Volume 135, Issue 22, 14 December 2011

Atomic motions in molecules are not linear. This infers that nonlinear dimensionality reduction methods can outperform linear ones in analysis of collective atomic motions. In addition, nonlinear collective motions can be used as potentially efficient guides for biased simulation techniques. Here we present a simulation with a bias potential acting in the directions of collective motions determined by a nonlinear dimensionality reduction method. Ad hoc generated conformations of trans,trans1,2,4trifluorocyclooctane were analyzed by Isomap method to map these 72dimensional coordinates to three dimensions, as described by Brown and coworkers [J. Chem. Phys.129, 064118 (2008)]. Metadynamics employing the threedimensional embeddings as collective variables was applied to explore all relevant conformations of the studied system and to calculate its conformationalfree energysurface. The method sampled all relevant conformations(boat, boatchair, and crown) and corresponding transition structures inaccessible by an unbiased simulation. This scheme allows to use essentially any parameter of the system as a collective variable in biased simulations. Moreover, the scheme we used for mapping outofsample conformations from the 72D to 3D space can be used as a general purpose mapping for dimensionality reduction, beyond the context of molecular modeling.
 COMMUNICATIONS


Communication: Branching ratio measurements in the predissociation of ^{12}C^{16}O by timeslice velocitymap ion imaging in the vacuum ultraviolet region
View Description Hide DescriptionThe first direct branching ratio measurement of the three lowest energy dissociation channels of CO that produce C(^{3}P) + O(^{3}P), C(^{1}D) + O(^{3}P), and C(^{3}P) + O(^{1}D) is reported. Rotational resolved carbon ion yield spectra for two Π bands (W(3sσ)^{1}Π (v^{′} = 3) at 108 012.6 cm^{−1} and ^{1}Π(v^{′} = 2) at 109 017 cm^{−1}) and two Σ bands ((4sσ)^{1}Σ^{+}(v^{′} = 4) at 109 452 cm^{−1} and (4pσ)^{1}Σ^{+}(v^{′} = 3) at 109 485 cm^{−1}) of CO were obtained. Our measurements show that the branching ratio in this energy region is strongly dependent on the electronic and vibrational energy but it is independent or just weakly dependent on the parity and rotational energy levels. To our knowledge, this is the first time that the triplet channel producing O(^{1}D) has been experimentally observed and this is also the first time that a direct measurement of the branching ratio for the different channels in the predissociation of CO in this energy region has been made.
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 ARTICLES

 Theoretical Methods and Algorithms

Diffusion in periodic twodimensional channels formed by overlapping circles: Comparison of analytical and numerical results
View Description Hide DescriptionWe study twodimensional diffusion in a channel formed by periodic overlapping circles. Periodic variation of the channel width leads to the slowdown of diffusion along the channel axis. There are several approximate approaches, which allow one to analyze the slowdown. We use these approaches to derive five expressions for the effective diffusion coefficient of a point Brownian particle in the channel. To check the accuracy of the expressions we compare their predictions with the effective diffusion coefficient obtained from Brownian dynamics simulations.

Interaction energies of large clusters from manybody expansion
View Description Hide DescriptionIn the canonical supermolecular approach, calculations of interactionenergies for molecular clusters involve a calculation of the whole cluster, which becomes expensive as the cluster size increases. We propose a novel approach to this task by demonstrating that interactionenergies of such clusters can be constructed from those of small subclusters with a much lower computational cost by applying progressively lowerlevel methods for subsequent terms in the manybody expansion. The efficiency of such “stratified approximation” manybody approach (SAMBA) is due to the rapid convergence of the manybody expansion for typical molecular clusters. The method has been applied to waterclusters (H_{2}O)_{ n }, n = 6, 16, 24. For the hexamer, the best results that can be obtained with current computational resources in the canonical supermolecular method were reproduced to within about one tenth of the uncertainty of the canonical approach while using 24 times less computer time in the manybody expansion calculations. For , SAMBA is particularly beneficial and we report interactionenergies with accuracy that is currently impossible to obtain with the canonical supermolecular approach. Moreover, our results were computed using two orders of magnitude smaller computer resources than used in the previous best calculations for this system. We also show that the basisset superposition errors should be removed in calculations for large clusters.

