Volume 122, Issue 4, 22 January 2005
 ARTICLES

 Theoretical Methods and Algorithms

Conical intersections and semiclassical trajectories: Comparison to accurate quantum dynamics and analyses of the trajectories
View Description Hide DescriptionSemiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, fulldimensional quantum mechanical scattering calculations are carried out for all five systems at energies that allow for electronic deexcitation via the seam of CIs. Several semiclassical trajectory methods are tested against the accurate quantum mechanical results. For four of the five model systems, the diabatic representation is the preferred (most accurate) representation for semiclassical trajectories, as correctly predicted by the Calaveras County criterion. Four surface hopping methods are tested and have overall relative errors of 40%–60%. The semiclassical Ehrenfest method has an overall error of 66%, and the selfconsistent decay of mixing (SCDM) and coherent switches with decay of mixing (CSDM) methods are the most accurate methods overall with relative errors of ∼32%. Furthermore, the CSDM method is less representation dependent than both the SCDM and the surface hopping methods, making it the preferred semiclassical trajectory method. Finally, the behavior of semiclassical trajectories near conical intersections is discussed.

Interpolated potential energy surfaces: How accurate do the second derivatives have to be?
View Description Hide DescriptionA global potential energy surface for the water dimer is constructed using the modified Shepard interpolation scheme of Collins et al. According to this interpolation scheme, the energy at an arbitrary geometry is expressed as a weighted sum of Taylor series expansions from neighboring data points, where the energy and derivative data required are obtained from ab initio calculations. For some ab initio methods, errors are introduced into the second derivative matrix, either by numerical differencing of ab initio energies or numerical integration during the ab initio calculation. Therefore, we test the accuracy required of the second derivative data by truncation of the exact second derivatives to a series of approximate second derivatives, and assess the effect on the results of a quantum diffusionMonte Carlo (QDMC) simulation. Our results show that the calculated zeropoint energy and wave function histograms converge to within the numerical uncertainty of the QDMC simulation by inclusion of either three significant figures or three decimal places in the second derivatives.

Improving the orbitalfree density functional theory description of covalent materials
View Description Hide DescriptionThe essential challenge in orbitalfree density functional theory (OFDFT) is to construct accurate kinetic energydensity functionals (KEDFs) with general applicability (i.e., transferability). During the last decade, several linearresponse (LR)based KEDFs have been proposed. Among them, the WangGovindCarter (WGC) KEDF, containing a densitydependent response kernel, is one of the most accurate that still affords a linear scaling algorithm. For nearlyfreeelectronlike metals such as Al and its alloys, OFDFT employing the WGC KEDF produces bulk properties in good agreement with orbitalbased KohnSham (KS) DFT predictions. However, when OFDFT, using the WGC KEDF combined with a recently proposed bulkderived local pseudopotential (BLPS), was applied to semiconducting and metallic phases of Si, problems arose with convergence of the selfconsistent density and energy, leading to poor results. Here we provide evidence that the convergence problem is very likely caused by the use of a truncated Taylor series expansion of the WGC response kernel. Moreover, we show that a defect in the ansatz for the firstorder reduced density matrix underlying the LR KEDFs limits the accuracy of these KEDFs. By optimizing the two free parameters involved in the WGC KEDF, the twobody Fermi wave vector mixing parameter γ and the reference density used in the Taylor expansion, OFDFT calculations with the BLPS can achieve semiquantitative results for nine phases of bulk silicon. These new parameters are recommended whenever the WGC KEDF is used to study nonmetallic systems.

