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This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e., the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating “memory” effects: the derived exchange-correlation potential will depend not only on present densities but also on the past. In order to ensure the potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn–Sham equations. The exchange-correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal exchange-correlation vector potential for the Kohn–Sham equations incorporating memory effects. We show explicitly that the net exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit). © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The Coulomb hole does not have its largest depth around an electron in or near the bond midplane. It splits into two parts, localized on both nuclear sites forming the bond. Even counterintuitive positive values of the “hole” around such a position may be observed. This happens when the Fermi hole is deeper than the total exchange-correlation hole at the reference electron position. This Coulomb “heap” is shown to arise from correlation effects on the one-electron density rather than correlation effects in the pair density. Left-right correlation tends to enhance the effect of the nuclear attraction, contracting the electron density around the nuclear positions and depleting the bond center region. Possible alternative definitions of the Coulomb hole are discussed, including one based on the exact Kohn–Sham exchange hole. Approximate density functional theory methods (generalized gradient approximation) are not accurate enough to realize the advantages of this definition. [ABSTRACT FROM AUTHOR]

The effect of diffuse electron density at the boundary surfaces of Au-core Ag-shell bimetallic nanospheres on their optical properties such as extinction spectra is investigated by considering a multiple shell model for both the interfaces consisting of exponentially decreasing electron density profiles corresponding to a minimized energy density functional. The dielectric constants for the shells of varying electron density have been obtained by proposing a new simple approach. The diffuseness of the electron density at the boundary surfaces is found to give rise to peak broadening to some extent and also seems to favor the experimental spectra. [ABSTRACT FROM AUTHOR]

There is a number of explicit kinetic energy density functionals for noninteracting electron systems that are obtained in terms of the electron density and its derivatives. These semilocal functionals have been widely used in the literature. In this work, we present a comparative study of the kinetic energy density of these semilocal functionals, stressing the importance of the local behavior to assess the quality of the functionals. We propose a quality factor that measures the local differences between the usual orbital-based kinetic energy density distributions and the approximated ones, allowing us to ensure if the good results obtained for the total kinetic energies with these semilocal functionals are due to their correct local performance or to error cancellations. We have also included contributions coming from the Laplacian of the electron density to work with an infinite set of kinetic energy densities. For all but one of the functionals, we have found that their success in the evaluation of the total kinetic energy is due to global error cancellations, whereas the local behavior of their kinetic energy density becomes worse than that corresponding to the Thomas-Fermi functional. [ABSTRACT FROM AUTHOR]

The central role of the shape function σ(r_) from the density functional theory (DFT), the ratio of the electron density ρ(r_) and the number of electrons N of the system (density per particle), is investigated. Moreover, its relationship with DFT based reactivity indices is established. In the first part, it is shown that an estimate for the chemical hardness can be obtained from the long range behavior of the shape function and its derivative with respect to the number of electrons at a fixed external potential. Next, the energy of the system is minimized with the constraint that the shape function should integrate to unity; the associated Lagrange multiplier is shown to be related to the electronic chemical potential μ of the system. Finally, the importance of the shape function for both molecular structure, reactivity, and similarity is outlined. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In methods based on frozen-density embedding theory or subsystem formulation of density functional theory, the non-additive kinetic potential (vtnad(r)) needs to be approximated. Since vtnad(r) is defined as a bifunctional, the common strategies rely on approximating vtnad[ρA,ρB](r). In this work, the exact potentials (not bifunctionals) are constructed for chemically relevant pairs of electron densities (ρA and ρB) representing: dissociating molecules, two parts of a molecule linked by a covalent bond, or valence and core electrons. The method used is applicable only for particular case, where ρA is a one-electron or spin-compensated two-electron density, for which the analytic relation between the density and potential exists. The sum ρA + ρB is, however, not limited to such restrictions. Kohn-Sham molecular densities are used for this purpose. The constructed potentials are analyzed to identify the properties which must be taken into account when constructing approximations to the corresponding bifunctional. It is comprehensively shown that the full von Weizsäcker component is indispensable in order to approximate adequately the non-additive kinetic potential for such pairs of densities. [ABSTRACT FROM AUTHOR]