Volume 119, Issue 8, 22 August 2003
 ARTICLES

 Theoretical Methods and Algorithms

Extended Douglas–Kroll transformations applied to the relativistic manyelectron Hamiltonian
View Description Hide DescriptionA new generalized Douglas–Kroll (DK) approach is proposed for the relativistic manyelectron Hamiltonian including the electron–electron interaction. In order to consider the higherorder DK transformation to the twoelectron interaction, the present approach adopts the effective oneelectron potential in the Dirac–Hartree–Fock/Dirac–Kohn–Sham operator as an expansion parameter in the DK transformation. Its numerical performance is tested for the atomic Hg and molecular HAt and systems. The thirdorder DK transformation to both oneelectron and twoelectron Hamiltonians, which is the highest level of theory treated in this study, gives excellent agreement with the fourcomponent relativistic approach. The firstorder DK correction to the twoelectron interaction is shown to be satisfactory for both atomic and molecular systems.

Wave function instabilities in the cis–trans isomerization and singlet–triplet energy gaps in a push–pull compound
View Description Hide DescriptionThe energy barriers for the cis–transisomerization are obtained for a sample of push–pull compounds. The appropriate trend in the values for the barriers is obtained after an instability treatment of the restricted Kohn–Sham solution. At the instability zone, some compounds exhibit a singlet openshell configuration. The width of the instability region around the transition state is characterized in an asymmetric push–pull compound. These results show that the instabilities in the twisted configuration of double bonds are mainly related to spin symmetry effects rather than to the molecular symmetry. For the openshell singlet, an ensemble model is used to compute the electronic properties. The singlet–triplet energy gap along the rotation coordinate is qualitatively described by the use of spin potential and hardness.

Improved Fermi operator expansion methods for fast electronic structure calculations
View Description Hide DescriptionLinear scaling algorithms based on Fermi operator expansions (FOE) have been considered significantly slower than other alternative approaches in evaluating the density matrix in Kohn–Sham density functional theory, despite their attractive simplicity. In this work, two new improvements to the FOE method are introduced. First, novel fast summation methods are employed to evaluate a matrix polynomial or Chebyshev matrix polynomial with matrix multiplications totalling roughly twice the square root of the degree of the polynomial. Second, six different representations of the Fermi operators are compared to assess the smallest possible degree of polynomial expansion for a given target precision. The optimal choice appears to be the complementary error function. Together, these advances make the FOE method competitive with the best existing alternatives.

On Löwdin’s projection technique and the energycorrected approaches
View Description Hide DescriptionRecently, a new energy correction to standard approaches of the coupledcluster (CC) method has been proposed, namely the socalled (complete) renormalized CC method [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 5644 (2000) and references therein], as well as the energycorrected CCSD approach [X. Li and J. Paldus, J. Chem. Phys. 117, 1941 (2002) and references therein], which are based on the method of moments of the CC method of Kowalski and Piecuch [Computational Chemistry: Reviews of Current Trends (World Scientific, Singapore, 2000), Vol. 5, p. 1]. These methods provide an efficient and noniterative, and thus less demanding, approach than do the iterative approaches and avoid, e.g., the fallacies of the standard CCSD(T) method. We show how this type of energy corrections may be related to Löwdin’s projection and bracketing techniques and also to a standard extrapolation scheme which is applied here to the results of the new energy corrections.

Current transport through molecular electronic devices
View Description Hide DescriptionA new formalism for the calculation of the conductance of a molecule attached to two macroscopic metal contacts is proposed. Starting from an effective oneelectron picture, the contacts are accounted for by certain potentials that are added to the molecular Hamiltonian. By choosing appropriate boundary conditions for the molecular eigenvalue problem, stationary states can be obtained describing the current transport through the molecule. The approach presented here is not restricted to the zerovoltage and zerocurrent limit. A simple and transparent formula for the conductance is derived that resembles Fermi’s golden rule. The relation of the proposed method to nonequilibrium transport theory is discussed.

