Volume 133, Issue 14, 14 October 2010

The grand canonical Monte Carlo method is used to simulate the adsorption isotherms of water molecules on different types of model soot particles. These soot models are constructed by first removing atoms from onionfullerene structures in order to create randomly distributed pores inside the soot, and then performing molecular dynamics simulations, based on the reactive adaptive intermolecular reactive empirical bond order (AIREBO) description of the interaction between carbon atoms, to optimize the resulting structures. The obtained results clearly show that the main driving force of wateradsorption on soot is the possibility of the formation of new waterwater hydrogen bonds with the already adsorbed water molecules. The shape of the calculated wateradsorption isotherms at 298 K strongly depends on the possible confinement of the water molecules in pores of the carbonaceous structure. We found that there are two important factors influencing the adsorption ability of soot. The first of these factors, dominating at low pressures, is the ability of the soot of accommodating the first adsorbed water molecules at strongly hydrophilic sites. The second factor concerns the size and shape of the pores, which should be such that the hydrogen bonding network of the water molecules filling them should be optimal. This second factor determines the adsorption properties at higher pressures.
 COMMUNICATIONS


Communication: Thermodynamics of water modeled using ab initio simulations
View Description Hide DescriptionWe regularize the potential distribution framework to calculate the excess free energy of liquid water simulated with the BLYPD density functional. Assuming classical statistical mechanical simulations at 350 K model the liquid at 298 K, the calculated free energy is found in fair agreement with experiments, but the excess internal energy and hence also the excess entropy are not. The utility of thermodynamic characterization in understanding the role of high temperatures to mimic nuclear quantum effects and in evaluating ab initio simulations is noted.

Communication: ROHF theory made simple
View Description Hide DescriptionRestricted openshell Hartree–Fock (ROHF) theory is formulated as a projected selfconsistent unrestricted HF (UHF) model by mathematically constraining spin density eigenvalues. This constrained UHF (CUHF) wave function is identical to that obtained from Roothaan’s effective Fock operator. The and CUHF Fock operators are parameterfree and have eigenvalues (orbital energies) that are physically meaningful as in UHF, except for eliminating spin contamination. This new way of solving ROHF leads to orbitals that turn out to be identical to semicanonical orbitals. The present approach removes ambiguities in ROHF orbital energies.

Communication: Secondorder multireference perturbation theory with explicit correlation: CASPT2F12
View Description Hide DescriptionAn explicitly correlated complete active space secondorder perturbation (CASPT2F12) method is presented which strongly accelerates the convergence of CASPT2 energies and properties with respect to the basis set size. A Slatertype geminal function is employed as a correlation factor to represent the electronelectron cusp of the wave function. The explicitly correlated terms in the wave function are internally contracted. The required density matrix elements and coupling coefficients are the same as in conventional CASPT2, and the additional computational effort for the F12 correction is small. The CASPT2F12 method is applied to the singlettriplet splitting of methylene, the dissociation energy of ozone, and lowlying excited states of pyrrole.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

Effective numbers of modes applied to analysis of internal dynamics of weakly bound clusters
View Description Hide DescriptionThe dependence of the volume of the chaotic component in the internal dynamics of triatomic van der Waals clusters on the angular momentum is calculated using the Monte Carlo and molecular dynamics methods. It has been found that this dependence is nonmonotonic and that its functional form varies for different values of the total energy. The effective number of rotational modes was used to clarify why a change in the volume of chaotic component of the phase space happens for certain values of the angular momentum. We conclude that a large fraction of regular trajectories in relation to all trajectories appears only when there is a possibility for the regular motion to perform a rotation different from that for a chaotic motion. When such difference is small, the regular motion disappears. The effective number of rotational modes can be used to estimate the difference in the type of rotation and is a convenient parameter which controls changes in the dynamics of the system.

