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Response field with supercell size
Vibrational frequencies calculation
B. Civalleri, F. Pascale and Y. Noel

Overview and goals

The crystal lattice is never rigid. Atoms actually move around their equilibrium positions inside the crystalline structure. Lattice dynamics provides the key to understand many physical phenomena mainly related to thermal effects, phase transitions, transport properties, and so forth. Theoretical calculation of atom vibrations then gives access to a number of properties such as the calculation of vibrational spectra, the prediction of structure stability or instability of a crystalline phase and the computation of thermodynamical properties (e.g. heat capacity, entropy, ...). 

Vibrational frequencies calculation in CRYSTAL is performed at the G point. The dynamical matrix is computed by numerical evaluation of the first-derivative of the analytical atomic gradients. The point group symmetry of the system is fully exploited to reduce the number of points (SCF+gradient) to be considered. On each numerical step, the residual symmetry is preserved during the SCF process and the gradients calculation.

In this tutorial you will learn how to run a vibrational frequencies calculation with CRYSTAL. Available options will be discussed along with commented examples. Because of the computational cost no explicit calculations will be required; rather selected outputs are discussed. They will be simply obtained by restarting from previous runs. a-Quartz and Calcite are considered as test case systems. The last part of this tutorial will also give an introduction to the calculation of anharmonic corrections to X-H stretching modes.

Harmonic vibrational frequencies

Vibrational frequencies are computed at the G point within the harmonic approximation.
The dynamical matrix, Hij (i.e. the matrix of the second-derivatives), is computed by numerical evaluation of the first-derivatives

of the analytical atomic gradients

at u=0, where u is the displacement vector with respect to equilibrium structure.

The mass-weighted dynamical matrix is calculated

where Ma and Mb are the masses of the atoms a and b associated with the i-th and j-th coordinates, respectively; and then diagonalized to obtain eigenvalues (i.e. frequencies) and eigenvectors (i.e. normal modes).

Special properties of the G point (q=0)

The point group symmetry of the system is fully exploited to reduce the number of points (SCF+gradient) to be considered. On each numerical step, the residual symmetry is preserved during the SCF process and the gradients calculation.
 

Input and output

The keyword FREQCALC opens the vibrational frequencies calculation input. The keyword must be inserted in the geometry input section (block 1) as the last keyword of the section. It is worth noting that meaningful vibrational frequencies are only computed when the crystalline structure is a stationary point on the potential energy surface, generally a minimum.
Note that the transverse optical (TO) modes are computed by default.

The CRYSTAL input and output are discussed in more detail in the Quick tour of CRYSTAL vibrational frequencies calculation input and output.

Exercise: 
Analyze the output for a-Quartz (qua_hf_2d_f.out). Locate where the relevant information on the vibrational frequencies calculation are reported. 
Which are the irreducible representations? Which modes are IR active? And Raman active? 
Compare the computed frequencies to the experimental data reported in ref. [1,2].  
Analyze the normal modes by using visualization tools.
 

Vibrational frequencies calculation restart

Restart is possible for a job which is abruptly terminated. The calculation restarts exactly from the last step of the previous run. Information is recovered from fortran unit FREQINFO.DAT, saved at each step of the calculation. The script runcry06 saves FREQINFO.DAT as inpfilename.allopt, and recovers the data when required.
The keyword RESTART must be specified in same input deck as for the initial geometry optimization. For instance:

 
Initial input
 
Restart input
QUARTZ ALFA (init. geom.: expt.) HF base 2d
CRYSTAL
0 0 2
154
0 0 16
4.91458 5.40486
2
14 4.705925E-01 0.000000E+00 0.000000E+00
8  4.151440E-01 2.670973E-01 1.199927E-01		   QUARTZ ALFA (init. geom.: expt.) HF base 2d
CRYSTAL
0 0 2
154
0 0 16
4.91458 5.40486
2
14 4.705925E-01 0.000000E+00 0.000000E+00
8  4.151440E-01 2.670973E-01 1.199927E-01
FREQCALC
END[FREQ]		   FREQCALC
RESTART (file FREQINFO.DAT and fort.9 must exist)
END[FREQ]
END   END

This keyword is also useful when a previous calculation has been complete and one would like to change some of the computational parameters such as:

  • computing the LO-TO splitting
  • performing an isotopic substitution
  • changing the default thermodynamical conditions (i.e. temperature and pressure)
All of those options will be discussed below.
 

