Volume 114, Issue 4, 22 January 2001
 ARTICLES

 Theoretical Methods and Algorithms

Correct dissociation behavior of radical ions such as in density functional calculations
View Description Hide DescriptionIn this contribution it is shown that the unphysical dissociation energy curves of dimeric ions bearing a small odd number of electrons as obtained with DFT calculations can be cured by a posteriori corrections. The selfinteraction error, which is known to be at the origin of the unphysical dissociation behavior, is corrected by a Slater’s transition state calculation. A very satisfactory dissociation energy curve is obtained for However for it is also necessary to introduce fractional occupation numbers to obtain a good description of the system.

A semiclassical approach to the dynamics of manybody Bose/Fermi systems by the path integral centroid molecular dynamics
View Description Hide DescriptionWe present a formalism of the path integral centroid molecular dynamics (CMD) extended to Bose and Fermi statistics as a semiclassical approach to explore the dynamics of quantum manybody systems. The validity of the method is examined in relation to the time correlation functions. The presently proposed scheme, refined from our previous derivation [Chem. Phys. Lett. 307, 187 (1999)], is aimed at the calculations of not the exact quantummechanical dynamics but the semiclassical dynamics under certain approximations. The formalism is based on the projection operator with which the Bose/Fermi system is mapped onto a particular type of pseudoBoltzmann system. In the pseudoBoltzmann system the correlation due to the Bose/Fermi statistics is introduced via an extra pseudopotential called the permutation potential and its relevant operator. Using the present semiclassical formalism, the time correlation function of centroid position, which is evaluated from the CMD trajectories in the pseudoBoltzmann system, is an approximation to the Kubo canonical correlation function of position operator of the exact quantumstatistical system composed of bosons or fermions. There is no such apparent relation between the momentum operator and the corresponding momentum centroid.

A single Lanczos propagation method for calculating transition amplitudes. II. Modified QL and symmetry adaptation
View Description Hide DescriptionThe recently proposed single Lanczos propagation method [J. Chem. Phys. 111, 9944 (1999)] for calculating multiple transition amplitudes is made more efficient in several aspects. It is shown that the amplitudes can be calculated without the explicit calculation and storage of the Lanczos eigenvectors, thus significantly reducing the computational costs, particularly for long propagation. It is also shown that symmetry adaptation can be implemented in the Lanczos propagation in a straightforward manner. In particular, eigenspectra in multiple irreducible representations can be determined from a single recursion by projecting the symmetrized Lanczos states at each step. The accuracy and efficiency of the improved methods are ascertained by numerical tests of realistic triatomic and tetratomic systems.

A symmetryadapted Lanczos method for calculating energy levels with different symmetries from a single set of iterations
View Description Hide DescriptionWe present a symmetryadapted Lanczos method that uses projection operators to calculate energy levels with different symmetries from a single sequence of matrix–vector products. Compared with the conventional Lanczos method, this method has the advantage that energy levels are computed more efficiently and with symmetry labels. Highlying stretching energy levels of a coupled Morse oscillator Hamiltonian describing are calculated to demonstrate the advantage of the symmetryadapted method.

Relativistic dynamics of two spinhalf particles in a homogeneous magnetic field
View Description Hide DescriptionRelativistic dynamics of two spin1/2 particles in an external, homogeneous magnetic field is investigated here. The problem is important for a preliminary understanding of the effect of magnetic field on atoms and molecules at the relativistic level. The relativistic Hamiltonian is formulated in three distinct forms which involve the Bethe–Salpeter interaction, generalized Breit interaction and projected Breit interaction. The total pseudomomentum of the twoparticle system is conserved in each case, and its components are distinct in the zerocharge sector. This permits the separation of the center of mass motion from the Hamiltonian of the neutral twoparticle system. The resulting Hamiltonian operator describes the movement of the two particles in relative coordinates. It is further simplified by using suitable unitary transformations so as to reduce the oneparticle operator for the first particle into a diagonal form. The effective equation of motion for the movement of the second particle in relative coordinates is then identified. A second set of transformations convert the twoparticle relative Hamiltonian into a form where the oneparticle operator for each spin1/2 particle is completely diagonalized and separable into positive and negative energy states. The correspondingly transformed interaction operators can be written in an order by order expansion from which the odd terms are removable by using suitable Foldy–Wouthuysen type transformations in a systematic way. The resulting Hamiltonian operator reduces to previously known expressions when the magnetic field is switched off. Thus the two sets of transformations which convert the one particle parts completely into separable as well as diagonal forms also transform the interaction operator to generate terms consistently through order The field dependence lies entirely in the diagonalized oneparticle parts, which is a consequence of the initial choice of interaction operators. Our results also include expressions corresponding to the interaction operator being projected. The Bethe–Salpeter and projected Breit cases lead to the same interaction operators for a hydrogen atom in the nonrelativistic limit. In the same limit the methodology directly yields the anomalous Zeeman interaction term, some correction to it, and terms which can account for nuclear magnetic resonance. All these terms are embedded in the final twoparticle Hamiltonian operator. These, along with the previously known, fieldindependent, terms which describe the hyperfine interactions, can account for electronic and magnetic resonancespectroscopies on the basis of the same Hamiltonian.

