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Relative enthalpies of isomers - Comparison of 0K enthalpies (kJ mol-1)

Isomers of C4H6O

17 10 10 15 39
index Species CAS number Name Relative experimental enthalpy (kJ mol-1) sketch
a CH2CHOCHCH2 109933 Vinyl ether   sketch of Vinyl ether
b C4H6O 1191953 Cyclobutanone   sketch of Cyclobutanone
c C4H6O 1191997 Furan, 2,3-dihydro-   sketch of Furan, 2,3-dihydro-
d C4H6O 1708298 Furan, 2,5-dihydro-   sketch of Furan, 2,5-dihydro-
e CHOCHCHCH3 4170303 2-Butenal   sketch of 2-Butenal
f C4H6O 15798648 cis-2-butenal   sketch of cis-2-butenal
The calculated enthalpies include the calculated and scaled vibrational zero-point energy.
Methods with predefined basis sets
composite G1
NC
NC
G2MP2
NC
NC
G2 0.0 a
-84.6 f
G3 0.0 a
-82.3 f
G3B3 0.0 a
-50.5 c
CBS-Q 0.0 a
-85.2 f

Methods with standard basis sets
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) TZVP cc-pVDZ cc-pVTZ aug-cc-pVDZ aug-cc-pVTZ cc-pV(T+d)Z daug-cc-pVTZ
hartree fock HF 0.0 a
-174.5 b
-193.2 c
-172.4 d
-83.9 e
-82.6 f
0.0 a
-55.0 b
-53.1 c
-42.5 d
-66.7 e
-67.4 f
0.0 a
-55.1 b
-53.1 c
-42.5 d
-66.7 e
-67.4 f
0.0 a
-62.9 b
-48.7 c
-46.0 d
-97.6 e
-93.4 f
0.0 a
-93.6 b
-63.7 c
-57.0 d
-112.2 e
-106.4 f
0.0 a
-90.5 b
-61.2 c
-54.8 d
-110.0 e
-104.3 f
0.0 a
-82.0 b
-55.2 c
-49.8 d
-107.0 e
-99.2 f
0.0 a
-87.0 b
-57.4 c
-51.5 d
-110.8 e
-104.6 f
0.0 a
-81.0 b
-53.6 c
-106.7 e
-100.4 f
0.0 a
-85.4 b
-57.8 c
-51.5 d
-106.4 e
-99.1 f
0.0 a
-69.6 b
-46.9 c
-41.4 d
-98.9 e
-89.2 f
0.0 a
-50.9 c
-44.6 d
-103.4 e
-95.6 f
0.0 a
-83.6 b
-56.0 c
-50.5 d
-110.0 e
-104.2 f
0.0 a
-68.7 b
-47.4 c
-41.8 d
-98.8 e
-90.1 f
0.0 a
-81.7 b
-55.4 c
-51.2 d
-107.0 e
-97.3 f
0.0 a
-67.9 b
-47.2 c
-41.8 d
-98.3 e
0.0 a
-68.7 b
-47.4 c
-41.8 d
-98.8 e
-90.1 f
0.0 a
-49.6 c
-44.2 d
-100.8 e
-90.9 f
density functional LSDA
NC
NC
NC
NC
NC
0.0 a
-95.9 b
-86.7 c
-58.1 d
-66.5 e
-66.7 f

NC
NC
NC
NC
NC

NC
NC
NC
NC
NC
0.0 a
-102.5 b
-91.7 c
-71.6 d
-85.9 e
-80.3 f
0.0 a
-100.3 b
-89.6 c
-69.3 d
-83.9 e
-78.4 f
0.0 a
-99.4 b
-87.0 c
-68.1 d
-86.3 e
-78.1 f
0.0 a
-101.4 b
-86.3 c
-65.6 d
-88.1 e
-82.2 f
0.0 a
-94.9 b
-81.3 c
-60.7 d
-83.2 e
-77.2 f
0.0 a
-95.5 b
-88.3 c
-68.5 d
-78.0 e
-72.1 f
    0.0 a
-97.9 b
-87.7 c
-67.3 d
-81.2 e
-76.0 f
0.0 a
-86.7 b
-79.6 c
-61.0 d
-78.5 e
-70.3 f
0.0 a
-98.4 b
-89.0 c
-71.8 d
-84.5 e
-75.4 f
 
