New Born radii deriving method for Generalized Born model

Here we report a method to calculate Born radii, an important parameter used in a Generalized Born model. Traditional methods to derive Born radii are mostly based on a complicated formula, while our method is easier and more direct. Atoms are classified according to their atom type, and the Born radii of each type are obtained by fitting to experimental solvation free energy. The SMARTS language is used for the exact definition of atoms types, and Ullmann's subgraph isomorphism algorithm is used to deduce the environment. A generic algorithm is used for the parameter fitting because of its efficiency in searching a huge phase space, and its results are then optimized by using the conjugate gradient method. The final parameter set is fitting from a training set containing 357 molecules and is tested using a test set of 44 small organic molecules, and the average error is 0.58 kcal/mol for 36 neutral molecules and is 1.67 kcal/mol for 8 ions. The model is further tested under organic molecules, biopolymers, and a protein-inhibitor complex and yields reliable results in all these cases. This method can be used to accelerate molecular docking calculations.     

Effective Born radii in the generalized Born approximation: the importance of being perfect

Generalized Born (GB) models provide, for many applications, an accurate and computationally facile estimate of the electrostatic contribution to aqueous solvation. The GB models involve two main types of approximations relative to the Poisson equation (PE) theory on which they are based. First, the self-energy contributions of individual atoms are estimated and expressed as "effective Born radii." Next, the atom-pair contributions are estimated by an analytical function f(GB) that depends upon the effective Born radii and interatomic distance of the atom pairs. Here, the relative impacts of these approximations are investigated by calculating "perfect" effective Born radii from PE theory, and enquiring as to how well the atom-pairwise energy terms from a GB model using these perfect radii in the standard f(GB) function duplicate the equivalent terms from PE theory. In tests on several biological macromolecules, the use of these perfect radii greatly increases the accuracy of the atom-pair terms; that is, the standard form of f(GB) performs quite well. The remaining small error has a systematic and a random component. The latter cannot be removed without significantly increasing the complexity of the GB model, but an alternative choice of f(GB) can reduce the systematic part. A molecular dynamics simulation using a perfect-radii GB model compares favorably with simulations using conventional GB, even though the radii remain fixed in the former. These results quantify, for the GB field, the importance of getting the effective Born radii right; indeed, with perfect radii, the GB model gives a very good approximation to the underlying PE theory for a variety of biomacromolecular types and conformations.     

Comparative study of generalized born models: Born radii and peptide folding

In this study, we have implemented four analytical generalized Born (GB) models and investigated their performance in conjunction with the GROMOS96 force field. The four models include that of Still and co-workers, the HCT model of Cramer, Truhlar, and co-workers, a modified form of the AGB model of Levy and co-workers, and the GBMV2 model of Brooks and co-workers. The models were coded independently and implemented in the GROMOS software package and in TINKER. They were compared in terms of their ability to reproduce the results of Poisson-Boltzmann (PB) calculations and in their performance in the ab initio peptide folding of two peptides, one that forms a beta-hairpin in solution and one that forms an alpha-helix. In agreement with previous work, the GBMV2 model is most successful in reproducing PB results while the other models tend to underestimate the effective Born radii of buried atoms. In contrast, stochastic dynamics simulations on the folding of the two peptides, the C-terminus beta-hairpin of the B1 domain of protein G and the alanine-based alpha-helical peptide 3K(I), suggest that the simpler GB models are more effective in sampling conformational space. Indeed, the Still model used in conjunction with the GROMOS96 force field is able to fold the hairpin peptide to a native-like structure without the benefit of enhanced sampling techniques. This is due in part to the properties of the united-atom GROMOS96 force field which appears to be more flexible, and hence to sample more efficiently, than force fields such as OPLSAA. Our results suggest a general strategy which involves using different combinations of force fields and solvent models in different applications, for example, using GROMOS96 and a simple GB model in sampling and OPLSAA and a more accurate GB model in refinement. The fact that various methods have been implemented in a unified way should facilitate the testing and subsequent use of different methods to evaluate conformational free energies in different applications. Our results also bear on some general issues involved in peptide folding and structure prediction which are addressed in the Discussion.     

