Volume 126, Issue 12, 28 March 2007
 ARTICLES

 Theoretical Methods and Algorithms

Energyconsistent relativistic pseudopotentials and correlation consistent basis sets for the elements Y–Pd
View Description Hide DescriptionScalarrelativistic pseudopotentials and corresponding spinorbit potentials of the energyconsistent variety have been adjusted for the simulation of the cores of the transition metal elements Y–Pd. These potentials have been determined in a onestep procedure using numerical twocomponent calculations so as to reproduce atomic valence spectra from fourcomponent allelectron calculations. The latter have been performed at the multiconfiguration DiracHartreeFock level, using the DiracCoulomb Hamiltonian and perturbatively including the Breit interaction. The derived pseudopotentials reproduce the allelectron reference data with an average accuracy of for configurational averages over nonrelativistic orbital configurations and for individual relativistic states. Basis sets following a correlation consistent prescription have also been developed to accompany the new pseudopotentials. These range in size from ccpVDZPP to ccpV5ZPP and also include sets for correlation (ccpwCVDZPP through ccpwCV5ZPP), as well as those with extra diffuse functions (augccpVDZPP, etc.). In order to accurately assess the impact of the pseudopotential approximation, allelectron basis sets of triplezeta quality have also been developed using the DouglasKrollHess Hamiltonian (ccpVTZDK, ccpwCVTZDK, and augccpVTZDK). Benchmark calculations of atomic ionization potentials and electronic excitation energies are reported at the coupled cluster level of theory with extrapolations to the complete basis set limit.

Gyrationradius dynamics in structural transitions of atomic clusters
View Description Hide DescriptionThis paper is concerned with the structural transition dynamics of the sixatom Morse cluster with zero total angular momentum, which serves as an illustrative example of the general reaction dynamics of isolated polyatomic molecules. It develops a methodology that highlights the interplay between the effects of the potential energy topography and those of the intrinsic geometry of the molecular internal space. The method focuses on the dynamics of three coarse variables, the molecular gyration radii. By using the framework of geometric mechanics and hyperspherical coordinates, the internal motions of a molecule are described in terms of these three gyration radii and hyperangular modes. The gyration radii serve as slow collective variables, while the remaining hyperangular modes serve as rapidly oscillating “bath” modes. Internal equations of motion reveal that the gyration radii are subject to two different kinds of forces: One is the ordinary force that originates from the potential energy function of the system, while the other is an internal centrifugal force. The latter originates from the dynamical coupling of the gyration radii with the hyperangular modes. The effects of these two forces often counteract each other: The potential force generally works to keep the internal mass distribution of the system compact and symmetric, while the internal centrifugal force works to inflate and elongate it. Averaged fields of these two forces are calculated numerically along a reaction path for the structural transition of the molecule in the threedimensional space of gyration radii. By integrating the sum of these two force fields along the reaction path, an effective energy curve is deduced, which quantifies the gross work necessary for the system to change its mass distribution along the reaction path. This effective energy curve elucidates the energydependent switching of the structural preference between symmetric and asymmetric conformations. The present methodology should be of wide use for the systematic reduction of dimensionality as well as for the identification of kinematic barriers associated with the rearrangement of mass distribution in a variety of molecular reaction dynamics in vacuum.

CarParrinello treatment for an approximate densityfunctional theory method
View Description Hide DescriptionThe authors formulate a CarParrinello treatment for the densityfunctionalbased tightbinding method with and without selfconsistent charge corrections. This method avoids the numerical solution of the secular equations, the principal drawback for large systems if the linear combination of atomic orbital ansatz is used. The formalism is applicable to finite systems and for supercells using periodic boundary conditions within the point approximation. They show that the methodology allows the application of modern computational techniques such as sparse matrix storage and massive parallelization in a straightforward way. All present bottlenecks concerning computer time and consumption of memory and memory bandwidth can be removed. They illustrate the performance of the method by direct comparison with BornOppenheimer molecular dynamics calculations. Water molecules, benzene, the fullerene, and liquid water have been selected as benchmark systems.

