Volume 136, Issue 17, 07 May 2012

Geometries, anharmonic vibrations, and torsionwagging (TW) multiplets of hydrazine and its deuterated species are studied using highlevel ab initio methods employing the secondorder MøllerPlesset perturbation theory (MP2) as well as the coupled cluster singles and doubles model including connected triple corrections, CCSD(T), in conjunction with extended basis sets containing diffuse and core functions. To describe the splitting patterns caused by tunneling in TW states, the 3D potential energy surface (PES) for the largeamplitude TW modes is constructed. Stationary points in the 3D PES, including equivalent local minima and saddle points are characterized. Using this 3D PES, a flexible Hamiltonian is built numerically and then employed to solve the vibrational problem for TW coupled motion. The calculated ground stater _{av} structure is expected to be more reliable than the experimental one that has been determined using a simplified structural model. The calculated fundamental frequencies allowed resolution of the assignment problems discussed earlier in the literature. The determined energy barriers, including the contributions from the smallamplitude vibrations, to the tunneling of the symmetric and antisymmetric wagging mode of 1997 cm^{−1} and 3454 cm^{−1}, respectively, are in reasonable agreement with the empirical estimates of 2072 cm^{−1} and 3312 cm^{−1}, respectively [W. Łodyga et al.J. Mol. Spectrosc.183, 374 (1997)10.1006/jmsp.1997.7271]. However, the empirical torsion barrier of 934 cm^{−1} appears to be overestimated. The ab initio calculations yield two torsion barriers: cis and trans of 744 cm^{−1} and 2706 cm^{−1}, respectively. The multiplets of the excited torsion states are predicted from the refined 3D PES.
 COMMUNICATIONS


Communication: Spectroscopic measurement of the binding energy of a carboxylic acidwater dimer
View Description Hide DescriptionInfraredultraviolet two color pumpprobe spectroscopy is used to measure the binding energy, D_{0,} of a carboxylic acidwater dimer where the acid is 9hydroxy9fluorenecarboxylic acid. The acidwater configuration presents a standard structure for the general acidwater interaction where the water bonds to the carboxylic acid group through two intermolecular hydrogen bonds. Photodissociation studies with product vibrational state resolution have enabled an accurate determination of the binding energy for this acidwater system to be D_{0} = 2975 ± 30 cm^{−1}. Quantum chemical calculations are performed to compare with the experimental observations and a recent measurement on the water dimer (D_{0} = 1105 ± 10 cm^{−1}).
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 ARTICLES

 Theoretical Methods and Algorithms

Optimizing transition states via kernelbased machine learning
View Description Hide DescriptionWe present a method for optimizing transition state theory dividing surfaces with support vector machines. The resulting dividing surfaces require no a priori information or intuition about reaction mechanisms. To generate optimal dividing surfaces, we apply a cycle of machinelearning and refinement of the surface by molecular dynamics sampling. We demonstrate that the machinelearned surfaces contain the relevant lowenergy saddle points. The mechanisms of reactions may be extracted from the machinelearned surfaces in order to identify unexpected chemically relevant processes. Furthermore, we show that the machinelearned surfaces significantly increase the transmission coefficient for an adatom exchange involving many coupled degrees of freedom on a (100) surface when compared to a distancebased dividing surface.

Equationofmotion coupledcluster method for ionized states with spinorbit coupling
View Description Hide DescriptionWe report implementation of the equation of motion coupledcluster approach for ionized states (EOMIPCC) with spinorbit coupling (SOC) using closedshell state as reference in this work. Ionization potentials (IPs) are calculated in the ionized 1h and 2h1p space with EOM at the CC singles (CCS) as well as the CC singles and doubles levels (CCSD). In this EOMIPCC approach, SOC is included either in both the CC and EOM steps or only in the EOM step. It should be noted that IPs provided by the EOMIPCC approach with SOC included only in the EOM step are not sizeintensive. Timereversal symmetry and spatial symmetry are exploited for D_{2h} and its subgroups to reduce computational effort. All these approaches have been shown to be able to afford acceptable estimates for SOC splittings. The EOMIPCCSD with SOC included only in the EOM step can provide reasonable IPs for systems containing up to 5th row elements. On the other hand, the EOMIPCCS approach with SOC included in both CC and EOM steps could not predict a bounded ^{2}∑_{g} ^{+} state for I_{2} ^{+} and should be used with care.

