Volume 135, Issue 3, 21 July 2011

Molecular dynamics simulations are performed to investigate the behavior of water molecules near goldmonolayer protected clusters (MPCs) with two different types of surfactant, HS(CH_{2})_{5}(OCH_{2}CH_{2})_{2}COOH (type1) and HS(CH_{2})_{11}COOH (type2). The effects of the different moieties of the two ligands on the local structure of the water molecules are quantified by means of the reduced density profiles of oxygen and hydrogen atoms, and the hydrogen bond statistics. The adsorption characteristics of water molecules are evaluated by means of their residence time near the MPCs. The results show that the hydrophilic oligo (ethylene glycol) segment increases the number of water molecules, which penetrate the protective layer of MPC. As a result, the interwater hydrogen bond network in the protective layer of type1 MPC is stronger than that in the protective layer of the type2 MPC. It is shown that the presence of interfacial hydrogen bonds increases the adsorption of water molecules near the MPCs and therefore constrains the motion of MPCs. As a result, the residence time of the water molecules adjacent to the type1 MPC is longer than that of the molecules adjacent to the type2 MPC.
 ARTICLES

 Theoretical Methods and Algorithms

Behavior of water molecules near monolayerprotected clusters with different terminal segments of ligand
View Description Hide DescriptionMolecular dynamics simulations are performed to investigate the behavior of water molecules near goldmonolayer protected clusters (MPCs) with two different types of surfactant, HS(CH_{2})_{5}(OCH_{2}CH_{2})_{2}COOH (type1) and HS(CH_{2})_{11}COOH (type2). The effects of the different moieties of the two ligands on the local structure of the water molecules are quantified by means of the reduced density profiles of oxygen and hydrogen atoms, and the hydrogen bond statistics. The adsorption characteristics of water molecules are evaluated by means of their residence time near the MPCs. The results show that the hydrophilic oligo (ethylene glycol) segment increases the number of water molecules, which penetrate the protective layer of MPC. As a result, the interwater hydrogen bond network in the protective layer of type1 MPC is stronger than that in the protective layer of the type2 MPC. It is shown that the presence of interfacial hydrogen bonds increases the adsorption of water molecules near the MPCs and therefore constrains the motion of MPCs. As a result, the residence time of the water molecules adjacent to the type1 MPC is longer than that of the molecules adjacent to the type2 MPC.

Optimized energy landscape exploration using the ab initio based activationrelaxation technique
View Description Hide DescriptionUnbiased openended methods for finding transition states are powerful tools to understand diffusion and relaxation mechanisms associated with defect diffusion, growth processes, and catalysis. They have been little used, however, in conjunction with ab initio packages as these algorithms demanded large computational effort to generate even a single event. Here, we revisit the activationrelaxation technique (ART nouveau) and introduce a twostep convergence to the saddle point, combining the previously used Lanczós algorithm with the direct inversion in interactive subspace scheme. This combination makes it possible to generate events (from an initial minimum through a saddle point up to a final minimum) in a systematic fashion with a net 300–700 force evaluations per successful event. ART nouveau is coupled with BigDFT, a KohnSham density functional theory (DFT) electronic structure code using a wavelet basis set with excellent efficiency on parallel computation, and applied to study the potential energy surface of C_{20} clusters, vacancydiffusion in bulk silicon, and reconstruction of the 4HSiC surface.

Quantum diffusive dynamics of macromolecular transitions
View Description Hide DescriptionWe study the role of quantum fluctuations of atomic nuclei in the realtime dynamics of nonequilibrium macromolecular transitions. To this goal we introduce an extension of the dominant reaction pathways formalism, in which the quantum corrections to the classical overdamped Langevin dynamics are rigorously taken into account to order ℏ^{2}. We first illustrate our approach in simple cases, and compare with the results of the instanton theory. Then we apply our method to study the C7_{ eq } → C7_{ ax } transition of alanine dipeptide. We find that the inclusion of quantum fluctuations can significantly modify the reaction mechanism for peptides. For example, the energy difference which is overcome along the most probable pathway is reduced by as much as 50%.

Efficient quantum trajectory representation of wavefunctions evolving in imaginary time
View Description Hide DescriptionThe Boltzmann evolution of a wavefunction can be recast as imaginarytime dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentumdependent quantum potential – computed approximately to be practical in highdimensional systems – influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys.132, 014112 (2010)]. For a nodelesswavefunction represented as ψ(x, t) = exp ( − S(x, t)/ℏ) with the trajectory momenta defined by ∇S(x, t), analysis of the Lagrangian and Eulerian evolution shows that for bound potentials the former is more accurate while the latter is more practical because the Lagrangian quantum trajectories diverge with time. Introduction of stationary and timedependent components into the wavefunction representation generates new Lagrangiantype dynamics where the trajectory spreading is controlled improving efficiency of the trajectory description. As an illustration, different types of dynamics are used to compute zeropoint energy of a strongly anharmonic well and lowlying eigenstates of a highdimensional coupled harmonic system.

