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 eigenvectors ? 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.
About hessian matrix printed out by .HESPUN

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 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
Best regards.
Ankit
Ankit

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 First name(s): Peter
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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 (postprocessing 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 matrixmatrix or matrixvector 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
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 (postprocessing 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 matrixmatrix or matrixvector 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

 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
Re: About hessian matrix printed out by .HESPUN
Thank you for your answer.
As mentioned by you the last block is in fact the optimized (final) geometry of the molecule. I checked it with the output.
As mentioned by you the last block is in fact the optimized (final) geometry of the molecule. I checked it with the output.
Best regards.
Ankit
Ankit
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