Molecular Structure

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
re	Equilibrium structure. Appears as a result of Born-Oppenheimer approximation in quantum mechanics.	QC
rg	Thermally averaged structure. rg distances are centers of gravity for corresponding distribution functions P(r), and thus can be physically defined as rg := <r>, where <> denotes averaging over the whole molecular ensemble in its specific state under observation.	GED
ra	Effective average structure parameter type resulting from fitting the theoretical model equation: Mtheo.(s)=const. Σi≠jN gij(s) exp(-0.5 lij2s2) sin[s(rij - κijs2)]/rij to experimental scattering data Mexp.(s) with respect to the parameters rij, lij and κij (distances, amplitudes and anharmonicity or "asymmetry" parameters). The resulting structure parameters rij are interpreted as "average structure parameters" of type "ra". gij(s) is the interatomic scattering cross sections function (for which ab-initio calculation based tabulated values are usually used). N is the number of scattering centers ("atoms"). In general it is not possible to assign a set of atoms to positions in a Euklidian space R3 such that values of a complete set of ra parameters correspond quantitatively exactly to the values of the distances between the atom positioned in R3 space. This is known also as the "shrinkage" problem, since due to zero point vibrational motions already for a single CO2 in the vibrational ground state: 2 ra(C-O) > ra(O-O'). In general these geometrical inconsistencies are worst for three-atom moieties describing large angles close to 180°. Since the structure parameters are obtained from diffraction patterns with Fourier-Transform relation to real space of molecular geometry an alternative (empirically motivated definition) is ra := 1/<1/r>, where <> denotes averaging over the whole molecular ensemble in its specific state under observation. From this point of view the former procedural definition of ra can be interpreted as an approximation to this quantity, holding to that extent that the model equation for sM(s) holds.	GED
rα = rh0	Distances between average nuclear positions. The averaging can be thought of to be carried out in a coordinate framework where all translational and rotational motions are projected out. Also for rα there is a procedural definition, allowing for a analytical approximation to the actual value starting from computed structures and harmonic force fields, this is the so called "rectilinear approximation" where interatomic motions are decomposed into a radial component along the bond and two rectilinear components perpendicular to the bond. In this way rectilinear rα corrections Δ =re-rα can be obtained.	GED, MW, HRMS
r0α, rz	Distances between average nuclear positions at 0 K, i.e. for ground vibrational state.	GED, MW, HRMS
rh1	Distances between average nuclear positions calculated taking into account nonlinear or "curvilinear" motion components perpendicular to the interatomic distance (similar as the above described rectili-linear corrections for rα). In this sense the rh1 is already a better approximation to re, than rα.	GED, MW, HRMS
ra3,1	Semi-experimental equilibrium structure obtained using corrections calculated by Shrink program utilizing cubic force fields.	GED, MW, HRMS
rsee	Semi-experimental equilibrium structure obtained using a set of theoretically calculated corrections to experimental and/or operational data.	GED, MW, HRMS
rs	Effective structure derived from isotopic differences in rotational constants.	MW, HRMS
r0	Effective structure derived from rotational constants of zero-point vibrational level.	MW, HRMS
rm	Effective structure derived from the mass-dependence method of Watson. Sometimes in the older literature e.g. Hargittai, Hargittai, "The molecular geometries of coordination compounds in the vapour phase", rm is used to refer to the maximum of the peaks in the radial distribution curves P(r)/r.	MW, HRMS, (GED)
rρm	Effective structure similar to rm obtained by a slightly modified method of Harmony et al.	MW, HRMS

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.<bib id="Kuchitsu1959" />