# Normal Mode Analysis

1. Oct 12, 2007

### Rajini

Hi Member,
does any one have some experience with normal mode analysis????I need to know from basics...i want to use this analysis for finding the vibrations of a complex molecule....(may be by using Urey- force constants,etc..or if u know any other method !).

eagerly waiting
Rajini

2. Oct 12, 2007

### quetzalcoatl9

you will be interested in calculating the Hessian matrix (i.e. the second derivatives of the energy with respect to the position and/or relative coordinates). in the harmonic approximation, the eigenvalues of the hessian will yield the spring constants (which is sounds like you are looking for).

a good intro is "Molecular Vibrations" by Wilson, Decius and Cross. also, there is a set of books on diatomic spectra by Herzberg...but really, there are a myriad of sources on NMA out there (another Dover book is "Symmetry and Spectroscopy" by Harris/Bertolucci).

most ab initio programs will calculate the hessian matrix for you, but you will need to have a careful understanding of how the energy is being (hopefully accurately) calculated.

also, most basis sets tend to overestimate the vibrational modes and so typically 6-31G* basis sets are used and then an empirical scaling factor of 0.89 is applied (i know this sounds hokey, but this is how we parameterize modern force fields).

3. Oct 14, 2007

### jdstokes

Group theoretical methods can also prove very useful in this game. If you know the symmetry group of your molecule, this will allow you to find what types of modes can exist.

If you want to calculate the eigenmodes analytically, this can be a problem for even small molecules because you end up needing to solve very high order polynomials. Again, group theory comes to the rescue here allowing analytical expressions for each mode frequency and its corresponding basis of vibrations.

The following texts are very good for this stuff:
J. F. Cornwell, Group theory in physics, vol. 1, (Harcourt Brace Jonavich, London 1984) p. 92, p. 190.

P. P. Teodorescu and N-A. P. Nicorovici, Applications of the theory of groups in mechanics and physics, (Kluwer Academic Publishers, Dordrecht, 2004)

4. Oct 22, 2007

### Rajini

thanks

hi thanks for ur reply...now i am on holidays..will try to find those books....after my holidays
thanks again
rajini

5. Jan 7, 2008

### Rajini

that book (by wilson) is really nice..thanks again..also i found another book by nakamoto..which is also good...(basics are same in both books)

6. Jan 8, 2008

### physicist888

hey rajini
sorry cause i didnt reply you. infact, the coordinates that ive calculate it in terms of x,y and z coordinates was it the symmetry coordinates and not the normal coordinates.
actually, im still searching for a method to calculate it manualy, but it seems that's so hard , cause we should resolve a matrix of the molecular orbitals of the representation A that we have built it based on the x,y and z coordiantes.
i didnt find the method till now, so really sorry.