Linear-response free energy

Carlson, H. A., Jorgensen, W. L. An extended linear response method for determining free energies of hydration. J. Phys. Chem. 99 (1995) 10667-10673... 

Appendix 11.3 Expansion of Zwanzig Expression for the Free Energy Difference for the Linear Response Method... 

Carlson H A and W L Jorgensen 1995. An Extended Linear Response Method for Determining Free Energies of Hydration. Journal of Physical Chemistry 99 10667-10673. 

X Chen, A Tropsha. A generalized linear response method Application to the hydration free energy calculations. J Comput Chem 20 749-759, 1999. 

LD model, see Langevin dipoles model (LD) Linear free-energy relationships, see Free energy relationships, linear Linear response approximation, 92,215 London, see Heitler-London model Lysine, structure of, 110 Lysozyme, (hen egg white), 153-169,154. See also Oligosaccharide hydrolysis active site of, 157-159, 167-169, 181 calibration of EVB surfaces, 162,162-166, 166... 

CPU time. In response to these slow and rigorous calculations, many fast heuristic approaches have been developed that are based on intuitive concepts such as docking [10], matching pharmacophores [19], or linear free energy relationships [20], A disadvantage of many simple heuristic approaches is their susceptibility to generalization error [17], where accuracy of the predictions is limited to the training data. 

In order to find the relation between Eq. (122) and the Marcus theory, we employ the linear response approximation. In this case, the free energies Fj )(i =1)2) for the donor and acceptor become a parabolic function of as... 

Henchman, R.H., Essex, J.W., Free energies of hydration using restrained electrostatic potential derived charges via free energy perturbations and linear response, J. Comput. Chem. 1999, 20, 499-510... 

We present and analyze the most important simplified free energy methods, emphasizing their connection to more-rigorous methods and the underlying theoretical framework. The simplified methods can all be superficially defined by their use of just one or two simulations to compare two systems, as opposed to many simulations along a complete connecting pathway. More importantly, the use of just one or two simulations implies a common approximation of a near-linear response of the system to a perturbation. Another important theme for simplified methods is the use, in many cases, of an implicit description of solvent usually a continuum dielectric model, often supplemented by a simple description of hydrophobic effects [11]. 

The cumulants [26] are simple functions of the moments of the probability distribution of 5V-.C2 = (V- V))2),C3 = (V- V)f),C4 = ((]/-(]/))4) 3C22,etc. Truncation of the expansion at order two corresponds to a linear-response approximation (see later), and is equivalent to assuming V is Gaussian (with zero moments and cumulants beyond order two). To this order, the mean and width of the distribution determine the free energy to higher orders, the detailed shape of the distribution contributes. 

Linear Response Theory and Free Energy Calculations... 

The dielectric response of a solvated protein to a perturbing charge, such as a redox electron or a titrating proton, is related to the equilibrium fluctuations of the unperturbed system through linear response theory [49, 50]. In the spirit of free energy... 

We now turn to the problem of proton binding to proteins, an important area for simplified free energy methods. The linear response formalism earlier underlies most of the methods used today. It leads directly to one of the more useful practical methods, the so-called LRA, or linear response approximation method [59], presented here. 

The idea is to do simulations of the system before and after the proton binding i.e., to simulate the reactant and product states. With the assumption of linear response, these provide all the information needed to compute AA. Indeed, the free energy to introduce a fractional charge Aq into the reactant state (0 < A < 1) is a parabolic function of Aq, which can be written ... 

McDonald, N.A. Carlson, H.A. Jorgensen, W.L., Free energies of solvation in chloroform and water from a linear response approach, J. Phys. Org. Chem. 1997,10, 563-576... 

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