Molecular Properties

Tutorial: Calculation of Molecular Properties of HF molecule.

Dipole moments in molecules are responsible for the behavior of a substance in the presence of external electric fields. The dipoles tend to be aligned to the external field which can be constant or time-dependent. This effect forms the basis of a modern experimental technique called dielectric spectroscopy.


Dipole Moment

1. Calculation of dipole moment of HF molecule by using analytical and numerical method.

Normally Gaussian program automatically prints out the information of molecule about its molecular properties such as dipole moment, polarization, quadrupole, magnetic dipole moment, etc. Predict of those are able to be performed using the analytical method which has more accuracy than numerical method since the error of latter method increase caused by many reason. Therefore, with analytical method provides an acceptable results that agrees well with experimental evidence. To overcome numerical problems, the scientists mostly calculate dipole moment and other properties through molecule's wave functions. As long as knowing the eigen-operator of them, we could directly solve the problem.

Ex. of Gaussian input to calculation of the dipole moment at different (+/-) applied electric field.

%chk=HF-mol-prop-field-plus10-z.chk
%mem=1GB
%nproc=1
#p B3LYP/6-311g(D,P) gfinput field=Z+10             ! applying E of 10 in gaussian unit to molecule.
                                                    ! Note that 1 Gaussian unit = 0.0001 a.u.
Title and comment is here

0  1
H   0.0  0.0  0.0
F   0.0  0.0  0.9201

The calculation setup above means that I am going to calculate electronics structure properties of HF with an applied electric dipole field of 0.001 a.u. along direction of +Z. On the other hand, for field=Z-10 indicates applying the same E in Z axis but opposite direction.

Output Analysis

How to get dipole moment of your simulated molecule from Gaussian output file.

The most of molecular properties are printed when the calculation almost finishes which means that those results close to the bottom of the output file, you should find the predicted mulliken atomic charges and dipole moment , quadupole moment, and etc of the molecule by this part of output.

This is the example of calculated total atomic charges of H2CO:

1 C .134575

2 O -.415727

3 H .140576

4 H .140576

So far, as we would expect from electronegativities, the oxygen atom is negatively charged. This produces a dipole moment (pointing toward the negative end) along the z-axis. The below data is dipole moment in Debye.

Dipole moment (Debye): X= .0000 Y= .0000 Z= -2.6663 Tot= 2.666

If you want to find dipole moment in a.u., see at the bottom file or use the following command

grep 'Dipole=' your_output_file.log

Computational Results: Comparison dipole moment and the applied electric dipole field.

CM645-DipoleMoment-Tutorial.xlsx

Estimation of dipole moment from relation between Total Energy and Applied Electric Dipole Field

Equation 1:
dW/dE = u
where W = Total energy (a.u.)
      E = Electric dipole field (a.u.)
      u = Dipole moment (a.u.)

If we make the relation between total energy and increments/decrements of the electric field, therefore dipole moment of HF molecule can be numerically calculated as a slope of the line equation. The total energies in following graphs has been compared with various step-size of applied electric field from 0.0005 up to 0.002 a.u. with increment = 0.0005 a.u. So the slope of each line is assumed to be equal to dipole moment in a.u. as well. Then just multiply those slope values by 2.54174 to convert a.u. to Debye.

Ex. The graph no. 1 is total energies with -0.0005 and +0.0005 a.u. of electric field. The linear slope of this line is -0.735400 which indicates to calculated dipole moment of HF molecule in atomic unit. Therefore, dipole moment of HF is also equal to -1.869195596 D, which very closed to the experimental dipole moment of 1.8692 D.

Summary

This table compares the error of ...

Polarization of Molecule

Polarizability is the ability to form instantaneous dipole. With the command of "polar" in Gaussian program, the program usually always calculate and print out those results with regarding of molecular properties. The first one is dipole we just have learnt before. Secondly, the chemist is also interested in polarization of molecule (used alpha symbol). On the other hand, we could numerically approximate a polarization likewise dipole moment.

The polarization can be approximately calculated as second derivative of total energy by applied electric dipole field.

The relation between numerically calculated dipole moment and applied electric field in A.U. unit

From an information above, the linear equation of dipole moment as a function of applied electric dipole field is

y = 4.3802 (x) + 0.7355

The slope of this equation is 4.3802 A.U. = polarization of HF molecule.

Supplement

  • 1 gaussian unit = 0.0001 a.u. electirc field
  • 1 a.u. electric field = 2.541746230211 D
  • Dipole moment EXPT = 1.86 D
  • H-F Bond distance = 0.917 Angstrom

References:

  1. http://gaussian.com/field/