Volume 135, Issue 18, 14 November 2011

Zeolites of type ferrierite are exploited as a host system for monitoring the evolution of guest concentration (methanol) in nanoporous host materials upon adsorption. Additional transport resistances at the crystal surface have been removed so that uptake is exclusively controlled by the diffusion resistance of the pore space. Since the crystal shape deviates from a simple parallelepiped, the primary imaging data do not immediately reflect true local concentrations. A simple algorithm is developed which overcomes this complication. The determined transient concentration profiles ideally comply with the requirements for the application of the BoltzmannMatano integration method for determining diffusivities. The resulting diffusivities (along the direction of the “10ring channels”) are found to exceed those along the 8ring channels by three orders of magnitude.
 COMMUNICATIONS


Communication: Regularizing binding energy distributions and thermodynamics of hydration: Theory and application to water modeled with classical and ab initio simulations
View Description Hide DescriptionThe highenergy tail of the distribution of solutesolvent interactionenergies is poorly characterized for condensed systems, but this tail region is of principal interest in determining the excess free energy of the solute. We introduce external fields centered on the solute to modulate the shortrange repulsive interaction between the solute and solvent. This regularizes the binding energy distribution and makes it easy to calculate the free energy of the solute with the field. Together with the work done to apply the field in the presence and absence of the solute, we calculate the excess chemical potential of the solute. We present the formal development of this idea and apply it to study liquid water.

Communication: Inferring the equation of state of a metastable hardsphere fluid from the equation of state of a hardsphere mixture at high densities
View Description Hide DescriptionA possible approximate route to obtain the equation of state of the monodisperse hardsphere system in the metastable fluid region from the knowledge of the equation of state of a hardsphere mixture at high densities is discussed. The proposal is illustrated by using recent Monte Carlo simulation data for the pressure of a binary mixture. It is further shown to exhibit high internal consistency.

Communication: Limitations of the stochastic quasisteadystate approximation in open biochemical reaction networks
View Description Hide DescriptionIt is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasisteadystate approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the MichaelisMenten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation.
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 ARTICLES

 Theoretical Methods and Algorithms

Semibottomup coarse graining of water based on microscopic simulations
View Description Hide DescriptionThe generalized dissipative particle dynamics (DPD) equation derived from the generalized Langevin equation under Markovian approximations is used to simulate coarsegrained (CG) water cells. The mean force and the friction coefficients in the radial and transverse directions needed for DPD equation are obtained directly from the all atomistic molecular dynamics (AAMD) simulations. But the dissipative friction forces are overestimated in the Markovian approximation, which results in wrong dynamic properties for the CG water in the DPD simulations. To account for the nonMarkovian dynamics, a rescaling factor is introduced to the friction coefficients. The value of the factor is estimated by matching the diffusivity of water. With this semibottomup mapping method, the radial distribution function, the diffusion constant, and the viscosity of the coarsegrained water system computed with DPD simulations are all in good agreement with AAMD results. It bridges the microscopic level and mesoscopic level with consistent length and time scales.

Photodissociation of methyl iodide embedded in a hostguest complex: A full dimensional (189D) quantum dynamics study of CH_{3}I@resorc[4]arene
View Description Hide DescriptionAccurate full dimensional quantum dynamics calculations studying the photodissociation of CH_{3}I@resorc[4]arene on an ab initio based potential energy surface (PES) model are reported. The converged 189D quantum dynamics calculations are facilitated by the multilayer multiconfigurational timedependent Hartree (MLMCTDH) approach combined with the correlation discrete variable representation (CDVR) for the evaluation of potential energy matrix elements. The potential employed combines an established ab initio PES describing the photodissociation of methyl iodide in the A band with a harmonic description of the resorc[4]arene host and a bilinear modeling of the hostguest interaction. All potential parameters required in the description of the vibrations of the host molecule and the hostguest interaction are derived from ab initio calculations on the hostguest complex. Absorption spectra at and are calculated and the electronic population dynamics during the bond breaking process occurring in the first 20–30 fs after the photoexcitation is investigated. Weak but significant effects resulting from the hostguest interaction on this time scale are found and interpreted. The present study demonstrates that accurate fully quantum mechanical dynamics calculations can be preformed for systems consisting of more than 50 atoms using the MLMCTDH/CDVR approach. Utilizing an efficient statistical approach for the construction of the ensemble of initial wavepackets, these calculations are not restricted to zero temperature but can also study the dynamics at 300 K.

