Optical Properties of Monolayer-Protected Aluminum Clusters: Time-Dependent Density Functional Theory Study

We examine the electronic and optical properties of experimentally known monolayer-protected aluminum clusters Al4(C5H5)4, Al50(C5Me5)12, and Al69(N(SiMe3)2)183– using time-dependent density functional theory. By comparing Al4(C5H5)4 and the theoretical Al4(N(SiMe3)2)4 cluster, we observe significant changes in the optical absorption spectra caused by different hybridization between metal core and ligands. Using these initial observations, we explain the calculated spectra of Al50(C5Me5)12 and Al69(N(SiMe3)2)183–. Al50(C5Me5)12 shows a structured spectrum with clear regions of low-intensity core-to-core transitions followed by high-intensity ligand-to-core transitions due to its high symmet…

Covalent and non-covalent coupling of a Au102 nanocluster with a fluorophore: energy transfer, quenching and intracellular pH sensing

Interactions between an atomically precise gold nanocluster Au102(p-MBA)44 (p-MBA = para mercaptobenzoic acid) and a fluorescent organic dye molecule (KU, azadioxatriangulenium) are studied. In solution, the constituents form spontaneously a weakly bound complex leading to quenching of fluorescence of the KU dye via energy transfer. The KU can be separated from the complex by lowering pH, leading to recovery of fluorescence, which forms a basis for an optical reversible pH sensor. However, the sensor is not a stable entity, which could be delivered inside cells. For this purpose, a covalently bound hybrid is synthesized by linking the KU dye to the ligand layer of the cluster via an ester b…

Solvation of triplet Rydberg states of molecular hydrogen in superfluid helium

We report ab initio interaction potentials, transition dipole moments, and radiative lifetimes for the four lowest triplet states of ${\mathrm{H}}_{2}:$ $b$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+},$ $c$ ${}^{3}{\ensuremath{\Pi}}_{u},$ $a$ ${}^{3}{\ensuremath{\Sigma}}_{g}^{+},$ and $e$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+},$ and their response to the perturbation due to approaching ground state He atom. Hybrid density functional\char21{}quantum Monte Carlo calculations employing the ab initio interaction potentials are then used for calculating the liquid structure around the molecular excimers in bulk superfluid ${}^{4}\mathrm{He}.$ Calculations demonstrate a wide variety of possible solvation …

Dithiol-Induced Oligomerization of Thiol-Protected Gold Nanoclusters

Controlled synthesis of nanostructure oligomers requires detailed understanding of their wet chemistry and the forces driving the polymerization process. In this paper, we report the main factors affecting the reaction yields of a dithiol-induced synthesis of covalently bound nanocluster dimers and oligomers and present a detailed analysis of possible reaction mechanisms. We synthesize the nanocluster oligomers using monodisperse para-mercaptobenzoic acid (p-MBA)-protected gold nanoclusters with a nominal composition of Au∼250(p-MBA)n to minimize ensemble effects on size, shape, and surface structure. Ligand exchange was performed on the nanoclusters with five different dithiol linkers: 5,5…

Covalent and non-covalent coupling of a Au102 nanocluster with a fluorophore : energy transfer, quenching and intracellular pH sensing

Interactions between an atomically precise gold nanocluster Au102(p-MBA)44 (p-MBA = para mercaptobenzoic acid) and a fluorescent organic dye molecule (KU, azadioxatriangulenium) are studied. In solution, the constituents form spontaneously a weakly bound complex leading to quenching of fluorescence of the KU dye via energy transfer. The KU can be separated from the complex by lowering pH, leading to recovery of fluorescence, which forms a basis for an optical reversible pH sensor. However, the sensor is not a stable entity, which could be delivered inside cells. For this purpose, a covalently bound hybrid is synthesized by linking the KU dye to the ligand layer of the cluster via an ester b…

Time-dependent density-functional theory in the projector augmented-wave method

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born–Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear e…

Crystal Structures and Density Functional Theory Calculations of o-and p-Nitroaniline Derivatives: Combined Effect of Hydrogen Bonding and aromatic interactions on dimerization energy

The interplay of strong and weak hydrogen bonds, dipole–dipole interactions, and aromatic interactions of o- and p-nitroaniline derivatives was studied by combining crystal structure analysis and density functional theory (DFT) calculations. Crystal structures of four 2-nitroaniline derivatives, 2-((2-nitrophenyl)amino)ethyl methanesulfonate (1A), 2-((2-nitrophenyl)amino)ethyl 4-methylbenzenesulfonate (2A), N,N′-((1,3-phenylenebis(oxy))bis(ethane-2,1-diyl))bis(2-nitroaniline) (3A), and N-(2-chloroethyl)-2-nitroaniline (4A), and crystal structures of three 4-nitroaniline derivatives, 2-((4-nitrophenyl)amino)ethyl methanesulfonate (1B), 2-((4-nitrophenyl)amino)ethyl 4-methylbenzenesulfonate (…

Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method.