Theory of multichromophoric coherent resonance energy transfer: A polaronic quantum master equation approach
View Description Hide DescriptionThe approach of second order time local quantum master equation in the polaron picture, which has been employed for a theory of coherent resonance energy transfer, is extended for general multichromophore systems. Explicit expressions for all the kernel and inhomogeneous terms are derived, which can be calculated by any standard numerical procedure. The theory is then applied to a model of donorbridgeacceptor system moderately coupled to bosonic bath. The results are compared with those based on the theory of Förster's resonance energy transfer. It is shown that coherently coupled multichromophores can speed up the transfer of energy substantially and in a way insensitive to the disorder.

Implementation of pseudopotential in the G3 theory for molecules containing first, second, and nontransition thirdrow atoms
View Description Hide DescriptionCompact effective pseudopotential (CEP) is adapted in the G3 theory providing a theoretical alternative referred to as G3CEP for calculations involving the first, second, and nontransition thirdrow elements. These modifications tried to preserve as much as possible the original characteristics of G3. G3CEP was used in the study of 247 enthalpies of formation, 22 atomization energies, 104 ionization potentials, 63 electron affinities, and 10 proton affinities, resulting in the calculation of 446 species for the first, second, and thirdrow atoms. The final average total absolute deviation was of 1.29 kcal mol^{−1} against 1.16 kcal mol^{−1} from allelectron G3 for the same calculations. The CPU time has been reduced by 7% to 56%, depending on the size of the molecules and the type of atoms considered.

Ab initio calculations on the excited states of Na_{3} cluster to explore beyond BornOppenheimer theories: Adiabatic to diabatic potential energy surfaces and nuclear dynamics
View Description Hide DescriptionWe perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na_{3} cluster and present the adiabatic PESs for the electronic states 2^{2} E′ and , and the nonadiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 2^{2} E′ and demonstrate the numerical validity of so called “Curl Condition,” such states closely form a subHilbert space. For this subspace, we employ the NAC terms to solve the “adiabaticdiabatic transformation (ADT)” equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond BornOppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na_{3} cluster and thereby, to explore the numerical validity of the theoretical development on beyond BornOppenheimer approach for adiabatic to diabatic transformation.

Simulating structural transitions by direct transition current sampling: The example of LJ_{38}
View Description Hide DescriptionReaction paths and probabilities are inferred, in a usual Monte Carlo or molecular dynamic simulation, directly from the evolution of the positions of the particles. The process becomes timeconsuming in many interesting cases in which the transition probabilities are small. A radically different approach consists of setting up a computation scheme where the object whose time evolution is simulated is the transition current itself. The relevant timescale for such a computation is the one needed for the transition probability rate to reach a stationary level, and this is usually substantially shorter than the passage time of an individual system. As an example, we show, in the context of the “benchmark” case of 38 particles interacting via the LennardJones potential (“LJ_{38}” cluster), how this method may be used to explore the reactions that take place between different phases, recovering efficiently known results, and uncovering new ones with small computational effort.

Size evolution study of “molecular” and “atomincluster” polarizabilities of mediumsize gold clusters
View Description Hide DescriptionA study on static polarizabilities for a family of goldclusters(Au_{n}, n = 6, 12, 20, 34, 54) is presented. For each cluster, a density functional theory perturbation theory calculation was performed to compute the clusterpolarizability and the polarizability of each atom in the cluster using Bader´s “quantum theory of atoms in molecules” formalism. The clusterpolarizabilitytensor,, is expressed as a sum of the atominmolecule tensors,. A strong quadratic correlation (R^{2} = 0.98) in the isotropic polarizability of atoms in the cluster and their distance to the cluster center of mass was observed. The clusterpolarizabilities are in agreement with previous calculations.

Implementation of screened hybrid density functional for periodic systems with numerical atomic orbitals: Basis function fitting and integral screening
View Description Hide DescriptionWe present an efficient O(N) implementation of screened hybrid density functional for periodic systems with numerical atomic orbitals (NAOs). NAOs of valence electrons are fitted with gaussiantype orbitals, which is convenient for the calculation of electron repulsion integrals and the construction of HartreeFock exchange matrix elements. All other parts of Hamiltonian matrix elements are constructed directly with NAOs. The strict locality of NAOs is adopted as an efficient twoelectron integral screening technique to speed up calculations.