An approximation to the ensemble Kohn–Sham exchange potential for excited states of atoms
View Description Hide DescriptionAn approximation to the Kohn–Sham exchange potential in the Gross–Oliveira–Kohn theory of ensemble of states is proposed for excited states of atoms, making use of a coupled selfconsistent fitting procedure to the parameters of an approximate potential generated from a nonlocal potential coming from the Becke exchange energy density, the and the socalled shortranged response potential The parameter values are obtained when the sum of the Coulomb and the approximate exchange potentials shows the least deviation from the analogous potential in the recently derived generalized Krieger–Li–Iafrate (KLI) approximation of the optimized potential method of ensembles. To test the quality of the proposed exchange potential, calculations are performed for the first two or three (excitedstate) ensembles of Li, Be, Na,Mg, K, and Ca atoms and the ensemble energies and densities are compared with the ensemble KLI results. As the exact exchange potential is free from the ghostinteraction (i.e., the selfinteraction between the elements of the ensemble) the proposed fitted potential reduces the ghostinteraction error as well.

Quantum chemistry using the density matrix renormalization group II
View Description Hide DescriptionWe have compared different strategies for ab initio quantum chemistry density matrix renormalization group treatments. The two starting orbital blocks include all valence and active orbitals of the reference complete active space self consistent field wave function. To generate the remaining blocks, we propose following the order of the contributions to the correlation energy: a posteriori using approximate occupation numbers or a priori, using a Møller–Plesset type of arguments, by explicit evaluation of secondorder interactions. We have compared two different schemes for orbital localization to identify the important and less important orbital interactions and simplify the generation of the orbital blocks. To truncate the expansion we have compared two approaches, keeping constant the number m of components or the threshold λ to fix the residue of the expansion at each step. The extrapolation of the energies is found to provide accurate estimates of the full configuration interaction energy, making the expansion independent on the actual values of the two parameters m and λ. We propose to generate the factors for the two blocks from ground and excited eigenvectors of the Hamiltonian matrix.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Effects of intermolecular interaction on proton tunneling: Theoretical study on twodimensional potential energy surfaces for 9hydroxyphenalenone complexes
View Description Hide DescriptionThe effects of binding of or with 9hydroxyphenalenone (9HPO) on protontunneling in the state have been theoretically investigated. Highlevel ab initio calculations predict that is van der Waalsbonded to the C=O⋯OH moiety of 9HPO in the most stable structure. This planar structure is more stable than the nonplanar structure where is bonded above the aromatic rings of 9HPO. In the complex, is hydrogenbonded to the carbonyl group in the most stable structure. Twodimensional potential energy surfaces (PESs) for and have been calculated with the reactionsurface method, and the contour plots of PESs for the complexes are compared with those for the 9HPO monomer. The binding of with 9HPO induces slight asymmetry in the doubleminimum potential well, whereas the asymmetry of the PES is very large for the binding of The transition state energy for drastically decreases to be about a half that of 9HPO, while that for is only slightly smaller than the transition energy for 9HPO. The vibrational wave function for in is substantially delocalized over two potential minima, but that for is completely localized around a single potential minimum. The calculated tunneling splitting of the zeropoint level in is only 10% smaller than the corresponding splitting of 9HPO, whereas protontunneling is quenched in The calculated results are consistent with the prediction from the electronic spectra measured in a supersonic free jet.

Guided ion beam studies of the reactions of with Nickel cluster oxide and dioxide bond energies
View Description Hide DescriptionThe kinetic energy dependences of the reactions of with are studied in a guided ion beam tandem mass spectrometer. A variety of and product ions, where are observed, with the dioxide cluster ions dominating the products for all larger reactant cluster ions. Reaction efficiencies are near unity for all but the smallest clusters. The energy dependences of the product cross sections are analyzed in several different ways to determine thermochemistry for both the first and second oxygen atom binding to nickel cluster ions. These values show little dependence on cluster size for clusters larger than three atoms. The trends in this thermochemistry are discussed and compared to bulk phase oxidation values.

