Volume 139, Issue 19, 21 November 2013

Using numerical simulations and a simple scaling theory, we study the microphase separation of a mixture of polymer brushes with different chain lengths tethered to surfaces with nonuniform curvature. We measure the free energy difference of the phase separated configurations as a function of spheroid eccentricity and ordering of the microdomains formed on them. We find that there is a preference for the longer chains to locate in high curvature regions, and identify and quantify the driving forces associated with this phenomenon. We also find that nonuniform curvature typically limits the number of striped domains that would normally form on a spherical surface under identical physical conditions. Finally, we generalize the scaling theory developed for brushes on spherical surfaces to include prolate and oblate spheroids, and show explicitly that while immiscibility between the chains is required for phase separation to occur on spheroids, it is unnecessary for certain surfaces with regions of positive and negative curvature. We present a phase diagram showing the conditions under which curvaturedriven phase separation of miscible, but lengthwise asymmetric chains is expected to occur.
 COMMUNICATIONS


Communication: Reduced density matrices in molecular systems: Grandcanonical electron states
View Description Hide DescriptionGrandcanonical like descriptions of many electron atomic and molecular open systems which are characterized by a noninteger number of electrons are presented. Their associated reduced density matrices (RDMs) are obtained by introducing the contracting mapping for this type of distributions. It is shown that there is loss of information when connecting RDMs of different order by partial contractions. The energy convexity property of these systems simplifies the description. Consequently, this formulation opens the possibility to a new look for chemical descriptors such as chemical potential and reactivity among others. Examples are presented to discuss the theoretical aspects of this work.

Communication: Twocomponent ringcoupledcluster computation of the correlation energy in the randomphase approximation
View Description Hide DescriptionWithin the framework of densityfunctional theory, the correlation energy is computed in the randomphase approximation (RPA) using spinors obtained from a twocomponent relativistic Kohn–Sham calculation accounting for spin–orbit interactions. Ringcoupledcluster equations are solved to obtain the twocomponent RPA correlation energy. Results are presented for the hydrides of the halogens Br, I, and At as well as of the coinage metals Cu, Ag, and Au, based on twocomponent relativistic exactdecoupling Kohn–Sham calculations.

Communication: Electronic and transport properties of molecular junctions under a finite bias: A dual mean field approach
View Description Hide DescriptionWe show that when a molecular junction is under an external bias, its properties cannot be uniquely determined by the total electron density in the same manner as the density functional theory for ground state properties. In order to correctly incorporate biasinduced nonequilibrium effects, we present a dual mean field (DMF) approach. The key idea is that the total electron density together with the density of currentcarrying electrons are sufficient to determine the properties of the system. Two mean fields, one for currentcarrying electrons and the other one for equilibrium electrons can then be derived. Calculations for a graphene nanoribbon junction show that compared with the commonly used ab initio transport theory, the DMF approach could significantly reduce the electric current at low biases due to the nonequilibrium corrections to the mean field potential in the scattering region.
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 ARTICLES

 Theoretical Methods and Algorithms

Linearscaling explicitly correlated treatment of solids: Periodic local MP2F12 method
View Description Hide DescriptionTheory and implementation of the periodic local MP2F12 method in the 3*A fixedamplitude ansatz is presented. The method is formulated in the direct space, employing local representation for the occupied, virtual, and auxiliary orbitals in the form of Wannier functions (WFs), projected atomic orbitals (PAOs), and atomcentered Gaussiantype orbitals, respectively. Local approximations are introduced, restricting the list of the explicitly correlated pairs, as well as occupied, virtual, and auxiliary spaces in the strong orthogonality projector to the pairspecific domains on the basis of spatial proximity of respective orbitals. The 4index twoelectron integrals appearing in the formalism are approximated via the directspace density fitting technique. In this procedure, the fitting orbital spaces are also restricted to local fitdomains surrounding the fitted densities. The formulation of the method and its implementation exploits the translational symmetry and the sitegroup symmetries of the WFs. Test calculations are performed on LiH crystal. The results show that the periodic LMP2F12 method substantially accelerates basis set convergence of the total correlation energy, and even more so the correlation energy differences. The resulting energies are quite insensitive to the resolutionoftheidentity domain sizes and the quality of the auxiliary basis sets. The convergence with the orbital domain size is somewhat slower, but still acceptable. Moreover, inclusion of slightly more diffuse functions, than those usually used in the periodic calculations, improves the convergence of the LMP2F12 correlation energy with respect to both the size of the PAOdomains and the quality of the orbital basis set. At the same time, the essentially diffuse atomic orbitals from standard molecular basis sets, commonly utilized in molecular MP2F12 calculations, but problematic in the periodic context, are not necessary for LMP2F12 treatment of crystals.

