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The bond angle between the two hydrogen atoms is approximately 104.45°. [1] Nonlinear geometry is commonly observed for other triatomic molecules and ions containing only main group elements, prominent examples being nitrogen dioxide (NO 2), sulfur dichloride (SCl 2), and methylene (CH 2).
Yet, clearly the bond angles between all these molecules deviate from their ideal geometries in different ways. Bent's rule can help elucidate these apparent discrepancies. [5] [20] [21] Electronegative substituents will have more p character. [5] [20] Bond angle has a proportional relationship with s character and an inverse relationship with ...
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in ...
In practice the most significant of these is bond convexity, the second derivative of bond price with respect to interest rates. As the second derivative is the first non-linear term, and thus often the most significant, "convexity" is also used loosely to refer to non-linearities generally, including higher-order terms.
Molecular geometries can be specified in terms of 'bond lengths', 'bond angles' and 'torsional angles'. The bond length is defined to be the average distance between the nuclei of two atoms bonded together in any given molecule. A bond angle is the angle formed between three atoms across at least two bonds.
This difference in convexity can also be used to explain the price differential from an MBS to a Treasury bond. However, the OAS figure is usually preferred. The discussion of the "negative convexity" and "option cost" of a bond is essentially a discussion of a single MBS feature (rate-dependent cash flows) measured in different ways.
If the edge length of the cube is chosen as 2 units, then the two bonds OA and OB correspond to the vectors a = (1, –1, 1) and b = (1, 1, –1), and the bond angle θ is the angle between these two vectors. This angle may be calculated from the dot product of the two vectors, defined as a ⋅ b = ‖ a ‖ ‖ b ‖ cos θ where ‖ a ...
The convexity property can make optimization in some sense "easier" than the general case - for example, any local minimum must be a global minimum. Convex polygon - a 2-dimensional polygon whose interior is a convex set in the Euclidean plane. Convex polytope - an n-dimensional polytope which is also a convex set in the Euclidean n-dimensional ...