Evaluation of the Molecular Configuration Integral in All Degrees of Freedom for the Direct Calculation of Conformational Free Energies:  Prediction of the Anomeric Free Energy of Monosaccharides

1997 ◽  
Vol 101 (51) ◽  
pp. 9900-9905 ◽  
Author(s):  
István Kolossváry
Keyword(s):  
Free Energy ◽  
Degrees Of Freedom ◽  
Direct Calculation ◽  
Free Energies ◽  
Molecular Configuration ◽  
Configuration Integral

QUANTUM FIELDS VERSUS STRINGS AT FINITE TEMPERATURE

1992 ◽  
Vol 07 (18) ◽  
pp. 4275-4292 ◽  
Author(s):  
M.A.R. OSORIO
Keyword(s):  
Free Energy ◽  
Degrees Of Freedom ◽  
Quantum Fields ◽  
Free Energies ◽  
Analog Model ◽  
Modular Invariant ◽  
Light Cone Gauge ◽  
Physical Fields ◽  
The One ◽  
The Relationship

We study some aspects of the relationship between the one-loop free energy of closed superstrings computed as a sum over the free energies of the quantum fields present in the string (the analog model) and the modular invariant expression of the same quantity. In particular, by getting a generalized duality relation for the integrand of the modular invariant expression for the free energy of closed superstrings and using a regularization procedure, we connect the contribution to the vacuum energy from the bosonic degrees of freedom in the analog model (one half of the total number) with the coefficient governing the high temperature behavior of the free energy. We also study the physical meaning of this regularization and the role played by the left-right constraint defining the physical fields in the light-cone gauge.

scholarly journals The Automated Optimisation of a Coarse-Grained Force Field Using Free Energy Data

2020 ◽  
Author(s):  
Javier Caceres-Delpiano ◽  
Lee-Ping Wang ◽  
Jonathan W. Essex
Keyword(s):  
Free Energy ◽  
Force Field ◽  
Degrees Of Freedom ◽  
Coarse Grained ◽  
Free Energies ◽  
Energy Data ◽  
Molecular Systems ◽  
Atomistic Models ◽  
The Cost ◽  
Long Timescales

AbstractAtomistic models provide a detailed representation of molecular systems, but are sometimes inadequate for simulations of large systems over long timescales. Coarse-grained models enable accelerated simulations by reducing the number of degrees of freedom, at the cost of reduced accuracy. New optimisation processes to parameterise these models could improve their quality and range of applicability. We present an automated approach for the optimisation of coarse-grained force fields, by reproducing free energy data derived from atomistic molecular simulations. To illustrate the approach, we implemented hydration free energy gradients as a new target for force field optimisation in ForceBalance and applied it successfully to optimise the un-charged side-chains and the protein backbone in the SIRAH protein coarse-grain force field. The optimised parameters closely reproduced hydration free energies of atomistic models and gave improved agreement with experiment.

Understanding Conformational Entropy in Small Molecules

2020 ◽  
Author(s):  
Lucian Chan ◽  
Garrett Morris ◽  
Geoffrey Hutchison
Keyword(s):  
Small Molecules ◽  
Degrees Of Freedom ◽  
Absolute Error ◽  
Low Energy ◽  
Standard Entropy ◽  
Free Energies ◽  
Conformational Entropy ◽  
Wide Range ◽  
High Degree ◽  
Empirical Corrections

The calculation of the entropy of flexible molecules can be challenging, since the number of possible conformers grows exponentially with molecule size and many low-energy conformers may be thermally accessible. Different methods have been proposed to approximate the contribution of conformational entropy to the molecular standard entropy, including performing thermochemistry calculations with all possible stable conformations, and developing empirical corrections from experimental data. We have performed conformer sampling on over 120,000 small molecules generating some 12 million conformers, to develop models to predict conformational entropy across a wide range of molecules. Using insight into the nature of conformational disorder, our cross-validated physically-motivated statistical model can outperform common machine learning and deep learning methods, with a mean absolute error ≈4.8 J/mol•K, or under 0.4 kcal/mol at 300 K. Beyond predicting molecular entropies and free energies, the model implies a high degree of correlation between torsions in most molecules, often as- sumed to be independent. While individual dihedral rotations may have low energetic barriers, the shape and chemical functionality of most molecules necessarily correlate their torsional degrees of freedom, and hence restrict the number of low-energy conformations immensely. Our simple models capture these correlations, and advance our understanding of small molecule conformational entropy.

