Volume 140, Issue 24, 28 June 2014

When a flowing fluid is channeled by chemical or physical precipitation, then tubular structures form. These patterns are common in nature, however, there have been few quantitative studies of their formation. Here, we report measurements of the radius, length, and internal pressure, as functions of time and flow rate, for precipitation tubes growing in chemical gardens. Using these measurements we develop models for how single tubes grow and also for how multiple tubes interact with each other. In particular, when multiple tubes grow from the same source they compete for resources; short/wide tubes have less resistance to flow, and so consume more of the resources, “killing” the growth of long/narrow tubes. These tube interactions are described by an equation similar to an unstable logistic equation.
 COMMUNICATIONS


Communication: The description of strong correlation within selfconsistent Green's function secondorder perturbation theory
View Description Hide DescriptionWe report an implementation of selfconsistent Green's function manybody theory within a secondorder approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix form in an atomic orbital basis, where the Green's function and selfenergy are built on the imaginary frequency and imaginary time domain, respectively, and fast Fourier transform is used to efficiently transform these quantities as needed. We apply this method to several archetypical examples of strong correlation, such as a H32 finite lattice that displays a highly multireference electronic ground state even at equilibrium lattice spacing. In all cases, GF2 gives a physically meaningful description of the metal to insulator transition in these systems, without resorting to spinsymmetry breaking. Our results show that selfconsistent Green's function manybody theory offers a viable route to describing strong correlations while remaining within a computationally tractable singleparticle formalism.

Communication: Relative diffusion in two dimensions: Breakdown of the standard diffusive model for simple liquids
View Description Hide DescriptionUsing molecular dynamics simulations for a liquid of identical soft spheres we analyze the relative diffusion constant D Σn (r) and the self diffusion constant D n where r is the interparticle distance and n = 2, 3 denotes the dimensionality. We demonstrate that for the periodic boundary conditions, D n is a function of the system size and the relation: D Σn (r = L/2) ≅ 2D n (L), where L is the length of the cubic box edge, holds both for n = 2 and 3. For n = 2 both D Σ2(r) and D 2 (L) increase logarithmically with its argument. However, it was found that the diffusive process for large two dimensional systems is very sensitive to perturbations. The sensitivity increases with L and even a very low perturbation limits the increase of D 2 (L → ∞). Nevertheless, due to the functional form of D Σ2(r) the standard assumption for the Smoluchowski type models of reaction kinetics at three dimensions:D Σn (r) ≈ 2D n leads to giant errors if applied for n = 2.

Communication: DMRGSCF study of the singlet, triplet, and quintet states of oxoMn(Salen)
View Description Hide DescriptionWe use CHEMPS2, our free opensource spinadapted implementation of the density matrix renormalization group (DMRG) [S. Wouters, W. Poelmans, P. W. Ayers, and D. Van Neck, Comput. Phys. Commun.185, 1501 (2014)], to study the lowest singlet, triplet, and quintet states of the oxoMn(Salen) complex. We describe how an initial approximate DMRG calculation in a large active space around the Fermi level can be used to obtain a good set of starting orbitals for subsequent completeactivespace or DMRG selfconsistent field calculations. This procedure mitigates the need for a localization procedure, followed by a manual selection of the active space. Per multiplicity, the same active space of 28 electrons in 22 orbitals (28e, 22o) is obtained with the 631G^{*}, ccpVDZ, and ANORCCVDZP basis sets (the latter with DKH2 scalar relativistic corrections). Our calculations provide new insight into the electronic structure of the quintet.
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 ARTICLES

 Theoretical Methods and Algorithms

Density functional theory based generalized effective fragment potential method
View Description Hide DescriptionWe present a generalized KohnSham (KS) density functional theory (DFT) based effective fragment potential (EFP2DFT) method for the treatment of solvent effects. Similar to the original HartreeFock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2HF), EFP2DFT includes electrostatic, exchangerepulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchangerepulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, waterbenzene clusters, water clusters, and nalkane dimers benchmark sets, respectively. The corresponding EFP2HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2DFTD3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.

