Volume 129, Issue 24, 28 December 2008
 ARTICLES

 Theoretical Methods and Algorithms

Constructing diabatic states from adiabatic states: Extending generalized Mulliken–Hush to multiple charge centers with Boys localization
View Description Hide DescriptionThis article shows that, although Boys localization is usually applied to singleelectron orbitals, the Boys method itself can be applied to many electron molecular states. For the twostate chargetransfer problem, we show analytically that Boys localization yields the same chargelocalized diabatic states as those found by generalized Mulliken–Hush theory. We suggest that for future work in electron transfer, where systems have more than two charge centers, one may benefit by using a variant of Boys localization to construct diabatic potential energy surfaces and extract electronic coupling matrix elements. We discuss two chemical examples of Boys localization and propose a generalization of the Boys algorithm for creating diabatic states with localized spin density that should be useful for Dexter triplettriplet energy transfer.

Ab initio calculation of interatomic decay rates of excited doubly ionized states in clusters
View Description Hide DescriptionRecently, a computational technique for ab initio calculation of the interatomic and intermolecular nonradiative decay processes has been developed [V. Averbukh and L. S. Cederbaum, J. Chem. Phys.123, 204107 (2005)]. It combines the Fano formalism with the Green’s function method known as the algebraic diagrammatic construction. The problem of normalization of continuum wave functions stemming from the use of the Gaussian basis sets is solved by using the Stieltjes imaging technique. In the present paper, the methodology is extended in order to describe the interatomic decay of excited doubly ionized states of clusters. The new computational scheme is applied to compute the interatomic decay rates of doubly ionized states formed by Auger relaxation of core vacancies in NeAr and MgNe van der Waals clusters.

Structure and reactions of carbon and hydrogen on Ru(0001): A scanning tunneling microscopy study
View Description Hide DescriptionThe interaction between carbon and hydrogen atoms on a Ru(0001) surface was studied using scanning tunneling microscopy(STM),density functional theory(DFT) and STM image calculations. Formation of CH species by reaction between adsorbed H and C was observed to occur readily at 100 K. When the coverage of H increased new complexes of the form of (, 2, and 3) were observed. These complexes, never observed before, might be precursors for further hydrogenation reactions.DFT analysis reveals that a considerable energy barrier exists for the reaction.

Variational and perturbative formulations of quantum mechanical/molecular mechanical free energy with meanfield embedding and its analytical gradients
View Description Hide DescriptionConventional quantum chemical solvation theories are based on the meanfield embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum mechanical/molecular mechanical (QM/MM) analog of such a meanfieldtheory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent to the firstorder expansion of the QM energy (in the exact free energy expression) about the selfconsistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating nonmeanfield effects (i.e., statistical fluctuations of the QM wavefunction) that are neglected in the meanfield calculation. As an illustration, the method is applied to an Menshutkin reaction in water, , for which free energy profiles are obtained at the Hartree–Fock, MP2, B3LYP, and BHHLYP levels by integrating the free energy gradient. Nonmeanfield effects are evaluated to be using a Gaussian fluctuation model for the environment, which suggests that those effects are rather small for the present reaction in water.

Implementation and performance of a domainspecific basis set incremental approach for correlation energies: Applications to hydrocarbons and a glycine oligomer
View Description Hide DescriptionThe fully automated implementation of the incremental scheme for CCSD energies has been modified for the usage of a domainspecific basis set. We find that the computational effort can be reduced significantly without loss of accuracy. It is shown explicitly in applications on hydrocarbons and the oligomer that the error of the incremental expansion for the total energy is usually below 1 kcal/mol at third order. Furthermore, it is demonstrated that the proposed approach saves CPU time, random access memory, and disk space. Moreover, we show in various tests that the inherently parallel incremental calculations can be run on up to 50 CPUs without significant loss of computer time.

Quantum Monte Carlo formulation of volume polarization in dielectric continuum theory
View Description Hide DescriptionWe present a novel formulation based on quantum Monte Carlo techniques for the treatment of volume polarization due to quantum mechanical penetration of the solute charge density in the solvent domain. The method allows to accurately solve Poisson’s equation of the solvation model coupled with the Schrödinger equation for the solute. We demonstrate the performance of the approach on a representative set of solutes in water solvent and give a detailed analysis of the dependence of the volume polarization on the solute cavity and the treatment of electron correlation.