Orbitaloptimized thirdorder MøllerPlesset perturbation theory and its spincomponent and spinopposite scaled variants: Application to symmetry breaking problems
View Description Hide DescriptionIn this research, orbitaloptimized thirdorder MøllerPlesset perturbation theory (OMP3) and its spincomponent and spinopposite scaled variants (SCSOMP3 and SOSOMP3) are introduced. Using a Lagrangianbased approach, an efficient, quadratically convergent algorithm for variational optimization of the molecular orbitals (MOs) for thirdorder MøllerPlesset perturbation theory (MP3) is presented. Explicit equations for response density matrices, the MO gradient, and Hessian are reported in spinorbital form. The OMP3, SCSOMP3, and SOSOMP3 approaches are compared with the secondorder MøllerPlesset perturbation theory (MP2), MP3, coupledcluster doubles (CCD), optimizeddoubles (OD), and coupledcluster singles and doubles (CCSD) methods. All these methods are applied to the , O_{3}, and seven diatomic molecules. Results demonstrate that the OMP3 and its variants provide significantly better vibrational frequencies than MP3, CCSD, and OD for the molecules where the symmetrybreaking problems are observed. For , the OMP3 prediction, 1343 cm^{−1}, for ω_{6} (b _{3u }) mode, where symmetrybreaking appears, is even better than presumably more reliable methods such as Brueckner doubles (BD), 1194 cm^{−1}, and OD, 1193 cm^{−1}, methods (the experimental value is 1320 cm^{−1}). For O_{3}, the predictions of SCSOMP3 (1143 cm^{−1}) and SOSOMP3 (1165 cm^{−1}) are remarkably better than the more robust OD method (1282 cm^{−1}); the experimental value is 1089 cm^{−1}. For the seven diatomics, again the SCSOMP3 and SOSOMP3 methods provide the lowest average errors, Δω_{ e } = 44 and Δω_{ e } = 35 cm^{−1}, respectively, while for OD, Δω_{ e } = 161 cm^{−1}and CCSD Δω_{ e } = 106 cm^{−1}. Hence, the OMP3 and especially its spinscaled variants perform much better than the MP3, CCSD, and more robust OD approaches for considered test cases. Therefore, considering both the computational cost and the reliability, SCSOMP3 and SOSOMP3 appear to be the best methods for the symmetrybreaking cases, based on present application results. The OMP3 method offers certain advantages: it provides reliable vibrational frequencies in case of symmetrybreaking problems, especially with spinscaling tricks, its analytic gradients are easier to compute since there is no need to solve the coupledperturbed equations for the orbital response, and the computation of oneelectron properties are easier because there is no response contribution to the particle density matrices. The OMP3 has further advantages over standard MP3, making it promising for excited state properties via linear response theory.

Sensitivity field for nonautonomous molecular rotors
View Description Hide DescriptionWe propose a numerical approach to quantify the control of a nonautonomous molecular rotor motion. Unlike straightforward molecular dynamics simulations in an explicitly timedependent framework, our method is based on the theory of geometric phases. This theory allows us to define a sensitivity field (SF) in control parameter space that characterizes average motion of a molecule induced by a cyclic perturbation. We show that the SF can be obtained using only equilibrium free energy sampling techniques. A density plot of the SF quantifies response of a molecule to an arbitrary cyclic adiabatic evolution of parameters. For demonstration, we numerically find the SFs for two surface mounted molecular rotor molecules that can be driven, in practice, by strong timedependent electric fields of a STM tip.