Selfinteraction corrected density functional calculations of molecular Rydberg states
View Description Hide DescriptionA method is presented for calculating the wave function and energy of Rydberg excited states of molecules. A good estimate of the Rydberg state orbital is obtained using ground state density functional theory including PerdewZunger selfinteraction correction and an optimized effective potential. The total energy of the excited molecule is obtained using the Delta SelfConsistent Field method where an electron is removed from the highest occupied orbital and placed in the Rydberg orbital. Results are presented for the first few Rydberg states of NH3, H2O, H2CO, C2H4, and N(CH3)3. The mean absolute error in the energy of the 33 molecular Rydberg states presented here is 0.18 eV. The orbitals are represented on a real space grid, avoiding the dependence on diffuse atomic basis sets. As in standard density functional theory calculations, the computational effort scales as NM ^{2} where N is the number of orbitals and M is the number of grid points included in the calculation. Due to the slow scaling of the computational effort with system size and the high level of parallelism in the real space grid approach, the method presented here makes it possible to estimate Rydberg electron binding energy in large molecules.

Reversible diffusioninfluenced reactions of an isolated pair on some two dimensional surfaces
View Description Hide DescriptionWe investigate reversible diffusioninfluenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the survival probability of the irreversible reaction. Furthermore, we make use of the mean reaction time approximation to write the irreversible survival probability in restricted spaces as a single exponential. In this way, we obtain exact and approximative expressions in the time domain for the reversible survival probability for three different two dimensional spatial domains: The infinite plane, the annular domain, and the surface of a sphere. Our obtained results should prove useful in the context of membranebound reversible diffusioninfluenced reactions in cell biology.

Charge transfer interaction using quasiatomic minimalbasis orbitals in the effective fragment potential method
View Description Hide DescriptionThe charge transfer (CT) interaction, the most timeconsuming term in the general effective fragment potential method, is made much more computationally efficient. This is accomplished by the projection of the quasiatomic minimalbasisset orbitals (QUAMBOs) as the atomic basis onto the selfconsistent field virtual molecular orbital (MO) space to select a subspace of the full virtual space called the valence virtual space. The diagonalization of the Fock matrix in terms of QUAMBOs recovers the canonical occupied orbitals and, more importantly, gives rise to the valence virtual orbitals (VVOs). The CT energies obtained using VVOs are generally as accurate as those obtained with the full virtual space canonical MOs because the QUAMBOs span the valence part of the virtual space, which can generally be regarded as “chemically important.” The number of QUAMBOs is the same as the number of minimalbasis MOs of a molecule. Therefore, the number of VVOs is significantly smaller than the number of canonical virtual MOs, especially for large atomic basis sets. This leads to a dramatic decrease in the computational cost.

The Jastrow antisymmetric geminal power in Hilbert space: Theory, benchmarking, and application to a novel transition state
View Description Hide DescriptionThe Jastrowmodified antisymmetric geminal power (JAGP) ansatz in Hilbert space successfully overcomes two key failings of other pairing theories, namely, a lack of interpair correlations and a lack of multiple resonance structures, while maintaining a polynomially scaling cost, variational energies, and size consistency. Here, we present efficient quantum Monte Carlo algorithms that evaluate and optimize the JAGP energy for a cost that scales as the fifth power of the system size. We demonstrate the JAGP’s ability to describe both static and dynamic correlation by applying it to bond stretching in H2O, C2, and N2 as well as to a novel, multireference transition state of ethene. JAGP’s accuracy in these systems outperforms even the most sophisticated singlereference methods and approaches that of exponentially scaling active space methods.