A gaugeindependent zerothorder regular approximation to the exact relativistic Hamiltonian—Formulation and applications
View Description Hide DescriptionA simple modification of the zerothorder regular approximation (ZORA) in relativistic theory is suggested to suppress its erroneous gauge dependence to a high level of approximation. The method, coined gaugeindependent ZORA (ZORAGI), can be easily installed in any existing nonrelativistic quantum chemical package by programming simple oneelectron matrix elements for the quasirelativistic Hamiltonian. Results of benchmark calculations obtained with ZORAGI at the HartreeFock (HF) and secondorder MøllerPlesset perturbation theory (MP2) level for dihalogens are in good agreement with the results of fourcomponent relativistic calculations (HF level) and experimental data (MP2 level). ZORAGI calculations based on MP2 or coupledcluster theory with single and double perturbations and a perturbative inclusion of triple excitations [CCSD(T)] lead to accurate atomization energies and molecular geometries for the tetroxides of group VIII elements. With ZORAGI/CCSD(T), an improved estimate for the atomization energy of hassium tetroxide is obtained.

Multireference secondorder perturbation theory: How size consistent is “almost size consistent”
View Description Hide DescriptionA systematic study of the deviation from size consistency of the multireference secondorder MøllerPlesset perturbation theory (MRMP2) method is presented. The sizeconsistency error is shown to depend on the number of monomers in a supermolecule calculation, size of basis set, number of correlated valence electrons, and size of active space. HF, and are used as test cases, with stretched bonds, to include simple, welldefined multireference character. This is essential in ensuring that MRMP2 is being tested as a multireference method. It is concluded that the MRMP2 and other multireference perturbation theory methods can exhibit significant sizeconsistency errors, and that the size of the error depends on the manner in which the perturbation theory is implemented.

Path integral evaluation of the quantum instanton rate constant for proton transfer in a polar solvent
View Description Hide DescriptionThe quantum instanton approximation for thermal rate constants, a type of quantum transition state theory (QTST), is applied to a modelproton transferreaction in liquid methyl chloride developed by Azzouz and Borgis. Monte Carlopath integral methods are used to carry out the calculations, and two other closely related QTST’s, namely, the centroiddensity and Hansen–Andersen QTST, are also evaluated for comparison using the present path integral approach. A technique is then introduced that calculates the kinetic isotope effect directly via thermodynamic integration of the rate with respect to hydrogen mass, which has the practical advantage of avoiding costly evaluation of the activation free energy. The present application to the Azzouz–Borgis problem shows that the above three types of QTST provide very similar results for the rate, within 30% of each other, which is nontrivial considering the totally different derivations of these QTSTs; the latter rates are also in reasonable agreement with some other previous results (e.g., obtained via molecular dynamics with quantum transitions), within a factor of for the transfer, thus significantly diminishing the possible range of the exact rates. In addition, it is revealed that a small but nonnegligible inconsistency exists in the parametrization of the AzzouzBorgis model employed in previous studies, which resulted in the large apparent discrepancy in the calculated rates.

Isotropic periodic sum: A method for the calculation of longrange interactions
View Description Hide DescriptionThis work presents an accurate and efficient approach to the calculation of longrange interactions for molecular modeling and simulation. This method defines a local region for each particle and describes the remaining region as images of the local region statistically distributed in an isotropic and periodic way, which we call isotropic periodic images. Different from lattice sum methods that sum over discrete lattice images generated by periodic boundary conditions, this method sums over the isotropic periodic images to calculate longrange interactions, and is referred to as the isotropic periodic sum (IPS) method. The IPS method is not a lattice sum method and eliminates the need for a reciprocal space sum. Several analytic solutions of IPS for commonly used potentials are presented. It is demonstrated that the IPS method produces results very similar to that of Ewald summation, but with three major advantages, (1) it eliminates unwanted symmetry artifacts raised from periodic boundary conditions, (2) it can be applied to potentials of any functional form and to fully and partially homogenous systems as well as finite systems, and (3) it is more computationally efficient and can be easily parallelized for multiprocessor computers. Therefore, this method provides a general approach to an efficient calculation of longrange interactions for various kinds of molecular systems.

Calculations of nearthreshold cross sections for photodissociation of using the Lanczos algorithm
View Description Hide DescriptionWe combine the Lanczos algorithm with the absorbingpotential method, implemented in a discrete variable representation to calculate the nearthreshold photodissociation cross sections of The method is iterative, based on a continued fraction representation of the Green function and avoids any explicit matrix diagonalization. A very good agreement is found with experiment and closecoupling calculations.