NC
NC
NC
NC
NC
 
BLYP 0.0 a
-112.3 b
-129.5 c
-84.2 d
-58.5 e
-55.5 f
0.0 a
-61.9 b
-44.8 c
-20.4 d
-72.5 e
-72.2 f
0.0 a
-61.9 b
-44.8 c
-20.4 d
-72.5 e
-72.2 f
0.0 a
-57.5 b
-37.7 c
-22.2 d
-96.3 e
-91.2 f
0.0 a
-66.9 b
-43.7 c
-27.0 d
-95.0 e
-89.3 f
0.0 a
-64.6 b
-41.3 c
-24.6 d
-92.7 e
-87.0 f
0.0 a
-61.4 b
-36.4 c
-21.4 d
-94.3 e
-86.0 f
0.0 a
-63.6 b
-36.3 c
-19.2 d
-95.2 e
-89.3 f

NC
NC
NC
NC
0.0 a
-58.7 b
-38.1 c
-21.3 d
-86.7 e
-80.8 f
    0.0 a
-60.1 b
-37.6 c
-20.7 d
-88.4 e
0.0 a
-52.7 b
-32.0 c
-16.4 d
0.0 a
-61.5 b
-38.5 c
-92.0 e
 
NC
NC
NC
 
B1B95 0.0 a
-145.8 b
-155.1 c
-65.7 e
0.0 a
-93.0 b
-76.0 c
-78.3 e
0.0 a
-93.0 b
-76.0 c
-78.3 e
0.0 a
-88.6 b
-64.7 c
-98.4 e
0.0 a
-100.9 b
-81.7 c
-98.9 e
0.0 a
-95.9 b
-69.8 c
-95.5 e
0.0 a
-92.9 b
-66.3 c
-51.8 d
-96.0 e
-88.1 f
0.0 a
-95.9 b
-67.6 c
-98.8 e
0.0 a
-89.6 b
-62.8 c
-93.9 e
0.0 a
-90.5 b
-67.8 c
-89.5 e
    0.0 a
-92.3 b
-67.2 c
-93.5 e
0.0 a
-82.1 b
-62.1 c
-88.1 e
0.0 a
-94.1 b
-69.8 c
-95.2 e
0.0 a
-51.6 d
-90.9 e
0.0 a
-82.1 b
-62.1 c
-88.1 e
 
B3LYP 0.0 a
-132.6 b
-149.8 c
-110.7 d
-65.2 e
-62.7 f
0.0 a
-69.3 b
-54.9 c
-33.7 d
-72.4 e
-72.4 f
0.0 a
-69.3 b
-54.9 c
-33.7 d
-72.4 e
-72.4 f
0.0 a
-67.7 b
-48.7 c
-36.1 d
-97.1 e
-92.2 f
0.0 a
-79.8 b
-56.7 c
-42.3 d
-97.7 e
-92.0 f
0.0 a
-77.0 b
-54.0 c
-39.7 d
-95.2 e
-89.5 f
0.0 a
-73.1 b
-49.3 c
-36.3 d
-95.8 e
-87.7 f
0.0 a
-75.1 b
-49.3 c
-34.9 d
-97.7 e
-91.8 f
0.0 a
-68.9 b
-44.7 c
-92.7 e
-86.7 f
0.0 a
-70.4 b
-50.4 c
-35.9 d
-89.3 e
-83.1 f
0.0 a
-60.3 b
-40.8 c
-88.3 e
0.0 a
-65.9 b
-42.5 c
-28.8 d
-93.3 e
-85.4 f
0.0 a
-72.2 b
-50.3 c
-36.0 d
-92.0 e
-86.6 f
0.0 a
-59.3 b
-40.5 c
-27.3 d
-87.8 e
-79.7 f
0.0 a
-71.9 b
-50.2 c
-38.3 d
-94.0 e
-85.0 f
0.0 a
-41.1 c
-28.7 d
-88.2 e
-79.0 f
0.0 a
-59.3 b
-40.5 c
-27.3 d
-87.8 e
-79.7 f
 