General active space commutatorbased coupled cluster theory of general excitation rank for electronically excited states: Implementation and application to ScH
View Description Hide DescriptionWe present a new implementation of general excitation rank coupled cluster theory for electronically excited states based on the singlereference multireference formalism. The method may include activespace selected and/or general higher excitations by means of the general active space concept. It may employ molecular integrals over the fourcomponent LévyLeblond Hamiltonian or the relativistic spinorbitfree fourcomponent Hamiltonian of Dyall. In an initial application to ground and excited states of the scandium monohydride molecule we report spectroscopic constants using basis sets of up to quadruplezeta quality and up to full iterative triple excitations in the cluster operators. Effects due to spinorbit interaction are evaluated using twocomponent multireference configuration interaction for assessing the accuracy of the coupled cluster results.

Effect of an external electric field on the diffusioninfluenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. III. Groundstate ABCD reaction
View Description Hide DescriptionIn the presence of an external electric field, the groundstate diffusioninfluenced reversible reaction for a geminate pair, a neutral and a charged particle, is investigated in three dimensions. The probability density functions, the rates of reactions, and the survival probabilities of individual particles are analytically derived in the Laplace domain in terms of series solutions. The longtime kinetics of probability density functions and rates of reactions in rescaled forms shows a kinetic transition behavior from a t ^{−3/2} power law to a t ^{−3/2} e ^{ t } increase when the condition , which depends on the diffusivities of particles and the external electric fields, changes to . In the transition region , the longtime behavior also shows a t ^{−3/2} power law decay but with a different value of the prefactor. The rescaled survival probabilities only exhibit an exponentially increasing behavior at long times with no dependence on the various values of parameters.

A secondorder multireference perturbation method for molecular vibrations
View Description Hide DescriptionWe present a general multireference framework for treating strong correlation in vibrational structure theory, which we denote the vibrational active space selfconsistent field (VASSCF) approach. Active configurations can be selected according to excitation level or the degrees of freedom involved, or both. We introduce a novel statespecific secondorder multiconfigurational perturbation correction that accounts for the remaining weak correlation between the vibrational modes. The resulting VASPT2 method is capable of accurately and efficiently treating strong correlation in the form of large anharmonic couplings, at the same time as correctly resolving resonances between states. These methods have been implemented in our new dynamics package DYNAMOL, which can currently treat up to fourbody Hamiltonian coupling terms. We present a pilot application of the VASPT2 method to the trans isomer of formic acid. We have constructed a new analytic potential that reproduces frozen core CCSD(T)(F12*)/ccpVDZF12 energies to within 0.25% RMSD over the energy range 0–15 000 cm^{−1}. The computed VASPT2 fundamental transition energies are accurate to within 9 cm^{−1} RMSD from experimental values, which is close to the accuracy one can expect from a CCSD(T) potential energy surface.

Multiscale multiphysics and multidomain models—Flexibility and rigidity
View Description Hide DescriptionThe emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the PoissonBoltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CEWAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more timeconsuming dynamics is handled with continuum elasticity theory, while the less timeconsuming static analysis is pursued with atomic approaches. We propose a simple method, flexibilityrigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of at most, where N is the number of atoms or residues, in contrast to for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein BFactor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.

