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Density functional calculations of the energy surfaces of infinite helical chains of selenium have been performed for a wide range of geometries using the parameter-free local density approximation. The results are compared with our earlier calculations for the sulfur helix S∞ for which the calculated ground state geometry is in good agreement with experiment. The energy surfaces of both molecules are flat over large regions of configuration space—consistent with the extreme flexibility of these molecules—and are characterized by a variety of local minima and saddle points. Stretching each molecule results in planar zig-zag and linear geometries with overlapping conduction bands. The energy differences between helical and planar minima are small (∼0.2 eV). [ABSTRACT FROM AUTHOR]

Presents a correction to the article, entitled `Electronic structure of polyglycine as a function of proton position' published in the volume 112 issue of the `Journal of Chemical Physics'.

Using a first-principles density-functional method, we have calculated the single-chain band structure for the α-helical protein polyglycine as a function of proton position along the N...H...O hydrogen bond. Calculations have been carried out using both the local-density approximation (LDA) and the Perdew-Wang generalized gradient approximation (GGA) for the exchange-correlation potential. We present results for the total energy, band structure, charge densities, and Mulliken charges as a function of proton position. The total energy gives an asymmetric double-well potential for simultaneous proton shift, with the global minimum (at a N-H distance of 0.95 Å) 2.02 eV (46.6 kcal/mol) below the top of the barrier with the GGA, and 1.83 eV (42.2 kcal/mol) below with the LDA. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present an inverse-design method, the poor man's materials optimization, that is designed to identify materials within a very large class with optimized values for a pre-chosen property. The method combines an efficient genetic-algorithm-based optimization, an automatic approach for generating modified molecules, a simple approach for calculating the property of interest, and a mathematical formulation of the quantity whose value shall be optimized. In order to illustrate the performance of our approach, we study the properties of organic molecules related to those used in dye-sensitized solar cells, whereby we, for the sake of proof of principle, consider benzene as a simple test system. Using a genetic algorithm, the substituents attached to the organic backbone are varied and the best performing molecules are identified. We consider several properties to describe the performance of organic molecules, including the HOMO-LUMO gap, the sunlight absorption, the spatial distance of the orbitals, and the reorganisation energy. The results show that our method is able to identify a large number of good candidate structures within a short time. In some cases, chemical/physical intuition can be used to rationalize the substitution pattern of the best structures, although this is not always possible. The present investigations provide a solid foundation for dealing with more complex and technically relevant systems such as porphyrins. Furthermore, our "properties first, materials second" approach is not limited to solar-energy harvesting but can be applied to many other fields, as briefly is discussed in the paper.

A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.

The response to an electrostatic field is determined through simple model calculations, within both the restricted Hartree-Fock and density functional theory methods, for long, finite as well as infinite, periodic chains. The permanent dipole moment, μ0, the polarizability, α, and the hyperpolarizabilities β and γ, calculated using a finite-field approach, are extensively analyzed. Our simple model allows for treatment of large systems and for separation of the properties into atomic and unit-cell contributions. That part of the response properties attributable to the terminations of the finite system change into delocalized current contributions in the corresponding infinite periodic system. Special emphasis is placed on analyzing the reasons behind the dramatic overestimation of the response properties found with density functional theory methods presently in common use.

At first, three different methods devoted to extracting the periodic-system band structures from the results of finite-system calculations are being discussed. Special emphasis is put on the performance of these methods for a system that is exposed to an external electrostatic field. Using model calculations we found that the three methods converge to the same results in the absence of the electrostatic field, but they lead to small differences when the field is included, which can be ascribed to distortions of the spatial extensions of the orbitals generated by the field. These small differences become important when addressing the issue whether it is possible to identify uniquely a set of band structures for the infinite, periodic system exposed to an electrostatic field. This question, related to the question whether the phases of the periodic-system orbitals are of physical importance, has so far not been answered. Applying the results of the first part we ultimately suggest that it is not possible to identify a unique set of band structures when the periodic system is exposed to an electrostatic field.

Various periodic piecewise linear potentials for extracting the electronic response of an infinite periodic system to a uniform electrostatic field are examined. It is shown that discontinuous potentials, such as the sawtooth, cannot be used for this purpose. Continuous triangular potentials can be successfully employed to determine both even- and odd-order (hyper)polarizabilities, as demonstrated here for the first time, although the permanent dipole moment of the corresponding long finite chain remains out of reach. Moreover, for typical highly polarizable organic systems, the size of the repeated unit has to be much larger than that of the finite system in order to obtain convergence with respect to system size. All results are illustrated both through extensive model calculations and through ab initio calculations on poly- and oligoacetylenes.

A recently proposed approach for extracting band structures from finite-cluster calculations is improved so that (avoided) band crossings can be handled and the problems related to so-called doublings and holes are reduced. In particular, we demonstrate how the method can be combined with the elongation method for the finite-system calculations and apply it to extracting band structures for polymers from oligomer calculations. As illustrations of the approach we discuss a chain of water molecules, polyacetylene, polyethylene, and a BN nanotube without and with an impurity.

