Volume 135, Issue 4, 28 July 2011

We experimentally demonstrate a nonlinear spectroscopic method that is sensitive to excitonexciton interactions in a Frenkel exciton system. Spatial overlap of oneexciton wavefunctions leads to coupling between them, resulting in twoexciton eigenstates that have the character of many singleexciton pairs. The mixed character of the twoexciton wavefunctions gives rise to a fourwavemixing nonlinear frequency generation signal. When only part of the linear excitation spectrum of the complex is excited with three spectrally tailored pulses with separate spatial directions, a frequencyshifted thirdorder nonlinear signal emerges in the phasematched direction. We employ the nonlinear response function formalism to show that the emergence of the signal is mediated by and carries information about the twoexciton eigenstates of the system. We report experimental results for nonlinear frequency generation in the FennaMatthewsOlson (FMO) photosynthetic pigmentprotein complex. Our theoretical analysis of the signal from FMO confirms that the emergence of the frequencyshifted signal is due to the interaction of spatially overlapped excitons. In this method, the signal intensity is directly measured in the frequency domain and does not require scanning of pulse delays or signal phase retrieval. The wavefunctions of the twoexciton states contain information about the spatial overlap of excitons and can be helpful in identifying coupling strengths and relaxation pathways. We propose this method as a facile experimental means of studying exciton correlations in systems with complicated electronic structures.
 COMMUNICATIONS


Communication: The formation of helium cluster cations following the ionization of helium nanodroplets: Influence of droplet size and dopant
View Description Hide DescriptionThe He_{ n } ^{+}/He_{2} ^{+} (n ≥ 3) signal ratios in the mass spectra derived from electron impact ionization of pure heliumnanodroplets are shown to increase with droplet size, reaching an asymptotic limit at an average droplet size of approximately 50 000 helium atoms. This is explained in terms of a charge hopping model, where on average the positive charge is able to penetrate more deeply into the liquid helium as the droplet size increases. The deeper the point where the charge localizes to form He_{2} ^{+}, the greater the likelihood of collisions with the surrounding helium as the ion begins to leave the droplet, thus increasing the probability that helium will be ejected in the form of He_{ n } ^{+} (n ≥ 3) cluster ions rather than He_{2} ^{+}. The addition of a dopant alters the He_{ n } ^{+}/He_{2} ^{+} ratio for small heliumdroplets, an observation attributed to the potential energy gradient created by the cationdopant interaction and its effect in drawing the positive charge towards the dopant in the interior of the droplet.
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 ARTICLES

 Theoretical Methods and Algorithms

Quasidegenerate secondorder perturbation theory for occupation restricted multiple active space selfconsistent field reference functions
View Description Hide DescriptionA multiconfiguration quasidegenerate secondorder perturbation method based on the occupation restricted multiple active space (ORMASPT/ORMAS) reference wavefunction is presented. ORMAS gives one the ability to approximate a complete active space selfconsistent field (CASSCF) wavefunction using only a subset of the configurations from the CASSCF space. The essential idea behind ORMASPT is to use the multireference MøllerPlesset formalism to correct the ORMAS reference energy. A computational scheme employing direct CI methodology is presented. Several tests are presented to demonstrate the performance of the ORMASPT method.

On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies
View Description Hide DescriptionThe leading cause of error in standard coupled clustertheory calculations of thermodynamic properties such as atomization energies and heats of formation originates with the truncation of the oneparticle basis set expansion. Unfortunately, the use of finite basis sets is currently a computational necessity. Even with basis sets of quadruple zeta quality, errors can easily exceed 8 kcal/mol in small molecules, rendering the results of little practical use. Attempts to address this serious problem have led to a wide variety of proposals for simple complete basis set extrapolation formulas that exploit the regularity in the correlation consistent sequence of basis sets. This study explores the effectiveness of six formulas for reproducing the complete basis set limit. The W4 approach was also examined, although in lesser detail. Reference atomization energies were obtained from standard coupledcluster singles, doubles, and perturbative triples (CCSD(T)) calculations involving basis sets of 6ζ or better quality for a collection of 141 molecules. In addition, a subset of 51 atomization energies was treated with explicitly correlated CCSD(T)F12b calculations and very large basis sets. Of the formulas considered, all proved reliable at reducing the oneparticle expansion error. Even the least effective formulas cut the error in the raw values by more than half, a feat requiring a much larger basis set without the aid of extrapolation. The most effective formulas cut the mean absolute deviation by a further factor of two. Careful examination of the complete body of statistics failed to reveal a single choice that out performed the others for all basis set combinations and all classes of molecules.