Adaptive spectral clustering with application to tripeptide conformation analysis
View Description Hide DescriptionA decomposition of a molecular conformational space into sets or functions (states) allows for a reduced description of the dynamical behavior in terms of transition probabilities between these states. Spectral clustering of the corresponding transition probability matrix can then reveal metastabilities. The more states are used for the decomposition, the smaller the risk to cover multiple conformations with one state, which would make these conformations indistinguishable. However, since the computational complexity of the clustering algorithm increases quadratically with the number of states, it is desirable to have as few states as possible. To balance these two contradictory goals, we present an algorithm for an adaptive decomposition of the position space starting from a very coarse decomposition. The algorithm is applied to small data classification problems where it was shown to be superior to commonly used algorithms, e.g., kmeans. We also applied this algorithm to the conformation analysis of a tripeptide molecule where sixdimensional time series are successfully analyzed.
 Atoms, Molecules, and Clusters

Dehydrogenation of N _{2} H _{ X } (X = 2 − 4) by nitrogen atoms: Thermochemical and kinetics
View Description Hide DescriptionThermochemical and kinetics of sequential hydrogen abstraction reactions from hydrazine by nitrogen atoms were studied. The dehydrogenation was divided in three steps, N 2 H 4 + N, N 2 H 3 + N, and N 2 H 2 + N. The thermal rate constants were calculated within the framework of canonical variational theory, with zero and small curvature multidimensional tunnelling corrections. The reaction paths were computed with the BB1K/augccpVTZ method and the thermochemical properties were improved with the CCSD(T)/CBS//BB1K/augccpVTZ approach. The first dehydrogenation step presents the lowest rate constants, equal to 1.22 × 10^{−20} cm^{3} molecule^{−1} s^{−1} at 298 K.

A search for the sulphur hexafluoride cation with intense, few cycle laser pulses
View Description Hide DescriptionIt is well established that upon ionization of sulphur hexafluoride, the SF6 ^{+} ion is never observed in mass spectra. Recent work with ultrashort intense laser pulses has offered indications that when strong optical field are used, the resulting “bond hardening” can induce changes in the potential energy surfaces of molecular cations such that molecular ions that are normally unstable may, indeed, become metastable enough to enable their detection by mass spectrometry. Do intense, ultrashort laser pulses permit formation of SF6 ^{+}? We have utilized intense pulses of 5 fs, 11 fs, and 22 fs to explore this possibility. Our results are negative: no evidence is discovered for SF6 ^{+}. However, multiply charged sulphur and fluorine ions from highly charged SF6 ^{q+} ions are observed that enable us to resolve the controversy regarding the kinetic energy release accompanying formation of F^{+} fragment ions. Quantum chemical computations of fielddistorted potential energy curves of SF6 and its molecular ion enable us to rationalize our nonobservation of SF6 ^{+}. Our findings have implications for high harmonic generation from SF6 in the fewcycle regime.

Electronic transitions of palladium dimer
View Description Hide DescriptionThe laser induced fluorescence spectrum of palladium dimer (Pd2) in the visible region between 480 and 700 nm has been observed and analyzed. The gasphase Pd2 molecule was produced by laser ablation of palladium metal rod. Eleven vibrational bands were observed and assigned to the [17.1] transition system. The bond length (ro) and vibrational frequency (ΔG1/2) of the ground state were determined to be 2.47(4) Å and 211.4(5) cm^{−1}, respectively. A molecular orbital energy level diagram was used to understand the observed ground and excited electronic states. This is the first gasphase experimental investigation of the electronic transitions of Pd2.

Ab initio potential energy surface for the highly nonlinear dynamics of the KCN molecule
View Description Hide DescriptionAn accurate ab initio quantum chemistry study at level of quadratic configuration interaction method of the electronic ground state of the KCN molecule is presented. A fitting of the results to an analytical series expansion was performed to obtain a global potential energy surface suitable for the study of the associated vibrational dynamics. Additionally, classical Poincaré surfaces of section for different energies and quantum eigenstates were calculated, showing the highly nonlinear behavior of this system.

