Adiabatic free energy dynamics (AFED) was introduced by Rosso et al. [J. Chem. Phys. 2002, 116, 4389] for computing free energy profiles quickly and accurately using a dynamical adiabatic separation between a set of collective variables or reaction coordinates and the remaining degrees of freedom of a system. This approach has been shown to lead to a significant gain in efficiency versus traditional methods such as umbrella sampling, thermodynamic integration, and free energy perturbation for generating one-dimensional free energy profiles. More importantly, AFED is able to generate multidimensional free energy surfaces efficiently via full sweeps of the surface that rapidly map out the locations of the free energy minima. The most significant drawback to the AFED approach is the need to transform the coordinates into a generalized coordinate system that explicitly contains the collective variables of interest. Recently, Maragliano and Vanden-Eijnden built upon the AFED approach by introducing a set of extended phase-space variables, to which the adiabatic decoupling and high temperature are applied [Chem. Phys. Lett. 2006, 426, 168]. In this scheme, which the authors termed "temperature accelerated molecular dynamics" or TAMD, the need for explicit coordinate transformations is circumvented. The ability of AFED and TAMD to generate free energy surfaces efficiently depends on the thermostatting mechanism employed, since both approaches are inherently nonequilibrium due to the adiabatic decoupling. Indeed, Maragliano and Vanden-Eijnden did not report any direct generation of free energy surfaces within the overdamped Langevin dynamics employed by these authors. Here, we show that by formulating TAMD in a manner that is closer to the original AFED approach, including the generalized Gaussian moment thermostat (GGMT) and multiple time-scale integration, multidimensional free energy surfaces for complex systems can be generated directly from the probability distribution function of the extended phase-space variables. The new TAMD formulation, which we term driven AFED or d-AFED, is applied to compare the conformational preferences of small peptides both in gas phase and in solution for three force fields. The results show that d-AFED/TAMD accurately and efficiently generates free energy surfaces in two collective variables useful for characterizing the conformations, namely, the radius of gyration, R(G), and number of hydrogen bonds, N(H).

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.

Ramachandran surfaces for the alanine di- and tripeptides in gas phase and solution are mapped out using the recently introduced adiabatic free-energy dynamics (AFED) approach introduced by Rosso et al. (J. Chem. Phys. 2002, 116, 4389) as applied to the CHARMM22 force field. It is shown that complete surfaces can be mapped out with an order of magnitude of greater efficiency with the AFED approach than they can using the popular umbrella sampling method. In the alanine dipeptide, it is found, in agreement with numerous other studies using the CHARMM22 force field, that the lowest free-energy structure is the extended beta conformation, (phi, psi) = (-81, 81), while in solution, the extended beta, (phi, psi) = (-81, 153) and right-handed alpha-helical, (phi, psi) = (-81, 63) conformations are nearly isoenergetic. In solution, a secondary minimum at (phi, psi) = (63, -81), corresponding to a C(7)ax conformation, occurs approximately 2.3 kcal/mol above the global free-energy minimum. The alanine tripeptide, a system that has received considerably less attention in the literature, is found to exhibit a similar structure to the alanine dipeptide with the extended beta conformation being the free-energy minimum in the gas phase and the beta and right-handed alpha-helical conformations being isoenergetic in solution. These studies indicate that the AFED method can be a powerful tool for studying multidimensional free-energy surfaces in complex systems.

When students effectively engage with textbooks or videos prior to class, more active and collaborative learning activities can be incorporated into subsequent face-to-face learning. Such pre-lecture assignments are particularly important in flipped classrooms, where a portion of the content is delivered primarily before face-to-face instruction. While a large amount of research has addressed the need to improve active learning during lectures, little work has examined the need to improve out-of-class preparation. Most often, out-of-class preparation consists of videos or assigned textbook readings, but question-embedded videos have also been shown to be effective. When using question-embedded videos, students must pause the video and solve problems as they watch the video, transforming their passive video watching into an active learning experience. Here, we present the results of a randomized control trial study that compares learning behaviors and outcomes between students using content-equivalent resources: organic chemistry textbook readings or question-embedded videos. We found that students who used question-embedded videos for their preparation had significantly higher learning gains and metacognitive monitoring proficiencies than students who used textbook readings. These results indicate that question-embedded videos enforce more productive feedback-driven problem-solving behaviors than textbook readings, which leads to substantial gains in performance and metacognitive monitoring, better preparing students for in-class instruction.