Relating normal vibrational modes to local vibrational modes with the help of an adiabatic connection scheme

Abstract

Information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes. However, normal vibrational modes result from a coupling of local vibrational modes, which means that only the latter can provide detailed insight into bonding and other structural features. In this work, it is proven that the adiabatic internal coordinate vibrational modes of Konkoli and Cremer [Int. J. Quantum Chem. 67, 29 (1998)] represent a unique set of local modes that is directly related to the normal vibrational modes. The missing link between these two sets of modes are the compliance constants of Decius, which turn out to be the reciprocals of the local mode force constants of Konkoli and Cremer. Using the compliance constants matrix, the local mode frequencies of any molecule can be converted into its normal mode frequencies with the help of an adiabatic connection scheme that defines the coupling of the local modes in terms of coupling frequencies and reveals how avoided crossings between the local modes lead to changes in the character of the normal modes.

Description of pnicogen bonding with the help of vibrational spectroscopy—The missing link between theory and experiment

“…Beside complex binding energy, geometry, and vibrational frequencies, infrared and Raman spectra including the Raman depolarization ratio [16] were calculated. The local vibrational modes were derived according to Konkoli and Cremer [18,29] where the relationship between normal and local vibrational frequencies was determined with the adiabatic connection scheme (ACS) [30,31]. For each normal mode frequency the corresponding local mode and coupling frequencies were determined and checked whether they lead to the conservation of the zeropoint energy of the molecule.…”

“…Vibrational modes probe the electronic structure and the bonds of a molecule or a molecular complex. Therefore, the stretching force constants provide a direct measure of the strength of the bonds of a molecule and the bending force constants about bond-bond interactions based on hybridization, electrostatic, and/or polarization effects [18,29,17,32,30,35].…”

Periodicity and Covalency of [MX2]– (M = Cu, Ag, Au, Rg; X = H, Cl, CN) Complexes

“…[37] All-electron basis sets aug-ccpVTZ were used for H, Cl, [38] C, and N. By using the AIMALL program, [22] atom-in-molecule (AIM) analyses were performed to determine the electron delocalization between metals and ligands. The adiabatic force constants were determined by using the code developed by Cremer and co-workers [39] based on the force constant matrix from DFT/B3LYP calculations.…”

Are compliance constants ill-defined descriptors for weak interactions?

“…15,16 In addition, in comparison with independent physical properties, other groups have successfully applied compliance constants and confirmed the significance of our results. 3,17 Very recently, in an elegant series (see for example 18 ) of papers, Cremer et al have shown that the so called local mode force constants introduced in 1998 19 amount exactly to (inverse) compliance constants introduced as early as 1947. 20 It is important to note that, as a second order tensor, the compliance matrix contains non-zero coupling elements.…”

“…If this tensor property is ignored and/or oversimplified potential functions are used, problems concerning the interpretation of compliance constants may arise. [21][22][23][24] The interpretation of exactly those coupling terms seems to have caused some troubles in the literature, 18 culminating in the conclusion that ''compliance constants are not useful diagnostics of the strength of weak interatomic interactions'' at all. 21,22 In order to verify, or falsify, this finding and to further elucidate the interpretation of compliance off-diagonal terms, the following study was split into two parts: in part one, we present detailed results on a series of rare gas-hydrogen iodide complexes comprising solely of van der Waals bonding.…”