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Linear organic molecules, such as acetylene (HC≡CH), are often described by invoking sp orbital hybridization for their carbon centers. Two sp orbitals. According to the VSEPR model (Valence Shell Electron Pair Repulsion model), linear geometry occurs at central atoms with two bonded atoms and zero or three lone pairs (AX 2 or AX 2 E 3) in ...
For example, when there are two electron pairs surrounding the central atom, their mutual repulsion is minimal when they lie at opposite poles of the sphere. Therefore, the central atom is predicted to adopt a linear geometry. If there are 3 electron pairs surrounding the central atom, their repulsion is minimized by placing them at the ...
Angular: Angular molecules (also called bent or V-shaped) have a non-linear shape. For example, water (H 2 O), which has an angle of about 105°. A water molecule has two pairs of bonded electrons and two unshared lone pairs. Tetrahedral: Tetra-signifies four, and -hedral relates to a face of a solid, so "tetrahedral" literally means "having ...
3) is also based upon a trigonal bipyramid, but the actual molecular geometry is linear with terminal iodine atoms in the two axial positions only and the three equatorial positions occupied by lone pairs of electrons (AX 2 E 3); another example of this geometry is provided by xenon difluoride, XeF 2.
The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...
[5] [22] For instance, a modification of this analysis is still viable, even if the lone pairs of H 2 O are considered to be inequivalent by virtue of their symmetry (i.e., only s, and in-plane p x and p y oxygen AOs are hybridized to form the two O-H bonding orbitals σ O-H and lone pair n O (σ), while p z becomes an inequivalent pure p ...
The seesaw geometry occurs when a molecule has a steric number of 5, with the central atom being bonded to 4 other atoms and 1 lone pair (AX 4 E 1 in AXE notation). An atom bonded to 5 other atoms (and no lone pairs) forms a trigonal bipyramid with two axial and three equatorial positions, but in the seesaw geometry one of the atoms is replaced ...
For example, suppose L, L′ are distinct lines in determined by points x, y and x′, y′, respectively. Linear combinations of their determining points give linear combinations of their Plücker coordinates, generating a one-parameter family of lines containing L and L′. This corresponds to a one-dimensional linear subspace ...