Electronic properties of metalarene functionalized graphene
View Description Hide DescriptionWe have employed firstprinciples densityfunctional calculations to study the electronic characteristics of covalently functionalized graphene by metalbisarene chemistry. It is shown that functionalization with Mbisarene (M = Ti, V, Cr, Mn, Fe) molecules leads to an opening in the bandgap of graphene (up to 0.81 eV for the Cr derivative), and as a result, transforms it from a semimetal to a semiconductor. The bandgap induced by attachment of a metal atom topped by a benzene ring is attributed to modification of πconjugation and depends on the concentration of functionalizing molecules. This approach offers a means of tailoring the band structure of graphene and potentially its applications for future electronic devices.

Multicomponent diffusion in nanosystems
View Description Hide DescriptionWe present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different areas of liquid state theory, namely, kinetic and density functional theory and their implementation as an effective numerical method via the lattice Boltzmann approach. By combining the first two methods, it is possible to obtain a closed set of kinetic equations for the singlet phase space distribution functions of each species. The interactions among particles are considered within a selfconsistent approximation and the resulting effective molecular fields are analyzed. We focus on multispecies diffusion in systems with shortrange hardcore repulsion between particles of unequal sizes and weak attractive longrange interactions. As a result, the attractive part of the potential does not contribute explicitly to viscosity but to diffusivity and the thermodynamic properties. Finally, we obtain a practical scheme to solve the kinetic equations by employing a discretization procedure derived from the lattice Boltzmann approach. Within this framework, we present numerical data concerning the mutual diffusion properties both in the case of a quiescent bulk fluid and shear flow inducing Taylor dispersion.

Auxiliary basis sets for density fitting secondorder MøllerPlesset perturbation theory: Correlation consistent basis sets for the 5d elements HfPt
View Description Hide DescriptionAuxiliary basis sets specifically matched to the correlation consistent ccpVnZPP, ccpwCVnZPP, augccpVnZPP, and augccpwCVnZPP orbital basis sets (used in conjunction with pseudopotentials) for the 5dtransition metal elements HfPt have been optimized for use in density fitting secondorder MøllerPlesset perturbation theory and other correlated ab initio methods. Calculations of the secondorder MøllerPlesset perturbation theorycorrelation energy, for a test set of small to medium sized molecules, indicate that the density fitting error when utilizing these sets is negligible at three to four orders of magnitude smaller than the orbital basis set incompleteness error.

Functional derivative of the kinetic energy functional for spherically symmetric systems
View Description Hide DescriptionEnsemble noninteracting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A firstorder differential equation for the functional derivative of the ensemble noninteracting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution provides the original noninteracting kinetic energy of the density functional theory.

On the coupling between slow diffusion transport and barrier crossing in nucleation
View Description Hide DescriptionWe model the coupling between slow diffusion transport and nucleation using the diffusion equation, an OstwaldFreundlich boundary condition, and a mass balance linking nucleus size to flux across the nucleussolution interface. The model retains some characteristics of the classical nucleation theory because of the common theoretical foundations behind classical nucleation theory and the OstwaldFreundlich equation. For example, the classically criticalsized nucleus in the uniform supersaturated concentration field is an unstable equilibrium point. However, the model also shows that certain types of concentration profiles can drive a classically precritical nucleus over the nucleation barrier. We identify the separatrix as a function of both nucleus size and characteristics of the local concentration field. Our analysis may be useful for understanding the effects of local concentration fluctuations and especially for understanding the role of dense precursor particles in driving twostep nucleation processes. Our analysis may also provide a starting point for further statistical field theory analyses of local concentration fluctuations and their effects on nucleation rates.

