Scaled quantum mechanical force field method

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

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]. 

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. 

Quantum mechanics is essential for studying enzymatic processes [1-3]. Depending on the specific problem of interest, there are different requirements on the level of theory used and the scale of treatment involved. This ranges from the simplest cluster representation of the active site, modeled by the most accurate quantum chemical methods, to a hybrid description of the biomacromolecular catalyst by quantum mechanics and molecular mechanics (QM/MM) [1], to the full treatment of the entire enzyme-solvent system by a fully quantum-mechanical force field [4-8], In addition, the time-evolution of the macromolecular system can be modeled purely by classical mechanics in molecular dynamicssimulations, whereas the explicit incorporation... 

Therefore the scaling transformation of the quantum-mechanical force field is an empirical way to account for the electronic correlation effects. As far as the conditions listed above are not always satisfied (e.g. in the presence of delocalized 7r-electron wavefunctions) the real transformation is not exactly homogeneous but rather of Puley s type, involving n different scale constants. The need of inhomogeneous Puley s scaling also arises due to the fact that the quantum-mechanical calculations are never performed in the perfect Hartree-Fock level. The realistic calculations employ incomplete basis sets and often are based on different calculation schemes, e.g. semiempirical hamiltonians or methods which account for the electronic correlations like Cl and density-functional techniques. In this context we want to stress that the set of scale factors for the molecule under consideration is specific for a given set of internal coordinates and a given quantum-mechanical method. 

Optimized geometries, scaled quantum-mechanics (SQM) force fields, and the corresponding vibrational frequencies, IR absorption intensities, and scale factors were calculated for thiazole and the [2(2)-H], [4-H-2], and [2,5-H-2(2)] isotopomers of thiazole using the DFT and B3LYB/6-31G methods <1995JCM354, 1995JCM174>. 

Quantum mechanics is the bedrock upon which multi-scale models are built. For decades, it has been a source of parameters for force-field models, which are vastly less computationally expensive and hence able to reach much longer length and time scales. It is also being increasingly used in concert with force-field methods through mixed quantum mechanics/molecular mechanics... 

Merkle (5) conveniently divided molecular- and nano-scale simulations into two categories - those which rely on force-field based molecular-mechanics methods (no explicit electronic information) which are utilized for modeling nano-machines, and those that are quantum based, which are suitable for nano-electronic components and devices. Force field methods have been enq)loyed to simulate numerous nano-mechanical phenomena and conq)onents including Drexler-Merkle gears and neon pumps (6), carbon nanotube based gears (7), atomic-scale friction (8) and semiconductor nanostructures (9). 

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