Dissociative ionization of ethanol in chirped intense laser fields
View Description Hide DescriptionThe dissociativeionization of ethanol in an intense laser field is investigated with a chirped laser pulse. From the sensitive dependence of the relative yields of the fragment ions on the absolute values of the linear chirp rate, it is shown that the lightdressed potentialenergysurface (LDPES) at the singly charged stage governs the nuclear dynamics, and that the nuclear wave packet flow into the breaking of either of the C–C and C–O chemical bonds could be characterized by the holding time during which the LDPESs are maintained. It is also understood in term of the holding time that the enhanced ionization into the doubly charged stage followed by the Coulomb explosion at C–C or C–O proceeds when the nuclear wave packet at the singly charged stage reaches the critical distance for the further ionization.

Symmetryadapted direct product discrete variable representation for the coupled angular momentum operator: Application to the vibrations of
View Description Hide DescriptionThe theoretical (quantum) description of large amplitude vibrations of systems containing four or more atoms using orthogonal internal coordinates requires three or more angular coordinates. The basis commonly used to represent these coordinates is the coupled angular momentum basis. We show that a direct product angular discrete variable representation (DVR) can be used advantageously, particularly for systems with high permutationinversion symmetry and nonlinear equilibrium geometry. The DVR permits full symmetry projection and solution by the sequential diagonalization and truncation method. Application to the dimer of rigid demonstrates the accuracy and efficiency of the approach.

Variational calculations of HBN energy levels in the and states
View Description Hide DescriptionA theoretical study of the HBN radical in the and states, taking into account vibronic coupling effects, is reported. The lowest potential energy surfaces (PES) of the HBN–BNH system have been studied to identify all stationary points. The HBN minimum was found to be 20.0 kcal/mol above BNH, with an isomerization barrier of ≈11 000 cm^{−1} on the surface. For the HBN isomer, accurate nearequilibrium threedimensional diabatic PESs for the ground and first excited electronic states have been calculated at the multireference configuration interaction level of theory, with extended basis set. A vibronic coupling between bend and BN stretch, analogous to that found in the isoelectronic and radicals, has been found to take place due to the crossing of the and states at energies close to 11 000 cm^{−1}. Vibronic energy levels of HBN and DBN have been calculated variationally using a previously developed method [Carter et al., Mol. Phys. 98, 1967 (2000)] suitable for threeatomic molecules showing threestate vibronic interactions. Energy levels of Σ and Π symmetry up to 10 000 cm^{−1} for HBN, and 8800 cm^{−1} for DBN, are reported. It is shown that due to the highenergy surface crossing, the vibronic interaction becomes nonnegligible only for levels above 8500 cm^{−1}. For all levels, Renner–Teller effects and Fermi resonances are analyzed.

Quasiperiodic orbit analysis of nonadiabatic cis–trans photoisomerization dynamics
View Description Hide DescriptionAdopting a multidimensional model of nonadiabaticcis–trans photoisomerization, quantummechanical and classical simulations of the ultrafast wavepacket dynamics associated with this photoreaction are presented. The quantum calculations demonstrate that nonadiabatic photoisomerization typically leads to a largely delocalized and diffuse wave function, which hampers an intuitive understanding of the dynamics in terms of specific nuclear motion. To facilitate a classical description, a recently proposed theoretical formulation is employed that affords an exact mapping of discrete electronic states onto continuous degrees of freedom and therefore provides a welldefined classical limit of a nonadiabatically coupled system. It is shown that a simple quasiclassical implementation of the mapping formulation is able to reproduce at least qualitatively the complex quantum dynamics of the system. In addition, the classical description allows us to characterize the nonadiabatic photoisomerization dynamics in terms of a few “quasiperiodic orbits.” These orbits are close to a true unstable periodic orbit but are exactly periodic only with respect to the slow reaction coordinate of the system. Various types of quasiperiodic orbits of nonadiabatic photoisomerization are identified and analyzed. It is shown that the diffuse appearance of the quantummechanical wave function can be directly connected to irregular classical orbits propagating on vibronically coupled potentialenergysurfaces. The chaotic behavior of the system is mainly caused by the relatively high energy corresponding to photoexcitation, the large anharmonicity of the isomerization potentials, and the reflection of the trajectory at surface crossings. The results demonstrate that quasiperiodic orbits represent a concept well suited to analyze the quantum dynamics of complex systems in terms of classical trajectories without the cumbersome search for periodic orbits.

