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This work follows a companion article, which will be referred to as Paper I [Campeggio et al., J. Chem. Phys. 158, 244104 (2023)] in which a quantum-stochastic Liouville equation for the description of the quantum–classical dynamics of a molecule in a dissipative bath has been formulated in curvilinear internal coordinates. In such an approach, the coordinates of the system are separated into three subsets: the quantum coordinates, the classical relevant nuclear degrees of freedom, and the classical irrelevant (bath) coordinates. The equation has been derived in natural internal coordinates, which are bond lengths, bond angles, and dihedral angles. The resulting equation needs to be parameterized. In particular, one needs to compute the potential energy surfaces, the friction tensor, and the rate constants for the nonradiative jumps among the quantum states. While standard methods exist for the calculation of energy and dissipative properties, an efficient evaluation of the transition rates needs to be developed. In this paper, an approximated treatment is introduced, which leads to a simple explicit formula with a single adjustable parameter. Such an approximated expression is compared with the exact calculation of transition rates obtained via molecular dynamics simulations. To make such a comparison possible, a simple sandbox system has been used, with two quantum states and a single internal coordinate (together with its conjugate momentum). Results show that the adjustable parameter, which is an effective decoherence time, can be parameterized from the effective relaxation times of the autocorrelation functions of the conjugated momenta of the relevant nuclear coordinates. [ABSTRACT FROM AUTHOR]

Multiscale methods are powerful tools to describe large and complex systems. They are based on a hierarchical partitioning of the degrees of freedom (d.o.f.) of the system, allowing one to treat each set of d.o.f. in the most computationally efficient way. In the context of coupled nuclear and electronic dynamics, a multiscale approach would offer the opportunity to overcome the computational limits that, at present, do not allow one to treat a complex system (such as a biological macromolecule in explicit solvent) fully at the quantum mechanical level. Based on the pioneering work of Kapral and Ciccotti [R. Kapral and G. Ciccotti, J. Chem. Phys.110, 8919 (1999)], this work is intended to present a nonadiabatic theory that describes the evolution of electronic populations coupled with the dynamics of the nuclei of a molecule in a dissipative environment (condensed phases). The two elements of novelty that are here introduced are (i) the casting of the theory in the natural, internal coordinates, that are bond lengths, bond angles, and dihedral angles; (ii) the projection of those nuclear d.o.f. that can be considered at the level of a thermal bath, therefore leading to a quantum-stochastic Liouville equation. Using natural coordinates allows the description of structure and dynamics in the way chemists are used to describe molecular geometry and its changes. The projection of bath coordinates provides an important reduction of complexity and allows us to formulate the approach that can be used directly in the statistical thermodynamics description of chemical systems., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

The ethanol electro-oxidation catalyzed by Pd in an alkaline environment involves several intermediate reaction steps promoted by the hydroxyl radical, OH. In this work, we report on the dynamical paths of the first step of this oxidation reaction, namely the hydrogen atom abstraction CH 3 CH 2 OH + OH → CH 3 CHOH + H 2 O, occurring at the Pd(111) surface and address the thermodynamic stability of the adsorbed reactants by means of quantum and molecular mechanics calculations, with special focus on the effect of the solvent. We have found that the impact of the solvent is significant for both ethanol and OH, contributing to a decrease in their adsorption free energies by a few dozen kcal mol -1 with respect to the adsorption energy under vacuum. Furthermore, we observe that hydrogen atom abstraction is enhanced for those simulation paths featuring large surface-reactant distances, namely, when the reactants weakly interact with the catalyst. The picture emerging from our study is therefore that of a catalyst whose coverage in an aqueous environment is largely dominated by OH with respect to ethanol. Nevertheless, only a small amount of them, specifically those weakly bound to the catalyst, is really active in the ethanol electro-oxidation reaction. These results open the idea of a rational design of co-catalysts based on the tuning of surface chemical properties to eventually enhance exchange current density.

We estimate the kinetic constants of a series of archetypal S N 2 reactions, i.e. , the nucleophilic substitutions of halides in halomethane. A parameter free, multiscale approach recently developed [Campeggio et al. , Phys. Chem. Chem. Phys. , 2020, 22 , 3455] is employed. The protocol relies on quantum mechanical calculations for the description of the energy profile along the intrinsic reaction coordinate, which is then mapped onto a reaction coordinate conveniently built for the reactive process. A Kramers-Klein equation is used to describe the stochastic time evolution of the reaction coordinate and its velocity; friction is parameterized using a hydrodynamic model and Kramers theory is used to derive the rate constant of the reaction. The method is here applied to six S N 2 reactions in water at 295.15 K, which differ in the nucleophile and the leaving group. The computed reaction rates are in good agreement with the experimental data and correlate well with the trends observed for the activation energies.

We propose an approach to the evaluation of kinetic rates of elementary chemical reactions within Kramers' theory based on the definition of the reaction coordinate as a linear combination of natural, pseudo Z-matrix, internal coordinates of the system. The element of novelty is the possibility to evaluate the friction along the reaction coordinate, within a hydrodynamic framework developed recently [J. Campeggio et al., J. Comput. Chem. 2019, 40, 679-705]. This, in turn, allows to keep into account barrier recrossing, i.e. the transmission coefficient that is employed in correcting transition state theory evaluations. To test the capabilities and the flaws of the approach we use as case studies two archetypal SN2 reactions. First, we consider to the standard substitution of chloride ion to bromomethane. The rate constant at 295.15 K is evaluated to k/c⊖ = 2.7 × 10-6 s-1 (with c⊖ = 1 M), which compares well to the experimental value of 3.3 × 10-6 s-1 [R. H. Bathgate and E. A. Melwyn-Hughes, J. Chem. Soc 1959, 2642-2648]. Then, the method is applied to the SN2 reaction of methylthiolate to dimethyl disulfide in water. In biology, such an interconversion of thiols and disulfides is an important metabolic topic still not entirely rationalized. The predicted rate constant is k/c⊖ = 7.7 × 103 s-1. No experimental data is available for such a reaction, but it is in accord with the fact that the alkyl thiolates to dialkyl disulfides substitutions in water have been found to be fast reactions [S. M. Bachrach, J. M. Hayes, T. Dao and J. L. Mynar, Theor. Chem. Acc. 2002, 107, 266-271].

We report on an extended hydrodynamic modeling of the friction tensorial properties of flexible molecules including all types of natural, Z-Matrix like, internal coordinates. We implement the new methodology by extending and updating the software DiTe [Barone et al. J. Comput. Chem. 30, 2 (2009)]. DiTe (DIffusion TEnsor) implements a hydrodynamic modeling of the generalized translational, rotational, and configurational friction and diffusion tensors of flexible molecules in which flexibility is described in terms of dihedral angles. The new tool, DiTe2, has been renewed to include also stretching and bending types of internal mobility. Furthermore, DiTe2 is able to calculate the friction and diffusion tensors along collective (or reaction) coordinates defined as linear combinations of the internal natural ones. A number of tests are reported to show the new features of DiTe2. As leitmotiv for the tests, the calmodulin protein is taken into consideration, described both at all-atom and coarse-grained levels. © 2018 Wiley Periodicals, Inc., (© 2018 Wiley Periodicals, Inc.)