Knowledge of the Free Energy Landscape topology is the essential key to understanding many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers there are, what the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times and rate constants, or hierarchical relationships among basins, completes the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.
A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schrödinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast to other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large scale AIMD simulations.PACS numbers: 71.15.Pd, 31.15.Ew Ab initio molecular dynamics (AIMD) on the ground state Born-Oppenheimer (gsBOMD) potential energy surface for the nuclei has become a standard tool for simulating the conformational behaviour of molecules, bioand nano-structures and condensed matter systems from first principles [1]. However, gsBOMD (in the DFT [2] picture) requires that the Kohn-Sham (KS) energy functional be minimized for each value of the nuclei positions. As this minimization can be very demanding, Car and Parrinello (CP) [3] proposed an elegant and efficient "on the fly" scheme in which the KS orbitals are propagated with a fictitious dynamics that mimics gsBOMD. The CP method has had a tremendous impact in many scientific areas [4,5]. Nevertheless, the numerical cost of AIMD hinders the application of the method to large scale simulations, such as those of interest in biochemistry or material science. Recently, new methods that allow larger systems and longer simulation times to be studied have been reported [6], but the cost associated with the wave function orthogonalization is still a potential bottleneck for both gsBOMD and CP.Time-dependent density functional theory (TDDFT) [7,8] has been for a long time recognized as an orthogonalization-free alternative for both ground state [9] and excited state AIMD. In its simplest implementation, Ehrenfest TDDFT, the ions are treated classically following electronic Hellmann-Feynman forces. For systems where the gap between the ground and the first excited state is large, Ehrenfest tends to gsBOMD and can mimic adiabatic dynamics [1]. However, the rapid movement of the electrons in TDDFT requires the use of a very small time step, which, in many occasions, renders its numerical application non-practical [10].In this letter, we borrow some of the ideas of CP and introduce a new TDDFT Ehrenfest dynamics that reduces the cost of AIMD simulations while keeping the accuracy of the results in tolerable levels, similar to CP. The whole scheme can be obtained from the following Lagrangian (atomic units are used throughout this paper):whereI M IṘI ·Ṙ I is the kinetic energy of the nuclei, M I their masses and E the KS energy. Note that the major modification with respect to TDDFT is the scaling of the electronic velocities by a parameter µ (TDDFT is recovered when µ = 1). We show in what follows that, in the µ → 0 limit, the trajectories ...
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