Volume 131, Issue 17, 07 November 2009

We apply a simple model system of patchy particles to study monodisperse selfassembly using the Platonic solids as target structures. We find marked differences between the assembly behaviors of the different systems. Tetrahedra, octahedral, and icosahedra assemble easily, while cubes are more challenging and dodecahedra do not assemble. We relate these differences to the kinetics and thermodynamics of assembly, with the formation of large disordered aggregates a particular important competitor to correct assembly. In particular, the free energy landscapes of those targets that are easy to assemble are funnellike, whereas for the dodecahedral system the landscape is relatively flat with little driving force to facilitate escape from disordered aggregates.
 ARTICLES

 Theoretical Methods and Algorithms

Block correlated coupled cluster method with the complete activespace selfconsistentfield reference function: Applications for lowlying electronic excited states
View Description Hide DescriptionBlock correlated coupled cluster (BCCC) method with the complete activespace (CAS) selfconsistentfield reference function (CASBCCC) has been applied to investigate the vertical excitation energies of lowlying valence excited states in a number of mediumsized organic molecules, including unsaturated aliphatic hydrocarbons (ethene, Ebutadiene, cyclopropene, and cyclopentadiene), aromatic heterocycles (furan and pyrrole), and carbonyl compounds (formaldehyde, acetone, and formamide). An approximate CASBCCC with the cluster operator truncated up to the fourblock correlation level, CASBCCC4, is employed in the calculations. The results are compared with those from the multireference configuration interaction with singles and doubles (MRCISD and its corrected version, MR), the complete active space with secondorder perturbation theory (CASPT2), and CC3. Our results show that the overall performance of CASBCCC4 is competitive with that of the multistate CASPT2 (slightly inferior to MR), better than that of the singlestate CASPT2 and MRCISD approaches. For triplet excited states, various methods tend to give relatively consistent predictions. However, for singlet excited states, various methods lead to quite different excitation energies in some cases.

Geometry and stability of and clusters
View Description Hide DescriptionThe gradientcorrected density functional calculation is applied to search the lowestenergy configurations of clusters and the calculation indicated that cluster is the most stable one. Based on the result, we further investigate the equilibrium geometries and stabilities of the clusters. We found that in cluster, N atoms formed a separate molecule away from the other part of the cluster. Furthermore, it was shown that the lowestenergy configurations of are stable with the nitrogen atoms well separated by the copper atoms. Therefore, it can be concluded that the cluster can be used as a building block for the construction of the clusterassembled compounds.

Nonproduct quadrature grids for solving the vibrational Schrödinger equation
View Description Hide DescriptionThe size of the quadrature grid required to compute potential matrix elements impedes solution of the vibrational Schrödinger equation if the potential does not have a simple form. This quadrature gridsize problem can make computing (ro)vibrational spectra impossible even if the size of the basis used to construct the Hamiltonian matrix is itself manageable. Potential matrix elements are typically computed with a direct product Gauss quadrature whose grid size scales as , where is the number of points per coordinate and is the number of dimensions. In this article we demonstrate that this problem can be mitigated by using a pruned basis set and a nonproduct Smolyak grid. The constituent quadratures are designed for the weight functions important for vibrational calculations. For the stretch problem we obtain accurate results with a grid that is more than two orders of magnitude smaller than the direct product Gauss grid. If we expect an even bigger reduction.

On the difference between the transition properties calculated with linear response and equation of motionCCSD approaches
View Description Hide DescriptionIn this work, we quantitatively investigate the difference between the linear response (LR) and the equation of motion (EOM) coupled cluster (CC) approaches in the calculation of transition properties, namely, dipole and oscillator strengths, for the most widely used truncated CC wave function, which includes single and double excitation operators. We compare systems of increasing size, where the sizeextensivity may be important. Our results suggest that, for small molecules, the difference is small even with large basis sets. The difference increases with the size of the system, but it is numerically small until hundreds of electron pairs are correlated. Although these calculations may be possible in a few years, at present the EOM approach is more advantageous, albeit more approximate, because it is computationally less demanding.

Longrange corrected doublehybrid density functionals
View Description Hide DescriptionWe extend the range of applicability of our previous longrange corrected (LC) hybrid functional, [J.D. Chai and M. HeadGordon, J. Chem. Phys.128, 084106 (2008)], with a nonlocal description of electron correlation, inspired by secondorder Møller–Plesset (manybody) perturbation theory. This LC “doublehybrid” density functional, denoted as , is fully optimized both at the complete basis set limit (using 2point extrapolation from calculations using triple and quadruple zeta basis sets), and also separately using the somewhat less expensive basis. On independent test calculations (as well as training set results), yields high accuracy for thermochemistry, kinetics, and noncovalent interactions. In addition, owing to its high fraction of exact Hartree–Fock exchange, shows significant improvement for the systems where selfinteraction errors are severe, such as symmetric homonuclear radical cations.

