Volume 129, Issue 21, 07 December 2008
 ARTICLES

 Theoretical Methods and Algorithms

Implementation of transition moments between excited states in the approximate coupledcluster singles and doubles model
View Description Hide DescriptionAn implementation of transition moments between excited states for the approximate coupledcluster singles and doubles model (CC2) using the resolution of the identity (RI) approximation is reported. The accuracy of the RI approximation is analyzed for a testset of 7 molecules and 76 transitions. The RI error is found to be very small for both transition moments and oscillator strengths. Furthermore, the performance of the CC2 model in comparison with coupledcluster singles and doubles (CCSD) is studied for 40 transitions of the same testset, yielding deviations of about 12% for the transition moments and 24% for the oscillator strengths. In addition, for 13 transitions of the testset the behavior of the transition moments with respect to seven different basis sets (Dunnings , with for and for ) is analyzed, showing a strong dependence on the degree of augmentation and a rather small effect of the cardinal number . First applications are presented for the triplettriplet transition moments of benzene and polyacenes (naphthalene to pentacene), showing good agreement with experimental and theoretical results for transitions between single excitation dominated states. Somewhat problematic is the insufficient description of doubleexcitation dominated states by the CC2 model. As transitions to such states may be strongly allowed, unlike for excitations out of the ground state, important features of transient spectra may be missed. For triplettriplet excitations the problem is less evident as the lowest doubly excited triplet states are expected at higher energies.

A tightbinding potential for helium in carbon systems
View Description Hide DescriptionThe presence of helium in carbon systems, such as diamonds and fullerenes is of interest for planetary sciences, geophysics, astrophysics, and evolution biology. Such systems typically involve a large number of atoms and require a fast method for assessing the interaction potential and forces. We developed a tightbinding approach, based on density functional calculations, which includes a manybody potential term. This latter term is essential for consolidating the density functional results of helium in bulky diamond and Helium passing through a benzene ring which is important for heliumfullerene applications. The method is simple to apply and exhibits good transferability properties.

Efficient elimination of response parameters in molecular property calculations for variational and nonvariational energies
View Description Hide DescriptionA general method is presented for the efficient elimination of response parameters in molecular property calculations for variational and nonvariational energies. For variational energies, Wigner’s rule is obtained as a special case of the more general rule, which states that for a subset of perturbations within a total set of perturbations, response parameters may be eliminated according to the rule (normally applied to the full set of perturbations). Nonvariational energies may be treated by introducing Lagrange multipliers that satisfy the stronger rule for the perturbations, while the wavefunction parameters still satisfy the rule for the perturbations. The corresponding rule for nonvariational energies is referred to as the rule. For , the wellknown rule for the multipliers is reproduced, while the wavefunction parameters satisfy the rule. The application of the and rules minimizes the total number of response equations to be solved when the molecular property contains extensive perturbations (e.g., geometrical derivatives) and intensive perturbations (e.g., electric fields).

Photonexposuredependent photonstimulated desorption for obtaining photolysis cross section of molecules adsorbed on surface by monochromatic soft xray photons
View Description Hide DescriptionPhotonexposuredependent positive and negativeion photonstimulated desorption(PSD) was proposed to study the photoreactions and obtain the photolysis cross sections of molecules adsorbed on a singlecrystal surface by monochromatic soft xray photons with energy near the core level of adsorbate. The changes in the and PSD ion yields were measured from molecules adsorbed on at ( , monolayer) during irradiation of monochromatic soft xray photons near the edge. The PSD ion yield data show the following characteristics: (a) The dissociation of adsorbed molecules is due to a combination of direct photodissociation via excitation of core level and substratemediated dissociation [dissociative attachment and dipolar dissociation induced by the photoelectrons emitting from the silicon substrate]. (b) the ion desorption is associated with the bond breaking of the surface, , CFCl, and SiF species. (c) the yield is mainly due to DA and DD of the adsorbed molecules. (d) The surface SiF is formed by reaction of the surface Si atom with the neutral fluorine atom, , or ion produced by scission of C–F bond of , , or CFCl species. A kinetic model was proposed for the explanation of the photolysis of this submonolayercovered surface. Based on this model and the variation rates of the signals during fixedenergy monochromatic photon bombardment at 690.2 and [near the edge], the photolysis cross section was deduced as a function of energy.