Improved algorithm for cornercutting tunneling calculations
View Description Hide DescriptionWe present an improved version of the largecurvature tunneling method that more accurately treats the anharmonic potentials encountered along lowenergy cornercutting tunneling paths. The method is illustrated by applications to the reaction and to the double proton transfer in formamidine hydrate.

Efficiency of different numerical methods for solving Redfield equations
View Description Hide DescriptionThe numerical efficiency of different schemes for solving the Liouville–von Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the wellknown Runge–Kutta scheme in two different implementations as well as methods especially developed for time propagation: the short iterative Arnoldi, Chebyshev, and Newtonian propagators. In addition, an implementation of a symplectic integrator has been studied. For a simple example of a twocenter electron transfer system we discuss some aspects of the efficiency of these methods to integrate the equations of motion. Overall, for timeindependent potentials the Newtonian method is recommended. For timedependent potentials implementations of the Runge–Kutta algorithm are very efficient.

Spin correlation function of benzene and naphthalene from spincoupled wave functions
View Description Hide DescriptionIn this paper we report on the calculation of the spin correlation function describing the dipolar spin–spin interaction for benzene and naphthalene in their lowest excited triplet state. Spincoupled wave functions were used. The spin correlation function measures the contributions to the expectation value arising from electrons located at different points. An alternation of positive and negative correlation dependent on the separation of the unpaired electrons is found. The results are used to analyze and interpret the zerofield splitting parameter D of these molecules in terms of different contributions. The relationship between the spin correlation function and the sequence of the zerofield levels as well as the value of the parameter D and its dependence from molecular size is discussed.

Interplay of nonMarkovian relaxation and ultrafast optical state preparation in molecular systems: The Laguerre polynomial method
View Description Hide DescriptionThe interplay of femtosecond optical excitation and retarded vibrational relaxation in a molecular system is studied using the nonMarkovian version of the Quantum Master Equation. To solve nonMarkovian equations with an arbitrary memory kernel an expansion with respect to Laguerre polynomials is introduced and the applicability of the method is tested. The nonMarkovian effects are identified and parameter regimes are indicated where these effects become predominant. For an early time region just after the optical excited state preparation it is demonstrated that the convolutionless quantum master equation with a timedependent Redfieldtensor may give a reasonable approximation of the correct nonMarkovian dynamics.

Quantum dynamics using pseudoparticle trajectories: A new approach based on the multiconfiguration timedependent Hartree method
View Description Hide DescriptionQuantum moleculardynamics simulations are an important way of gaining information on the molecular level about chemical systems. In this paper, a new method for the approximate solution of the timedependent Schrödinger equation is presented. This is a reformulation of the multiconfiguration timedependent Hartree (MCTDH) wave packet propagation method, which is transformed so that the evolution of the wave function can be represented by pseudoparticle trajectories. In this way, the poor scaling of computational resources with system size attending all exact solutions of the timedependent Schrödinger equation are circumvented. The equations of motion for the trajectories and the wave function expansion coefficients (importance of each trajectory for the representation) are derived using a variational principle. Other than the MCTDH ansatz, no major approximations have been introduced, and the method converges on the numerically exact solution. Importantly, the trajectories are not classical trajectories, and are coupled by nonlocal effects. A strategy for the practical solution of the equations of motion is then detailed.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dimers of alkaline earth metal halide radicals, A theoretical study
View Description Hide DescriptionAlkaline earth metal halide radical dimers, Mg, Ca and Cl) have not yet been observed experimentally and their existence could be doubted since MX is known to disproportionate in the bulk. We study the species using DFT and MP2 methods and show that they are either thermodynamically or kinetically stable with respect to various reactions including disproportionation. Energetics, geometries, and vibrational frequencies of singlet and triplet equilibrium structures and some transition states are calculated. The ground states of are all singlet except which is triplet and, with the possible exception of the ground states have a rhombic structure in which the X atoms are shared equally with each M atom. The ionization potentials of the species are significantly lower than those of the corresponding MX species suggesting that their chemistry may be significantly different.

