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ZPVE: Zero point vibration / zero point energy (Read 1553 times)
Gerrit-Jan Linker
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ZPVE: Zero point vibration / zero point energy
19.03.09 at 15:11:21
 
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:
E0= (1/2)(h/2pi) (k/m)^0.5
 
Energy relation from the Zero Point Vibrational Energy:
ZPE = Evibr(0) = (1/2)h Σiνi
Note that vi 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
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« Last Edit: 20.05.12 at 10:20:14 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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Gerrit-Jan Linker
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Re: ZPVE: Zero point vibration / zero point energy
Reply #1 - 27.08.09 at 12:56:13
 
ZPE
 
The Zero Point Energy (ZPE):
ZPE = De - D0
 
De: electronic dissociation energy (depth of the curve with respect to the energy of free atoms)
D0: bond dissociation energy. Energy required to break the bond.
ZPE: zero point vibrational energy. In the harmonic approximation:
ZPE=½hωe
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Gerrit-Jan Linker
Linker IT Software
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