Volume 134, Issue 18, 14 May 2011

We demonstrate the power of high resolution, two dimensional laser induced fluorescence (2DLIF) spectroscopy for observing rovibronic transitions of polyatomic molecules. The technique involves scanning a tunable laser over absorption features in the electronic spectrum while monitoring a segment, in our case 100 cm^{−1} wide, of the dispersed fluorescencespectrum. 2DLIF images separate features that overlap in the usual laser induced fluorescencespectrum. The technique is illustrated by application to the S_{1}–S_{0} transition in fluorobenzene. Images of room temperature samples show that overlap of rotational contours by sequence band structure is minimized with 2DLIF allowing a much larger range of rotational transitions to be observed and high precision rotational constants to be extracted. A significant advantage of 2DLIF imaging is that the rotational contours separate into their constituent branches and these can be targeted to determine the three rotational constants individually. The rotational constants determined are an order of magnitude more precise than those extracted from the analysis of the rotational contour and we find the previously determined values to be in error by as much as 5% [G. H. Kirby, Mol. Phys.19, 289 (1970)10.1080/00268977000101291]. Comparison with earlier ab initio calculations of the S_{0} and S_{1} geometries [I. Pugliesi, N. M. Tonge, and M. C. R. Cockett, J. Chem. Phys.129, 104303 (2008)10.1063/1.2970092] reveals that the CCSD/6–311G** and RICC2/def2TZVPP levels of theory predict the rotational constants, and hence geometries, with comparable accuracy. Two ground state Fermi resonances were identified by the distinctive patterns that such resonances produce in the images. 2DLIF imaging is demonstrated to be a sensitive method capable of detecting weak spectral features, particularly those that are otherwise hidden beneath stronger bands. The sensitivity is demonstrated by observation of the three isotopomers of fluorobenzened_{1} in natural abundance in an image taken for a supersonically cooled sample. The ability to separate some of the ^{13}C isotopomers in natural abundance is also demonstrated. The equipment required to perform 2DLIF imaging with sufficient resolution to resolve the rotational features of large polyatomics is available from commercial suppliers.
 ARTICLES

 Theoretical Methods and Algorithms

Scaled oppositespin CC2 for ground and excited states with fourth order scaling computational costs
View Description Hide DescriptionAn implementation of scaled oppositespin CC2 (SOSCC2) for ground and excited stateenergies is presented that requires only fourth order scaling computational costs. The SOSCC2 method yields results with an accuracy comparable to the unscaled method. Furthermore the timedetermining fifth order scaling steps in the algorithm can be replaced by only fourth order scaling computational costs using a “resolution of the identity” approximation for the electron repulsion integrals and a Laplace transformation of the orbital energy denominators. This leads to a significant reduction of computational costs especially for large systems. Timings for ground and excited state calculations are shown and the error of the Laplace transformation is investigated. An application to a chlorophyll molecule with 134 atoms results in a speedup by a factor of five and demonstrates how the new implementation extends the applicability of the method. A SOS variant of the algebraic diagrammatic construction through second order ADC(2), which arises from a simplification of the SOSCC2 model, is also presented. The SOSADC(2) model is a costefficient alternative in particular for future extensions to spectral intensities and excited state structure optimizations.

Efficient firstprinciples electronic dynamics
View Description Hide DescriptionAn efficient firstprinciples electronic dynamics method is introduced in this article. The approach we put forth relies on incrementally constructing a timedependent Fock/KohnSham matrix using active space density screening method that reduces the cost of computing twoelectron repulsion integrals. An adaptive stepsize control algorithm is developed to optimize the efficiency of the electronic dynamics while maintaining good energy conservation. A selected set of model dipolar pushpull chromophore molecules are tested and compared with the conventional method of direct formation of the Fock/KohnSham matrix. While both methods considered herein take on identical dynamical simulation pathways for the molecules tested, the active space density screening algorithm becomes much more computationally efficient. The adaptive stepsize control algorithm, when used in conjunction with the dynamically active space method, yields a factor of ∼3 speedup in computational cost as observed in electronic dynamics using the time dependent density functional theory. The total computational cost scales nearly linear with increasing size of the molecular system.