A note on the Pulay force at finite electronic temperatures
View Description Hide DescriptionPulay’s original expression for the basisset dependent adjustment term to the Hellmann–Feynman force in electronic structuretheory, which occurs for nonorthogonal local basisset representations, is based on the idempotency condition of a pure ensemble. At finite electronic temperatures with a fractional occupation of the states, the conventional expression of the Pulay force is therefore no longer valid. Here we derive a simple and computationally efficient expression for a generalized Pulay force, which is suitable for largescale ab initio simulations at finite electronic temperatures using local nonorthogonal basisset representations. The generalized Pulay force expression is given in terms of the temperaturedependent density matrix. For the construction of the density matrix, we propose a recursive Fermi operator expansion algorithm that automatically converges to the correct chemical potential.

Application of improved virtual orbital based multireference methods to , LiF, and systems
View Description Hide DescriptionThe improved virtual orbital (IVO) complete active space configuration interaction (CASCI) based multiconfigurational quasidegenerate perturbation theory (MCQDPT) and its singleroot version (termed as MRMPPT) are applied to assess the efficacy and the reliability of these two methods. Applications involve the ground and/or excited state potential energy curves (PECs) of , LiF, and (butadiene) molecules, systems that are sufficiently complex to assess the applicability of these methods. The ionicneutral curve crossing involving the lowest two states of LiF molecule is studied using the IVOMCQDPT method, while its singleroot version (IVOMRMPPT) is employed to study the ground state PEC for isomerization of butadiene and to model the bonddissociation of molecule. Comparisons with the standard methods (full CI, coupled cluster with singles and doubles, etc.) demonstrate that the IVObased MRMPPT and MCQDPT approaches provide smooth and reliable PECs for all the systems studied. The IVOCASCI method is explored to enable geometry optimization for ground state of using numerical energy gradients. The ground spectroscopic constants of and LiF determined using the numerical gradient based IVOCASCI method are in accord with experiment and with other correlated calculations. As an illustration, we may point out that the maximum deviation from the experiment in our estimated normal mode frequency of LiF is , whereas for the bond length, the maximum error is just .

Variational, representable, and variableoccupationnumber perturbation theories
View Description Hide DescriptionDensityfunctional perturbation theory with variationally fitted Kohn–Sham (KS) potentials is described. Requiring the Fock matrix and density matrix to commute through each order of perturbation theory determines the offdiagonal elements of the density matrix, and thus the effect of changing occupation numbers in densityfunctional perturbation theory. At each order of perturbation theory, the change in occupation numbers at that order enters only the diagonal part of the density matrix. The theory contains no phases, and a limiting process relates the rest of the diagonal density matrix element, obtained from wave functionperturbation theory, to the offdiagonal part, obtained by commutation. representable densityfunctional theory is most practical when the KS potential is expanded in a finite basis to create the Sambe–Felton (SF) potential of analytic densityfunctional theory. This reduces the dimensionality of perturbation theory from order in the orbital basis to order N in the SF basis. Computing the , i.e., , sum over states once at the end of a selfconsistentfield molecular orbital calculation removes the orbitals from all higher orders of perturbation theory. The rank iterative coupledperturbed equations are replaced by rankN matrix inversion, to fit variationally the perturbed SF potential at each order. As an example of the rule of perturbation theory, the variational, firstorder potential is used to give precise second and third derivatives of the energy with respect to occupation number. The hardness and hyperhardness are computed for a standard set of molecules. Both are essentially independent of how the variational SF potential is constrained for four different constraint combinations. With variational fitting, the precision of derivatives and the fidelity of the fit to the SF potential are not related. Analytic derivatives are accurate to machine precision for any constraint and all fitting basis sets.

Calculation of first and second static hyperpolarizabilities of one to threedimensional periodic compounds. Implementation in the CRYSTAL code.
View Description Hide DescriptionA computational scheme for the evaluation of the static first and second hyperpolarizability tensors of systems periodic in 1D (polymers), 2D (slabs), 3D (crystals), and, as a limiting case, 0D (molecules) has been implemented, within the coupled perturbed Hartree–Fock framework (CPHF), in the CRYSTAL code, which uses a Gaussian type basis set. This generalizes to 2D and 3D the work by Bishop et al. (J. Chem. Phys.114, 7633 (2001)). CPHF is applied for and (the polarizabilitytensor is also reported for completeness) of LiF in different aggregation states: finite and infinite chains, slabs, and cubic crystal. Correctness of the computational scheme and its numerical efficiency are documented by the trend of and for increasing dimensionality: for a finite linear chain containing LiF units, the hyperpolarizability tends to the infinite chain value at large , parallel chains give the slab value when is sufficiently large, and superimposed slabs tend to the bulk value. High numerical accuracy can be achieved at relatively low cost, with a dependence on the computational parameters similar to that observed for fieldfree selfconsistent field (SCF) calculations.