CCSD(T) intermolecular potential between He atom and ClF molecule: Comparison with experiment
View Description Hide DescriptionThe potential energy surface of the He–ClF complex is calculated using for He atom an efficient basis set of augccpV5Z augmented with a set of set of midbond functions and augccpVTZ, augccpVQZ for Cl and F atoms, respectively, at coupledcluster with single and double excitations and a noniterative perturbation treatment of triple excitations [CCSD(T)] level. Three local minima are found for the He–ClF that correspond to linear He–Cl–F (collinear) and He–F–Cl (antilinear) configurations and a asymmetric Tshaped structure. The well depths and the equilibrium distances are and 3.54 Å (collinear), and 3.23 Å (Tshaped) and and 3.93 Å (antilinear). Bound states calculations are carried out for the CCSD(T) surface and the sensitivity of the rovibrational levels to the errors of the computed potential energy surface at different configuration regions is discussed. The computed energy levels up to a total angular momentum are in general accord with experimental data.

Ab initio molecular dynamics study on the excitation dynamics of psoralen compounds
View Description Hide DescriptionAb initiomolecular dynamics (AIMD) simulations are performed for studying the excitation dynamics of psoralen compounds; namely, nonsubstituted psoralen, 5methoxypsoralen (5MOP), and 8methoxypsoralen (8MOP). The density functional theory calculations at the B3LYP/D95V level are used for evaluating the atomic forces in every AIMD step. The specific behavior of 8MOP in the state, which has been reported by the experimental study, is found to be due to a unique openring structure, which leads to a different spin distribution in comparison with the cases of psoralen and 5MOP and further to a crossing between the and states.

Reaction dynamics of Rotational and vibrational distribution of HCl probed with timeresolved Fouriertransform spectroscopy
View Description Hide DescriptionFollowing laser irradiation of a flowing mixture of and at 308 nm to initiate the reaction of vibration–rotation resolved emission spectra of in the spectral region are detected with a stepscan timeresolved Fouriertransform spectrometer. The Boltzmanntype rotational distributions of and yield rotational temperatures that decrease with reaction time; extrapolation to time zero based on data in the range 0.5–4.0 μs yields nascent rotational temperatures of and respectively; an average rotational energy of is determined for much greater than a previous report. Observed temporal profiles of the vibrational population of are fitted with a kinetic model that includes formation and quenching of to yield a branching ratio of for formation of and a thermal rate coefficient of Combining an estimate of the vibrational population of based on a surprisal analysis of previous investigations on the reaction we report a ratio of vibrational distributions of which gives an average vibrational energy of for HCl. Internal energies, especially rotational energy, of HCl derived with this method is more reliable than with previous techniques; the fractions of available energy going into rotation and vibration of HCl are and respectively.

Ab initio calculation of the ground potential energy surface and theoretical rate constant for the reaction
View Description Hide DescriptionThe entrance channel of the reaction has been investigated for collinear and perpendicular approach of the silicon atom to the molecule by ab initio electronic structure calculations using the multireference configuration interaction (MRCI) method and Davidson correction (MRCI+Q). Results show that the reaction can proceed through the ground singlet and first triplet electronic states at low temperatures. The ground threedimensional potential energy surface (PES) which correlates the reactants to the products was computed at the MRCI+Q level of theory using the Woon and Dunning ccpVTZ basis sets. The reaction was found barrierless and three minima have been characterized on the PES with energy ordering: linear About 2500 ab initio data points have been fitted to a many body expansion using the method of Aguado and Paniagua, with a global rootmeansquare of 1.49 kcal/mol. The analytical PES has been used to determine the thermal rate constants in the temperature range 15–300 K by quasiclassical trajectory calculations. Comparison with experimental results shows a quite good agreement for temperature dependence of the rate constants when the spin–orbit structure of the reactants is taken into account. The rate constants are also compared with earlier results of adiabatic capture calculations. The excellent agreement between both theoretical results for temperatures above 50 K points out an increasing contribution of the first triplet state to reactivity when temperature increases.

