Volume 134, Issue 9, 07 March 2011

We describe a theoretical framework for understanding the heteronuclear version of the third spin assisted recoupling polarization transfer mechanism and demonstrate its potential for detecting longdistance intramolecular and intermolecular ^{15}N–^{13}C contacts in biomolecular systems. The pulse sequence, proton assisted insensitive nuclei cross polarization (PAINCP) relies on a cross term between ^{1}H–^{15}N and ^{1}H–^{13}C dipolar couplings to mediate zero and/or doublequantum ^{15}N–^{13}C recoupling. In particular, using average Hamiltonian theory we derive effective Hamiltonians for PAINCP and show that the transfer is mediated by trilinear terms of the form N ^{±} C ^{∓} H _{ z } (ZQ) or N ^{±} C ^{±} H _{ z } (DQ) depending on the rf field strengths employed. We use analytical and numerical simulations to explain the structure of the PAINCP optimization maps and to delineate the appropriate matching conditions. We also detail the dependence of the PAINCP polarization transfer with respect to local molecular geometry and explain the observed reduction in dipolar truncation. In addition, we demonstrate the utility of PAINCP in structural studies with ^{15}N–^{13}C spectra of two uniformly ^{13}C,^{15}N labeled model microcrystalline proteins—GB1, a 56 amino acid peptide, and Crh, a 85 amino acid domain swapped dimer (MW = 2 × 10.4 kDa). The spectra acquired at high magic angle spinning frequencies (ω_{r}/2π > 20 kHz) and magnetic fields (ω _{ 0H }/2π = 700–900 MHz) using moderate rf fields, yield multiple longdistance intramonomer and intermonomer ^{15}N–^{13}C contacts. We use these distance restraints, in combination with the available xray structure as a homology model, to perform a calculation of the monomer subunit of the Crh protein.
 COMMUNICATIONS


Communication: Direct angleresolved measurements of collision dynamics with electronically excited molecules: NO(A^{2}Σ^{+}) + Ar
View Description Hide DescriptionWe report direct doubly differential (quantum state and angleresolved) scattering measurements involving shortlived electronically excited molecules using crossed molecular beams. In our experiment, supersonic beams of nitric oxide and argon atoms collide at 90°. In the crossing region, NO molecules are excited to the A^{2}Σ^{+}state by a pulsed nanosecond laser, undergo rotationally inelastic collisions with Ar atoms, and are then detected 400 ns later (approximately twice the radiative lifetime of the A^{2}Σ^{+}state) by 1 + 1^{′} multiphoton ionization via the E^{2}Σ^{+} state. The velocity distributions of the scattered molecules are recorded using velocitymapped ion imaging. The resulting images provide a direct measurement of the statetostate differential scattering cross sections. These results demonstrate that sufficient scattering events occur during the short lifetimes typical of molecular excited states (∼200 ns, in this case) to allow spectroscopically detected quantumstateresolved measurements of products of excitedstate collisions.

Communication: CO oxidation by silver and gold cluster cations: Identification of different active oxygen species
View Description Hide DescriptionThe oxidation of carbon monoxide with nitrous oxide on massselected and clusters has been investigated under multicollision conditions in an octopole ion trap experiment. The comparative study reveals that for both gold and silver cations carbon dioxide is formed on the clusters. However, whereas in the case of the cluster itself acts as reactive species that facilitates the formation of CO_{2} from N_{2}O and CO, for silver the oxidizedclustersAg_{3}O_{ x } ^{+} (n = 1–3) are identified as active in the CO oxidationreaction. Thus, in the case of the silvercluster cations N_{2}O is dissociated and one oxygen atom is suggested to directly react with CO, whereas a second kind of oxygen strongly bound to silver is acting as a substrate for the reaction.
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 ARTICLES

