Release66:Hessians & Vibrational Frequencies

__NOTITLE__
=Hessians=

This section relates to the computation of analytic hessians which are available for open and closed shell SCF, except ROHF and for closed shell and unrestricted open shell DFT <ref>Johnson, B.G. and Frisch, M.J. (1994) "An implementation of analytic second derivatives of the gradient-corrected density functional energy", ''Journal of Chemical Physics'' '''100''' 7429-7442, doi:[http://dx.doi.org/10.1063/1.466887 10.1063/1.466887]</ref>. Analytic hessians are not currently available for SCF or DFT calculations relativistic all-electron methodologies or for charge fitting with DFT. The current algorithm is fully in-core and does not use symmetry.

There is no required input for the Hessian module. This module only impacts the hessian calculation. For options for calculating the frequencies, please see the [[Vibration|Vibrational]] module.

==Hessian Module Input==

All input for the Hessian Module is optional since the default definitions are usually correct for most purposes. The generic module input begins with hessian and has the form:

  hessian
    thresh <real tol default 1d-6>
    print ...
    profile
  end

===Defining the wavefunction threshold===

You may modify the default threshold for the wavefunction. This keyword is identical to [[Release66:Hartree-Fock Theory for Molecules#THRESH -- convergence threshold|THRESH]] in the SCF, and the [[Density Functional Theory for Molecules#CONVERGENCE -- SCF Convergence Control|CONVERGENCE]] gradient in the DFT. The usual defaults for the convergence of the wavefunction for single point and gradient calculations is generally not tight enough for analytic hessians. Therefore, the hessian, by default, tightens these up to 1d-6 and runs an additional energy point if needed. If, during an analytic hessian calculation, you encounter an error:

  cphf_solve:the available MOs do not satisfy the SCF equations

the convergence criteria of the wavefunction generally needs to be tightened.

===Profile===

The PROFILE keyword provides additional information concerning the computation times of different sections of the hessian code. Summary information is given about the maximum, minimum and average times that a particular section of the code took to complete. This is normally only useful for developers.

===Print Control===

Known controllable print options are shown in the table below:


<center>
{| border='1' cellspacing='0'
|+Hessian Print Control Specifications
| '''Name'''
| '''Print Level'''
| '''Description'''
|-
| "hess_follow"
| high
| more information about where the calculation is
|-
| "cphf_cont"
| debug
| detailed CPHF information
|-
| "nucdd_cont"
| debug
| detailed nuclear contribution information
|-
| "onedd_cont"
| debug
| detailed one electron contribution information
|-
| "twodd_cont"
| debug
| detailed two electron contribution information
|-
| "fock_xc"
| debug
| detailed XC information during the fock builds
|}
</center>

=Vibrational frequencies=

The nuclear hessian which is used to compute the vibrational frequencies can be computed by finite difference for any ab initio wave-function that has analytic gradients or by analytic methods for SCF and DFT (see [[#Hessians|Hessians]] for details). The appropriate nuclear hessian generation algorithm is chosen based on the user input when TASK <theory> frequencies is the task directive.

The vibrational package was integrated from the Utah Messkit and can use any nuclear hessian generated from the driver routines, finite difference routines or any analytic hessian modules. There is no required input for the "VIB" package. VIB computes the Infra Red frequencies and intensities for the computed nuclear hessian and the "projected" nuclear hessian. The VIB module projects out the translations and rotations of the nuclear hessian using the standard Eckart projection algorithm. It also computes the zero point energy for the molecular system based on the frequencies obtained from the projected hessian.

The default mass of each atom is used unless an alternative mass is provided via the [[Release66:Geometry|geometry]] input or redefined using the vibrational module input. The default mass is the mass of the most abundant isotope of each element. If the abundance was roughly equal, the mass of the isotope with the longest half life was used.

In addition, the vibrational analysis is given at the default standard temperature of 298.15 degrees.

==Vibrational Module Input==

All input for the Vibrational Module is optional since the default definitions will compute the frequencies and IR intensities. The generic module input can begin with vib, freq, frequency and has the form:

  {freq || vib || frequency}
    [reuse [<string hessian_filename>]]
    [mass <integer lexical_index> <real new_mass>]
    [mass <string tag_identifier> <real new_mass>]
    [{temp || temperature} <integer number_of_temperatures> \
          <real temperature1 temperature2 ...>]
    [animate [<real step_size_for_animation>]]
    [filename <string file_set_name> [overwrite]]
  end

===Hessian File Reuse===

By default the task <theory> frequencies directive will recompute the hessian. To reuse the previously computed hessian you need only specify reuse in the module input block. If you have stored the hessian in an alternate place you may redirect the reuse directive to that file by specifying the path to that file.

  reuse /path_to_hessian_file

This will reuse your saved Hessian data but one caveat is that the geometry specification at the point where the hessian is computed must be the default "geometry" on the current run-time-data-base for the projection to work properly.

