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Sigma bonds are the strongest type of covalent bonds due to the direct overlap of orbitals, and the electrons in these bonds are sometimes referred to as sigma electrons. [3] The symbol σ is the Greek letter sigma. When viewed down the bond axis, a σ MO has a circular symmetry, hence resembling a similarly sounding "s" atomic orbital.
In the usual analysis, the p-orbitals of the metal are used for σ bonding (and have the wrong symmetry to overlap with the ligand p or π or π * orbitals anyway), so the π interactions take place with the appropriate metal d-orbitals, i.e. d xy, d xz and d yz. These are the orbitals that are non-bonding when only σ bonding takes place.
In mathematics, computer science and logic, overlap, as a property of the reduction rules in term rewriting system, describes a situation where a number of different reduction rules specify potentially contradictory ways of reducing a reducible expression, also known as a redex, within a term.
The term "Z-order" refers to the order of objects along the Z-axis. In coordinate geometry, X typically refers to the horizontal axis (left to right), Y to the vertical axis (up and down), and Z refers to the axis perpendicular to the other two (forward or backward). One can think of the windows in a GUI as a series of planes parallel to the ...
The white and grey line visible in some MO's is the molecular axis passing through the nuclei. The orbital wave functions are positive in the red regions and negative in the blue. The right column shows virtual MO's which are empty in the ground state, but may be occupied in excited states.
The mutilated chessboard problem is an instance of domino tiling of grids and polyominoes, also known as "dimer models", a general class of problems whose study in statistical mechanics dates to the work of Ralph H. Fowler and George Stanley Rushbrooke in 1937. [1]
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space.There are several rather similar versions. In one version of the theorem, if both these sets are closed and at least one of them is compact, then there is a hyperplane in between them and even two parallel hyperplanes in between them separated by a gap.