Preference of cluster isomers as a result of quantum delocalization: Potential energy surfaces and intermolecular vibrational states of Ne⋯HBr, Ne⋯HI, and
View Description Hide DescriptionIntermolecular vibrational states are calculated for Ne⋯HBr, Ne⋯HI, and complexes using potential energy surfaces constructed by accurate ab initio methods. Potentials of rare gas–hydrogen halide clusters exhibit two collinear minima, one corresponding to hydrogen lying between the heavy atoms, and the other to hydrogen facing away from the rare gas atom. The relative depths of the two minima are a result of a subtle balance between polarization and dispersion interactions. Moreover, due to a large quantum delocalization in the hydrogen bending (librational) motion the relevance of a particular stationary point on the potential energy surface is only limited. It is more appropriate to discuss the isomers in terms of vibrationally averaged structures. For Ne⋯HBr the potential minimum and the vibrationally averaged structure correspond to the same isomer with hydrogen between neon and bromine. However, for Ne⋯HI the global minimum corresponds to the Ne–IH collinear geometry, while the vibrationally averaged structure has hydrogen between the heavy atoms. In the case of we show that one can flip between the two isomers by adding argon atoms, which reconciles the seemingly contradictory experimental results obtained for the photodissociation of HI⋯Ar on one side, and of large clusters on the other side.

Quantumclassical correspondence in the and reactions for total angular momentum
View Description Hide DescriptionA method for carrying out quasiclassical trajectory(QCT) calculations of reactive collisions for the special case of the total angular momentum is described. Since quantum reactive scattering calculations involving heavier atoms are not straightforward for the case, this method is useful to establish the extent to which classical mechanics is applicable to a particular reaction. The method is tested by comparing the results of trajectory calculations for the case with analogous quantummechanical (QM) calculations for the reaction and the reverse reaction The S4 potential surface, which is based on MRCI+Q/ccpVTZ energies scaled by the scaled external correlation method [B. Ramachandran et al., J. Chem. Phys. 111, 3862 (1999)], is used for these calculations. The QCT and QM cumulative reaction probabilities are found to be in good agreement, especially for the Cl+OH reaction. The agreement between the two types of stateresolved reaction probabilities is less striking but improves considerably as the initial diatomic rotational quantum number increases. A comparison is also made between the exact and QCT thermal rate coefficients. These are found to be in excellent agreement, which is in keeping with similar agreement observed in the case of the quantummechanical exact and thermal rate coefficients.

Infrared spectra and density functional calculations of platinum hydrides
View Description Hide DescriptionLaserablated and thermally evaporated Pt atoms react with to form which is characterized by infrared spectra of PtHD, and in solid argon and neon, and density functional theory calculations. The insertion reaction of Pt into dihydrogen is spontaneous on annealingsolid neon to 6–8 K and solid argon to 20–30 K. This observation requires spin–orbit coupling of the ground and excited states of Pt in the curvecrossing region to give the stable molecule. Laserablated Pt atoms with excess energy also react with to produce PtH. Further reactions of PtH with or with H atoms give evidence for a new asymmetric molecule, which is also characterized by isotopic substitution and frequency calculations.

Double proton transfer in the complex of acetic acid with methanol: Theory versus experiment
View Description Hide DescriptionTo test the approximate instanton approach to intermolecular protontransfer dynamics, we report multidimensional ab initio bimolecular rate constants of HH, HD, and DD exchange in the complex of acetic acid with methanol in tetrahydrofuran and compare them with the NMR(nuclear magnetic resonance) experiments of Gerritzen and Limbach. The bimolecular rate constants are evaluated as products of the exchange rates and the equilibrium rate constants of complex formation in solution. The two molecules form hydrogenbond bridges and the exchange occurs via concerted transfer of two protons. The dynamics of this transfer is evaluated in the complete space of 36 vibrational degrees of freedom. The geometries of the two isolated molecules, the complex, and the transition states corresponding to double proton transfer are fully optimized at QCISD (quadratic configuration interaction including single and double substitutions) level of theory, and the normalmode frequencies are calculated at MP2 (MøllerPlesset perturbation theory of second order) level with the 631G basis set. The presence of the solvent is taken into account via singlepoint calculations over the gas phase geometries with the PCM (polarized continuum model). The proton exchange rate constants, calculated with the instanton method, show the effect of the structure and strength of the hydrogen bonds, reflected in the coupling between the tunneling motion and the other vibrations of the complex. Comparison with experiment, which shows substantial kinetic isotopic effects (KIE), indicates that tunneling prevails over classic exchange for the whole temperature range of observation. The unusual behavior of the experimental KIE upon single and double deuterium substitution is well reproduced and is related to the synchronicity of twoatom tunneling.

