During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells1, graphite has been vaporized by laser irradiation, producing a remarkably stable cluster consisting of 60 carbon atoms. Concerning the question of what kind of 60-carbon atom structure might give rise to a superstable species, we suggest a truncated icosahedron, a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal. This object is commonly encountered as the football shown in Fig. 1. The C60 molecule which results when a carbon atom is placed at each vertex of this structure has all valences satisfied by two single bonds and one double bond, has many resonance structures, and appears to be aromatic. Before 1985, it was generally accepted that elemental carbon exists in two forms, or allotropes: diamond and graphite. Then, Kroto et al. identified the signature of a new, stable form of carbon that consisted of clusters of 60 atoms. They called this third allotrope of carbon 'buckminsterfullerene', and proposed that it consisted of polyhedral molecules in which the atoms were arrayed at the vertices of a truncated icosahedron. In 1990, the synthesis of large quantities of C60 [see Nature 347, 354–358 (1990)] confirmed this hypothesis.

C 60 : Buckminsterfullerene

A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

The density functional formalism, its applications and prospects

We present a systematic study for numerical atomic basis orbitals ranging from H to Kr, which could be used in large scale $\mathrm{O}(N)$ electronic structure calculations based on density-functional theories (DFT). The comprehensive investigation of convergence properties with respect to our primitive basis orbitals provides a practical guideline in an optimum choice of basis sets for each element, which well balances the computational efficiency and accuracy. Moreover, starting from the primitive basis orbitals, a simple and practical method for variationally optimizing basis orbitals is presented based on the force theorem, which enables us to maximize both the computational efficiency and accuracy. The optimized orbitals well reproduce convergent results calculated by a larger number of primitive orbitals. As illustrations of the orbital optimization, we demonstrate two examples: the geometry optimization coupled with the orbital optimization of a ${\mathrm{C}}_{60}$ molecule and the preorbital optimization for a specific group such as proteins. They clearly show that the optimized orbitals significantly reduce the computational efforts, while keeping a high degree of accuracy, thus indicating that the optimized orbitals are quite suitable for large scale DFT calculations.

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Numerical atomic basis orbitals from H to Kr

Synthesis of nanoparticles in the gas phase for electronic, optical and magnetic applications—a review

A pedagogical overview of intramolecular vibrational redistribution (IVR) phenomena in vibrationally excited molecules is presented. In the interest of focus and simplicity, the topics covered deal primarily with IVR in the ground electronic state, relying on examples from the literature to illustrate key points. The experimental topics discussed attempt to sample systematically three different energy regimes on the full potential surface corresponding to (i) “low”, e.g., moderate- to high-resolution vibrational spectroscopies, (ii) “intermediate”, e.g., stimulated emission pumping and high overtone spectroscopies, and (iii) “high”, e.g., photofragment/predissociation dynamical spectroscopies. The interplay between experiment and theory is highlighted here because it has facilitated enormous advances in the field over the past decade.

Vibrational Energy Flow in Highly Excited Molecules: Role of Intramolecular Vibrational Redistribution

Copper clusters ranging in size from 1 to 29 atoms have been prepared in a supersonic beam by laser vaporization of a rotating copper target rod within the throat of a pulsed supersonic nozzle using helium for the carrier gas. The clusters were cooled extensively in the supersonic expansion [T(translational) 1 to 4 K, T(rotational)=4 K, T(vibrational)=20 to 70 K]. These clusters were detected in the supersonic beam by laser photoionization with time‐of‐flight mass analysis. Using a number of fixed frequency outputs of an exciplex laser, the threshold behavior of the photoionization cross section was monitored as a function of cluster size. The 7.9 eV photon energy of the F2 excimer laser was found to be above the ionization potential of all clusters, and the photoion mass spectrum thus produced showed the copper cluster concentration in the beam to follow a monotonically decreasing function of cluster size. The 6.4 eV ArF exciplex laser photon energy was found to be above the photoionization threshold of clusters with three or more atoms in the case of odd‐numbered clusters, but only for clusters with eight or more atoms for even‐numbered clusters. Extending out to clusters as large as 29 atoms, laser photoionization at 6.4 eV produced a time‐of‐flight mass distribution with a pronounced even/odd alternation in cluster photoion intensity. This alternation in ionization threshold behavior was attributed to an even/odd alternation in the electronic structure of the copper clusters with the highest occupied molecular orbital (HOMO) of the even clusters being considerably more strongly bonding than it is in the clusters with an odd number of copper atoms. The 4.98 eV photon energy of the KrF exciplex laser was found to lie below the ionization threshold of all clusters in the 1 to 29 atom range. An extensive survey of the ultraviolet absorption spectrum of the copper dimer was also performed with this supersonic beam source. Resonance two‐photon ionization (R2PI) with mass selective detection allowed the detection of five new electronic band systems in the region between 2690 and 3200 A, for each of the three naturally occurring isotopic forms of Cu2. In the process of scanning the R2PI spectrum of these new electronic states, the ionization potential of the copper dimer was determined to be 7.894±0.015 eV.