Electronic correlation without double counting via a combination of spin projected HartreeFock and density functional theories
View Description Hide DescriptionSeveral schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spinprojected HartreeFock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+f c DFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+f c DFT can greatly improve the description of certain molecular properties (e.g., singlettriplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+f c DFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+f c DFT scheme are discussed in light of these results.

A stochastic reorganizational bath model for electronic energy transfer
View Description Hide DescriptionEnvironmentally induced fluctuations of the optical gap play a crucial role in electronic energy transfer dynamics. One of the simplest approaches to incorporate such fluctuations in energy transfer dynamics is the well known HakenStroblReineker (HSR) model, in which the energygap fluctuation is approximated as white noise. Recently, several groups have employed molecular dynamics simulations and excitedstate calculations in conjunction to account for excitation energies’ thermal fluctuations. On the other hand, since the original work of HSR, many groups have employed stochastic models to simulate the same transfer dynamics. Here, we discuss a rigorous connection between the stochastic and the atomistic bath models. If the phonon bath is treated classically, time evolution of the excitonphonon system can be described by Ehrenfest dynamics. To establish the relationship between the stochastic and atomistic bath models, we employ a projection operator technique to derive the generalized Langevin equations for the energygap fluctuations. The stochastic bath model can be obtained as an approximation of the atomistic Ehrenfest equations via the generalized Langevin approach. Based on this connection, we propose a novel scheme to take account of reorganization effects within the framework of stochastic models. The proposed scheme provides a better description of the population dynamics especially in the regime of strong excitonphonon coupling. Finally, we discuss the effect of the bath reorganization in the absorption and fluorescence spectra of ideal Jaggregates in terms of the Stokes shifts. We find a simple expression that relates the reorganization contribution to the Stokes shifts – the reorganization shift – to the ideal or nonideal exciton delocalization in a Jaggregate. The reorganization shift can be described by three parameters: the monomer reorganization energy, the relaxation time of the optical gap, and the exciton delocalization length. This simple relationship allows one to understand the physical origin of the Stokes shifts in molecular aggregates.

A new Gaussian MCTDH program: Implementation and validation on the levels of the water and glycine molecules
View Description Hide DescriptionWe report the main features of a new general implementation of the Gaussian MultiConfiguration TimeDependent Hartree model. The code allows effective computations of timedependent phenomena, including calculation of vibronic spectra (in one or more electronic states), relative state populations, etc. Moreover, by expressing the DiracFrenkel variational principle in terms of an effective Hamiltonian, we are able to provide a new reliable estimate of the representation error. After validating the code on simple onedimensional systems, we analyze the harmonic and anharmonic vibrational spectra of water and glycine showing that reliable and converged energy levels can be obtained with reasonable computing resources. The data obtained on water and glycine are compared with results of previous calculations using the vibrational secondorder perturbation theory method. Additional features and perspectives are also shortly discussed.

A method of orbital analysis for largescale firstprinciples simulations
View Description Hide DescriptionAn efficient method of calculating the natural bond orbitals (NBOs) based on a truncation of the entire density matrix of a whole system is presented for largescale density functional theory calculations. The method recovers an orbital picture for O(N) electronic structure methods which directly evaluate the density matrix without using KohnSham orbitals, thus enabling quantitative analysis of chemical reactions in largescale systems in the language of localized Lewistype chemical bonds. With the density matrix calculated by either an exact diagonalization or O(N) method, the computational cost is O(1) for the calculation of NBOs associated with a local region where a chemical reaction takes place. As an illustration of the method, we demonstrate how an electronic structure in a local region of interest can be analyzed by NBOs in a largescale firstprinciples molecular dynamics simulation for a liquid electrolyte bulk model (propylene carbonate + LiBF4).