Quantum reaction rate from higher derivatives of the thermal fluxflux autocorrelation function at time zero
View Description Hide DescriptionA quantum theory of thermal reaction rates is presented which may be viewed as an extension of the recently developed “quantum instanton” (QI) model [W. H. Miller, Y. Zhao, M. Ceotto, and S. Yang, J. Chem. Phys. 119, 1329 (2003)]. It is based on using higher derivatives of the fluxflux autocorrelation function (as given by Miller, Schwartz, and Tromp) at to construct a short time approximation for Tests of this theory on and collinear reactions, both symmetric and asymmetric, show it to be more accurate than the original QI model, giving rate constants to for a wide range of temperature.

Comparison of density functionals for energy and structural differences between the high and low spin states of iron(II) coordination compounds. II. More functionals and the hexaminoferrous cation,
View Description Hide DescriptionThe ability of different density functionals to describe the structural and energy differences between the high and low spin states of small octahedral ferrous compounds is studied. This work is an extension of our previous study of the hexaquoferrous cation, [J. Chem. Phys. 120, 9473 (2004)] to include a second compound—namely, the hexaminoferrous cation, and several additional functionals. In particular, the present study includes the highly parametrized generalized gradient approximations (GGAs) known as HCTH and the metaGGA VSXC [which together we refer to as highly parametrized density functionals (HPDFs)], now readily available in the GAUSSIAN03 program, as well as the hybrid functional PBE0. Since there are very few experimental results for these molecules with which to compare, comparison is made with best estimates obtained from secondorder perturbation theorycorrected complete active space selfconsistent field (CASPT2) calculations, with spectroscopy oriented configuration interaction (SORCI) calculations, and with ligand fieldtheory (LFT) estimations. While CASPT2 and SORCI are among the most reliable ab initio methods available for this type of problem, LFT embodies many decades of empirical experience. These three methods are found to give coherent results and provide best estimates of the adiabatic lowspin–highspin energy difference, of for and for All functionals beyond the purely local approximation produce reasonably good geometries, so long as adequate basis sets are used. In contrast, the energy splitting, is much more sensitive to the choice of functional. The local density approximation severely over stabilizes the lowspin state with respect to the highspin state. This “density functional theory(DFT) spin pairingenergy problem” persists, but is reduced, for traditional GGAs. In contrast the hybrid functional B3LYP underestimates by a few thousands of wave numbers. The RPBE GGA of Hammer, Hansen, and Nørskov gives good results for as do the HPDFs, especially the VSXC functional. Surprisingly the HCTH functionals actually over correct the DFT spin pairingenergy problem, destabilizing the lowspin state relative to the highspin state. Best agreement is found for the hybrid functional PBE0.

Excited electronic states of small water clusters
View Description Hide DescriptionThe lowest electronic states that are initially formed upon excitation of small water clusters having a central water molecule with one stretched OH bond are studied with electronic structure methods. It is found that in water dimer, trimer, and pentamer the lowest excited singlet and triplet states are each nondissociative for stretching of an OH bond that is hydrogen bonded in an icelike configuration to a neighboring water molecule. This is in marked contrast to the behavior of an isolated gas phase watermonomer, where it is well known that the lowest excited state is strongly dissociative upon OH stretching. The conclusions of this study may serve as a basis to interpret recent experimental evidence that suggests a significant lifetime for excited water in irradiated thin icefilms, and may also have important implications for the behavior of excitation of liquid water.

