Molecular surface, calculating

Connolly, M. L. Analytical molecular surface calculation. J. Appl. Crystallogr. 16 (1983) 548-558... 

C/jnnolly M L 1983b. Analytical Molecular Surface Calculation. Journal of Applied Crystallography 16 548-558. 

F. M. Richards, Areas, volumes, packing and protein structure, Annu. Rev. Biophys. Bioeng., 6 (1997) 151-176 M. L. Connolly, Analytical molecular surface calculation, J. Appl. Crys-tallogr., 16 (1983) 548-558. 

The area of the solvent-accessible surface is called the Solvent-Accessible Surface Area SASA (or Total Solvent-Accessible Surface Area, TSASA). Several algorithms were proposed that implement both the first original definition of SASA and that of Richards. One of the most popular algorithms that implements Richards solvent-accessible surface was proposed by Connolly [Connolly, 1983a]. It is an analytical method for computing molecular surface, and is based on surface decomposition into a set of curved regions of spheres and tori that join at circular arcs spheres, tori and arcs are defined by analytical expressions in terms of atomic coordinates, van der Waals radii and the probe radius. Ihe molecular surface calculated in such a way is sometimes referred to as Connolly surface area. This algorithm also allows the calculation of solvent-accessible atomic areas. 

Connolly, M.L. (1983a). Analytical Molecular Surface Calculation. J.Appl.Cryst, 16, 548-558. 

Gogonea V, Motsenigos A, Ciubotariu D, Deretey E, Chtriac A, Simon Z (1981) Molecular mechanics and molecular shape descriptors. 2. Comparative treatment of four methods for molecular surface calculation. Preprint, University of Timisoara, Ser. Chimie. 1-12 Gogonea V, Ciubotariu D, Deretey E, Popescu M, lorga I, Medeleanu M (1991) Rev Roum Chim 36 465-471... 

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

The theoretical treatments of Section III-2B have been used to calculate interfacial tensions of solutions using suitable interaction potential functions. Thus Gubbins and co-workers [88] report a molecular dynamics calculation of the surface tension of a solution of A and B molecules obeying Eq. III-46 with o,bb/ o,aa = 0.4 and... 

It was noted in connection with Eq. III-56 that molecular dynamics calculations can be made for a liquid mixture of rare gas-like atoms to obtain surface tension versus composition. The same calculation also gives the variation of density for each species across the interface [88], as illustrated in Fig. Ill-13b. The density profiles allow a calculation, of course, of the surface excess quantities. 

Molecular dynamics calculations have been made on atomic crystals using a Lennard-Jones potential. These have to be done near the melting point in order for the iterations not to be too lengthy and have yielded density functioi). as one passes through the solid-vapor interface (see Ref. 45). The calculations showed considerable mobility in the surface region, amounting to the presence of a... 

The summation of pair-wise potentials is a good approximation for molecular dynamics calculations for simple classical many-body problems [27], It has been widely used to simulate hyperthennal energy (>1 eV) atom-surface scattering ... 

A completely new method of determining siufaces arises from the enormous developments in electron microscopy. In contrast to the above-mentioned methods where the surfaces were calculated, molecular surfaces can be determined experimentally through new technologies such as electron cryomicroscopy [188]. Here, the molecular surface is limited by the resolution of the experimental instruments. Current methods can reach resolutions down to about 10 A, which allows the visualization of protein structures and secondary structure elements [189]. The advantage of this method is that it can be apphed to derive molecular structures of maaomolecules in the native state. 

The MEP at the molecular surface has been used for many QSAR and QSPR applications. Quantum mechanically calculated MEPs are more detailed and accurate at the important areas of the surface than those derived from net atomic charges and are therefore usually preferable [Ij. However, any of the techniques based on MEPs calculated from net atomic charges can be used for full quantum mechanical calculations, and vice versa. The best-known descriptors based on the statistics of the MEP at the molecular surface are those introduced by Murray and Politzer [44]. These were originally formulated for DFT calculations using an isodensity surface. They have also been used very extensively with semi-empirical MO techniques and solvent-accessible surfaces [1, 2]. The charged polar surface area (CPSA) descriptors proposed by Stanton and Jurs [45] are also based on charges derived from semi-empirical MO calculations. 

The calculation of autocorrelation vectors of surface properties [25] is similar (Eq. (21), with the distance d XiXj) between two points and Xj on the molecular surface within the interval between d[ and d a certain property p, e.g., the electrostatic potential (ESP) at a point on the molecular surface and the number of distance intervals 1). 

The representation of molecules by molecular surface properties was introduced in Section 2.10. Different properties such as the electrostatic potential, hydrogen bonding potential, or hydrophobicity potential can be mapped to this surface and seiwe for shape analysis [44] or the calculation of surface autocorrelation vectors (refer to Section 8.4.2). 

D descriptors), the 3D structure, or the molecular surface (3D descriptors) of a structure. Which kind of descriptors should or can be used is primarily dependent on the si2e of the data set to be studied and the required accuracy for example, if a QSPR model is intended to be used for hundreds of thousands of compounds, a somehow reduced accuracy will probably be acceptable for the benefit of short processing times. Chapter 8 gives a detailed introduction to the calculation methods for molecular descriptors. 

Non-covalent interactions between molecules often occur at separations where the van der Waals radii of the atoms are just touching and so it is often most useful to examine the electrostatic potential in this region. For this reason, the electrostatic potential is often calculated at the molecular surface (defined in Section 1.5) or the equivalent isodensity surface as shown in Figure 2.18 (colour plate section). Such pictorial representations... 

The solvent-excluded volume is a molecular volume calculation that finds the volume of space which a given solvent cannot reach. This is done by determining the surface created by running a spherical probe over a hard sphere model of molecule. The size of the probe sphere is based on the size of the solvent molecule. 

The level of theory necessary for computing PES s depends on how those results are to be used. Molecular mechanics calculations are often used for examining possible conformers of a molecule. Semiempiricial calculations can give a qualitative picture of a reaction surface. Ah initio methods must often be used for quantitatively correct reaction surfaces. Note that size consistent methods must be used for the most accurate results. The specific recommendations given in Chapter 18 are equally applicable to PES calculations. 

Molecular mechanics methods have been used particularly for simulating surface-liquid interactions. Molecular mechanics calculations are called effective potential function calculations in the solid-state literature. Monte Carlo methods are useful for determining what orientation the solvent will take near a surface. Molecular dynamics can be used to model surface reactions and adsorption if the force held is parameterized correctly. 

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