Topic

# Bent molecular geometry

About: Bent molecular geometry is a research topic. Over the lifetime, 9142 publications have been published within this topic receiving 59498 citations.

##### Papers published on a yearly basis

##### Papers

More filters

••

TL;DR: In this paper, a method for extracting a unique set of atomic hybrids and bond orbitals for a given molecule, thereby constructing its Lewis structure in an a priori manner, is described.

Abstract: From the information contained in the (exact or approximate) first-order density matrix, we describe a method for extracting a unique set of atomic hybrids and bond orbitals for a given molecule, thereby constructing its “Lewis structure” in an a priori manner. These natural hybrids are optimal in a certain sense, are efficiently computed, and seem to agree well with chemical intuition (as summarized, for example, in Bent’s Rule) and with hybrids obtained by other procedures. Using simple INDO-SCF-MO wave functions, we give applications of the natural hybrid orbital analysis to molecules exhibiting a variety of bonding features, including lone pairs, multiple bonds, strained rings, and “bent bonds”, multiple resonance structures, hydrogen bonds, and three-center bonds. Three examples are described in greater detail: (i) “orbital following” during ammonia umbrella inversion, (ii) the dimerization of water molecules, and (iii) the hydrogen-bridged bonds of diborane.

4,338 citations

••

TL;DR: The "coding theory" point of view for studying the existence of almost bent functions is developed, showing explicitly the links with cyclic codes and new characterizations are given by means of associated Boolean functions.

Abstract: Almost bent functions oppose an optimum resistance to linear and differential cryptanalysis. We present basic properties of almost bent functions; particularly we give an upper bound on the degree. We develop the "coding theory" point of view for studying the existence of almost bent functions, showing explicitly the links with cyclic codes. We also give new characterizations of almost bent functions by means of associated Boolean functions.

649 citations

••

TL;DR: In this article, the authors derived an expression for the vibration-rotation Hamiltonian of a triatomic molecule using a curvilinear bending coordinate and two rectilinear stretching coordinates in such a way that the Hamiltonian obtained is applicable for any linear or bent, and allows for large displacements of the bending coordinate.

538 citations

••

TL;DR: In this paper, the Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions is investigated, and it is shown that if the tube is non-straight and its curvature vanishes asymptotically, there is always a bound state below the bottom of the essential spectrum.

Abstract: Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions is investigated. It is shown that if the tube is non-straight and its curvature vanishes asymptotically, there is always a bound state below the bottom of the essential spectrum. An upper bound to the number of these bound states in thin tubes is derived. Furthermore, if the tube is only slightly bent, there is just one bound state; we derive its behaviour with respect to the bending angle. Finally, perturbation theory of these eigenvalues in any thin tube with respect to the tube radius is constructed and some open questions are formulated.

469 citations

••

TL;DR: In this article, a bond-valence analysis of the repulsion leads to the conclusion that strong and weak hydrogen bonds are different in kind, the stronger ones involve strain and are linear while the weaker ones (O-O greater than 2.7 A) have an extra degree of freedom and are generally bent.

Abstract: The asymmetry of hydrogen bonds arises from the repulsion between the O atoms forming the bonds. A bond-valence analysis of the repulsion leads to the conclusion that strong and weak hydrogen bonds are different in kind, the stronger ones (O-O less than 2.7 A) involve strain and are linear while the weaker ones (O-O greater than 2.7 A) have an extra degree of freedom and are generally bent. The strength of the hydrogen bond is determined by a number of factors such as the requirement that the bond valences around each atom add up to the atomic valence, a tendency for the O-O distance to be close to 2.7 A, and by crystal-packing considerations which often lead to the formation of bent, and hence weaker, hydrogen bonds. The bond-valence analysis correctly predicts the observed correlations between H⋯O distance and O-H-O angle. The frequency with which various hydrogen-bond configurations are observed in crystals is used to propose a method for determining hydrogen-bond energies. This analysis of hydrogen bonding leads to an understanding of the lengthening of hydrogen bonds in high-pressure ices and to proposals for hydrated ion structures which can be used, for example, to predict the acid strengths of anions and to show that in neutral aqueous solutions the oxygen atoms of complex anions each hydrogen-bond to two or three water molecules.

462 citations