 Theoretical Methods and Algorithms

Local ab initio methods for calculating optical band gaps in periodic systems. I. Periodic density fitted local configuration interaction singles method for polymers
View Description Hide DescriptionWe present a density fitted local configuration interaction singles (CIS) method for calculating optical band gaps in 1Dperiodic systems. The method is based on the Davidson diagonalization procedure, carried out in the reciprocal space. The oneelectron part of the matrix–vector products is also evaluated in the reciprocal space, where the diagonality of the Fock matrix can be exploited. The contraction of the CIS vectors with the two electron integrals is performed in the direct space in the basis of localized occupied (Wannier) and virtual (projected atomic) orbitals. The direct space approach allows to utilize the sparsity of the integrals due to the local representation and locality of the exciton. The density fitting approximation employed for the two electron integrals reduces the nominal scaling with unit cell size to . Test calculations on a series of prototypical systems demonstrate that the method in its present stage can be used to calculate the excitonic band gaps of polymers with up to a few dozens of atoms in the cell. The computational cost depends on the locality of the exciton, but even relatively delocalized excitons occurring in the polybiphenyl in the parallel orientation, can be routinely treated with this method.

Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration timedependent Hartree method
View Description Hide DescriptionIn this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration timedependent Hartree results with approximate solutions using continuous configuration timedependent selfconsistent field and local coherent state approximation.

Transitionmetal dioxides: A case for the intersite term in Hubbardmodel functionals
View Description Hide DescriptionTriatomic transitionmetal oxides in the “inserted dioxide” (O–M–O) structure represent one of the simplest examples of systems that undergo qualitative geometrical changes via subtle electronicstructure modulation. We consider here three transitionmetal dioxide molecules (MO_{2} where M = Mn, Fe, or Co), for which the equilibrium structural (e.g., bent or linear geometry) and electronic (e.g., spin or symmetry) properties have been challenging to assign both theoretically and experimentally. Augmenting a standard densityfunctional theory(DFT) approach with a Hubbard term (DFT+U) occasionally overlocalizes the 3dmanifold, leading to an incorrect bond elongation and, in turn, poor equilibrium geometries for MO_{2} molecules, while preserving good spinstate splittings. Proper description of both geometry and energetics for these molecules is recovered; however, through either calculating DFT+U relaxations at fixed M–O bond lengths or by inclusion of an intersite interaction term V that favors M(3d)–O(2p) interactions. In this latter case, both U and V are calculated fully from firstprinciples and are not fitting parameters. Finally, we identify an approach that more accurately determines the Hubbard U over a coordinate in which the covalent character of bonding varies.

Exponentially and preexponentially correlated Gaussians for atomic quantum calculations
View Description Hide DescriptionExplicitly correlated, nelectron, onecenter s Gaussian (ECG) functions that depend on the interelectron distances in the exponent are combined with s ECGs which also depend on the interelectron separations through preexponential multipliers. The preexponentially dependent ECGs are included in the basis to better describe the interelectron correlation and the interelectron cusps. The basis set is tested in the calculations of the ground state of the beryllium atom (^{9}Be).

Transport, phase transitions, and wetting in micro/nanochannels: A phase field/DDFT approach
View Description Hide DescriptionWhile the flow of a liquid in a macroscopic channel is usually described using hydrodynamics with noslip boundary conditions at the walls of the channel, transport phenomena in microchannels involve physics at many different scales due to the interplay between the micrometric section of the channel and the micro or nanometric roughness of the boundaries. Roughness can have many different effects such as increasing the friction between the liquid and the walls (leading to the macroscopic noslip boundary condition) or on the contrary reduce it thanks to the Wenzel–Cassie–Baxter wettingtransition induced by capillarity. Here we detail a phasefield/dynamic density functional theory model able to account for the wettingtransitions, the resulting friction between the wall and the fluid, and compressible hydrodynamics at high viscosity contrast.

