6. Pulay P (1969) Ab initio calculation of force constants and equilibrium geometries in
polyatomic molecules. I Theory Mol Phys 17:197–204
7. Pulay P, Meyer W (1974) Comparison of ab initio force constants of ethane, ethylene and
acetylene. Mol Phys 27:473–490
8. Pople JA, Krishnan R, Schlegel HB, Binkley JS (1979) Derivative studies in Hartree-Fock
and Moller-Plesset theories. Int J Quantum Chem 16:225–241
9. Willetts A, Handy NC, Green WH, Jayatilaka D (1990) Anharmonic corrections to vibrational
transition intensities. J Phys Chem 94:5608–5616
10. Barone V, Bloino J, Guido CA, Lipparini F (2010) A fully automated implementation of
VPT2 Infrared intensities. Chem Phys Lett 496:157–161
11. Pulay P, Fogarasi G, Boggs JE (1981) Force field, dipole moment derivatives, and vibronic
constants of benzene from a combination of experimental and ab initio quantum chemical
information. J Chem Phys 74:3999–4014
12. Pulay P, Fogarasi G, Pongor G, Boggs JE, Vargha A (1983) Combination of theoretical
ab initio and experimental information to obtain reliable harmonic force-constants—scaled
quantum-mechanical (SQM) force-fields for glyoxal, acrolein, butadiene, formaldehyde, and
ethylene. J Am Chem Soc 105:7037–7047
13. Borowski P, Fernández-Gómez M, Fernández-Liencres M-P, Peña Ruiz T, Quesada Rincón
M (2009) An effective scaling frequency factor method for scaling of harmonic vibrational
frequencies: application to toluene, styrene and its 4-methyl derivative. J Mol Struct 924:493–
503
14. McQuarrie DA (1976) Statistical mechanics. HarperCollinsPublishers, New York
15. Merrick JP, Moran D, Radom L (2007) An evaluation of harmonic vibrational frequency scale
factors. J Phys Chem A 111:11683–11700
16. Pople JA, Schlegel HB, Krishnan R, Defrees DJ, Binkley JS, Frisch MJ, Whiteside RA,
Hout RF, Hehre WJ (1981) Molecular-orbital studies of vibrational frequencies. Int J
Quantum Chem 15:269–278
17. Hout RF, Levi BA, Hehre WJ (1982) Effect of electron correlation on theoretical vibrational
frequencies. J Comput Chem 3:234–250
18. Pople JA, Scott AP, Wong MW, Radom L (1993) Scaling factors for obtaining fundamental
vibrational frequencies and zero-point energies from HF/6-31 g-asterisk and MP2/
6-31 g-asterisk harmonic frequencies. Isr J Chem 33:345–350
19. Scott AP, Radom L (1996) Harmonic vibrational frequencies: an evaluation of Hartree-Fock,
Moller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J Phys Chem 100:16502–16513
20. Wong MW (1996) Vibrational frequency prediction using density functional theory. Chem
Phys Lett 256:391–399
21. Patton LF, Corchado J, Sanchez ML, Truhlar DG (1999) Optimized parameters for scaling
correlation energy. J Phys Chem A 103:3139–3143
22. Lynch BJ, Truhlar DG (2001) How well can hybrid density functional methods predict
transition state geometries and barrier heights? J Phys Chem A 105:2936–2941
23. Zhao Y, Lynch BJ, Truhlar DG (2004) Doubly hybrid meta DFT: new multi-coefficient
correlation and density functional methods for thermochemistry and thermochemical kinetics.