Performance of W4 theory for spectroscopic constants and electrical properties of small molecules
View Description Hide DescriptionAccurate spectroscopic constants and electrical properties of small molecules are determined by means of W4 and postW4 theories. For a set of 28 first and secondrow diatomic molecules for which very accurate experimental spectroscopic constants are available, W4 theory affords nearspectroscopic or better predictions. Specifically, the rootmeansquare deviations (RMSDs) from experiment are 0.04 pm for the equilibrium bond distances , for the harmonic frequencies , for the first anharmonicity constants , for the second anharmonicity constants , and for the vibrationrotation coupling constants . These RMSDs imply 95% confidence intervals of about 0.1 pm for , for , for , and for . We find that postCCSD(T) contributions are essential to achieve such narrow confidence intervals for and , but have little effect on and , and virtually none on . Higherorder connected triples improve the agreement with experiment for the hydride systems, but their inclusion (in the absence of ) tends to worsen the agreement with experiment for the nonhydride systems. Connected quadruple excitations have significant and systematic effects on , , and , in particular they universally increase (by up to 0.5 pm), universally reduce (by up to ), and universally increase (by up to ). Connected quintuple excitations are spectroscopically significant for of the nonhydride systems, affecting by up to . Diagonal Born–Oppenheimer corrections have systematic and spectroscopically significant effects on and of the hydride systems, universally increasing by 0.01–0.06 pm and decreasing by . Obtaining and of the pathologically multireference BN and BeO systems with nearspectroscopic accuracy requires large basis sets in the corevalence CCSD(T) step and augmented basis sets in the valence postCCSD(T) steps in W4 theory. The triatomic molecules , , and are also considered. The equilibrium geometries and harmonic frequencies (with the exception of the asymmetric stretch of ) are obtained with nearspectroscopic accuracy at the W4 level. The asymmetric stretch of ozone represents a severe challenge to W4 theory, in particular the connected quadruple contribution converges very slowly with the basis set size. Finally, the importance of postCCSD(T) correlation effects for electrical properties, namely, dipole moments, polarizabilities, and first hyperpolarizabilities , is evaluated.

A theoretical investigation of electric properties of Larginine phosphate monohydrate including environment polarization effects
View Description Hide DescriptionThe dipole moment, linear polarizability, and first hyperpolarizability of the asymmetric unit of Larginine phosphate (LAP) monohydrate crystal are investigated using the supermolecule approach in combination with an iterative electrostaticpolarization scheme. Environment polarization effects are attained by assuring the convergence of the dipole moment of LAP embedded in the polarization field of the surrounding molecules whose atomic sites are treated as point charges. The results obtained show that in the presence of the embedding charges, the value of is increased by 9% but the static values of and are decreased, respectively, by 3% and 13%, as compared with the isolated situation. The model predicts for the incrystal dipole moment the converged value of 33 D, in good concordance with the available experimental result of 32 D. Our estimates for the converged results of and are, respectively, and . Dispersion effects are found to have a small impact on the nonlinear optical responses of LAP in the visible region. In addition, MP2/6311G results obtained for by using isolated and embedded LAP dimers show that crystal packing effects have a significant contribution of the electrostaticinteractions. Our results suggest that the role of the crystal environment is to minimize the effects of the intermolecular interactions in the electric properties. That is, and gain a more additive character in the presence of the field of the embedding charges. This is specially marked for .

On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the secondorder reduced density matrix
View Description Hide DescriptionIn this paper we propose a functional of the manybody cumulant of the secondorder reduced density matrix within the spinfree formalism of quantum chemistry which quantifies the idea of electron correlation and allows one to detect spin entanglement. Its properties are rigorously stated and discussed for spinadapted pure states. Numerical determinations are performed for both equilibrium conformations and dissociation processes in molecular systems.

Energy surface, chemical potentials, Kohn–Sham energies in spinpolarized density functional theory
View Description Hide DescriptionOn the basis of the zerotemperature grand canonical ensemble generalization of the energy for fractional particle and spin numbers, the energy surface over the plane is displayed and analyzed in the case of homogeneous external magnetic fields. The (negative of the) left/rightside derivatives of the energy with respect to , , and give the fixed, spinup, and spindown ionization potentials/electron affinities, respectively, while the derivative of with respect to gives the (signed) half excitation energy to the lowestlying state with increased (or decreased) by 2. The highest occupied and lowest unoccupied Kohn–Sham spinorbital energies are identified as the corresponding spinup and spindown ionization potentials and electron affinities. The excitation energies to the lowestlying states with can be obtained as the differences between the lowest unoccupied and the oppositespin highest occupied spinorbital energies, if the representation of the Kohn–Sham spinpotentials is used. The cases where the convexity condition on the energy does not hold are also discussed. Finally, the discontinuities of the energy derivatives and the Kohn–Sham potential are analyzed and related.

Benchmarking NMR indirect nuclear spinspin coupling constants: SOPPA, SOPPA(CC2), and SOPPA(CCSD) versus CCSD
View Description Hide DescriptionAccurate calculations of NMR indirect nuclear spinspin coupling constants require especially optimized basis sets and correlated wave function methods such as CCSD or SOPPA(CCSD). Both methods scale as , where N is the number of orbitals, which prevents routine applications to molecules with more than 10–15 nonhydrogen atoms. We have therefore developed a modification of the SOPPA(CCSD) method in which the CCSD singles and doubles amplitudes are replaced by CC2 singles and doubles amplitudes. This new method, called SOPPA(CC2), scales only as , like the original SOPPAmethod. The performance of the SOPPA(CC2) method for the calculation of indirect nuclear spinspin coupling constants is compared to SOPPA and SOPPA(CCSD) employing a set of benchmark molecules. We also investigate the basis set dependence by employing three different basis sets optimized for spinspin coupling constants, namely the HuzIVsu4, ccJpVTZ, and ccJpVQZ basis sets. The results of the corresponding CCSD calculations are used as a theoretical reference.