B3LYPultrafine         0.0 a
-79.9 b
-56.7 c
-97.6 e
                0.0 a
-59.4 b
-87.7 e
  0.0 a
-59.5 b
-41.1 c
-28.7 d
-88.2 e
-79.0 f
   
B3PW91 0.0 a
-151.8 b
-161.9 c
-121.4 d
-73.4 e
-70.5 f
0.0 a
-91.5 b
-71.8 c
-48.8 d
-77.9 e
-77.3 f
0.0 a
-91.5 b
-71.8 c
-48.8 d
-77.9 e
-77.3 f
0.0 a
-88.7 b
-64.5 c
-50.4 d
-101.4 e
-96.4 f
0.0 a
-101.7 b
-74.4 c
-58.4 d
-102.7 e
-96.7 f
0.0 a
-97.3 b
-70.3 c
-54.3 d
-98.8 e
-92.7 f
0.0 a
-94.2 b
-67.0 c
-52.6 d
-99.3 e
-91.1 f
0.0 a
-98.0 b
-69.0 c
-53.6 d
-103.5 e
-97.3 f
0.0 a
-90.5 b
-62.9 c
-97.1 e
-90.8 f
0.0 a
-91.2 b
-67.4 c
-51.7 d
-93.1 e
-86.6 f
    0.0 a
-93.6 b
-67.8 c
-52.4 d
-96.9 e
-91.2 f
0.0 a
-81.2 b
-59.6 c
-45.4 d
-91.4 e
-83.2 f
0.0 a
-93.6 b
-68.5 c
-98.2 e
  0.0 a
-81.2 b
-59.6 c
-45.4 d
-91.4 e
-83.2 f
 
mPW1PW91 0.0 a
-158.5 b
-169.3 c
-130.2 d
-74.8 e
-72.1 f
0.0 a
-90.2 b
-72.3 c
-54.6 d
-72.4 e
-77.0 f
0.0 a
-94.9 b
-76.9 c
-54.6 d
-77.2 e
-77.0 f
0.0 a
-92.9 b
-69.4 c
-55.9 d
-101.4 e
-96.6 f
0.0 a
-101.7 b
-75.1 c
-63.9 d
-98.3 e
-97.2 f
0.0 a
-99.0 b
-72.7 c
-61.6 d
-96.1 e
-94.9 f
0.0 a
-50.5 b
-69.2 c
-59.4 d
-96.7 e
-93.1 f
0.0 a
-98.0 b
-69.8 c
-59.2 d
-99.3 e
-97.8 f
0.0 a
-96.7 b
-69.7 c
-99.2 e
-93.1 f
0.0 a
-96.2 b
-72.9 c
-57.6 d
-93.8 e
-87.4 f
    0.0 a
-95.7 b
-70.5 c
-60.3 d
-95.1 e
-94.2 f
0.0 a
-85.9 b
-64.9 c
-51.0 d
-91.9 e
-83.7 f
0.0 a
-98.3 b
-73.7 c
-98.9 e
  0.0 a
-85.9 b
-64.9 c
-51.0 d
-91.9 e
-83.7 f
 
M06-2X     0.0 a
-69.3 b
-68.2 c
-49.0 d
-60.1 e
-62.2 f
  0.0 a
-69.0 c
-54.1 d
-88.3 e
-83.8 f
                         
PBEPBE 0.0 a
-137.8 b
-149.3 c
-100.8 d
-66.3 e
-62.8 f
0.0 a
-91.3 b
-69.9 c
-43.0 d
-77.7 e
-77.2 f
0.0 a
-91.2 b
-69.9 c
-43.0 d
-77.7 e
-77.2 f
0.0 a
-86.7 b
-60.9 c
-43.1 d
-101.4 e
-96.3 f
0.0 a
-97.4 b
-69.8 c
-51.1 d
-101.0 e
-95.0 f
0.0 a
-93.1 b
-65.6 c
-47.0 d
-96.9 e
-91.0 f
0.0 a
-91.0 b
-62.0 c
-44.9 d
-98.5 e
-90.1 f
0.0 a
-95.0 b
-64.5 c
-45.9 d
-101.7 e
-95.7 f
0.0 a
-87.3 b
-58.0 c
-95.1 e
-89.0 f
0.0 a
-87.9 b
-63.9 c
-45.3 d
-91.1 e
-84.8 f
    0.0 a
-89.4 b
-62.9 c
-44.4 d
-93.8 e
-88.3 f
0.0 a
-78.8 b
-55.4 c
-38.3 d
-90.1 e
-81.9 f
0.0 a
-90.4 b
-63.9 c
-96.5 e
  0.0 a
-78.8 b
-55.4 c
-38.3 d
-90.1 e
-81.9 f
 
