Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the “free-energy” analog of the minimum potential energy path and to take the activation free energy, [Formula: see text], as the difference between the maximum at the transition state and the minimum at R. We show that this approximation can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different [Formula: see text]. We derive an exact expression for the activation free energy that avoids this ambiguity. We find [Formula: see text] to be a combination of the probability of the system being in the reactant state, the probability density on the dividing surface, and the thermal de Broglie wavelength associated with the transition. We apply our formalism to simple analytic models and realistic chemical systems and show that the FEP-based approximation applies only at low temperatures for CVs with a small effective mass. Most chemical reactions occur on complex, high-dimensional PES that cannot be treated analytically and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, [Formula: see text] is quite sensitive.

We explore and show the usefulness of the density of states function for computing vibrational free energies and free energy differences between small systems. Therefore, we compare this density of states integration method (DSI) to more established schemes such as Bennett’s Acceptance Ratio method (BAR), the Normal Mode Analysis (NMA), and the Quasiharmonic Analysis (QHA). The strengths and shortcomings of all methods are highlighted with three numerical examples. Furthermore, the free energy of the ionization of ammonia and the mutation from serine to cysteine are computed using extensive ab initio molecular dynamics simulations. We conclude that DSI improves upon the other frequency-based methods (NMA and QHA) regarding the treatment of anharmonicity and yielding results comparable to BAR in all cases without the need for alchemical transformations. Low-frequency modes lead to larger errors indicating that long simulation times might be required for larger systems. In addition, we introduce the use of DSI for the localization of the vibrational free energy to specific atoms or residues, leading to insights into the underlying process, a unique feature that is only offered by this method.

Thymine DNA glycosylase (TDG) initiates the base excision repair mechanism for the deamination and oxidation products of cytosine and 5-methylcytosine. This enzyme has a key role in epigenetic regulation, and its catalytic inactivation results in, e.g., mice embryo lethality. Here, we employ molecular dynamics simulations and quantum mechanics/molecular mechanics calculations to investigate the reaction mechanism of the TDG-catalyzed N-glycosidic bond hydrolysis of the modified base 5-formylcytosine. Our results reveal a reaction pathway, which in its first step features a reorganization of the substrate that lowers the barrier height for the subsequent C1′−N1 bond dissociation. The suggested mechanism is consistent with the experimental data, as it is not acidcatalyzed and proceeds through an oxocarbenium-like transition state. It also provides insights into the catalytic roles of the Thr197 and Asn140 residues.