Volume 126, Issue 15, 21 April 2007
 COMMUNICATIONS


Interaction of an infrared surface plasmon with an excited molecular vibration
View Description Hide DescriptionThe interaction of an infrared surface plasmon and an excited molecular vibration was investigated by using a square array of subwavelength holes in a Nifilm which supports propagating, surfaceplasmonmediated, transmission resonances. The largest transmission resonance [the ] was tuned through the rocking vibration of the hexadecane molecule (at ) in a hexadecane film on the mesh by varying the thickness of the film. The interaction of the rocking vibration and surface plasmon is characterized spectroscopically by an increase in the intensity of the vibrational band by more than a factor of 2, variation of the vibrational line shape relative to the spectrum on a nonmetallic surface, and shifts in vibrational peak position by as much as . Relationships are developed between the transmission resonance position and the thickness and dielectric properties of the coating.
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 ARTICLES

 Theoretical Methods and Algorithms

Frequencydependent nonlinear optical properties with explicitly correlated coupledcluster response theory using the CCSD(R12) model
View Description Hide DescriptionResponse theory up to infinite order is combined with the explicitly correlated coupledcluster singles and doubles model including linear corrections, CCSD(R12). The additional terms introduced by the linear contributions, not present in the conventional CCSD calculation, are derived and discussed with respect to the extra costs required for their evaluation. An implementation is presented up to the cubic response function for oneelectron perturbations, i.e., up to frequencydependent second hyperpolarizabilities. As first applications the authors computed the electronic polarizabilities and second hyperpolarizabilities of BH, , and formaldehyde and show that the improvement in the oneelectron basis set convergence known from the R12 method for ground state energies is retained for higherorder optical properties. Frequencydependent results are presented for the second hyperpolarizability of .

Chemical origin of blue and redshifted hydrogen bonds: Intramolecular hyperconjugation and its coupling with intermolecular hyperconjugation
View Description Hide DescriptionUpon formation of a H bond, intramolecular hyperconjugation of the proton donor plays a key role in red and blueshift characters of H bonds and must be introduced in the concepts of hyperconjugation and rehybridization. Intermolecular hyperconjugation transfers electron density from Y to and causes elongation and stretch frequency redshift of the X–H bond; intramolecular hyperconjugation couples with intermolecular hyperconjugation and can adjust electron density in ; rehybridization causes contraction and stretch frequency blueshift of the X–H bond on complexation. The three factors—intra and intermolecular hyperconjugations and rehybridization determine commonly red or blueshift of the formed H bond. A proton donor that has strong intramolecular hyperconjugation often forms blueshifted H bonds.

Calculation of the electric hypershielding at the nuclei of molecules in a strong magnetic field
View Description Hide DescriptionThe thirdrank electric hypershielding at the nuclei of 14 small molecules has been evaluated at the HartreeFock level of accuracy, by a pointwise procedure for the geometrical derivatives of magnetic susceptibilities and by a straightforward use of its definition within the RayleighSchrödinger perturbation theory. The connection between these two quantities is provided by the HellmannFeynman theorem. The magnetically induced hypershielding at the nuclei accounts for distortion of molecular geometry caused by strong magnetic fields and for related changes of magnetic susceptibility. In homonuclear diatomics , , and , a field along the bond direction squeezes the electron cloud toward the center, determining shorter but stronger bond. It is shown that constraints for rotational and translational invariances and hypervirial theorems provide a natural criterion for HartreeFock quality of computed nuclear electric hypershielding.

Computation of correlation functions and wave function projections in the context of quantum trajectory dynamics
View Description Hide DescriptionThe de BroglieBohm formulation of the Schrödinger equation implies conservation of the wave functionprobability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate as it requires fitting or interpolation procedures. In this paper we present a method of computing wave packet correlation functions and wave function projections, which typically contain all the desired information about dynamics, without the full knowledge of the wave function by making quadratic expansions of the wave function phase and amplitude near each trajectory similar to expansions used in semiclassical methods. Computation of the quantities of interest in this procedure is linear with respect to the number of trajectories. The introduced approximations are consistent with approximate quantum potential dynamics method. The projection technique is applied to model chemical systems and to the exchange reaction in three dimensions.

