AbstractThe first quantum-mechanical calculations of all relevant potential constants in both the iron-molybdenum cofactor and the iron-vanadium cofactor of nitrogenase suggest that the carbide is bound to the center of the enzyme much more strongly than hitherto assumed. Previous studies seemed to indicate a dummy function of the interstitial carbon, with a weak force constant (ca. 0.32 N cm−1). Our new investigations confirm a different picture: the central carbon atom binds the iron-sulfur cluster through six covalent C−Fe bonds. With a potential constant of more than 1.3 N cm−1, the interstitial carbon also appears to be dynamically persistent. According to our investigations, the values for the elasticity within the iron-sulfur cluster have to be corrected too. These new details on the mechano-chemical properties of the FeMo cofactor will be important for elucidating the catalytic cycle of nitrogen fixation. By implementing our new algorithm in the freely available COMPLIANCE program, the dependence on the coordinates during the calculation of Hesse matrices is eliminated completely.

AbstractDie erste quantenmechanische Berechnung aller relevanten Potentialkonstanten (Compliance-Konstanten) im Eisen-Molybdän-Cofaktor und Eisen-Vanadium-Cofaktor der Nitrogenase deutet darauf hin, dass das Kohlenstoffatom im Zentrum des Enzyms deutlich stärker gebunden ist als bisher angenommen wurde. Frühere Untersuchungen schienen mit einer schwachen Kraftkonstante (≈0.32 N cm−1) auf eine Platzhalterfunktion des interstitiellen Kohlenstoffs hinzudeuten. Dagegen bestätigen unsere Untersuchungen ein anderes Bild: Der zentrale Kohlenstoff fixiert den Eisen-Schwefel-Cluster deutlich durch sechs kovalente C-Fe-Bindungen. Mit einer quantenchemisch berechneten Potentialkonstante von über 1.3 N cm−1 scheint dieser auch dynamisch persistent. Nach unseren Untersuchungen müssen auch die Werte für die Festigkeit innerhalb des Eisen-Schwefel-Clusters nach oben korrigiert werden. Durch die Implementierung eines neuen Algorithmus in unser frei verfügbares Programm COMPLIANCE fällt in Zukunft die Koordinatenabhängigkeit bei der Berechnung von Hesse-Matrizen weg. Die neu gewonnenen Informationen über die mechanochemischen Eigenschaften des FeMo-Cofaktors werden in Zukunft bei der Aufklärung des Katalysezyklus der Stickstoff-Fixierung von Bedeutung sein.

In a recent publication, the interpretation of Braunschweig's diboryne NHC–BB–NHC as a true triple bond is questioned. The analysis by Köppe and Schnöckel is based, inter alia, on the calculation of rigid coupling force constants. Nevertheless, since it is known for a long time that the use of rigid force constants as bond strength descriptors is by no means straightforward, we recomputed the rigid force constants for a model diboryne, applying different coordinate systems and compared the values with the relaxed force constants (generalized compliance constants, GCC). In contrast with the results by Schnöckel and Köppe, the true coupling between the boron–boron bond and the boron–carbon bond, that is, after the elimination of all numerical artifacts, is negligible (fBB/BC = −0.003).

Different force fields and approximate density functional theory were applied in order to study the rotamer space of the telomeric G-quadruplex DNA. While some force fields show an erratic behavior when it comes to the reproduction of the higher-order DNA conformer space, OPLS and MMFF implementations are able to reproduce the experimentally known energy order. The stabilizing effect of the AA (anti–anti) versus SA (syn–anti) conformer is analyzed applying mechanical bond strength descriptors (compliance constants). The fact that we observe the correct energy order using appropriate force fields is in contrast with results previously reported, which suggested the general inappropriateness of force fields for the description of G-quadruplex structures.

Just as the potential energy can be written as a quadratic form in internal coordinates, so it can also be expanded in terms of generalized forces. The resulting coefficients are termed compliance constants. In this article, the suitability of compliance constants as non-covalent bond strength descriptors is studied (a) for a series of weakly bound hydrogen halide–rare gas complexes applying a configuration interaction theory, (b) for a double stranded DNA 4-mer using approximate density functional methods and finally (c) for a double stranded DNA 20-mer using empirical force fields. Our results challenge earlier studies, which concluded the inappropriateness of compliance constants as soft matter descriptors. The discrepancy may be ascribed, inter alia, to the application of an oversimplified potential function in these earlier studies, assuming a central forces approximation.