Regularity in highly excited vibrational dynamics of NOCl Quantum mechanical calculations on a new potential energy surface
View Description Hide DescriptionA new potential energy surface (PES) of NOCl in the ground electronic state is constructed based on multireference configuration interaction calculations. Almost all the vibrational eigenstates up to the dissociation threshold are obtained using filter diagonalization method with the present PES. The vibrational excitation energies are in good agreement with the experimental values. The nearest neighbor level spacing distribution shows that the vibrational structure is regarded as regular up to the dissociation threshold. The distribution of radiative coupling elements also supports the regularity. It is further found out that the NO stretching mode is strongly decoupled from the other modes. Taking advantage of this result, the twodimensional (2D) analyses are carried out with the NO distance fixed. The 2D wave functions have clear nodal patterns even near the dissociation threshold, indicating that the 2D quantum dynamics is regular as in the threedimensional case. Comparing the 2D classical dynamics with the 2D wave functions, quasiperiodic trajectories closely related to the corresponding quantum dynamics are extracted. Although it is generally believed that the phase space becomes fully chaotic with approaching to the dissociation threshold, two stable islands of regular motion still remain even at this energy region.

Orbital interactions and charge redistribution in weak hydrogen bonds: The Watson–Crick AT mimic adenine2,4difluorotoluene
View Description Hide DescriptionThe discovery by Kool and coworkers that 2,4difluorotoluene (F) mimics thymine (T) in DNA replication has led to a controversy about the question if this mimic has the capability of forminghydrogen bonds with adenine (A). In the present study, we address not only the question about the strengths of the hydrogen bonds in AF as compared to those in AT but we focus in particular on the nature of these interactions. Thus, we have analyzed AF and AT at the BP86/TZ2P level of density functional theory(DFT). In line with previous experience, this approach is shown to achieve close agreement with the available data from ab initio computations and experiment: the complexation energy of AF (−3.2 kcal/mol) is confirmed to be much weaker indeed than that of AT (−13.0 kcal/mol). Interestingly, the weak hydrogen bonds in AF still possess a significant orbital interaction component that resembles the situation for the more strongly bound AT, as follows from (1) an analysis of the orbital electronic structure of AF and AT, (2) a quantitative decomposition of the A–F and A–T bondenergies, as well as (3) a quantitative decomposition of the charge redistribution associated with the A–F and A–T interactions based on the Voronoi deformation density (VDD) method. The VDD method has been further developed such that the charge redistribution per atom can be decomposed into a component associated with the Pauli repulsive orbital interactions and a component associated with the bonding orbital interactions: Implications of our findings for the mechanism of DNA replication are discussed.

Hydrogen bonding and proton transfer in small hydroxylammonium nitrate clusters: A theoretical study
View Description Hide DescriptionStructures and energies of gasphase hydroxylammonium nitrate (HAN), are determined using density functional theory and the basis set. Three stable configurations are found for HAN which involve strong hydrogen bonding between hydroxylamine and nitric acid molecules. In the most stable configuration, both the oxygen and the nitrogen of hydroxylamine are hydrogen bonded to sites on the nitric acid molecule. In the less stable HAN structures only the oxygen or the nitrogen of hydroxylamine are hydrogen bonded. Two stable structures for the complex are investigated. The more stable structure is ionic, with the nitric acidproton having transferred to the nitrogen of hydroxylamine. Strong electrostatic and hydrogenbonding interactions stabilize this structure. The other stable form of has fewer hydrogen bonds and is composed of interacting neutral nitric acid and hydroxylamine molecules. Binding energies are determined for all structures along with corrections for basis set superposition errors in the HAN molecules. Proton exchange reaction paths are studied for the HAN configurations. The saddle points for the proton exchange process are ionic forms of HAN with interacting and moieties. These ionic structures are 13.5 and 13.6 kcal/mol higher in energy than the neutral hydrogenbonded complexs of and from which they are formed. The electrostatic attractions between the ions are sufficient to stabilize the ionic form of whereas in the HAN “monomer” the interaction energy for single and ions is not sufficient to compensate for the energy required for proton transfer from nitric acid to the hydroxylamine group. A correlation based on the bondvalence theory which describes the bond lengths of the hydrogen bonds is examined for the complexes. All the hydrogen bonds follow the correlation well.