Accurate Equilibrium Structures

Finally, we focus on the derivation of highly accurate structural information, by mixed experimental-theoretical analysis. As already mentioned, the equilibrium structure is directly related to the instead of experimentally measured Bq rotational constants. As a consequence, its elucidation requires explicit consideration of vibrational effects, which, within a pure experimental approach, would require the knowledge of experimental vibrational corrections to rotational constants for all isotopic species considered. A viable alternative is provided by the QM computations of the corresponding vibrational corrections [29], which can be obtained very effectively by second-order vibrational perturbation theory (VPT2) [210, 214] applied to a cubic force field [214-216] (see Section 10.3.2 for an extended account on VPT2). The combination of experimental ground-state rotational constants with computed vibrational corrections see Eq. 10.6) allows 

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Recent microwave data for the potential interstellar molecule Sis is used together with high-level coupled-cluster calculations to extract an accurate equilibrium structure. Observed rotational constants for several isotopomers have been corrected for effects of vibration-rotation interaction subsequent least-squares refinements of structural parameters provide the equilibrium structure. This combined experimental-theoretical approach yields the following parameters for this C2v molecule re(SiSi) = 2.173 0.002A and 0e(SiSiSi) = 78.1 O.2 ... 

The purpose of this report is to demonstrate the ease with which highly accurate equilibrium structures can be determined by combining laboratory microwave data with the results of ab initio calculations. In this procedure, the effects of vibration-rotation interaction are calculated and removed from the observed rotational constants, Aq, Bq and Cq. The resulting values correspond to approximate rigid-rotor constants and and are thus inversely... 

Equilibrium Structure Accurate equilibrium structures are required in... 

The corresponding required calculations have been presented that is, to fulfil point (a) accurate equilibrium structures as well as harmonic and anharmonic force field computations are necessary, for point (b) accurate dipole moment evaluations are needed, and for point (c) electric field gradient, spin-rotation and spin-spin tensor calculations are required. Furthermore, for meaningful predictions and/or comparisons to experiment, the vibrational corrections related to points (a) to (c) are also required. 

As with hydrocarbons, accurate descriptions of equilibrium structures for molecules with heteroatoms from density functional and MP2 models requires polarization basis sets. As shown in Table A5-20 (Appendix A5), bond distances in these compounds obtained from (EDF 1 and B3LYP) density functional models and from MP2 models... 

It is not known if the effect of flexibility is an equilibrium or kinetic effect. The flexibility might allow the compounds to expand or contract to fill available space in the VP1 hydrophobic pocket. Alternatively, the flexibility may allow the compounds to achieve a conformation required to enter or leave the pocket, but this conformation would not be seen in the crystallographic experiment. If this is true, modeling of the equilibrium structure of compounds in the pocket will not be accurate predictors of compound potency. 

Hartree-Fock theory is a rigorous ab initio theory of electronic structure and has a vast array of successes to its credit. Equilibrium structures of most molecules are calculated almost to experimental accuracy, and reasonably accurate properties (e.g., dipole moments and IR and Raman intensities) can be calculated from HF wave functions. Rela-... 

The most common response nowadays is to supplement the experimental data with the highest quality ab initio data that can be had (either from molecular orbital or density functional calculations). A pleasant feature of using theoretical data is that one can compare regions on a PES that are far from equilibrium structures by direct computation rather than by trying to interpret vibrational spectra. Furthermore, one can attempt to make force-field energy derivatives correspond to those computed ab initio. The only limitation to this approach is the computational resources that are required to ensure that the ab initio data are sufficiently accurate. 

A molecule contains a nuclear distribution and an electronic distribution there is nothing else in a molecule. The nuclear arrangement is fully reflected in the electronic density distribution, consequently, the electronic density and its changes are sufficient to derive all information on all molecular properties. Molecular bodies are the fuzzy bodies of electronic charge density distributions consequently, the shape and shape changes of these fuzzy bodies potentially describe all molecular properties. Modern computational methods of quantum chemistry provide practical means to describe molecular electron distributions, and sufficiently accurate quantum chemical representations of the fuzzy molecular bodies are of importance for many reasons. A detailed analysis and understanding of "static" molecular properties such as "equilibrium" structure, and the more important dynamic properties such as vibrations, conformational changes and chemical reactions are hardly possible without a description of the molecule itself that implies a description of molecular bodies. 

It was, therefore, clear in 1974 that electronic-structure methods were not sufficiently advanced to reproduce experimental data accurately for even a simple ionic oxide such as MgO. The emphasis at the time was on the determination of the effects of different approximations upon the calculated results. Comparison was usually made between one calculation and another rather than between calculation and experiment. The theoretical papers reported the quantities arising directly from the calculations, such as orbital eigenvalues and atomic-orbital charge decompositions, and spectral properties were interpreted primarily in terms of orbital energies. No attempt was made to evaluate equilibrium structural or energetic properties. 

Both CO2-HF and CO2-HCI complexes were first examined in the gas phase by Klemperer and co-workers, using the molecular beam electric resonance technique, with the radio-frequency and microwave spectra of CO2-HF and CO2-HCI indicating nearly linear, hydrogen-bonded structures [35, 36], Accurate determinations of rotational constants allowed the separations between the centers-of-mass of each sub-unit to be obtained, and assuming that neither CO2 nor HX underwent intramolecular change, the O—H bond lengths could be estimated for each complex. A comparison of CO2-HF and CO2-HCI showed the O—H separation in the former to be 10% less than in the latter. Equilibrium structures for CO2-HF and CO2HCI are shown in Fig. 10, and Table 1 lists structural parameters for all known CO2-HX complexes. 

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