Hardness of molecules and bandgap of solids from a generalized gradient approximation exchange energy functional.

The deviations from linearity of the energy as a function of the number of electrons that arise with current approximations to the exchange-correlation (XC) energy functional have important consequences for the frontier eigenvalues of molecules and the corresponding valence-band maxima for solids. In this work, we present an analysis of the exact theory that allows one to infer the effects of such approximations on the highest occupied and lowest unoccupied molecular orbital eigenvalues. Then, we show the importance of the asymptotic behavior of the XC potential in the generalized gradient approximation (GGA) in the case of the NCAPR functional (nearly correct asymptotic potential revised) for determining the shift of the frontier orbital eigenvalues toward the exact values. Thereby we establish a procedure at the GGA level of refinement that allows one to make a single calculation to determine the ionization potential, the electron affinity, and the hardness of molecules (and its solid counterpart, the bandgap) with an accuracy equivalent to that obtained for those properties through energy differences, a procedure that requires three calculations. For solids, the accuracy achieved for the bandgap lies rather close to that which is obtained through hybrid XC energy functionals, but those also demand much greater computational effort than what is required with the simple NCAPR GGA calculation.

Analysis of the kinetic energy functional in the generalized gradient approximation.

A new density functional for the total kinetic energy in the generalized gradient approximation is developed through an enhancement factor that leads to the correct behavior in the limits when the reduced density gradient tends to 0 and to infinity and by making use of the conjoint conjecture for the interpolation between these two limits, through the incorporation, in the intermediate region of constraints that are associated with the exchange energy functional. The resulting functional leads to a reasonable description of the kinetic energies of atoms and molecules when it is used in combination with Hartree-Fock densities. Additionally, in order to improve the behavior of the kinetic energy density, a new enhancement factor for the Pauli kinetic energy is proposed by incorporating the correct behavior into the limits when the reduced density gradient tends to 0 and to infinity, together with the positivity condition, and imposing through the interpolation function that the sum of its integral over the whole space and the Weiszacker energy must be equal to the value obtained with the enhancement factor developed for the total kinetic energy.

Constrained dipole moment density functional theory for charge distributions in force fields for the study of molecular fluids.

A new procedure, based on electronic structure calculations that only requires a dipole moment value for a given molecule as input and, from which the charges for all the atoms in it are uniquely determined, is developed and applied to the study of molecular fluids with classical dynamics. The dipole moment value considered for the isolated molecule is the one that reproduces the dielectric constant of its corresponding fluid. Following previous work, the Lennard-Jones parameters are determined to reproduce the liquid density and the surface tension at the liquid-vapor interface. The force field thus obtained leads to a reasonable description of several properties such as heats of vaporization, self-diffusion coefficients, shear viscosities, isothermal compressibilities, and volumetric expansion coefficients of pure substances.

Negative Electron Affinities and Derivative Discontinuity Contribution from a Generalized Gradient Approximation Exchange Functional.

Two methods to calculate negative electron affinities systematically from ground-state density functional methods are presented. One makes use of the lowest unoccupied molecular orbital energy shift provided by approximate inclusion of derivative discontinuity in the nearly correct asymptotic potential (NCAP) nonempirical, constraint-based generalized gradient approximation exchange functional. The other uses a second-order perturbation calculation of the derivative discontinuity based on the NCAP exchange-correlation potential. On a set of thirty-eight molecules, NCAP leads to a rather accurate description that is improved further through the perturbation correction. The results presented show the importance of the asymptotic behavior of the exchange-correlation potential in the calculation of negative electron affinities as well as demonstrating the versatility of the NCAP functional.

Generalized Gradient Approximation Exchange Energy Functional with Near-Best Semilocal Performance.

