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The effect of solvation on the free energy of reaction intermediates adsorbed on electrocatalyst surfaces can significantly change the thermochemical overpotential, but accurate calculations of this are challenging. Here, we present computational estimates of the solvation energy for reaction intermediates in oxygen reduction reaction (ORR) on a B-doped graphene (BG) model system where the overpotential is found to reduce by up to 0.6 V due to solvation. BG is experimentally reported to be an active ORR catalyst but recent computational estimates using state-of-the-art hybrid density functionals in the absence of solvation effects have indicated low activity. To test whether the inclusion of explicit solvation can bring the calculated activity estimates closer to the experimental reports, up to 4 layers of water molecules are included in the simulations reported here. The calculations are based on classical molecular dynamics and local minimization of energy using atomic forces evaluated from electron density functional theory. Data sets are obtained from regular and coarse-grained dynamics, as well as local minimization of structures resampled from dynamics simulations. The results differ greatly depending on the method used and the solvation energy estimates are deemed untrustworthy. It is concluded that a significantly larger number of water molecules is required to obtain converged results for the solvation energy. As the present system includes up to 139 atoms, it already strains the limits of computational feasibility, so this points to the need for a hybrid simulation approach where efficient simulations of much larger number of solvent molecules is carried out using a lower level of theory while retaining the higher level of theory for the reacting molecules as well as their near neighbors and the catalyst. The results reported here provide a word of caution to the computational catalysis community: activity predictions can be inaccurate if too few solvent molecules are included in the calculations.

The energetics and atomic structure associated with the localized hole formed near an Al-atom dopant in α-quartz are calculated using a variational, self-consistent implementation of the Perdew–Zunger self-interaction correction with complex optimal orbitals. This system has become an important test problem for theoretical methodology since generalized gradient approximation energy functionals, as well as commonly used hybrid functionals, fail to produce a sufficiently localized hole due to the self-interaction error inherent in practical implementations of Kohn–Sham density functional theory. The self-interaction corrected calculations are found to give accurate results for the energy of the defect state with respect to both valence and conduction band edges as well as the experimentally determined atomic structure where only a single Al–O bond is lengthened by 11%. The HSE hybrid functional, as well as the PW91 generalized gradient approximation functional, however, gives too small an energy gap between the defect state and the valence band edge, overly delocalized spin density and lengthening of more than one Al–O bond.

Coordination chemistry has been a consistently active branch of chemistry since Werner’s seminal theory of coordination compounds inaugurated in 1893, with the central focus on transition metal complexes. However, control and measurement of metal–ligand interactions at the single-molecule level remain a daunting challenge. Here we demonstrate an interdisciplinary and systematic approach that enables measurement and modulation of the coordinative bonding forces in a transition metal complex. Terpyridine is derived with a thiol linker, facilitating covalent attachment of this ligand on both gold substrate surfaces and gold-coated atomic force microscopy tips. The coordination and bond breaking between terpyridine and osmium are followed in situ by electrochemically controlled atomic force microscopy at the single-molecule level. The redox state of the central metal atom is found to have a significant impact on the metal–ligand interactions. The present approach represents a major advancement in unravelling the nature of metal–ligand interactions and could have broad implications in coordination chemistry. The nature of metal–ligand interactions remains unclear in coordination chemistry. Hao et al. address this question using in situ electrochemically controlled atomic force microscopy, which can monitor and modulate the coordinative bonding in a transition metal complex at a molecular level.

The energetics and atomic structure associated with the localized hole formed near an Al-atom dopant in -quartz are calculated using a variational, self-consistent implementation of the Perdew-Zunger self-interaction correction with complex optimal orbitals. This system has become an important test problem for theoretical methodology since generalized gradient approximation energy functionals, as well as commonly used hybrid functionals, fail to produce a sufficiently localized hole due to the self-interaction error inherent in practical implementations of Kohn-Sham density functional theory. The self-interaction corrected calculations are found to give accurate results for the energy of the defect state with respect to both valence and conduction band edges as well as the experimentally determined atomic structure where only a single Al-O bond is lengthened by 11%. The HSE hybrid functional, as well as the PW91 generalized gradient approximation functional, however, gives too small an energy gap between the defect state and the valence band edge, overly delocalized spin density and lengthening of more than one Al-O bond.

