Scaling factor optimization method

The resonant -trajectories from different decouplings are displayed in figs. 8a and 8b where it is seen that optimal value of the radial scale factor a is different for the methods with (E2 and E2ph TDA) and without (E°, E2, E2ph TDA) orbital relaxation. 

Other optimization paths are possible. One can think that a covering of the exponential product e b niay be better achieved by a simultaneous n-dimensional optimization process like Newton-Raphson procedure [58]. In fact, however, the overlap as described in equation (4.19) is an irregular function of the p,e parameter pairs, and possesses multiple maxima and minima with respect to the scale factors variation. A method with a scanning or sweep feature among a given parameter range will be perhaps superior in this case than a global search procedure, and so was adopted. 

Geometry level al which the structure is optimized higher-order correlation method(s) for estimating higher-order correlation effects thermo level at which the thermodynamical corrections are calculated [vibrational scale factor] MAD Mean Absolute Deviation for reference data set in kcal/mol. 

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>. 

The ease of applicability and effectiveness of the proposed optimization method for determining the scale factor oc in the case where an exponential type of mapping transformation was utilized. 

Gl, G2, G2(MP2), and G3 are composite computations using the 6-311G basis set and MP2/6-31G geometry optimization. The protocols are designed for efficient calculation of energies and electronic properties. The G2 method calculates electron correlation at the MP4 level, while G2(MP2) correlation calculations are at the MP2 level. A scaling factor derived from a series of calibration molecules is applied to energies. 

The MAS technique is effective because of the fact that the interaction Hamiltonian includes a static term proportional to the scale factor P2(cos0). Consequently, the anisotropy can be partly restored when the samples rotate at an angle other than the magic angle. This method can be implemented in one-dimensional experiments, for example, in the measurement of chemical shift anisotrojw, 323,468-473 optimally when the fast spinning condition... 

The DFT method at B3LYP/6-311G(d,p), is used to determine the optimized geometries [211, 212, 213] of the species. Zero-point vibrational energies (ZPVE), vibrational frequencies and thermal correction contributions to enthalpy from harmonic frequencies are scaled in accordance to the scaling factors recommended by Scott and Radom [120], These geometries, frequencies and moment of inertia are reported in appendix B. 

---