Spinfree intermediate Hamiltonian Fock space coupledcluster theory with full inclusion of triple excitations for restricted Hartree Fock based triplet states
View Description Hide DescriptionThe recently reported inclusion of the connected triples into the intermediate Hamiltonian realization of the Fock space coupledcluster (IHFSCC) theory [M. Musial and R. J. Bartlett, J. Chem. Phys.129, 044101 (2008)] is extended to produce the triplet states. This is done entirely in spatial orbitals on the basis of the double occupancy in the restricted Hartree Fock reference function. New equations for the triplet state amplitudes expressed in terms of the Goldstone diagrams are derived and implemented. Several applications show the usefulness of the IHFSCC scheme to describe the triplet states with the computational gains inherent to a spinfree implementation.

Enhanced identification and exploitation of time scales for model reduction in stochastic chemical kinetics
View Description Hide DescriptionWidely different time scales are common in systems of chemical reactions and can be exploited to obtain reduced models applicable to the time scales of interest. These reduced models enable more efficient computation and simplify analysis. A classic example is the irreversible enzymatic reaction, for which separation of time scales in a deterministic mass action kinetics model results in approximate rate laws for the slow dynamics, such as that of Michaelis–Menten. Recently, several methods have been developed for separation of slow and fast time scales in chemical master equation (CME) descriptions of stochastic chemical kinetics, yielding separate reduced CMEs for the slow variables and the fast variables. The paper begins by systematizing the preliminary step of identifying slow and fast variables in a chemical system from a specification of the slow and fast reactions in the system. The authors then present an enhanced timescaleseparation method that can extend the validity and improve the accuracy of existing methods by better accounting for slow reactions when equilibrating the fast subsystem. The resulting method is particularly accurate in systems such as enzymatic and protein interaction networks, where the rates of the slow reactions that modify the slow variables are not a function of the slow variables. The authors apply their methodology to the case of an irreversible enzymatic reaction and show that the resulting improvements in accuracy and validity are analogous to those obtained in the deterministic case by using the total quasisteadystate approximation rather than the classical Michaelis–Menten. The other main contribution of this paper is to show how mass fluctuation kinetics models, which give approximate evolution equations for the means, variances, and covariances of the concentrations in a chemical system, can feed into timescaleseparation methods at a variety of stages.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Contribution of the Gouy phase to twopathway coherent control of the photoionization and photodissociation of vinyl chloride
View Description Hide DescriptionThe electric field of a light wave accumulates a phase shift as it passes through a focus. We show here how this effect, known as the Gouy phase, may be used to control the branching ratio of a unimolecular reaction when the products are formed with different numbers of photons. We demonstrate this control method for the ionization and dissociation of vinyl chloride, using absorption of 177 and photons to induce a pair of interfering paths. Excellent agreement between the observed and calculated phase shift as a function of the axial coordinate of the laser focus indicates that fragmentation occurs via a ladder switching mechanism. The axial dependence of the modulation depth is evidence of loss of coherence at higher internal temperatures of the molecule.

Gasphase infrared multiple photon dissociation spectroscopy of isolated and anions
View Description Hide DescriptionResonantly enhanced multiple photondissociation of gasphase and is studied using tunable infrared light from the FELIX free electron laser. The photodissociationspectrum of the sulfur hexafluoride anion, producing , is recorded over the spectral range of . The infrared multiple photondissociation cross section exhibits a strong, broad resonance enhancement at in agreement with the calculated value of , one of the two IRactive fundamental vibrational modes predicted for the symmetry ion. Much weaker absorption features are observed in the spectral region of as well as at that are not easily assigned to the other IRactive fundamental of since these resonances are observed at a much higher energy than the calculated values for the IRactive mode. The potential role of binary combination bands is considered. Photodissociation from the sulfur pentafluoride anion produced only , but photodetachment was also observed through associative electron capture. The IR multiple photondissociationspectrum of shows multiple resonances within the region of and agreement with calculations is clear, including the observation of three fundamental frequencies: at , at , and at . Comparisons of the measured frequencies with ab initio and density functional theory calculations confirm an anion of symmetry. Similar comparisons for are not inconsistent with an anion of symmetry.

Interaction of with rare gas atoms: Potential energy surfaces and spectroscopy
View Description Hide DescriptionWe present the results of an ab initio study of the interaction of electronically excited with rare gas (Rg) atoms. The bound states of each species are determined from potential energy surfaces calculated at the RCCSD(T) level of theory. Making use of the vibrational wavefunctions, we then simulate electronic spectra. For NO–Kr and NO–Xe we obtain good qualitative agreement with the previously published experimental spectra. For NO–Ar, the shallowness of the surface gives rise to agreement that is less satisfactory, but a global scaling provides better qualitative agreement. The assignment of the spectra is far from straightforward and is only possible with guidance from the calculated energies and wavefunctions of the energy levels of the complex. Previous assignments are discussed in the light of this conclusion.

