Molecular model autocorrelation

The shape of the vibration-rotation bands in infrared absorption and Raman scattering experiments on diatomic molecules dissolved in a host fluid have been used to determine2,15 the autocorrelation functions unit vector pointing along the molecular axis and P2(x) is the Legendre polynomial of index 2. These correlation functions measure the rate of rotational reorientation of the molecule in the host fluid. The observed temperature- and density-dependence of these functions yields a great deal of information about reorientation in solids, liquids, and gases. These correlation functions have been successfully evaluated on the basis of molecular models.15... 

Molecular modeling has been used to calculate viscosity using a variety of different well-developed approaches, including velocity autocorrelation [26], kinetic energy exchange [27], and simulating Poiseuille or Couette flow (also called the confined shear method) [28-34],... 

Let us start with a classic example. We had a dataset of 31 steroids. The spatial autocorrelation vector (more about autocorrelation vectors can be found in Chapter 8) stood as the set of molecular descriptors. The task was to model the Corticosteroid Ringing Globulin (CBG) affinity of the steroids. A feed-forward multilayer neural network trained with the back-propagation learning rule was employed as the learning method. The dataset itself was available in electronic form. More details can be found in Ref. [2]. 

Raman intensities of the molecular vibrations as well as of their crystal components have been calculated by means of a bond polarizibility model based on two different intramolecular force fields ([87], the UBFF after Scott et al. [78] and the GVFF after Eysel [83]). Vibrational spectra have also been calculated using velocity autocorrelation functions in MD simulations with respect to the symmetry of intramolecular vibrations [82]. 

Wagener, M., Sadowski, J., and Gasteiger, J. (1995) Autocorrelation of molecular surface properties for modeling corticosteriod binding globulin and cytosolic Ah receptor activity by neural networks. J. Am. Chem. Soc. 117, 7769-7775. 

No single model can exactly describe molecular reorientation in plastic crystals. Models which include features of the different models described above have been considered. For example, diffusion motion interrupted by orientation jumps has been considered to be responsible for molecular reorientation. This model has been somewhat successful in the case of cyclohexane and neopentane (Lechner, 1972 De Graaf Sciesinski, 1970). What is not completely clear is whether the reorientational motion is cooperative. There appears to be some evidence for coupling between the reorientational motion and the motions of neighbouring molecules. Comparative experimental studies employing complementary techniques which are sensitive to autocorrelation and monomolecular correlation would be of interest. 

The dipole autocorrelation function, , defined previously. The full-time dependence of this function for liquid carbon monoxide has been successfully determined experimentally from Fourier inversion of infrared band shapes.2,15 In fact, this was one of the reasons this system was studied. This function has also been successfully evaluated in terms of models of the molecular reorientation process.58 s memory function, KD(t), is defined by... 

K. Singer, J. V. L. Singer, and A. J, Taylor. Molecular dynamics of liquids modelled by 2-Lennard-Jones centres pair potentials II. Translational and rotational autocorrelation functions. Molec. Phys., 57 1239-1262 (1979). 

The properties p of the atoms i and j are considered for a particular topological distance d. Sjj is a Kronecker delta that represents additional constraints or conditions. The topological distance may also be replaced by the Euclidean distance, thus accounting for two- or three-dimensional arrangement of atoms. Three-dimensional spatial autocorrelation of physicochemical properties has been used to model the biological activity of compound classes [24]. In this case, a set of randomly distributed points is selected on the molecular surface, and all distances between the surface points are calculated and sorted into preset intervals. These points are used to calculate the spatial autocorrelation coefficient for particular molecular properties, such as the molecular electrostatic potential (MEP). The resulting descriptor is a condensed representation of the distribution of the property on the molecular surface. 

It was demonstrated that to obtain the best surface autocorrelation vectors for QSAR modeling, the van der Waals surface is better than other molecular surfaces. Then, surface should have no fewer than five grid points per A, and a distance interval not more than 1A should be used in the distance binning scheme (Figure Al). 

---