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These combinations are chosen to satisfy two conditions. First, the total amount of s and p orbital contributions must be equivalent before and after hybridisation. Second, the hybrid orbitals must be orthogonal to each other. [27] [28] If two hybrid orbitals were not orthogonal, by definition they would have nonzero orbital overlap. Electrons ...
Orthogonal ligand-protein pairs (also known as re-engineered ligand-receptor interfaces or re-engineered enzyme-substrate interactions) are a protein-ligand binding pair made to be independent of the original binding pair. This is done by taking a mutant protein (naturally occurring or selectively engineered), which is activated by a different ...
An example is cyclopropane which, because of its planar geometry, has six fully eclipsed carbon and axial hydrogen bonds making the strain 116 kJ/mol (27.7 kcal/mol). [5] Strain can also be decreased when the carbon-carbon bond angles are close or at the preferred bond angle of 109.5°, meaning a ring having six tetrahedral carbons is typically ...
Example of a localized Wannier function of titanium in barium titanate (BaTiO3) Although, like localized molecular orbitals, Wannier functions can be chosen in many different ways, [3] the original, [1] simplest, and most common definition in solid-state physics is as follows.
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
This definition can be formalized in Cartesian space by defining the dot product and specifying that two vectors in the plane are orthogonal if their dot product is zero. Similarly, the construction of the norm of a vector is motivated by a desire to extend the intuitive notion of the length of a vector to higher-dimensional spaces.
The overlap matrix is a square matrix, used in quantum chemistry to describe the inter-relationship of a set of basis vectors of a quantum system, such as an atomic orbital basis set used in molecular electronic structure calculations. In particular, if the vectors are orthogonal to one another, the
The concepts of syn and anti addition are used to characterize the different reactions of organic chemistry by reflecting the stereochemistry of the products in a reaction. The type of addition that occurs depends on multiple different factors of a reaction, and is defined by the final orientation of the substituents on the parent molecule .