2/6-311G(d), although the distortions are negligible in the observed structures of 3-1a–3-3a.
Such distortions are not predicted for 3-1a–3-4a with MP2/6-311G(3d) (see Table 3-A5 of the Appendix). Therefore, MP2/6-311G(3d) is also employed to evaluate the interactions, in addition to MP2/6-311G(d), although the species are limited to 3-1a–3-7a, and 3-9a–3-11a. The frequency analysis is not applied to 3-4a, due to too large number of primitive gaussians. Indeed, the magnitudes of the differences between predicted and observed values in r1 and 3 amount to 0.03 Å and 1°, respectively, if calculated at the MP2 level, but they would not affect so severely on the behavior of the --- interactions.
Table 3-1. Structural parameters evaluated for 3-1a,a with the observed valuesb
Level/Basis set R1 R2 r1 r2 1 2 3 4 1
(Å) (Å) (Å) (Å) (°) (°) (°) (°) (°)
MP2/6-311+G(3d) 3.0394 2.6283 1.3450 1.4995 97.9 114.1 123.4 96.1 0.0 MP2/6-311G(3d) 3.0396 2.6279 1.3439 1.4997 97.9 114.1 123.4 96.3 0.0 MP2/6-311G(d) 3.0419 2.6335 1.3471 1.5026 97.8 114.1 123.5 96.5 0.0 Observed (average) 3.032 2.620 1.315 1.500 97.9 114.5 124.4 96.8 -0.5
a The structural parameters being defined in Scheme 3-1. b Ref. 8.