Volume 136, Issue 15, 21 April 2012

A semiempirical counterpoisetype correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pairwise potential corrects for the inter and intramolecular BSSE in supermolecular HartreeFock (HF) or density functional theory(DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wavefunction is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of noncovalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, splitvalence, 631G*), but reliable results are also obtained for larger tripleζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%–30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanineglycinephenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and doubleζ basis sets combined with gCP and the dispersion corrections DFTD3 and DFTNL are successfully benchmarked on the S22 and S66 sets of noncovalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3refit) is obtained at the gCPcorrected HFD3/(minimal basis) level for the S66 benchmark. The gCPcorrected B3LYPD3/631G* model chemistry yields MAD=0.68 kcal/mol, which represents a huge improvement over plain B3LYP/631G* (MAD=2.3 kcal/mol). Application of gCPcorrected B97D3 and HFD3 on a set of large proteinligand complexes prove the robustness of the method. Analytical gCP gradients make optimizations of large systems feasible with small basis sets, as demonstrated for the interring distances of 9helicene and most of the complexes in Hobza's S22 test set. The method is implemented in a freely available FORTRAN program obtainable from the author's website.
 ARTICLES

 Theoretical Methods and Algorithms

A geometrical correction for the inter and intramolecular basis set superposition error in HartreeFock and density functional theory calculations for large systems
View Description Hide DescriptionA semiempirical counterpoisetype correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pairwise potential corrects for the inter and intramolecular BSSE in supermolecular HartreeFock (HF) or density functional theory(DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wavefunction is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of noncovalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, splitvalence, 631G*), but reliable results are also obtained for larger tripleζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%–30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanineglycinephenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and doubleζ basis sets combined with gCP and the dispersion corrections DFTD3 and DFTNL are successfully benchmarked on the S22 and S66 sets of noncovalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3refit) is obtained at the gCPcorrected HFD3/(minimal basis) level for the S66 benchmark. The gCPcorrected B3LYPD3/631G* model chemistry yields MAD=0.68 kcal/mol, which represents a huge improvement over plain B3LYP/631G* (MAD=2.3 kcal/mol). Application of gCPcorrected B97D3 and HFD3 on a set of large proteinligand complexes prove the robustness of the method. Analytical gCP gradients make optimizations of large systems feasible with small basis sets, as demonstrated for the interring distances of 9helicene and most of the complexes in Hobza's S22 test set. The method is implemented in a freely available FORTRAN program obtainable from the author's website.

Adaptive GreenKubo estimates of transport coefficients from molecular dynamics based on robust error analysis
View Description Hide DescriptionWe present a rigorous GreenKubo methodology for calculating transport coefficients based on onthefly estimates of: (a) statistical stationarity of the relevant process, and (b) error in the resulting coefficient. The methodology uses time samples efficiently across an ensemble of parallel replicas to yield accurate estimates, which is particularly useful for estimating the thermal conductivity of semiconductors near their Debye temperatures where the characteristic decay times of the heat flux correlation functions are large. Employing and extending the error analysis of Zwanzig and Ailawadi [Phys. Rev.182, 280 (1969)]10.1103/PhysRev.182.280 and Frenkel [in Proceedings of the International School of Physics “Enrico Fermi”, Course LXXV (NorthHolland Publishing Company, Amsterdam, 1980)] to the integral of correlation, we are able to provide tight theoretical bounds for the error in the estimate of the transport coefficient. To demonstrate the performance of the method, four test cases of increasing computational cost and complexity are presented: the viscosity of Ar and water, and the thermal conductivity of Si and GaN. In addition to producing accurate estimates of the transport coefficients for these materials, this work demonstrates precise agreement of the computed variances in the estimates of the correlation and the transport coefficient with the extended theory based on the assumption that fluctuations follow a Gaussian process. The proposed algorithm in conjunction with the extended theory enables the calculation of transport coefficients with the GreenKubo method accurately and efficiently.

