The Linear Interaction Energy LIE Method

The first version of the LIE method employed the linear response approximation to estimate the electrostatic part of the solvation/binding free energies. The linear response result for this component of the solvation 

The electrostatic interactions within the ligand V t could, in principle, also 

Our initial parametrization of the LIE equation was subsequently used for HIV protease and trypsin inhibitors as well as in a study of sugar binding to a bacterial receptor protein. While it was at first suspected that a 

and perhaps the most important result, is that the binding free 

3 with p=Vi yields a binding free energy of about -2 kcal/mol for the K -18-crown-6 complex in agreement with experiment21 and the relationship 

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Stjernschantz E, Marelius J, Medina C, Jacobsson M, Vermeulen NP, Oosten-brink C. Are automated molecular dynamics simulations and binding free energy calculations realistic tools in lead optimization An evaluation of the linear interaction energy (LIE) method. J Chem Inf Model 2006 46 1972-83. 

Bortolato, A. and Moro, S. (2007) In silico binding free energy predictability by using the linear interaction energy (LIE) method bromobenzrmidazole CK2 inhibitors as a case study. Journal of Chemical Information and Modeling, 47, 572-582. 

To rectify this problem, efforts are underway to develop methods that predict binding free energies, at least qualitatively, for a medium-sized compound library (100-200 compounds) over a relatively short time period. The most promising methods to date include Linear Interaction Energy (LIE) analysis. Molecular Mechanics Poisson Boltzmann Surface Area (MM-... 

In addition to these SBD methods the ERa crystal structure has recently been used in evaluating linear interaction energy (LIE) methodology for lead optimization [125], and in calculating ab initio molecular interactions between ERa and 17p-estradiol [126],... 

Wang W, Wang J, Kollman PA (1999) What determines the van der Waals coefficient 3 in die LIE (linear interaction energy) method to estimate binding free energies using molecular dynamic simulation, Proteins, 34 395 102... 

Wang W, J Wang and P A Kollman 1999. What Determmes the van der Waals Coefficient f m the LIE (Linear Interaction Energy) Method to Estimate Bindmg Free Energies Using Molecular Dymamics Simulations Proteins- Structure, Function and Genetics 34 395-402. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

The K-matrix method is essentially a configuration interaction (Cl) performed at a fixed energy lying in the continuum upon a basis of "unperturbed funetions that (at the formal level) includes both diserete and eontinuous subsets. It turns the Schrodinger equation into a system of integral equations for the K-matrix elements, which is then transformed into a linear system by a quadrature upon afinite L basis set. 

The few attempts at describing excited states in transition metal complexes within the Restricted Hartree Fock (RHF) formalism were rapidly abandoned due to the computational difficulties (convergence of the low-lying states in the open-shell formalism) and theoretical deficiencies (inherent lack of electronic correlation, inconsistent treatment of states of different multiplicities and d shell occupations). The simplest and most straightforward method to deal with correlation energy errors is the Configuration Interaction (Cl) approach where the single determinant HF wave function is extended to a wave function composed of a linear combination of many de-... 

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