A separable shadow Hamiltonian hybrid Monte Carlo method
View Description Hide DescriptionHybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC’s performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a secondorder integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc).

A softcore Gay–Berne model for the simulation of liquid crystals by Hamiltonian replica exchange
View Description Hide DescriptionThe Gay–Berne (GB) potential has proved highly successful in the simulation of liquid crystal phases, although it is fairly demanding in terms of resources for simulations of large (e.g., ) systems, as increasingly required in applications. Here, we introduce a softcore GBmodel, which exhibits both liquid crystal phase behavior and rapid equilibration. We show that the Hamiltonian replica exchange method, coupled with the newly introduced softcore GBmodel, can effectively speed up the equilibration of a GBliquid crystal phase by frequent exchange of configurations between replicas, while still recovering the mesogenic properties of the standard GB potential.

Firstprinciples molecular dynamics simulations at solidliquid interfaces with a continuum solvent
View Description Hide DescriptionContinuum solvent models have become a standard technique in the context of electronic structure calculations, yet no implementations have been reported capable to perform molecular dynamics at solidliquid interfaces. We propose here such a continuum approach in a density functional theory framework using planewave basis sets and periodic boundary conditions. Our work stems from a recent model designed for Car–Parrinello simulations of quantum solutes in a dielectric medium [D. A. Scherlis et al., J. Chem. Phys.124, 074103 (2006)], for which the permittivity of the solvent is defined as a function of the electronic density of the solute. This strategy turns out to be inadequate for systems extended in two dimensions: the dependence of the dielectric function on the electronic density introduces a new term in the Kohn–Sham potential, which becomes unphysically large at the interfacial region, seriously affecting the convergence of the selfconsistent calculations. If the dielectric medium is properly redefined as a function of the atomic coordinates, a good convergence is obtained and the constant of motion is conserved during the molecular dynamics simulations. The Poisson problem is solved using a multigrid method, and in this way Car–Parrinello molecular dynamics simulations of solidliquid interfaces can be performed at a very moderate computational cost. This scheme is employed to investigate the acidbase equilibrium at the water interface. The aqueous behavior of titania surfaces has stimulated a large amount of experimental research, but many open questions remain concerning the molecular mechanisms determining the chemistry of the interface. Here we make an attempt to answer some of them, putting to the test our continuum model.

Cumulant decomposition of reduced density matrices, multireference normal ordering, and Wicks theorem: A spinfree approach
View Description Hide DescriptionWe propose a spinfree approach to the cumulant decomposition of reduced density matrices of singlet and spinrotation or invariant ensemble of nonsinglet states as in [W. Kutzelnigg and D. Mukherjee, J. Chem. Phys.110, 2800 (1999); 116, 4787 (2002)]. We provide a simple recursive procedure to obtain expressions which relate different spin components of spinorbital reduced density matrices and cumulants of such states to the spinfree counterparts. These results are used to set up a spinsummation procedure to arrive at a definition of spinfree cumulants of any order. Alternatively, an analytic formula for the spinfree form resulting from a spin summation involving product of two spinorbital cumulants is derived and its utility in spinfree cumulant decomposition of reduced density matrices is demonstrated. This leads to suitable definitions of spinfree analog of multireference normal ordering and the associated Wicks theorem. The results of this formulation are expected to be useful in investigations of spinfree multireference internally contracted coupledcluster methods where cumulant approximations to the active reduced density matrices are employed.

Ca impurity in small mixed clusters
View Description Hide DescriptionThe structure of small mixed helium clustersdoped with one calcium atom has been determined within the diffusion Monte Carlo framework. The results show that the calcium atom sits at the interface. This is in agreement with previous studies, both experimental and theoretical, performed for large clusters. A comparison between the results obtained for the largest cluster we have considered for each isotope shows a clear tendency of the Ca atom to reside in a deep dimple at the surface of the cluster for clusters, and to become fully solvated for clusters. We have calculated the absorptionspectrum of Ca around the transition and have found that it is blueshifted from that of the freeatom transition by an amount that depends on the size and composition of the cluster.

The Landau free energy of a melt of graft copolymers
View Description Hide DescriptionNew graphical algorithm is proposed to find vertex functions which are the coefficients of expansion of the Landau free energy of polydisperse multigraft copolymers whose macromolecules comprise an arbitrary number of types of side chains. This algorithm imposes no restriction on length distributions of side chains in copolymermacromolecules as well as on distribution of distances between two successive grafting points along the backbone. By way of example, with this algorithm the expressions for the second, third, and fourth order contributions into the free energy have been derived. The obtained results can be used for construction of the phase diagrams of polydisperse multigraft copolymers.