A general formula for the rate of resonant transfer of energy between two electric multipole moments of arbitrary order using molecular quantum electrodynamics
View Description Hide DescriptionA general expression is derived for the matrix element for the resonant transfer of energy between an initially excited donor species and an acceptor moiety in the ground state, with each entity possessing an electric multipole moment of arbitrary order. In the quantum electrodynamical framework employed, the coupling between the pair is mediated by the exchange of a single virtual photon. The probability amplitude found from secondorder perturbation theory is a product of the electric moments located at each center and the resonant multipolemultipole interaction tensor. Using the Fermi golden rule, a general formula for the rate of energy transfer is obtained. As an illustration of the efficacy of the theory developed, rates of excitation energy exchange are calculated for systems interacting through dipolequadrupole, dipoleoctupole, quadrupolequadrupole, and the familiar dipoledipole coupling. For each of the cases examined, the near and farzone limits of the migration rate are calculated from the result valid for all donoracceptor separations beyond wave function overlap. Expression of the octupole contribution to the transfer rate in terms of its irreducible components of weights 1 and 3 leads to new features. The octupole weight1 term is found to contribute only when the interaction is retarded, while the dipoleoctupole weight1 contribution appears as a higherorder correction term to the dipoledipole rate. Order of magnitude estimates are given for the contributions of dipolequadrupole and dipoleoctupole terms relative to the leading dipoledipole rate for near, intermediate, and farzone separations to further understand the role played by higher multipole moments in the transfer of excitation and the mechanism dominating the process.

Resonant transfer of excitation between two molecules using Maxwell fields
View Description Hide DescriptionThe matrix element for the resonant transfer of excitation between two molecules possessing electric and magnetic multipole moments of arbitrary order is calculated using quantum electrodynamical response theory. A prerequisite of the method is the functional form for the lth order linear electric and magnetic multipole dependent electric displacement and magnetic field operators in the neighborhood of a molecule, whose derivation is also given. The initially unexcited species is viewed as a test body accepting energy resonantly via coupling to the Maxwell fields of the excited multipole source molecule. The generalized electricelectric multipole contribution to the matrix element is shown to agree with an earlier calculation using timedependent perturbation theory. As an application involving both electric and magnetic terms, the rate of excitation transfer between two chiral molecules is computed and found to depend on the handedness of each species.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Polarizabilities and hyperpolarizabilities for the atoms Al, Si, P, S, Cl, and Ar: Coupled cluster calculations
View Description Hide DescriptionAccurate static dipole polarizabilities and hyperpolarizabilities are calculated for the ground states of the Al, Si, P, S, Cl, and Ar atoms. The finitefield computations use energies obtained with various ab initio methods including Møller–Plesset perturbation theory and the coupled cluster approach. Excellent agreement with experiment is found for argon. The experimental for Al is likely to be in error. Only limited comparisons are possible for the other atoms because hyperpolarizabilities have not been reported previously for most of these atoms. Our recommended values of the mean dipole polarizability (in the order Al–Ar) are 37.17, 24.93, 19.37, 14.57, and 11.085 with an error estimate of The recommended values of the mean second dipole hyperpolarizability (in the order Al–Ar) are and with an error estimate of Our recommended polarizabilityanisotropy values are 8.41, and 1.71 for Al, Si, S, and Cl respectively, with an error estimate of The recommended hyperpolarizability anisotropies are and for Al, Si, S, and Cl, respectively, with an error estimate of

A theoretical study on the innervalence photoelectron spectra lying between 21 and 26 eV of the molecule
View Description Hide DescriptionAb initio calculations were carried out to study the structures of the photoelectron spectra of the molecule using complete active space selfconsistent field and multireference single and double excitation configuration interaction methods. We focused our attention primarily on the innervalence ionized states lying below 26 eV. Vibrational levels were calculated using adiabatic potential curves and vibrational wave functions were used to obtain Franck–Condon factors. We show that not only discrete vibrational levels of but also the continuum of nuclear motion in contribute to the bands of vibrational progression and the broad peak of the continuum between 22.5 and 26 eV. Other states with weak intensity lying between 19 and 26 eV are also discussed.