A perturbation density functional theory for the competition between inter and intramolecular association
View Description Hide DescriptionUsing the framework of Wertheim's thermodynamic perturbation theory we develop the first density functional theory which accounts for intramolecular association in chain molecules. To test the theory new Monte Carlo simulations are performed at a fluid solid interface for a 4 segment chain which can both intra and intermolecularly associate. The theory and simulation results are found to be in excellent agreement. It is shown that the inclusion of intramolecular association can have profound effects on interfacial properties such as interfacial tension and the partition coefficient.

Density functional theory with fractional orbital occupations
View Description Hide DescriptionIn contrast to the original KohnSham (KS) formalism, we propose a density functional theory(DFT) with fractional orbital occupations for the study of ground states of manyelectron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFTLDA is shown to improve upon KSLDA for multireference systems, such as dissociation of H_{2} and N_{2}, and twisted ethylene, while performing similar to KSLDA for singlereference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KSLDA), this DFTLDA is applied to the study of the singlettriplet energy gaps (ST gaps) of acenes, which are “challenging problems” for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and highlevel ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.

A study of the accuracy of momentclosure approximations for stochastic chemical kinetics
View Description Hide DescriptionMomentclosure approximations have in recent years become a popular means to estimate the mean concentrations and the variances and covariances of the concentration fluctuations of species involved in stochastic chemical reactions, such as those inside cells. The typical assumption behind these methods is that all cumulants of the probability distribution function solution of the chemical master equation which are higher than a certain order are negligibly small and hence can be set to zero. These approximations are ad hoc and hence the reliability of the predictions of these class of methods is presently unclear. In this article, we study the accuracy of the two moment approximation (2MA) (third and higher order cumulants are zero) and of the three moment approximation (3MA) (fourth and higher order cumulants are zero) for chemical systems which are monostable and composed of unimolecular and bimolecular reactions. We use the systemsize expansion, a systematic method of solving the chemical master equation for monostable reaction systems, to calculate in the limit of large reaction volumes, the first and secondorder corrections to the mean concentration prediction of the rate equations and the firstorder correction to the variance and covariance predictions of the linearnoise approximation. We also compute these corrections using the 2MA and the 3MA. Comparison of the latter results with those of the systemsize expansion shows that: (i) the 2MA accurately captures the firstorder correction to the rate equations but its firstorder correction to the linearnoise approximation exhibits the wrong dependence on the rate constants. (ii) the 3MA accurately captures the first and secondorder corrections to the rate equation predictions and the firstorder correction to the linearnoise approximation. Hence while both the 2MA and the 3MA are more accurate than the rate equations, only the 3MA is more accurate than the linearnoise approximation across all of parameter space. The analytical results are numerically validated for dimerization and enzymecatalyzed reactions.

Anisotropic behavior of organic molecules on prepatterned surfaces
View Description Hide DescriptionThe nucleation of organic molecules on surfaces, prepatterned with stripes, is investigated with emphasis on anisotropy effects. Representing the molecules as ellipsoids, the related particleparticle interaction is modeled by means of a generalized GayBerne potential for similar biaxial particles. The orientation behavior of these ellipsoidal molecules induced by the stripe pattern is studied for the first monolayer by performing kinetic Monte Carlo simulations. It is shown how the properties of the particle alignment depend on energy scales, temperature, and flux. Based on the fact the particles strictly arrange in rows, it is furthermore instructive to analyze the orientation behavior within the different rows. Finally, the transfer of orientation from a preset row of molecules with fixed orientation to other nucleating particles is examined.

Quantization and fractional quantization of currents in periodically driven stochastic systems. I. Average currents
View Description Hide DescriptionThis article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically timedependent transition rates that satisfy the detailed balance condition at any time. We show that under general conditions, the currents in the system on average become quantized or fractionally quantized for adiabatic driving at sufficiently low temperature. We develop the quantitative theory of this quantization and interpret it in terms of topological invariants. By implementing the celebrated Kirchhoff theorem we derive a general and explicit formula for the average generated current that plays a role of an efficient tool for treating the current quantization effects.