Chemical reaction versus vibrational quenching in low energy collisions of vibrationally excited OH with O
View Description Hide DescriptionQuantum scattering calculations are reported for statetostate vibrational relaxation and reactive scattering in O + OH(v = 2 − 3, j = 0) collisions on the electronically adiabatic ground state ^{2} A′′ potential energy surface of the HO2 molecule. The timeindependent Schrödinger equation in hyperspherical coordinates is solved to determine energy dependent probabilities and cross sections over collision energies ranging from ultracold to 0.35 eV and for total angular momentum quantum number J = 0. A Jshifting approximation is then used to compute initial state selected reactive rate coefficients in the temperature range T = 1 − 400 K. Results are found to be in reasonable agreement with available quasiclassical trajectory calculations. Results indicate that rate coefficients for O2 formation increase with increasing the OH vibrational level except at low and ultralow temperatures where OH(v = 0) exhibits a slightly different trend. It is found that vibrational relaxation of OH in v = 2 and v = 3 vibrational levels is dominated by a multiquantum process.

Resonant photoelectron spectroscopy of Au_{2} ^{−} via a Feshbach state using highresolution photoelectron imaging
View Description Hide DescriptionPhotodetachment cross sections are measured across the detachment threshold of Au 2 ^{−} between 1.90 and 2.02 eV using a tunable laser. In addition to obtaining a more accurate electron affinity for Au 2 (1.9393 ± 0.0003 eV), we observe eight resonances above the detachment threshold, corresponding to excitations from the vibrational levels of the Au 2 ^{−} ground state (X ^{2}Σu ^{+}) to those of a metastable excited state of Au 2 ^{−} (or Feshbach resonances) at an excitation energy of 1.9717 ± 0.0003 eV and a vibrational frequency of 129.1 ± 1.5 cm^{−1}. Highresolution photoelectron spectra of Au 2 ^{−} are obtained using photoelectron imaging to follow the autodetachment processes by tuning the detachment laser to all the eight Feshbach resonances. We observe significant nonFranckCondon behaviors in the resonant photoelectron spectra due to autodetachment from a given vibrational level of the Feshbach state to selective vibrational levels of the neutral final state. Using the spectroscopic data for the ground states of Au 2 ^{−} (X ^{2}Σu ^{+}) and Au 2 (X ^{1}Σg ^{+}), we estimate an equilibrium bond distance of 2.53 ± 0.02 Å for the Feshbach state of Au 2 ^{−} by simulating the FranckCondon factors for the resonant excitation and autodetachment processes.

Solvent dependent branching between CI and CBr bond cleavage following 266 nm excitation of CH_{2}BrI
View Description Hide DescriptionIt is well known that ultraviolet photoexcitation of halomethanes results in halogencarbon bond cleavage. Each halogencarbon bond has a dominant ultraviolet (UV) absorption that promotes an electron from a nonbonding halogen orbital (nX) to a carbonhalogen antibonding orbital (σ*CX). UV absorption into specific transitions in the gas phase results primarily in selective cleavage of the corresponding carbonhalogen bond. In the present work, broadband ultrafast UVvisible transient absorption studies of CH2BrI reveal a more complex photochemistry in solution. Transient absorption spectra are reported spanning the range from 275 nm to 750 nm and 300 fs to 3 ns following excitation of CH2BrI at 266 nm in acetonitrile, 2butanol, and cyclohexane. Channels involving formation of CH2Br + I radical pairs, isoCH2BrI, and isoCH2IBr are identified. The solvent environment has a significant influence on the branching ratios, and on the formation and stability of isoCH2BrI. Both isoCH2BrI and isoCH2IBr are observed in cyclohexane with a ratio of ∼2.8:1. In acetonitrile this ratio is 7:1 or larger. The observation of formation of isoCH2IBr photoproduct as well as isoCH2BrI following 266 nm excitation is a novel result that suggests complexity in the dissociation mechanism. We also report a solvent and concentration dependent lifetime of isoCH2BrI. At low concentrations the lifetime is >4 ns in acetonitrile, 1.9 ns in 2butanol and ∼1.4 ns in cyclohexane. These lifetimes decrease with higher initial concentrations of CH2BrI. The concentration dependence highlights the role that intermolecular interactions can play in the quenching of unstable isomers of dihalomethanes.