Frequency normalized

D. Perahia and L. Mouawad. Computation of low-frequency normal modes in macromolecules Improvements to the method of diagonalization in a mixed basis and application to hemoglobin. Comput. Chem., 19 241-246, 1995. 

Nonnal mode analysis was first applied to proteins in the early 1980s [1-3]. Much of the literature on normal mode analysis of biological molecules concerns the prediction of functionally relevant motions. In these studies it is always assumed that the soft normal modes, i.e., those with the lowest frequencies and largest fluctuations, are the ones that are functionally relevant. The ultimate justification for this assumption must come from comparisons to experimental data. Several studies have been made in which the predictions of a normal mode analysis have been compared to functional transitions derived from two X-ray conformers [4-7]. These smdies do indeed suggest that the low frequency normal modes are functionally relevant, but in no case has it been found that the lowest frequency normal mode corresponds exactly to a functional mode. Indeed, one would not expect this to be the case. 

Combining all these techniques suggests that, provided minimization has been achieved, a number of the lowest frequency normal modes of any protein can be accurately determined. 

A block Lanczos algorithm (where one starts with more than one vector) has been used to calculate the first 120 normal modes of citrate synthase [4]. In this calculation no apparent use was made of symmetry, but it appears that to save memory a short cutoff of 7.5 A was used to create a sparse matrix. The results suggested some overlap between the low frequency normal modes and functional modes detennined from the two X-ray conformers. 

The normal mode refinement method is based on the idea of the normal mode important subspace. That is, there exists a subspace of considerably lower dimension than 3N, within which most of the fluctuation of the molecule undergoing the experiment occurs, and a number of the low frequency normal mode eigenvectors span this same subspace. In its application to X-ray diffraction data, it was developed by Kidera et al. [33] and Kidera and Go [47,48] and independently by Diamond [49]. Brueschweiler and Case [50] applied it to NMR data. 

Slip frequency is the difference between synchronous speed and actual running speed of the motor. A narrowband filter should be established to monitor electrical line frequency. The window should have enough resolution to clearly identify the frequency and the modulations, or sidebands, that represent slip frequency. Normally, these modulations are spaced at the difference between synchronous and actual speed, and the number of sidebands is equal to the number of poles in the motor. 

Fig. 39. Crossover from 0- to good solvent conditions in dilute solutions. Calculated characteristic frequencies, normalized to 0-conditions, as dependent on reduced temperature for two different chain lengths N at various values of (QS). To the right of each curve the increase in Qred (q,x) between t = 0 and t = 0.9 is given...

Schuyler, A. D., Chirikjian, G. S., Efficient determination of low-frequency normal modes of large protein structures by cluster-NMA, J. Mol. Graph. Model. 2005, 24, 46-58... 

As 7u(x t) are relative frequencies normalized to unity, we can define the statistical averages ... 

One is intended to produce structural diversity in the model by grid-sampling the amphtudes of (at most) two of the lo west-frequency normal modes ... 

Delarue, M. and Dumas, P. (2004) On the use of low-frequency normal modes to enforce collective movements in refining macromolecular structural models. Proc. Natl. Acad. Sci. USA 101, 6957-6962. 

Figure 6 The calculation of the effectiveforce in the Dimer method. A pair of images, spaced apart by a small distance, on the order q/ 0.1A is rotated to minimize the energy. This gives the direction of the lowest frequency normal mode. The component of the force in the direction of the dimer is then inverted and the minimization of this effectiveforce leads to convergence to a saddle point. No reference is made to the final state.

The Rearrangement of 1,2,6-Heptatriene. The experimental facts and basic mechanistic idea behind this reaction were outlined in section 1.2. The molecular dynamics study began with a single CASSCF(8,8)/6-31G(d) trajectory started from TSl (see Fig. 21.2) with no kinetic energy (not even ZPE) in any of the real-frequency normal modes. The purpose of such an unphysical trajectory calculation is to see what is the steepest descent path down from the transition state... 

Fig. 2. Time evolution of the average OH frequency (normalized to its initial value) of the molecules remaining in the ground state as a result of laser excitation.

To scale frequency to a more convenient range, IR spectroscopists have defined a frequency unit called wave number v given by v = 1 /X, where X is the wavelength in centimeters. The units of v are reciprocal centimeters (cm-1). The wave number is the number of vibrations which occur over a 1-cm distance. Thus the higher the wave number, the more vibrations occur in a 1-cm distance and thus the higher the frequency. Normally IR spectra are recorded between 4000 and 650 cm 1 (2.5 and 15 p,m). 

Dimensionless collision frequency (for electrolyte solutions Normalized collision frequency Normalized complex frequency (for electrolyte solutions)... 

For cases in which the spectra do not share a common band, it might be better to normalize the spectra so that the total area under the spectrum is 1.0. Prior to normalizing by any method, it is important to zero the baseline of the spectra by subtracting the minimum intensity from the intensities at every frequency. Normalizing the total area under the spectral curve is most useful for searching libraries and for putting the unknown and library spectra on the same scale. In this method, the intensity at each frequency in the spectrum is divided by the square root of the sum of the squares of all the intensities, i.e.,... 

The F2 frequency normally corresponds to a chemical shift axis, for example, H or l3C. When the Fx axis also corresponds to a chemical shift scale, we describe the result as a... 

In general, the accuracy of a simulated spectrum depends on the quality of the description of both the initial and the final electronic states of the transition. This is obviously related to the proper choice of a well-suited computational model a reliable description of equilibrium structures, harmonic frequencies, normal modes, and electronic transition energy is necessary. In the study of the A Bj Aj electronic transition of phenyl radical the structural and vibrational properties have been obtained with the B3LYP/TDB3LYP//N07D model, designed for computational studies of free radicals. Unconstrained geometry optimizations lead to planar... 

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