Trimer Geometry Research Articles

Self-assembly of trimer colloids: effect of shape and interaction range.

Trimers with one attractive bead and two repulsive beads, similar to recently synthesized trimer patchy colloids, were simulated with flat-histogram Monte Carlo methods to obtain the stable self-assembled structures for different shapes and interaction potentials. Extended corresponding states principle was successfully applied to self-assembling systems in order to approximately collapse the results for models with the same shape, but different interaction range. This helps us directly compare simulation results with previous experiment, and good agreement was found between the two. In addition, a variety of self-assembled structures were observed by varying the trimer geometry, including spherical clusters, elongated clusters, monolayers, and spherical shells. In conclusion, our results help to compare simulations and experiments, via extended corresponding states, and we predict the formation of self-assembled structures for trimer shapes that have not been experimentally synthesized.

Strengthening gold–gold bonds by complexing gold clusters with noble gases

We report an unexpectedly strong and complex chemical bonding of rare-gas atoms to neutral gold clusters. The bonding features are consistently reproduced at different levels of approximation within density-functional theory and beyond: from GGA, through hybrid and double-hybrid functionals, up to renormalized second-order perturbation theory. The main finding is that the adsorption of Ar, Kr, and Xe reduces electron–electron repulsion within gold dimer, causing strengthening of the AuAu bond. Differently from the dimer, the rare-gas adsorption effects on the gold trimer's geometry and vibrational frequencies are mainly due to electron occupation of the trimer's lowest unoccupied molecular orbital. For the trimer, the theoretical results are also consistent with far-infrared multiple photon dissociation experiments.

A Polarizable and Transferable PHAST N2 Potential for Use in Materials Simulation.

A polarizable and transferable intermolecular potential energy function, potentials with high accuracy, speed, and transferability (PHAST), has been developed from first principles for molecular nitrogen to be used in the modeling of heterogeneous processes such as materials sorption and separations. A five-site (van der Waals and point charge) anisotropic model, that includes many-body polarization, is proposed. It is parametrized to reproduce high-level electronic structure calculations (CCSD(T) using Dunning-type basis sets extrapolated to the CBS limit) for a representative set of dimer potential energy curves. Thus it provides a relatively simple yet robust and broadly applicable representation of nitrogen. Two versions are developed, differing by the type of mixing rules applied to unlike Lennard-Jones potential sites. It is shown that the Waldman-Hagler mixing rules are more accurate than Lorentz-Berthelot. The resulting potentials are demonstrated to be effective in modeling neat nitrogen but are designed to also be useful in modeling N2 interactions in a large array of environments such as metal-organic frameworks and zeolites and at interfaces. In such settings, capturing anisotropic forces and interactions with (open and coordinated) metals and charged/polar environments is essential. In developing the potential, it was found that adding a seemingly redundant dimer orientation, slip-parallel (S), improved the transferability of the potential energy surface (PES). Notably, one of the solid phases of nitrogen was not as accurately represented energetically without including S in the representative set. Liquid simulations, however, were unaffected and worked equally well for both potentials. This suggests that accounting for a wide variety of configurations is critical in designing a potential that is intended for use in heterogeneous environments where many orientations, including those not commonly explored in the bulk, are possible. Testing and validation of the potential are achieved via simulations of a thermal distribution of trimer geometries compared to analogous high level electronic structure calculations and molecular simulations of bulk pressure-density isotherms across the vapor, supercritical, and liquid phases. Crystal lattice parameters and energetics of the α-N2 and γ-N2 solid phases are also evaluated and determined to be in good agreement with experiment. Thus the proposed potential is shown to be efficacious for gas, liquid, and solid use, representing both disordered and ordered configurations.

Theoretical Investigation of the Cooperativity in CH3CHO·2H2O, CH2FCHO·2H2O, and CH3CFO·2H2O Systems

The hydrogen bond interaction between CH3CHO, CH2FCHO, and CH3CFO and two water molecules is investigated at the B3LYP/6-311++G(d,p) level. The results are compared with the complexes involving the same carbonyl derivatives and one water molecule. The calculations involve the optimization of the structure, the harmonic vibrational frequencies, and relevant NBO (natural bond orbital) parameters such as the NBO charges, the occupation of antibonding orbitals, and intra- and intermolecular hyperconjugation energies. Two stable cyclic structures are predicted. The two structures are stabilized by C=O⋯HO hydrogen bond. The A structures are further stabilized by CH⋯O bond involving the CH3 (CH2F) group. This bond results in an elongation of the CH bond and red shift of the ν(CH) vibration. The B structures are stabilized by CH⋯O interaction involving the aldehydic CH bond. The formation of this bond results in a marked contraction of the CH bond and blue shift of the ν(CH) vibration indicating the predominance of the lone pair effect in determining the CH distances. The total interaction energies range from −12.40 to −13.50 kcal mol−1. The cooperative energies calculated at the trimer geometry are comprised between −2.30 and −2.60 kcal mol−1.

