Background
The FREQCALC keyword activates one of the
most interesting features of
the CRYSTAL code.
The dynamical matrix (mass weighted Hessian matrix) is built by numerical differentiation of the analytical first derivative of the total energy. Supported Hamiltonians span the HartreeFock, LDA, GGA and hybrid functionals. Accuracy can be checked by varying step and number of points used for numerically calculating the Hessian matrix from the analytical first derivative. Frequencies at the Gamma point only are computed by diagonalizing the dynamic matrix, and the full harmonic set of frequencies can be compared with IR and RAMAN spectra. IR intensities are optionally computed, whereas Raman intensities are still to be implemented. Extension to the full Brillouin Zone is, at the moment, not yet available.
Implemented tools
Many interpretative tools can be activated through keywords, including isotopic substitution, restart options, computing frequencies for a fragments of the full system, LOTO splitting, calculation of the static dielectric tensor, graphical representation by means of the freerly available
MOLDRAW program, whereas all modes can also be rendered directly on the web by means of JMOL graphical engine.
Modes are automatically classified by symmetry. This is an extremely useful tool which simplify the comparison with experiment and allows a full classification of the spectrum to be carried out; IR and RAMAN activity of the modes is indicated in the output. A full potential energy
decomposition (PED) of all modes is automatically performed.
General reference work
The accuracy of the method, the influence of the computational parameters, basis set and hamiltonian have been explored extensively; see for example
[1, 5] where alphaquartz is used as a test system and reference [2] in which brucite vibrational spectra has been fully characterized.
Similar tests are also reported for pyrope [3] (Mg_{3}
Al_{2}Si_{3}O_{12}, 80 atoms in the unit cell, cubic), calcite [4] CaCO_{3};
these tests confirm that the produced frequencies are stable to within 24 cm^{1}
with respect to all the numerical parameters.
Overall, the mean absolute error obtained with respect to accurate experimental data
for a relatively large family of compounds (about 15) is of the order of 79 cm^{1},
when a good basis set is used and the B3LYP hamiltonian is adopted. HF, LDA and GGA perform worse [5].
Even more important, the automatic classification of modes by symmetry
and their animation permit to solve many of the interpretation problems very frequently
affecting experimental investigations (together with overtones, background problems, intensity problems).
Recent applications to rather complex systems are the
hydrogarnet katoite Ca_{3}Al_{2},[(OH}_{4}], [16],
the forsterite
Mg_{2}SiO_{4} [17], the open shell garnet andradite [7]
Ca_{3}Fe_{2}Si_{3}O_{12} and the vibrational spectra of titanosilicalite ETS10 [8].
Anharmonicity of the H containing bonds
Special attention has been devoted to the XH bonds, OH in particular.
For the OH stretching, the harmonic approximation is known to be in error by as much as 150200 cm^{1} .
Luckely, due to the light H mass, the OH stretching is fully separated from the other modes, and can be treated as a onedimensional vibrational problem.
A keyword is available (ANHARM) that permits to solve numerically the nuclear Schroedinger equation (NSE) of this onedimensional problem [9].
Extensive investigations have been performed [10] on the numerical parameters, basis set and hamiltonian [2], showing that:

the present scheme provides very accurate OH stretching frequencies (within 510 cm^{1}) for non Hbonded systems, when the B3LYP scheme is used.
 HF, LDA and GGA errors are much larger (80200 cm^{1})
 for strongly Hbonded systems like betaBe(OH)_{2} [11], B3LYP OH stretchings are off by about 100 cm^{1}, whereas HartreeFock error can reach +350 cm^{1}, GGA 400 cm^{1}, and LDA 800 cm^{1}.
Other applications are listed concerning the OH stretching only, namely the LiOH and NaOH crystals [12],
the vibrational features of H
_{2} adsorbed on acid chabazite [13] and the anharmonic treatment of the acid OH group in interaction with carbon monoxide in chabazite [14].
The combined use of the FREQUENCY option (full set of modes at Gamma in the harmonic approximation) and of the ANHARM option (anharmonic treatment of the single OH modes) permits to investigate at high level of accuracy many different and complex hydroxydes [15].
References
 1

F. Pascale, C.M. ZicovichWilson, F. Lopez Gejo, B. Civalleri, R. Orlando,
R. Dovesi, ``The calculation of vibrational frequencies of crystalline
compounds and its implementation in the CRYSTAL code'',
J. Comput. Chem. 25, 888897 (2004).

 2

Pascale F, Tosoni S, ZicovichWilson C, Ugliengo P, Orlando R, Dovesi R,
``Vibrational spectrum of brucite, Mg(OH)_{2}: a periodic ab initio quantum
mechanical calculation including OH anharmonicity'',
Chem. Phys. Lett. 396, 46 (2004).