Longrange corrected density functional calculations of chemical reactions: Redetermination of parameter
View Description Hide DescriptionChemical reaction calculations were carried out using the longrange correction (LC) scheme, which improves longrange exchange effects in density functional theory(DFT) [J. Chem. Phys.115, 3540 (2001); 120, 8425 (2004)]. A new determination of the LC scheme parameter was made by a root mean square fit of the percent error in calculated atomization energies. As a result, the parameter was optimized as 0.47, which is higher than the previous one . Using this new parameter , LCDFT was firstly applied to geometry optimizations of the G2 benchmark set molecules. Consequently, this new LCDFT gave more accurate bond lengths and bond angles than previous LCDFT and hybrid B3LYP results. Following this result, the authors calculated reaction barrier height energies of benchmark reaction sets, which have been underestimated in conventional DFT calculations. Calculated results showed that LCDFT provided much more accurate barrier height energies with errors less than half those of previous LCDFT and B3LYP studies. To test the general validity of the new LCDFT, the authors finally calculated reactionenthalpies. As a result, they found that the LC scheme using the new clearly improved the accuracy of calculated enthalpies. The authors therefore conclude that the insufficient inclusion of longrange exchange effects is responsible for the underestimation of reaction barriers in DFT calculations and that LCDFT using the new parameter is a powerful tool for theoretically investigating chemical reactions.

Relativistic twocomponent infinite order method for atomic core ionization potentials
View Description Hide DescriptionIn this paper the authors have applied the infiniteorder twocomponent method (IOTC) to compute the valence and inner shell ionization potentials for the Ne, Ar, Kr, and Xe elements. The obtained results show the very good performance of the recently defined relativistic IOTC method. They also confirm the importance of the relativistic effects in the determination of the inner shell ionization potentials.

Decay rates of innervalence excitations in noble gas atoms
View Description Hide DescriptionA Fano  algebraic diagrammatic construction  Stieltjes method has been recently developed for ab initio calculations of nonradiative decay rates [V. Averbukh and L. S. Cederbaum, J. Chem. Phys.123, 204107 (2005)] of singly ionized states. In the present work this method is generalized for the case of electronic decay of excited states. The decay widths of autoionizing innervalenceexcited states of Ne, Ar, and Kr are calculated. Apart from the lowest excitation of Kr, they are found to be in good to excellent agreement with the experimental values. Comparison with the other theoretical studies shows that in many cases the new method performs better than the previously available techniques.

Linearscaling implementation of molecular response theory in selfconsistent field electronicstructure theory
View Description Hide DescriptionA linearscaling implementation of HartreeFock and KohnSham selfconsistent field theories for the calculation of frequencydependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the oneelectron density matrix in the atomicorbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomicorbital subspace method equivalent to that of molecularorbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecularorbital theory, with five to ten iterations needed for convergence. As in traditional direct HartreeFock and KohnSham theories, the calculations are dominated by the construction of the effective Fock/KohnSham matrix, once in each iteration. Linear complexity is achieved by using sparsematrix algebra, as illustrated in calculations of excitation energies and frequencydependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Tests of functionals for systems with fractional electron number
View Description Hide DescriptionIn the exact theory, the ground state energy of an open system varies linearly when the electron number is changed between two adjacent integers. This linear dependence is not reproduced by common approximate density functionals. Deviation from linearity in this dependence has been suggested as a basis for the concept of manyelectron selfinteraction error (SIE). In this paper, we quantify manyelectron SIE of a number of approximations by performing calculations on fractionally charged atoms. We demonstrate the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge transfer. Semilocal approximations have the largest manyelectron SIE, which is only slightly reduced in typical global hybrids. In these approximations the energy versus fractional electron number curves upward, while in HartreeFock theory the energy curves downward. PerdewZunger selfinteraction correction [Phys. Rev. B23, 5048 (1981)] significantly reduces the manyelectron SIE of semilocal functionals but impairs their accuracy for equilibrium properties. In contrast, a longrange corrected hybrid functional can be nearly manyelectron SIEfree in many cases (for reasons we discuss) and at the same time performs remarkably well for many molecular properties.

Fully automated implementation of the incremental scheme: Application to CCSD energies for hydrocarbons and transition metal compounds
View Description Hide DescriptionA general fully automated implementation of the incremental scheme for molecules and embedded clusters in the framework of the coupled cluster singles and doubles theory is presented. The code can be applied to arbitrary order of the incremental expansion and is parallelized in a master/slave structure. The authors found that the error in the total correlation energy is lower than with respect to the canonical CCSD calculation if the incremental series is truncated in a proper way.

Gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach. II. Density functional and coupled cluster theory
View Description Hide DescriptionThe quantum mechanical current density induced in a molecule by an external magnetic field is invariant to translations of the coordinate system. This fundamental symmetry is exploited to formally annihilate the diamagnetic contribution to the current density via the approach of “continuous transformation of the origin of the current densitydiamagnetic zero” (CTOCDDZ). The relationships obtained by this method for the magnetic shielding at the nuclei are intrinsically independent of the origin of the coordinate system for any approximate computational scheme relying on the algebraic approximation. The authors report for the first time an extended series of originindependent estimates of nuclear magnetic shielding constants using the CTOCDDZ approach at the level of density functional theory(DFT) with four different types of functionals and unrelaxed coupled cluster singles and doubles linear response (CCSDLR) theory. The results obtained indicate that in the case of DFT the procedure employed is competitive with currently adopted computational methods allowing for basis sets of gaugeincluding atomic orbitals, whereas larger differences between CTOCDDZ and common origin CCSDLR results are observed due to the incomplete fulfillment of hypervirial relations in standard CCSDLR theory. It was found furthermore that the unrelaxed CCSDLR calculations predict larger correlation corrections for the shielding constants of almost all nonhydrogen atoms in their set of molecules than the usual relaxed energy derivative CCSD calculations. Finally the results confirm the excellent performance of Keal and Tozer’s third functional, in particular, for the multiply bonded systems with a lot of electron correlation, but find also that the simple local density functional gives even better results for the few singly bonded molecules in their study where correlation effects are small.

Density functional selfconsistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde
View Description Hide DescriptionA combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a selfconsistent scheme linear in the solventpolarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the densityfunctional theory(DFT) and the HartreeFock (HF) theory. Sample calculations presented for groundstate energies, firstorder groundstate properties, excitation energies, firstorder excited state properties, polarizabilities, firsthyperpolarizabilities, and twophoton absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to highlevel theory, such as coupledcluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for groundstate and firstorder properties. However, to obtain such accuracy an exchangecorrelation functional capable of describing the diffuse Rydberg states must be chosen.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photodissociation of in water clusters via RennerTeller and conical interactions
View Description Hide DescriptionThe photochemistry of mass selected , cluster anions is investigated using photofragment spectroscopy and theoretical calculations. Similar to the previous experiment [Habteyes et al., Chem. Phys. Lett.424, 268 (2006)], the fragmentation at yields two types of anionic products: (coredissociation products) and (solventevaporation products). Despite the same product types, different electronic transitions and dissociation mechanisms are implicated at 355 and . The dissociation is initiated by excitation to the first excited electronic state of the cluster core, the state, and proceeds via a glancing RennerTeller intersection with the ground electronic state at a linear geometry. The dissociation involves the second excited electronic state of , the state, which exhibits a conical intersection with the state at a bent geometry. The asymptotic based products are believed to be formed via this state. By analyzing the fragmentation results, the bond dissociation energy of to in hydrated clusters is estimated as , compared to for bare . The enthalpy of evaporation of one water molecule from asymptotically large clusters is determined to be . This result compares very favorably with the heat of evaporation of bulk water, .

Yield of excited CO molecules from dissociative recombination of and ions with electrons
View Description Hide DescriptionThe authors have investigated CO band emissions arising from the dissociative recombination of and ions with thermal electrons in a flowing afterglow plasma. The quantitative analysis of the band intensities showed that recombination forms the longlived state with a yield of , while recombination favors formation of and with a combined yield of greater than 0.4. The observed vibrational distribution for the state reproduces theoretical predictions quite well. The vibrational distributions for and are, in part, inverted, presumably as a consequence of a change in CO equilibrium bond length during recombination. The observations are compatible with current knowledge of the potential surfaces of states of HCO and .

Yield of electronically excited CN molecules from the dissociative recombination of with electrons
View Description Hide DescriptionThe authors have studied and emissions produced by the dissociative recombination of ions with thermal electrons in a flowing afterglow experiment. A separate drift tube study showed that the reaction, the precursor reaction used in the flowtube experiment, produces predominantly rather than the more energetic isomer. Models simulating the ionchemical processes, diffusion, and gas mixing in the afterglow plasma were fitted to observed position dependent and band intensities. Absolute yields of and were then obtained by comparing the CN band intensities to those of CO bands produced by recombination of ions. It was concluded that the recombination coefficient of is close to , that is formed with a yield of and with a yield of . By comparison to synthetic spectra, the rotational temperature of was estimated to be approximately . It was also found that recombination produces and with far greater vibrational excitation than would be expected from the “impulse model” of Bates [Mon. Not. R. Astron. Soc.263, 369 (1993)].