Osmotic ensemble methods for predicting adsorptioninduced structural transitions in nanoporous materials using molecular simulations
View Description Hide DescriptionOsmotic framework adsorbed solution theory is a useful molecular simulation method to predict the evolution of structural transitions upon adsorption of guest molecules in flexible nanoporoussolids. One challenge with previous uses of this approach has been the estimation of free energy differences between the solid phases of interest in the absence of adsorbed molecules. Here we demonstrate that these free energy differences can be calculated without reference to experimental data via the vibrational density of states of each phase, a quantity that can be obtained from molecular dynamics simulations. We show the applicability of this method through case studies of the swelling behaviors of two representative systems in which swelling upon adsorption of water is of importance: singlewalled aluminosilicate nanotube bundles and cesium montmorillonite. The resulting predictions show that the aluminosilicate nanotube bundles swell significantly with increasing interstitial adsorption and that the layer spacing of cesium montmorillonite expands up to about 12.5 Å, giving good agreement with experiments. The method is applicable to a wide range of flexible nanoporous materials, such as zeolites, metalorganic frameworks, and layered oxide materials, when candidate structures can be defined and a force field to describe the material is available.

Explicitly correlated multireference configuration interaction with multiple reference functions: Avoided crossings and conical intersections
View Description Hide DescriptionWe develop an explicitly correlated multireference configuration interaction method (MRCIF12) with multiple reference functions. It can be routinely applied to nearly degenerate molecular electronic structures near conical intersections and avoided crossings, where the reference functions are strongly mixed in the correlated wave function. This work is a generalization of the MRCIF12 method for electronic ground states, reported earlier by Shiozaki et al. [J. Chem. Phys.134, 034113 (2011)]10.1063/1.3528720. The socalled F12b approximation is used to arrive at computationally efficient formulas. The doubly external part of the wave function is expanded in terms of internally contracted configurations generated from all the reference functions. In addition, we introduce a singles correction to the CASSCF reference energies, which is applicable to multistate calculations. As examples, we present numerical results for the avoided crossing of LiF, excited states of ozone, and the H_{2} + OH (A ^{2}Σ^{+}) reaction.

Comparing modern density functionals for conjugated polymer band structures: Screened hybrid, Minnesota, and Rung 3.5 approximations
View Description Hide DescriptionSemiconducting polymers with πconjugated backbones show promise in fields such as photovoltaics. Practical applications of conjugated polymers require precise control over the polymer's electronic band structure. Several new classes of density functional approximation, including screened hybrids, semilocal Minnesota functionals, and Rung 3.5 functionals, show potential for improved predictions of conjugated polymerband structures. This work compares these methods to standard global hybrid density functionals for bandgaps and band structures of representative conjugated polymers. The new methods exhibit particular promise for modeling threedimensionally periodic bulk polymers, which can be problematic for global hybrids.

Stress and heat flux for arbitrary multibody potentials: A unified framework
View Description Hide DescriptionA twostep unified framework for the evaluation of continuum field expressions from molecular simulations for arbitrary interatomic potentials is presented. First, pointwise continuum fields are obtained using a generalization of the Irving–Kirkwood procedure to arbitrary multibody potentials. Two ambiguities associated with the original Irving–Kirkwood procedure (which was limited to pair potential interactions) are addressed in its generalization. The first ambiguity is due to the nonuniqueness of the decomposition of the force on an atom as a sum of central forces, which is a result of the nonuniqueness of the potential energy representation in terms of distances between the particles. This is in turn related to the shape space of the system. The second ambiguity is due to the nonuniqueness of the energy decomposition between particles. The latter can be completely avoided through an alternate derivation for the energy balance. It is found that the expressions for the specific internal energy and the heat flux obtained through the alternate derivation are quite different from the original Irving–Kirkwood procedure and appear to be more physically reasonable. Next, in the second step of the unified framework, spatial averaging is applied to the pointwise field to obtain the corresponding macroscopic quantities. These lead to expressions suitable for computation in molecular dynamics simulations. It is shown that the important commonlyused microscopic definitions for the stress tensor and heat flux vector are recovered in this process as special cases (generalized to arbitrary multibody potentials). Several numerical experiments are conducted to compare the new expression for the specific internal energy with the original one.