IR intensities

The IR intensity of the i-th mode is defined as

i.e. it is proportional to the square of the first-derivative of the dipole moment with respect to the normal mode coordinate Qi times the di degeneracy of the i-th mode. The dipole moment derivative is evaluated numerically by using the unit cell well-localized Wannier functions. 
The dipole moment is related to the Born effective charge tensor which is the first derivative of the polarization per unit cell with respect to the atomic displacements when the applied electric field is zero

From the Born effective charge tensor, atomic charges, Z*a, are then defined as one-third of the trace of the tensor in Cartesian coordinates. In molecular physics they are also known as generalized atomic polarizability tensor (GAPT) charges.

To include the calculation of the intensities of IR active modes, the keyword INTENS must be specified. In the output file a column with the values (in km/mol) of the computed IR intensities is printed in the list of vibrational frequencies.
 
FREQCALC
INTENS
ENDFREQ 		  Keyword to perform a vibrational frequencies calculation
Keyword to activate calculation of IR intensities
End of the vibrational frequencies input block
END   End of the geometry input section


Note that the evaluation of the IR intensities requires a full calculation of the vibrational frequencies as well. To restart a calculation the fort.80 is needed, along with the FREQINFO.DAT and fort.9 fortran units.  

Exercise: Analyze the output for a-Quartz (qua_hf_2d_f_ir-int.out) to locate where IR intensities are reported. Atomic Born effective charges are also reported in the output file. Compare them to the Mulliken ones (Si = 1.86 e, O = -0.93 e).
 

LO-TO splitting

In the case of ionic compounds, long-range Coulomb effects due to coherent displacement of the crystal nuclei are neglected, as a consequence of imposing the periodic boundary conditions. Therefore, Wij needs to be corrected for obtaining the longitudinal optical (LO) modes. This additional contribution, the so-called non analitycal term, is

where W is the cell volume. It depends on

  • the dynamic (i.e. electronic or clamped nuclei) dielectric tensor
  • the Born effective charge tensor associated to atom a:

To compute the LO-TO splitting the cartesian components of the dynamic dielectric tensor must be specified by using the keyword DIELTENS,
The dynamic dielectric tensor is evaluated by means of a finite field saw-tooth model (see the The calculation of static dielectric constants tutorial), whereas the Born effective charge tensor is obtained from well-localized Wannier functions by specifying the keyword INTENS. 
An example of input for a-Quartz is given below
 
FREQCALC
INTENS
DIELTENS
2.018 0.000 0.000
0.000 2.018 0.000
0.000 0.000 2.071
ENDFREQ 		  Keyword to perform a vibrational frequencies calculation
Keyword to compute IR intensities
Keyword to compute LO-TO splitting

Cartesian components of the dynamic dielectric tensor

End of the vibrational frequencies input block
END   End of the geometry input section

In this case, as a supplementary result, the static dielectric tensor (i.e. ionic contribution) is calculated by means of the eigenvalues, , and the eigenvectors, , as

where


Exercise: Analyze the output for a-Quartz (qua_hf_2d_f_lo-to.out). Locate where the static dielectric tensor is printed and the LO-TO part. Which is the mode with the largest LO-TO splitting?
 

Isotopic substitution

Isotopic substitution is a well-known technique adopted by experimentalists as a tool to help the assignment of an observed band in the vibrational spectrum. The same strategy can easily be implemented once the dynamical matrix is available. Frequency shifts due to isotopic substitutions are calculated simply by changing the masses Ma (Mb) in the mass-weighted Wai,bj matrix.
The following input allows to change the mass of the Si atoms of a-Quartz to 29 amu.
 
FREQCALC
ISOTOPES
3
1 29
2 29
3 29
ENDFREQ 		  Keyword to perform a vibrational frequencies calculation
Keyword for isotopic substitution
Number of atomic masses to be changed

Label of the atoms and isotopic mass

End of the vibrational frequencies input block
END   End of the geometry input section

Exercise: Analyze the output for a-Quartz (qua_hf_2d_f_iso-si29.out). Compare the vibrational frequencies computed with the standard atomic masses to the ones obtained with the new isotopes.