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability an…

Efficient numerical method for simulating static and dynamic properties of superfluid helium

Density functional theory (DFT) offers computationally affordable way of describing static and dynamic properties of superfluid 4He. In general, the DFT models yield single particle-like Schrodinger equations with a nonlinear potential term that accounts for all the many-body interactions. The resulting equations can be solved for small amplitude plane wave excitations in the bulk whereas fully numerical solution must be sought in more complicated cases. In this paper we propose a numerical method that can be used in solving the time-dependent nonlinear Schrodinger equation in both real and imaginary times. The method is based on operator splitting technique where each component operator is…

Crystal Structures and Density Functional Theory Calculations of o-and p-Nitroaniline Derivatives: Combined Effect of Hydrogen Bonding and aromatic interactions on dimerization energy

The interplay of strong and weak hydrogen bonds, dipole–dipole interactions, and aromatic interactions of o- and p-nitroaniline derivatives was studied by combining crystal structure analysis and density functional theory (DFT) calculations. Crystal structures of four 2-nitroaniline derivatives, 2-((2-nitrophenyl)amino)ethyl methanesulfonate (1A), 2-((2-nitrophenyl)amino)ethyl 4-methylbenzenesulfonate (2A), N,N′-((1,3-phenylenebis(oxy))bis(ethane-2,1-diyl))bis(2-nitroaniline) (3A), and N-(2-chloroethyl)-2-nitroaniline (4A), and crystal structures of three 4-nitroaniline derivatives, 2-((4-nitrophenyl)amino)ethyl methanesulfonate (1B), 2-((4-nitrophenyl)amino)ethyl 4-methylbenzenesulfonate (…

Localized surface plasmon resonance in silver nanoparticles: Atomistic first-principles time-dependent density-functional theory calculations

We observe using ab initio methods that localized surface plasmon resonances in icosahedral silver nanoparticles enter the asymptotic region already between diameters of 1 and 2 nm, converging close to the classical quasistatic limit around 3.4 eV. We base the observation on time-dependent density-functional theory simulations of the icosahedral silver clusters Ag$_{55}$ (1.06 nm), Ag$_{147}$ (1.60 nm), Ag$_{309}$ (2.14 nm), and Ag$_{561}$ (2.68 nm). The simulation method combines the adiabatic GLLB-SC exchange-correlation functional with real time propagation in an atomic orbital basis set using the projector-augmented wave method. The method has been implemented for the electron structure…

Covalently linked multimers of gold nanoclusters Au102(p-MBA)44 and Au∼250(p-MBA)n

We present the synthesis, separation, and characterization of covalently-bound multimers of para-mercaptobenzoic acid (p-MBA) protected gold nanoclusters. The multimers were synthesized by performing a ligand-exchange reaction of a pre-characterized Au102(p-MBA)44 nanocluster with biphenyl-4,4′-dithiol (BPDT). The reaction products were separated using gel electrophoresis yielding several distinct bands. The bands were analyzed by transmission electron microscopy (TEM) revealing monomer, dimer, and trimer fractions of the nanocluster. TEM analysis of dimers in combination with molecular dynamics simulations suggest that the nanoclusters are covalently bound via a disulfide bridge between BP…

Covalently linked multimers of gold nanoclusters Au102(p-MBA)44and Au∼250(p-MBA)n

We present the synthesis, separation, and characterization of covalently-bound multimers of para-mercaptobenzoic acid (p-MBA) protected gold nanoclusters. The multimers were synthesized by performing a ligand-exchange reaction of a pre-characterized Au102(p-MBA)44 nanocluster with biphenyl-4,4′-dithiol (BPDT). The reaction products were separated using gel electrophoresis yielding several distinct bands. The bands were analyzed by transmission electron microscopy (TEM) revealing monomer, dimer, and trimer fractions of the nanocluster. TEM analysis of dimers in combination with molecular dynamics simulations suggest that the nanoclusters are covalently bound via a disulfide bridge between BP…

Au-40(SR)(24) Cluster as a Chiral Dimer of 8-Electron Superatoms: Structure and Optical Properties

We predict and analyze density-functional theory (DFT)-based structures for the recently isolated Au(40)(SR)(24) cluster. Combining structural information extracted from ligand-exchange reactions, circular dichroism and transmission electron microscopy leads us to propose two families of low-energy structures that have a chiral Au-S framework on the surface. These families have a common geometrical motif where a nonchiral Au(26) bi-icosahedral cluster core is protected by 6 RS-Au-SR and 4 RS-Au-SR-Au-SR oligomeric units, analogously to the "Divide and Protect" motif of known clusters Au(25)(SR)(18)(-/0), Au(38)(SR)(24) and Au(102)(SR)(44). The strongly prolate shape of the proposed Au(26) c…