Unified treatment of coherent and incoherent electronic energy transfer dynamics using classical electrodynamics
View Description Hide DescriptionRecent experiments on resonance energy transfer (RET) in photosynthetic systems have found evidence of quantum coherence between the donor and the acceptor. Under these conditions, Förster’s theory of RET is no longer applicable and no theory of coherent RET advanced to date rivals the intuitive simplicity of Förster’s theory. Here, we develop a framework for understanding RET that is based on classical electrodynamics but still captures the essence of the quantum coherence between the molecules. Our theory requires only a knowledge of the complex polarizabilities of the two molecules participating in the transfer as well as the distance between them. We compare our results to quantum mechanical calculations and show that the results agree quantitatively.

An efficient method for computing steady state solutions with Gillespie’s direct method
View Description Hide DescriptionGillespie’s direct method is a stochastic simulation algorithm that may be used to calculate the steady state solution of a chemically reacting system. Recently the all possible states method was introduced as a way of accelerating the convergence of the simulations. We demonstrate that while the all possible states (APS) method does reduce the number of required trajectories, it is actually much slower than the original algorithm for most problems. We introduce the elapsed time method, which reformulates the process of recording the species populations. The resulting algorithm yields the same results as the original method, but is more efficient, particularly for large models. In implementing the elapsed time method, we present robust methods for recording statistics and empirical probability distributions. We demonstrate how to use the histogram distance to estimate the error in steady state solutions.

A transferable classical potential for the water molecule
View Description Hide DescriptionWe developed a new model for the water molecule which contains only three Gaussian charges. Using the gasphase geometry the dipole moment of the molecule matches, the quadrupole moment closely approximates the experimental values. The negative charge is connected by a harmonic spring to its gasphase position. The polarized state is identified by the equality of the intermolecular electrostatic force and the spring force acting on the negative charge. In each timestep the instantaneous position of the massless negative charge is determined by iteration. Using the technique of Ewald summation, we derived expressions for the potential energy, the forces, and the pressure for Gaussian charges. The only properties to be fitted are the halfwidth values of the Gaussian charge distributions and the parameters of the nonelectrostatic repulsionattraction potential. We determined the properties of gasphase clusters up to six molecules, the internal energy and density of ambient water and hexagonal ice. We calculated the equilibrium density of ice VII as a function of pressure. As an additional test, we calculated the paircorrelation function, the isotherm compressibility, the heat capacity, and the selfdiffusion coefficients for ambient water. As far as we know, this is the first classical model of water which is able to estimate both ends of the phase diagram, the high pressureice VII, and the gas clusters of water with excellent accuracy.

Simulation of loss mechanisms in organic solar cells: A description of the mesoscopic Monte Carlo technique and an evaluation of the first reaction method
View Description Hide DescriptionIn this letter we evaluate the accuracy of the first reaction method (FRM) as commonly used to reduce the computational complexity of mesoscale Monte Carlo simulations of geminate recombination and the performance of organic photovoltaic devices. A wide range of carrier mobilities, degrees of energetic disorder, and applied electric field are considered. For the ranges of energetic disorder relevant for most polyfluorene, polythiophene, and alkoxy poly(phenylene vinylene) materials used in organic photovoltaics, the geminate separation efficiency predicted by the FRM agrees with the exact model to better than 2%. We additionally comment on the effects of equilibration on lowfield geminate separation efficiency, and in doing so emphasize the importance of the energy at which geminate carriers are created upon their subsequent behavior.

Basis set representation of the electron density at an atomic nucleus
View Description Hide DescriptionIn this paper a detailed investigation of the basis set convergence for the calculation of relativistic electron densities at the position of finitesized atomic nuclei is presented. The development of Gausstype basis sets for such electron densities is reported and the effect of different contraction schemes is studied. Results are then presented for picturechange corrected calculations based on the Douglas–Kroll–Hess Hamiltonian. Moreover, the role of electron correlation, the effect of the numerical integration accuracy in density functional calculations, and the convergence with respect to the order of the Douglas–Kroll–Hess Hamiltonian and the picturechangetransformed property operator are studied.