When the isotopic mass of one atom symmetry related to others is modified, the symmetry is reduced according to the point group symmetry.
If a previous calculation was performed with standard atomic masses, new frequencies from isotopic substitutions can be computed from the previous dynamical matrix  by simply restarting the calculation.
 

Working with subunits

The keyword ISOTOPES can also be used to decompose the vibrational spectrum in subunits. This is attained by freezing atoms which are not part of the subunits, as if they have an infinite mass (i.e. by attributing a very large mass to some of the atoms). In this way, steric, electrostatic and short range repulsion effects, as well as symmetry of the crystalline environment, which would be lost in an isolated fragment, are preserved.
 

Thermodynamic analysis

Thermodynamic information are printed at the end of the calculation. By default, they are referred to room temperature (T=298.15 K) and pressure (P=1.01325 105 Pa). Those conditions can be modified by using the keywords TEMPERATURE and PRESSURE, respectively. A range of temperature (or pressure) must be entered by specifying the number of intervals in the range, the initial and the final temperature (or pressure).
 
FREQCALC
TEMPERAT
15 20.0 300.0
ENDFREQ 		  Keyword to perform a vibrational frequencies calculation
Keyword to change temperature in thermodynamic analysis
Number of intervals, initial and final temperature
End of the vibrational frequencies input block
END   End of the geometry input section

The output file contains a series of 15 calculations of the thermodynamic part at different temperature going from 20.0 to 300.0 K.

Exercise: Analyze the output for a-Quartz (qua_hf_2d_f_thermo.out) and locate where thermodynamical data are reported. Restart the calculation and change the range of temperature to 20.0-1000.0 K with 25 intervals and then plot the constant volume heat capacity vs T by using gnuplot.

Note that for a full thermodynamic analysis the phonon dispersion relation should be available in order to have the phonon density of states to be used in the thermodynamic relations. The error is larger for the acustic bands and low-frequency phonons.
 

Frequencies of a fragment

The numerical procedure implemented for the vibrational frequencies calculation allows to limit the calculation to an atomic fragment. The keyword FRAGMENT must be specified along with the number of atoms in the fragment and the corresponding labels. For instance, the following input performs the calculation of the vibrational frequencies of a hydroxyl group at the (100) surface of the pure silica edingtonite zeolite: 
  
EDI(Si) slab con OH[6-31+G(d,p)]
SLAB
27
6.47559     6.97941
9
14    -1.155432E-01 -2.695484E-01  0.000000E+00
14    -4.956097E-01  2.230743E-20  0.000000E+00
14     1.245946E-01  2.230743E-20  1.884433E+00
 1     1.360395E-02  2.230743E-20  4.035403E+00
 8    -3.534958E-01 -1.928605E-01  0.000000E+00
 8     3.618417E-01  2.230743E-20  1.344337E+00
108    1.385407E-01  2.230743E-20  3.513412E+00
 8    -1.166139E-01 -5.000000E-01  0.000000E+00
 8     3.021910E-03 -1.911223E-01  1.339109E+00
   Title
Slab model
Layer group symmetry number
Cell parameters of the bidimensional lattice
Number of irreducible atoms in the 2D unit cell Atomic number and Mixed fractionary (x,y) and cartesian (z) coordinates
FREQCALC
FRAGMENT
3
4 12 6
ENDFREQ 		  Keyword to perform a vibrational frequencies calculation
Keyword to compute vibrational frequencies on a fragment
Number of atoms in the fragment
Labels of the atoms belonging to the fragment
End of the vibrational frequencies input block
END   End of the geometry input section

A reduced Dynamical matrix is computed and diagonalized. 

Note that: (i) the symmetry may be broken, so that the number of SCF+gradient calculation changes according to the new symmetry; (ii) the residual symmetry is not exploited in the wavefunction and gradient calculation (i.e. the symmetry is removed). 

Exercise: Analyze the output of EDI(100) -SiOH group (slab_b3_f_frag.out) and full vibrational frequencies calculations (slab_b3_f.out).
Compare the results for the OH stretching mode in the two cases.
What about the other vibrational modes involving the OH group (e.g. Si-OH stretching)?
How does the harmonic OH stretching mode frequency compare with the experimental value of 3747 cm-1?