Penning ionization electron spectroscopy of by collision with metastable atoms and classical trajectory calculations: Optimization of ab initio model potentials
View Description Hide DescriptionThe potential energy surface of benzene with a atom was obtained by comparison of experimental data in collisionenergyresolved twodimensional Penning ionizationelectron spectroscopy with classical trajectory calculations. The ab initiomodel interaction potentials for were successfully optimized by the overlap expansion method; the model potentials were effectively modified by correction terms proportional to the overlap integrals between orbitals of the interacting system, and Classical trajectory calculations with optimized potentials gave excellent agreement with the observed collisionenergy dependence of partial ionization cross sections. Important contributions to corrections were found to be due to interactions between unoccupied molecular orbitals and the orbital. A molecule attracts a atom widely at the region where π electrons distribute, and the interaction of (ca. just cover the carbon hexagon. The binding energy of a molecule and a atom was 107 meV at a distance of 2.40 Å on the sixfold axis from the center of a molecule, which is similar to that of and is much larger than those of the systems.

Structure and energetics of two and threedimensional neutral, cationic, and anionic gold clusters
View Description Hide DescriptionLowenergy structures are found on the potential energy surfaces of the neutral, cationic, and anionic gold clusters and on the neutral potential energy surface of These structures provide insights on the two to three dimensional (2D⇒3D) transition in small neutral and chargedgold clusters. It is demonstrated that the size threshold for the 2D3D coexistence is lower for cationic than neutral gold clusters: the 2D3D coexistence develops for and on the cationic potential energy surfaces while only for on the neutral. Two metastable longlived dianions of gold clusters are also reported.

Ab initio calculations, potential representation and vibrational dynamics of van der Waals complex
View Description Hide DescriptionAn intermolecular potential energy surface for complex in the ground state is calculated at the levels of fourthorder (MP4) Møller–Plesset and coupledcluster [CCSD(T)] approximations, using largecore pseudopotential for Br atoms and the augccpV5Z basis set for He. The surface is characterized by three minima and the minimum energy pathways through them. The global minimum corresponds to a linear configuration, while the two other ones to “policenightstick” and tetrahedral structures. The corresponding well depths are and respectively, at MP4/CCSD(T) levels of theory. It is found that results obtained by summing threebody parametrized interactions and the He–He interaction are in very good accord with the corresponding MP4/CSSD(T) configuration energies of the Variational calculations using a sum of threebody interactions are presented to study the bound states of the vdW complex. The binding energy and the corresponding vibrationally averaged structure are determined for different isomers of the cluster and their comparison with the available experimental data is discussed.

Photoelectron spectroscopy of nickelbenzene cluster anions
View Description Hide Descriptioncluster anions were studied by both mass spectrometry and anion photoelectron spectroscopy. Only species for which were observed in the mass spectra. No singlenickel species were seen. Adiabatic electron affinities, vertical detachment energies, and second transition energies were determined for (2,2), (3,1), and (3,2). For the most part, calculations on species by B. K. Rao and P. Jena [J. Chem. Phys. 117, 5234 (2002)] were found to be consistent with our results. The synergy between their calculations and our experiment provided enhanced confidence in the theoretically implied magnetic moments of several nickelbenzene complexes. The magnetic moments of small nickel clusters were seen to be extremely sensitive to immediate molecular environmental effects.

Molecular beam studies of the F atom reaction with propyne: Site specific reactivity
View Description Hide DescriptionThe dynamics of the F atom reaction with propyne has been investigated using a universal crossed molecular beam apparatus. Two reaction channels have been clearly observed: and The substitution of F for H occurs mainly via a complex formation mechanism, producing reaction products with some contribution from a direct reaction mechanism. The HF product, however, appears to be dominantly forward scattered relative to the F atom beam direction, suggesting that the HF formation occurs via a direct abstraction mechanism. Branching ratios for the two observed reaction channels are also determined. The H formation channel is found to be the major reaction pathway, while the HF formation channel is also significant. From the measurements of DF versus HF products from the F atom reaction with deuterated propyne, the H atom picked up by the F atom in the reaction with normal propyne seems to come mostly from the group. In addition, the H atom produced in the H atom formation channel appears to be mostly from the group with some contribution from the CCH group.