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are generally complex-valued. Real-valued orbitals can be formed as linear combinations of mℓ and −mℓ orbitals, and are often labeled using associated harmonic...

In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new hybrid orbitals (with different energies,...

whole, so the atomic orbitals combine to form molecular orbitals. The electrons from the constituent atoms occupy the molecular orbitals. Mathematically...

molecular orbitals. It is assumed that the molecular orbital wave function ψj can be written as a simple weighted sum of the n constituent atomic orbitals χi...

combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry...

covalent chemical bond. They are formed by head-on overlapping between atomic orbitals along the internuclear axis. Sigma bonding is most simply defined for...

electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom is...

properties. When atomic orbitals overlap during metallic or covalent bonding, they create both bonding and antibonding molecular orbitals of equal capacity...

which includes orbital hybridization and resonance, and molecular orbital theory which includes the linear combination of atomic orbitals and ligand field...

orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals has...

are normally higher in energy than bonding molecular orbitals. Bonding and antibonding orbitals form when atoms combine into molecules. If two hydrogen...

of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This...

combination of atomic orbitals. These atomic orbitals are called Slater-type orbitals. Furthermore, it is very common for the "atomic orbitals" in use to...

Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method. They are named...

orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of...

between the atoms. This tunneling splits (hybridizes) the atomic orbitals into molecular orbitals with different energies.: 117–122  Similarly, if a large...

quantized) set of these orbitals exist around the nucleus, as other possible wave patterns rapidly decay into a more stable form. Orbitals can have one or more...

have also been proposed in which nucleons occupy orbitals, much like the atomic orbitals in atomic physics theory. These wave models imagine nucleons...

instance, the n = 1 shell has only orbitals with ℓ = 0 {\displaystyle \ell =0} , and the n = 2 shell has only orbitals with ℓ = 0 {\displaystyle \ell =0}...

of atomic orbitals can be used: Gaussian-type orbitals, Slater-type orbitals, or numerical atomic orbitals. Out of the three, Gaussian-type orbitals are...