Elucidating the effects of adsorbent flexibility on fluid adsorption using simple models and flathistogram sampling methods
View Description Hide DescriptionUsing flathistogram Monte Carlo methods, we investigate the adsorptive behavior of the squarewell fluid in two simple slitporelike models intended to capture fundamental characteristics of flexible adsorbent materials. Both models require as input thermodynamic information about the flexible adsorbent material itself. An important component of this work involves formulating the flexible pore models in the appropriate thermodynamic (statistical mechanical) ensembles, namely, the osmotic ensemble and a variant of the grandcanonical ensemble. Twodimensional probability distributions, which are calculated using flathistogram methods, provide the information necessary to determine adsorption thermodynamics. For example, we are able to determine precisely adsorption isotherms, (equilibrium) phase transition conditions, limits of stability, and free energies for a number of different flexible adsorbent materials, distinguishable as different inputs into the models. While the models used in this work are relatively simple from a geometric perspective, they yield nontrivial adsorptive behavior, including adsorptiondesorption hysteresis solely due to material flexibility and socalled “breathing” of the adsorbent. The observed effects can in turn be tied to the inherent properties of the bare adsorbent. Some of the effects are expected on physical grounds while others arise from a subtle balance of thermodynamic and mechanical driving forces. In addition, the computational strategy presented here can be easily applied to more complex models for flexible adsorbents.

Efficient and accurate treatment of weak pairs in local CCSD(T) calculations. II. Beyond the ring approximation
View Description Hide DescriptionIn order to arrive at linear scaling of the computational cost with molecular size, local coupled cluster methods discriminate pairs of local molecular orbitals according to the spatial separation R of the latter. Only strong pairs are treated at the full coupled cluster level, whereas for weak pairs a lower level of theory (usually MøllerPlesset perturbation theory of second order, MP2) is used. Yet an MP2 treatment of weak pairs is inadequate in certain situations (for example, for describing πstacking), which calls for an improved but still inexpensive method for dealing with the weak pairs. In a previous contribution, we proposed as a substituent for MP2 the LrCCD3 method, which is based on ring coupled cluster doubles (ringCCD) and includes all thirdorder diagrams with energy contributions decaying not quicker than R ^{−6}. In the present work, we explore a still more accurate method, which is based on the same principles. It turned out to be essential to abandon the restriction to ringCCD, i.e., to include further CCD diagrams beyond the ring approximation. The occurring intermediates turn out to be formally very similar to LMP2 density matrices, such that an efficient evaluation of these nonring CCD diagrams is possible. Furthermore, a computationally cheap a posteriori estimate for the fourthorder singles contribution to the weak pair energy, which also exhibits a decay behavior of R ^{−6}, is introduced. The resulting method, denoted as LCCD[S]R^{−6}, indeed provides a substantial improvement in accuracy over the previous LrCCD3 method at a relatively modest additional computational cost.

Dynamics of excitonpolaron transition in molecular assemblies: The variational approach
View Description Hide DescriptionDynamics of excitonic polaron formation in molecular systems coupled to an overdamped bath are investigated using the DiracFrenkel variational principle and Davydov D 1 Ansatz. Using a twosite model system we show that a few qualitatively distinct relaxation regimes of an optically created exciton are possible, depending on the timescale of bath fluctuations. A slow bath always leads to adiabatic polaron formation. Nonadiabatic exciton selftrapping occurs when the system is strongly coupled to a fast bath. Weak coupling to such bath does not perturb the excitonic picture. The complex systembath dynamics can then be mapped to an effective model where the resonant coupling between sites is quenched during relaxation. The timescale of the polaron formation can be defined by the timescale of resonant coupling quenching, and is found to directly correlate with the bath relaxation time.

Variational nature of the frozen density energy in densitybased energy decomposition analysis and its application to torsional potentials
View Description Hide DescriptionThe densitybased energy decomposition analysis (DEDA) is the first of its kind to calculate the frozen density energy variationally. Defined with the constrained search formulation of density functional theory, the frozen density energy is optimized in practice using the WuYang (WY) method for constrained minimizations. This variational nature of the frozen density energy, a possible reason behind some novel findings of DEDA, will be fully investigated in this work. In particular, we systematically study the dual basis set dependence in WY: the potential basis set used to expand the Lagrangian multiplier function and the regular orbital basis set. We explain how the convergence progresses differently on these basis sets and how an apparent basisset independence is achieved. We then explore a new development of DEDA in frozen energy calculations of the ethane molecule, focusing on the internal rotation around the carboncarbon bond and the energy differences between staggered and eclipsed conformations. We argue that the frozen density energy change at fixed bond lengths and bond angles is purely steric effects. Our results show that the frozen density energy profile follows closely that of the total energy when the dihedral angle is the only varying geometry parameter. We can further analyze the contributions from electrostatics and Pauli repulsions. These results lead to a meaningful DEDA of the torsional potential in ethane.

