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It is given by the square of a mathematical function known as the "wavefunction", which is a solution of the Schrödinger equation. The lowest energy equilibrium state of the hydrogen atom is known as the ground state. The ground state wave function is known as the wavefunction.
This table shows the real hydrogen-like wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of all elements in the periodic table up to radium and some beyond. "ψ" graphs are shown with − and + wave function phases shown in two different colors (arbitrarily red and blue).
The wave function of the ground state of a hydrogen atom is a spherically symmetric distribution centred on the nucleus, which is largest at the center and reduces exponentially at larger distances. The electron is most likely to be found at a distance from the nucleus equal to the Bohr radius .
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. In chemistry, a molecular orbital (/ ɒr b ə d l /) is a mathematical function describing the location and wave-like behavior of an electron in a ...
The atomic orbitals used are typically those of hydrogen-like atoms since these are known analytically i.e. Slater-type orbitals but other choices are possible such as the Gaussian functions from standard basis sets or the pseudo-atomic orbitals from plane-wave pseudopotentials. Example of a molecular orbital diagram.
The Bohr model gives an incorrect value L=ħ for the ground state orbital angular momentum: The angular momentum in the true ground state is known to be zero from experiment. Although mental pictures fail somewhat at these levels of scale, an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to revolve ...
The ground state energy would then be 8E 1 = −109 eV, where E 1 is the Rydberg constant, and its ground state wavefunction would be the product of two wavefunctions for the ground state of hydrogen-like atoms: [2]: 262 (,) = (+) /. where a 0 is the Bohr radius and Z = 2, helium's nuclear charge.
Quantum chemistry and Physics textbooks usually treat the binding of the molecule in the electronic ground state by the simplest possible ansatz for the wave function: the (normalized) sum of two 1s hydrogen wave functions centered on each nucleus. This ansatz correctly reproduces the binding but is numerically unsatisfactory.