A Lanczos algorithm for linear response

An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic accuracy of the basic mean-field approximation, avoiding the problem of solving very large matrices. For local interactions, the computational effort for the method scales with the number of particles N_p as O(N_p^3).Comment: 12 pages including 3 figures; Late

Oscillator strengths with pseudopotentials

The time-dependent local-density approximation (TDLDA) is shown to remain accurate in describing the atomic response of IB elements under the additional approximation of using pseudopotentials to treat the effects of core electrons. This extends the work of Zangwill and Soven who showed the utility of the all-electron TDLDA in the atomic response problem.Comment: 13 pages including 3 Postscript figure

Application of time-dependent density functional theory to optical activity

As part of a general study of the time-dependent local density approximation (TDLDA), we here report calculations of optical activity of chiral molecules. The theory automatically satisfies sum rules and the Kramers-Kronig relation between circular dichroism and optical rotatory power. We find that the theory describes the measured circular dichroism of the lowest states in methyloxirane with an accuracy of about a factor of two. In the chiral fullerene C_76 the TDLDA provides a consistent description of the optical absorption spectrum, the circular dichroism spectrum, and the optical rotatory power, except for an overall shift of the theoretical spectrum.Comment: 17 pages and 13 PostScript figure

Wavelet-Based Linear-Response Time-Dependent Density-Functional Theory

Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BigDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program deMon2k for the calculation of electronic absorption spectra of N2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BigDFT than for deMon2k. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BigDFT, while all virtual orbitals are included in TD-DFT calculations in deMon2k. As a reality check, we report the x-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1,2-a]pyridin-3-amine

Efficient Benzodithiophene/Benzothiadiazole-Based n-Channel Charge Transporters

A series of donor–acceptor small molecules based on electrondeficient benzothiadiazole (BTD) and electron-rich benzodithiophene (BDT) featuring an A-D-A structure is presented. Exhaustive spectroscopic, electrochemical, and computational studies evidence their electroactive nature and their ability to form well-ordered thin films with broad visible absorptions and low band gaps (ca. 2 eV). Time-resolved microwave conductivity (TRMC) studies unveil unexpected n-type charge transport displaying high electron mobilities around 0.1 cm2V1 s 1 . Efficient electron transport properties are consistent with the low electron reorganization energies (0.11–0.17 eV) theoretically predicted

Quasiparticle Density-Matrix Representation of Nonlinear TDDFT Response Functions

The time-dependent density functional (TDDFT) equations may be written either for the Kohn-Sham orbitals in Hilbert space or for the single electron density matrix in Liouville space. A collective-oscillator, quasiparticle, representation of the density response of many-electron systems which explicitly reveals the relevant electronic coherence sizes is developed using the Liouville space representation of adiabatic TDDFT. Closed expressions for the nonlinear density-density response are derived, eliminating the need to solve nonlinear integral equations, as required in the Hilbert space formulation of the response.Comment: 24 page

Three real-space discretization techniques in electronic structure calculations

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status solidi (b) - basic solid state physics" devoted to the CECAM workshop "State of the art developments and perspectives of real-space electronic structure techniques in condensed matter and molecular physics". v2: Minor stylistic and typographical changes, partly inspired by referee comment

Transition-metal dimers and physical limits on magnetic anisotropy

Recent advances in nanoscience have raised interest in the minimum bit size required for classical information storage, i.e. for bistability with suppressed quantum tunnelling and energy barriers that exceed ambient temperatures. In the case of magnetic information storage much attention has centred on molecular magnets[1] with bits consisting of ~ 100 atoms, magnetic uniaxial anisotropy energy barriers ~ 50 K, and very slow relaxation at low temperatures. In this article we draw attention to the remarkable magnetic properties of some transition metal dimers which have energy barriers approaching ~ 500 K with only two atoms. The spin dynamics of these ultra small nanomagnets is strongly affected by a Berry phase which arises from quasi-degeneracies at the electronic Highest Occupied Molecular Orbital (HOMO) energy. In a giant spin-approximation, this Berry phase makes the effective reversal barrier thicker. [1] Gatteschi, D., Sessoli, R. & Villain, J. Molecular Nanomagnets. (Oxford, New York 2006).Comment: 14 pages, 1 figur

Neutral and Oxidized Triisopropylsilyl End-Capped Oligothienoacenes: A Combined Electrochemical, Spectroscopic, and Theoretical Study

This work presents an analysis of the structural, electrochemical, and optical properties of a family of triisopropylsilyl end-capped oligothienoacenes (TIPS- T n -TIPS, n =4–8) by combining cyclic voltammetry, spectroscopic techniques, and quantum-chemical calculations. TIPS- T n -TIPS compounds form stable radical cations, and dications are only obtained for the longest oligomers ( n =7 and 8). Oxidation leads to the quinoidization of the conjugated backbone, from which electrons are mainly extracted. The absorption and fluorescence spectra show partially resolved vibronic structures even at room temperature, due to the rigid molecular geometry. Two well-resolved vibronic progressions are observed at low temperatures due to the vibronic coupling, with normal modes showing wavenumbers of ≈1525 and ≈480 14cm −1 . Optical absorption bands display remarkable bathochromic dispersion with the oligomer length, indicative of the extent of Π conjugation. The optical properties of the oxidized compounds are characterized by in situ UV/Vis/NIR spectroelectrochemistry. The radical cation species show two intense absorption bands emerging at energies lower than in the neutral compounds. The formation of the dication is only detected for the heptamer and the octamer, and shows a new band at intermediate energies. Optical data are interpreted with the help of density functional theory calculations performed at the B3LYP/6-31G** level, both for the neutral and the oxidized compounds.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75765/1/5481_ftp.pd

A well-tempered density functional theory of electrons in molecules

Reporting extensions of a recently developed approach to density functional theory with correct long-range be-havior (Phys. Rev. Lett. 94, 043002 (2005)). The central quantities are a splitting functional gamma[n] and a complementary exchange-correlation functional. We give a practical method for determining the value of \gamma in molecules, assuming an approximation for XC energy is given. The resulting theory shows good ability to reproduce the ionization potentials for various molecules. However it is not of sufficient accuracy for forming a satisfactory framework for studying molecular properties. A somewhat different approach is then adopted, which depends on a density-independent \gamma and an additional parameter w eliminating part of the local exchange functional. The values of these two parameters are obtained by best-fitting to experimental atomization energies and bond-lengths of the molecules in the G2(1) database. The optimized values are gamma=0.5 a_0^{-1} and w=0.1 . We then examine the performance of this slightly semi-empirical functional for a variety of molecular properties, comparing to related works and to experiment. We show that this approach can be used for describing in a satisfactory manner a broad range of molecular properties, be they static or dynamic. Most satisfactory is the ability to describe valence, Rydberg and inter-molecular charge-transfer excitations