Linearscaling symmetric squareroot decomposition of the overlap matrix
View Description Hide DescriptionWe present a robust linearscaling algorithm to compute the symmetric squareroot or Löwdin decomposition of the atomicorbital overlap matrix. The method is based on NewtonSchulz iterations with a new approach to starting matrices. Calculations on 12 chemically and structurally diverse molecules demonstrate the efficiency and reliability of the method. Furthermore, the calculations show that linear scaling is achieved.

Nonequilibrium multiscale computational model
View Description Hide DescriptionA computational multiscale method is proposed to simulate coupled, nonequilibrium thermomechanical processes. This multiscale framework couples together thermomechanical equations at the coarse scale with nonequilibrium molecular dynamics at the fine scale. The novel concept of distributed coarse scale thermostats enables subsets of fine scale atoms to be attached to different coarse scale nodes which act as thermostats. The fine scale dynamics is driven by the coarse scale mean field. A coarsegrained Helmholtz free energy is used to derive macroscopic quantities. This new framework can reproduce the correct thermodynamics at the fine scale while providing an accurate coarsegrained result at the coarse scale.

The electrostatic surface term: (I) Periodic systems
View Description Hide DescriptionThe authors propose a new approach to understand the electrostaticsurface contributions to the interactions of large but finite periodic distributions of charges. They present a simple method to derive and interpret the surface contribution to any electrostatic field produced by a periodic distribution of charges. They discuss the physical and mathematical interpretations of this term. They present several examples and physical details associated with the calculation of the surface term. Finally, they provide a simple derivation of the surface contribution to the virial. This term does not disappear even if tinfoilboundary conditions are applied.

Optimized theory for simple and molecular fluids
View Description Hide DescriptionAn optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between PerkusYevick and hypernetted chain closures is optimized by minimizing the free energy selfconsistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys.123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic LennardJones fluids were analyzed, obtaining sitesite correlation functions in excellent agreement with simulation data.

Exact stochastic simulation of coupled chemical reactions with delays
View Description Hide DescriptionGillespie’s exact stochastic simulation algorithm (SSA) [J. Phys. Chem.81, 2350 (1977)] has been widely used to simulate the stochastic dynamics of chemically reacting systems. In this algorithm, it is assumed that all reactions occur instantly. While this is true in many cases, it is also possible that some chemical reactions, such as gene transcription and translation in living cells, take certain time to finish after they are initiated. Thus, the product of such reactions will emerge after certain delays. Apparently, Gillespie’s SSA is not an exact algorithm for chemical reaction systems with delays. In this paper, the author develops an exact SSA for chemical reaction systems with delays, based upon the same fundamental premise of stochastic kinetics used by Gillespie in the development of his SSA. He then shows that an algorithm modified from Gillespie’s SSA by Barrio et al. [PLOS Comput. Biol.2, 1017 (2006)] is also an exact SSA for chemical reaction systems with delays, but it needs to generate more random variables than the author’s algorithm.

A simple density functional fractional occupation number procedure to determine the low energy transition region of spinflip reactions
View Description Hide DescriptionA computationally simple threestep procedure to survey the energy landscape and to determine the molecular transition structure and activation energy at the intersection of two weakly coupled electronic potential energy surfaces of different symmetry is suggested. Only commercial software is needed to obtain the transition states of, for instance, spinflip reactions. The computational expense is only two to three times larger than that of the standard determination of an adiabatic reaction path. First, the structures of the two electronic initial and final states along a chosen reaction coordinate are individually optimized. At the “projected crossing,” the two states have the same energy at the same value of the reaction coordinate, but different stateoptimized partial structures. Second, the unique optimized structure of a low energy crossing point between the two states is determined with the help of the density functional fractional occupation number approach. Finally, the respective energy of the two states at the crossing is estimated by a single point calculation. The prescription is successfully applied to some simple topical examples from organic and from inorganic chemistry, respectively, concerning the spinflip reactions and .

Local integrals and their globally connected invariant structure in phase space giving rise to a promoting mode of chemical reaction
View Description Hide DescriptionWe develop a method to extract local integrals, that is, integrals defined locally in the linear regime of an arbitrary point in phase space. The individual integral represents a vibrational mode. We also propose an index that quantifies the extent of connection between neighboring local integrals. Those pieces that are smoothly connected over a wide range represent a global structure of phase space. With a sixatomic LennardJones cluster, we show that it is possible to identify which vibrational mode in the potential basin correlates smoothly to that in the area of transition state, which is nothing but a reactive mode. As an application of the method, we attempt to enhance the structural transition by exciting the reactive mode thus found. This method works successfully as shown in numerical calculations.