Localized orbital corrections applied to thermochemical errors in density functional theory: The role of basis set and application to molecular reactions
View Description Hide DescriptionThis paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [R. A. Friesner et al., J. Chem. Phys.125, 124107 (2006); E. H. Knoll and R. A. Friesner, J. Phys. Chem. B110, 18787 (2006).] This methodology allows one to redress systematic density functional theory(DFT) errors, rooted in DFT’s inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3LYP (denoted as B3LYPLOC), were previously applied to enthalpies of formation, ionization potentials, and electron affinities and showed impressive reduction in the errors. In this paper, we demonstrate for the first time that the B3LYPLOC scheme is robust across different basis sets [, , ccpVTZ, and augccpVTZ] and reaction types (atomization reactions and molecular reactions). For example, for a test set of 70 molecular reactions, the LOC scheme reduces their mean unsigned error from 4.7 kcal/mol [obtained with ] to 0.8 kcal/mol. We also verified whether the LOC methodology would be equally successful if applied to the promising M052X functional. We conclude that although M052X produces better reactionenthalpies than B3LYP, the LOC scheme does not combine nearly as successfully with M052X than with B3LYP. A brief analysis of another functional, M062X, reveals that it is more accurate than M052X but its combination with LOC still cannot compete in accuracy with B3LYPLOC. Indeed, B3LYPLOC remains the best method of computing reactionenthalpies.

On collisional energy transfer in recombination and dissociation reactions: A Wiener–Hopf problem and the effect of a near elastic peak
View Description Hide DescriptionThe effect of the large impact parameter nearelastic peak of collisional energy transfer for unimolecular dissociation/bimolecular recombination reactions is studied. To this end, the conventional single exponential model, a biexponential model that fits the literature classical trajectory data better, a model with a singularity at zero energy transfer, and the most realistic model, a model with a nearsingularity, are fitted to the trajectory data in the literature. The typical effect of the energy transfer on the recombination rate constant is maximal at low pressures and this region is the one studied here. The distribution function for the limiting dissociationrate constant at low pressures is shown to obey a Wiener–Hopf integral equation and is solved analytically for the first two models and perturbatively for the other two. For the single exponential model, this method yields the trial solution of Troe. The results are applied to the dissociation of in the presence of argon, for which classical mechanical trajectory data are available. The ’s for various models are calculated and compared, the value for the nearsingularity model being about ten times larger than that for the first two models. This trend reflects the contribution to the cross section from collisions with larger impact parameter. In the present study of the nearsingularity model, it is found that is not sensitive to reasonable values for the lower bound. Energy transfer values ’s are also calculated and compared and can be similarly understood. However, unlike the values, they are sensitive to the lower bound, and so any comparison of a classical trajectory analysis for ’s with the kinetic experimental data needs particular care.

Molecular dynamics with time dependent quantum Monte Carlo
View Description Hide DescriptionIn this paper we propose an ab initio method to solve quantum manybody problems of molecular dynamics where both electronic and nuclear degrees are represented by ensembles of trajectories and guiding waves in physical space. Both electrons and nuclei can be treated quantum mechanically where the guiding waves obey a set of coupled Schrödinger equations (quantumquantum description) or, alternatively, coupled Schrödinger–Newtonian equations are solved for the quantumclassical approximation. The method takes into account local and nonlocal quantum correlationeffects in a selfconsistent manner. The general formalism is applied to one and twodimensional hydrogen molecules subjected to a strong ultrashort optical pulse. Comparison is made with the results from the “exact” Ehrenfest molecular dynamics for the molecular ionization and for the evolution of the internuclear distance as the molecule dissociates.

A density matrixbased quasienergy formulation of the Kohn–Sham density functional response theory using perturbation and timedependent basis sets
View Description Hide DescriptionA general method is presented for the calculation of molecular properties to arbitrary order at the Kohn–Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linearscaling methodology to be used. Timedependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequencydependent perturbations may be used, e.g., frequencydependent London atomic orbitals. The rule may be applied if computationally favorable, but alternative formulations using higherorder perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the firstorder geometrical derivative of the hyperpolarizability.