Analytic energy gradient in combined timedependent density functional theory and polarizable force field calculation
View Description Hide DescriptionFormulas for evaluating analytic energy gradient are derived for combined timedependent density functional theory (TDDFT) and polarizable force field methods that incorporate dipole polarizability tensors and linearly induced point dipoles. The vector method for determining relaxed oneparticle difference density matrix in regular TDDFT methods is extended to include induced dipoles. The analytic gradient of the mutual polarizationenergy of the force field and the TDDFT excited state can be formulated by using the TDDFT difference densityinduced dipoles and the transition state densityinduced dipoles. All the forces and torques involving induced dipoles can be efficiently evaluated using standard electrostatic formulas as if the induced dipoles were permanent dipoles. The formulas are given in the most general form and are applicable to various flavors of polarizable force fields. Implementation and tests with a polarizable fivepoint water model show that the formulas are rigorous. The carbonyl vibration modes and infrared spectrum intensities of a cluster formed by acetone and two water molecules are studied.

A Bayesian method for construction of Markov models to describe dynamics on various timescales
View Description Hide DescriptionThe dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markovmodels from simulation data. A Markovmodel is specified by , where is the mesoscopic time step, is a partition of configuration space into mesostates, and is an transition rate matrix for transitions between the mesostates in one mesoscopic time step, where is the number of mesostates in . The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markovmodel for any chosen mesoscopic timescale . (3) It constructs Markovmodels for which the diagonal elements of are all equal to or greater than 0.5. Such a model will be called a “consistent mesoscopic Markov model” (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic timescale. The Bayesian method uses simulation data to find a posterior probability distribution for for any chosen . This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic timescale was generated by the CMMM specified by . An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markovmodel construction to several toy systems(random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic timescales.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Negative ions of transition metalhalogen clusters
View Description Hide DescriptionA systematic density functional theory based study of the structure and spectroscopic properties of neutral and negatively charged clusters formed by a transition metal atom and up to seven halogen atoms has revealed a number of interesting features: (1) Halogen atoms are bound chemically to Sc, Ti, and V for , where the maximal valence equals to 3, 4, and 5 for Sc, Ti, and V, respectively. For , two halogen atoms became dimerized in the neutral species, while dimerization begins at , 6, and 7 for negatively charged clusters containing Sc, Ti, and V. (2) Magnetic moments of the transition metal atoms depend strongly on the number of halogen atoms in a cluster and the cluster charge. (3) The number of halogen atoms that can be attached to a metal atom exceeds the maximal formal valence of the metal atom. (4) The electron affinities of the neutral clusters abruptly rise at , reaching values as high as 7 eV. The corresponding anions could be used in the synthesis of new salts, once appropriate counterions are identified.

Electronic states of MgO: Spectroscopy, predissociation, and cold atomic Mg and O production
View Description Hide DescriptionWe used multiconfigurational methods and a large basis set to compute the potential energy curves of the valence and valenceRydberg electronic states of MgO molecule. New bound electronic states are found. Using these highly correlated wave functions, we evaluated their mutual spinorbit couplings and transition moment integrals. For the bound electronic states of MgO, we deduced an accurate set of spectroscopic constants that agree remarkably well with experimental results. Moreover, our potentials, transition moments, and spinorbit coupling evolutions are incorporated into Fermi golden rule calculations to deduce the radiative lifetimes of rovibrational levels and the natural lifetimes of vibrational levels, where a good agreement is found with experimental values. Finally, we suggest new routes for the production of cold Mg and O atoms and cold MgO molecules.

photodetachment: The effect of electronmolecule interactions in cluster anion photodetachment spectra and angular distributions
View Description Hide DescriptionThe electron kinetic energy dependence of the photoelectron spectra and angular distributions of cluster anions are measured via velocity mapped imaging at wavelengths between 350 and 270 nm. Processes analogous to those encountered in free electron interactions are revealed. In particular, the presence and energies of resonances associated with a low lying state have a marked effect on the results of photoexcitation. These effects (vibrational excitation, product anion production, and alteration of the photoelectron angular distribution) are far more prominent for . However, in the vicinity of the threshold there is a sharp deviation in the channel angular distribution and an enhancement of the channel vibrational structure of all three cluster anions. These latter effects are specific to the cluster anion environment through the relaxation of the partner excited I atom and subsequent electronic autodetachment.

Photoelectron spectroscopic study of the hydrated nucleoside anions: , , and
View Description Hide DescriptionThe hydrated nucleoside anions, , , and , have been prepared in beams and studied by anion photoelectron spectroscopy in order to investigate the effects of a microhydrated environment on parent nucleoside anions. Vertical detachment energies (VDEs) were measured for all eight anions, and from these, estimates were made for five sequential anion hydration energies. Excellent agreement was found between our measured VDE value for and its calculated value in the companion article by S. Kim and H. F. Schaefer III.