Density scaling and relaxation of the Pauli principle
View Description Hide DescriptionThe relaxation of the Pauli principle associated with density scaling is examined. Scaling the density has been investigated in the development of density functionalcomputational methods with higher accuracy. Scaling the density by reduces the number of electrons to when . The minimum kinetic energy of the scaled density, , can be scaled back to the electron system by multiplying the electron KohnShamtype occupation numbers by to produce . This relaxes the Pauli principle when the orbital occupation numbers are greater than 1 in the electron system. The effects of antisymmetry on solutions to the KohnSham equations are examined for Ne and the Be isoelectronic series. The changes in and the exchange energy when is varied show that these two quantities are inextricably linked.

Polarization energy gradients in combined quantum mechanics, effective fragment potential, and polarizable continuum model calculations
View Description Hide DescriptionA method that combines quantum mechanics (QM), typically a solute, the effective fragment potential (EFP) discrete solvent model, and the polarizable continuum model is described. The EFP induced dipoles and polarizable continuum model (PCM) induced surface charges are determined in a selfconsistent fashion. The gradients of these two energies with respect to molecular coordinate changes are derived and implemented. In general, the gradients can be formulated as simple electrostatic forces and torques among the QM nuclei, electrons, EFP static multipoles, induced dipoles, and PCM induced charges. Molecular geometry optimizations can be performed efficiently with these gradients. The formulas derived for EFP∕PCM can be generally applied to other combined molecular mechanics and continuum methods that employ induced dipoles and charges.

Seams near seams: The JahnTeller effect in the state of
View Description Hide DescriptionThe electronic state of cyclic arising from the singly excited electron configuration is studied using multireference configuration interactionwave functions and a quadratic JahnTeller Hamiltonian determined from those calculations. It is shown that these two states have both a symmetryrequired seam of conical intersections at geometries and three proximal symmetry equivalent seams, located on a circle with radius from the intersection. , a function of , the breathing mode, is quite small but only attains a value of zero at , resulting in a confluence or intersection node of the three seams with the seam. At this point only, , the norm of half the energy difference gradient, the linear JahnTeller term, vanishes and the intersection is of the RennerTeller type. The close proximity of the previously unreported seams to the seam over the range of considered is a consequence of the small values of , compared to the quadratic JahnTeller term. The present analysis has important implications in the study of JahnTeller effects in ring systems and provides insight into a recent report that characterized this seam as a RennerTeller or glancing intersection.

Polarizable atomic multipole solutes in a PoissonBoltzmann continuum
View Description Hide DescriptionModeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager [J. Am. Chem. Soc.58, 1486 (1936)] used vacuum properties of small molecules, including polarizability,dipole moment, and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the PoissonBoltzmann equation. Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here the authors describe the theory underlying a newly developed polarizable multipole PoissonBoltzmann (PMPB) continuum electrostatics model, which builds on the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit AMOEBA water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and prediction. Introduction of salt lowered the electrostatic solvation energy between 2 and , depending on the formal charge of the protein, but had only a small influence on dipole moments.

