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We propose a direct method for reducing the dimension of the space of orbital products that occur, for example, in the calculation of time dependent density functional theory linear response and in Hedin’s GW approximation to the electron propagator. We do this by defining, within the linear space of orbital products, a subspace of dominant directions that are associated with a certain eigenvalue problem. These directions span the entire linear space of products with an error that decreases approximately exponentially with their number. Our procedure works best for atomic orbitals of finite range and it avoids the use of extra sets of auxiliary fit functions. [ABSTRACT FROM AUTHOR]

The key characteristics of electronic excitations of many-electron systems, the excitation energies ωα and the oscillator strengths fα, can be obtained from linear response theory. In one-electron models and within the adiabatic approximation, the zeros of the inverse response matrix, which occur at the excitation energies, can be obtained from a simple diagonalization. Particular cases are the eigenvalue equations of time-dependent density functional theory (TDDFT), time-dependent density matrix functional theory, and the recently developed phase-including natural orbital (PINO) functional theory. In this paper, an expression for the oscillator strengths fα of the electronic excitations is derived within adiabatic response PINO theory. The fα are expressed through the eigenvectors of the PINO inverse response matrix and the dipole integrals. They are calculated with the phase-including natural orbital functional for two-electron systems adapted from the work of Lowdin and Shull on two-electron systems (the phase-including Löwdin-Shull functional). The PINO calculations reproduce the reference fα values for all considered excitations and bond distances R of the prototype molecules H2 and HeH+ very well (perfectly, if the correct choice of the phases in the functional is made). Remarkably, the quality is still very good when the response matrices are severely restricted to almost TDDFT size, i.e., involving in addition to the occupied-virtual orbital pairs just (HOMO+1)-virtual pairs (R1) and possibly (HOMO+2)-virtual pairs (R2). The shape of the curves fα(R) is rationalized with a decomposition analysis of the transition dipole moments. [ABSTRACT FROM AUTHOR]

Meta-generalized gradient approximation (meta-GGA) exchange-correlation density functionals depend on the Kohn-Sham (KS) orbitals through the kinetic energy density. The KS orbitals in turn depend functionally on the electron density. However, the functional dependence of the KS orbitals is indirect, i.e., not given by an explicit expression, and the computation of analytic functional derivatives of meta-GGA functionals with respect to the density imposes a challenge. The practical solution used in many computer implementations of meta-GGA density functionals for ground-state calculations is abstracted and generalized to a class of density functionals that is broader than meta-GGAs and to any order of functional differentiation. Importantly, the TDDFT working equations for meta-GGA density functionals are presented here for the first time, together with the technical details of their computer implementation. The analysis presented here also uncovers the implicit assumptions in the practical solution to computing functional derivatives of meta-GGA density functionals. The connection between the approximation that is invoked in taking functional derivatives of density functionals, the non-uniqueness with respect to the KS orbitals, and the non-locality of the resultant potential is also discussed. [ABSTRACT FROM AUTHOR]

Adsorption of O2 molecule on Al surface has been a long standing puzzle for the first principles calculation. We have studied the adsorption of O2 molecule on the Al(111) surface using hybrid functionals. In contrast to the previous local-density approximation/gradient-corrected approximation, the present calculations with hybrid functionals successfully predict that O2 molecule can be absorbed on the Al(111) surface with a barrier around 0.2-0.4 eV, which is in good agreement with experiments. Our calculations predict that the lowest unoccupied molecular orbital of O2 molecule is higher than the Fermi level of the Al(111) surface, which is responsible for the barrier of the O2 adsorption. [ABSTRACT FROM AUTHOR]

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z→∞, presenting a new method to extract the coefficients from oscillating numerical data. Recovery of the correct expansion yields a condition on the Kohn–Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules, and solids. For example, this determines the small gradient limit of any generalized gradient approximation and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters using densities constructed from Kohn–Sham orbitals. We also give a modern, highly accurate parametrization of the Thomas–Fermi density of neutral atoms. [ABSTRACT FROM AUTHOR]

The electronic and atomic structure of the family of hydrogenated Al clusters AlnHn+2 with n=4–11 has been studied using the density functional theory with the generalized gradient approximation (GGA) for exchange and correlation. All these clusters have substantial gaps between the highest occupied and the lowest unoccupied molecular orbitals (HOMO-LUMO) and, consequently, they are chemically very stable. The largest gap of 2.81 eV occurs for Al6H8. Five clusters of the family, Al4H6, Al5H7, Al6H8, Al7H9, and Al10H12, fulfill the Wade–Mingos rule. That is, in AlnHn+2, the Al matrix forms a polyhedron of n vertices and n H atoms form strong H–Al terminal bonds; one pair of electrons is involved in each of those bonds. The remaining n+1 electron pairs form a delocalized cloud over the surface of the Al cage. The clusters fulfilling the Wade–Mingos rule have wider HOMO-LUMO gaps and are chemically more stable. The trends in the gap have some reflections in the form of the photoabsorption spectra, calculated in the framework of time-dependent density functional theory using the GGA single-particle energies and orbitals and a local density approximation exchange-correlation kernel. [ABSTRACT FROM AUTHOR]