Theoretical investigation of resonance Raman scattering of dye molecules absorbed on semiconductor surfaces
View Description Hide DescriptionA method in time domain is proposed to investigate resonance Raman spectra of absorbed molecules on semiconductor surfaces. The charge transfer at the moleculesurface interface is incorporated with the use of an AndersonNewns type Hamiltonian, where the surface continuum state is dealt with an expansion of Legendre polynomials for fast numerical convergence. From a model test, it is found that the intensities of Raman modes in the sole molecule generally decrease as the moleculesurface interaction is switched on, except that the energy gaps between the molecular excited state and the bottom of the band are at special values. New Raman peaks which are not observed in the sole molecule, however, appear and are greatly enhanced. The enhancement depends on the electronic coupling and the energy gap. It is also highly sensitive to the modespecific reorganization energy in the charge transfer state, and a thousand times enhancement can be obtained at a certain reorganization energy. The corresponding electron dynamics is revealed by the population decay from the absorbed molecule.

Introduction of the FloquetMagnus expansion in solidstate nuclear magnetic resonance spectroscopy
View Description Hide DescriptionIn this article, we present an alternative expansion scheme called FloquetMagnus expansion (FME) used to solve a timedependent linear differential equation which is a central problem in quantum physics in general and solidstate nuclear magnetic resonance(NMR) in particular. The commonly used methods to treat theoretical problems in solidstate NMR are the average Hamiltonian theory (AHT) and the Floquet theory (FT), which have been successful for designing sophisticated pulse sequences and understanding of different experiments. To the best of our knowledge, this is the first report of the FME scheme in the context of solid state NMR and we compare this approach with other series expansions. We present a modified FME scheme highlighting the importance of the (timeperiodic) boundary conditions. This modified scheme greatly simplifies the calculation of higher order terms and shown to be equivalent to the Floquet theory (single or multimode timedependence) but allows one to derive the effective Hamiltonian in the Hilbert space. Basic applications of the FME scheme are described and compared to previous treatments based on AHT, FT, and static perturbation theory. We discuss also the convergence aspects of the three schemes (AHT, FT, and FME) and present the relevant references.

Analytic energy gradient for secondorder MøllerPlesset perturbation theory based on the fragment molecular orbital method
View Description Hide DescriptionThe first derivative of the total energy with respect to nuclear coordinates (the energy gradient) in the fragment molecular orbital (FMO) method is applied to second order MøllerPlesset perturbation theory (MP2), resulting in the analytic derivative of the correlation energy in the external selfconsistent electrostatic field. The completely analytic energy gradient equations are formulated at the FMOMP2 level. Both for molecular clusters (H_{2}O)_{64} and a system with fragmentation across covalent bonds, a capped alanine decamer, the analytic FMOMP2 energy gradients with the electrostatic dimer approximation are shown to be complete and accurate by comparing them with the corresponding numeric gradients. The developed gradient is parallelized with the parallel efficiency of about 97% on 32 Pentium4 nodes connected by Gigabit Ethernet.

Fluctuating hydrodynamics for multiscale simulation of inhomogeneous fluids: Mapping allatom molecular dynamics to capillary waves
View Description Hide DescriptionWe introduce a multiscale framework to simulate inhomogeneous fluids by coarsegraining an allatom molecular dynamics (MD) trajectory onto sequential snapshots of hydrodynamic fields. We show that the field representation of an atomistic trajectory is quantitatively described by a dynamic fieldtheoretic model that couples hydrodynamicfluctuations with a GinzburgLandaufree energy. For liquidvapor interfaces of argon and water, the parameters of the field model can be adjusted to reproduce the bulk compressibility and surface tension calculated from the positions and forces of atoms in an MD simulation. These optimized parameters also enable the field model to reproduce the static and dynamic capillary wave spectra calculated from atomistic coordinates at the liquidvapor interface. In addition, we show that a densitydependent gradient coefficient in the GinzburgLandaufree energy enables bulk and interfacial fluctuations to be controlled separately. For water, this additional degree of freedom is necessary to capture both the bulk compressibility and surface tension emergent from the atomistic trajectory. The proposed multiscale framework illustrates that bottomup coarsegraining and topdown phenomenology can be integrated with quantitative consistency to simulate the interfacial fluctuations in nanoscale transport processes.