A semigrand canonical Monte Carlo simulation model for ion binding to ionizable surfaces: Proton binding of carboxylated latex particles as a case study
View Description Hide DescriptionIn this paper, we present a computer simulation study of the ion binding process at an ionizable surface using a semigrand canonical Monte Carlo method that models the surface as a discrete distribution of charged and neutral functional groups in equilibrium with explicit ions modelled in the context of the primitive model. The parameters of the simulation model were tuned and checked by comparison with experimental titrations of carboxylated latex particles in the presence of different ionic strengths of monovalent ions. The titration of these particles was analysed by calculating the degree of dissociation of the latex functional groups vs. pH curves at different background salt concentrations. As the charge of the titrated surface changes during the simulation, a procedure to keep the electroneutrality of the system is required. Here, two approaches are used with the choice depending on the ion selected to maintain electroneutrality: counterion or coion procedures. We compare and discuss the difference between the procedures. The simulations also provided a microscopic description of the electrostaticdouble layer(EDL) structure as a function of pH and ionic strength. The results allow us to quantify the effect of the size of the background salt ions and of the surface functional groups on the degree of dissociation. The nonhomogeneous structure of the EDL was revealed by plotting the counterion density profiles around charged and neutral surface functional groups.

The nuclear magnetic resonance relaxation data analysis in solids: General R _{1}/R _{1} _{ ρ } equations and the modelfree approach
View Description Hide DescriptionThe advantage of the solid state NMR for studying molecular dynamics is the capability to study slow motions without limitations: in the liquid state, if orienting media are not used, all anisotropic magnetic interactions are averaged out by fast overall Brownian tumbling of a molecule and thus investigation of slow internal conformational motions (e.g., of proteins) in solution can be conducted using only isotropic interactions. One of the main tools for obtaining amplitudes and correlation times of molecular motions in the μs time scale is measuring relaxation rate R _{1} _{ ρ }. Yet, there have been a couple of unresolved problems in the quantitative analysis of the relaxation rates. First, when the resonance offset of the spinlock pulse is used, the spinlock field can be oriented under an arbitrary angle in respect to B _{0}. Second, the spinlock frequency can be comparable or even less than the magic angle spinning rate. Up to now, there have been no equations for R _{1} _{ ρ } that would be applicable for any values of the spinlock frequency, magic angle spinning rate and resonance offset of the spinlock pulse. In this work such equations were derived for two most important relaxation mechanisms: heteronuclear dipolar coupling and chemical shift anisotropy. The validity of the equations was checked by numerical simulation of the R _{1} _{ ρ } experiment using SPINEVOLUTION program. In addition to that, the applicability of the wellknown modelfree approach to the solid state NMR relaxation data analysis was considered. For the wobbling in a cone at 30º and 90º cone angles and twosite jump models, it has been demonstrated that the autocorrelation functions G _{0}(t), G _{1}(t), G _{2}(t), corresponding to different spherical harmonics, for isotropic samples (powders, polycrystals, etc.) are practically the same regardless of the correlation time of motion. This means that the modelfree approach which is widely used in liquids can be equally applied, at least assuming these two motional models, to the analysis of the solid state NMR relaxation data.