Vibrational subsystem analysis: A method for probing free energies and correlations in the harmonic limit
View Description Hide DescriptionA new vibrational subsystem analysis (VSA) method is presented for coupling global motion to a local subsystem while including the inertial effects of the environment. The premise of the VSA method is a partitioning of a system into a smaller region of interest and a usually larger part referred to as environment. This method allows the investigation of localglobal coupling, a more accurate estimation of vibrational free energy contribution for parts of a large system, and the elimination of the “tip effect” in elastic network model calculations. Additionally, the VSA method can be used as a probe of specific degrees of freedom that may contribute to free energy differences. The VSA approach can be employed in many ways, but it will likely be most useful for estimating activation free energies in QM/MM reaction path calculations. Four examples are presented to demonstrate the utility of this method.

Dimensional scaling treatment of stability of simple diatomic molecules induced by superintense, highfrequency laser fields
View Description Hide DescriptionWe present results obtained using dimensional scaling with highfrequency Floquet theory to evaluate the stability of gas phase simple diatomic molecules in superintense laser fields. The large limit provides a simple model that captures the main physics of the problem, which imposes electron localization along the polarization direction of the laser field. This localization markedly reduces the ionization probability and can enhance chemical bonding when the laser strength becomes sufficiently strong. We find that energy and structure calculations at the largedimensional limit for stabilities of , , and in superintense laser fields are much simpler than at , yet yield similar results to those found from demanding ab initio calculations. We also use the large model to predict the stability of and the field strength needed to bind the “extra” electron to the molecule.

Thermodynamics of droplet formation around a soluble condensation nucleus in the atmosphere of a solvent vapor
View Description Hide DescriptionAn expression for the work of formation of a spherical droplet condensing on a soluble condensation nucleus out of a solvent vapor is derived. The dependence of the formation work on the solvent vapor chemical potential and the droplet and the nucleus residue sizes is analyzed. The balance of the solute matter between the liquid film and the nucleus residue and the effect of overlapping the surface layers of the thin film have been taken into account. It is shown that the equations of the chemical equilibrium of a solute and a solvent in the droplet, resulting from the generating properties of the formation work, coincide with the generalized Gibbs–Kelvin–Köhler and Ostwald–Freundlich equations. The numerical solution of these equations at a fixed number of molecules of the nucleus matter (at an initial size of the nucleus specified) has been performed in the case of the solvent vapor undersaturated over the bulk liquidsolvent phase. The solution links the equilibrium sizes of the droplet and the soluble nucleus residue with the chemical potential or the pressure of the solvent vapor saturated over the droplet. It also determines the limiting sizes of the droplet with small nucleus residue above which the chemical equilibrium of the residue surface and the solutionfilm does not exist. The existence of the limiting sizes is responsible for the specific behavior of the droplet thermodynamic characteristics and the work of dropletformation at deliquescence transition from the droplet state with a partly dissolved nucleus to the state of complete dissolution of the nucleus.

Estimating errors in free energy calculations from thermodynamic integration using fitted data
View Description Hide DescriptionA procedure to estimate the statistical uncertainties associated with free energies computed from thermodynamic integration using fitted data is described. The method involves generating synthetic data sets from the actual simulation data and performing an analysis of the resulting distribution of free energy values. These values follow a Gaussian distribution, and the corresponding standard deviation is associated with the error in the computed value of the free energy. The impact of these uncertainties on the coexistence pressure is examined for firstorder transitions. The approach is demonstrated with an examination of finitesize effects at the freezing transition of hard spheres.