JahnTeller effect in and : Conformational isomerism, tunnelingrotation structure, and the location of conical intersections
View Description Hide DescriptionHighresolution pulsedfieldionization zerokineticenergy photoelectron spectra of and have been recorded at rotational resolution from the adiabatic ionization energy up to of internal energy of the respective cations. The spectra are characterized by the effects of a largeamplitude pseudorotational motion exchanging the equivalent nuclei in each molecule. With increasing internal energy, a transition from the tunneling regime with splittings of the order of to the free pseudorotation regime is observed. A theoretical model that treats the simultaneous rotational and pseudorotational motions and incorporates the effects of the geometric phase has been developed. The model provides the appropriate rovibronic symmetries in the molecular symmetry group and reaches a nearquantitative agreement with the experimental data. The complete grouptheoretical analysis of the rovibronic problem is also given. The analysis of the spectra has revealed the existence of two different isomers for both and , which differ in the bond length between the carbon atom and the unique ligand atom. All isomers are subject to a fast pseudorotational motion between three equivalent minima with a period of in and in . The analysis has also provided the ordering of the tunneling sublevels for each isomer, which enables the location of the twofold conical intersections on the potential energy surface that could not be determined from experiments on .

Ab initio study of the torsional potential energy surfaces of and : Origin of the torsional barriers
View Description Hide DescriptionIntrinsic reaction coordinate (IRC) torsional potentials were calculated for and based on optimized B3LYP/augccpVDZ geometries of the respective 90°twisted saddle points. These potentials were refined by obtaining energies [in the complete basis set (CBS) limit] of points along the IRC. A comparison is made between these ab initio potentials and an analytical form based on a twoterm cosine expansion in terms of the N–N dihedral angle. The shapes of these two potential curves are in close agreement. The torsional barriers in and obtained from the CCSD(T)/CBS//B3LYP/augccpVDZ calculations are 2333 and , respectively. For the torsion fundamental frequency from the IRC potential is , which is in good agreement with the experimentally reported value of . However, in the case of the torsional frequency found from the IRC potential, , is considerably larger than the reported experimental values . Consistent with this discrepancy, the torsional barrier obtained from several different calculations, , is higher than the value of deduced from experimental studies. It is suggested that the assignment of the torsional mode in should be reexamined. and exhibit strong hyperconjugative interactions of inplane O lone pairs with the central N–N antibond. Hyperconjugative stabilization is somewhat stronger at the planar geometries because 1,4 interactions of lone pairs on cis O atoms promote delocalization of electrons into the N–N antibond. Calculations therefore suggest that the torsional barriers in these molecules arise principally from a combination of 1,4 interactions and hyperconjugation.

Closecoupling study of rotational energy transfer and differential scattering in collisions with He atoms
View Description Hide DescriptionQuantum closecoupling scattering calculations of rotational energy transfer (RET) of rotationally excited due to collisions with He are presented for collision energies between and with para initially in levels , , , and and ortho in levels , , and . Quenching cross sections and rate coefficients for statetostate RET were computed. Both elastic and inelastic differential cross sections are also calculated and compared with relative experimental results giving generally good agreement in all cases, but less so for inelastic results. Significant differences in the computed collisional parameters, obtained on three different potential energy surfaces (PESs), were found particularly in the ultracold regime. In the thermal regime, the rate coefficients calculated on each of the surfaces are generally in better agreement and comparable, but typically larger, than those obtained in a previous calculation. Unfortunately, a lack of absolute differential or integral inelastic experimental data prevents firm determination of a preferred PES.

Bright, guided molecular beam with hydrodynamic enhancement
View Description Hide DescriptionThe authors realize a novel high flux source of cold atoms and molecules employing hydrodynamic enhancement of an effusive aperture at cryogenic temperatures. Molecular oxygen from the source is coupled to a magnetic guide, delivering a cold, continuous, guided flux of . The dynamics of the source are studied by creating and spectroscopically analyzing high flux beams of atomic ytterbium.