Adaptive integration grids in instanton theory improve the numerical accuracy at low temperature
View Description Hide DescriptionThe instanton method allows to accurately calculate tunneling rates down to very low temperature. However, with lowering the temperature, the computational effort steeply increases as many more discretization points are required. This is caused in practical applications by the majority of the discretization points accumulating at a very small region in configuration space. Here, we describe a method to flexibly discretize the instanton path adapted to the temperature. Chosen appropriately, the discretization leads to a much more uniform distribution of the images (control points) along the path which reduces the number of required images by about a factor of two. Combined with a modified Newton–Raphson optimizer and successive updates of the Hessians, the proposed method provides converged reaction rates at computational costs reduced by more than an order of magnitude. We show the success of the method on analytic test potentials and on molecules with energies directly obtained from density functional theory calculations.

External coupledcluster perturbation theory: Description and application to weakly interaction dimers. Corrections to the random phase approximation
View Description Hide DescriptionThe formalism for developing perturbation theory by using an arbitrary fixed (external) set of amplitudes as an initial approximation is presented in a compact form: external coupledclusterperturbation theory (xCCPT). Nonperturbative approaches also fit into the formalism. As an illustration, the weakly interacting dimers Ne^{2} and Ar^{2} have been studied in the various ringcoupledcluster doubles (CCD) approximations; ring, directring, antisymmetrized ring, and antisymmetrized direct ring, and a secondorder correction in the xCCPT approach is added. The direct approaches include the summation of just Coulomb terms with the intention of selectively summing the largest terms in the perturbation first. “Coulomb attenuation” is effected by taking the random phase approximation to define such amplitudes, whose results are then improved upon using perturbation theory.Interaction energies at the ringCCD level are poor but the xCCPT correction employed predicts binding energies which are only a few percent from the coupledcluster single double (triple) values for the direct ringCCD variants. Using the MP2 amplitudes which neglect exchange, the initial Coulombonly term, leads to very accurate Ne^{2} and Ar^{2} potentials. However, to accurately compute the Na^{2} potential required a different initial wavefunction, and hence perturbation. The potential energy surfaces of Ne^{2} and Ar^{2} are much too shallow using linear coupledcluster doubles. Using xCCPT(2) with these amplitudes as the initial wavefunction led to slightly worse results. These observations suggest that an optimal external set of amplitudes exists which minimizes perturbational effects and hence improve the predictability of methods.

The central cell model: A mesoscopic hopping model for the study of the displacement autocorrelation function
View Description Hide DescriptionOn the mesoscale, the molecular motion in a microporous material can be represented as a sequence of hops between different pore locations and from one pore to the other. On the same scale, the memory effects in the motion of a tagged particle are embedded in the displacement autocorrelation function (DACF), the discrete counterpart of the velocity autocorrelation function (VACF). In this paper, a mesoscopic hopping model, based on a latticegas automata dynamics, is presented for the coarsegrained modeling of the DACF in a microporous material under conditions of thermodynamic equilibrium. In our model, that we will refer to as central cellmodel, the motion of one tagged particle is mimicked through probabilistic hops from one location to the other in a small lattice of cells where all the other particles are indistinguishable; the cells closest to the one containing the tagged particle are simulated explicitly in the canonical ensemble, whereas the border cells are treated as meanfieldcells in the grandcanonical ensemble. In the present paper, numerical simulation of the central cellmodel are shown to provide the same results as a traditional latticegas simulation. Along with this a meanfieldtheory of selfdiffusion which incorporates time correlations is discussed.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Two dimensional laser induced fluorescence spectroscopy: A powerful technique for elucidating rovibronic structure in electronic transitions of polyatomic molecules
View Description Hide DescriptionWe demonstrate the power of high resolution, two dimensional laser induced fluorescence (2DLIF) spectroscopy for observing rovibronic transitions of polyatomic molecules. The technique involves scanning a tunable laser over absorption features in the electronic spectrum while monitoring a segment, in our case 100 cm^{−1} wide, of the dispersed fluorescencespectrum. 2DLIF images separate features that overlap in the usual laser induced fluorescencespectrum. The technique is illustrated by application to the S_{1}–S_{0} transition in fluorobenzene. Images of room temperature samples show that overlap of rotational contours by sequence band structure is minimized with 2DLIF allowing a much larger range of rotational transitions to be observed and high precision rotational constants to be extracted. A significant advantage of 2DLIF imaging is that the rotational contours separate into their constituent branches and these can be targeted to determine the three rotational constants individually. The rotational constants determined are an order of magnitude more precise than those extracted from the analysis of the rotational contour and we find the previously determined values to be in error by as much as 5% [G. H. Kirby, Mol. Phys.19, 289 (1970)10.1080/00268977000101291]. Comparison with earlier ab initio calculations of the S_{0} and S_{1} geometries [I. Pugliesi, N. M. Tonge, and M. C. R. Cockett, J. Chem. Phys.129, 104303 (2008)10.1063/1.2970092] reveals that the CCSD/6–311G** and RICC2/def2TZVPP levels of theory predict the rotational constants, and hence geometries, with comparable accuracy. Two ground state Fermi resonances were identified by the distinctive patterns that such resonances produce in the images. 2DLIF imaging is demonstrated to be a sensitive method capable of detecting weak spectral features, particularly those that are otherwise hidden beneath stronger bands. The sensitivity is demonstrated by observation of the three isotopomers of fluorobenzened_{1} in natural abundance in an image taken for a supersonically cooled sample. The ability to separate some of the ^{13}C isotopomers in natural abundance is also demonstrated. The equipment required to perform 2DLIF imaging with sufficient resolution to resolve the rotational features of large polyatomics is available from commercial suppliers.