Calculation of the exchange coupling constants of copper binuclear systems based on spinflip constricted variational density functional theory
View Description Hide DescriptionWe have recently developed a methodology for the calculation of exchange coupling constants J in weakly interacting polynuclear metal clusters. The method is based on unrestricted and restricted second order spinflip constricted variational density functional theory (SFCV(2)DFT) and is here applied to eight binuclear copper systems. Comparison of the SFCV(2)DFT results with experiment and with results obtained from other DFT and wave function based methods has been made. Restricted SFCV(2)DFT with the BH&HLYP functional yields consistently J values in excellent agreement with experiment. The results acquired from this scheme are comparable in quality to those obtained by accurate multireference wave function methodologies such as difference dedicated configuration interaction and the complete active space with secondorder perturbation theory.

Multipolar polarizabilities and twobody dispersion coefficients for Na by a variationally stable procedure
View Description Hide DescriptionBased on the weakest bound electron potential model theory, the groundstatewave function of Na is investigated. The variationally stable procedure of Gao and Starace is then employed to evaluate the static multipolar polarizabilities of Na, and the twobody dispersion coefficients for the Na–Na system. Calculated values show that our results are in general agreement with those previously reported in the literature.

A tiered approach to Monte Carlo sampling with selfconsistent field potentials
View Description Hide DescriptionA “tiered” approach to Monte Carlo sampling of nuclear configurations is presented for ab initio, selfconsistent field (SCF)based potentials, including HartreeFock and density functional theory. Rather than Metropolis testing only the final SCF energy, individual cycle energies are tested in a tiered fashion, without approximation. Accordingly, rejected configurations are terminated early in the SCF procedure. The method is shown to properly obey detailed balance, and effective modifications are presented for cases in which the initial SCF guess is particularly poor. Demonstrations on simple systems are provided, including an assessment of the thermal properties of the neutral water dimer with B3LYP/631++G**. Cost analysis indicates a factoroftwo reduction in SCF cycles, which makes the method competitive with accelerated molecular dynamics sampling techniques, without the need for forces.

Magnetic exchange couplings from constrained density functional theory: An efficient approach utilizing analytic derivatives
View Description Hide DescriptionWe introduce a method for evaluating magnetic exchange couplings based on the constrained density functional theory (CDFT) approach of Rudra, Wu, and Van Voorhis [J. Chem. Phys.124, 024103 (2006)10.1063/1.2145878]. Our method shares the same physical principles as CDFT but makes use of the fact that the electronic energy changes quadratically and bilinearly with respect to the constraints in the range of interest. This allows us to use coupled perturbed KohnSham spin density functional theory to determine approximately the corrections to the energy of the different spin configurations and construct a priori the relevant energylandscapes obtained by constrained spin density functionaltheory. We assess this methodology in a set of binuclear transitionmetal complexes and show that it reproduces very closely the results of CDFT. This demonstrates a proofofconcept for this method as a potential tool for studying a number of other molecular phenomena. Additionally, routes to improving upon the limitations of this method are discussed.

Prospects for releasenode quantum Monte Carlo
View Description Hide DescriptionWe perform releasenode quantum Monte Carlo simulations on the first row diatomic molecules in order to assess how accurately their groundstate energies can be obtained. An analysis of the fermionboson energy difference is shown to be strongly dependent on the nuclear charge, Z, which in turn determines the growth of variance of the releasenode energy. It is possible to use maximum entropyanalysis to extrapolate to groundstate energies only for the low Z elements. For the higher Z dimers beyond boron, the error growth is too large to allow accurate data for long enough imaginary times. Within the limit of our statistics we were able to estimate, in atomic units, the groundstate energy of Li_{2} (−14.9947(1)), Be_{2} (−29.3367(7)), and B_{2}(−49.410(2)).