PBEPBEultrafine         0.0 a
-69.9 c
-100.9 e
                         
PBE1PBE         0.0 a
-82.2 c
-66.3 d
-103.1 e
-97.3 f
                         
HSEh1PBE   0.0 a
-76.5 c
-54.0 d
-77.3 e
-77.0 f
    0.0 a
-79.4 c
-63.7 d
-103.2 e
-97.2 f
 
NC
NC
NC
NC
            0.0 a
-64.4 c
-50.3 d
-92.0 e
-83.7 f
       
TPSSh         0.0 a
-91.4 b
-69.5 c
-53.1 d
-96.8 e
-91.1 f
  0.0 a
-84.8 b
-63.6 c
-49.0 d
-95.0 e
-87.0 f
    0.0 a
-82.7 b
-64.8 c
-48.8 d
-89.5 e
-83.3 f
      0.0 a
-72.5 b
-56.9 c
-42.7 d
-87.5 e
-79.4 f
       
wB97X-D     0.0 a
-96.3 b
-71.2 c
-47.9 d
-78.4 e
-79.1 f
  0.0 a
-106.5 b
-75.5 c
-59.0 d
-102.1 e
-97.4 f
  0.0 a
-100.0 b
-69.6 c
-54.8 d
-100.4 e
-93.5 f
  0.0 a
-96.1 b
-64.9 c
-49.2 d
-98.4 e
-93.4 f
    0.0 a
-94.5 b
-63.6 c
-48.0 d
-98.9 e
-92.1 f
0.0 a
-100.0 b
-69.6 c
-54.8 d
-100.4 e
-93.5 f
0.0 a
-88.2 b
-62.7 c
-47.9 d
-94.0 e
-86.9 f
  0.0 a
-88.8 b
-63.4 c
-49.1 d
-94.7 e
-86.5 f
   
B97D3   0.0 a
-73.2 b
-53.3 c
-28.0 d
-78.6 e
-77.8 f
    0.0 a
-54.4 c
-37.1 d
-102.4 e
-96.4 f
  0.0 a
-48.6 c
-32.9 d
-101.2 e
-92.9 f
  0.0 a
-72.8 b
-45.1 c
-28.0 d
-98.6 e
-92.3 f
  0.0 a
-66.4 b
-42.6 c
-27.7 d
-95.5 e
-86.5 f
0.0 a
-69.9 b
-42.7 c
-26.4 d
-99.0 e
-91.1 f
  0.0 a
-42.1 c
-26.4 d
-94.4 e
-86.4 f
  0.0 a
-65.2 b
-42.9 c
-28.1 d
-95.3 e
-86.3 f
   
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) TZVP cc-pVDZ cc-pVTZ aug-cc-pVDZ aug-cc-pVTZ cc-pV(T+d)Z daug-cc-pVTZ
Moller Plesset perturbation MP2 0.0 a
-162.4 b
-147.8 c
-116.5 d
-110.2 e
-108.2 f
0.0 a
-76.2 b
-53.4 c
-32.6 d
-86.5 e
-86.2 f
0.0 a
-76.2 b
-53.4 c
-32.6 d
-86.5 e
-86.2 f
0.0 a
-80.4 b
-51.2 c
-39.4 d
-114.2 e
-108.7 f
0.0 a
-104.7 b
-76.0 c
-60.7 d
-111.5 e
-105.9 f
0.0 a
-103.0 b
-75.4 c
-60.1 d
-110.5 e
-104.8 f
0.0 a
-70.2 c
-55.8 d
-99.4 f
0.0 a
-106.7 b
-72.8 c
-111.5 e
-105.7 f
0.0 a
-103.5 b
-72.0 c
-109.5 e
-103.1 f
0.0 a
-102.8 b
-76.5 c
-60.0 d
-102.1 e
-96.2 f
  0.0 a
-89.4 b
-66.7 c
-104.1 e
-96.4 f
0.0 a
-103.8 b
-71.2 c
-54.0 d
-111.5 e
-106.0 f
0.0 a
-88.6 b
-69.1 c
-53.6 d
-98.5 e
-90.3 f
0.0 a
-58.0 d
-97.7 f
0.0 a
-88.1 b
-55.6 d
-98.1 e