SAMPL6 Octanol-Water Partition Coefficients from Alchemical Free Energy Calculations with MBIS Atomic Charges

2019 ◽  
Author(s):  
Maximiliano Riquelme ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Free Energy ◽  
Electron Density ◽  
Free Energy Calculations ◽  
Basis Set ◽  
Energetic Cost ◽  
Atomic Charges ◽  
Free Energies ◽  
Energy Calculations ◽  
Alchemical Free Energy ◽  
Alchemical Free Energy Calculations

In molecular modeling the description of the interactions between molecules forms the basis for a correct prediction of macroscopic observables. Here, we derive atomic charges from the implicitly polarized electron density of eleven molecules in the SAMPL6 challenge using the Hirshfeld-I and Minimal Basis Set Iterative Stockholder(MBIS) partitioning method. These atomic charges combined with other parameters in the GAFF force field and different water/octanol models were then used in alchemical free energy calculations to obtain hydration and solvation free energies, which after correction for the polarization cost, result in the blind prediction of the partition coefficient. From the tested partitioning methods and water models the S-MBIS atomic charges with the TIP3P water model presented the smallest deviation from the experiment. Conformational dependence of the free energies and the energetic cost associated with the polarization of the electron density are discussed.

Molecular orientation of liquid aliphatic hydrocarbons on the surface and at the interface with water

1989 ◽  
Vol 54 (12) ◽  
pp. 3171-3186 ◽  
Author(s):  
Jan Kloubek
Keyword(s):  
Free Energy ◽  
Surface Free Energy ◽  
Molecular Orientation ◽  
Phase Changes ◽  
Aliphatic Hydrocarbons ◽  
Water Molecules ◽  
Free Energies ◽  
Dispersion Component ◽  
System Water ◽  
Orientation Of Molecules

The validity of the Fowkes theory for the interaction of dispersion forces at interfaces was inspected for the system water-aliphatic hydrocarbons with 5 to 16 C atoms. The obtained results lead to the conclusion that the hydrocarbon molecules cannot lie in a parallel position or be randomly arranged on the surface but that orientation of molecules increases there the ration of CH3 to CH2 groups with respect to that in the bulk. This ratio is changed at the interface with water so that the surface free energy of the hydrocarbon, γH, rises to a higher value, γ’H, which is effective in the interaction with water molecules. Not only the orientation of molecules depends on the adjoining phase and on the temperature but also the density of hydrocarbons on the surface of the liquid phase changes. It is lower than in the bulk and at the interface with water. Moreover, the volume occupied by the CH3 group increases on the surface more than that of the CH2 group. The dispersion component of the surface free energy of water, γdW = 19.09 mJ/m2, the non-dispersion component, γnW = 53.66 mJ/m2, and the surface free energies of the CH2 and CH3 groups, γ(CH2) = 32.94 mJ/m2 and γ(CH3) = 15.87 mJ/m2, were determined at 20 °C. The dependence of these values on the temperature in the range 15-40 °C was also evaluated.

Chemical equilibrium and chemical kinetics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Free Energy ◽  
Equilibrium Constant ◽  
Gibbs Free Energy ◽  
Chemical Kinetics ◽  
Chemical Equilibrium ◽  
First Principles ◽  
Effect Of Temperature ◽  
Total System ◽  
Free Energies

Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, expressing the total Gibbs free energy of a reaction mixture at any time as the sum of the instantaneous Gibbs free energies of each component, as expressed in terms of the extent-of-reaction. The equilibrium reaction mixture is then defined as the point at which the total system Gibbs free energy is a minimum, from which concepts such as the equilibrium constant emerge. The chapter also explores the temperature dependence of equilibrium, this being one example of Le Chatelier’s principle. Finally, the chapter links thermodynamics to chemical kinetics by showing how the equilibrium constant is the ratio of the forward and backward rate constants. We also introduce the Arrhenius equation, closing with a discussion of the overall effect of temperature on chemical equilibrium.

scholarly journals Automation of absolute protein-ligand binding free energy calculations for docking refinement and compound evaluation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Germano Heinzelmann ◽  
Michael K. Gilson
Keyword(s):  
Free Energy ◽  
Early Stage ◽  
Binding Free Energy ◽  
Low Cost ◽  
Free Energy Calculations ◽  
Free Energies ◽  
Energy Calculations ◽  
Drug Candidates ◽  
Binding Free Energy Calculations ◽  
Binding Free Energies

AbstractAbsolute binding free energy calculations with explicit solvent molecular simulations can provide estimates of protein-ligand affinities, and thus reduce the time and costs needed to find new drug candidates. However, these calculations can be complex to implement and perform. Here, we introduce the software BAT.py, a Python tool that invokes the AMBER simulation package to automate the calculation of binding free energies for a protein with a series of ligands. The software supports the attach-pull-release (APR) and double decoupling (DD) binding free energy methods, as well as the simultaneous decoupling-recoupling (SDR) method, a variant of double decoupling that avoids numerical artifacts associated with charged ligands. We report encouraging initial test applications of this software both to re-rank docked poses and to estimate overall binding free energies. We also show that it is practical to carry out these calculations cheaply by using graphical processing units in common machines that can be built for this purpose. The combination of automation and low cost positions this procedure to be applied in a relatively high-throughput mode and thus stands to enable new applications in early-stage drug discovery.

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

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