Doubly hybrid density functional xDHPBE0 from a parameterfree global hybrid model PBE0
View Description Hide DescriptionFollowing the XYG3 model which uses orbitals and density from B3LYP, an empirical doubly hybrid (DH) functional is developed by using inputs from PBE0. This new functional, named xDHPBE0, has been tested on a number of different molecular properties, including atomization energies,bonddissociationenthalpies,reaction barrier heights, and nonbonded interactions. From the results obtained, xDHPBE0 not only displays a significant improvement with respect to the parent PBE0, but also shows a performance that is comparable to XYG3. Arguably, while PBE0 is a parameterfree global hybrid (GH) functional, the B3LYP GH functional contains eight fit parameters. From a more general point of view, the present work points out that reliable and generalpurpose DHs can be obtained with a limited number of fit parameters.

Long range excitonic transport in a biomimetic system inspired by the bacterial lightharvesting apparatus
View Description Hide DescriptionPhotosynthesis, the process by which energy from sunlight drives cellular metabolism, relies on a unique organization of lightharvesting and reaction center complexes. Recently, the organization of lightharvesting LH2 complexes and dimeric reaction centerlightharvesting IPufX core complexes in membranes of purple nonsulfur bacteria was revealed by atomic force microscopy [S. Bahatyrova et al., Nature (London)430, 1058 (2004)]. Here, we discuss optimal exciton transfer in a biomimetic system closely modeled on the structure of LH2 and its organization within the membrane using a Markovian quantum model with dissipation and trapping added phenomenologically. In a deliberate manner, we neglect the high level detail of the bacterial lightharvesting complex and its interaction with the phonon bath in order to elucidate a set of design principles that may be incorporated in artificial pigmentscaffold constructs in a supramolecular assembly. We show that our scheme reproduces many of the most salient features found in their natural counterpart and may be largely explained by simple electrostatic considerations. Most importantly, we show that quantum effects act primarily to enforce robustness with respect to spatial and spectral disorder between and within complexes. The implications of such an arrangement are discussed in the context of biomimetic photosynthetic analogs capable of transferring energy efficiently across tens to hundreds of nanometers.

Discontinuous phase transition in a dimer lattice gas
View Description Hide DescriptionI study a dimer model on the square lattice with nearest neighbor exclusion as the only interaction. Detailed simulations using tomographic entropic sampling show that as the chemical potential is varied, there is a strongly discontinuous phase transition, at which the particle density jumps by about 18% of its maximum value, 1/4. The transition is accompanied by the onset of orientational order, to an arrangement corresponding to the {1/2, 0, 1/2} structure identified by Phares et al. [Physica B409, 1096 (2011)] in a dimer model with finite repulsion at fixed density. Using finitesize scaling and Binder's cumulant, the expected scaling behavior at a discontinuous transition is verified in detail. The discontinuous transition can be understood qualitatively given that the model possesses eight equivalent maximumdensity configurations, so that its coarsegrained description corresponds to that of the q = 8 Potts model.

Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolutionoftheidentity approximation
View Description Hide DescriptionWe present an implementation of static and frequencydependent polarizabilities for the approximate coupled cluster singles and doubles model CC2 and static polarizabilities for secondorder MøllerPlesset perturbation theory. Both are combined with the resolutionoftheidentity approximation for electron repulsion integrals to achieve unprecedented low operation counts, input–output, and disc space demands. To avoid the storage of double excitation amplitudes during the calculation of derivatives of density matrices, we employ in addition a numerical Laplace transformation for orbital energy denominators. It is shown that the error introduced by this approximation is negligible already with a small number of sampling points. Thereby an implementation of secondorder oneparticle properties is realized, which avoids completely the storage of quantities scaling with the fourth power of the system size. The implementation is tested on a set of organic molecules including large fused aromatic ring systems and the C_{60} fullerene. It is demonstrated that exploiting symmetry and shared memory parallelization, secondorder properties for such systems can be evaluated at the CC2 and MP2 level within a few hours of calculation time. As large scale applications, we present results for the 7, 9, and 11ring helicenes.