A unified theoretical framework for fluctuatingcharge models in atomspace and in bondspace
View Description Hide DescriptionOur previously introduced QTPIE (charge transfer with polarization current equilibration) model [J. Chen and T. J. Martínez, Chem. Phys. Lett.438, 315 (2007)] is a fluctuatingcharge model with correct asymptotic behavior. Unlike most other fluctuatingcharge models, QTPIE is formulated in terms of chargetransfer variables and pairwise electronegativities, not atomic charge variables and electronegativities. The pairwise character of the electronegativities in QTPIE allows us to avoid spurious charge transfer when bonds are broken. However, the increased number of variables leads to considerable computational expense and a rankdeficient set of working equations, which is numerically inconvenient. Here, we show that QTPIE can be exactly reformulated in terms of atomic charge variables, leading to a considerable reduction in computational complexity. The transformation between atomic and bond variables is generally applicable to arbitrary fluctuating charge models and uncovers an underlying topological framework that can be used to understand the relation between fluctuatingcharge models and the classical theory of electrical circuits.

A Bayesian statistics approach to multiscale coarse graining
View Description Hide DescriptionCoarsegrained (CG) modeling provides a promising way to investigate many important physical and biological phenomena over large spatial and temporal scales. The multiscale coarsegraining (MSCG) method has been proven to be a thermodynamically consistent way to systematically derive a CG model from atomistic force information, as shown in a variety of systems, ranging from simple liquids to proteins embedded in lipid bilayers. In the present work, Bayes’ theorem, an advanced statistical tool widely used in signal processing and pattern recognition, is adopted to further improve the MSCG force field obtained from the CG modeling. This approach can regularize the linear equation resulting from the underlying forcematching methodology, therefore substantially improving the quality of the MSCG force field, especially for the regions with limited sampling. Moreover, this Bayesian approach can naturally provide an error estimation for each force field parameter, from which one can know the extent the results can be trusted. The robustness and accuracy of the Bayesian MSCG algorithm is demonstrated for three different systems, including simple liquid methanol, polyalanine peptide solvated in explicit water, and a much more complicated peptide assembly with 32 NNQQNY hexapeptides.

Elimination of fast variables in chemical Langevin equations
View Description Hide DescriptionInternal and external fluctuations are ubiquitous in cellular signaling processes. Because biochemical reactions often evolve on disparate time scales, mathematical perturbation techniques can be invoked to reduce the complexity of stochastic models. Previous work in this area has focused on direct treatment of the master equation. However, eliminating fast variables in the chemical Langevin equation is also an important problem. We show how to solve this problem by utilizing a partial equilibrium assumption. Our technique is applied to a simple birthdeathdimerization process and a more involved gene regulation network, demonstrating great computational efficiency. Excellent agreement is found with results computed from exact stochastic simulations. We compare our approach with existing reduction schemes and discuss avenues for future improvement.

H/D isotope effect in methyl torsional interaction of acetone as calculated by a multicomponent molecular orbital method
View Description Hide DescriptionWe analyzed the H/D isotope effect in the methyl torsional interactions accompanying two methyl internal rotations for acetone and deuterated acetone ( and ) in the ground state by means of the multicomponent molecular orbital (MC_MO) method, which directly accounts for the quantum effects of protons and deuterons. Our estimated rotational constants and moments of inertia for and agreed well with the experimental results because of the adequate treatment of protonic and deuteronic quantum effects afforded by the MC_MO method. Because the C–D bond distance in the group was shorter than the C–H distance in owing to the anharmonicity of the potential, the difference in potential energy surfaces of , , and was strongly related to the differences induced in geometrical parameters by the H/D isotope effect. The potential energy obtained by the MC_MO method was estimated as for , which is in excellent agreement with the experimental results. For , two potential energies were obtained for and internal rotations. The MC_MO method successfully elucidated the H/D isotope effect for methylmethyl repulsive interactions by allowing the adequate treatment of protonic and deuteronic wave functions. The potential energies and bond distances associated with methyl internal rotation induced by the H/D isotope effect were also controlled by the distribution of wave functions of protons and deuterons.