Development of threedimensional sitesite SmoluchowskiVlasov equation and application to electrolyte solutions
View Description Hide DescriptionSitesite SmoluchowskiVlasov (SSSV) equation enables us to directly calculate van Hove time correlation function, which describes diffusion process in molecular liquids. Recently, the theory had been extended to treat solutesolvent system by Iida and Sato [J. Chem. Phys.137, 034506 (2012)]. Because the original framework of SSSV equation is based on conventional pair correlation function, time evolution of system is expressed in terms of onedimensional solvation structure. Here, we propose a new SSSV equation to calculate time evolution of solvation structure in threedimensional space. The proposed theory was applied to analyze diffusion processes in 1M NaCl aqueous solution and in lithium ion battery electrolyte solution. The results demonstrate that these processes are properly described with the theory, and the computed van Hove functions are in good agreement with those in previous works.

Improved master equation approach to quantum transport: From Born to selfconsistent Born approximation
View Description Hide DescriptionBeyond the secondorder Born approximation, we propose an improved master equation approach to quantum transport under selfconsistent Born approximation. The basic idea is to replace the free Green's function in the tunneling selfenergy diagram by an effectivereduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.

Equilibrium limit of thermal conduction and boundary scattering in nanostructures
View Description Hide DescriptionDetermining the lattice thermal conductivity (κ) of nanostructures is especially challenging in that, aside from the phononphonon scattering present in large systems, the scattering of phonons from the system boundary greatly influences heat transport, particularly when system length (L) is less than the average phonon mean free path (MFP). One possible route to modeling κ in these systems is through molecular dynamics (MD) simulations, inherently including both phononphonon and phononboundary scattering effects in the classical limit. Here, we compare current MD methods for computing κ in nanostructures with both L ⩽ MFP and L ≫ MFP, referred to as mean free path constrained (c MFP) and unconstrained (u MFP), respectively. Using a (10,0) CNT (carbon nanotube) as a benchmark case, we find that while the u MFP limit of κ is welldefined through the use of equilibrium MD and the timecorrelation formalism, the standard equilibrium procedure for κ is not appropriate for the treatment of the c MFP limit because of the large influence of boundary scattering. To address this issue, we define an appropriate equilibrium procedure for c MFP systems that, through comparison to highfidelity nonequilibrium methods, is shown to be the low thermal gradient limit to nonequilibrium results. Further, as a means of predicting κ in systems having L ≫ MFP from c MFP results, we employ an extrapolation procedure based on the phenomenological, boundary scattering inclusive expression of Callaway [Phys. Rev.113, 1046 (1959)]. Using κ from systems with L ⩽ 3 μm in the extrapolation, we find that the equilibrium u MFP κ of a (10,0) CNT can be predicted within 5%. The equilibrium procedure is then applied to a variety of carbonbased nanostructures, such as graphene flakes (GF), graphene nanoribbons (GNRs), CNTs, and icosahedral fullerenes, to determine the influence of size and environment (suspended versus supported) on κ. Concerning the GF and GNR systems, we find that the supported samples yield consistently lower values of κ and that the phononboundary scattering remains dominant at large lengths, with L = 0.4 μm structures exhibiting a third of the periodic result. We finally characterize the effect of shape in CNTs and fullerenes on κ, showing the angular components of conductivity in CNTs and icosahedral fullerenes are similar for a given circumference.

Correlation functions for fully or partially stateresolved reactive scattering calculations
View Description Hide DescriptionFlux correlation functions and the quantum transition state concept are important tools for the accurate description of polyatomic reaction processes. Combined with the multiconfigurational timedependent Hartree approach, they facilitate rigorous fulldimensional calculations of cumulative and initialstate selected reaction probabilities for six atom reactions. In recent work [R. Welsch, F. HuarteLarrañaga, and U. Manthe, J. Chem. Phys.136, 064117 (2012)], an approach which allows one to calculate also statetostate reaction probabilities within the quantum transition state concept has been introduced. This article presents further developments. Alternative generalized flux correlation functions are introduced and discussed. Equations for the calculation of fully stateresolved differential cross section using arbitrary definitions of the body fixed frame are derived. An approach for the efficient calculation of partially stateresolved observables as a function of the collision energy is introduced. Finally, numerical test studying the D + H2 reaction illustrate important aspects of the formalism.