Fragmentation and reactivity in collisions of protonated diglycine with chemically modified perfluorinated alkylthiolateselfassembled monolayer surfaces
View Description Hide DescriptionDirect dynamics simulations are reported for quantum mechanical (QM)/molecular mechanical (MM) trajectories of Nprotonated diglycine (gly_{2}H^{+}) colliding with chemically modified perfluorinated octanethiolate selfassembled monolayer (SAM)surfaces. The RM1 semiempirical theory is used for the QM component of the trajectories. RM1 activation and reaction energies were compared with those determined from higherlevel ab initio theories. Two chemical modifications are considered in which a head group (–COCl or –CHO) is substituted on the terminal carbon of a single chain of the SAM. These surfaces are designated as the COClSAM and CHOSAM, respectively. Fragmentation, peptidereaction with the SAM, and covalent linkage of the peptide or its fragments with the SAMsurface are observed. Peptide fragmentation via concerted CH_{2}–CO bond breakage is the dominant pathway for both surfaces. HCl formation is the dominant species produced by reaction with the COClSAM, while for the CHOSAM a concerted Hatom transfer from the CHOSAM to the peptide combined with either a Hatom or radical transfer from the peptide to the surface to form singlet reaction products is the dominant pathway. A strong collision energy dependence is found for the probability of peptide fragmentation, its reactivity, and linkage with the SAM.Surface deposition, i.e., covalent linkage between the surface and the peptide, is compared to recent experimental observations of such bonding by Laskin and coworkers [Phys. Chem. Chem. Phys. 10, 1512 (2008)]. Qualitative differences in reactivity are seen between the COClSAM and CHOSAM showing that chemical identity is important for surface reactivity. The probability of reactive surface deposition, which is most closely analogous to experimental observables, peaks at a value of around 20% for a collision energy of 50 eV.

Ab initio interatomic decay widths of excited states by applying Stieltjes imaging to Lanczos pseudospectra
View Description Hide DescriptionElectronically excited states of atoms and molecules in an environment may decay in interatomic processes by transferring excess energy to neighboring species and ionizing them. The corresponding interatomic decay width is the most important characteristic of the decay allowing to calculate its efficiency and the final states’ distribution. In this paper we present calculations of interatomic widths by the Fano–Stieltjes method applied to Lanczos pseudospectra, which has been previously shown to provide accurate autoionization widths in atoms and molecules. The use of Lanczos pseudospectra allows one to avoid the full diagonalization bottleneck and makes the method applicable to larger systems. We apply the present method to the calculation of interatomic decay widths in NeMg, NeAr and HCN·Mg_{ n }, n = 1, 2 clusters. The results are compared with widths obtained analytically and by other ab initio methods where available.

Accurate freezing and melting equations for the LennardJones system
View Description Hide DescriptionAnalyzing three approximate methods to locate liquid–solid coexistence in simple systems, an observation is made that all of them predict the same functional dependence of the temperature on density at freezing and melting of the conventional LennardJones (LJ) system. The emerging equations can be written as in normalized units. We suggest to determine the values of the coefficients at freezing and melting from the hightemperature limit, governed by the inverse 12th power repulsive potential. The coefficients can be determined from the triple point parameters of the LJ fluid. This produces freezing and meltingequations which are exact in the hightemperature limit and at the triple point and show remarkably good agreement with numerical simulation data in the intermediate region.

The effect of electron interactions on the universal properties of systems with optimized offresonant intrinsic hyperpolarizability
View Description Hide DescriptionBecause of the potentially large number of important applications of nonlinear optics, researchers have expended a great deal of effort to optimize the secondorder molecular nonlinearoptical response, called the hyperpolarizability. The focus of our present studies is the intrinsic hyperpolarizability, which is a scaleinvariant quantity that removes the effects of simple scaling, thus being the relevant quantity for comparing molecules of varying sizes. Past theoretical studies have focused on structural properties that optimize the intrinsic hyperpolarizability, which have characterized the structure of the quantum system based on the potential energy function, placement of nuclei, geometry, and the effects of external electric and magnetic fields. Those previous studies focused on singleelectron models under the influence of an average potential. In the present studies, we generalize our calculations to twoelectron systems and include electron interactions. As with the singleelectron studies, universal properties are found that are common to all systems—be they molecules, nanoparticles, or quantum gases—when the hyperpolarizability is near the fundamental limit.

Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: Application to formaldehyde
View Description Hide DescriptionWe have demonstrated the use of ab initiomolecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SCIVR). A relatively low level of electronic structure theory (HF/321G) was used in this proofofprinciple study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMDSCIVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational selfconsistent field/vibrational configuration interaction with perturbation selected interactionssecondorder perturbation theory (VSCF/VCIPSIPT2) and correlationcorrected vibrational selfconsistent field (ccVSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SCIVR method a practical tool for firstprinciples quantum dynamics simulations.

On the relation between orbitallocalization and selfinteraction errors in the density functional theory treatment of organic semiconductors
View Description Hide DescriptionIt is commonly argued that the selfinteraction error (SIE) inherent in semilocal density functionals is related to the degree of the electronic localization. Yet at the same time there exists a latent ambiguity in the definitions of the terms “localization” and “selfinteraction,” which ultimately prevents a clear and readily accessible quantification of this relationship. This problem is particularly pressing for organic semiconductor molecules, in which delocalized molecular orbitals typically alternate with localized ones, thus leading to major distortions in the eigenvaluespectra. This paper discusses the relation between localization and SIEs in organic semiconductors in detail. Its findings provide further insights into the SIE in the orbital energies and yield a new perspective on the failure of selfinteraction corrections that identify delocalized orbital densities with electrons.

Coarsegraining errors and numerical optimization using a relative entropy framework
View Description Hide DescriptionThe ability to generate accurate coarsegrained models from reference fully atomic (or otherwise “firstprinciples”) ones has become an important component in modeling the behavior of complex molecular systems with large length and time scales. We recently proposed a novel coarsegraining approach based upon variational minimization of a configurationspace functional called the relative entropy,S _{rel}, that measures the information lost upon coarsegraining. Here, we develop a broad theoretical framework for this methodology and numerical strategies for its use in practical coarsegraining settings. In particular, we show that the relative entropy offers tight control over the errors due to coarsegraining in arbitrary microscopic properties, and suggests a systematic approach to reducing them. We also describe fundamental connections between this optimization methodology and other coarsegraining strategies like inverse Monte Carlo, force matching, energy matching, and variational meanfieldtheory. We suggest several new numerical approaches to its minimization that provide new coarsegraining strategies. Finally, we demonstrate the application of these theoretical considerations and algorithms to a simple, instructive system and characterize convergence and errors within the relative entropy framework.

Inversion of twodimensional potentials from frequencyresolved spectroscopic data
View Description Hide DescriptionWe report the first successful reconstruction of twodimensional potential energy surfaces (PES) using the magnitudes and positions of a set of frequencyresolved fluorescence (or absorption) lines. The inversion proceeds by first extracting the phases of the transitiondipole matrix elements, yielding, together with the (ground) PES to (from) which emission (absorption) occurs, a point by point reconstruction of the twodimensional excited state PES. The inversion procedure is highly accurate even for PES with multiple minima and many missing lines, with typical RMS errors <0.002 cm^{−1} in the classically allowed region and <0.018 cm^{−1} in the classically forbidden region.

Langevin–Bloch equations for a spin bath
View Description Hide DescriptionWe derive the Bloch equations for a twolevel system coupled to a spin bath of infinitely many twolevel atoms to examine phase and energy relaxation of an optically excited system. We show that increasing temperature assists coherence. This is reflected in a number of anomalous features of relaxation of the system, e.g., decrease of integrated absorption coefficient with temperature, nonlinear variation of linewidth with incident power. We also predict that thermally induced coherence may result in anomalous narrowing of linewidth, reminiscent (but distinct) of “motional narrowing” of spectral line. The theoretical results are discussed in the light of absorption–emission experiments on single quantum dots.

