Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state.
In quantum mechanics an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). The temperature of a group of particles is indicative of the level of excitation (with the notable exception of systems that exhibit Negative temperature).
The lifetime of a system in an excited state is usually short: spontaneous or induced emission of a quantum of energy (such as a photon or a phonon) usually occurs shortly after the system is promoted to the excited state, returning the system to a state with lower energy (a less excited state or the ground state). This return to a lower energy level is often loosely described as decay and is the inverse of excitation.
Atomic excitation 
A simple example of this concept comes by considering the hydrogen atom.
The ground state of the hydrogen atom corresponds to having the atom's single electron in the lowest possible orbit (that is, the spherically symmetric "1s" wavefunction, which has the lowest possible quantum numbers). By giving the atom additional energy (for example, by the absorption of a photon of an appropriate energy), the electron is able to move into an excited state (one with one or more quantum numbers greater than the minimum possible). If the photon has too much energy, the electron will cease to be bound to the atom, and the atom will become ionised.
After excitation the atom may return to the ground state or a lower excited state, by emitting a photon with a characteristic energy. Emission of photons from atoms in various excited states leads to an electromagnetic spectrum showing a series of characteristic emission lines (including, in the case of the hydrogen atom, the Lyman, Balmer, Paschen and Brackett series.)
An atom in a high excited state is termed Rydberg atom. A system of highly excited atoms can form a long-lived condensed excited state e.g. a condensed phase made completely of excited atoms: Rydberg matter. Hydrogen can also be excited by heat or electricity.
Perturbed gas excitation 
A collection of molecules forming a gas can be considered in an excited state if one or more molecules are elevated to kinetic energy levels such that the resulting velocity distribution departs from the equilibrium Boltzmann distribution. This phenomenon has been studied in the case of a two-dimensional gas in some detail, analyzing the time taken to relax to equilibrium.
Calculation of excited states 
Excited states are often calculated using Coupled cluster, Møller–Plesset perturbation theory, Multi-configurational self-consistent field, Configuration interaction, and Time-dependent density functional theory. These calculations are more difficult than non-excited state calculations.
A further consequence is reaction of the atom in the excited state, as in photochemistry. Excited states give rise to chemical reaction.
See also 
- Hehre, Warren J. (2003). A Guide to Molecular Mechanics and Quantum Chemical Calculations. Irvine, California: Wavefunction, Inc. ISBN 1-890661-06-6.
- Glaesemann, Kurt R.; Govind, Niranjan; Krishnamoorthy, Sriram; Kowalski, Karol (2010). "EOMCC, MRPT, and TDDFT Studies of Charge Transfer Processes in Mixed-Valence Compounds: Application to the Spiro Molecule". The Journal of Physical Chemistry A 114 (33): 8764–8771. doi:10.1021/jp101761d. PMID 20540550.
- Dreuw, Andreas; Head-Gordon, Martin (2005). "Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules". Chemical Reviews 105 (11): 4009–37. doi:10.1021/cr0505627. PMID 16277369.
- Knowles, Peter J.; Werner, Hans-Joachim (1992). "Internally contracted multiconfiguration-reference configuration interaction calculations for excited states". Theoretica Chimica Acta 84: 95. doi:10.1007/BF01117405.
- Foresman, James B.; Head-Gordon, Martin; Pople, John A.; Frisch, Michael J. (1992). "Toward a systematic molecular orbital theory for excited states". The Journal of Physical Chemistry 96: 135. doi:10.1021/j100180a030.
- Glaesemann, Kurt R.; Gordon, Mark S.; Nakano, Haruyuki (1999). "A study of FeCO+ with correlated wavefunctions". Physical Chemistry Chemical Physics 1 (6): 967–975. Bibcode:1999PCCP....1..967G. doi:10.1039/a808518h.