A density functional investigation of thiolate-protected bimetal PdAu24(SR)18z clusters: doping the superatom complex

Structure, electronic properties, optical absorption and charging properties of methylthiolate-protected bimetal PdAu(24)(SR)(18)(z) (R = Me) clusters with various charge states (-3or=zor= +3) are investigated by using density functional theory. The results are compared to properties of the well-understood singly anionic pure gold complex Au(25)(SR)(18)((-1)) [J. Akola, M. Walter, H. Häkkinen and H. Grönbeck, J. Am. Chem. Soc., 2008, 130, 3756]. The atomic structure of this all-gold complex can be written in a "divide-and-protect" way [H. Häkkinen, M. Walter and H. Grönbeck, J. Phys. Chem. B, 2006, 110, 9927] as Au(13)[Au(2)(SR)(3)](6)((-1)) where 6 v-shaped Au(2)(SR)(3) ligands protect the…

All-thiol-stabilized Ag44 and Au12Ag32 nanoparticles with single-crystal structures

Noble metal nanoparticles stabilized by organic ligands are important for applications in assembly, site-specific bioconjugate labelling and sensing, drug delivery and medical therapy, molecular recognition and molecular electronics, and catalysis. Here we report crystal structures and theoretical analysis of three Ag44(SR)30 and three Au12Ag32(SR)30 intermetallic nanoclusters stabilized with fluorinated arylthiols (SR=SPhF, SPhF2 or SPhCF3). The nanocluster forms a Keplerate solid of concentric icosahedral and dodecahedral atom shells, protected by six Ag2(SR)5 units. Positive counterions in the crystal indicate a high negative charge of 4(-) per nanoparticle, and density functional theory…

Towards Controlled Synthesis of Water-Soluble Gold Nanoclusters : Synthesis and Analysis

Water-soluble gold nanoclusters with well-defined molecular structures and stability possess particular biophysical properties making them excellent candidates for biological applications as well as for fundamental spectroscopic studies. The currently existing synthetic protocols for atomically monodisperse thiolate-protected gold nanoclusters (AuMPCs) have been widely expanded with organothiolates, yet the direct synthesis reports for water-soluble AuMPCs are still deficient. Here, we demonstrate a wet-chemistry pH-controlled synthesis of two large water-soluble nanoclusters utilizing p-mercaptobenzoic acid (pMBA), affording different sizes of plasmonic AuMPCs on the preparative scale (∼7 …

Elektroniset aaltopaketit atomeissa ja pienissä molekyyleissä

Solution of time-independent Schrödinger equation by the imaginary time propagation method

Numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and non-linear Schrodinger equations using the imaginary time propagation (ITP) method is described. Convergence properties and accuracy of 2nd and 4th order operator-splitting methods for the ITP method are studied using numerical examples. The natural convergence of the method is further accelerated with a new dynamic time step adjustment method. The results show that the ITP method has better scaling with respect to matrix size as compared to the implicitly restarted Lanczos method. An efficient parallel implementation of the ITP method for shared memory computers is also demons…

Birth of the Localized Surface Plasmon Resonance in Monolayer-Protected Gold Nanoclusters

Gold nanoclusters protected by a thiolate monolayer (MPC) are widely studied for their potential applications in site-specific bioconjugate labeling, sensing, drug delivery, and molecular electronics. Several MPCs with 1-2 nm metal cores are currently known to have a well-defined molecular structure, and they serve as an important link between molecularly dispersed gold and colloidal gold to understand the size-dependent electronic and optical properties. Here, we show by using an ab initio method together with atomistic models for experimentally observed thiolate-stabilized gold clusters how collective electronic excitations change when the gold core of the MPC grows from 1.5 to 2.0 nm. A …

TDDFT Analysis of Optical Properties of Thiol Monolayer-Protected Gold and Intermetallic Silver–Gold Au144(SR)60 and Au84Ag60(SR)60 Clusters

The optical absorption spectra of atomistic model structures for experimentally isolated all-gold Au144(SR)60 and intermetallic Au84Ag60(SR)60 clusters are systematically analyzed from linear-response time-dependent density functional theory (LR-TDDFT) and time-dependent density functional perturbation theory (TD-DFPT) calculations. The computed spectra, utilizing the atomistic model for Au144(SR)60 published by us in 2009, reproduce closely the experimental observations for corresponding isolated compounds, reported previously by Kumara and Dass in 2011. A collective dipole oscillation within the metal cores of the all-gold and intermetallic clusters is formed as response to light in the v…