The lowest singlet states of octatetraene revisited
View Description Hide DescriptionThe two lowest excited singlet states of alltrans1,3,5,7octatetraene, 2 ^{1}A^{−} _{ g } and 1 ^{1}B^{+} _{ u }, are studied by means of high level ab initio methods computing the vertical and adiabatic excitation energies for both states and the vertical emission energy for the ←2 ^{1}A^{−} _{ g } transition. The results confirm the known assignment of two energies, the 2 ^{1}A^{−} _{ g } adiabatic excitation energy and the 2 ^{1}A^{−} _{ g } vertical emission energy, for which well defined experimental values are available, with an excellent agreement between theory and experiment. In the experimental absorptionspectrum, the maximum of the band describing the 1 ^{1}B^{+} _{ u }← excitation is the first peak and it has been assigned to the (00) vibrational transition, but in literature it is normally compared with the theoretical vertical excitation energy. This comparison has been questioned in the past, but a conclusive demonstration of its lack of foundation has not been given. The analysis reported here, while confirming the assignment of the highest peak in the experimental spectrum to the (00) adiabatic transition, indicates that it cannot be used as a reference for the vertical excitation energy. The theoretical vertical excitation energies for the 2 ^{1}A^{−} _{ g } and 1 ^{1}B^{+} _{ u } states are found to be almost degenerate, with a value, ≃ 4.8 eV, higher than that normally accepted in the literature, 4.4 eV. The motivations which have induced in the past other authors to consider this a correct value are discussed and the origin of their feebleness are analyzed.

Statetostate quantum dynamics of the H + HBr reaction: Competition between the abstraction and exchange reactions
View Description Hide DescriptionQuantum statetostate dynamics for the H + HBr(υ_{ i } = 0,j _{ i } =0) reaction was studied on an accurate ab intio potential energy surface for the electronic ground state of BrH_{2}. Both the H + HBr → H_{2} + Br abstraction reaction and the H^{′} + HBr → H^{′}Br + H exchange reaction were investigated up to a collision energy of 2.0 eV. It was found that the abstraction channel is dominant at lower collision energies, while the exchange channel becomes dominant at higher collision energies. The total integral cross section of the abstraction reaction at a collision energy of 1.6 eV was found to be 1.37 Å^{2}, which is larger than a recent quantum mechanical result (1.06 Å^{2}) and still significantly smaller than the experimental value (3 ± 1 Å^{2}). Meanwhile, similar to the previous theoretical study, our calculations also predicted much hotter product rotational state distributions than those from the experimental study. This suggests that further experimental investigations are highly desirable to elucidate the dynamic properties of the title reactions.

