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A new approach to quantify hydrogen bond strengths based on interaction coordinates (HBSBIC) is proposed and is very promising. In this research, it is assumed that the projected force field of the fictitious three atoms fragment (DHA) where D is the proton donor and A is the proton acceptor from the full molecular force field of the H-bonded complex characterizes the hydrogen bond. The "interaction coordinate (IC)" derived from the internal compliance matrix elements of this three-atom fragment measures how the DH covalent bond (its electron density) responds to constrained optimization when the HA hydrogen bond is stretched by a known amount (its electron density is perturbed by a specified amount). This response of the DH bond, based on how the IC depends on the electron density along the HA bond, is a measure of the hydrogen bond strength. The inter- and intramolecular hydrogen bond strengths for a variety of chemical and biological systems are reported. When defined and evaluated using the IC approach, the HBSBIC index leads to satisfactory results. Because this involves only a three-atom fragment for each hydrogen bond, the approach should open up new directions in the study of "appropriate small fragments" in large biomolecules.

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Attempts to establish degrees of aromaticity in molecules are legion. In the present study, we begin with a fictitious fragment arising from only those atoms contributing to the aromatic ring and having a force field projected from the original system. For example, in benzene, we adopt a fictitious C6 fragment with a force field projected from the full benzene force field. When one bond or angle is stretched and kept fixed, followed by a partial optimization for all other internal coordinates, structures change from their respective equilibria. These changes are the responses of all other internal coordinates for constraining the bond or angle by unit displacements and relaxing the forces on all other internal coordinates. The "interaction coordinate" derived from the redundant internal coordinate compliance constants measures how a bond (its electron density) responds for constrained optimization when another bond or angle is stretched by a specified unit (its electron density is perturbed by a finite amount). The sum of interaction coordinates (responses) of all bonded neighbors for all internal coordinates of the fictitious fragment is a measure of the strength of the σ and π electron interactions leading to aromatic stability. This sum, based on interaction coordinates, appears to be successful as an aromaticity index for a range of chemical systems. Since the concept involves analyzing a fragment rather than the whole molecule, this idea is more general and is likely to lead to new insights.