Effect of the geometric phase on nuclear dynamics at a conical intersection: Extension of a recent topological approach from one to two coupled surfaces
View Description Hide DescriptionA recent approach [S. C. Althorpe, J. Chem. Phys.124, 084105 (2006)] for interpreting geometric phase (GP) effects in a nuclear wave function confined to the lower of two conically intersecting potential energy surfaces is extended to treat coupled dynamics on both surfaces. The approach is exact, and uses simple topology to separate the wave function into contributions from Feynman paths that wind different numbers of times, and in different senses, around the conical intersection. We derive the approach first, by mapping the timedependent wave packet describing the coupled dynamics onto a double space, and second, by classifying the Feynman paths within a timeordered expansion of the path integral. The approach is demonstrated numerically for a simple Jahn–Teller system and for a model of the intersection in pyrrole. The approach allows one to investigate and interpret the effect of the GP on population transfer between the surfaces, and also to extract contributions to the coupled nuclear wave function from different reaction paths.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Anion photoelectron spectroscopy of transition metal and lanthanide metalsilicon clusters:
View Description Hide DescriptionThe electronic properties of siliconclusters containing a transition or lanthanide metal atom from group 3, 4, or 5, , (, Ti, V, Y, Zr, Nb, Lu, Tb, Ho, Hf, and Ta) were investigated by anion photoelectron spectroscopy at . In the case of the group 3 elements Sc, Y, Lu, Tb, and Ho, the threshold energy of electron detachment exhibits local maxima at and 16, while in case of the group 4 elements Ti, Zr, and Hf, the threshold energy exhibits a local minimum at , associated with the presence of a small bump in the spectrum. These electronic characteristics of are closely related to a cooperative effect between their geometric and electronic structures, which is discussed, together with the results of experiments that probe their geometricstability via their reactivity to adsorption, and with theoretical calculations.

Potential energy curves and electronic structure of transition metal hydrides and their cations
View Description Hide DescriptionWe investigate gasphase neutral and cationic hydrides formed by transition metals from Sc to Cu with density functional theory(DFT) methods. The performance of two exchangecorrelation functionals, Boese–Martin for kinetics (BMK) and Tao–Perdew–StaroverovScuseria (TPSS), in predicting bond lengths and energetics, electronic structures, dipole moments, and ionization potentials is evaluated in comparison with available experimental data. To ensure a unique selfconsistent field (SCF) solution, we use stability analysis, Fermi smearing, and continuity analysis of the potential energy curves. Brokensymmetry approach was adapted in order to get the qualitatively correct description of the bonddissociation. We found that on average BMK predicted values of dissociation energies and ionization potentials are closer to experiment than those obtained with high level wave functiontheory methods. This agreement deteriorates quickly when the fraction of the Hartree–Fock exchange in DFT functional is decreased. Natural bond orbital (NBO) population analysis was used to describe the details of chemical bonding in the systems studied. The multireference character in the wave function description of the hydrides is reproduced in brokensymmetry DFT description, as evidenced by NBO analysis. We also propose a new scheme to correct for spin contamination arising in brokensymmetry DFT approach. Unlike conventional schemes, our spin correction is introduced for each spinpolarized electron pair individually and therefore is expected to yield more accurate energy values. We derive an expression to extract the energy of the pure singlet state from the energy of the brokensymmetry DFT description of the low spin state and the energies of the high spin states (pentuplet and two spincontaminated triplets in the case of two spinpolarized electron pairs). The high spin states are build with canonical natural orbitals and do not require SCF convergence.

Effects of intense femtosecond pumping on ultrafast electronicvibrational dynamics in molecular systems with relaxation
View Description Hide DescriptionWe investigate the influence of strong femtosecond optical pulses on the ultrafast dynamics of molecular systems. The study is based on a series of generic molecular models of increasing complexity, which incorporate multiple and mutually coupled electronic states, electronicvibrational interaction, and vibrational relaxation. The influence of vibrational relaxation is treated using multilevel Redfield theory. Comparisons to benchmark results of the multilayer multiconfiguration timedependent Hartree (MLMCTDH) method demonstrate the validity of the fieldfree implementation of Redfield theory employed in this work for weak systembath interaction. The calculated electronic population and vibrational wavepacket dynamics demonstrate the intricate interplay of strongfield excitation, laserinduced Rabi oscillations, electronic interaction, vibronic coupling, and dissipation. In particular, we show that the interaction with a strong laser pulse may result in pronounced coherent vibrational motion in a dissipative system, even for laser pulses that are longer than the vibrational period. Furthermore, vibrational relaxation in combination with strong laser pulse excitation can lead to revivals of the electronic population after the excitation pulse is over.