Electron Phases

In physical chemistry, Electron Phases describe the sign (positive or negative) of the wave function, which is a solution to the Schrödinger equation. When two wave functions describing two atomic orbitals on the same atom are combined, a hybrid orbital is created. When wave functions for atomic orbitals on two different atoms are combined, the result is a molecular orbital.

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In terms of molecular orbitals (MOs), the type of interaction between the two wave functions being added depends on their signs. This interaction may be either constructive (both wave functions are of the same sign) or destructive (opposite signs). The phases of a wave function can be represented as a simple sine curve, y=sinx, in which the values above the x-axis are positive and the values below the x-axis are negative. When two wave functions of the same phase (meaning both positive sine curves) are combined, in-phase overlap is observed and mathematically speaking, the amplitude of the wave increases. When two wave functions of opposite phases (this time one is a positive sine curve while the other is negative) are combined, the phases "cancel out" and the addition of wave functions results in a straight line with zero amplitude. Bonding orbitals are created via constructive interaction, while antibonding orbitals are created due to destructive interaction.

When two atomic orbitals come in contact, they may form a sigma bond, pi bond, delta bond, or other form of interaction. These atomic orbitals may undergo in-phase overlap to produce a bonding orbital, as well as out-of-phase overlap to produce an antibonding orbital. As defined by phase space, an electron has a position and a momentum, and when two electron orbitals merge and form a bonding interaction, the electrons from both orbitals must have the same position and momentum. Thus, when the phases of both electron orbitals are similar, a bond is formed; when they are different, the two orbitals repel each other to form an antibonding pair. Relationships that are antibonding are denoted by the letter (sigma, pi, delta, etc.) followed by an asterisk (*) and are pronounced, for example, "sigma star".

Regarding energy, bonding pairs are always more stable than the two original atomic orbitals that combined. Antibonding pairs are higher in energy than the atomic orbitals. The number of atomic orbitals that overlap during this process is equal to the number of molecular orbitals that result; one MO is lower energy (bonding) and the other is higher energy (antibonding).

See also

• Antibonding
• Molecular Orbital Theory
• Molecular orbital diagram

References

• Moore, Walter J. Physical Chemistry. New Jersey: 1972, 4th ed. ISBN 0-13-665968-3
• Whitten, Kenneth W. "General Chemistry". 2000, 6th ed. ISBN 0-03-021214-6