Particleparticle particlemesh method for dipolar interactions: On error estimates and efficiency of schemes with analytical differentiation and mesh interlacing
View Description Hide DescriptionThe interlaced and noninterlaced versions of the dipolar particleparticle particlemesh (P^{3}M) method implemented using the analytic differentiation scheme (ADP^{3}M) are presented together with their respective error estimates for the calculation of the forces, torques, and energies. Expressions for the optimized lattice Green functions, and for the Madelung selfforces, selftorques and selfenergies are given. The applicability of the theoretical error estimates are thoroughly tested and confirmed in several numerical examples. Our results show that the accuracy of the calculations can be improved substantially when the approximate (mesh computed) Madelung selfinteractions are subtracted. Furthermore, we show that the interlaced dipolar ADP^{3}M method delivers a significantly higher accuracy (which corresponds approximately to using a twice finer mesh) than the conventional method, allowing thereby to reduce the mesh size with respect to the noninterlaced version for a given accuracy. In addition, we present similar expressions for the dipolar ikdifferentiation interlaced scheme, and we perform a comparison with the AD interlaced scheme. Rough tests for the relative speed of the dipolar P^{3}M method using ikdifferentiation and the interlaced/noninterlaced AD schemes show that when FFT computing time is the bottleneck, usually when working at high precisions, the interlaced ADscheme can be several times faster than the other two schemes. For calculations with a low accuracy requirement, the interlaced version can perform worse than the ik and the noninterlaced AD schemes.

Analytical approach for the excitedstate Hessian in timedependent density functional theory: Formalism, implementation, and performance
View Description Hide DescriptionThe paper presents the formalism, implementation, and performance of the analytical approach for the excitedstate Hessian in the timedependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys.135, 014113 (2011)] on the analytical Hessian in TDDFT within TammDancoff approximation (TDA) to full TDDFT. In contrast to TDATDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excitedstate harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized groundstate and excitedstate scale factors to scale the calculated excitedstate harmonic frequencies and find that the scaling decreases the rootmeansquare errors. The optimized scale factors derived from the excitedstate calculations are slightly smaller than those from the groundstate calculations.
 Advanced Experimental Techniques

Microimaging of transient guest profiles in nanochannels
View Description Hide DescriptionZeolites of type ferrierite are exploited as a host system for monitoring the evolution of guest concentration (methanol) in nanoporous host materials upon adsorption. Additional transport resistances at the crystal surface have been removed so that uptake is exclusively controlled by the diffusion resistance of the pore space. Since the crystal shape deviates from a simple parallelepiped, the primary imaging data do not immediately reflect true local concentrations. A simple algorithm is developed which overcomes this complication. The determined transient concentration profiles ideally comply with the requirements for the application of the BoltzmannMatano integration method for determining diffusivities. The resulting diffusivities (along the direction of the “10ring channels”) are found to exceed those along the 8ring channels by three orders of magnitude.

Can stimulated Raman pumping cause large population transfers in isolated molecules?
View Description Hide DescriptionWhen stimulated Raman pumping (SRP) is applied to a stream of isolated molecules, such as found in a supersonic molecular beam expansion, we show that SRP can neither saturate nor power broaden a molecular transition connecting two metastable levels that is resonant with the energy difference between the pump and Stokes laser pulses. Using the optical BlochFeynman equations, we discuss the pumping of the hydrogen molecule from H_{2} (v = 0, J = 0, M = 0) to H_{2} (v = 1, J = 2, M = 0) as an illustration of how coherent population return severely reduces the SRP pumping efficiency unless the pump and Stokes laser pulses are applied with an appropriate relative delay and ratio of intensities.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Resonance electron attachment and longlived negative ions of phthalimide and pyromellitic diimide
View Description Hide DescriptionResonance attachment of low energy (0–15 eV) electrons to imidecontaining molecules, phthalimide (PTI) and pyromellitic diimide (PMDI), was investigated in the gasphase by means of Electron Transmission Spectroscopy (ETS) and Dissociative Electron Attachment Spectroscopy (DEAS). Among a variety of low intensity negatively charged fragments formed by DEA, in both compounds the dominant species was found to be a longlived (μs) parent molecular anion formed at zero energy. In addition, in PMDI longlived molecular anions were also observed at 0.85 and 2.0 eV. The experimentally evaluated detachment times from the molecular anions as a function of incident electron energy are modeled with a simple computational approach based on the RRKM theory. The occurrence of radiationless transitions to the ground anion state, followed by internal vibrational relaxation, is believed to be a plausible mechanism to explain the exceptionally long lifetime of the PMDI molecular anions formed above zero energy.