Particlebased multiscale coarse graining with densitydependent potentials: Application to molecular crystals (hexahydro1,3,5trinitrostriazine)
View Description Hide DescriptionWe describe the development of isotropic particlebased coarsegrain models for crystalline hexahydro1,3,5trinitrostriazine (RDX). The coarse graining employs the recently proposed multiscale coarsegraining (MSCG) method, which is a particlebased forcematching approach for deriving freeenergy effective interaction potentials. Though onesite and foursite coarsegrain (CG) models were parameterized from atomistic simulations of nonordered (molten and ambient temperature amorphous) systems, the focus of the paper is a detailed study of the onesite model with a brief recourse to the foursite model. To improve the ability of the onesite model to be applied to crystalline phases at various pressures, it was found necessary to include explicit dependence on a particle density, and a new theory of local densitydependent MSCG potentials is subsequently presented. The densitydependency is implemented through interpolation of MSCG force fields derived at a preselected set of reference densities. The computationally economical procedure for obtaining the reference force fields starting from the interaction at ambient density is also described. The onesite MSCG model adequately describes the atomistic lattice structure of αRDX at ambient and high pressures, elastic and vibrational properties, pressurevolume curve up to P = 10 GPa, and the melting temperature. In the molten state, the model reproduces the correct pair structure at different pressures as well as higher order correlations. The potential of the MSCG model is further evaluated in simulations of shocked crystalline RDX

Approximate variational coupled cluster theory
View Description Hide DescriptionWe show that it is possible to construct an accurate approximation to the variational coupled cluster method, limited to double substitutions, from the minimization of a functional that is rigorously extensive, exact for isolated twoelectron subsystems and invariant to transformations of the underlying orbital basis. This approximate variational coupled clustertheory is a modification and enhancement of our earlier linked pair functionaltheory. It is first motivated by the constraint that the inverse square root of the matrix that transforms the cluster amplitudes must exist. Loworder corrections are then included to enhance the accuracy of the approximation of variational coupled cluster, while ensuring that the computational complexity of the method never exceeds that of the standard traditional coupled cluster method. The effects of single excitations are included by energy minimization with respect to the orbitals defining the reference wavefunction. The resulting quantum chemical method is demonstrated to be a robust approach to the calculation of molecular electronic structure and performs well when static correlation effects are strong.

Diabatic couplings for charge recombination via Boys localization and spinflip configuration interaction singles
View Description Hide DescriptionWe describe a straightforward technique for obtaining diabatic couplings applicable to charge transfer from or charge recombination to the electronic ground state. Our method is nearly black box, requiring minimal chemical intuition from the user, and merges two wellestablished approaches in electronic structuretheory: first, smooth and balanced adiabatic states are generated using spinflipconfiguration interaction singles (SFCIS) based on a triplet HF state; second, Boys localization is applied to rotate all adiabatic states into chargelocalized diabatic states. The method is computationally inexpensive, scaling only with the cost of CIS, and does not require a choice of active space, which is usually required for such intrinsically multiconfigurational problems. Molecular LiF in vacuum and LiF solvated by a single water molecule are examined as model systems. We find nearly smooth diabatic potential energy surfaces and couplings and we find that the Condon approximation is obeyed approximately for this model problem.

Empirical valence bond models for reactive potential energy surfaces: A parallel multilevel genetic program approach
View Description Hide DescriptionWe describe a new method for constructing empirical valence bond potential energy surfaces using a parallel multilevel genetic program (PMLGP). Genetic programs can be used to perform an efficient search through function space and parameter space to find the best functions and sets of parameters that fit energies obtained by ab initio electronic structure calculations. Building on the traditional genetic program approach, the PMLGP utilizes a hierarchy of genetic programming on two different levels. The lower level genetic programs are used to optimize coevolving populations in parallel while the higher level genetic program (HLGP) is used to optimize the genetic operator probabilities of the lower level genetic programs. The HLGP allows the algorithm to dynamically learn the mutation or combination of mutations that most effectively increase the fitness of the populations, causing a significant increase in the algorithm's accuracy and efficiency. The algorithm's accuracy and efficiency is tested against a standard parallel genetic program with a variety of onedimensional test cases. Subsequently, the PMLGP is utilized to obtain an accurate empirical valence bond model for proton transfer in 3hydroxygammapyrone in gas phase and protic solvent.

