**ZPVE:Zero point vibration / zero point energy** The zero-point energy is the lowest possible energy that a quantum mechanical physical system may have and is the energy of the ground state at 0K.

The energy of the ground vibrational state is often referred to as "zero point vibration" or "zero point energy". The energy of a system described by a harmonic oscillator potential cannot have zero energy. Physical systems such as atoms in a solid lattice or in polyatomic molecules in a gas cannot have zero energy even at absolute zero temperature. The zero point energy is sufficient to prevent liquid helium-4 from freezing at atmospheric pressure, no matter how low the temperature.

Energy expression from the quantum harmonic oscillator:

E(n) = (n+1/2).(h/2pi).(k/m)^0.5

The zero point enery is at n=0:

E

_{0}= (1/2)(h/2pi) (k/m)^0.5

Energy relation from the Zero Point Vibrational Energy:

ZPE = E

_{vibr}(0) = (1/2)h Σ

_{i}ν

_{i} Note that v

_{i} is a normal-mode vibrational frequency.

ZPE is a quantum mechanical effect which is a consequence of the uncertainty principle.

ZPVE = the energy of vibration of a system at absolute zero (0K).

ZPE = the energy of a system at absolute zero, i.e. the electronic energy + ZPVE.

See also:

Quantum harmonic oscillator

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1236257037 Quantum Harmonic Oscillator: Energy Minimum from Uncertainty Principle

http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/hosc4.html Zero-point energy

http://en.wikipedia.org/wiki/Zero-point_energy zero-point vibrational energy (ZPVE)

http://www.iupac.org/goldbook/ZT07133.pdf