===Redefining Masses of Elements===

You may also modify the mass of a specific center or a group of centers via the input.

To modify the mass of a specific center you can simply use:

  mass 3 4.00260324

which will set the mass of center 3 to 4.00260324 AMUs. The lexical index of centers is determined by the geometry object.

To modify all Hydrogen atoms in a molecule you may use the tag based mechanism:

  mass hydrogen 2.014101779

The mass redefinitions always start with the default masses and change the masses in the order given in the input. Care must be taken to change the masses properly. For example, if you want all hydrogens to have the mass of Deuterium and the third hydrogen (which is the 6th atomic center) to have the mass of Tritium you must set the Deuterium masses first with the tag based mechanism and then set the 6th center's mass to that of Tritium using the lexical center index mechanism.

The mass redefinitions are not fully persistent on the run-time-data-base. Each input block that redefines masses will invalidate the mass definitions of the previous input block. For example,

 freq
   reuse
   mass hydrogen 2.014101779
 end
 task scf frequencies
 freq
   reuse
   mass oxygen 17.9991603
 end
 task scf frequencies

will use the new mass for all hydrogens in the first frequency analysis. The mass of the oxygen atoms will be redefined in the second frequency analysis but the hydrogen atoms will use the default mass. To get a modified oxygen and hydrogen analysis you would have to use:

 freq
   reuse
   mass hydrogen 2.014101779
 end
 task scf frequencies
 freq
   reuse
   mass hydrogen 2.014101779
   mass oxygen 17.9991603
 end
 task scf frequencies

===Temp or Temperature===

The "VIB" module can generate the vibrational analysis at various temperatures other than at standard room temperature. Either temp or temperature can be used to initiate this command.

To modify the temperature of the computation you can simply use:

  temp 4 298.15 300.0 350.0 400.0

At this point, the temperatures are persistant and so the user must "reset" the temperature if the standard behavior is required after setting the temperatures in a previous "VIB" command, i.e.

  temp 1 298.15

===Animation===

The "VIB" module also can generate mode animation input files in the standard xyz file format for graphics packages like RasMol or XMol There are scripts to automate this for RasMol in $NWCHEM_TOP/contrib/rasmolmovie. Each mode will have 20 xyz files generated that cycle from the equilibrium geometry to 5 steps in the positive direction of the mode vector, back to 5 steps in the negative direction of the mode vector, and finally back to the equilibrium geometry. By default these files are not generated. To activate this mechanism simply use the following input directive

  animate

anywhere in the frequency/vib input block.

Given an ordered list of files containing molecular coordinates
in XYZ format, the rasmolmovie shell script generates an animated
gif for each of the six possible views down a Cartesian axis.

It uses the free utilities
  - rasmol 
    (http://www.umass.edu/microbio/rasmol) 
    to manipulate the molecule and generate the individual frames
  - convert from ImageMagick 
    (http://www.imagemagick.org/)
    to combine the frames into an animated gif

It should be easy to modify the script to other file formats
or animation tools.

====Controlling the Step Size Along the Mode Vector====

By default, the step size used is 0.15 a.u. which will give reliable animations for most systems. This can be changed via the input directive

  animate real <step_size>

where <step_size> is the real number that is the magnitude of each step along the eigenvector of each nuclear hessian mode in atomic units.

===Specifying filenames for animated normal modes===

By default, normal modes will be stored in files that start with "freq.m-<mode number>". This is inconvenient if more than vibrational analysis
is run in a single input file. To specify different filename for a particular vibrational analysis use the directive

 filename <file_set_name> [overwrite]

where <file_set_name> is the name that will be prepended to the usual filenames. In addition the code by default requires all files to be new
files. When the option "overwrite" is provided any pre-existing files will simply be overwritten.

===An Example Input Deck===

This example input deck will optimize the geometry for the given basis set, compute the frequencies for <math>H_{2}O</math>, <math>H_{2}O</math> at different temperatures, <math>D_{2}O</math>, HDO, and TDO.

 start  h2o
 title Water 
 geometry units au autosym
   O      0.00000000    0.00000000    0.00000000
   H      0.00000000    1.93042809   -1.10715266
   H      0.00000000   -1.93042809   -1.10715266
 end
 basis noprint
   H library sto-3g 
   O library sto-3g
 end
 scf; thresh 1e-6; end
 driver; tight; end
 task scf optimize
 
 scf; thresh 1e-8; print none; end
 task scf freq 
 
 freq
  reuse; temp 4 298.15 300.0 350.0 400.0
 end
 task scf freq
 
 freq 
  reuse; mass H 2.014101779
  temp 1 298.15
 end
 task scf freq
 
 freq
  reuse; mass 2 2.014101779
 end
 task scf freq
 
 freq
  reuse; mass 2 2.014101779 ; mass 3 3.01604927
 end
 task scf freq

==References==
<references/>