Quantization and fractional quantization of currents in periodically driven stochastic systems. II. Full counting statistics
View Description Hide DescriptionWe study Markovian stochastic motion on a graph with finite number of nodes and adiabatically periodically driven transition rates. We show that, under general conditions, the quantized currents that appear at low temperatures are a manifestation of topological invariants in the counting statistics of currents. This observation provides an approach for classification of topological properties of the counting statistics, as well as for extensions of the phenomenon of the robust quantization of currents at low temperatures to the properties of the counting statistics which persist to finite temperatures.

Longrange corrected hybrid metageneralizedgradient approximations with dispersion corrections
View Description Hide DescriptionWe propose a longrange corrected hybrid metageneralizedgradient approximation (GGA) functional, based on a global hybrid metaGGA functional, M05 [Y. Zhao, N. E. Schultz, and D. G. Truhlar, J. Chem. Phys.123, 161103 (2005)10.1063/1.2126975], and empirical atomatom dispersion corrections. Our resulting functional, ωM05D, is shown to be accurate for a very wide range of applications, such as thermochemistry, kinetics, noncovalent interactions, equilibrium geometries, frontier orbital energies, fundamental gaps, and excitation energies. In addition, we present three new databases, IP131 (131 ionization potentials), EA115 (115 electron affinities), and FG115 (115 fundamental gaps), consisting of experimental molecular geometries and accurate reference values, which will be useful in the assessment of the accuracy of density functional approximations.
 Advanced Experimental Techniques

Dualetalon frequencycomb cavity ringdown spectrometer
View Description Hide DescriptionWe have demonstrated a spectroscopic technique for simultaneously obtaining broad spectral bandwidth and high frequency resolution absorption measurements, with 5 μs temporal resolution, continuously for tens of microseconds in an apparatus with no active stabilization. The technique utilizes two passive airgap etalons to imprint two frequency comb patterns onto a single pulsed light source. The airgap etalons also serve as cavity ringdown cells increasing the sensitivity of the absorption spectroscopy by increasing the interrogation path length. Here, we demonstrate the operation of the spectrometer utilizing a ∼0.15 cm^{−1} bandwidth pulsed dye laser and two nearly identical 300 MHz freespectral range confocal airgap etalons each with a finesse of ∼1 × 10^{5}, to investigate the (1,1,3) overtone of water and the R(7) transition of the O _{2} (2,0) band with high spectral resolution.

Source of slow lithium atoms from Ne or H_{2} matrix isolation sublimation
View Description Hide DescriptionWe have studied, via laser absorption spectroscopy, the velocity distribution of ^{7}Li atoms released from cryogenic matrices of solid neon or molecular hydrogen. The Li atoms are implanted into the Ne or H_{2} matrices – grown onto a sapphire substrate – by laser ablation of a solid Li or LiH precursor. A heat pulse is then applied to the sapphire substrate sublimating the matrix together with the isolated atoms. With a NiCr filmresistor deposited directly onto the sapphire substrate we are able to transfer high instantaneous power to the matrix, thus reaching a fast sublimation regime. In this regime the Li atoms can get entrained in the released matrix gas, and we were also able to achieve matrix sublimation times down to 10 μs for both H_{2} or Ne matrix, enabling us to proceed with the trapping of the species of our interest such as atomic hydrogen, lithium, and molecules. The sublimation of the H_{2} matrix, with its large centerofmass velocity, provides evidence for a new regime of onedimensional thermalization. The laser ablated Li seems to penetrate the H_{2} matrix deeper than it does in Ne.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electronic, vibrational, and rotational structures in the S _{0} ^{1} A _{1} and S _{1} ^{1} A _{1} states of phenanthrene
View Description Hide DescriptionElectronic and vibrational structures in the S _{0} ^{1} A _{1} and S _{1} ^{1} A _{1} states of jetcooled phenanthreneh _{10} and phenanthrened _{10} were analyzed by highresolution spectroscopy using a tunable nanosecond pulsed laser. The normal vibrational energies and molecular structures were estimated by ab initio calculations with geometry optimization in order to carry out a normalmode analysis of observed vibronic bands. The rotational structure was analyzed by ultrahighresolution spectroscopy using a continuouswave singlemode laser. It has been demonstrated that the stable geometrical structure is markedly changed upon the S _{1} ← S _{0} electronic excitation. Nonradiative internal conversion in the S _{1} state is expected to be enhanced by this structural change. The observed fluorescence lifetime has been found to be much shorter than the calculated radiative lifetime, indicating that the fluorescence quantum yield is low. The lifetime of phenanthrened _{10} is longer than that of phenanthreneh _{10} (normal deuterium effect). This fact is in contrast with anthracene, which is a structural isomer of phenanthrene. The lifetime at the S _{1} zerovibrational level of anthracened _{10} is much shorter than that of anthraceneh _{10} (inverse deuterium effect). In phenanthrene, the lifetime becomes monotonically shorter as the vibrational energy increases for both isotopical molecules without marked vibrational dependence. The vibrational structure of the S _{0} state is considered to be homogeneous and quasicontinuous (statistical limit) in the S _{1}energy region.

