Frequency analysis of H2O
Some background
- no output should be analised until the structure has been confirmed as a minimum on the potential energy surface, this is achieved by computing the second derivatives for every degree of fredom.
- it also relates to determining the force constants and vibrational spectrum of the molecule
- assume we expand the potential V(R) in a Taylor Series about the minimum R0. At the minimum the first derivative is zero, and we can define our axis system so that V(R0)=0, then we can truncate our expansion ignoring all the terms of O(Rn) n>2, and this leaves us with only a single remaining term which contains the second derivative:
- Where have defined k to be the (partial) second derivative, thus if k is positive there is a minimum on the PES.
- k is also called the force constant, for example a large force constant indicates a strong bond, and to stretch or contract a strong bond takes a large amount of energy. These are the force constants used in the development of classical potentials.
- The solution of the HO problem also gives you the frequencies or vibrational modes of a molecule. Do you remember the relationship between k and the wavenumber where μ is the reduced mass? (shown above)
- however, the potential energy surface, as you know does not depend on a single coordinate, it is multi-dimensional. Now that we have a multi-dimensional surface dependent on many coordinates, how do we determine the stable geometries and transition states? Before we differentiated the energy with respect to one coordinate R, now we have to differentiate with respect to each coordinate. At minima the force for every coordinate must be zero. If we write a list of the derivatives it would look something like the vector.
- we can also calculate a second derivative for each coordinate, however this is a little more complex than calculating the forces. The second derivative turns out to be a matrix, sometimes it is called the Hessian, and sometimes it is called the force constant matrix.
- In its basic form the Hessian matrix is not very useful, it is diagonalised to give us a new a new set of coordinates Q which are just linear combinations of the old coordinates and are called normal coordinates.
- Normal coordinates are just the vibrational modes!
- Only at a minimum on the PES can the second derivative be equated to the vibrational force constant, as this is the only time they are all positive and real and observable. There is no physical relevance to a negative force constant or imaginary frequency.
Computing the Hessian or Vibrational Modes of H2O
- copy your water_queue.com file to water_freq.com file and open the new file in vi (or your favourite text editior)
- change the %chk filename to the new filename
- edit the command line to replace the opt keyword with the freq keyword.
- The geometry in the current file is incorrect it is the starting geometry and not the final optimised one, so we need to tell gaussian to read the optimised electronic structure and geometry from the checkpoint file, to do this we add the keywords guess=read and geom=checkpoint.
- remove the now wrong geometry from the input file. Make sure you leave the charge and multiplicity line and then a blank line in the file.
- we also need to copy the checkpoint file from the water_queue.chk to the new file name of water_freq.chk
%chk=water_freq.chk %mem=3600MB %nproc=2 # b3lyp/6-311g(d,p) freq guess=read geom=checkpoint single molecule water frequency analysis 0 1
- then you are ready to submit to the queue
qsub -N water_freq -v in=water_freq rng2_4 - when the job completes first check that the file terminates noramlly, you can see this by looking at the last line of the file:
Job cpu time: 0 days 0 hours 0 minutes 10.5 seconds. File lengths (MBytes): RWF= 5 Int= 0 D2E= 0 Chk= 1 Normal termination of Gaussian 09 at Sun Jan 23 15:27:27 2011.
- then vi the file and search forward for the string Harmonic, in vi the command is /Harm
Full mass-weighted force constant matrix: Low frequencies --- -72.7153 -68.4952 -57.2148 -0.0011 -0.0009 0.0015 Low frequencies --- 1637.9196 3812.7536 3909.9019 Diagonal vibrational polarizability: 0.0000000 0.0440726 0.5895645 Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU), depolarization ratios for plane and unpolarized incident light, reduced masses (AMU), force constants (mDyne/A), and normal coordinates: 1 2 3 A1 A1 B2 Frequencies -- 1637.9196 3812.7536 3909.9019 Red. masses -- 1.0823 1.0456 1.0812 Frc consts -- 1.7107 8.9552 9.7382 IR Inten -- 58.1101 3.5959 25.0362 Atom AN X Y Z X Y Z X Y Z 1 8 0.00 0.00 0.07 0.00 0.00 0.05 0.00 0.07 0.00 2 1 0.00 -0.43 -0.56 0.00 0.58 -0.40 0.00 -0.56 0.44 3 1 0.00 0.43 -0.56 0.00 -0.58 -0.40 0.00 -0.56 -0.44 - the important bits are the two lines labeled "Low frequencies", you know that every molecule has 3N-6 vibrational frequencies, the frequencies listed are the "-6", these are just the motions of the center of mass of the molecule, and should be much smaller than the first vibration listed, for example the first vibration has A2" symmetry and has a frequency of 1637cm-1, the largest "zero" frequency is about 73cm-1 which is an order of magnitude smaller ... so this looks ok.
- The better the method employed the closer to zero these six frequencies should be, we normally require them to be within plus/minus 10cm-1. They are not that accurate in this case because we have used a relatively low level method.
- however we now know that a true minimum has been found and we can go on to analyze the electrostatic and electronic structure of this molecule.
- now to animate the frequencies to see what they look like. Open the frequency analysis log file in gaussview, choose open from the Results tab, don't forget to change the file extension from *.com to *.log in the dialog box that appears:
- once the file opens choose vibrations from the File tab. Animate the individual vibrations and also have a look at the spectrum (red boxes).
- now we are ready to analyze some of the electronic and electostatic information for the moleucle