A relook at the compliance constants in redundant internal coordinates and some new insights
View Description Hide DescriptionThe compliance constants, the inverse of the force constant matrix elements offer the advantage that any one of them could be calculated directly without the need to calculate the full Hessian. Here we show that such a direct calculation produces accurate results. Since the diagonal and the compliance matrix elements give unique values that are independent of the other internal coordinates, an internal frequency is defined which could be effectively used to study related molecules. The conventional coordinates used for benzene and cubane give some of the compliance constants, which differ from the values obtained by the direct method by 5%–40%, indicating that the coordinate systems used are deficient. We identify the source of this discrepancy and find a way to form the correct coordinate system in the sense that the Hessian method and the direct method will lead to the same compliance constants. This procedure takes away the simplicity of local coordinates at least in highly symmetric molecules and it is advantageous to have the potential energy distribution in redundant internal coordinates. A method is proposed for this purpose. All these imply that the most satisfactory way of describing the molecular force field is in terms of redundant internal compliance constants.

Improving replica exchange using driven scaling
View Description Hide DescriptionReplica exchange is a powerful simulation method in which simulations are run at a series of temperatures, with the highest temperature chosen so phase space can be sampled efficiently. In order for swaps to be accepted, the energy distributions of adjacent replicas must have some overlap. This can create the need for many replicas for large systems. In this paper, we present a new method in which the potential energy is scaled by a parameter, which has an explicit time dependence. Scaling the potential energy broadens the distribution of energy and reduces the number of replicas necessary to span a given temperature range. We demonstrate that if the system is driven by the timedependent potential sufficiently slowly, then equilibrium is maintained and energetic and structural properties are identical to those of conventional replica exchange. The method is tested using two systems, the alanine dipeptide and the trpzip2 polypeptide, both in water.

Phase diagram and structural properties of a simple model for onepatch particles
View Description Hide DescriptionWe study the thermodynamic and structuralproperties of a simple, onepatch fluid model using the reference hypernettedchain (RHNC) integral equation and specialized Monte Carlo simulations. In this model, the interacting particles are hard spheres, each of which carries a single identical, arbitrarily oriented and attractive circular patch on its surface; two spheres attract via a simple squarewell potential only if the two patches on the spheres face each other within a specific angular range dictated by the size of the patch. For a ratio of attractive to repulsive surface of 0.8, we construct the RHNC fluidfluid separation curve and compare with that obtained by Gibbs ensemble and grand canonical Monte Carlo simulations. We find that RHNC provides a quick and highly reliable estimate for the position of the fluidfluid critical line. In addition, it gives a detailed (though approximate) description of all structuralproperties and their dependence on patch size.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photodissociation cross sections of ClOOCl at 248.4 and 266 nm
View Description Hide DescriptionThis study utilized a massresolved detection of ClOOCl to determine its photodissociation cross section, which is the product of the absorption cross section and dissociation quantum yield. An effusive molecular beam of ClOOCl was generated and its photodissociation probability was determined through measuring the decrease in the ClOOCl beam intensity upon laser irradiation. By comparing with a reference molecule, the absolute cross sections of ClOOCl were obtained without knowing its absolute concentration. The determined cross section of ClOOCl at 248.4 nm is at 200 K, significantly larger than previously reported values. The temperature dependence of the cross section was investigated at 248.4 nm in the range of 160–260 K; only a very small and negative temperature effect was observed. Because 248.4 nm is very close to the peak of the UVabsorption band of ClOOCl, this work provides a new calibration point for normalizing relative absorption spectra of ClOOCl. In this work, the photodissociation cross section at 266 nm and 200 K was also reported to be .

Structure and optical properties of coreshell bimetallic clusters: Comparison with pure silver and nickel clusters
View Description Hide DescriptionWe present the structural, electronic, and optical properties of bimetallic clusters investigated in the framework of the density functional theory(DFT)(DFT and timedependent DFT). The structure of clusters is found to be governed essentially by the formation of a Nicore surrounded by silver atoms. The cohesive energies and the ionization potentials are calculated. The UVvisible absorption spectra of bimetallic clusters are compared to those of pure silver and nickel clusters. An interpretation of spectroscopic patterns in terms of contribution from  and type excitations is also given. In particular the electrons of nickel atoms are found to play a crucial role in the optical transitions in Nirich systems.