A molecular H2 potential for heterogeneous simulations including polarization and many-body van der Waals interactions

A highly accurate aniostropic intermolecular potential for diatomic hydrogen has been developed that is transferable for molecular modeling in heterogeneous systems. The potential surface is designed to be efficacious in modeling mixed sorbates in metal-organic materials that include sorption interactions with charged interfaces and open metal sites. The potential parameters are compatible for mixed simulations but still maintain high accuracy while deriving dispersion parameters from a proven polarizability model. The potential includes essential physical interactions including: short-range repulsions, dispersion, and permanent and induced electrostatics. Many-body polarization is introduced via a point-atomic polarizability model that is also extended to account for many-body van der Waals interactions in a consistent fashion. Permanent electrostatics are incorporated using point partial charges on atomic sites. However, contrary to expectation, the best potentials are obtained by permitting the charges to take on values that do not reproduce the first non-vanishing moment of the electrostatic potential surface, i.e., the quadrupole moment. Potential parameters are fit to match ab initio energies for a representative range of dimer geometries. The resulting potential is shown to be highly effective by comparing to electronic structure calculations for a thermal distribution of trimer geometries, and by reproducing experimental bulk pressure-density isotherms. The surface is shown to be superior to other similarly portable potential choices even in tests on homogeneous systems without strong polarizing fields. The present streamlined approach to developing such potentials allows for a simple adaptation to other molecules amenable to investigation by high-level electronic structure methods.

Cooperative mechanism for anchoring highly polar molecules at an ionic surface

Structure formation of the highly polar molecule cytosine on the (111) cleavage plane of calcium fluoride is investigated in ultrahigh vacuum using noncontact atomic force microscopy at room temperature. Molecules form well-defined trimer structures, covering the surface as homogeneously distributed stable structures. Density-functional theory calculations yield a diffusion barrier of about 0.5 eV for individual molecules suggesting that they are mobile at room temperature. Furthermore, it is predicted that the molecules can form trimers in a configuration allowing all molecules to attain their optimum adsorption position on the substrate. As the trimer geometry facilitates hydrogen bonding between the molecules within the trimer, we conclude that the stabilization of individual diffusing molecules into stable trimers is due to a cooperative mechanism involving polar interactions between molecules and substrate as well as hydrogen bonding between molecules.

Effects of cluster formation on spectra of benzo[ a]pyrene and benzo[ e]pyrene

Absorption and fluorescence emission spectra of the polycyclic aromatic hydrocarbons benzo[ a]pyrene (BaP) and benzo[ e]pyrene (BeP) in solution and adsorbed on silica have been obtained and compared to examine the spectroscopic effects of clustering. Molecular mechanics calculations with the UFF potential were done to optimize monomer, dimer and trimer geometries, and energy differences were determined by MP2/6-31G∗ calculations. Fluorescence emission spectra of adsorbed BeP and BaP display a red shift that progresses with increased loading, and the two differ in their photodegradation kinetics. The experimental and theoretical results are found to be consistent.

Ab initio three-body interactions for water. I. Potential and structure of water trimer

A new ab initio three-body potential for water has been generated from the Hartree–Fock method and symmetry-adapted perturbation theory calculations performed at 7533 trimer geometries. The calculated nonadditive energies were then fitted to a physically motivated analytic formula containing representations of short-range exchange contributions and damped induction terms. To our knowledge, this is the first time the short-range nonadditive interactions have been explicitly included in a potential for water. The fitted nonadditive potential was then applied, together with an accurate ab initio pair potential, SAPT-5s, to evaluate the effects of nonadditivity on the structure and energetics of water trimer.

Self-assembly of a porphyrin array via the molecular recognition approach: synthesis and properties of a cyclic zinc(II) porphyrin trimer based on coordination and hydrogen bonding.

