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Mod:Hunt Research Group/molecular volume

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Calculating Molecular Volumes

Why do this?


The Basics

  • Within Gaussian molecular volumes can be computed using the "volume" keyword.
  • By default this is defined as the volume within a contour of 0.001 electrons/Bohr3 density.
  • The density to be used can be specified with the "density" keyword. By default this is the SCF density. For post-SCF methods, the default is therefore the HF density. Hence, for MP2, for example, need to specify "density=MP2" to ensure that the MP2 density is used.
  • The volume information can be found at the end of the log file (example shown below). The computed volume is listed as the Molar volume and is given in both units of Bohr3/mol and cm3/mol (from which the molecular volume could then be calculated).
  • The "Recommended a0 for SCRF calculation" is the radius recommended for use with the Onsager solvent model (quite old now) and is 0.5 Å larger than the radius corresponding to the computed volume.
Evaluate density.
Using the total density.
Monte-Carlo method of calculating molar volume:
based on  0.001 e/bohr**3 density envelope.
Number of points per bohr**3 =  100 CutOff= 1.00D-04
Using the SCF density.
There are      1628 points.  Will hold      1628 in memory.
LenV=    33496491 MDV=    33554432.
Box volume = 4316.320 fraction occupied=0.076
Integrated density= 4.0986229256571240D+00 error=-1.3901377074342875D+01
Molar volume =  326.110 bohr**3/mol ( 29.102 cm**3/mol)
Recommended a0 for SCRF calculation =  2.99 angstrom (  5.64 bohr)


Accuracy of Molecular Volume Calculations

  • In order to compute the molecular volume, Gaussian employs a Monte-Carlo integration write more about this
  • This results in an "accuracy" of only 2 significant figures (however, this is adequate for the Onsager solvent model).
  • To improve the accuracy to approximately 10%, the "volume=tight" option can be used. This increases the density of points resulting in a more accurate integration (the number of points is increased from the default of 20 to 100). The above example was run with the volume=tight option and, as expected, the output tells us that the calculation was run with 100 points per Bohr3.
  • To further increase the number of points per Bohr3, can employ IOp(6/45) e.g. IOp(6/45=N) , where N= number of points. (Note: just add the IOp to the route section, as shown below).


Example route section using an IOp to request an increased number of points: 

# b3lyp/6-311+g(d,p) volume iop(6/45=200) scf=conver=9 int=ultrafine


Example output from test calculation using 200 points/Bohr3. 

Evaluate density.
Using the total density.
Monte-Carlo method of calculating molar volume:
based on  0.001 e/bohr**3 density envelope.
Number of points per bohr**3 =  200 CutOff= 1.00D-04
Using the SCF density.
There are      3256 points.  Will hold      3256 in memory.
LenV=    33439511 MDV=    33554432.
Box volume = 4316.320 fraction occupied=0.082
Integrated density= 2.8381094033928647D+01 error= 1.0381094033928647D+01
Molar volume =  353.949 bohr**3/mol ( 31.586 cm**3/mol)
Recommended a0 for SCRF calculation =  3.06 angstrom (  5.77 bohr)
  • Due to use of a Monte Carlo algorithm, even with an increased number of points used for the integration, there is still variation in the molar volumes obtained when repeated for the same structure. Therefore,the best approach may be to repeat the volume calculation multiple times for any given structure and take the average molar volume. In Table 1, molar volumes for an example IL cation, using different number of points and each calculation repeated 10 times, are listed.


Table 1. Computed molar volumes (cm3/mol) for the same IL cation. N is the number of points requested using IOp(6/45=N)
Run N=100 N=150 N=300
1 135.501 137.696 132.391
2 131.609 126.378 134.513
3 131.963 130.622 137.578
4 124.534 130.387 128.736
5 125.241 130.151 133.805
6 133.378 141.704 133.334
7 137.978 134.866 137.460
8 135.501 132.744 128.029
9 129.487 124.492 128.854
10 133.025 134.631 129.679

Additional Options

  • The density contour used can be altered using IOp(6/46=N), N=density threshold used for the molecular volume calculation. The value used will be N x 10-4 e.g. if N=20 is specified, the 0.002 density surface will be used.


Example output for test calculation with IOp(6/46=20) included: 

Monte-Carlo method of calculating molar volume:
based on  0.002 e/bohr**3 density envelope.
Number of points per bohr**3 =  100 CutOff= 2.00D-04
Using the SCF density.
There are      1628 points.  Will hold      1628 in memory.
LenV=    33496491 MDV=    33554432.
Box volume = 4316.320 fraction occupied=0.055
Integrated density= 2.2134317874629794D+01 error= 4.1343178746297937D+00
Molar volume =  235.966 bohr**3/mol ( 21.057 cm**3/mol)
Recommended a0 for SCRF calculation =  2.73 angstrom (  5.16 bohr)
  • IOp(6/47) can be used to scale the vdW radii for the box size during the volume calculation. However, we do not really understand what this does!


Things to Think About

Why is the density contour surface of 0.001 e/Bohr3 used as default?

  • Bader. explain.


How "accurate" are experimental atomic radii and molecular volumes?

  • Discuss (refer to Bondii and problems with vdW)


What if my molecule has multiple conformations?

  • May need to undertake a conformational analysis and then average volume over the different conformers.
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