Geometric integration in BornOppenheimer molecular dynamics
View Description Hide DescriptionGeometric integration schemes for extended Lagrangian selfconsistent BornOppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate selfconsistent field (SCF) convergence. We investigate three different geometric integration schemes: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics.

Spinorbit relativistic longrange corrected timedependent density functional theory for investigating spinforbidden transitions in photochemical reactions
View Description Hide DescriptionA longrange corrected (LC) timedependent density functional theory (TDDFT) incorporating relativistic effects with spinorbit couplings is presented. The relativistic effects are based on the twocomponent zerothorder regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkalineearth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans’ theorem. We found that both longrange exchange and spinorbit couplingeffects are required to obtain Koopmans’ IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for firstrow transition metals and systems containing large shortrange exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydbergexcitations of rare gas atoms using spinorbit relativistic LCTDDFT. We found that the longrange exchange and spinorbit couplingeffects significantly contribute to the electronic spectra of even light atoms if the atoms have lowlying excitations between orbital spinors of quite different electron distributions.

Electrostatic embedding in largescale first principles quantum mechanical calculations on biomolecules
View Description Hide DescriptionBiomolecular simulations with atomistic detail are often required to describe interactions with chemical accuracy for applications such as the calculation of free energies of binding or chemical reactions in enzymes. Force fields are typically used for this task but these rely on extensive parameterisation which in cases can lead to limited accuracy and transferability, for example for ligands with unusual functional groups. These limitations can be overcome with first principles calculations with methods such as density functional theory (DFT) but at a much higher computational cost. The use of electrostatic embedding can significantly reduce this cost by representing a portion of the simulated system in terms of highly localised charge distributions. These classical charge distributions are electrostatically coupled with the quantum system and represent the effect of the environment in which the quantum system is embedded. In this paper we describe and evaluate such an embedding scheme in which the polarisation of the electronic density by the embedding charges occurs selfconsistently during the calculation of the density. We have implemented this scheme in a linearscaling DFT program as our aim is to treat with DFT entire biomolecules (such as proteins) and large portions of the solvent. We test this approach in the calculation of interaction energies of ligands with biomolecules and solvent and investigate under what conditions these can be obtained with the same level of accuracy as when the entire system is described by DFT, for a variety of neutral and charged species.

Efficient exploration of reaction paths via a freezing string method
View Description Hide DescriptionThe ability to efficiently locate transition states is critically important to the widespread adoption of theoretical chemistry techniques for their ability to accurately predict kinetic constants. Existing surface walking techniques to locate such transition states typically require an extremely good initial guess that is often beyond human intuition to estimate. To alleviate this problem, automated techniques to locate transition state guesses have been created that take the known reactant and product endpoint structures as inputs. In this work, we present a simple method to build an approximate reaction path through a combination of interpolation and optimization. Starting from the known reactant and product structures, new nodes are interpolated inwards towards the transition state, partially optimized orthogonally to the reaction path, and then frozen before a new pair of nodes is added. The algorithm is stopped once the string ends connect. For the practical user, this method provides a quick and convenient way to generate transition state structure guesses. Tests on three reactions (cyclization of cis,cis2,4hexadiene, alanine dipeptide conformation transition, and ethylene dimerization in a Niexchanged zeolite) show that this “freezing string” method is an efficient way to identify complex transition states with significant cost savings over existing methods, particularly when high quality linear synchronous transit interpolation is employed.