 

Phonon dispersion calculations


As in the case of electronic energy levels, the discrete molecular vibrational frequencies become phonon bands in solids. Phonon dispersion arises because the interaction is not confined inside the volume of the primitive cell. This means that as the phase difference of the motion of atoms in different cells varies, so do the energy and the frequency.

It is explained at the beginning of this section that performing a frequency calculation with CRYSTAL gives the harmonic  vibrational frequencies at the Gamma point. This is the zone central point of the First Brillouin Zone (FBZ), which corresponds to the motion in phase of the atoms  in different cells. The numerical procedure which is used to compute the Hessian matrix elements implies that all translationally equivalent atoms in the crystal are displaced at the same time.

Gamma point   

The calculation of phonon dispersion is possible by means of the supercell approach. The construction of a supercell implies the partial breaking of the translational symmetry, thus allowing a certain set of phase differences, say FBZ points, to be sampled.  This sampling depends on the size and shape of the supercell: the reciprocal lattice of the supercell defines the sampling net on the primitive FBZ.

Dispersion   

As an example, in the monodimensional system in the above figures, the supercell in the second one permits to compute the frequencies at 3 reciprocal space points, namely 0, 1/3 and 2/3.
Symmetry is exploited in order to reduce as much as possible the cost of the calculations. In particular the number of SCF+G calculations is almost constant and does not depend on the size of the supercell. Indeed the number of SCF+G calculations may depend on the shape of the supercell. The choice of non isotropic supercell expansions may lead to point symmetry breaking which in turn decreases the ratio between the reducible and the irreducible information.
 
To perform a phonon dispersion calculation, the usual input of a frequency calculation needs to be modified in two ways:
  1. The SCELPHONO keyword needs to be inserted in the geometry input block. This keyword builds a supercell where the first atoms are the primitive ones, and builds all the symmetry information which is needed for a phonon dispersion calculation. The usual SUPERCELL keyword will not work in this context.
  2. Inside the FREQCALC block the keyword DISPERSI is needed.

COMMENT LINE
CRYSTAL
0 0 0
...
...
...
SCELPHONO
2 0 0
0 2 0
0 0 2
END
FREQCALC
DISPERSI
ENDFREQ 		  CRYSTAL Geometry input block



Crystal group and atomic fractional coordinates

SCELPHONO keyword
supercell expansion for dispersion calculations



Keyword to perform a vibrational frequencies calculation
Keyword to perform a phonon dispersion calculation
END   End of the geometry input section
Basis block

SCF block

 

Exercise:

Analyze the output for MgO (MgO-222-DISP.out)
Locate where the relevant information on the phonon dispersion sampling is reported.
Which reciprocal space points correspond to the supercell given in input?
How does the number of dispacements change with respect to a Gamma calculation (MgO-prim.out)?
How does the number of dispacements change with respect to a traditional frequency calculation performed on a supercell constructed using keyword SUPERCELL (MgO-222.out)?
How do the thermodynamical properties change ?
(Note: the thermodynamical properties calculated with DISPERSI need to be divided by the number of primitive cells which are contained in the supercell.)


Anharmonic correction to X-H stretching modes

Vibrational normal modes that involve H atoms can be largely affected by anharmonicity. This is especially true for X-H stretching mode. To take into account the anharmonicity for X-H stretching mode a numerical procedure has been implemented in CRYSTAL. The calculation consists in:

  1. consider the X-H distance as a normal mode decoupled from all other modes
  2. calculate the total energy of the system for a set of X-H values around equilibrium
  3. fit the points with a sixth-order polynomial
  4. solve the one-dimensional nuclear Schrodinger equation for the fitted PES
as shown in the figure below

From the energy of the vibrational levels the fundamental frequency and the anharmonic contribution are obtained as:

where we is the harmonic frequency and wexe the anharmonic correction. w01 is the corrected X-H stretching frequency to be compared with the fundamental frequency from experiments.

The keyword ANHARM opens the anharmonicity calculation section. The keyword must be inserted in the geometry input section (block 1) as the last keyword of the section. As shown in the input below, the label of the hydrogen atom of the X-H bond must be indicated. Atom linked to H is automatically found by looking for the nearest neighbour. To preserve the symmetry of the system, the keyword KEEPSYMM must be specified.
 