J Phys Chem A 108:4786–4791
24. Zhao Y, Lynch BJ, Truhlar DG (2004) Development and assessment of a new hybrid density
functional model for thermochemical kinetics. J Phys Chem A 108:2715–2719
25. Zhao Y, Truhlar DG (2004) Hybrid meta density functional theory methods for
thermochemistry, thermochemical kinetics, and noncovalent interactions: the MPW1B95
and MPWB1K models and comparative assessments for hydrogen bonding and van der Waals
interactions. J Phys Chem A 108:6908–6918
26. Schultz NE, Zhao Y, Truhlar DG (2005) Databases for transition element bonding: metal–
metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta
density functionals and generalized gradient approximations. J Phys Chem A 109:4388–4403
92
O. Bąk and P. Borowski
polyatomic molecules. I Theory Mol Phys 17:197–204
7. Pulay P, Meyer W (1974) Comparison of ab initio force constants of ethane, ethylene and
acetylene. Mol Phys 27:473–490
8. Pople JA, Krishnan R, Schlegel HB, Binkley JS (1979) Derivative studies in Hartree-Fock
and Moller-Plesset theories. Int J Quantum Chem 16:225–241
9. Willetts A, Handy NC, Green WH, Jayatilaka D (1990) Anharmonic corrections to vibrational
transition intensities. J Phys Chem 94:5608–5616
10. Barone V, Bloino J, Guido CA, Lipparini F (2010) A fully automated implementation of
VPT2 Infrared intensities. Chem Phys Lett 496:157–161
11. Pulay P, Fogarasi G, Boggs JE (1981) Force field, dipole moment derivatives, and vibronic
constants of benzene from a combination of experimental and ab initio quantum chemical
information. J Chem Phys 74:3999–4014
12. Pulay P, Fogarasi G, Pongor G, Boggs JE, Vargha A (1983) Combination of theoretical
ab initio and experimental information to obtain reliable harmonic force-constants—scaled
quantum-mechanical (SQM) force-fields for glyoxal, acrolein, butadiene, formaldehyde, and
ethylene. J Am Chem Soc 105:7037–7047
13. Borowski P, Fernández-Gómez M, Fernández-Liencres M-P, Peña Ruiz T, Quesada Rincón
M (2009) An effective scaling frequency factor method for scaling of harmonic vibrational
frequencies: application to toluene, styrene and its 4-methyl derivative. J Mol Struct 924:493–
503
14. McQuarrie DA (1976) Statistical mechanics. HarperCollinsPublishers, New York
15. Merrick JP, Moran D, Radom L (2007) An evaluation of harmonic vibrational frequency scale
factors. J Phys Chem A 111:11683–11700
16. Pople JA, Schlegel HB, Krishnan R, Defrees DJ, Binkley JS, Frisch MJ, Whiteside RA,
Hout RF, Hehre WJ (1981) Molecular-orbital studies of vibrational frequencies. Int J
Quantum Chem 15:269–278
17. Hout RF, Levi BA, Hehre WJ (1982) Effect of electron correlation on theoretical vibrational
frequencies. J Comput Chem 3:234–250
18. Pople JA, Scott AP, Wong MW, Radom L (1993) Scaling factors for obtaining fundamental
vibrational frequencies and zero-point energies from HF/6-31 g-asterisk and MP2/
6-31 g-asterisk harmonic frequencies. Isr J Chem 33:345–350
19. Scott AP, Radom L (1996) Harmonic vibrational frequencies: an evaluation of Hartree-Fock,
Moller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J Phys Chem 100:16502–16513
20. Wong MW (1996) Vibrational frequency prediction using density functional theory. Chem
Phys Lett 256:391–399
21. Patton LF, Corchado J, Sanchez ML, Truhlar DG (1999) Optimized parameters for scaling
correlation energy. J Phys Chem A 103:3139–3143
22. Lynch BJ, Truhlar DG (2001) How well can hybrid density functional methods predict
transition state geometries and barrier heights? J Phys Chem A 105:2936–2941
23. Zhao Y, Lynch BJ, Truhlar DG (2004) Doubly hybrid meta DFT: new multi-coefficient
correlation and density functional methods for thermochemistry and thermochemical kinetics.
J Phys Chem A 108:4786–4791
24. Zhao Y, Lynch BJ, Truhlar DG (2004) Development and assessment of a new hybrid density
functional model for thermochemical kinetics. J Phys Chem A 108:2715–2719
25. Zhao Y, Truhlar DG (2004) Hybrid meta density functional theory methods for
thermochemistry, thermochemical kinetics, and noncovalent interactions: the MPW1B95
and MPWB1K models and comparative assessments for hydrogen bonding and van der Waals
interactions. J Phys Chem A 108:6908–6918
26. Schultz NE, Zhao Y, Truhlar DG (2005) Databases for transition element bonding: metal–
metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta
density functionals and generalized gradient approximations. J Phys Chem A 109:4388–4403
92
O. Bąk and P. Borowski