Plasmonic twinned silver nanoparticles with molecular precision

Determining the structures of nanoparticles at atomic resolution is vital to understand their structure–property correlations. Large metal nanoparticles with core diameter beyond 2 nm have, to date, eluded characterization by single-crystal X-ray analysis. Here we report the chemical syntheses and structures of two giant thiolated Ag nanoparticles containing 136 and 374 Ag atoms (that is, up to 3 nm core diameter). As the largest thiolated metal nanoparticles crystallographically determined so far, these Ag nanoparticles enter the truly metallic regime with the emergence of surface plasmon resonance. As miniatures of fivefold twinned nanostructures, these structures demonstrate a subtle dis…

Electronic Structure and Optical Properties of the Intrinsically Chiral 16-Electron Superatom Complex [Au20(PP3)4]4+

The recently solved crystal structure of the [Au20(PP3)4]Cl4 cluster (PP3: tris(2-(diphenylphophino)ethyl)phosphine) is examined using density functional theory (DFT). The Au20 core of the cluster is intrinsically chiral by the arrangement of the Au atoms. This is in contrast to the chirality of thiolate-protected gold clusters, in which the protecting Au-thiolate units are arranged in chiral patterns on achiral cores. We interpret the electronic structure of the [Au20(PP3)4]Cl4 cluster in terms of the superatom complex model. The 16-electron cluster cannot be interpreted as a dimer of 8-electron clusters (which are magic). Instead, a superatomic electron configuration of 1S(2) 1P(6) 1D(6) …

A DFT Study of Linear Gold–Thiolate Superclusters Absorbing in the Therapeutic NIR Window

A series of linear clusters up to an aspect ratio of 1:6, formed as multimers of smaller clusters with an icosahedral Au13(5+) core having an eight-electron superatom configuration, are computationally predicted to have a greatly enhanced size-dependent absorption in the near-infrared (NIR) region extending to the biologically important NIR window. A novel structural model is presented for the previously isolated thiol-stabilized Au54(SR)30 cluster, where the metal core is formed as a heterodimer of the cores of the known Au25(SR)18(-/0) and Au38(SR)24 clusters.

Supramolecular functionalization and concomitant enhancement in properties of Au25 clusters

We present a versatile approach for tuning the surface functionality of an atomically precise 25 atom gold cluster using specific host-guest interactions between ?-cyclodextrin (CD) and the ligand anchored on the cluster. The supramolecular interaction between the Au25 cluster protected by 4-(t-butyl)benzyl mercaptan, labeled Au25SBB18, and CD yielding Au25SBB18�?�CDn (n = 1, 2, 3, and 4) has been probed experimentally using various spectroscopic techniques and was further analyzed by density functional theory calculations and molecular modeling. The viability of our method in modifying the properties of differently functionalized Au25 clusters is demonstrated. Besides modifying their optoe…

Superatomic S2 Silver Clusters Stabilized by a Thiolate–Phosphine Monolayer: Insight into Electronic and Optical Properties of Ag14(SC6H3F2)12(PPh3)8 and Ag16(SC6H3F2)14(DPPE)4

The electronic structure of two recently crystallographically solved, thiolate–phosphine protected silver clusters Ag14 and Ag16 are analyzed via density functional theory (DFT) and their optical excitations are analyzed from time-dependent DFT perturbation theory. Both clusters can be characterized as having the S2 free-electron configuration in the metal core, which is the first time such a configuration is confirmed for structurally known ligand-protected noble metal clusters. However, their different core shapes and ligand layer induce significantly different optical spectra. Performance of gradient-corrected DFT functionals is discussed and it is shown that the asymptotically correct L…

CCDC 930278: Experimental Crystal Structure Determination

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CCDC 930279: Experimental Crystal Structure Determination

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CCDC 1496141: Experimental Crystal Structure Determination

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CCDC 953878: Experimental Crystal Structure Determination

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CCDC 953880: Experimental Crystal Structure Determination

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CCDC 930281: Experimental Crystal Structure Determination

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CCDC 953881: Experimental Crystal Structure Determination

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CCDC 930282: Experimental Crystal Structure Determination

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CCDC 953883: Experimental Crystal Structure Determination

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CCDC 953879: Experimental Crystal Structure Determination

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CCDC 953882: Experimental Crystal Structure Determination

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CCDC 1496142: Experimental Crystal Structure Determination

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CCDC 930280: Experimental Crystal Structure Determination

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CCDC 930283: Experimental Crystal Structure Determination

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CCDC 930277: Experimental Crystal Structure Determination

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