Mg(OH)2 brucite 75/16 p
CRYSTAL
0 0 0
164
3.171065 4.858475
3
12 0.000000000  0.000000000 0.000000000
8  0.333333333 -0.333333333 0.213989313
1  0.333333333 -0.333333333 0.412022411
   Title
3D crystalline system
Space group symmetry number
Cell parameters of the bidimensional lattice
Number of irreducible atoms in the unit cell
Atomic number and fractionary coordinates
ANHARM
4
KEEPSYMM
END		   Keyword to perform anharmonic correction to X-H stretching 
Label of the hydrogen atoms
Keyword to preserve the symmetry
End of the vibrational frequencies input block
END   End of the geometry input section


This input corresponds to the calculation of the anharmonic correction of the frequency value for the OH stretching mode in Mg(OH)2. Two stretching modes are available, the correction is only computed for the symmetric one. The following output is printed concerning information on the calculation: isotopic masses, number of points and the exploitation of the symmetry (i.e. atom 5 symmetry related to 4 is also displaced).

 THE OSCILLATOR IS DEFINED BY THESE TWO ATOMS:
 ATOM SYMBOL   MASS(AMU)  NEIGHBOR IN THE CELL
    4     H     1.00782
    2     O   15.99491

 THE EQUILIBRIUM DISTANCE (ANGS) IS:                0.96214
 THE REDUCED MASS (AMU) IS:                         0.94809


 ATOM N.   4 AT. N.   1 DISPLACED BY (A)   0.00000   0.00000   1.00000



  7 ENERGY CALCULATIONS ARE PERFORMED:
 THE SELECTED ATOM IS DISPLACED ALONG THE VECTOR TO ITS FIRST NEIGHBOR

 THE FIRST CALCULATION CORRESPONDS TO THE EQUILIBRIUM
 GEOMETRY AND IS USED AS AN INITIAL GUESS FOR THE OTHER GEOMETRIES.
 FIXINDEX POINT (SEE MANUAL) AT THE EQUILIBRIUM GEOMETRY.


 KEEPSYMM OPTION:
 THE SYMMETRY OF THE CRYSTAL IS KEPT AND APPLIED TO THE PERTURBATION

 THERE ARE     2 EQUIVALENT ATOMS MOVED DURING THE ANHARMONIC CALCULATION.
 THE CRYSTAL ENERGY WILL BE DIVIDED BY  2 - LABEL OF THE ATOMS:

    4    5

After the first SCF, the output reports the total energy for the selected set of points and results of the evaluation of the anharmonicity 

 HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
                        STRETCHING OF THE OSCILLATOR
 HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH


     PT        DISPL (BOHR)        ENERGY (AU)       N.CYC      DE
      1        -3.77945E-01     -3.517750623855E+02   16     1.2578E-01
      2        -3.02356E-01     -3.518287388496E+02   12     7.2099E-02
      3        -1.13384E-01     -3.518930912322E+02   14     7.7465E-03
      4         0.00000E+00     -3.519008377258E+02   19     0.0000E+00
      5         3.02356E-01     -3.518666663959E+02   18     3.4171E-02
      6         4.53534E-01     -3.518359931504E+02   20     6.4845E-02
      7         5.66918E-01     -3.518112125962E+02   21     8.9625E-02

     A POLYNOMIAL FIT OF ORDER 6 IS PERFORMED.
     THE ONE-DIMENSIONAL SCHROEDINGER EQUATION IS SOLVED NUMERICALLY.

 XMU =  0.948087E+00 amu

 New minimum distance (A)     -1.00000
 New maximum distance (A)      1.50000

     EIGENVALUES OF THE ANHARMONIC OSCILLATOR

     N           A.U            EV         KCAL/MOLE      CM-1

     E 1       0.00868       0.23614         5.446        1904.6
     E 2       0.02540       0.69129        15.942        5575.6
     E 3       0.04132       1.12426        25.926        9067.8
     E 4       0.05645       1.53602        35.421       12388.8
     E 5       0.07097       1.93108        44.532       15575.2
     E 6       0.08520       2.31852        53.466       18700.1
     E 7       0.09955       2.70899        62.471       21849.5
     E 8       0.11430       3.11030        71.725       25086.3
     E 9       0.12959       3.52639        81.320       28442.2
     E10       0.14548       3.95871        91.290       31929.2

     THE THREE LOWEST EIGENVALUES E0, E1 AND E2 ARE USED TO COMPUTE
          W(0-1)=E1-E0, W(0-2)=E2-E0, WeXe=[2W(0-1)-W(0-2)]/2 AND We=W(0-1)+2WeXe