Harmonic electron correlation operator
View Description Hide DescriptionAn appealing way to model electron correlation within the single determinantwave function formalism is through the expectation value of a linear twoelectron operator. For practical reasons, it is desirable for such an operator to be universal, i.e., not depend on the positions and types of nuclei in a molecule. We show how a perturbation theory applied to a hookium atom provides for a particular form of a correlation operator, hence called the harmonic correlation operator. The correlation operator approach is compared and contrasted to the traditional ways to describe electron correlation. To investigate the twoelectron approximation of this operator, we apply it to manyelectron hookium systems. To investigate the harmonic approximation, we apply it to the small atomic systems. Directions of future research are also discussed.

Constrainedpairing meanfield theory. V. Triplet pairing formalism
View Description Hide DescriptionDescribing strong (also known as static) correlation caused by degenerate or nearly degenerate orbitals near the Fermi level remains a theoretical challenge, particularly in molecular systems. Constrainedpairing meanfieldtheory has been quite successful, capturing the effects of static correlation in bond formation and breaking in closedshell molecular systems by using singlet electron entanglement to model static correlation at meanfield computational cost. This work extends the previous formalism to include triplet pairing. Additionally, a spin orbital extension of the “oddelectron” formalism is presented as a method for understanding electron entanglement in molecules.

A global, high accuracy ab initio dipole moment surface for the electronic ground state of the water molecule
View Description Hide DescriptionA highly accurate, global dipole momentsurface (DMS) is calculated for the water molecule using ab initio quantum chemistry methods. The new surface is named LTP2011 and is based on allelectron, internally contracted multireference configuration interaction, including sizeextensivity corrections in the augccpCV6Z basis set. Dipoles are computed as energy derivatives and small corrections due to relativistic effects included. The LTP2011 DMS uses an appropriate functional form that guarantees qualitatively correct behaviour even for most high energies configuration (up to about 60 000 cm^{−1}), including, in particular, along the water dissociation channel. Comparisons with high precision experimental data show agreement within 1% for mediumstrength lines. The new DMS and all the ab initio data are made available in the supplementary material.

Identifying low variance pathways for free energy calculations of molecular transformations in solution phase
View Description Hide DescriptionImproving the efficiency of free energy calculations is important for many biological and materials design applications, such as proteinligand binding affinities in drug design, partitioning between immiscible liquids, and determining molecular association in soft materials. We show that for any pair potential, moderately accurate estimation of the radial distribution function for a solute molecule is sufficient to accurately estimate the statistical variance of a sampling along a free energy pathway. This allows inexpensive analytical identification of low statistical error free energy pathways. We employ a variety of methods to estimate the radial distribution function (RDF) and find that the computationally cheap twobody “dilute gas” limit performs as well or better than 3D–RISM theory and other approximations for identifying low variance free energy pathways. With a RDF estimate in hand, we can search for pairwise interaction potentials that produce low variance. We give an example of a search minimizing statistical variance of solvation free energy over the entire parameter space of a generalized “soft core” potential. The free energy pathway arising from this optimization procedure has lower curvature in the variance and reduces the total variance by at least 50% compared to the traditional soft core solvation pathway. We also demonstrate that this optimized pathway allows free energies to be estimated with fewer intermediate states due to its low curvature. This free energy variance optimization technique is generalizable to solvation in any homogeneous fluid and for any type of pairwise potential and can be performed in minutes to hours, depending on the method used to estimate g(r).

Symmetry exploitation in closedshell coupledcluster theory with spinorbit coupling
View Description Hide DescriptionIn the present work, we report exploitation of spatial symmetry in calculations of ground stateenergy and analytic first derivatives of closedshell molecules based on our previously developed coupledcluster (CC) approach with spinorbit coupling. Both timereversal symmetry and spatial symmetry for D_{2h} and its subgroups are exploited in the implementation. The symmetry of a certain spin case for the amplitude, intermediate, or density matrix is determined by the symmetry of the corresponding spin functions and the direct product decomposition method is employed in computations involving these quantities. The reduction in computational effort achieved through the use of spatial symmetry is larger than the order of the molecular single point group. Symmetry exploitation renders application of the CC approaches with spinorbit coupling to larger closedshell molecules containing heavy elements with high accuracy.

