## About hessian matrix printed out by .HESPUN

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ankit7540
Posts: 46
Joined: 05 Sep 2015, 10:49
First name(s): ANKIT
Last name(s): RAJ
Affiliation: National Chiao Tung University
Country: Taiwan, Province of China

### About hessian matrix printed out by .HESPUN

Hello all,
This question is related to learning with DALTON.

By using .HESPUN directive under *VIBANA the molecular hessian is given in the DALTON.HES file. Upon analyzing it I see 3N blocks of numbers with each block having 3N numbers. So this is the (3N x 3N) hessian matrix. I also see another block in the bottom which might be the (1/sqrt(mass)) or maybe the norm for eigen-vectors ? Not sure ?

So my question(s)

1) What is this last block of numbers in the DALTON.HES file.

2) In the output file we again see the molecular hessian printed (with .VIBANA) but this appears as a triangular matrix ? How is this hessian different from DALTON.HES ?

Sorry for this rather descriptive/ explanatory type of question but I am learning. External links are welcome.
Best regards.
Ankit

taylor
Posts: 600
Joined: 15 Oct 2013, 05:37
First name(s): Peter
Middle name(s): Robert
Last name(s): Taylor
Affiliation: Tianjin University
Country: China

### Re: About hessian matrix printed out by .HESPUN

I think that the last block of numbers should be the (presumably converged, if you are doing an optimization --- hard to know without your output file...) molecular geometry. In an optimization, at steps that are not a stationary point if I remember correctly the program will also write the molecular gradient vector to the file.

The Hessian is a symmetric matrix. Hence it can be (and is) printed in the listing as a symmetric matrix, printing only the lower triangle of the matrix. But in almost any subsequent operation that uses the Hessian (post-processing of vibrational stuff, or using it to start the next phase of a geometry optimization perhaps at a different computational level for the wave function) it will need to be expanded to square form anyway to use in some sort of matrix-matrix or matrix-vector multiply operation. Given that it is hard to see that any (useful or meaningful) calculation with Dalton (LSDalton is different!) can use much more than 100 or so atoms, the value of 3N is not that large and it is simplest to write the square Hessian to file. But it takes up space in the output file, and it makes sense there to print only the distinct elements of one triangle of the matrix.

Best regards
Pete

ankit7540
Posts: 46
Joined: 05 Sep 2015, 10:49
First name(s): ANKIT
Last name(s): RAJ
Affiliation: National Chiao Tung University
Country: Taiwan, Province of China