NC
NC
NC
NC
NC
 
MP2=FULL 0.0 a
-116.8 d
-108.3 f
0.0 a
-76.1 b
-32.7 d
-86.1 f
0.0 a
-76.1 b
-32.7 d
-86.1 f
0.0 a
-80.3 b
-39.6 d
-108.6 f
0.0 a
-104.9 b
-76.4 c
-60.9 d
-111.1 e
-105.6 f
0.0 a
-103.3 b
-75.8 c
-60.4 d
-110.0 e
-104.3 f
0.0 a
-94.2 b
-70.5 c
-56.2 d
-107.1 e
-98.9 f
0.0 a
-107.7 b
-73.6 c
-55.3 d
-111.6 e
-105.7 f
0.0 a
-104.6 b
-73.0 c
-109.6 e
-103.2 f
0.0 a
-66.5 d
-99.0 f
    0.0 a
-103.7 b
-54.2 d
-105.9 f
0.0 a
-88.9 b
-55.3 d
-99.3 e
-90.8 f
   
NC
NC
 
MP3         0.0 a
-92.4 b
-71.9 c
-101.1 e
                         
MP3=FULL         0.0 a
-93.5 b
-73.3 c
-61.9 d
-101.7 e
-95.9 f
 
NC
NC
NC
NC
NC
                     
B2PLYP         0.0 a
-64.5 c
-49.7 d
-104.5 e
-99.0 f
               
NC
NC
NC
NC
NC
       
Configuration interaction CID   0.0 a
-41.8 d
-71.9 f
0.0 a
-41.8 d
-71.9 f
0.0 a
-46.9 d
-94.3 f
0.0 a
-75.0 c
-64.7 d
-106.6 e
-101.2 f
    0.0 a
-59.6 d
-100.7 f
                   
CISD   0.0 a
-40.4 d
-72.5 f
0.0 a
-40.4 d
-72.5 f
0.0 a
-45.6 d
-95.2 f
0.0 a
-74.4 c
-63.6 d
-106.7 e
-101.4 f
    0.0 a
-58.8 d
-101.2 f
                   
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) TZVP cc-pVDZ cc-pVTZ aug-cc-pVDZ aug-cc-pVTZ cc-pV(T+d)Z daug-cc-pVTZ
Quadratic configuration interaction QCISD   0.0 a
-59.2 b
-46.7 c
-29.5 d
-72.8 e
-73.2 f
0.0 a
-29.5 d
-73.2 f
0.0 a
-61.6 b
-33.8 d
-94.2 f
0.0 a
-92.7 b
-54.1 d
-99.1 f
0.0 a
-90.8 b
-66.4 c
-54.0 d
-103.1 e
-98.5 f
0.0 a
-51.2 d
-100.6 e
-93.7 f
0.0 a
-49.6 d
-100.0 f
0.0 a
-103.7 e
-98.4 f
0.0 a
-54.0 d
-91.7 f
    0.0 a
-92.8 b
         
QCISD(T)         0.0 a
-33.6 f
                         
Coupled Cluster CCD   0.0 a
-33.7 d
-69.4 f
0.0 a
-33.7 d
-69.4 f
0.0 a
-60.9 b
-38.2 d
-88.8 f
0.0 a
-93.2 b
-58.7 d
-101.9 e
-96.3 f
0.0 a
-58.8 d
-95.6 f
0.0 a
-55.0 d
-90.7 f
0.0 a
-53.5 d
-96.6 f
0.0 a
-94.9 f
0.0 a
-57.6 d
-89.3 f
               