Convergence of the multipole expansions of the polarization and dispersion interactions for atoms under confinement
View Description Hide DescriptionThe multipole expansion of the polarization interaction between a charged particle and an electrically neutral object has long been known to be asymptotic in nature, i.e., the multiple expansion diverges at any finite distance from the atom. However, the multipole expansion of the polarization potential of a confined hydrogen atom is shown to be absolutely convergent at a distance outside the confinement radius, R _{0}, of the atom. The multipole expansion of the dispersion potential between two confined hydrogen atoms is also shown to be absolutely convergent provided the two atoms satisfy R > 2R _{0}, where R is the internuclear separation. These results were established analytically using oscillator strength sum rules and verified numerically using a Bspline description of the hydrogen ground state and its excitation spectrum.

Experiment and theoretical modeling of the luminescence of silver nanoclusters dispersed in oxyfluoride glass
View Description Hide DescriptionDensity functional theory(DFT) and complete active space perturbation theory (CASPT2) have been applied for modeling the configuration, charge, energy states, and spin of luminescent Agnanoclusters dispersed within the bulk of oxyfluoride glass host. The excitation spectra of luminescence of the Agnanoclusters have been measured and simulated by means of the DFT and CASPT2. Electron spin resonancespectra have been recorded and suggest diamagnetic state of Agnanoclusters. The silvernanoclusters have been argued to consist mostly of pairs of Ag_{2} ^{+} dimers, or Ag_{4} ^{2+} tetramers, with different extent of distortion along the tetramer diagonal. The sites for the Agnanoclusters have been suggested where the pairs of Ag ions substitute onto metal and hole cation sites and are surrounded by fluorine ions within a fluoritetype lattice.

Van der Waals interactions in solids using the exchangehole dipole moment model
View Description Hide DescriptionThe exchangehole dipole moment model of dispersion interactions of Becke and Johnson [J. Chem. Phys.127154108 (2007)10.1063/1.2795701] is implemented for calculations in solids using the pseudopotentials/planewaves approach. The resulting functional retains the simplicity and efficiency of semilocal functionals while accurately treating dispersion interactions via a semiempirical asymptotic expansion. The dispersion coefficients are calculated completely ab initio using local quantities alone (density, gradient, Laplacian, and kinetic energy density). The two empirical parameters in the damping function are calculated by fit to a 65molecule training set recalculated under periodic boundary conditions. Calculations in simple solids offer good results with minimal computational cost compared to electronic relaxation.

On the representation of coupled adiabatic potential energy surfaces using quasidiabatic Hamiltonians: A distributed origins expansion approach
View Description Hide DescriptionIn two previous papers we have introduced a method to generate coupled quasidiabatic Hamiltonians (H ^{d}) that are capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, two new synergistic features are introduced. Firstly, the functional form of H ^{d} is generalized. Rather than requiring there to be a low energy point of high symmetry to serve as the unique origin, functions centered on points distributed in nuclear coordinate space are used in the polynomials that comprise the matrix elements in H ^{d}. The use of functions with distributed origins, allows reproduction of the ab initio data with lower order expansions, and offers the possibility of describing multichannel dissociation. The fitting algorithm is combined with a threestep procedure in which the domain of H ^{d} is extended from a core set of nuclear configurations to a region of nuclear coordinate space appropriate for nuclear dynamics, with a prescribed accuracy. This significant extension of the domain of definition compared to our original work, which is facilitated by the distributed origin approach, is achieved largely through the use of surface hopping trajectories. The 1,2^{1}A states of NH_{3}, which provide an archetypical example of nonadiabaticdynamics, are used to demonstrate the utility of this approach. The representation describes 21 points on the 1^{1}A–2^{1}A seam of conical intersection and their local topography flawlessly and on the entire domain, the electronic structure data is represented to an accuracy of 77.00 (46.90) cm^{−1}, as measured by the root mean square (mean unsigned) error for energies lower than 50 000 cm^{−1}. This error is a factor of 10 lower than that of the most accurate representation of high quality ab initio data, on a comparable domain, previously reported for this system.