Self-assembly of [5-(pyrazol-4-yl)-10,20-bis(p-tolyl)-15- (2-ethoxycarbonylphenyl)porphyrinato]-zinc(II) (1), designed to have both a coordination site and a hydrogen bonding site, leads to a stable cyclic trimer array where coordination of the pyrazole nitrogen to the zinc(II) ion as well as hydrogen bonding between carbonyl oxygen and pyrazole NH holds each zinc(II) porphyrin. The recognition event for pyrazole has been confirmed preliminarily in the model studies using [5-(2-ethoxycarbonylphenyl)tris(p-tolyl)porphyrinato]-zinc(II) (3). The zinc(II) porphyrin 3 has large affinity for pyrazole due to the hydrogen bond between pyrazole and the 2-ethoxycarbonyl group in addition to the coordination bonding accompanied by the conformational change of the ethoxycarbonyl group in the coordination process. The (1)H NMR, IR, and UV-vis spectra of 1 and its ESI-MS and VPO measurements have revealed the cyclic trimer structure with an overall association constant of 6.0 x 10(13) M(-2) at 22 degrees C. The contribution of the hydrogen bond to the total free energy change in trimer formation is estimated to be 7.5 kcal/mol based on a reference trimer system without a hydrogen bonding site. The trimer geometry causes characteristic exitonic interaction between porphyrin units to yield a broad Soret band which is deconvoluted into four components by UV-vis and MCD spectral analyses. Electrochemical measurements have shown that only the first ring-oxidation process proceeds stepwise in the trimer.

Transferable ab Initio Intermolecular Potentials. 1. Derivation from Methanol Dimer and Trimer Calculations

An intermolecular potential was derived from ab initio calculations on methanol dimers and trimers. Ninety-four methanol dimer geometries and seventeen trimer geometries have been studied using an interaction-optimized basis set. Because we aimed at transferability, all terms of the model were fitted separately, in order to obtain a potential in which these energy terms have a well-defined physical meaning. Electrostatic interactions were described by atomic multipole moments obtained by fitting to the monomer electrostatic potential. The polarization energy was modeled using atomic dipole polarizabilities. Scaled empirical polarizabilities reproduced the energy nonadditivity in methanol trimers very accurately. The dispersion energy was described by a damped r-6 atom−atom potential, which was fitted to separately calculated dispersion energies. Exchange energy and remaining short-ranged terms were modeled by an exponential repulsion term, including some anisotropic features. This repulsion model was fitt...

All-electron local and gradient-corrected density-functional calculations of Nan dipole polarizabilities for n=1-6.

Sodium clusters represent an experimentally accessible and seemingly simple system for studying the size dependence of the optical properties of metal clusters. Nevertheless, with the exception of the atom and dimer, previous ab initio calculations have either been restricted to correlated calculations in which pseudopotentials were used in order to reduce sodium to an effective one-electron atom or correlation effects were entirely neglected. The present study presents the results of correlated all-electron density-functional calculations of sodium-cluster dipole polarizabilities for clusters through the hexamer. In particular, polarizabilities were calculated at the local-density-approximation- (LDA-) optimized geometries using the LDA functional, with the Perdew-Wang 1986 exchange plus the Perdew 1986 correlation (PW86x+P86c) gradient corrections, and with the Becke 1988 exchange plus the Perdew 1986 correlation (B88x+P86c) gradient corrections. The results are compared with the available experimental and ab initio theoretical values. Of the three exchange-correlation functionals presented in this paper, the mean polarizabilities calculated using the B88x+P86c functional are in best agreement with the experimental values, with discrepancies between theory and experiment of only 3.5% for the atom and 5% for the dimer. Differences between the experimental and B88x+P86c optimized dimer and trimer geometries are also significantly smaller than in the LDA case. However, there is little difference between mean polarizabilities calculated at the LDA-optimized, B88x+P86c optimized, and experimental geometries. In particular, this cannot explain the 11--22 % discrepancies found here between the experimental polarizabilities for the trimer and higher-order clusters and those calculated at the LDA-optimized geometries using the B88x+P86c functional. It is suggested that molecular motion may need to be taken into account before a completely satisfactory explanation of the experimental polarizabilities of these floppy molecules can be given.

The photoionization and dissociation dynamics of energy-selected acetylene dimers, trimers, and tetramers

The photoionization and dissociation characteristics of (C2H2)n (n=2, 3, and 4) have been studied by the threshold photoelectron–photoion coincidence technique applied to a molecular beam. For photon energies between 10.20 and 11.27 eV, only dissociative ionization pathways were observed for the clusters; no direct ionization of (C2H2)2, (C2H2)3, and (C2H2)4 to the stable ions C4H4+, C6H6+, and C8H8+ was observed. The shape of the time of flight peaks is consistent with statistical dissociation dynamics, and statistical analysis of the fragment peak shapes suggests that the dimer, trimer, and tetramer produce the fragments C4H2+/C4H3+, C4H4+, and C6H6+, respectively. Consistent with these observations, ab initio calculations are presented which indicate that the neutral T-shaped dimer and triangular trimer geometries are unstable on the ionic potential energy surface, and indeed have vertical ionization energies well above the dissociation limits of many of their possible product channels. The statistical modeling of the C4H4+ peak width is consistent with a process in which the trimer neutral produces a C4H4+–C2H2 complex, which then dissociates via monomer evaporation without exploring any of the covalent C6H6+ potential energy surface, i.e., benzene ion is not formed. The heat of formation of the observed C4H4+ daughter is estimated to be 1240±15 kJ/mol, indicating that it is cyclobutadiene, butatriene, or vinylacetylene ion. The peak width of C6H6+ is also analyzed, and suggests a process whereby the tetramer produces a C6H6+–C2H2 complex, which dissociates via monomer evaporation without exploring any of the covalent C8H8+ potential energy surface. The heat of formation of the C6H6+ daughter fragment is estimated as 1160±15 kJ/mol, which is consistent with the formation of benzvalene ion.