Milestoning with transition memory
View Description Hide DescriptionMilestoning is a method used to calculate the kinetics and thermodynamics of molecular processes occurring on time scales that are not accessible to brute force molecular dynamics (MD). In milestoning, the conformation space of the system is sectioned by hypersurfaces (milestones), an ensemble of trajectories is initialized on each milestone, and MD simulations are performed to calculate transitions between milestones. The transition probabilities and transition time distributions are then used to model the dynamics of the system with a Markov renewal process, wherein a long trajectory of the system is approximated as a succession of independent transitions between milestones. This approximation is justified if the transition probabilities and transition times are statistically independent. In practice, this amounts to a requirement that milestones are spaced such that trajectories lose position and velocity memory between subsequent transitions. Unfortunately, limiting the number of milestones limits both the resolution at which a system's properties can be analyzed, and the computational speedup achieved by the method. We propose a generalized milestoning procedure, milestoning with transition memory (MTM), which accounts for memory of previous transitions made by the system. When a reaction coordinate is used to define the milestones, the MTM procedure can be carried out at no significant additional expense as compared to conventional milestoning. To test MTM, we have applied its version that allows for the memory of the previous step to the toy model of a polymer chain undergoing Langevin dynamics in solution. We have computed the mean first passage time for the chain to attain a cyclic conformation and found that the number of milestones that can be used, without incurring significant errors in the first passage time is at least 8 times that permitted by conventional milestoning. We further demonstrate that, unlike conventional milestoning, MTM permits milestones to be spaced such that trajectories do not have enough time to lose their velocity memory between successively crossed milestones.

A scheme to interpolate potential energy surfaces and derivative coupling vectors without performing a global diabatization
View Description Hide DescriptionSimulation of nonadiabatic molecular dynamics requires the description of multiple electronic state potential energy surfaces and their couplings. Ab initiomolecular dynamics approaches provide an attractive avenue to accomplish this, but at great computational expense. Interpolation approaches provide a possible route to achieve flexible descriptions of the potential energy surfaces and their couplings at reduced expense. A previously developed approach based on modified Shepard interpolation required global diabatization, which can be problematic. Here, we extensively revise this previous approach, avoiding the need for global diabatization. The resulting interpolated potentials provide only adiabatic energies, gradients, and derivative couplings. This new interpolation approach has been integrated with the ab initio multiple spawning method and it has been rigorously validated against direct dynamics. It is shown that, at least for small molecules, constructing an interpolated PES can be more efficient than performing direct dynamics as measured by the total number of ab initio calculations that are required for a given accuracy.

Thermodynamic integration from classical to quantum mechanics
View Description Hide DescriptionWe present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a wellestablished method with an analysis of a onedimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.

The problem of hole localization in innershell states of N_{2} and CO_{2} revisited with complete active space selfconsistent field approach
View Description Hide DescriptionPotential energy curves for innershell states of nitrogen and carbon dioxide molecules are calculated by innershell complete active space selfconsistent field (CASSCF) method, which is a protocol, recently proposed, to obtain specifically converged innershell states at multiconfigurational level. This is possible since the collapse of the wave function to a lowlying state is avoided by a sequence of constrained optimization in the orbital mixing step. The problem of localization of Kshell states is revisited by calculating their energies at CASSCF level based on both localized and delocalized orbitals. The localized basis presents the best results at this level of calculation. Transition energies are also calculated by perturbation theory, by taking the above mentioned MCSCF function as zeroth order wave function. Values for transition energy are in fairly good agreement with experimental ones. Bond dissociation energies for N_{2} are considerably high, which means that these states are strongly bound. Potential curves along ground statenormal modes of CO_{2} indicate the occurrence of RennerTeller effect in innershell states.

Boiling point determination using adiabatic Gibbs ensemble Monte Carlo simulations: Application to metals described by embeddedatom potentials
View Description Hide DescriptionThe normal boiling points are obtained for a series of metals as described by the “quantumcorrected Sutton Chen” (qSC) potentials [S.N. Luo, T. J. Ahrens, T. Çağın, A. Strachan, W. A. Goddard III, and D. C. Swift, Phys. Rev. B68, 134206 (2003)]. Instead of conventional Monte Carlo simulations in an isothermal or expanded ensemble, simulations were done in the constantNPH adabatic variant of the Gibbs ensemble technique as proposed by Kristóf and Liszi [Chem. Phys. Lett.261, 620 (1996)]. This simulation technique is shown to be a precise tool for direct calculation of boiling temperatures in highboiling fluids, with results that are almost completely insensitive to system size or other arbitrary parameters as long as the potential truncation is handled correctly. Results obtained were validated using conventional NVTGibbs ensemble Monte Carlo simulations. The qSC predictions for boiling temperatures are found to be reasonably accurate, but substantially underestimate the enthalpies of vaporization in all cases. This appears to be largely due to the systematic overestimation of dimer binding energies by this family of potentials, which leads to an unsatisfactory description of the vapor phase.
 Advanced Experimental Techniques

