Difference between revisions of "Molecular Structure"
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| ''r''<sub>g</sub> | | ''r''<sub>g</sub> | ||
− | | Thermally averaged structure.<ref group="gt" name="tav">Interatomic distances are averaged over molecular vibrations for a given temperature. Generally such distances are geometrically inconsistent.</ref> ''r''<sub>g</sub> distances are centers of gravity for corresponding distribution functions ''P''(''r''). | + | | Thermally averaged structure.<ref group="gt" name="tav">Interatomic distances are averaged over molecular vibrations for a given temperature. Generally such distances are geometrically inconsistent. </ref> ''r''<sub>g</sub> distances are centers of gravity for corresponding distribution functions ''P''(''r''). |
| GED | | GED | ||
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| ''r''<sub>a</sub> | | ''r''<sub>a</sub> | ||
− | | Average structure <ref group="gt" name="tav" /> used for calculation of molecular scattering intensity in GED theory. | + | | Average structure <ref group="gt" name="tav" /> used for calculation of molecular scattering intensity in GED theory. The parameters correspond to ''r''<sub>ij</sub> from the model equation ''M(s)''=''const.'' Σ<sub>''i''≠''j''</sub><sup>''N''</sup> ''g''<sub>''ij''</sub>(''s'') exp(-0.5 ''l''<sub>''ij''</sub><sup>2</sup>) sin[''s''(''r''<sub>ij</sub> - κ<sub>ij</sub>''s''<sup>2</sup>)]/''r''<sub>ij</sub> with parameters ''l''<sub>''ij''</sub> interpreted as amplitudes of vibration, κ<sub>ij</sub> as anharmonicity or "asymmetry" parameters and interatomic scattering cross sections ''g''<sub>''ij''</sub>(''s''). ''N'' is the number of scattering centers ("atoms"). |
| GED | | GED | ||
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Revision as of 09:45, 15 September 2017
Molecular structure (molecular geometry) is a one of the most fundamental properties of molecules, which characterizes spatial positions of the atoms that constitute a molecule. This term is usually referred to the geometrical structure of molecules in gas phase.
Types of molecular structure
Abbreviations are:
- QC — Quantum-chemical calculations
- GED — Gas electron diffraction
- MW — Microwave spectroscopy
- HRMS — High resolution molecular spectroscopy
Type | Description | Methods |
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r_{e} | Equilibrium structure. Appears as a result of Born-Oppenheimer approximation in quantum mechanics. | QC |
r_{g} | Thermally averaged structure.^{[gt 1]} r_{g} distances are centers of gravity for corresponding distribution functions P(r). | GED |
r_{a} | Average structure ^{[gt 1]} used for calculation of molecular scattering intensity in GED theory. The parameters correspond to r_{ij} from the model equation M(s)=const. Σ_{i≠j}^{N} g_{ij}(s) exp(-0.5 l_{ij}^{2}) sin[s(r_{ij} - κ_{ij}s^{2})]/r_{ij} with parameters l_{ij} interpreted as amplitudes of vibration, κ_{ij} as anharmonicity or "asymmetry" parameters and interatomic scattering cross sections g_{ij}(s). N is the number of scattering centers ("atoms"). | GED |
r_{α} = r_{h0} | Distances between average nuclear positions.^{[gt 2]} | GED, MW, HRMS |
r^{0}_{α}, r_{z} | Distances between average nuclear positions at 0 K, i.e. for ground vibrational state.^{[gt 2]} | GED, MW, HRMS |
r_{h1} | Distances between average nuclear positions calculated taking into account nonlinear relationships between internal and Cartesian coordinates.^{[gt 2]} | GED, MW, HRMS |
r_{a3,1} | Semi-experimental equilibrium structure obtained using corrections calculated by Shrink program utilizing cubic force fields. | GED, MW, HRMS |
r^{se}_{e} | Semi-experimental equilibrium structure obtained using a set of theoretically calculated corrections to experimental and/or operational data. | GED, MW, HRMS |
r_{s} | Effective structure derived from isotopic differences in rotational constants. | MW, HRMS |
r_{0} | Effective structure derived from rotational constants of zero-point vibrational level. | MW, HRMS |
r_{m} | Effective structure derived from the mass-dependence method of Watson. | MW, HRMS |
r^{ρ}_{m} | Effective structure similar to r_{m} obtained by a slightly modified method of Harmony et al. | MW, HRMS |
- ↑ ^{1.0} ^{1.1} Interatomic distances are averaged over molecular vibrations for a given temperature. Generally such distances are geometrically inconsistent.
- ↑ ^{2.0} ^{2.1} ^{2.2} In contrast to r_{g}, where subject to averaging are interatomic distances, here atomic positions are averaged. Therefore this structure is geometrically consistent.
In some of the old GED papers the parameter types r_{g}(0) and r_{g}(1) are used. They are equivalent to normal r_{g} and r_{a} types, respectively.[Kuchitsu1959]Author: Kuchitsu, Kozo
Journal: Bulletin of the Chemical Society of Japan
Number: 7
Pages: 748-769
Title: Electron Diffraction Investigation on the Molecular Structure of n-Butane
Volume: 32
Year: 1959