 3

F. Pascale, C.M. ZicovichWilson, R. Orlando, C. Roetti, P. Ugliengo, R.
Dovesi, ``Vibration frequencies of Mg_{3}
Al_{2}Si_{3}O_{12}
pyrope. An ab
initio study with the CRYSTAL code'',
J. Phys. Chem. B 109, 61466152 (2005).

 4

M. Prencipe, F. Pascale, C.M. ZicovichWilson, V.R. Saunders, R. Orlando,
R. Dovesi, ``The vibrational spectrum of calcite (CaCO_{3}): an ab initio
quantummechanical calculation'',
Phys. Chem. Minerals 31, 559564 (2004).

 5

C.M. ZicovichWilson, F. Pascale, C. Roetti, V.R. Saunders, R. Orlando, R.
Dovesi, ``Calculation of vibration frequencies of alphaquartz: the effect
of hamiltonian and basis set'',
J. Comput. Chem. 25, 18731881 (2004).

 6

Merawa M, Noel Y, Civalleri B, Brown R, Dovesi R, ``Raman and infrared
vibrational frequencies and elastic properties of solid BaFCl calculated with
various Hamiltonians: an ab initio study'',
J. PhysCondems. Mat. 17, 535548 (2005).

 7

F. Pascale, M. Catti, A. Damin, R. Orlando, V.R. Saunders, R. Dovesi,
``Vibration frequencies of Ca_{3}Fe_{2}Si_{3}O_{12}
andradite: An ab initio study with the CRYSTAL code``
J. Phys. Chem. B 109, 1852218527 (2005)

 8

A. Damin, F.X. Llabres i Xamena, C. Lamberti, B. Civalleri,
C.M. ZicovichWilson,n A. Zecchina, ``Structural, electronic and vibrational
properties of the titanosilicate ETS10: an abinitio periodic study'',
J. Phys. Chem. B 108, 13281336 (2004).

 9

P. Ugliengo, ``ANHARM. A program to solve monodimensional nuclear Schroedinger equation``,
unpublished, (1989).

 10

S. Tosoni, F. Pascale, P. Ugliengo, R. Orlando, V.R. Saunders, R. Dovesi,
``Quantum mechanical calculation of the OH vibrational frequency in
crystalline solids'',
Mol. Phys. 103, 25492558 (2005).

 11

P. Ugliengo, F. Pascale, M. Merawa, P. Labéguerie, S. Tosoni, R. Dovesi,
``Infrared spectra of Hydrogenbonded ionic crystals: Ab initio study of
Mg(OH)_{2} and betaBe(OH)_{2}. ,
J. Phys. Chem. B 108, 136213637 (2004).

 12

M. Merawa, P. Labeguerie, P. Ugliengo, K. Doll, R. Dovesi, ``The structural,
electronic and vibrational properties of LiOH and NaOH: an ab initio study'',
Chem. Phys. Lett. 387, 453459 (2004).

 13

X. SolansMonfort, V. Branchadell, M. Sodupe, C.M. ZicovichWilson, E. Gribov, G. Spoto, C. Busco, P. Ugliengo
``Can Cu+Exchanged Zeolites Store Molecular Hydrogen? An AbInitio Periodic Study
Compared with LowTemperature FTIR``
J. Phys. Chem. B 108, 82788286 (2004).

 14

P. Ugliengo, C. Busco, B. Civalleri, C.M. ZicovichWilson,
``Carbon monoxide adsorption on alkali and protonexchanged chabazite:
an abinitio periodic study using the CRYSTAL code``
Mol. Phys. 103, 25592571 (2005)

 15

F. Pascale, P. Ugliengo, B. Civalleri, R. Orlando, P. D'Arco, R. Dovesi
``The katoite hydrogarnet Sifree Ca_{3}Al_{2}([OH]_{4})_{3
}:
A periodic HartreeFock and B3LYP study``
J. Chem. Phys. 121, 10051013 (2004).

 16

R. Orlando, J. Torres, F. Pascale, P. Ugliengo, C.M. ZicovichWilson, R. Dovesi,
``Vibrational spectrum of katoite Ca_{3}Al_{2}[(OH)_{4]}]_{3}:
a periodic ab initio study``
J. Phys. Chem.,in press

 17

Y. Noel, M. Catti, Ph. D'Arco, R. Dovesi,
``The vibrational frequencies of forsterite Mg_{2}SiO_{4}:
an allelectron ab initio study with the CRYSTAL code.``
Phys. Chem. Minerals, in press