The free energy of expansion and contraction: Treatment of arbitrary systems using the Jarzynski equality
View Description Hide DescriptionThermodynamic integration, free energyperturbation, and slow change techniques have long been utilised in the calculation of free energy differences between two states of a system that has undergone some transformation. With the introduction of the Jarzynski equality and the Crooks relation, new approaches are possible. This paper investigates an important phenomenon – systems undergoing a change in volume/density – and derives both the Jarzynski equality and Crooks relation of such systems using a statistical mechanical approach. These results apply to systems with arbitrary particle interactions and densities. The application of this approach to the expansion/compression of particles confined within a vessel with a piston and within a periodic system is considered.

The role of axis embedding on rigid rotor decomposition analysis of variational rovibrational wave functions
View Description Hide DescriptionApproximate rotational characterization of variational rovibrational wave functions via the rigid rotor decomposition (RRD) protocol is developed for Hamiltonians based on arbitrary sets of internal coordinates and axis embeddings. An efficient and general procedure is given that allows employing the Eckart embedding with arbitrary polyatomic Hamiltonians through a fully numerical approach. RRD tables formed by projecting rotationalvibrational wave functions into products of rigidrotor basis functions and previously determined vibrational eigenstates yield rigidrotor labels for rovibrational eigenstates by selecting the largest overlap. Embeddingdependent RRD analyses are performed, up to high energies and rotational excitations, for the H_{2} ^{16}O isotopologue of the water molecule. Irrespective of the embedding chosen, the RRD procedure proves effective in providing unambiguous rotational assignments at low energies and J values. Rotational labeling of rovibrational states of H_{2} ^{16}O proves to be increasingly difficult beyond about 10 000 cm^{−1}, close to the barrier to linearity of the water molecule. For medium energies and excitations the Eckart embedding yields the largest RRD coefficients, thus providing the largest number of unambiguous rotational labels.

Exact expressions for ensemble functionals from particle number dependence
View Description Hide DescriptionSome properties of exact ensemble density functionals can be determined by examining the particle number dependence of ground state ensemble density matrices for systems where the integer ground state energies satisfy a convexity condition. The results include the observation that the integral of the product of the functional derivative and Fukui function of functionals that can be expressed as the trace of an operator is particle number independent for particle numbers between successive integers and the integral itself is equal to the difference between functionals evaluated at successive integer particle numbers. Expressions that must be satisfied by 2nd and higher order functional derivatives are formulated and equations that must be satisfied point by point in space are derived. Using the analytic Hooke's atom model, it is shown that commonly used correlation functional approximations do not bear any resemblance to a spatially dependent expression derived from the exact second order functional derivative of the correlation functional. It is also shown that two expressions for the mutual Coulomb energy are not equal when approximate exchange and correlation functionals are used.

Multicomponent density functional theory study of the interplay between electronelectron and electronproton correlation
View Description Hide DescriptionThe interplay between electronelectron and electronproton correlation is investigated within the framework of the nuclearelectronic orbital density functional theory (NEODFT) approach, which treats electrons and select protons quantum mechanically on the same level. Recently two electronproton correlation functionals were developed from the electronproton pair densities obtained from explicitly correlated wavefunctions. In these previous derivations, the kinetic energy contribution arising from electronproton correlation was neglected. In this paper, an electronproton correlation functional that includes this kinetic energy contribution is derived using the adiabatic connection formula in multicomponent DFT. The performance of the NEODFT approach using all three electronproton correlation functionals in conjunction with three wellestablished electronic exchangecorrelation functionals is assessed. NEODFT calculations with these electronproton correlation functionals capture the increase in the hydrogen vibrational stretching frequencies arising from the inclusion of electronelectron correlation in model systems. Electronproton and electronelectron correlation are found to be uncoupled and predominantly additive effects to the total energy for the model systems studied. Thus, electronproton correlation functionals and electronic exchangecorrelation functionals can be developed independently and subsequently combined together without reparameterization.

