First-principles calculations of electronic excitations in clusters (original) (raw)
Related papers
First-principles approach to the calculation of electronic spectra in clusters
Computational Materials Science, 1998
We discuss a method for first-principles calculations of photoemission spectra in small clusters, going well beyond a standard density functional theory-local density approximation (DFT-LDA) approach. Starting with a DFT-LDA calculation, we evaluate self-energy contributions to the quasiparticle energies of an electron or hole in the G W scheme, where the selfenergy C = G W is constructed from the one-particle Green's function G and the RPA screened Coulomb interaction W. The contributions of structural relaxation are taken into account. We show the importance of these effects at the example of the photoemission spectrum of SiH4. We also briefly discuss results for longer hydrogenated silicon chains, and address the problem of optical absorption.
WIREs Computational Molecular Science, 2019
While methodological developments in the last decade made it possible to compute coupled cluster (CC) energies including excitations up to a perturbative triples correction for molecules containing several hundred atoms, a similar breakthrough has not yet been reported for excited state computations. Accurate CC methods for excited states are still expensive, although some promising candidates for an efficient and accurate excited state CC method have emerged recently. This review examines the various approximation schemes with particular emphasis on their performance for excitation energies and summarizes the best state-of-the-art results which may pave the way for a robust excited state method applicable to molecules of hundreds of atoms. Among these, special attention will be given to exploiting the techniques of similarity transformation, perturbative approximations as well as integral decomposition, local and embedding techniques within the equation of motion CC framework.
The Journal of chemical …, 1996
Algorithms for calculating singlet excitation energies in the coupled cluster singles and doubles ͑CCSD͒ model are discussed and an implementation of an atomic-integral direct algorithm is presented. Each excitation energy is calculated at a cost comparable to that of the CCSD ground-state energy. Singlet excitation energies are calculated for benzene using up to 432 basis functions. Basis-set effects of the order of 0.2 eV are observed when the basis is increased from augmented polarized valence double-zeta ͑aug-cc-pVDZ͒ to augmented polarized valence triple-zeta ͑aug-cc-pVTZ͒ quality. The correlation problem is examined by performing calculations in the hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3, as well as by using the CCSDR͑3͒ perturbative triples corrections. The effect of triple excitations are less than 0.2 eV for all excitations except for the 2 1 E 2g state. The calculated excitation energies are compared with experiment and other theoretical results.
Theoretical Studies of Structural, Energetic, and Electronic Properties of Clusters
Zeitschrift für Physikalische Chemie, 2008
Size in combination with low symmetry makes theoretical studies of the properties of clusters a challenge. This is in particular the case when the studies also shall identify the structures of the lowest total energy. We discuss here various methods for calculating the structural, energetic, and electronic properties of nanoparticles, emphasizing that the computational method always should be chosen carefully according to the scientific questions that shall be addressed. Therefore, different approximate methods for calculating the total energy of a given structure are discussed, including the embedded-atom method and a parameterized density-functional method. Moreover, different approaches for choosing/determining the structures are presented, including an Aufbau/Abbau method and genetic algorithms. In order to illustrate the approaches we present results from calculations on metallic and semiconducting nanoparticles as well as on nanostructured HAlO.
Physical Review A, 2001
All-electron calculations in large basis sets of excitation energies, oscillator strengths, and polarizabilities of small alkali-metal clusters of Li, Na, and K, with up to eight atoms, are performed using time-dependent density-functional theory. It is shown that the use of the recently developed statistical average of orbital potentials ͑SAOP͒ exchange-correlation ͑xc͒ potential ͓P.R.T. Schipper et al., J. Chem. Phys. 112, 1344 ͑2000͔͒ leads to polarizabilities of these alkali-metal clusters which are 10-15 % larger than polarizabilities calculated with the xc potential of the local-density approximation ͑LDA͒. The lower LDA polarizabilities ͑in comparison to the SAOP͒ are shown to originate from differences in the low-lying excitation energies, which are determined by the xc potential in the molecular inner and valence region. In spite of such differences, both SAOP and LDA results are shown to provide reliable assignments of the experimental absorption spectra, with typical errors in peak positions of only 0.1-0.2 eV, or even less.
