Transcript Thermochemistry in Gaussian

Thermochemistry in Gaussian
The Internal Thermal Energy

The internal thermal energy can be
obtaine from the partition function, q.
  ln q 
E  Nk BT 

 T V
2

The contributions to partition functions.
q  qe qt qr qv
 Translational
partition function; qt
 Rotational partition function; qr
 Vibrational partition function; qv
 Electronic partition function; qe
Contributions from Translation

Translational partition function
 2mkBT 
qt  

2
 h


3/ 2
k BT
P
Contribution to internal thermal energy
2   ln qt 
Et  N A k BT 

 T V
3
 RT
2
Contributions from Electronic
motion

Electronic partition function
qe   i e
 i / k BT
i 0

Contribution to internal thermal energy
Ee  0
Contributions from Rotation

Rotational partition function

 1/ 2 
T 3/ 2

qr 
1/ 2 

 r   r , x  r , y  r , z  

Contribution to internal thermal energy
2   ln qr 
Er  RT 

 T V
3
 RT
2
Contributions from Vibration

Vibrational partition function
1
qv  
  v ,K / T
K 1 e

Contribution to internal thermal energy
1
1

Ev  R v , K   v ,K / T

1 
2 e
K
Symbols
Output from Gaussian

Frequency Calculation

Zero point energy
Thermal Correction
Thermal Correction to Energy
Etot  Et  Er  Ev  Ee
 Thermal Correction to Enthalpy
Ecorr  Etot  kBT


Thermal Correction To Gibbs Free Energy
Gcorr  H corr  TStot
Total Energy
0
 Sum of electronic & ZPE =  0   ZPE
 Sum of electronic & T energy =  0   tot
 Sum of electronic & T enthalpy =  0  H corr
 Sum of electronic & T free energy =  0  Gcorr

Total electronic energy =
Individual Contributions

Individual contributions to Etot, Ctot and Stot

Individual contributions to partition functions
Example

H-abstraction reaction
C2 H5   H 2  C2 H 6  H 
Rate of Reaction
FH  Cl  [ FHCl]  F  HCl
Energies Calculation

Atomization energy of molecule

Heat of formation of atoms at 0 K (expt.)

Enthalpy correction of atomic element

Enthalpy correction for molecule
=

Entropy for atoms 25 °C (expt.)

Entropy for molecules 25 °C
Heat of Formation