CRYSTAL - Vibrational frequencies

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 Hartree-Fock, 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, LO-TO 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 alpha-quartz 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] (Mg3 Al2Si3O12, 80 atoms in the unit cell, cubic), calcite [4] CaCO3; these tests confirm that the produced frequencies are stable to within 2-4 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 7-9 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 Ca3Al2,[(OH}4], [16], the forsterite Mg2SiO4 [17], the open shell garnet andradite [7] Ca3Fe2Si3O12 and the vibrational spectra of titanosilicalite ETS-10 [8].

Anharmonicity of the H containing bonds

Special attention has been devoted to the X-H bonds, O-H in particular. For the O-H stretching, the harmonic approximation is known to be in error by as much as 150-200 cm-1 . Luckely, due to the light H mass, the O-H stretching is fully separated from the other modes, and can be treated as a one-dimensional vibrational problem. A keyword is available (ANHARM) that permits to solve numerically the nuclear Schroedinger equation (NSE) of this one-dimensional problem [9]. Extensive investigations have been performed [10] on the numerical parameters, basis set and hamiltonian [2], showing that:

Other applications are listed concerning the O-H stretching only, namely the LiOH and NaOH crystals [12], the vibrational features of H2 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 O-H modes) permits to investigate at high level of accuracy many different and complex hydroxydes [15].

References

1
F. Pascale, C.M. Zicovich-Wilson, 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, 888-897 (2004).
 
2
Pascale F, Tosoni S, Zicovich-Wilson 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, 4-6 (2004).
 
3
F. Pascale, C.M. Zicovich-Wilson, R. Orlando, C. Roetti, P. Ugliengo, R. Dovesi, ``Vibration frequencies of Mg3 Al2Si3O12 pyrope. An ab initio study with the CRYSTAL code'',
J. Phys. Chem. B 109, 6146-6152 (2005).
 
4
M. Prencipe, F. Pascale, C.M. Zicovich-Wilson, V.R. Saunders, R. Orlando, R. Dovesi, ``The vibrational spectrum of calcite (CaCO3): an ab initio quantum-mechanical calculation'',
Phys. Chem. Minerals 31, 559-564 (2004).
 
5
C.M. Zicovich-Wilson, F. Pascale, C. Roetti, V.R. Saunders, R. Orlando, R. Dovesi, ``Calculation of vibration frequencies of alpha-quartz: the effect of hamiltonian and basis set'',
J. Comput. Chem. 25, 1873-1881 (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. Phys-Condems. Mat. 17, 535-548 (2005).
 
7
F. Pascale, M. Catti, A. Damin, R. Orlando, V.R. Saunders, R. Dovesi, ``Vibration frequencies of Ca3Fe2Si3O12 andradite: An ab initio study with the CRYSTAL code``
J. Phys. Chem. B 109, 18522-18527 (2005)
 
8
A. Damin, F.X. Llabres i Xamena, C. Lamberti, B. Civalleri, C.M. Zicovich-Wilson,n A. Zecchina, ``Structural, electronic and vibrational properties of the titanosilicate ETS-10: an ab-initio periodic study'',
J. Phys. Chem. B 108, 1328-1336 (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, 2549-2558 (2005).
 
11
P. Ugliengo, F. Pascale, M. Merawa, P. Labéguerie, S. Tosoni, R. Dovesi, ``Infrared spectra of Hydrogen-bonded ionic crystals: Ab initio study of Mg(OH)2 and beta-Be(OH)2. ,
J. Phys. Chem. B 108, 1362-13637 (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, 453-459 (2004).
 
13
X. Solans-Monfort, V. Branchadell, M. Sodupe, C.M. Zicovich-Wilson, E. Gribov, G. Spoto, C. Busco, P. Ugliengo ``Can Cu+-Exchanged Zeolites Store Molecular Hydrogen? An Ab-Initio Periodic Study Compared with Low-Temperature FTIR``
J. Phys. Chem. B 108, 8278-8286 (2004).
 
14
P. Ugliengo, C. Busco, B. Civalleri, C.M. Zicovich-Wilson, ``Carbon monoxide adsorption on alkali and proton-exchanged chabazite: an ab-initio periodic study using the CRYSTAL code``
Mol. Phys. 103, 2559-2571 (2005)
 
15
F. Pascale, P. Ugliengo, B. Civalleri, R. Orlando, P. D'Arco, R. Dovesi ``The katoite hydrogarnet Si-free Ca3Al2([OH]4)3 : A periodic Hartree-Fock and B3-LYP study``
J. Chem. Phys. 121, 1005-1013 (2004). 
 
16
R. Orlando, J. Torres, F. Pascale, P. Ugliengo, C.M. Zicovich-Wilson, R. Dovesi, ``Vibrational spectrum of katoite Ca3Al2[(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 Mg2SiO4: an all-electron ab initio study with the CRYSTAL code.``
Phys. Chem. Minerals, in press
cry98 2005-12-28