Work functions, ionization potentials, and in-between: Scaling relations based on the image charge model

We revisit a model in which the ionization energy of a metal particle is associated with the work done by the image charge force in moving the electron from infinity to a small cut-off distance just outside the surface. We show that this model can be compactly, and productively, employed to study the size dependence of electron removal energies over the range encompassing bulk surfaces, finite clusters, and individual atoms. It accounts in a straightforward manner for the empirically known correlation between the atomic ionization potential (IP) and the metal work function (WF), IP/WF$\sim$2. We formulate simple expressions for the model parameters, requiring only a single property (the atomic polarizability or the nearest neighbor distance) as input. Without any additional adjustable parameters, the model yields both the IP and the WF within $\sim$10% for all metallic elements, as well as matches the size evolution of the ionization potentials of finite metal clusters for a large fraction of the experimental data. The parametrization takes advantage of a remarkably constant numerical correlation between the nearest-neighbor distance in a crystal, the cube root of the atomic polarizability, and the image force cutoff length. The paper also includes an analytical derivation of the relation of the outer radius of a cluster of close-packed spheres to its geometric structure.Comment: Original submission: 8 pages with 7 figures incorporated in the text. Revised submission (added one more paragraph about alloy work functions): 18 double spaced pages + 8 separate figures. Accepted for publication in PR

Ab initio studies of structures and properties of small potassium clusters

We have studied the structure and properties of potassium clusters containing even number of atoms ranging from 2 to 20 at the ab initio level. The geometry optimization calculations are performed using all-electron density functional theory with gradient corrected exchange-correlation functional. Using these optimized geometries we investigate the evolution of binding energy, ionization potential, and static polarizability with the increasing size of the clusters. The polarizabilities are calculated by employing Moller-Plesset perturbation theory and time dependent density functional theory. The polarizabilities of dimer and tetramer are also calculated by employing large basis set coupled cluster theory with single and double excitations and perturbative triple excitations. The time dependent density functional theory calculations of polarizabilities are carried out with two different exchange-correlation potentials: (i) an asymptotically correct model potential and (ii) within the local density approximation. A systematic comparison with the other available theoretical and experimental data for various properties of small potassium clusters mentioned above has been performed. These comparisons reveal that both the binding energy and the ionization potential obtained with gradient corrected potential match quite well with the already published data. Similarly, the polarizabilities obtained with Moller-Plesset perturbation theory and with model potential are quite close to each other and also close to experimental data.Comment: 33 pages including 10 figure

Structure and Stability of Zn, Cd, and Hg Atom Doped Golden Fullerene (Au₃₂)

Structures and properties of various complexes formed between the “golden fullerene”, Au₃₂, and group IIB atoms such as Zn, Cd, and Hg have been investigated using density functional theory (DFT). Binding energy values indicate that the group IIB atoms can form stable clusters in most of the different isomeric forms of the Au₃₂ cage. The HOMO–LUMO gap of the Au₃₂ cage remains almost the same even after doping of Zn, Cd, and Hg atoms for high symmetry clusters, while it decreases for the low symmetry isomers. The highest stable isomer for the Hg-doped Au₃₂ cluster is found to be associated with <i>I</i>_<i>h</i> symmetry with a large energy difference from the other low symmetry isomers, using generalized gradient approximation (GGA) type functionals. However, for the Zn and Cd encapsulated Au₃₂ clusters, the highest stable structures are of <i>C_s</i>[1] and <i>C</i>_5<i>v</i> symmetry, respectively, along with one low symmetry isomer for each of them, having energy very close to the respective most stable isomer. Nevertheless, depending on the energy density functional, the relative energy orderings for the various isomers are found to be modified strongly. In fact, the meta-GGA TPSS functional predicts low symmetry compact isomers to be more stable for all the metal atom doped Au₃₂ clusters. Moreover, low symmetry compact isomers are found to be more stable with the dispersion-corrected GGA type PBE functional for the Zn- and Cd-doped cluster, in agreement with the TPSS results; however, the same dispersion correction fails to reproduce the TPSS results for the Hg-doped Au₃₂ system. Structural data, energetic parameters, and spectral analysis point toward the possible experimental observation of group IIB atom doped golden fullerene, which in turn might help to understand the nature of interactions between the metal atom and the Au₃₂ cage. Furthermore, experimental investigations would likely confirm the predictive ability of the different functionals used in this work

Twisting dynamics in the excited singlet state of Michler's ketone

Ultrafast relaxation dynamics of the excited singlet (S<SUB>1</SUB>) state of Michler's ketone (MK) has been investigated in different kinds of solvents using a time-resolved absorption spectroscopic technique with 120 fs time resolution. This technique reveals that conversion of the locally excited (LE) state to the twisted intramolecular charge transfer (TICT) state because of twisting of the N,N-dimethylanilino groups with respect to the central carbonyl group is the major relaxation process responsible for the multi-exponential and probe-wavelength-dependent transient absorption dynamics of the S<SUB>1</SUB> state of MK, but solvation dynamics does not have a significant role in this process. Theoretical optimization of the ground-state geometry of MK shows that the dimethylanilino groups attached to the central carbonyl group are at a dihedral angle of about 51&#176; with respect to each other because of steric interaction between the phenyl rings. Following photoexcitation of MK to its S<SUB>1</SUB> state, two kinds of twisting motions have been resolved. Immediately after photoexcitation, an ultrafast "anti-twisting" motion of the dimethylanilino groups brings back the pretwisted molecule to a near-planar geometry with high mesomeric interaction and intramolecular charge transfer (ICT) character. This motion is observed in all kinds of solvents. Additionally, in solvents of large polarity, the dimethylamino groups undergo further twisting to about 90&#176; with respect to the phenyl ring, to which it is attached, leading to the conversion of the ICT state to the TICT state. Similar characteristics of the absorption spectra of the TICT state and the anion radical of MK establish the nearly pure electron transfer (ET) character of the TICT state. In aprotic solvents, because of the steep slope of the potential energy surface near the Franck-Condon (FC) or LE state region, the LE state is nearly nonemissive at room temperature and fluorescence emission is observed from only the ICT and TICT states. Alternatively, in protic solvents, because of an intermolecular hydrogen-bonding interaction between MK and the solvent, the LE region is more flat and stimulated emission from this state is also observed. However, a stronger hydrogen-bonding interaction between the TICT state and the solvent as well as the closeness between the two potential energy surfaces due to the TICT and the ground states cause the nonradiative coupling between these states to be very effective and, hence, cause the TICT state to be weakly emissive. The multi-exponentiality and strong wavelength-dependence of the kinetics of the relaxation process taking place in the S<SUB>1</SUB> state of MK have arisen for several reasons, such as strong overlapping of transient absorption and stimulated emission spectra of the LE, ICT, and TICT states, which are formed consecutively following photoexcitation of the molecule, as well as the fact that different probe wavelengths monitor different regions of the potential energy surface representing the twisting motion of the excited molecule