Scaled quantum mechanical force

Williams, R. W., V. F. Kalasinsky, and A. H. Lowrey. 1993. Scaled Quantum Mechanical Force Field for Cis- and Trans-glycine in Acidic Solution. J. Mol. Struct. (Theochem) 281, 157-171. 

However, the most reliable and widely used is the method developed by Puley [16], which is now referred to as Scaled Quantum Mechanical Force Field (SQMF). In SQMF a scale constant Xs is ascribed to each internal coordinate qH such that the corrected (scaled) force-constants are calculated according to the equation ... 

Normally the scaling factors are extracted by minimizing the squared deviation (4) considered as a functional R A) of the variable set A, - The frequency parameters z alc now correspond to the harmonic normal frequencies calculated with the scaled quantum-mechanical force-field (6). The first and second derivatives of R( A) with respect to the scaling factors can be calculated analytically [17,18], which permits to implement rapidly converging minimization procedures of the Newton-Gauss type. Alternative iterative minimization methods were also proposed [19]. 

A. Aamouche et al., Neutron inelastic scattering, optical spectroscopies and scaled quantum mechanical force fields for analyzing the vibrational dynamics of pyrimidine nucleic acid bases. 1. Uracil. J. Phys. Chem. 100, 5224-5234 (1996)... 

V. Scaled Quantum Mechanical Force-Field Method.240... 

Scaled quantum-mechanical force fields for furan (and thiophene) and its isotopomers have been calculated with the B3LYP/6-31G method. Corresponding MP2 and FIE calculations gave less satisfactory results. Excellent agreement... 

The application of ab initio methods in the calculation of harmonic force fields of transition metal complexes has been hampered by the size of these systems and the need to employ costly post-Hartree-Fock methods, in which electron correlation is taken into account. Thus, the fruitful symbiosis between ab initio theory and experiment, to determine empirically scaled quantum mechanical force fields, has been virtually absent in studies of transition metal complexes. 

Baker, Jarzecki, A. A., 8c Pulay, P. (1998). Direct scaling of primitive valence force constants An alternative approach to scaled quantum mechanical force fields. Journal of Physical Chemistry A,... 

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