We develop and validate a nonempirical generalized gradient approximation (GGA) exchange (X) density functional that performs as well as the SCAN (strongly constrained and appropriately normed) meta-GGA on standard thermochemistry tests. Additionally, the new functional (NCAP, nearly correct asymptotic potential) yields Kohn-Sham eigenvalues that are useful approximations of the density functional theory (DFT) ionization potential theorem values by inclusion of a systematic derivative discontinuity shift of the X potential. NCAP also enables time-dependent DFT (TD-DFT) calculations of good-quality polarizabilities, hyper-polarizabilities, and one-Fermion excited states without modification (calculated or ad hoc) of the long-range behavior of the exchange potential or other patches. NCAP is constructed by reconsidering the imposition of the asymptotic correctness of the X potential (-1/ r) as a constraint. Inclusion of derivative discontinuity and approximate integer self-interaction correction treatments along with first-principles determination of the effective second-order gradient expansion coefficient yields a major advance over our earlier correct asymptotic potential functional [CAP; J. Chem. Phys. 2015 , 142 , 054105 ]. The new functional reduces a spurious bump in the CAP atomic exchange potential and moves it to distances irrelevantly far from the nucleus (outside the tail of essentially all practical basis functions). It therefore has nearly correct atomic exchange-potential behavior out to rather large finite distances r from the nucleus but eventually goes as - c/ r with an estimated value for the constant c of around 0.3, so as to achieve other important properties of exact DFT exchange within the restrictions of the GGA form. We illustrate the results with the Ne atom optimized effective potentials and with standard molecular benchmark test data sets for thermochemical, structural, and response properties.

Revisiting the definition of local hardness and hardness kernel.

An analysis of the hardness kernel and local hardness is performed to propose new definitions for these quantities that follow a similar pattern to the one that characterizes the quantities associated with softness, that is, we have derived new definitions for which the integral of the hardness kernel over the whole space of one of the variables leads to local hardness, and the integral of local hardness over the whole space leads to global hardness. A basic aspect of the present approach is that global hardness keeps its identity as the second derivative of energy with respect to the number of electrons. Local hardness thus obtained depends on the first and second derivatives of energy and electron density with respect to the number of electrons. When these derivatives are approximated by a smooth quadratic interpolation of energy, the expression for local hardness reduces to the one intuitively proposed by Meneses, Tiznado, Contreras and Fuentealba. However, when one combines the first directional derivatives with smooth second derivatives one finds additional terms that allow one to differentiate local hardness for electrophilic attack from the one for nucleophilic attack. Numerical results related to electrophilic attacks on substituted pyridines, substituted benzenes and substituted ethenes are presented to show the overall performance of the new definition.

Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential.

A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement.

Time-dependent auxiliary density perturbation theory.

The recently developed auxiliary density perturbation theory is extended to time-dependent perturbations. As its static counterpart, it is based on auxiliary density functional theory in which the Coulomb and exchange-correlation potentials are expressed through one auxiliary function density. As in the case of static perturbations a noniterative alternative to the corresponding coupled perturbed Kohn-Sham method is formulated. The new methodology is validated by local and gradient corrected dynamical polarizability calculations. Comparison with experiment indicates that for low frequencies reliable dynamical polarizabilities are obtained. Our discussion also shows that the computational performance of time-dependent auxiliary density perturbation theory is similar to the previously described static approach. In order to demonstrate the potential of this new methodology, dynamic polarizabilities of C(60), C(180), and C(240) are calculated.

Comparison of the auxiliary density perturbation theory and the noniterative approximation to the coupled perturbed Kohn-Sham method: case study of the polarizabilities of disubstituted azoarene molecules.

We present a theoretical study of the polarizabilities of free and disubstituted azoarenes employing auxiliary density perturbation theory (ADPT) and the noniterative approximation to the coupled perturbed Kohn-Sham (NIA-CPKS) method. Both methods are noniterative but use different approaches to obtain the perturbed density matrix. NIA-CPKS is different from the conventional CPKS approach in that the perturbed Kohn-Sham matrix is obtained numerically, thereby yielding a single-step solution to CPKS. ADPT is an alternative approach to the analytical CPKS method in the framework of the auxiliary density functional theory. It is shown that the polarizabilities obtained using these two methods are in good agreement with each other. Comparisons are made for disubstituted azoarenes, which give support to the push-pull mechanism. Both methods reproduce the same trend for polarizabilities because of the substitution pattern of the azoarene moiety. Our results are consistent with the standard organic chemistry "activating/deactivating" sequence. We present the polarizabilities of the above molecules calculated with three different exchange-correlation functionals and two different auxiliary function sets. The computational advantages of both methods are also discussed.