The Pt_{2} (1,0) band of System VI in the near infrared by intracavity laser absorption spectroscopy
View Description Hide DescriptionIntracavity laser absorption spectroscopy has been used to record rotationally resolved electronic spectra of Pt_{2} in the near infrared. The metal dimers were created using a 50 mmlong, platinumlined hollow cathode plasma discharge. The observed transition at 12 937 cm^{−1} is identified as the (1,0) band of System VI, with state symmetries Ω = 0 – X Ω = 0.

O1s photoionization dynamics in oriented NO_{2}
View Description Hide DescriptionWe have performed extensive density functional theory(DFT) calculations, partial cross sections, dipole prepared continuum orbitals, dipole amplitudes and phase shifts, asymmetry parameters β, and molecular frame photoelectron angular distributions, to elucidate the O1s photoionizationdynamics of NO_{2} molecule with emphasis on the shape resonances in the O1s ionization continuum. In the shape resonance region, the β parameters and photoelectron angular distributions have been compared with our experimental results. Fairly good agreement between the theory and experiment has confirmed that the DFT level calculations can well describe the photoionizationdynamics of the simple molecule such as NO_{2}. Interference due to equivalent atom photoionization is theoretically considered, and the possibility of detection of the effect in the two degenerate channels with different combinations of light polarization and photoemission direction is discussed.

Photoelectron spectra of dihalomethyl anions: Testing the limits of normal mode analysis
View Description Hide DescriptionWe report the 364nm negative ion photoelectron spectra of CHX_{2} ^{−} and CDX_{2} ^{−}, where X = Cl, Br, and I. The pyramidal dihalomethyl anions undergo a large geometry change upon electron photodetachment to become nearly planar, resulting in multiple extended vibrational progressions in the photoelectron spectra. The normal modeanalysis that successfully models photoelectron spectra when geometry changes are modest is unable to reproduce qualitatively the experimental data using physically reasonable parameters. Specifically, the harmonic normal modeanalysis using Cartesian displacement coordinates results in much more CH stretch excitation than is observed, leading to a simulated photoelectron spectrum that is much broader than that which is seen experimentally. A (2 + 1)dimensional anharmonic coupledmode analysis much better reproduces the observed vibrational structure. We obtain an estimate of the adiabatic electron affinity of each dihalomethyl radical studied. The electron affinity of CHCl_{2} and CDCl_{2} is 1.3(2) eV, of CHBr_{2} and CDBr_{2} is 1.9(2) eV, and of CHI_{2} and CDI_{2} is 1.9(2) eV. Analysis of the experimental spectra illustrates the limits of the conventional normal mode approach and shows the type of analysis required for substantial geometry changes when multiple modes are active upon photodetachment.

Timeresolved photoelectron spectroscopy of coupled electronnuclear motion
View Description Hide DescriptionWe investigate pumpprobe electron detachment spectroscopy in a model system which is ideally suited to study coupled electronic and nuclear wavepacket dynamics. Timeresolvedphotoelectron spectra are calculated within the adiabatic approximation and a discretization of the detachment continuum. These spectra are compared to those which derive from a nonBornOppenheimer description and a numerically exact treatment of the detachment process. In this way it is possible to identify the influence of nonadiabatic effects on the spectra in a systematic way and also to test commonly applied approximations.

