65. Fogarasi G, Zhou X, Taylor PW, Pulay P (1992) The calculation of ab initio molecular
geometries: efficient optimization by natural internal coordinates and empirical correction by
offset forces. J Am Chem Soc 114:8191–8201
66. Borowski P (2012) An evaluation of scaling factors for multiparameter scaling procedures
based on DFT force fields. J Phys Chem A 116:3866–3880
67. Kalincsák F, Pongor G (2002) Extension of the density functional derived scaled quantum
mechanical force field procedure. Spectrochim Acta A 58:999–1011
68. Borowski P, Drzewiecka A, Fernández-Gómez M, Fernández-Liencres M-P, Peña Ruiz T
(2008) An effective scaling frequency factor method for harmonic vibrational frequencies: the
factors’ transferability problem. Chem Phys Lett 465:290–294
69. Borowski P, Drzewiecka A, Fernández-Gómez M, Fernández-Liencres M-P, Peña Ruiz T
(2010) A new, reduced set of scaling factors for both SQM and ESFF calculations. Vib Spect
52:16–21
70. Borowski P, Peña Ruiz T, Barczak M, Pilorz K, Pasieczna-Patkowska S (2012) Application of
the multi-parameter SQM harmonic force field, and ESFF harmonic frequencies scaling
procedures to the determination of the vibrational spectra of silicon- and sulfur(II)-containing
compounds. Spectrochim Acta A 86:571–585
71. Borowski P, Pilorz K, Pitucha M (2010) An effective scaling frequency factor method for
scaling of harmonic vibrational frequencies: application to 1,2,4-triazole derivatives.
Spectrochim Acta A 75:1470–1475
72. Fábri C, Szidarovszky T, Magyarfalvi G, Tarczay G (2011) Gas-phase and Ar-matrix SQM
scaling factors for various DFT functionals with basis sets including polarization and diffuse
functions. J Phys Chem A 115:4640–4649
73. Morino Y, Kuchitsu K (1952) A note on the classification of normal vibrations of molecules.
J Chem Phys 20:1809–1810
74. Borowski P, Fernández-Gómez M, Fernández-Liencres M-P, Peña Ruiz T (2007) An effective
scaling frequency factor method for scaling of harmonic vibrational frequencies: theory and
preliminary application to toluene. Chem Phys Lett 446:191–198
75. Borowski P (2010) An effective scaling frequency factor method for scaling of harmonic
vibrational frequencies: the use of redundant primitive coordinates. J Mol Spectr 264:66–74
76. Martı ́ nez-Torres E (2000) Formulation of the vibrational theory in terms of redundant internal
coordinates. J Mol Struct 520:53–61
77. Borowski P, Pasieczna-Patkowska S, Barczak M, Pilorz K (2012) Theoretical determination
of the infrared spectra of amorphous polymers. J Phys Chem A 116:7424–7435
78. Reiher M, Neugebauer J (2003) A mode-selective quantum chemical method for tracking
molecular vibrations applied to functionalized carbon nanotubes. J Chem Phys 118:1634–
1641
79. Herrmann C, Neugebauer J, Reiher M (2007) Finding a needle in a haystack: direct
determination of vibrational signatures in complex systems. New J Chem 31:818–831
80. Luber S, Neugebauer J, Reiher M (2009) Intensity tracking for theoretical infrared
spectroscopy of large molecules. J Chem Phys 130:064105
81. Kiewisch K, Luber S, Neugebauer J, Reiher M (2009) Intensity tracking for vibrational
spectra of large molecules. Chimia 63:270–274
2 Scaling Procedures in Vibrational Spectroscopy
95
geometries: efficient optimization by natural internal coordinates and empirical correction by
offset forces. J Am Chem Soc 114:8191–8201
66. Borowski P (2012) An evaluation of scaling factors for multiparameter scaling procedures
based on DFT force fields. J Phys Chem A 116:3866–3880
67. Kalincsák F, Pongor G (2002) Extension of the density functional derived scaled quantum
mechanical force field procedure. Spectrochim Acta A 58:999–1011
68. Borowski P, Drzewiecka A, Fernández-Gómez M, Fernández-Liencres M-P, Peña Ruiz T
(2008) An effective scaling frequency factor method for harmonic vibrational frequencies: the
factors’ transferability problem. Chem Phys Lett 465:290–294
69. Borowski P, Drzewiecka A, Fernández-Gómez M, Fernández-Liencres M-P, Peña Ruiz T
(2010) A new, reduced set of scaling factors for both SQM and ESFF calculations. Vib Spect
52:16–21
70. Borowski P, Peña Ruiz T, Barczak M, Pilorz K, Pasieczna-Patkowska S (2012) Application of
the multi-parameter SQM harmonic force field, and ESFF harmonic frequencies scaling
procedures to the determination of the vibrational spectra of silicon- and sulfur(II)-containing
compounds. Spectrochim Acta A 86:571–585
71. Borowski P, Pilorz K, Pitucha M (2010) An effective scaling frequency factor method for
scaling of harmonic vibrational frequencies: application to 1,2,4-triazole derivatives.
Spectrochim Acta A 75:1470–1475
72. Fábri C, Szidarovszky T, Magyarfalvi G, Tarczay G (2011) Gas-phase and Ar-matrix SQM
scaling factors for various DFT functionals with basis sets including polarization and diffuse
functions. J Phys Chem A 115:4640–4649
73. Morino Y, Kuchitsu K (1952) A note on the classification of normal vibrations of molecules.
J Chem Phys 20:1809–1810
74. Borowski P, Fernández-Gómez M, Fernández-Liencres M-P, Peña Ruiz T (2007) An effective
scaling frequency factor method for scaling of harmonic vibrational frequencies: theory and
preliminary application to toluene. Chem Phys Lett 446:191–198
75. Borowski P (2010) An effective scaling frequency factor method for scaling of harmonic
vibrational frequencies: the use of redundant primitive coordinates. J Mol Spectr 264:66–74
76. Martı ́ nez-Torres E (2000) Formulation of the vibrational theory in terms of redundant internal
coordinates. J Mol Struct 520:53–61
77. Borowski P, Pasieczna-Patkowska S, Barczak M, Pilorz K (2012) Theoretical determination
of the infrared spectra of amorphous polymers. J Phys Chem A 116:7424–7435
78. Reiher M, Neugebauer J (2003) A mode-selective quantum chemical method for tracking
molecular vibrations applied to functionalized carbon nanotubes. J Chem Phys 118:1634–
1641
79. Herrmann C, Neugebauer J, Reiher M (2007) Finding a needle in a haystack: direct
determination of vibrational signatures in complex systems. New J Chem 31:818–831
80. Luber S, Neugebauer J, Reiher M (2009) Intensity tracking for theoretical infrared
spectroscopy of large molecules. J Chem Phys 130:064105
81. Kiewisch K, Luber S, Neugebauer J, Reiher M (2009) Intensity tracking for vibrational
spectra of large molecules. Chimia 63:270–274
2 Scaling Procedures in Vibrational Spectroscopy
95