Spectroscopy and dynamics of bariumdoped helium nanodroplets
View Description Hide DescriptionExcitation spectra up to the ionization threshold are reported for barium atoms located on the surface of helium nanodroplets. For states with low principal quantum number, the resonances are substantially broadened and shifted towards higher energy with respect to the gas phase. This has been attributed to the repulsive interaction of the excited atom with the helium at the FranckCondon region. In contrast, for states with high principal quantum number the resonances are narrower and shifted towards lower energies. Photoelectron and ZEKE spectroscopy reveal that the redshift results from a lowering of the ionization threshold due to polarization of the helium by the barium ionic core. As a result of the repulsive interaction with the helium, excited barium atoms desorb from the surface of the droplets. Only when excited to the 6s6p ^{1}P_{1} state, which reveals an attractive interaction with the helium, the atoms remain attached to the droplets.

Nearthreshold shape resonance in the photoionization of 2butyne
View Description Hide DescriptionPhotoelectron velocity map imaging is combined with one and twophotonionization to study the near threshold photoionization of the 2butyne molecule. In this region, the photoabsorption and photoionization cross sections display a very intense broad feature that is assigned to an ℓ = 4, π_{g} shape resonance. The effect of this shape resonance on the vibrational branching ratios and photoelectron angular distributions is explored. Theoretical calculations of the photoionization cross section and photoelectron angular distributions are in good agreement with the experiments. The results for 2butyne are compared with those of acetylene, propyne, and 1butyne, none of which show such significant enhancements near threshold, and the differences are rationalized in terms of the symmetries and orbital angular momenta of the highest occupied orbitals and the corresponding shape resonances. Expectations for larger alkynes and alkynyl radicals are also discussed. A preliminary measurement of the ionization energy of the 2butyne dimer is also presented.

A new method for investigating infrared spectra of protonated benzene (C_{6}H_{7} ^{+}) and cyclohexadienyl radical (cC_{6}H_{7}) using parahydrogen
View Description Hide DescriptionWe use protonated benzene (C_{6}H_{7} ^{+}) and cyclohexadienyl radical (cC_{6}H_{7}) to demonstrate a new method that has some advantages over other methods currently used. C_{6}H_{7} ^{+} and cC_{6}H_{7} were produced on electron bombardment of a mixture of benzene (C_{6}H_{6}) and parahydrogen during deposition onto a target at 3.2 K. Infrared (IR) absorption lines of C_{6}H_{7} ^{+} decreased in intensity when the matrix was irradiated at 365 nm or maintained in the dark for an extended period, whereas those of cC_{6}H_{7} increased in intensity. Observed vibrational wavenumbers, relative IR intensities, and deuterium isotopic shifts agree with those predicted theoretically. This method, providing a wide spectral coverage with narrow lines and accurate relative IR intensities, can be applied to larger protonated polyaromatic hydrocarbons and their neutral species which are difficult to study with other methods.