Ultrasensitive highprecision spectroscopy of a fast molecular ion beam
View Description Hide DescriptionDirect spectroscopy of a fast molecular ion beam offers many advantages over competing techniques, including the generality of the approach to any molecular ion, the complete elimination of spectral confusion due to neutral molecules, and the mass identification of individual spectral lines. The major challenge is the intrinsic weakness of absorption or dispersion signals resulting from the relatively low number density of ions in the beam. Direct spectroscopy of an ion beam was pioneered by Saykally and coworkers in the late 1980s, but has not been attempted since that time. Here, we present the design and construction of an ion beamspectrometer with several improvements over the Saykally design. The ion beam and its characterization have been improved by adopting recent advances in electrostatic optics, along with a timeofflightmass spectrometer that can be used simultaneously with optical spectroscopy. As a proof of concept, a noiseimmune cavityenhanced optical heterodyne molecular spectroscopy (NICEOHMS) setup with a noise equivalent absorption of ∼2 × 10^{−11} cm^{−1} Hz^{−1/2} has been used to observe several transitions of the Meinel 1–0 band of with linewidths of ∼120 MHz. An optical frequency comb has been used for absolute frequency calibration of transition frequencies to within ∼8 MHz. This work represents the first direct spectroscopy of an electronic transition in an ion beam, and also represents a major step toward the development of routine infrared spectroscopy of rotationally cooled molecular ions.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Coherent control of molecular torsion
View Description Hide DescriptionWe propose a coherent, strongfield approach to control the torsional modes of biphenyl derivatives, and develop a numerical scheme to simulate the torsional dynamics. By choice of the field parameters, the method can be applied either to drive the torsion angle to an arbitrary configuration or to induce free internal rotation. Transient absorption spectroscopy is suggested as a probe of torsional control and the usefulness of this approach is numerically explored. Several consequences of our ability to manipulate molecular torsional motions are considered. These include a method for the inversion of molecular chirality and an ultrafast chiral switch.

Infrared absorption of gaseous benzoylperoxy radical C_{6}H_{5}C(O)OO recorded with a stepscan Fouriertransform spectrometer
View Description Hide DescriptionA stepscan Fouriertransform infrared spectrometer coupled with a multipass absorption cell was utilized to monitor the transient species produced in gaseous reactions of benzoyl radical, C_{6}H_{5}CO, with O_{2}. C_{6}H_{5}CO was produced either from photolysis of acetophenone, C_{6}H_{5}C(O)CH_{3}, at 248 nm, or from photolysis of a mixture of benzaldehyde, C_{6}H_{5}CHO, and Cl_{2} at 355 nm. Two intense bands near 1830 and 1226 cm^{−1} are assigned to the C=O stretching (ν _{6}) and the C−C stretching mixed with C−H deformation (ν _{13}) modes, and two weaker bands near 1187 and 1108 cm^{−1} are assigned to the ν _{14} (C−H deformation) and ν _{16} (O−O stretching /C−H deformation) modes of C_{6}H_{5}C(O)OO, the benzoylperoxy radical. These observed vibrational wave numbers and relative infrared intensities agree with those reported for synC_{6}H_{5}C(O)OO isolated in solid Ar and values predicted for synC_{6}H_{5}C(O)OO with the B3LYP/ccpVTZ method. The simulated rotational contours of the two intense bands based on rotational parameters predicted with the B3LYP/ccpVTZ method fit satisfactorily with experimental results.

