Heats of adsorption of methane, ethane, and propane in H-chabazite (Si/Al = 14.4) have been measured and entropies have been derived from adsorption isotherms. For these systems quantum chemical ab initio calculations of Gibbs free energies have been performed. The deviations from the experimental values for methane, ethane, and propane are below 3 kJ/mol for the enthalpy, and the Gibbs free energy. A hybrid high-level (MP2/CBS): low-level (DFT+dispersion) method is used to determine adsorption structures and energies. Vibrational entropies and thermal enthalpy contributions are obtained from vibrational partition functions for the DFT+dispersion potential energy surface. Anharmonic corrections have been evaluated for each normal mode separately. One-dimensional Schrodinger equations are solved for potentials obtained by (curvilinear) distortions of the normal modes using a representation in internal coordinates.

We introduce a method to obtain one-dimensional collective variables for studying rarely occurring transitions between two metastable states separated by a high free energy barrier. No previous information, not even approximated, on the path followed during the transition is needed. The only requirement is to know the fluctuations of the system while in the two metastable states. With this information in hand, we build the collective variable using a modified version of Fisher's linear discriminant analysis. The usefulness of this approach is tested on the metadynamics simulation of two representative systems. The first is the freezing of silver iodide into the superionic α-phase, and the second is the study of a classical Diels-Alder reaction. The collective variable works very well in these two diverse cases.

The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an appropriate set of collective variables. These are meant to describe the system’s modes that most slowly approach equilibrium under the action of the sampling algorithm. Once identified, the equilibration of these modes is accelerated by the enhanced sampling method of choice. An attractive way of determining the collective variables is to relate them to the eigenfunctions and eigenvalues of the transfer operator. Unfortunately, this requires knowing the long-term dynamics of the system beforehand, which is generally not available. However, we have recently shown that it is indeed possible to determine efficient collective variables starting from biased simulations. In this paper, we bring the power of machine learning and the efficiency of the recently developed on the fly probability-enhanced sampling method to bear on this approach. The result is a powerful and robust algorithm that, given an initial enhanced sampling simulation performed with trial collective variables or generalized ensembles, extracts transfer operator eigenfunctions using a neural network ansatz and then accelerates them to promote sampling of rare events. To illustrate the generality of this approach, we apply it to several systems, ranging from the conformational transition of a small molecule to the folding of a miniprotein and the study of materials crystallization.

The effect of anharmonic corrections to the vibrational energies of extended systems is explored. Particular attention is paid to the thermodynamics of adsorption of small molecules on catalytically relevant systems typically affected by anharmonicity. The implemented scheme obtains one-dimensional anharmonic model potentials by distorting the equilibrium structure along the normal modes using both rectilinear (Cartesian) or curvilinear (internal) representations. Only in the latter case, the modes are decoupled also at higher order of the potential and the thermodynamic functions change in the expected directions. The method is applied to calculate ab initio enthalpies, entropies, and Gibbs free energies for the adsorption of methane in acidic chabazite (H-CHA) and on MgO(001) surface. The values obtained for the adsorption of methane in H-CHA (273.15 K, 0.1 MPa, θ = 0.5) are ΔH = -19.3, -TΔS = 11.9, and ΔG = -7.5 kJ/mol. For methane on the MgO(001) (47 K, 1.3 × 10(-14) MPa, θ = 1) ΔH = -14.4, -TΔS = 16.6, and ΔG = 2.1 kJ/mol are obtained. The calculated desorption temperature is 44 K, and the desorption prefactor is 4.26 × 10(12) s(-1). All calculated results agree within chemical accuracy limits with experimental data.

The surface plasmon resonance has been theoretically investigated in gold nanowires by means of time-dependent density functional theory. Linear chains of Au atoms and nanowires with the structure of the fcc bulk gold grown along the ⟨110⟩ and ⟨111⟩ directions have been considered. The effects of changing the length and the section on the plasmon have been studied. Strong photoabsorption is found when the length is above 2 nm: in that case the absorption profile is characterized by a sharp peak, and its analysis reveals that many configurations contribute to the transition, confirming its collective nature as an s ← s intraband transition. As expected, the effect of increasing the length is reflected in a red shift of the plasmon

The ab initio prediction of reaction rate constants for systems with hundreds of atoms with an accuracy that is comparable to experiment is a challenge for computational quantum chemistry. We present a divide‐and‐conquer strategy that departs from the potential energy surfaces obtained by standard density functional theory with inclusion of dispersion. The energies of the reactant and transition structures are refined by wavefunction‐type calculations for the reaction site. Thermal effects and entropies are calculated from vibrational partition functions, and the anharmonic frequencies are calculated separately for each vibrational mode. This method is applied to a key reaction of an industrially relevant catalytic process, the methylation of small alkenes over zeolites. The calculated reaction rate constants (free energies), pre‐exponential factors (entropies), and enthalpy barriers show that our computational strategy yields results that agree with experiment within chemical accuracy limits (less than one order of magnitude).

For CO and N on Mg sites of the metal-organic framework CPO-27-Mg (Mg-MOF-74), ab initio calculations of Gibbs free energies of adsorption have been performed. Combined with the Bragg-Williams/Langmuir model and taking into account the experimental site availability (76.5%), we obtained adsorption isotherms in close agreement with those in experiment. The remaining deviations in the Gibbs free energy (about 1 kJ/mol) are significantly smaller than the "chemical accuracy" limit of about 4 kJ/mol. The presented approach uses (i) a DFT dispersion method (PBE+D2) to optimize the structure and to calculate anharmonic frequencies for vibrational partition functions and (ii) a "hybrid MP2:(PBE+D2)+ΔCCSD(T)" method to determine electronic energies. With the achieved accuracy (estimated uncertainty ±1.4 kJ/mol), the ab initio energies become useful benchmarks for assessing different DFT + dispersion methods (PBE+D2, B3LYP+D*, and vdW-D2), whereas the ab initio heats, entropies, and Gibbs free energies of adsorption are used to assess the reliability of experimental values derived from fitting isotherms or from variable-temperature IR studies.

A computational protocol is presented that uses normal mode coordinates for structure optimization and for obtaining harmonic frequencies by numerical differentiation. It reduces numerical accuracy problems encountered when density functional theory with plane wave basis sets is applied to systems with flat potential energy surfaces. The approach is applied to calculate Gibbs free energies for adsorption of methane, ethane, and propane on the Brønsted acidic sites of zeolite H-CHA. The values obtained (273.15 K, 0.1 MPa,), -0.25, -5.95, and -16.76 kJ/mol, respectively, follow the trend of the experimental values, which is not the case for results obtained with the standard approach (Cartesian optimization, frequencies from Cartesian distortions). Anharmonicity effects have been approximately taken into account by solving one-dimensional Schrödinger equations along each normal mode. This leads to a systematic increase of the Gibbs free energy of adsorption of 4.5, 5.0, and 3.1 kJ/mol for methane, ethane, and propane, respectively, making adsorption at a given pressure and temperature less likely. This is due to an increase of low vibrational frequencies associated with hindered translations and rotations of the adsorbed molecules and the floppy modes of the zeolite framework.