An electric field-based approach for quantifying effective volumes and radii of chemically affected space

Chemical shape and size play a critical role in chemistry. The van der Waals (vdW) radius, a familiar manifold used to quantify size by assuming overlapping spheres, provides rapid estimates of size in atoms, molecules, and materials. However, the vdW method may be too rigid to describe highly polarized systems and chemical species that stray from spherical atomistic environments. To deal with these exotic chemistries, numerous alternate methods based on electron density have been presented. While each boasts inherent generality, all define the size of a chemical system, in one way or another, by its electron density. Herein, we revisit the longstanding problem of assessing sizes of atoms and molecules, instead through examination of the local electric field produced by them. While conceptually different than nuclei-centered methods like that of van der Waals, the field assesses chemically affected volumes. This approach implicitly accounts for long-range fields in highly polar systems and predicts that cations should affect more space than neutral counterparts.

Computing atomic and molecular volumes from DFT and ab initio-based electric fields.     

New expressions for the overlap integral of two linear harmonic oscillator wavefunctions

Three new compact analytical expressions for the overlap integral of the wavefunctions of two distorted and displaced linear harmonic oscillators have been otained: unlike Ansbacher's formula, the do not lead to divergence when there is no distortion.     

A new method of determination of radii of ions with arbitrary effective charges

An equation for calculation of the radii of ions with an arbitrary effective charge has been derived. The ionic radii of halogens, chalcogens, and other atoms with different charges have been calculated. Under the assumption of pure ionic bond character, these values have been used for calculating the R ₁₂ distances for a large group of different molecules—halogens, interhalides, oxygen, chalcogens, and nitrogen and their compounds—by the previously derived equation for the a priori determination of internuclear distances. The error of calculation of the internuclear distance for halogens and interhalides is no more than 0.07 Å (3–4%). The internuclear distance in dihalogen cations Hal ₂ ⁺ and binary ionic molecules of p elements and their oxides and sulfides have been calculated. It has been demonstrated that the coordination (environment) of atoms should be taken into account and that there is a possibility of estimating the bond multiplicity and the character of bonding electron pairs in a molecule.     

正离子的边界半径

本文建议和讨论了离子的边界半径, 给出了一价正离子的边界半径的周期表以及某些常见正离子的边界半径。正离子的边界半径与SP半径、Pauling离子半径、晶体离子半径等有一定的关联, 显示了其合理性和可应用性。由这些关联性质, 还可以预言某些元素的难以测定的电离能。     

Metallic radii of nonmetals

Experimental data are used to determine the atomic volumes and radii of the elements of subgroups IV–VIIA in the structures of metallic phases at high pressures. Metallic radii of nonmetals are compared with values based on Pauling and Goldschmidt calculations.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 220–222, February, 1994.     

Comparative study on solvation free energy expressions in reference interaction site model integral equation theory

The performance of the recently proposed partial wave (PW) free energy functional is compared with those of two previous expressions, Gaussian fluctuation (GF) and hypernetted chain (HNC), within the reference interaction site model framework. The applications to the calculations of ambient and supercritical water, solvation free energies of organic molecules, and partition coefficients clearly show that the PW and GF free energy expressions provide more reliable results than the HNC functional, indicating rather associative situations of geometry in ordinary liquids of medium-sized molecules.     

The radii of spherical ions

A set of most probable ionic radii have been formulated using a combination of deduction from r ₀ values and experimental electron density maps. The relationship of the new radii to the free energies of hydration of gaseous ions is discussed.     

The quantitative relationship between metal radii, cationic radii and electronic configurations of elements

A close relationship has been found between the metal radii, cationic radii and electronic configurations of elements. A unified formula for calculating metal radii is presented, whose paramatem are only related to the electronic configuration. Meanwhile theoretical relation between cationic radii and electronic configuration can be revealed by combining quantitative analysis with qualitative analysis. The calculated results and the charts of standard deviations are coincident with those given by reference books. Our work indicates that the metal radius and cationic radius of an element reflect in essence the element's configuration.     

Ionic radii for Group 1 halide crystals and ion-pairs

Internuclear separations calculated from empirical soft-sphere radii for seventeen crystalline Group 1 halides with rock-salt structures and from empirical hovering-sphere radii for fourteen gaseous Group 1 halide ion-pairs agree well with experimental measurements. Two lithium and four fluoride ion-pairs appear to be anomalous. Soft-sphere ionic radii are compared with atomic radii of noble gases.