Spinorbit and rotational couplings in radiative association of C(^{3} P) and N(^{4} S) atoms
View Description Hide DescriptionThe role of spinorbit and rotational couplings in radiative association of C(^{3} P) and N(^{4} S) atoms is investigated. Couplings among doublet electronic states of the CN radical are considered, giving rise to a 6state model of the process. The solution of the dynamical problem is based on the L^{2} method, where a complex absorbing potential is added to the Hamiltonian operator in order to treat continuum and bound levels in the same manner. Comparison of the energydependent rate coefficients calculated with and without spinorbit and rotational couplings shows that the couplings have a strong effect on the resonance structure and lowenergy baseline of the rate coefficient.

Millimeterwave rotational spectroscopy of FeCN (X ^{4}Δ_{i}) and FeNC (X ^{6}Δ_{i}): Determining the lowest energy isomer
View Description Hide DescriptionThe pure rotational spectrum of FeCN has been recorded in the frequency range 140500 GHz using millimeter/submillimeter direct absorption techniques. The species was created in an ac discharge of Fe(CO)_{5} and cyanogen. Spectra of the ^{13}C, ^{54}Fe, and ^{57}Fe isotopologues were also measured, confirming the linear cyanide structure of this free radical. Lines originating from several RennerTeller components in the v _{2} bending mode were also observed. Based on the observed spinorbit pattern, the ground state of FeCN is ^{4}Δ_{i}, with small lambdadoubling splittings apparent in the Ω = 5/2, 3/2, and 1/2 components. In addition, a much weaker spectrum of the lowest spinorbit component of FeNC, Ω = 9/2, was recorded; these data are consistent with the rotational parameters of previous optical studies. The data for FeCN were fit with a Hund's case (a) Hamiltonian and rotational, spinorbit, spinspin, and lambdadoubling parameters were determined. Rotational constants were also established from a case (c) analysis for the other isotopologues, excited vibronic states, and for FeNC. The r_{0}bond lengths of FeCN were determined to be r_{Fe−C} = 1.924 Å and r_{C−N} = 1.157 Å, in agreement with theoretical predictions for the ^{4}Δ_{i} state. These measurements indicate that FeCN is the lower energy isomer and is more stable than FeNC by ∼1.9 kcal/mol.

Spectroscopic studies of the – electronic spectrum of the βhydroxyethylperoxy radical: Structure and dynamics
View Description Hide DescriptionThe jetcooled – near IR origin band spectra of the G_{1}G_{2}G_{3} conformer of four βhydroxyethylperoxy isotopologues, βHEP (HOCH_{2}CH_{2}OO), βDHEP (DOCH_{2}CH_{2}OO), βHEPd_{4} (HOCD_{2}CD_{2}OO), and βDHEPd_{4} (DOCD_{2}CD_{2}OO), have been recorded by a cavity ringdown spectrometer with a laser source linewidth of ∼70 MHz. The spectra of all four isotopologues have been analyzed and successfully simulated with an evolutionary algorithm, confirming the cyclic structure of the molecule responsible for the observed origin band. The analysis also provides experimental and state rotational constants and the orientation of the transition dipole moment in the inertial axis system; these quantities are compared to results from electronic structure calculations. The observed, broad linewidth (Δν > 2 GHz) is attributed to a shortened lifetime of the state associated with dynamics along the reaction path for hydrogen transfer from the OH to OO group.