In quantum mechanics, atomic orbitals describe the probability distribution of finding an electron in a given region of space around an atom. Atomic orbitals can be classified as either real or complex, depending on their mathematical representation.
- Real Orbitals: Real orbitals are wave functions that have a real-valued probability density. They represent regions in space where the electron has a non-zero probability of being found. Real orbitals are associated with the familiar s, p, d, and f orbitals that are commonly taught in chemistry. These orbitals have specific shapes and orientations that are determined by their quantum numbers.
- The s orbital is spherical and has a maximum probability density at the nucleus.
- The p orbitals are dumbbell-shaped and oriented along the x, y, and z axes.
- The d orbitals have more complex shapes and orientations.
Real orbitals are often used to describe the behavior and properties of electrons in atoms and molecules. They are typically depicted as three-dimensional probability density plots or as two-dimensional representations showing electron density contours.
- Complex Orbitals: Complex orbitals are wave functions that have complex-valued probability density. They are also known as "complex conjugate" orbitals. Complex orbitals are used to describe systems that involve constructive and destructive interference of electronic wave functions. The imaginary component of complex orbitals represents the phase or "wave-like" nature of the electron's behavior.
Complex orbitals are commonly used in molecular orbital theory (MOT) to describe the formation of molecular orbitals from atomic orbitals. When atomic orbitals combine, they can form molecular orbitals with real and complex components. The complex components describe the phase relationship and nodal patterns in the molecular orbitals.
It's important to note that while complex orbitals have complex-valued wave functions, the probability density calculated from the square of the wave function is always real and positive. This probability density represents the likelihood of finding an electron in a particular region of space.
In summary, real orbitals have a real-valued probability density and are commonly encountered in atomic orbitals, while complex orbitals have a complex-valued probability density and are used in molecular orbital theory to describe phase relationships and nodal patterns in molecular orbitals.