Analysis of selfconsistency effects in rangeseparated densityfunctional theory with MøllerPlesset perturbation theory
View Description Hide DescriptionRangeseparated densityfunctional theory combines wave functiontheory for the longrange part of the twoelectron interaction with densityfunctional theory for the shortrange part. When describing the longrange interaction with nonvariational methods, such as perturbation or coupledcluster theories, selfconsistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze selfconsistency when using MøllerPlessettype (MP) perturbation theory for the long range interaction. The lowestorder selfconsistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the oneelectron reduced density matrix. The computational implementation of the latter is based on a Neumann series which, interestingly, even though the effect is small, usually diverges. A convergence technique, which perhaps can be applied in other uses of Neumann series in perturbation theory, is proposed. The numerical results thus obtained show that, in weakly bound systems, selfconsistency can be neglected since the longrange correlation does not affect the density significantly. Although MP is not adequate for multireference systems, it can still be used as a reliable analysis tool. Though the density change is not negligible anymore in such cases, selfconsistency effects are found to be much smaller than longrange correlation effects (less than 10% for the systems considered). For that reason, a sensible approximation might be to update the shortrange energy functional term while freezing its functional derivative, namely, the shortrange local potential, in the wave function optimization. The accuracy of such an approximation still needs to be assessed.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Fieldfree molecular orientation enhanced by two dualcolor laser subpulses
View Description Hide DescriptionIn this paper, we theoretically show that the fieldfree molecular orientation created by a single dualcolor laser pulse can be significantly enhanced by separating it into two timedelayed dualcolor subpulses. It is indicated that the maximum enhancement of the molecular orientation created by two timedelayed dualcolor subpulses can be achieved with their intensity ratio of about 1:2 and by simultaneously applying the second one at the beginning of the rotational wave packet rephasing or the end of the rotational wave packet dephasing induced by the first one. It is also shown that the enhancement or suppression of the molecular orientation can be coherently manipulated by varying the relative phase between the fundamental field and its second harmonic field of the second dualcolor subpulse, and its enhancement is obtained around half rotational period.

Analyzing velocity map images to distinguish the primary methyl photofragments from those produced upon C–Cl bond photofission in chloroacetone at 193 nm
View Description Hide DescriptionWe use a combination of crossed lasermolecular beamscattering experiments and velocity map imaging experiments to investigate the three primary photodissociation channels of chloroacetone at 193 nm: C–Cl bondphotofission yielding CH_{3}C(O)CH_{2} radicals, C–C bondphotofission yielding CH_{3}CO and CH_{2}Cl products, and C–CH_{3}bondphotofission resulting in CH_{3} and C(O)CH_{2}Cl products. Improved analysis of data previously reported by our group quantitatively identifies the contribution of this latter photodissociation channel. We introduce a forward convolution procedure to identify the portion of the signal, derived from the methyl image, which results from a twostep process in which C–Cl bondphotofission is followed by the dissociation of the vibrationally excited CH_{3}C(O)CH_{2} radicals to CH_{3} + COCH_{2}. Subtracting this from the total methyl signal identifies the methyl photofragments that result from the CH_{3} + C(O)CH_{2}Cl photofission channel. We find that about 89% of the chloroacetone molecules undergo C–Cl bondphotofission to yield CH_{3}C(O)CH_{2} and Cl products; approximately 8% result in C–C bondphotofission to yield CH_{3}CO and CH_{2}Cl products, and the remaining 2.6% undergo C–CH_{3}bondphotofission to yield CH_{3} and C(O)CH_{2}Cl products.

On the rotational temperature and structure dependence of electric field deflection experiments: A case study of germanium clusters
View Description Hide DescriptionMolecular beamelectric field deflection experiments offer a probe to the structural and dielectric properties of isolated particles in the gas phase. However, their quantitative interpretation is still a formidable task. Despite the benefits of this method, the analysis of the deflection behavior is often complicated by various experimental and theoretical problems, including the amount of energy stored in internal and rotational modes of the deflected particle and the amount of structural asymmetry. In this contribution, we address these issues by discussing the experimentally observed fieldinduced deflection of Ge_{9}, Ge_{10}, and Ge_{15} clusters in comparison to quantum mechanical and classical deflection models. Additionally, we derive simple formulas to describe how the molecular beam deflection depends on the rotational temperature and the symmetry of the particle. Based on these results, we discuss to what extend molecular beamelectric field deflection experiments can be used as a tool for structure determination of isolated clusters in the gas phase.

Geometrical and substituent effects in conical intersections: Linking chemical structure and photoreactivity in polyenes
View Description Hide DescriptionThe knowledge of the intersection space topography of electronic states is essential for deciphering and predicting photoinduced reactions. Michl and Bonac̆ićKoutecký developed a twoelectron twoorbital model that allowed first systematic studies of the chemical origin of conical intersections in strongly polar systems. We generalize this approach to arbitrary functionalized and unfunctionalized polyene systems. For the extended model, a set of mathematical conditions for the formation of conical intersections are derived. These conditions are translated into geometrical motions and electronic effects, which help to explain and predict the structure and energetics of conical intersections. A threestep strategy for the conceptual search of conical intersections is outlined. Its universal validity is demonstrated using the textbook example cyclohexadiene and its functionalized derivative trifluoromethylindolylfulgide, a chromophore studied for possible application as a molecular switch.