     FUNDAMENTAL ANHARMONIC FREQUENCY  W(0-1)     3671.0 cm-1
     FIRST OVERTONE                    W(0-2)     7163.2 cm-1
     HARMONIC FREQUENCY                We         3849.9 cm-1
     ANHARMONIC CONSTANT               WeXe         89.4 cm-1

 

Exercise: Analyze the output file of Mg(OH)2 (mgoh2_oh_anharm.out) and locate the relevant information on the calculation of the OH stretching anharmonicity. Compare the results with the full harmonic value of 3847 cm-1 and the available experimental data of 3654 cm-1. Data obtained with different Hamiltonians are available from ref. [3] 
 

Examples and exercises

Technical notes
Vibrational frequencies calculation can be rather expensive. To avoid running time consuming jobs, you will find output files ready to be analyzed.
Input decks and some output files for the proposed examples and exercises are listed below

Input decks can also be used to restart from a previous calculation:

  1. copy the filename.freqinfo fortran unit in your local directory
  2. modify the input deck by inserting the keyword RESTART in the FREQCALC...ENDFREQ input block
  3. run the runcry06 script by specifying the filename of the input and then the name of the file from which the data will be recovered

Hint: Use visualization tools to analyze normal modes.
For instance, vibrational frequencies normal modes can be visualized with jmoledit.
   

Example 1: a-Quartz (a-quartz)
 
Outputs of the previously proposed exercises on a-Quartz are available to be analyzed. Calculations can be restarted from the qua_hf_2d_f.freqinfo unit by following instructions above.
 

Exercise 1: Calcite (calcite)
 
Repeat calculations proposed for a-Quartz. Use available fortran units to restart calculations (calcite_b3_bsa.freqinfo).

Start from the analysis of the output for the calculation of vibrational frequencies and IR intensities of Calcite (calcite_b3_bsa.out). The smallest basis of ref. [5] (i.e. BSA) has been adopted.

  • Which are the irreducible representations? Which modes are IR active? And Raman active?
  • Identify the external modes and the internal ones
  • Compare the computed frequencies to the experimental data reported in ref. [5].
  • Analyze the normal modes by using visualization tools.
  • Compare the atomic Born effective charges with the Mulliken ones

Compute the LO-TO splitting by inserting the DIELTENS keyword. Use the static dielectric tensor of xx=yy=2.749, zz=2.208 and xy=xz=yx=zx=0.000, as reported in ref. [5] for basis set BSD.

Perform an isotopic substitution of Ca, C and O. How do vibrational frequencies change with respect to standard isotopic masses? Which is the largest isotopic shift?

Change the range of temperature to 20.0-1000.0 K with 25 intervals and then plot the constant volume heat capacity vs T by using gnuplot.
 

Exercise 2: EDI(100) (edislab)
 
Analyze the output file (slab_b3_f.out) and animate normal modes by using visualization tools. Is there something strange?

Identify relevant vibrational modes, namely: OH stretching mode, Si-OH stretching mode, SiOH bending mode and SiOH torsion mode.
 
Restart the full vibrational frequencies calculation by using the atomic fragment adopted in the example above. Modify the atomic fragment to include SiOH first-neighbours oxygen atoms (i.e. to be O3SiOH).

Compare the computed vibrational frequencies of the modes indicated above to the experimental values for amorphous silica of 3747, 980, 760, 127 cm-1, respectively.

A large discrepancy is observed for the OH stretching mode. Why?
Analyze the slab_b3_anharm.out and compare results for the OH stretching mode with the experimental value.


List of available input decks and output files

Here a list of the available input decks is reported. In some cases the corresponding output files are also available. Vibrational frequencies output files can be used to visualize the animation of the normal modes with the jmoledit tool.
 

