The tacit assumption underlying all science is that, of two competing theories, the one in closer agreement with experiment is the better one. In structural chemistry the same principle applies but, when calculated and experimental structures are compared, closer is not necessarily better. Structures from ab initio calculations, specifically, must not be the same as the experimental counterparts the way they are observed. This is so because ab initio geometries refer to nonexistent, vibrationless states at the minimum of potential energy, whereas structural observables represent specifically defined averages over distributions of vibrational states. In general, if one wants to make meaningful comparisons between calculated and experimental molecular structures, one must take recourse of statistical formalisms to describe the effects of vibration on the observed parameters. Among the parameters of interest to structural chemists, internuclear distances are especially important because other variables, such as bond angles, dihedral angles, and even crystal spacings, can be readily derived from them. However, how a rigid torsional angle derived from an ab initio calculation compares with the corresponding experimental value in a molecule subject to vibrational anharmonicity, is not so easy to determine. The same holds for the lattice parameters of a molecule in a dynamical crystal, and their temperature dependence as a function of the molecular potential energy surface. In contrast, vibrational effects are readily defined and best described for internuclear distances, bonded and non-bonded ones. In general, all observed internuclear distances are vibrationally averaged parameters. Due to anharmonicity, the average values will change from one vibrational state to the next and, in a molecular ensemble distributed over several states, they are temperature dependent. All these aspects dictate the need to make statistical definitions of various conceivable, different averages, or structure types. In addition, since the two main tools for quantitative structure determination in the vapor phase—gas electron diffraction and microwave spectroscopy—interact with molecular ensembles in different ways, certain operational definitions are also needed for a precise understanding of experimental structures. To illustrate how the operations of an experimental technique affect the nature of its observables, gas electron diffraction shall be used as an example.
Comparison of molecular structures of cis-bis[8-(dimethylphosphanyl)quinoline]nickel(II) and -platinum(II) complex cations