Vibrational Fano resonances in dipolebound anions
View Description Hide DescriptionThis paper explores Fano resonances due to nonadiabatic coupling of vibrational modes and the electron continuum in dipolebound anions. We adopt a simple oneelectron model consisting of a point dipole and an auxiliary potential to represent the electron interaction with the neutral core. Nuclear motion is added by assuming that harmonic vibrations modulate the dipole moment. When the model is parameterized to simulate key features of the water tetramer anion, the resultant photodetachment lineshape closely resembles that observed experimentally and analyzed as a Fano resonance with a parameter q close to −1. Other parameterizations are explored for the model and it is found that large changes in the auxiliary potential are required to change the sign of q. This is consistent with the experimental finding that q is negative for all water cluster sizes studied.

Photoelectron spectroscopy of the molecular anions, ZrO^{−}, HfO^{−}, HfHO^{−}, and HfO_{2}H^{−}
View Description Hide DescriptionNegative ion photoelectron spectra of ZrO^{−}, HfO^{−}, HfHO^{−}, and HfO_{2}H^{−} are reported. Even though zirconium and hafniumcontaining molecules typically exhibit similar chemistries, the negative ion photoelectron spectral profiles of ZrO^{−} and HfO^{−} are dramatically different from one another. By comparing these data with relevant theoretical and experimental studies, as well as by using insights drawn from atomic spectra, spinorbit interactions, and relativistic effects, the photodetachment transitions in the spectra of ZrO^{−} and HfO^{−} were assigned. As a result, the electron affinities of ZrO and HfO were determined to be 1.26 ± 0.05 eV and 0.60 ± 0.05 eV, respectively. The anion photoelectron spectra of HfHO^{−} and HfO_{2}H^{−} are similar to one another and their structural connectivities are likely to be H–Hf–O^{−} and O–Hf–OH^{−}, respectively. The electron affinities of HfHO and HfO_{2}H are 1.70 ± 0.05 eV and 1.73 ± 0.05 eV, respectively.

A systematic investigation of the ground state potential energy surface of
View Description Hide DescriptionBased on different ab initio electronic structure calculations (CIR12 and Gaussian Geminals) of the BornOppenheimer electronic energy E _{ BO } of from high to highest quality, we build up a potential energy surface which represents a highly reliable form of the topology of the whole potential region, locally and globally. We use the CIR12 method in order to get within reasonable CPUtime a relatively dense grid of energy points. We demonstrate that CIR12 is good enough to give an accurate surface, i.e., Gaussian Geminals are not absolutely necessary. For different types of potential energy surface fits, we performed variational calculations of all bound vibrational states, including resonances above the dissociation limit, for total angular momentum J = 0. We clarify the differences between different fits of the energy to various functional forms of the potential surface. Small rmsvalues (<1 cm^{−1}) of the fit do not provide precise information about the interpolatory behaviour of the fit functions.

Resonant Auger spectroscopy at the carbon and nitrogen Kedges of pyrimidine
View Description Hide DescriptionThe resonant Auger electron spectra obtained after photoexcitation below the C and N 1sionization thresholds in the pyrimidine molecule have been measured at several photonenergies. The results show the relevance of the localization of the inner hole and of the matching between the symmetries of the intermediate and final states in the decay spectra via participator transitions. The comparison with the Auger electron spectra suggests some assignment for the twoholeoneparticle states reached via spectator transitions. The analysis of the participator decay is supported by stateofthe art density functional theory calculations.

Structures of small bismuth cluster cations
View Description Hide DescriptionThe structures of bismuthcluster cations in the range between 4 and 14 atoms have been assigned by a combination of gas phase ion mobility and trapped ion electron diffraction measurements together with density functional theory calculations. We find that above 8 atoms the clusters adopt prolate structures with coordination numbers between 3 and 4 and highly directional bonds. These open structures are more like those seen for clusters of semiconductinginbulk elements (such as silicon) rather than resembling the compact structures typical for clusters of metallicinbulk elements. An accurate description of bismuthclusters at the level of density functional theory, in particular of fragmentation pathways and dissociation energetics, requires taking spinorbit coupling into account. For n = 11 we infer that low energy isomers can have fragmentation thresholds comparable to their structural interconversion barriers. This gives rise to experimental isomer distributions which are dependent on formation and annealing histories.