Accurate and efficient approaches to predict the optical properties of organic semiconducting compounds could accelerate the search for efficient organic photovoltaic materials. Nevertheless, predicting the optical properties of organic semiconductor
s has been plagued by the inaccuracy or computational cost of conventional first-principles calculations. In this work, we demonstrate that orbital-dependent density-functional theory based upon Koopmans condition [Phys. Rev. B 82, 115121 (2010)] is apt at describing donor and acceptor levels for a wide variety of organic molecules, clusters, and oligomers within a few tenths of an electron-volt relative to experiment, which is comparable to the predictive performance of many-body perturbation theory methods at a fraction of the computational cost.
In surface catalysis, the adsorption of carbon monoxide on transition-metal electrodes represents the prototype of strong chemisorption. Notwithstanding significant changes in the molecular orbitals of adsorbed CO, spectroscopic experiments highlight
a close correlation between the adsorbate stretching frequency and equilibrium bond length for a wide range of adsorption geometries and substrate compositions. In this work, we study the origins of this correlation, commonly known as Badgers rule, by deconvoluting and examining contributions from the adsorption environment to the intramolecular potential using first-principles calculations. Noting that intramolecular anharmonicity is preserved upon CO chemisorption, we show that Badgers rule for adsorbed CO can be expressed solely in terms of the tabulated Herzberg spectroscopic constants of isolated CO. Moreover, although it had been previously established using finite-cluster models that Badgers rule is not affected by electrical conditions, we find here that Badgers rule breaks down when the electrified surface is represented as a periodic slab. Examining this breakdown in terms of anharmonic contributions from the effective surface charge reveals limitations of conventional finite-cluster models in describing electrical conditions at metal electrodes.
The solvation model proposed by Fattebert and Gygi [Journal of Computational Chemistry 23, 662 (2002)] and Scherlis et al. [Journal of Chemical Physics 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and
extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multi-grid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [Physical Review Letters 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation (SCCS) model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the PCM model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond forming compounds.
Plane-wave electronic-structure predictions based upon orbital-dependent density-functional theory (OD-DFT) approximations, such as hybrid density-functional methods and self-interaction density-functional corrections, are severely affected by comput
ational inaccuracies in evaluating electron interactions in the plane-wave representation. These errors arise from divergence singularities in the plane-wave summation of electrostatic and exchange interaction contributions. Auxiliary-function corrections are reciprocal-space countercharge corrections that cancel plane-wave singularities through the addition of an auxiliary function to the point-charge electrostatic kernel that enters into the expression of interaction terms. At variance with real-space countercharge corrections that are employed in the context of density-functional theory (DFT), reciprocal-space corrections are computationally inexpensive, making them suited to more demanding OD-DFT calculations. Nevertheless, there exists much freedom in the choice of auxiliary functions and various definitions result in different levels of performance in eliminating plane-wave inaccuracies. In this work, we derive exact point-charge auxiliary functions for the description of molecular structures of arbitrary translational symmetry, including the yet unaddressed one-dimensional case. In addition, we provide a critical assessment of different reciprocal-space countercharge corrections and demonstrate the improved accuracy of point-charge auxiliary functions in predicting the electronic levels and electrical response of conjugated polymers from plane-wave OD-DFT calculations.
In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors that pervad
e many fundamental aspects of density-functional predictions. Here, we first examine self-interaction in terms of the discrepancy between total and partial electron removal energies, and then highlight the importance of imposing the generalized Koopmans condition -- that identifies orbital energies as opposite total electron removal energies -- to resolve this discrepancy. In the process, we derive a correction to approximate functionals that, in the frozen-orbital approximation, eliminates the unphysical occupation dependence of orbital energies up to the third order in the single-particle densities. This non-Koopmans correction brings physical meaning to single-particle energies; when applied to common local or semilocal density functionals it provides results that are in excellent agreement with experimental data -- with an accuracy comparable to that of GW many-body perturbation theory -- while providing an explicit total energy functional that preserves or improves on the description of established structural properties.
We have studied the vibrational properties of CO adsorbed on platinum and platinum-ruthenium surfaces using density-functional perturbation theory within the Perdew-Burke-Ernzerhof generalized-gradient approximation. The calculated C-O stretching fre
quencies are found to be in excellent agreement with spectroscopic measurements. The frequency shifts that take place when the surface is covered with ruthenium monolayers are also correctly predicted. This agreement for both shifts and absolute vibrational frequencies is made more remarkable by the frequent failure of local and semilocal exchange-correlation functionals in predicting the stability of the different adsorption sites for CO on transition metal surfaces. We have investigated the chemical origin of the C-O frequency shifts introducing an orbital-resolved analysis of the force and frequency density of states, and assessed the effect of donation and backdonation on the CO vibrational frequency using a GGA + molecular U approach. These findings rationalize and establish the accuracy of density-functional calculations in predicting absolute vibrational frequencies, notwithstanding the failure in determining relative adsorption energies, in the strong chemisorption regime.
We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained from a Four
ier transform, and the potential satisfying any other boundary conditions can be characterized analytically. In light of this observation, we present an efficient real-space method to correct periodic-image errors, based on a multigrid solver for the potential difference, and demonstrate that exponential convergence of the energy with respect to cell size can be achieved in practical calculations. Additionally, we derive rapidly convergent expansions for determining the Madelung constants of point-charge assemblies in one, two, and three dimensions.