Double-hybrid density functionals are based on a mixing of standard generalized gradient approximations (GGAs) for exchange and correlation with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional (dubbed B2PLYP) contains only two empirical parameters that describe the mixture of HF and GGA exchange (ax) and of the PT2 and GGA correlation (ac), respectively. Extensive testing has recently demonstrated the outstanding accuracy of this approach for various ground state problems in general chemistry applications. The method is extended here without any further empirical adjustments to electronically excited states in the framework of time-dependent density functional theory (TD-DFT) or the closely related Tamm-Dancoff approximation (TDA-DFT). In complete analogy to the ground state treatment, a scaled second-order perturbation correction to configuration interaction with singles (CIS(D)) wave functions developed some years ago by Head-Gordon et al. [Chem. Phys. Lett. 219, 21 (1994)] is computed on the basis of density functional data and added to the TD(A)-DFT/GGA excitation energy. The method is implemented by applying the resolution of the identity approximation and the efficiency of the code is discussed. Extensive tests for a wide variety of molecules and excited states (of singlet, triplet, and doublet multiplicities) including electronic spectra are presented. In general, rather accurate excitation energies (deviations from reference data typically <0.2 eV) are obtained that are mostly better than those from standard functionals. Still, systematic errors are obtained for Rydberg (too low on average by about 0.3 eV) and charge-transfer transitions but due to the relatively large ax parameter (0.53), B2PLYP outperforms most other functionals in this respect. Compared to conventional HF-based CIS(D), the method is more robust in electronically complex situations due to the implicit account of static correlation effects by the GGA parts. The (D) correction often works in the right direction and compensates for the overestimation of the transition energy at the TD level due to the elevated fraction of HF exchange in the hybrid GGA part. Finally, the limitations of the method are discussed for challenging systems such as transition metal complexes, cyanine dyes, and multireference cases. [ABSTRACT FROM AUTHOR]

We report a method for the efficient evaluation of analytic energy second derivatives with respect to in-phase nuclear coordinate displacements within Hartree-Fock and Kohn-Sham density functional theories using Gaussian orbitals and periodic boundary conditions. The use of an atomic orbital formulation for all computationally challenging steps allows us to adapt the direct space fast multipole method for the Coulomb-type infinite summations. Our implementation also exploits the local character of the exact Hartree-Fock exchange in nonconducting systems. Exchange-correlation contributions are computed using extensive screening and fast numerical quadratures. We benchmark our scheme for in-phase vibrational frequencies of a trans-polyacetylene chain, a two-dimensional boron nitride sheet, and bulk diamond with the 6-31G** basis set and various density functionals. A study of computational scaling with the size of the unit cell for trans-polyacetylene reveals subquadratic scaling for our scheme. [ABSTRACT FROM AUTHOR]

The evaluation of ≤S⁁2> in density functional theory (DFT) is considered. Wang et al. [J. Chem. Phys. 102, 3477 (1995)] have derived an approximate, local density expression for <<⁁2> and in the present study their formula is evaluated using densities from unrestricted Hartree-Fock (UHF) and a range of DFT exchange-correlation functionals. The results are compared with those obtained by evaluating the conventional UHF expression using the Kohn-Sham orbitals, which is appropriate for the noninteracting system. A generalized gradient approximation for ≤S⁁2> is then proposed and investigated [ABSTRACT FROM AUTHOR]

The small-bias conductance of the C[sub 6] molecule, stretched between two metallic leads, is studied using time-dependent density functional theory within the adiabatic local density approximation. The leads are modeled by jellium slabs, the electronic density and the current density are described on a grid, whereas the core electrons and the highly oscillating valence orbitals are approximated using standard norm-conserving pseudopotentials. The jellium leads are supplemented by a complex absorbing potential that serves to absorb charge reaching the edge of the electrodes and hence mimic irreversible flow into the macroscopic metal. The system is rapidly exposed to a ramp potential directed along the C[sub 6] axis, which gives rise to the onset of charge and current oscillations. As time progresses, a fast redistribution of the molecular charge is observed, which translates into a direct current response. Accompanying the dc signal, alternating current fluctuations of charge and currents within the molecule and the metallic leads are observed. These form the complex impedance of the molecule and are especially strong at the plasmon frequency of the leads and the lowest excitation peak of C[sub 6]. We study the molecular conductance in two limits: the strong coupling limit, where the edge atoms of the chain are submerged in the jellium and the weak coupling case, where the carbon atoms and the leads do not overlap spatially. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]