The analysis of NMR Jcouplings of saturated and unsaturated compounds by the localized second order polarization propagator approach method
View Description Hide DescriptionCalculations of NMR Jcoupling with polarization propagators are not invariant under unitary transformations at second order level of approach, second order polarization propagator approach (SOPPA). They are only invariant at first order or random phase level of approach (RPA). We performed “localized” SOPPA (LocSOPPA), calculations of Jcouplings applying two different schemes for the localization of molecular orbitals(LMO): FosterBoys and PipekMezey. We show here that results of such LocSOPPA calculations are different though not much: they are less than 6% different in the worst case. Therefore it is possible to apply them with confidence in the analysis of the transmission of different coupling mechanisms within the molecule. We are able now to get reliable information on what LMOs are the most important (and so which are not important) for a given Jcoupling in a molecule. This information can then be used for selecting which are the paths that should be described with the highest possible accuracy for that Jcoupling calculation. A few unsaturated compounds are analyzed: ethene, transdifluoroethene or DiFethene, and imine. It is shown that different lone pairs (of p_{ z } or p_{ x/y } type) are responsible for the vicinal FF Jcoupling in DiFethene; and also the fact that the main LP contributor is not the same for the fermi contact and the spindipolar mechanisms. We also studied phosphorous containing compounds such as phosphine and cispropylene phosphine. In both cases the analysis of the main LMO contributing to onebond PH coupling and throughspace PC coupling were performed. The above mentioned unsaturated molecular systems have quasiinstability problems that arise at RPA level of approach. We show here that they are mostly originated in the antibonding π* LMO, corresponding to the C=C or C=N double bonds. We performed the analysis of the origin of quasiinstabilities for the SD mechanism. The contribution of each kind of excitation terms to SOPPA calculations were considered, meaning the main contributions by single and double excitations. It is shown that one can get more than 97% of the total electron correlation contribution when including terms that mainly contain single excitations (though doubleexcitation matrix elements should still be calculated).

The extended Koopmans’ theorem: Vertical ionization potentials from natural orbital functional theory
View Description Hide DescriptionThe Piris natural orbital functional, PNOF5, has been used to predict vertical ionization potentials of a selected set of 30 organic and inorganic spincompensated molecules by means of the extended Koopmans’ theorem.Electron affinities of 10 selected radicals have also been estimated as the inverse of the ionization potentials of the anionic species, calculated at the experimental geometries of the neutral radicals. The basis set limit effects have been assessed by inspecting the data obtained for the Dunning's basis set series ccpVXZ and augccpVXZ (X = D, T, Q, 5). The performance of the PNOF5 is established by carrying out a statistical analysis of the mean absolute errors (MAEs) with respect to the experiment values. The calculated PNOF5 ionization potentials and electron affinities agree satisfactorily with the corresponding experimental data, with MAEs smaller than 0.5 eV.

Twodimensional stimulated resonance Raman spectroscopy of molecules with broadband xray pulses
View Description Hide DescriptionExpressions for the twodimensional stimulated xrayRaman spectroscopy (2DSXRS) signal obtained using attosecond xray pulses are derived. The 1D and 2DSXRS signals are calculated for transNmethyl acetamide (NMA) with broad bandwidth (181 as, 14.2 eV FWHM) pulses tuned to the oxygen and nitrogen Kedges. Crosspeaks in 2D signals reveal electronic FranckCondon overlaps between valence orbitals and relaxed orbitals in the presence of the corehole.

Nonstationary forward flux sampling
View Description Hide DescriptionWe present a method, NonStationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and nonstationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform sampling of trajectories in phase space and time, leading to accurate estimates for timedependent switching propensities and timedependent phase space probability densities. It is suitable for equilibrium or nonequilibrium systems, in or out of stationary state, including nonMarkovian or externally driven systems. We demonstrate the validity of the technique by applying it to a onedimensional barrier crossing problem that can be solved exactly, and show its usefulness by applying it to the timedependent switching of a genetic toggle switch.

Rare switching events in nonstationary systems
View Description Hide DescriptionPhysical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For timehomogeneous systems with shortterm memory these transitions are fully characterized by a set of rate constants. We consider the question how to extend such a coarsegrained description to nonstationary systems and to systems with finite memory. We identify the physical regimes in which timedependent rates are meaningful, and state microscopic expressions that can be used to measure both externally timedependent and historydependent rates in microscopic simulations. Our description can be used to generalize Markov state models to timedependent Markovian or nonMarkovian systems.