Supersonic copper clusters

Laser vaporization of a rotating metal target within a pulsed supersonic nozzle has been used to produce ultracold beams of copper clusters Photoionization with an argon fluoride excimer laser followed by time-of-flight mass spectrometric analysis showed the cold beam to contain clusters in the range from 1 through 13 copper atoms The ionization potential (IP) of the small clusters was seen to alternate above and below the 64-eV laser photon energy depending upon whether the cluster contained an een (high IP) or odd (low IP) number of copper atoms The absorption spectrum of Cu/sub 2/ was recorded in the 4480 to 4660-A region by using two-color resonant two-photon ionization The Cu/sub 2/ cluster beam was found to have translational, rotational, and vibrational temperatures of < 5, < 10, and 50 to 100/sup 0/K, respectively In addition to the known B /sup 1/sigma/sup +//sub u/ reverse arrow X /sup 1/sigma/sup +//sub g/ band system, a new system was found in the same spectral range Parameters for the new system were T/sub e/ = 21,867 +- 4 cm/sup -1/, omega'/sub e/ = 226 +- 3 cm/sup -1/, omega/sub e/ chi'/sub e/ = 3 +- 2 cm/sup -1/ The lifetime of the Bmore » state was found to be 35 +- 10 ns for the vibrational levels nu' = 0 and 1, and it is argued this short lifetime is likely due to predissociation The lifetime of the new C state was found to be 10 +- 02 mus 4 figures, 1 table« less

Supersonic metal cluster beams: laser photoionization studies of copper cluster (Cu2)

Fluorescence excitation spectra of a series of alkylbenzenes cooled in a supersonic free jet have been obtained for the first 1000 cm−1 region of the 1B2(ππ*)←1A1 ultraviolet absorption spectrum. The series includes all n‐alkylbenzenes up to n‐hexyl together with isopropyl‐ and tert‐butylbenzene. As with toluene, the spectra in this region for all alkylbenzenes is found to be dominated by vibrations of five ring modes: 6a, 6b, 1, 12, and 18a. Three of these—the ’’system modes’’ (6b, 12, 18a)—are found to be largely invariant to changes in the alkyl chain length and type— the ’’bath.’’ For n‐alkylbenzenes with chain length of three or higher, spectra of two distinct conformations are observed with roughly equal intensity. These conformations are distinguished by configuration about the 1–2 carbon–carbon bond of the alkyl chain. When this configuration is trans [n‐(t)‐alkylbenzene], the alkyl chain extends away from the phenyl ring leaving the ring free to van der Waals complex binding on both sides of the ...

Vibrational relaxation in jet‐cooled alkyl benzenes. I.Absorption spectra

Fluorescence excitation spectra have been recorded for the first 6000 cm−1 of the ultraviolet spectrum of h8‐ and d8‐naphthalene cooled in a supersonic free jet. Measured profiles of vibronic bands in these spectra display a monotonically increasing width as a function of vibrational energy (Ev) in the excited electronic state. The high fluorescence quantum yield and relatively constant fluorescence lifetimes in these spectral regions require the measured line broadening to be assigned to intramolecular vibrational relaxation (IVR) within the excited electronic state. The rate of this IVR process as measured by the width of the broadened profiles increases smoothly from 9×1010 sec−1 at Ev=3068 cm−1 to 7×1011 sec−1 at Ev=5200 cm−1 for h8‐naphthalene. Line profiles of d8‐naphthalene in this same spectral region are found to be ∼50% wider.

D. E. Powers

Papers

Supersonic copper clusters

Supersonic metal cluster beams: laser photoionization studies of copper cluster (Cu2)

Vibrational relaxation in jet‐cooled alkyl benzenes. I.Absorption spectra

Jet‐cooled naphthalene. I. Absorption spectra and line profiles

Mass-selective two-color photoionization of benzene clusters