We present results of an investigation of small Ti(m)C(n) clusters with different stoichiometries in order to throw light on the occurrence of carbon dimers in these structures. Previous studies of transition metal (M) metallocarbohedrene (metcar) clusters M(m)C(n) have proposed that C(2) dimers play a special role. In the special case of Ti(m)C(n) metcars these dimers have been observed in several studies. We shall show that clusters containing C(2) dimers are energetically favored with respect to those containing only single carbon atoms or trimers, especially when the dimers occupy the corner positions of cubic clusters. Moreover, we find that cubic structures are more stable than corresponding double-cage metcars. Finally, a highly symmetric Ti(6)C(10) metcar cluster is presented and proposed to be the global-minimum structure of this stoichiometry.

The basin-hopping algorithm combined with the Gupta many-body potential is used to study the structural and energetic properties of (KCs)(n) and (RbCs)(n) bimetallic clusters with N=2n up to 50 atoms. Each binary structure is compared to those of the pure clusters of the same size. For the cluster size N=28 and for the size range of N=34-50, the introduction of K and Rb atoms in the Cs alkali metal cluster results in new ground state structures different from those of the pure elements. In the size range N>/=38 the binary and pure clusters show not only structural differences, but they also display different magic numbers. Most of the magic Rb-Cs and K-Cs clusters possess highly symmetric structures. They belong to a family of pIh structures, where a fivefold pancake is a dominant structural motif. Such geometries have not been reported for alkali binary clusters so far, but have been found for series of binary transition metal clusters with large size mismatch. Moreover, tendency to phase separation (shell-like segregation) is predicted for both K-Cs and Rb-Cs clusters with up to 1000 atoms. Our finding of a surface segregation in Rb-Cs clusters is different from that of theoretical and experimental studies on bulk Rb-Cs alloys where phase separation does not occur.

Reparametrization of Wigner's correlation energy density functional yields a very close fit to the correlation energies of the helium isoelectronic sequence. However, a quite different reparametrization is required to obtain an equally close fit to the isoelectronic sequence of Hooke's atom. In an attempt to avoid having to reparametrize the functional for different choices of the one-body potential, we propose a parametrization that depends on global characteristics of the ground-state electron density as quantified by scale-invariant combinations of expectation values of local one-body operators. This should be viewed as an alternative to the density-gradient paradigm, allowing one to introduce the nonlocal dependence of the density functional on the density in a possibly more effective way. Encouraging results are obtained for two-electron systems with one-body potentials of the form r(zeta) with zeta=-12,+12,1, which span the range between the Coulomb potential (zeta=-1) and the Hooke potential (zeta=2).

The response of periodic systems to external electric fields is a challenging theoretical problem. The authors show how the vector potential approach yields a numerically efficient treatment of the combined electronic and nuclear response to a finite static field. Their method is based on a self-consistent reformulation of the charge flow term in the single particle Hamiltonian. Careful numerical implementation yields a treatment whose computational needs are only marginally larger than those of a conventional field-free calculation. To prove the method exemplary polymer calculations are done for a model Hamiltonian. The latter contains all essential elements of an ab initio Kohn-Sham or Hartree-Fock Hamiltonian but allows for extensive testing. The extension to three-dimensional systems is described.

The correlation energies of the helium isoelectronic sequence and of Hooke's atom isoelectronic sequence have been evaluated using an assortment of local, gradient, and metagradient density functionals. The results are compared with the exact correlation energies, showing that while several of the more recent density functionals reproduce the exact correlation energies of the helium isoelectronic sequence rather closely, none is satisfactory for Hooke's atom isoelectronic sequence. It is argued that the uniformly acceptable results for the helium sequence can be explained through simple scaling arguments that do not hold for Hooke's atom sequence, so that the latter system provides a more sensitive testing ground for approximate density functionals. This state of affairs calls for further effort towards formulating correlation-energy density functionals that would be truly universal at least for spherically symmetric two-fermion systems.

The correlation energies of the helium isoelectronic sequence (IS) and of Hooke's IS are very similar and are both weakly increasing upon increasing the nuclear charge/force constant, respectively. However, their separation into radial and angular correlations shows interesting differences. First, for intermediate (and high) values of the force constant radial correlation in Hooke's IS is surprisingly low. Second, both systems exhibit a decrease in the relative contribution of radial versus angular correlation upon strengthening the one-body attractive potential; however, unlike the helium IS, in Hooke's IS the radial correlation energy increases in absolute value upon strengthening the attractive one-body potential. The contribution of radial correlation to the Coulomb hole is examined and the asymptotic behavior at both strong and weak attractive potentials is considered. Radial correlation in Hooke's IS is found to constitute about 9.3% of the total correlation energy when the spring constant approaches the limit k-->infinity, but 100% of the total correlation energy for k-->0. Our results highlight both the similarities and the differences between the helium and Hooke's ISs.

Some aspects of the adiabatic connection method are studied for two-particle spherically symmetric systems. Ground-state wave functions that are constrained by means of a set of moments to have the same density as a corresponding fully interacting system are obtained for noninteracting or partially interacting systems. Local one-body potentials that support these constrained wave functions are generated using a simple method. We examine an interacting two-particle system with a parameter-dependent one-body potential, which for a particular value of that parameter exhibits an intersection between the (3)S and the (3)P states, whereas the 2s and 2p eigenvalues of the corresponding Kohn-Sham potentials do not intersect along with the total energies. These results show that there do exist cases where occupying the orbitals from below in energy may not lead to the ground state, and that the inherent assumptions behind the adiabatic connection can sometimes be violated., ((c) 2004 American Institute of Physics.)