CCSD         0.0 a
-55.3 d
                         
CCSD(T)         0.0 a
-97.3 f
                         
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) TZVP cc-pVDZ cc-pVTZ aug-cc-pVDZ aug-cc-pVTZ cc-pV(T+d)Z daug-cc-pVTZ

Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 0.0 a
-90.4 b
-70.5 c
-70.3 d
-110.5 e
-104.2 f
0.0 a
-119.4 b
-84.1 c
-78.8 d
-125.2 e
-116.9 f
0.0 a
-75.5 b
-62.1 c
-62.3 d
-101.2 e
-95.8 f
0.0 a
-96.2 b
-67.5 c
-63.1 d
-113.6 e
-106.1 f
0.0 a
-69.1 b
-55.8 c
-55.3 d
-96.7 e
-91.0 f
0.0 a
-70.0 b
-56.3 c
-55.7 d
-96.9 e
-91.2 f
    0.0 a
-68.5 b
-46.7 c
-41.3 d
-98.9 e
-89.6 f
density functional B1B95 0.0 a
-115.7 b
-88.3 c
-74.1 d
-105.2 e
-98.1 f
0.0 a
-129.4 b
-98.2 c
-80.8 d
-107.9 e
-99.5 f
             
B3LYP 0.0 a
-91.4 b
-68.1 c
-57.1 d
-103.7 e
-96.4 f
0.0 a
-105.8 b
-76.5 c
-62.8 d
-109.6 e
-101.2 f
0.0 a
-73.7 b
-57.9 c
-48.7 d
-95.6 e
-89.7 f
0.0 a
-82.5 b
-59.5 c
-47.6 d
-98.6 e
-91.5 f
0.0 a
-73.5 b
-55.1 c
-43.0 d
-91.3 e
-84.9 f
0.0 a
-73.5 b
-54.7 c
-42.5 d
-91.4 e
-85.0 f
    0.0 a
-60.7 b
-41.1 c
-28.3 d
-88.8 e
-80.2 f
PBEPBE                 0.0 a
-79.9 b
-55.8 c
-39.2 d
-91.2 e
-82.4 f
Moller Plesset perturbation MP2 0.0 a
-99.4 b
-66.9 c
-57.2 d
-121.5 e
-113.7 f
0.0 a
-133.0 b
-94.5 c
-78.6 d
-124.6 e
-116.2 f
0.0 a
-80.5 b
-57.4 c
-49.1 d
-111.9 e
-105.3 f
0.0 a
-107.5 b
-79.8 c
-64.3 d
-112.1 e
-105.2 f
0.0 a
-75.4 b
-51.6 c
-40.5 d
-106.0 e
-99.3 f
0.0 a
-76.0 b
-51.8 c
-40.6 d
-106.4 e
-99.5 f
    0.0 a
-89.5 b
-70.0 c
-54.8 d
-98.7 e
-89.8 f

Single point energy calculations (select basis sets)
cc-pVDZ cc-pVTZ aug-cc-pVTZ cc-pV(T+d)Z
Moller Plesset perturbation MP2FC// MP2FC/6-31G*    
NC
NC
NC
 
Coupled Cluster CCSD(T)// HF/6-31G*
NC
NC
     
CCSD(T)//B3LYP/6-31G(2df,p)  
NC
NC
NC
 
NC
NC
NC
CCSD// MP2FC/6-31G*    
NC
NC
NC
 
CCSD(T)// MP2FC/6-31G*    
NC
NC
NC
 
NC = not calculated
For descriptions of the methods (AM1, HF, MP2, ...) and basis sets (3-21G, 3-21G*, 6-31G, ...) see the glossary in section I.C. Predefined means the basis set used is determined by the method.
gaw refers to the group additivity method implemeted in the NIST Chemistry Webbook.
See section Calculated; Vibrations; Scale Factors; Scale factors to list vibrational scaling factors.
See section Calculated; Vibrations; Scale Factors; Calculate a scale factor to calculate a vibrational scaling factor for a given set of molecules.