Low-energy electron diffraction studies of Si(111)-(√3 × √3)R30°-Bi system: Observation and structural determination of two phases

The initial epitaxial growth of Bi on a Si(111)-7 × 7 surface has been studied as a function of overlayer coverage and deposition conditions using low-energy electron diffraction (LEED) and Auger electron spectroscopy (AES). Experiments show for the first time that two equilibrium phases are formed in the growth process, each displaying a (√3 × √3)R30° LEED symmetry: an α-phase occurring at 1 3 ML Bi coverage and substrate temperature of 360° C, and a β-phase at 1 ML and 300°C. Quantitative structural information for each phase was determined by multiple scattering analysis of I- V curves. The analysis is facilitated by comparing LEED intensity data measured for each phase with calculated values using appropriate structural models. The T 4 geometry for the α-phase and a trimer geometry for the β-phase are revealed to be the “best” models; detailed atomic coordinates have been determined for each phase.

The state of detergent solubilised light-harvesting chlorophyll- a/ b protein complex as monitored by picosecond time-resolved fluorescence and circular dichroism

Steady-state and picosecond time-resolved fluorescence techniques in conjunction with circular dichroism have been used to study the light-harvesting chlorophyll- a/ b protein complex (LHC) isolated from pea chloroplasts. In particular, the effect of changing the detergent / chlorophyll ratio on the state of the LHC has been investigated. Our results have been interpreted in light of the known protein geometry of the LHC in 2-dimensional crystals (Kühlbrandt, W. (1984) Nature 307, 478–479). The fluorescence lifetime data reveals 1 / e-lifetimes of 3.53 (±0.04) ns and 1.10 (±0.01) ns for a stable, efficiently energy-transferring state of the LHC. Subnanosecond lifetimes are observed under conditions leading to aggregation, while a long component of 5.50 (±0.16) ns corresponding to free Chl a is found when the detergent / chlorophyll ratio is high. The circular dichroism shows a major Chl- b exciton, a Chl- a / b exciton and a further ‘quenching’ Chl- b exciton. These have been attributed to: a C 3 symmetric Chl- b interaction for which the intact C 3 protein trimer geometry is a prerequisite; a dimeric Chl- a / b interaction, the presence of which is critically dependent on the detergent type; and a further Chl- b interaction which arises from the presence of aggregated trimers, respectively. We have found that the degree of heterogeneity with respect to the oligomeric state of the pigment-protein trimers is dependent upon the detergent / chlorophyll ratio used. Low detergent / chlorophyll ratios result in extensive aggregation of the trimers with a geometry similar to that found in 2-dimensional crystals of the LHC. Moderate detergent conditions yield predominantly non-aggregated trimers. Excess detergent conditions result in considerable chromophore heterogeneity and loss of the main Chl- b exciton consistent with protein denaturation through an initial break up of the trimer geometry. From these results we believe that in vitro the minimum stable functional unit corresponds to a C 3 symmetric protein trimer.

Infrared vibration-rotation spectrum of acetylene trimer

The infrared spectrum of acetylene trimer has been obtained in the 3 μm wavelength region by observing direct absorption of color center laser radiation by a pulsed molecular beam. The rotational structure of this band was that of a planar oblate symmetric top. The B rotational constant is 1885.8 MHz, which fixes the distance between the center of mass of each monomer and the center of mass of the trimer at 2.513 Å. This monomer separation is consistent with a trimer geometry of D 3h or C 3h symmetry, having atoms of adjacent monomer units close to van der Waals contact.

Structure of mixed group IB metal trimers

The structures of all mixed group IB trimers have been calculated in the diatomics-in-molecules (DIM) approximation. The optimum trimer geometries correspond to bent structures in C 2 or C 2 v symmetry. All trimers are bound with respect to dissociation to an atom plus a diatomic. The structures can all be characterized as having an “obtuse” structure with a bond angle greater than 60°. The structure of the trimer is controlled by the atom which forms the strongest diatomic bonds. This is confirmed by calculations on the possible linear structures. The most stable linear structure has the atom which forms the strongest diatomic bonds in the central position.