Vibrational frequencies¶

Overview¶

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 for details). The appropriate nuclear hessian generation algorithm is chosen based on the user input when TASK 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 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>]]  
 end

Hessian File Reuse¶

By default the task 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.

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

Changing the Suffix of the Animation Files¶

The filename option sets a new name for the animated natural modes so you can have more than one vibrational analysis in a run (e.g. find minimum, calculate frequencies, follow mode to TS, calculate frequencies again). The optional keyword overwrite allows old animated modes to be overwritten if they exist.

filename <filename> [overwrite]

An Example Input Deck¶

This example input deck will optimize the geometry for the given basis set, compute the frequencies for H₂O, H₂O at different temperatures, D₂O, 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