The anomer selectivity of artificial carbohydrate receptors was studied using in silico methods in order to shed light on the thermodynamic driving forces at work during molecular recognition in general. The contributions of relevant intermolecular hydrogen bonds were investigated by means of generalized compliance constants in order to dissect important from less important non-covalent interactions. Even at this moderately low rung on the ladder of complexity essential aspects of molecular recognition are not explainable in terms of additive intermolecular interactions. Though molecular recognition seems to be a complex and emergent property, a rationale for the diastereoselectivity of carbohydrate receptors was obtained by a combination of experimental data, free energy simulations and ab initio calculations.

Knowledge about individual covalent or non-covalent bond strengths is the Holy Grail of many modern molecular sciences. Recent developments of new descriptors for such interaction strengths based on potential constants are summarised in this tutorial review. Several publications for and against the use of compliance matrices (inverse force constants matrix) have appeared in the literature in the last few years. However the mathematical basis for understanding, and therefore interpreting, compliance constants is still not well developed. We therefore summarise the theoretical foundations and point to the advantages and disadvantages of the use of force constants versus compliance constants for the description of both non-covalent and covalent interactions.

A systematic search for a quick and cost-effective theoretical method suitable for simultaneous studies of the structures, spectra and atomization energies of polyphosphorus compounds has been performed. It is demonstrated that density functional theory in BPW91/cc-pVTZ formulation provides a reasonable description of small Pn (n = 2, 3, 4, 6) clusters and PnRm molecules (R = H, C(SiH3)3, n = 1, 2; m = 1, 2, 4), close to that achieved by far more expensive coupled cluster calculations. In order to assign intrinsic PP bond strengths compliance matrices have been calculated. It is shown that compliance constants of PP bonds provide a unique tool for assigning individual mechanical bond strengths in small cluster systems.

The vibrational spectra of 3,3′′,5,5″-tetrachloro-p-terphenyl, 2,2″,4,4″-tetrachloro-p-terphenyl, 2′,3,3″,5,5″-pentachloro-p-terphenyl and 3,3″,5,5″-tetrachloro-m-terphenyl have been calculated using hybrid density functional theory (B3LYP/6-31G*) and a single scaling factor. The calculated spectra have been compared to experimental gas phase spectra. The agreement between theoretical and experimental spectra is excellent and allows the identification of an unknown congener just by pattern recognition. Differences of individual C–Cl bond strengths were studied by compliance matrix calculations.

In a recent publication, the interpretation of Braunschweig's diboryne NHC–BB–NHC as a true triple bond is questioned. The analysis by Köppe and Schnöckel is based, inter alia, on the calculation of rigid coupling force constants. Nevertheless, since it is known for a long time that the use of rigid force constants as bond strength descriptors is by no means straightforward, we recomputed the rigid force constants for a model diboryne, applying different coordinate systems and compared the values with the relaxed force constants (generalized compliance constants, GCC). In contrast with the results by Schnöckel and Köppe, the true coupling between the boron–boron bond and the boron–carbon bond, that is, after the elimination of all numerical artifacts, is negligible (fBB/BC = −0.003).

Knowledge about individual covalent or non-covalent bond strengths is the Holy Grail of many modern molecular sciences. Recent developments of new descriptors for such interaction strengths based on potential constants are summarised in this tutorial review. Several publications for and against the use of compliance matrices (inverse force constants matrix) have appeared in the literature in the last few years. However the mathematical basis for understanding, and therefore interpreting, compliance constants is still not well developed. We therefore summarise the theoretical foundations and point to the advantages and disadvantages of the use of force constants versus compliance constants for the description of both non-covalent and covalent interactions.

The anomer selectivity of artificial carbohydrate receptors was studied using in silico methods in order to shed light on the thermodynamic driving forces at work during molecular recognition in general. The contributions of relevant intermolecular hydrogen bonds were investigated by means of generalized compliance constants in order to dissect important from less important non-covalent interactions. Even at this moderately low rung on the ladder of complexity essential aspects of molecular recognition are not explainable in terms of additive intermolecular interactions. Though molecular recognition seems to be a complex and emergent property, a rationale for the diastereoselectivity of carbohydrate receptors was obtained by a combination of experimental data, free energy simulations and ab initio calculations.