Analytic derivatives for perturbatively corrected “double hybrid” density functionals: Theory, implementation, and applications
View Description Hide DescriptionA recently proposed new family of density functionals [S. Grimme, J. Chem. Phys.124, 34108 (2006)] adds a fraction of nonlocal correlation as a new ingredient to density functional theory(DFT). This fractional correlation energy is calculated at the level of secondorder manybody perturbation theory (PT2) and replaces some of the semilocal DFTcorrelation of standard hybrid DFT methods. The new “double hybrid” functionals (termed, e.g., B2PLYP) contain only two empirical parameters that have been adjusted in thermochemical calculations on parts of the G2/3 benchmark set. The methods have provided the lowest errors ever obtained by any DFT method for the full G3 set of molecules. In this work, the applicability of the new functionals is extended to the exploration of potential energy surfaces with analytic gradients. The theory of the analytic gradient largely follows the standard theory of PT2 gradients with some additional subtleties due to the presence of the exchangecorrelation terms in the selfconsistent field operator. An implementation is reported for closedshell as well as spinunrestricted reference determinants. Furthermore, the implementation includes external point charge fields and also accommodates continuum solvation models at the level of the conductor like screening model. The density fitting resolution of the identity (RI) approximation can be applied to the evaluation of the PT2 part with large gains in computational efficiency. For systems with basis functions the evaluation of the double hybrid gradient is approximately four times more expensive than the calculation of the standard hybrid DFT gradient. Extensive test calculations are provided for main group elements and transition metal containing species. The results reveal that the B2PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Doorway mechanism for dissociative electron attachment to fructose
View Description Hide DescriptionRecently, the three sugars ribose, deoxyribose, and fructose have been shown to undergo dissociative electron attachment at threshold, that is, to fragment upon capture of a zeroenergy electron. Here the electron acceptor properties of three fructose isomers are investigated in view of a doorway mechanism. Two key ingredients for a doorway mechanism, a weakly bound state able to support a vibrational Feshbach resonance, and a valence anion more stable than neutral fructose are characterized. Moreover, possible structures for the observed fragment anion are suggested.

Statetostate inelastic scattering of OH by HI: A comparison with OH–HCl and OH–HBr
View Description Hide DescriptionRelative statetostate cross sections and steric asymmetries have been measured for the scattering process: , at collision energy. Comparison with the previously studied systems OH–HCl and OH–HBr reveals relevant features of the potential energy surfaces of these molecular systems. Some measured differences concerning the internal energy distribution after collision and the propensities for the impact with one or the other side of the OH molecule in scattering by HCl, HBr, and HI molecules are discussed.

Fermi resonance in : A combined electronic coupledcluster and vibrational configurationinteraction prediction
View Description Hide DescriptionThe authors present a firstprinciples prediction of the energies of the eight lowestlying anharmonic vibrational states of , including the fundamental symmetric stretching mode and the first overtone of the fundamental bending mode, which undergo a strong coupling known as Fermi resonance. They employ coupledcluster singles, doubles, and (perturbative) triples [CCSD(T) and CCSDT] in conjunction with a range of Gaussian basis sets (up to ccpV5Z, augccpVQZ, and augccpCVTZ) to calculate the potential energy surfaces (PESs) of the molecule, with the errors arising from the finite basisset sizes eliminated by extrapolation. The resulting vibrational manybody problem is solved by the vibrational selfconsistentfield and vibrational configurationinteraction (VCI) methods with the PESs represented by a fourthorder Taylor expansion or by numerical values on a GaussHermite quadrature grid. With the VCI, the best theoretical estimates of the anharmonic energy levels agree excellently with experimental values within (the mean absolute deviation). The theoretical (experimental) anharmonic frequencies of the Fermi doublet are 1288.9 (1285.4) and 1389.3 .

Spinorbit effect in the energy pooling reaction
View Description Hide DescriptionFivedimensional nonadiabatic quantum dynamics studies have been carried out on two new potential energy surfaces of and states for the title oxygen molecules collision with coplanar configurations, along with the spinorbit coupling between them. The ab initio calculations are based on complete active state secondorder perturbation theory with the basis set. The calculated spinorbit induced transition probability as a function of collision energy is found to be very small for this energy pooling reaction. The rate constant obtained from a uniform shifting approach is compared with the existing theoretical and experimental data, and the spinorbit effect is also discussed in this electronic energytransfer process.

Building transition probabilities for any condition using reduced cumulative energy transfer functions in collisions
View Description Hide DescriptionThe energy transfer process between highly vibrationally excited in thermal equilibrium with a gas bath of at different internal energies and temperatures has been studied by classical trajectory calculations. The results were analyzed using a cumulative probability distribution of the amount of energy transferred, obtained by direct count of the number of trajectories that transfer an amount of energy equal to or greater than a certain value . Scaling in terms of the mean down and up energies transferred for each group of trajectories results in a unique distribution. This fact and the use of detailed balance constrains were used to propose a methodology that make it possible to build the whole for any condition by knowing and a series of parameters that depend only on the system under study.