Valence ionization spectra of group six metal hexacarbonyls studied by the symmetryadapted clusterconfiguration interaction method
View Description Hide DescriptionThe valence ionization spectra up to 20 eV of group six metal carbonyls, chromium hexacarbonyl, molybdenum hexacarbonyl, and tungsten hexacarbonyl were studied by the symmetryadapted clusterconfiguration interaction (SACCI) method. The assignments of the spectra are given based on reliable SACCI calculations. The relativistic effects including the spinorbit effects are important for the ionization spectrum of . The relation between the metalCO distance and ionization energies was examined. The lowest ionization energies of the three metal carbonyls are approximately the same because of the energy dependence of the metalCO length and relativistic effects. In , the Cr–CO interaction significantly increases the lowest ionization energy in comparison with and because of the relatively short metalCO bond length. The relativistic effect reduces the lowest ionization energy of because the effective core potential of 5d electrons is more efficiently screened as a result of the relativistic contraction of the inner electrons.

On the kinetics of the reaction: Cluster degradation in consecutive steps
View Description Hide DescriptionThe kinetics of the reaction system initiated by the reaction was experimentally studied in a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer. The clusters were produced by laser desorption/ionization of , then transferred into the ICR cell, cooled by collisions with Ar, and exposed to an excess of with a concentration of . Relative concentrationtime profiles of clusters with , 11, 9, and 7 as well as profiles of ions have been recorded. Other ionic species, besides traces of , were not found, which indicates a doublestep degradation mechanism via the oddnumbered clusters. From a kinetic analysis of the experimental results, a rate coefficient of for the reaction was obtained. Furthermore, it is inferred from a simultaneous fit of all concentrationtime profiles that the reactions for , 11, 9, and 7 occur with rate coefficients near the Langevin limit in the range . The branching ratios between the producing and producing channels of a given cluster indicate an increasing contribution of the producing channels with decreasing cluster size. Statistical rate theory calculations on the basis of molecular data from quantum chemical calculations show that the experimental profiles are compatible with a sequence of associationelimination reactions proceeding via the formation of highly excited adducts followed by a sequential elimination of two AlCl molecules. Rate coefficients for these reactions were calculated, and the production of was shown probably not to proceed via these intermediates.

Comparison of the resonanceenhanced multiphoton ionization spectra of pyrrole and 2,5dimethylpyrrole: Building toward an understanding of the electronic structure and photochemistry of porphyrins
View Description Hide DescriptionThe photophysical properties of porphyrins have relevance for their use as lightactivated drugs in cancer treatment and sensitizers in solidstate solar cells. However, the appearance of their UVvisible spectra is usually explained inadequately by qualitative molecularorbital theories. We intend to gain a better insight into the intense absorption bands, and excitedstate dynamics, that make porphyrins appropriate for both of these applications by gradually building toward an understanding of the macrocyclic structure, starting with studies of smaller pyrrolic subunits. We have recorded the and resonanceenhanced multiphoton ionization (REMPI) spectra of pyrrole and 2,5dimethylpyrrole between (390 nm) and (206 nm). We did not observe a REMPI signal through the optically bright and states in pyrrole due to ultrafast deactivation via conical intersections with the dissociative and states. However, we did observe REMPI through Rydberg states with a dominant feature at (twophoton energy, ) assigned to a transition. In contrast, 2,5dimethylpyrrole has a broad and structured REMPI spectrum between and as a result of vibronic transitions to the state, and it does not show the Rydberg transition via REMPI. We have complemented the experimental studies by a theoretical treatment of the excited states of both molecules using timedependent density functional theory (TDDFT) and accounted for the contrasting features in the spectra. TDDFT modeled the photochemical activity of both the optically dark states (dissociative) and optically bright states well, predicting the barrierless deactivation of the state of pyrrole and the bound minimum of the state in 2,5dimethylpyrrole. However, the quantitative agreement between vibronic transition energies and the excitedstate frequencies calculated by TDDFT was hampered by inaccurate modeling of Rydberg orbital mixing with the valence states, caused by the lack of an asymptotic correction to the exchangecorrelation functionals used.

Fragmentation properties of threemembered heterocyclic molecules by partial ion yield spectroscopy: and
View Description Hide DescriptionWe investigated the photofragmentation properties of two threemembered ring heterocyclic molecules, and , by total and partial ion yield spectroscopy. Positive and negative ions have been collected as a function of photon energy around the and ionization thresholds in , and around the and thresholds in . We underline similarities and differences between these two analogous systems. We present a new assignment of the spectral features around the edge and the sulfur edges in . In both systems, we observe high fragmentation efficiency leading to positive and negative ions when exciting these molecules at resonances involving coretoRydberg transitions. The system, with one electron in an orbital far from the ionic core, relaxes preferentially by spectator Auger decay, and the resulting singly charged ion with two valence holes and one electron in an outer diffuse orbital can remain in excited states more susceptible to dissociation. A stateselective fragmentation pattern is analyzed in which leads to direct production of following the decay of virtualorbital excitations to final states above the doubleionization threshold.