Binarycollisioninduced longitudinal relaxation in gasphase
View Description Hide DescriptionDensity dependent NMRrelaxation measurements of noble gases can provide complementary information to that obtained from relaxation studies of molecular gases. However, conventional noble gas NMR is typically hindered by low sensitivity or prohibitively long relaxation times. In this work, the low sensitivity of was overcome by spin exchange optical pumping, and the quadrupolar interaction dominated times of enabled rapid collection of relaxation data. The density dependence of the longitudinal relaxation in pure krypton was found to be about . Experiments were also performed in krypton mixtures containing either helium or nitrogen as a buffer gas. By varying the composition and the density of these mixtures, the density dependence of buffer gas induced relaxation and the relaxation efficiency of buffer gas collisions were determined. The results from these gas mixtures are compared with those from pure krypton.

Extended negative glow and “hollow anode” discharges for submillimeterwave observation of , , and
View Description Hide DescriptionThree molecular anions, , , and , have been detected in an extended negative glow discharge and a “hollow anode” discharge in the submillimeterwave region. These electrical discharges have been unexpectedly found to be reasonable anion sources. The measurements have been extended up to 830 GHz, and the molecular constants have been improved significantly compared with those determined by microwave and millimeterwave spectroscopy. The parent gas mixture of or of 2 mTorr and Ar or Ne buffer of 15 mTorr was used for the production of or and . The number densities of the anions in the cell were estimated to be , , and for , , and , respectively.

Pathways and reduceddimension fivedimensional potential energy surface for the reactions and
View Description Hide DescriptionTo obtain theoretical insight regarding the stability and formation dynamics of the interstellar ions and , stationary points and the associated vibrational frequencies on the full ninedimensional potential energy surface for the electronic ground state have been calculated using coupledcluster theory with both single and double substitutions (CCSD). The energetics were refined with a higherlevel coupledcluster method CCSD(T), with corevalence electron correlation treated at the complete basis set limit. To elucidate the formation mechanism and internal relaxation processes, the reaction paths for the reactions and were calculated at the secondorder Møller–Plesset (MP2) level, and corresponding singlepoint energies were obtained at the higher CCSD(T)/augccpVTZ level. Based on the analysis of the main reaction processes, a reduceddimension fivedimensional potential energy surface for this system was constructed from ab initio points calculated at the CCSD(T)/augccpVTZ level.

Renner–Teller coupledchannel dynamics of the reaction and the role of the electronic state
View Description Hide DescriptionWe present Renner–Teller (RT) and Born–Oppenheimer (BO) coupledchannel (CC) dynamics of the reaction, considering both coupled electronic states, and , and Coriolis interactions. We use the best available potential energy surfaces (PESs), and we obtain initialstateresolved reaction probabilities, cross sections, and rate constants through the real wavepacket and flux methods, taking into account the nuclearspin statistics for both electronic states. Contrasting RTCC with more approximate results, we point out the role of RT and Coriolis couplings, and discuss the importance of the excited state on the initialstateresolved dynamics and on the thermal kinetic rate. Confirming the previous results, RT couplings transfer partly the reactivity from to , and CC calculations are necessary to obtain accurate highenergy cross sections. When is initially rotating, RT couplings enhance strongly the electronicstateresolved reactivity. Considering the nuclearspin statistics for both electronic states, we find out that the state plays a significant role in the rotationally resolved dynamics of . However, the approximation gives a thermal rate that is slightly smaller than the one obtained by the RTCC calculations. This implies that this usual approximation is acceptable to calculate unresolved kinetic data of the title reaction. Our calculated rate constant values within the 213–300 K temperature interval are in excellent agreement with the experimental ones.

Photoelectron imaging of atomic chlorine and bromine following photolysis of
View Description Hide DescriptionPhotoionization of chlorine and bromine atoms following photodissociation of was studied in the wavelength range of 231–238 nm by photoelectron imaging technique. Final statespecific speed and angular distributions of the photoelectron were recorded. Analysis of relative branching ratios to different levels of and revealed that the final ion level distributions are generally dominated by the preservation of the ioncore configuration of the intermediate resonant state. Some numbers of the intermediate states were newly assigned according to this regulation. The configuration interaction between resonant states and the autoionization in the continuum were also believed to play an important role in the ionization process since some ions that deviate from the regulation mentioned ahead were observed. The angular distributions of the electrons were found to be well characterized by and , although the ionization process of chlorine and bromine atoms involves three photons.