A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density dependent functionals (ODD) including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate \\(\\pi^\\ast\\) orbitals where the importance of complex orbitals is illustrated. An application of the method to several metal-to-ligand charge-transfer and metal-centred excited states of an Fe\\(^{\\rm II}\\) photosensitizer complex is described and the results compared to reported experimental estimates. The method is also used to study the effect of Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented as a function of the elements of a skew-Hermitian matrix that can be optimized directly using unconstrained minimization methods. An implementation based on the limited memory Broyden-Fletcher-Goldfarb-Shanno approach with inexact line search and a preconditioner is presented and the performance compared with that of the commonly used self-consistent field approach. Results are presented for the G2 set of 148 molecules, liquid water configurations with up to 576 molecules and some insulating crystals. A general preconditioner is presented that is applicable to systems with fractional orbital occupation as is, for example, needed in the k-point sampling for periodic systems. This exponential transformation direct minimization approach is found to outperform the standard implementation of the self-consistent field approach in that all the calculations converge with the same set of parameter values and it requires less computational effort on average. The formulation of the exponential transformation and the gradients of the energy presented here are quite general and can be applied to energy functionals that are not unitary invariant such as self-interaction corrected functionals.

Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.

Qualitatively incorrect results are obtained for the Mn dimer in density functional theory calculations using the generalized gradient approximation (GGA) and similar results are obtained from local density and meta-GGA functionals. The coupling is predicted to be ferromagnetic rather than antiferromagnetic and the bond between the atoms is predicted to be an order of magnitude too strong and about an Ångstrøm too short. Explicit, self-interaction correction (SIC) applied to a commonly used GGA energy functional, however, provides close agreement with both experimental data and high-level, multi-reference wave function calculations. These results show that the failure is not due to strong correlation but rather the single electron self-interaction that is necessarily introduced in estimates of the classical Coulomb and exchange-correlation energy when only the total electron density is used as input. The corrected functional depends explicitly on the orbital densities and can, therefore, avoid the introduction of self-Coulomb interaction. The error arises because of over-stabilization of bonding \\(d\\)-states in the minority spin channel resulting from an overestimate of the \\(d\\)-electron self-interaction in the semi-local exchange-correlation functionals. Since the computational effort in the self-interaction corrected calculations scales with system size in the same way as for regular semi-local functional calculations, this approach provides a way to calculate properties of Mn nanoclusters as well as biomolecules and extended solids where Mn dimers and larger cluster are present, while multi-reference wave function calculations can only be applied to small systems.

Copper is a good CO2 electroreduction catalyst as products beyond CO form, but efficiency and selectivity is low. Experiments have shown that admixture of other elements can help, and computational screening studies have pointed out various promising candidates based on the adsorption of a single CO molecule as a descriptor. Our calculations of CO adsorption on surfaces where a first row transition metal atom replaces a Cu atom show that multiple CO molecules, not just one, bind to the substitutional atom. For Fe, Co, and Ni atoms, a decrease in binding energy is found, but the reverse trend, namely increasing bond strength, is found for V, Cr, and Mn and the first three CO molecules. Magnetic moment, charge, and position of the substitutional atom are also strongly affected by the CO adsorption in most cases. Magnetic moment is stepwise reduced to zero, and the outward displacement of the substitutional atom increased.

The structure of the solvation shell of aqueous Fe\\(^{+3}\\) ion has been a subject of controversy due to discrepancies between experiments and different levels of theory. We address this issue by performing simulations for a wide range of ion concentrations, using various empirical potential energy functions, as well as density functional theory calculations of selected configurations. The solvation shell undergoes abrupt transitions between two states: an octahedral (OH) state with 6-fold coordination, and a capped trigonal prism (CTP) state with 7-fold coordination. The lifetime of these states is concentration dependent. In dilute \\(\\mathrm{FeCl_3}\\) solutions, the lifetime of the two states is similar (\\(\\approx 1\\) ns). However, the lifetime of the OH state increases with ion concentration, while that of the CTP state decreases slightly. When a uniform negative background charge is used instead of explicit counterions, the lifetime of the OH state is greatly overestimated. These findings underscore the need for further experimental measurements as well as high-level simulations over sufficiently long timescales and low concentration.