Experimental characterization of the weakly anisotropic CN X ^{2}Σ^{+} + Ne potential from IRUV double resonance studies of the CNNe complex
View Description Hide DescriptionIRUV double resonance spectroscopy has been used to characterize hindered internal rotor states (n ^{ K } = 0^{0}, 1^{1}, and 1^{0}) of the CNNe complex in its ground electronic state with various degrees of CN stretch (ν_{CN}) excitation. Rotationally resolved infrared overtone spectra of the CNNe complex exhibit perturbations arising from Coriolis coupling between the closely spaced hindered rotor states (1^{1} and 1^{0}) with two quanta of CN stretch (ν_{CN} = 2). A deperturbation analysis is used to obtain accurate rotational constants and associated average CN centerofmass to Ne separation distances as well as the coupling strength. The energetic ordering and spacings of the hindered internal rotor states provide a direct reflection of the weakly anisotropic intermolecular potential between CN X ^{2}Σ^{+} and Ne, with only an 8 cm^{−1} barrier to CN internal rotation, from which radially averaged anisotropy parameters (V _{10} and V _{20}) are extracted that are consistent for ν_{CN} = 03. Complementary ab initio calculation of the CN X ^{2}Σ^{+} + Ne potential using MRCI+Q extrapolated to the complete oneelectron basis set limit is compared with the experimentally derived anisotropy by optimizing the radial potential at each angle. Experiment and theory are in excellent accord, both indicating a bent minimum energy configuration and nearly free rotor behavior. Analogous experimental and theoretical studies of the CNNe complex upon electronic excitation to the CN B ^{2}Σ^{+} state indicate a slightly more anisotropic potential with a linear CNNe minimum energy configuration. The results from these IRUV double resonance studies are compared with prior electronic spectroscopy and theoretical studies of the CNNe system.

Distinguishing between relaxation pathways by combining dissociative ionization pump probe spectroscopy and ab initio calculations: A case study of cytosine
View Description Hide DescriptionWe present a general method for tracking molecular relaxation along different pathways from an excited state down to the ground state. We follow the excited state dynamics of cytosine pumped near the S_{0}–S_{1} resonance using ultrafast laser pulses in the deep ultraviolet and probed with strong field near infrared pulses which ionize and dissociate the molecules. The fragment ions are detected via time of flight mass spectroscopy as a function of pump probe delay and probe pulse intensity. Our measurements reveal that different molecular fragments show different timescales, indicating that there are multiple relaxation pathways down to the ground state. We interpret our measurements with the help of ab initio electronic structure calculations of both the neutral molecule and the molecular cation for different conformations en route to relaxation back down to the ground state. Our measurements and calculations show passage through two seams of conical intersections between ground and excited states and demonstrate the ability of dissociativeionization pump probe measurements in conjunction with ab initio electronic structure calculations to track molecular relaxation through multiple pathways.

Multiple isomers in the photoelectron spectra of small mononiobium carbide clusters
View Description Hide DescriptionWe calculate the photoelectron spectrum of small mononiobium carbide clusters (NbC_{n}) using density functional theory for clusters with n = 2–7 and the symmetry adapted cluster configuration interaction method for the smallest clusters (n = 2–4). Theoreticalspectra of a single structure cannot explain all peaks present in the spectrum measured by Zhai et al. [J. Chem. Phys.115, 5170 (2001)]. However, we can match all peaks in the experimental spectra if we assume that the beam contains a combination of cyclic and linear structures. This finding is even more surprising given the fact that some of the excited metastable geometries have energies as large as 0.5 eV above the ground state. Our result is confirmed by both theoretical approaches. We suggest further experiments, using additional beam cooling, to corroborate this observation.

Solventmediated charge redistribution in photodissociation of IBr^{−} and IBr^{−}(CO_{2})
View Description Hide DescriptionA combined experimental and theoretical investigation of photodissociationdynamics of IBr^{−} and IBr^{−}(CO_{2}) on the B () excited electronic state is presented. Timeresolved photoelectron spectroscopy reveals that in bare IBr^{−} prompt dissociation forms exclusively I* + Br^{−}. Compared to earlier dissociation studies of IBr^{−} excited to the A′ (^{2}Π_{1/2}) state, the signal rise is delayed by 200 ± 20 fs. In the case of IBr^{−}(CO_{2}), the product distribution shows the existence of a second major (∼40%) dissociation pathway, Br* + I^{−}. In contrast to the primary product channel, the signal rise associated with this pathway shows only a 50 ± 20 fs delay. The altered product branching ratio indicates that the presence of one solventlike CO_{2} molecule dramatically affects the electronic structure of the dissociating IBr^{−}. We explore the origins of this phenomenon with classical trajectories, quantum wave packet studies, and MRSOCISD calculations of the six lowestenergy electronic states of IBr^{−} and 36 lowestenergy states of IBr. We find that the CO_{2} molecule provides sufficient solvation energy to bring the initially excited state close in energy to a lowerlying state. The splitting between these states and the time at which the crossing takes place depend on the location of the solvating CO_{2} molecule.