Dynamical meanfield theory from a quantum chemical perspective
View Description Hide DescriptionWe investigate the dynamical meanfieldtheory (DMFT) from a quantum chemical perspective. Dynamical meanfieldtheory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical meanfieldtheory to connect to quantum chemical language. Next, we describe an implementation of dynamical meanfieldtheory where we start from an ab initio Hartree–Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.

Laserinduced breathing modes in metallic nanoparticles: A symmetric molecular dynamics study
View Description Hide DescriptionA highly efficient simulation method based on molecular dynamics and group theory is adopted to investigate the laserinduced breathing oscillation of gold and silvernanospheres.Nanoparticles with size ranging from 5.8 to 46.2 nm are discussed. The effect due to laserinduced heating is modeled by a symmetric sudden expansion of the nanospheres by increasing the interatomic distances. A longrange empirical potential model which is capable of describing the phonon dispersion curves of noble metals in the full frequency range is established. Group theory is fully exploited to increase the computation efficiency, and the oscillation behavior of nanospheres of over 3 × 10^{6} atoms can be simulated efficiently. Oscillation frequencies of nanospheres are obtained by calculating the Fourier transform of the velocity autocorrelation function. The breathing modes of nanospheres are identified as the excitation of A _{1g } modes with inphase radial displacement of atoms in the nanospheres. The resulting oscillation spectra are in very good agreement with experimental data.

Complex wave patterns in an effective reaction–diffusion model for chemical reactions in microemulsions
View Description Hide DescriptionAn effective medium theory is employed to derive a simple qualitative model of a pattern formingchemical reaction in a microemulsion. This spatially heterogeneous system is composed of water nanodroplets randomly distributed in oil. While some steps of the reaction are performed only inside the droplets, the transport through the extended medium occurs by diffusion of intermediate chemical reactants as well as by collisions of the droplets. We start to model the system with heterogeneous reaction–diffusion equations and then derive an equivalent effective spatially homogeneous reaction–diffusion model by using earlier results on homogenization in heterogeneous reaction–diffusion systems [S.Alonso, M.Bär, and R.Kapral, J. Chem. Phys.134, 214102 (2009)]. We study the linear stability of the spatially homogeneous state in the resulting effective model and obtain a phase diagram of pattern formation, that is qualitatively similar to earlier experimental results for the Belousov–Zhabotinsky reaction in an aerosol OT (AOT)waterinoil microemulsion [V. K.Vanag and I. R.Epstein, Phys. Rev. Lett.87, 228301 (2001)]. Moreover, we reproduce many patterns that have been observed in experiments with the Belousov–Zhabotinsky reaction in an AOT oilinwater microemulsion by direct numerical simulations.

An efficient, fragmentbased electronic structure method for molecular systems: Selfconsistent polarization with perturbative twobody exchange and dispersion
View Description Hide DescriptionWe report a fragmentbased electronic structure method, intended for the study of clusters and molecular liquids, that incorporates electronic polarization (induction) in a selfconsistent fashion but treats intermolecular exchange and dispersion interactions perturbatively, as postselfconsistent field corrections, using a form of pairwise symmetryadapted perturbation theory. The computational cost of the method scales quadratically as a function of the number of fragments (monomers), but could be made to scale linearly by exploiting distancedependent thresholds. Extensive benchmark calculations are reported using the S22 database of highlevel ab initio binding energies for dimers, and we find that average errors can be reduced to <1 kcal/mol with a suitable choice of basis set. Comparison to ab initio benchmarks for water clusters as large as demonstrates that the method recovers ≳90% of the binding energy in these systems, at a tiny fraction of the computational cost. As such, this approach represents a promising path toward accurate, systematically improvable, and parameterfree simulation of molecular liquids.