Physical Review B, 1996
The ground state geometries of some small clusters have been obtained via ab initio molecular dynamical simulations by employing density based energy functionals. The approximate kinetic energy functionals that have been employed are the standard Thomas-Fermi (TTF)(T_{TF})(TTF) along with the Weizsacker correction TWT_WTW and a combination F(Ne)TTF+TWF(N_e)T_{TF} + T_WF(Ne)TTF+TW. It is shown that the functional involving F(Ne)F(N_e)F(Ne) gives superior charge densities and bondlengths over the standard functional. Apart from dimers and trimers of Na, Mg, Al, Li, Si, equilibrium geometries for LinAl,n=1,8Li_nAl, n=1,8LinAl,n=1,8 and Al13Al_{13}Al13 clusters have also been reported. For all the clusters investigated, the method yields the ground state geometries with the correct symmetries with bondlengths within 5\% when compared with the corresponding results obtained via full orbital based Kohn-Sham method. The method is fast and a promising one to study the ground state geometries of large clusters.
The Journal of Chemical Physics, 2001
An extensive benchmarking of exchange-correlation functionals, pseudopotentials, and basis sets on real X-ray resolved nanoclusters has been carried out and reported here for the first time. The systems investigated and used for the tests are two undecagold and one Au + 24 -based nanoparticles stabilized by thiol and phosphine ligands. Time-dependent density-functional calculations have been performed for comparing results with experimental data on optical gaps. It has been observed that GGA functionals employing PBE-like correlation (viz. PBE itself, BPBE, BP86, and BPW91) coupled with an improved version of the LANL2DZ pseudopotential and basis set provide fairly accurate results for both structure and optical gaps of gold nanoparticles, at a reasonable computational cost. Good geometries have been also obtained using some global hybrid (e.g. PBE0, B3P86, B3PW91) and range separated hybrid (e.g. HSE06, LC-BLYP) functionals, even though they yield optical gaps that constantly overestimate the experimental findings. To probe the effect of the stabilizing organic ligands on the structural and electronic properties of the metal core, we have simulated the full metalorganic nanoparticles (whose diameter exceed the 2 nm threshold) with an ONIOM QM/QM' approach and at the density-functional level of theory. This work represents a first step toward the simulations of structural and opto-electronic properties of larger metal-organic particles suitable for a wide range of nanotechnological applications.
Electronic excitations: density-functional versus many-body Green’s-function approaches
Reviews of Modern Physics, 2002
Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.
Molecular electronic excitations calculated from a solid-state approach: Methodology and numerics
Physical Review B, 2005
We investigate the applicability and accuracy of a solid-state approach, which was developed originally for the relatively homogeneous electron gas, to describe electronic single-particle and electron-hole pair excitations in molecules. Thereby we start from the determination of the molecular ground state within the local density functional theory using repeated supercells and pseudopotentials for the electron-ion interaction. The electronic spectra are obtained from the Green's function formalism. The exchange-correlation self-energy ⌺ is linearly expanded in the screened Coulomb interaction, i.e., the GW approximation is used. Optical spectra are obtained from the Bethe-Salpeter equation for the irreducible polarization propagator. The numerical implementation and possible pitfalls of this methodology are discussed using silane, disilane, and water molecules as examples. In particular the influence of the dynamics of the screening, the supercell size, and the number of empty states are studied. The resulting single-and two-particle excitation energies are compared with experiment and previous theoretical work.
Coupled cluster methods including triple excitations for excited states of radicals
The Journal of Chemical Physics, 2005
We report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock ͑UHF͒ and spin-restricted open-shell Hartree-Fock ͑ROHF͒ reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N 7) computational steps and avoids storage of the triple-excitation amplitudes for both the ground-and excited-state calculations. The excitation-energy program makes use of a Löwdin projection formalism ͑comparable to that of earlier implementations͒ that allows computational reduction of the Davidson algorithm to only the single-and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence 2 B 1 state of the allyl radical, low-lying states of the CH and CO ϩ diatomics, and the nitromethyl radical show substantial improvement over ROHF-and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the 2 ⌺ ϩ state of CH, significant errors of more than 0.4 eV remain.