Directory

Input

Output

Description
a-quartz qua_hf_2d_f.d12 qua_hf_2d_f.out a-Quartz HF/BS(2d) vibrational frequencies calculation
  qua_hf_2d_f.freqinfo   a-Quartz HF/BS(2d) vibrational frequencies FREQINFO.DAT unit
  qua_hf_2d_f_ir-int.d12 qua_hf_2d_f_ir-int.out a-Quartz HF/BS(2d) vibrational frequencies calculation with IR intensities
  qua_hf_2d_f_lo-to.d12 qua_hf_2d_f_lo-to.out a-Quartz HF/BS(2d) vibrational frequencies calculation with LO-TO splitting
  qua_hf_2d_f_iso-si29.d12 qua_hf_2d_f_iso-si29.out a-Quartz HF/BS(2d) vibrational frequencies calculation with isotopic substitution: 29Si
  qua_hf_2d_f_thermo.d12 qua_hf_2d_f_thermo.out a-Quartz HF/BS(2d) vibrational frequencies calculation with thermodynamical analysis
       
calcite calcite_b3_bsa.d12 calcite_b3_bsa.out Calcite B3LYP/BSA vibrational frequencies calculation with IR intensities
  calcite_b3_bsa.freqinfo   Calcite B3LYP/BSA vibrational frequencies FREQINFO.DAT unit
       
edislab slab_b3_f.d12 slab_b3_f.out Hydroxylated EDI(100) full harmonic calculation 
  slab_b3_f.freqinfo   Hydroxylated EDI(100) full harmonic calculation FREQINFO.DAT unit
  slab_b3_f_frag.d12 slab_b3_f_frag.out Hydroxylated EDI(100) calculation on Si-OH fragment
  slab_b3_anharm.d12 slab_b3_anharm.out Hydroxylated EDI(100) OH anharmonicity
       
mgoh2 mgoh2_oh_f.d12 mgoh2_oh_f.out Mg(OH)2 full harmonic calculation
  mgoh2_oh_f.freqinfo   Mg(OH)2 full harmonic calculation FREQINFO.DAT unit
  mgoh2_oh_anharm.d12 mgoh2_oh_anharm.out Mg(OH)2 OH anharmonicity calculation
       
mgo MgO-prim.d12 MgO-prim.out MgO primitive cell calculation
  MgO-222.d12 MgO-222.out MgO 222 supercell calculation
  MgO-222-DISP.d12 MgO-222-DISP.out MgO 222 phonon dispersion calculation

References

Vibrational frequencies calculation of crystalline compounds

[1] F. Pascale, C.M. Zicovich-Wilson, F. Lopez, B. Civalleri, R. Orlando, R. Dovesi
The calculation of the vibration frequencies of crystalline compounds and its implementation in the CRYSTAL code
J. Comput. Chem. 25 (2004) 888-897

[2] C.M. Zicovich-Wilson, F. Pascale, C. Roetti, V.R. Saunders, R. Orlando, R. Dovesi
The calculation of the vibration frequencies of alpha-quartz: the effect of hamiltonian and basis set
J. Comput. Chem. 25 (2004) 1873-1881

Anharmonicity of X-H stretching modes

[3] F. Pascale, S. Tosoni, C.M. Zicovich-Wilson, P. Ugliengo, R. Orlando, R. Dovesi
Vibrational spectrum of brucite Mg(OH)2: A periodic ab initio quantum-mechanical calculation including OH anharmonicity
Chem. Phys. Letters 396 (2004) 4-6

[4] P. Ugliengo, F. Pascale, M. Merawa, P. Labeguerie, S. Tosoni, R. Dovesi
Iinfrared spectra of hydrogen-bonded ionic crystals: ab initio study of Mg(OH)2 and b-Be(OH)2
J. Phys. Chem. B 108 (2004) 13632-13637

Selected applications

[5] L. Valenzano, F.J. Torres, K. Doll, F. Pascale, C.M. Zicovich-Wilson, R. Dovesi
Ab initio study of the vibrational spectrum and related properties of crystalline compounds; the case of CaCO3 calcite
Z. Phys. Chem. 220 (2006) 893-912

[6] F. Pascale, C.M. Zicovich-Wilson, R. Orlando, C. Roetti, P. Ugliengo, R. Dovesi
Vibration frequencies of Mg3Al2Si3O12 pyrope. An ab initio study with the CRYSTAL code
J. Phys. Chem. B 109 (2005) 6146-6152

[7] B. Montanari, B. Civalleri, C.M. Zicovich-Wilson, R. Dovesi
Influence of the exchange-correlation functional in all-electron calculations of the vibrational frequencies of corundum (alpha-Al2O3)
Int. J. Quantum Chem. 106 (2006) 1703-1714

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