Onthefly ab initio semiclassical dynamics: Identifying degrees of freedom essential for emission spectra of oligothiophenes
View Description Hide DescriptionVibrationally resolved spectra provide a stringent test of the accuracy of theoretical calculations. We combine the thawed Gaussian approximation (TGA) with an onthefly ab initio (OTFAI) scheme to calculate the vibrationally resolved emission spectra of oligothiophenes with up to five rings. The efficiency of the OTFAITGA permits treating all vibrational degrees of freedom on an equal footing even in pentathiophene with 105 vibrational degrees of freedom, thus obviating the need for the global harmonic approximation, popular for large systems. Besides reproducing almost perfectly the experimental emission spectra, in order to provide a deeper insight into the associated physical and chemical processes, we also develop a novel systematic approach to assess the importance and coupling between individual vibrational degrees of freedom during the dynamics. This allows us to explain how the vibrational line shapes of the oligothiophenes change with increasing number of rings. Furthermore, we observe the dynamical interplay between the quinoid and aromatic characters of individual rings in the oligothiophene chain during the dynamics and confirm that the quinoid character prevails in the center of the chain.

Control scheme of nonadiabatic transitions with the dynamical shift of potential curve crossing
View Description Hide DescriptionWe investigate how the nuclear dynamics at an avoided crossing is affected and can be controlled by the introduction of a laser field whose cycle is comparable to the timescale of the nuclear dynamics. By introducing the concepts of lightinduced effective potential energy curves and dynamical avoided crossing, we describe the laser controlled nuclear dynamics and present basic control scenarios, giving a detailed explanation of the underlying dynamical mechanisms. The scenarios presented allow for examples to understand from a different perspective the results of dynamic Stark control experiments. The proposed interpretation is applied to the lasercontrolled nonadiabatic dynamics between the two lowest ^{1}Σ^{+} states of LiF, where the usefulness of the concepts developed is elucidated.

Longtime selfdiffusion of charged spherical colloidal particles in parallel planar layers
View Description Hide DescriptionThe longtime selfdiffusion coefficient, D ^{ L }, of charged spherical colloidal particles in parallel planar layers is studied by means of Brownian dynamics computer simulations and modecoupling theory. All particles (regardless which layer they are located on) interact with each other via the screened Coulomb potential and there is no particle transfer between layers. As a result of the geometrical constraint on particle positions, the simulation results show that D ^{ L } is strongly controlled by the separation between layers. On the basis of the socalled contraction of the description formalism [C. ContrerasAburto, J. M. MéndezAlcaraz, and R. CastañedaPriego, J. Chem. Phys.132, 174111 (2010)], the effective potential between particles in a layer (the socalled observed layer) is obtained from integrating out the degrees of freedom of particles in the remaining layers. We have shown in a previous work that the effective potential performs well in describing the static structure of the observed layer (loc. cit.). In this work, we find that the D ^{ L } values determined from the simulations of the observed layer, where the particles interact via the effective potential, do not agree with the exact values of D ^{ L }. Our findings confirm that even when an effective potential can perform well in describing the static properties, there is no guarantee that it will correctly describe the dynamic properties of colloidal systems.

Fragment transition density method to calculate electronic coupling for excitation energy transfer
View Description Hide DescriptionA general approach, the Fragment Transition Density (FTD) scheme, is introduced to estimate electronic coupling for excitation energy transfer in a molecular system. Within this method, the excitation energies and transition densities of the system are used to derive the coupling matrix element. The scheme allows one to treat systems where exciton donor and acceptor are close together and their exchange interaction and orbital overlap are significant. The FTD method can be applied in combination with any quantum mechanical approach to treat excited states of general nature including single, double, and higher excitations. Using FTD approach, we derive excitonic couplings for several systems computed with the CIS, TD DFT and MSCASPT2 methods. In particular, it is shown that the estimated coupling values in DNA πstacks are strongly affected by the shortrange electronic interaction of adjacent nucleobases.