A new perspective on transition states: χ_{1} separatrix
View Description Hide DescriptionWe present a new definition of the transition state for chemical reactions, named the χ_{1} separatrix. In contrast to previous transition state definitions which depend on the choice of reaction coordinates, the χ_{1} separatrix is defined by choosing a time scale for observation and is connected to exact rate constants in the high friction limit. We demonstrate that this separatrix appears in the isomerization of alanine dipeptide as a stationary population in quasiequilibrium, without assuming a particular coordinate system or reactant and product surfaces.

GVVPT2 energy gradient using a Lagrangian formulation
View Description Hide DescriptionA Lagrangian based approach was used to obtain analytic formulas for GVVPT2 energy nuclear gradients. The formalism can use either complete or incomplete model (or reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. An efficient means of evaluating the gradient equations is described. Demonstrative calculations were performed and compared with finite difference calculations on several molecules and show that the GVVPT2 gradients are accurate. Of particular interest, the suggested formalism can straightforwardly use stateaveraged MCSCF descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited singlet states of LiH, including calculations near an avoided crossing. The accuracy and usefulness of the GVVPT2 method and its gradient are highlighted by comparing the geometry of the nearC_{2v} minimum on the conical intersection seam between the 1 ^{1} A _{1} and 2 ^{1} A _{1} surfaces of O_{3} with values that were calculated at the multireference configuration interaction, including single and double excitations (MRCISD), level of theory.

Density functional study of multiplicitychanging valence and Rydberg excitations of pblock elements: Delta selfconsistent field, collinear spinflip timedependent density functional theory (DFT), and conventional timedependent DFT
View Description Hide DescriptionA database containing 17 multiplicitychanging valence and Rydbergexcitation energies of pblock elements is used to test the performance of density functional theory(DFT) with approximate density functionals for calculating relative energies of spin states. We consider only systems where both the lowspin and highspin state are well described by a single Slater determinant, thereby avoiding complications due to brokensymmetry solutions. Because the excitations studied involve a spin change, they require a balanced treatment of exchange and correlation, thus providing a hard test for approximate density functionals. We test three formalisms for predicting the multiplicitychanging transition energies. First is the ΔSCF method; we also test timedependent density functional theory (TDDFT), both in its conventional form starting from the lowspin state and in its collinear spinflip form starting from the highspin state. Very diffuse basis functions are needed to give a qualitatively correct description of the Rydberg excitations. The scalar relativistic effect needs to be considered when quantitative results are desired, and we include it in the comparisons. With the ΔSCF method, most of the tested functionals give mean unsigned errors (MUEs) larger than 6 kcal/mol for valence excitations and MUEs larger than 3 kcal/mol for Rydberg excitations, but the performance for the Rydberg states is much better than can be obtained with timedependent DFT. It is surprising to see that the longrange corrected functionals, which have 100% Hartree–Fock exchange at large interelectronic distance, do not improve the performance for Rydberg excitations. Among all tested density functionals, ΔSCF calculations with the O3LYP, M08HX, and OLYP functionals give the best overall performance for both valence and Rydberg excitations, with MUEs of 2.1, 2.6, and 2.7 kcal/mol, respectively. This is very encouraging since the MUE of the CCSD(T) coupled cluster method with quintuple zeta basis sets is 2.0 kcal/mol; however, caution is advised since many popular density functionals give poor results, and there can be very significant differences between the ΔSCF predictions and those from TDDFT.

Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy
View Description Hide DescriptionWe explore the concept of seniority number (defined as the number of unpaired electrons in a determinant) when applied to the problem of electroncorrelation in atomic and molecular systems. Although seniority is a good quantum number only for certain model Hamiltonians (such as the pairing Hamiltonian), we show that it provides a useful partitioning of the electronic full configuration interaction (FCI) wave function into rapidly convergent Hilbert subspaces whose weight diminishes as its seniority number increases. The primary focus of this study is the adequate description of static correlation effects. The examples considered are the ground states of the helium, beryllium, and neon atoms, the symmetric dissociation of the N_{2} and CO_{2} molecules, as well as the symmetric dissociation of an H_{8} hydrogen chain. It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion. The energy relevance of the seniority zero sector (determinants with all paired electrons) increases dramatically if orbitals of broken spatial symmetry (as those commonly used for Hubbard Hamiltonian studies) are allowed in the wave function construction.