Efficient and precise solvation free energies via alchemical adiabatic molecular dynamics

Abstract

A new molecular dynamics method for calculating free energies associated with transformations of the thermodynamic state or chemical composition of a system (also known as alchemical transformations) is presented. The new method extends the adiabatic dynamics approach recently introduced by Rosso et al. [J. Chem. Phys. 116, 4389 (2002)] and is based on the use of an additional degree of freedom, lambda, that is used as a switching parameter between the potential energy functions that characterize the two states. In the new method, the coupling parameter lambda is introduced as a fictitious dynamical variable in the Hamiltonian, and a system of switching functions is employed that leads to a barrier in the lambda free energy profile between the relevant thermodynamic end points. The presence of such a barrier, therefore, enhances sampling in the end point (lambda = 0 and lambda = 1) regions which are most important for computing relevant free energy differences. In order to ensure efficient barrier crossing, a high temperature T(lambda) is assigned to lambda and a fictitious mass m(lambda) is introduced as a means of creating an adiabatic separation between lambda and the rest of the system. Under these conditions, it is shown that the lambda free energy profile can be directly computed from the adiabatic probability distribution function of lambda without any postprocessing or unbiasing of the output data. The new method is illustrated on two model problems and in the calculation of the solvation free energy of amino acid side-chain analogs in TIP3P water. Comparisons to previous work using thermodynamic integration and free energy perturbation show that the new lambda adiabatic free energy dynamics method results in very precise free energy calculations using significantly shorter trajectories.

Accelerating equilibrium isotope effect calculations. I. Stochastic thermodynamic integration with respect to mass

“…As a result, several variants of λ-dynamics bias the sampling of λ towards the endpoints and then calculate the free energy difference from the ratio of probability densities at λ = 0 and λ = 1. 49,50 Indeed, our STI approach would also allow obtaining a well converged result by sampling mainly in the regions of λ close to the endpoints λ = 0 and λ = 1 if one used a modified partition functioñ…”

Molecular grand-canonical ensemble density functional theory and exploration of chemical space

“…In addition, arbitrary paths connecting different molecules or functional groups via chemical or "alchemical" transformations can be used for the purpose of computing relative free energies within classical Monte Carlo or molecular dynamics ͑MD͒ calculations via thermodynamic integration or other -sampling techniques. [9][10][11][12][13][14][15][16] As noted above, a general description of chemical space involving the breaking and forming of chemical bonds is possible within a first-principles or ab initio theory. An electronic GCE theory was established decades ago within the development of Kohn-Sham ͑KS͒ density functional theory ͑DFT͒.…”

Improving replica exchange using driven scaling

“…In addition, rather than enforcing the condition that stays in the interval from 0 to 1 by changing variables as done previously, 22 we placed elastic hard walls at −⑀ and 1 + ⑀, with ⑀ = 0.005 Å. 31 The scaled replicas have T A and T B values equal to the temperatures of the adjacent replicas; for the scaled replica with the lowest temperature, T A equals 250 K. All replicas for both methods started from an unfolded state, which was generated by starting with the folded structure of trpzip2, 36 running at 640 K for 1.2 ns, and then equilibrating this unfolded structure at lower temperatures. The REDS results represent 10 ns per replica and the REDS2 results represent 14 ns per replica.…”

“…The variable is made to vary by treating it as a dynamical variable, with a mass and equations of motion, as is done in other -dynamics applications. [23][24][25][26][27][28][29][30][31] In the first application of this method to the alanine dipeptide with 512 water molecules, the scaled replica was shown to replace about ten conventional replicas, reducing the number of replicas from 22 to 5. The method has some other advantages.…”