Assessing computationally efficient isomerization dynamics: ΔSCF densityfunctional theory study of azobenzene molecular switching
View Description Hide DescriptionWe present a detailed comparison of the S0, S1 (n → π*) and S2 (π → π*) potential energy surfaces (PESs) of the prototypical molecular switch azobenzene as obtained by Δselfconsistentfield (ΔSCF) densityfunctional theory(DFT), timedependent DFT (TDDFT) and approximate coupled cluster singles and doubles (RICC2). All three methods unanimously agree in terms of the PES topologies, which are furthermore fully consistent with existing experimental data concerning the photoisomerization mechanism. In particular, summethod corrected ΔSCF and TDDFT yield very similar results for S1 and S2, when based on the same groundstate exchangecorrelation (xc) functional. While these techniques yield the correct PES topology already on the level of semilocal xc functionals, reliable absolute excitation energies as compared to RICC2 or experiment require an xc treatment on the level of longrange corrected hybrids. Nevertheless, particularly the robustness of ΔSCF with respect to state crossings as well as its numerical efficiency suggest this approach as a promising route to dynamical studies of larger azobenzenecontaining systems.

Highresolution threshold photoelectron study of the propargyl radical by the vacuum ultraviolet laser velocitymap imaging method
View Description Hide DescriptionBy employing the vacuum ultraviolet (VUV) laser velocitymap imaging (VMI) photoelectron scheme to discriminate energetic photoelectrons, we have measured the VUVVMIthreshold photoelectrons (VUVVMITPE) spectra of propargyl radical [C_{3}H_{3}()] near its ionization threshold at photoelectron energy bandwidths of 3 and 7 cm^{−1} (fullwidth at halfmaximum, FWHM). The simulation of the VUVVMITPE spectra thus obtained, along with the Stark shift correction, has allowed the determination of a precise value 70 156 ± 4 cm^{−1} (8.6982 ± 0.0005 eV) for the ionization energy (IE) of C_{3}H_{3}. In the present VMITPE experiment, the Stark shift correction is determined by comparing the VUVVMITPE and VUV laser pulsed field ionizationphotoelectron (VUVPFIPE) spectra for the origin band of the photoelectron spectrum of the transition of chlorobenzene. The fact that the FWHMs for this origin band observed using the VUVVMITPE and VUVPFIPE methods are nearly the same indicates that the energy resolutions achieved in the VUVVMITPE and VUVPFIPE measurements are comparable. The IE(C_{3}H_{3}) value obtained based on the VUVVMITPE measurement is consistent with the value determined by the VUV laser PIE spectrum of supersonically cooled C_{3}H_{3}() radicals, which is also reported in this article.

Copper doping of small gold cluster cations: Influence on geometric and electronic structure
View Description Hide DescriptionThe effect of Cudoping on the properties of small gold cluster cations is investigated in a joint experimental and theoretical study. Temperaturedependent Ar tagging of the clusters serves as a structural probe and indicates no significant alteration of the geometry of Au_{ n } ^{+} (n = 1–16) upon Cudoping. Experimental cluster–argon bond dissociation energies are derived as a function of cluster size from equilibrium mass spectra and are in the 0.10–0.25 eV range. NearUV and visible light photodissociation spectroscopy is employed in conjunction with timedependent density functional theory calculations to study the electronic absorption spectra of Au_{4m }Cu_{ m } ^{+} (m = 0, 1, 2) and their Ar complexes in the 2.00−3.30 eV range and to assign their fragmentation pathways. The tetramers Au_{4} ^{+}, Au_{4} ^{+}·Ar, Au_{3}Cu^{+}, and Au_{3}Cu^{+}·Ar exhibit distinct optical absorption features revealing a pronounced shift of electronic excitations to larger photon energies upon substitution of Au by Cu atoms. The calculated electronic excitationspectra and an analysis of the character of the optical transitions provide detailed insight into the compositiondependent evolution of the electronic structure of the clusters.