Locally designed pulse shaping for selective preparation of enantiomers from their racemate
View Description Hide DescriptionWe present a method for the design of laser fields to control a selective preparation of enantiomers from their racemate. An expression for two components of the laser pulses and propagating along the Z axis is derived using a locally optimized control theory in the density operator formalism. This expression was applied to a selective preparation of (R, L) enantiomers from preoriented phosphinotioic acid at low temperatures. The target operator was set for the populations to be localized in one side of the doublewell potential. First, a simple onedimensional model was treated. Then, a twodimensional model in which a free rotation around the preoriented torsional axis is included was briefly considered. In the onedimensional model, almost complete preparation of the enantiomers was obtained. The optimal electric field consists of a sequence of two linearly polarized pulses with the same phases but with different magnitudes. This means that the resultant electric field is linearly polarized with the polarization for obtaining the Rform nearly parallel to its S–H bond. The optimal electric field transfers the Lform into the Rform while suppressing the reverse process. In the twodimensional model, the enantiomer selective preparation is controlled by a sequence of circularly polarized pulses.

Tautomerism of 6thioxanthine in the gas and aqueous phases using AM1 and PM3 methods
View Description Hide DescriptionHeats of formation, entropies,Gibbs free energies, relative tautomerization energies, tautomeric equilibrium constants, relative proton affinities, dipole moments, and ionization potentials for the fourteen possible tautomers of 6thioxanthine have been studied by using semiempirical AM1 and PM3 quantumchemical calculations at the selfconsistent field level, both in the gas and aqueous phases, with full geometry optimization. The conductorlike screening solvation model was employed for aqueous solution calculations. The calculations show that the two oxothione tautomers, TX (1,3,7) and TX (1,3,9), are the predominant species at room temperature in both phases, but the oxothione form is more stable than the oxothione form. The energy difference between TX (1,3,7) and TX (1,3,9) is predicted to be significantly lowered by the polar solution. The results are in good agreement with available experimental results. The entropy effect on the Gibbs free energy of the 6thioxanthine base is very small and has practically no significance for the tautomeric equilibrium of the base. The enthalpic term is dominant in the determination of the equilibrium constant. The protonation of 6thioxanthine in both phases occurs at the imidazole nitrogen (N7 or N9), then pyrimidine nitrogen (N1 or N3).

Ground and valence excited states of and transients: Ab initio geometries, electronic structures, and molecular properties
View Description Hide DescriptionGeometric and vibrational characterization of and systems have been done using fullvalence complete active space SCF (CASSCF) method. The Renner–Teller interaction parameter, ε, is calculated for Π electronic states with CASSCF potentials. Excitation energies with zeropoint corrections, electric field gradient (efg), and dipole moment, μ, are calculated using CASSCF, complete active space second order perturbation theory (CASPT2) and multireference singles and doubles configuration interaction (MRDCI) levels of theory. The fact that CASSCF values of the principal components and of the efg tensor listed through two quantities and are not very different from their CASPT2 counterparts, suggests that secondorder perturbation involving all singles and doubles over the onedimensional space spanned by the CASSCF wave function are not important for the efg and μ. However, the important contributions come from the higher excitations (triple, quadruples, etc.), which are included in MRDCI wave function, by taking multireference zerothorder wave function. The use of iterative natural orbital seems to be necessary to obtain stable values of the efg and μ in the MRDCI method.

Quantum wavepacket method for statetostate reactive cross sections
View Description Hide DescriptionWe present a 3D quantum wavepacket method for calculating statetostate reactive cross sections for the reaction. The method avoids the coordinate problem (of arrangements being difficult to represent by coordinates, and vice versa) by solving the reactantproduct decoupling (RPD) equations [T. Peng and J. Z. H. Zhang, J. Chem. Phys. 105, 6072 (1996)] in their further partitioned form [S. C. Althorpe, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. 107, 7816 (1997)]. These equations decouple the nuclear dynamics Schrödinger equation into separate reactant, stronginteraction, and product regions, permitting different coordinates to be used in each region. We solve the equations using Jacobi coordinates in the reactant region, and Jacobi coordinates in the stronginteraction and product regions. In test calculations on the reaction, we show that this partitioning of coordinate systems is much more efficient than using coordinates in the stronginteraction region (as was done in all previous applications of the RPD equations). We apply the method to the reaction (for and obtain the first statetostate differential cross sections to be calculated by an exact quantum wavepacket method. The method will allow statetostate cross sections to be calculated for the same reactions for which wavepacket methods can currently calculate total cross sections.

Photodissociation dynamics of at 157.6 nm. I. Experimental study using photofragment translational spectroscopy
View Description Hide DescriptionPhotofragment translational spectroscopy of at 157.6 nm was carried out using a crossed lasermolecular beams technique. Detected species are Br, Cl, and From the analyses of timeofflight (TOF) spectra for these three species, the molecules were found to dissociate competitively through and channels with the branching ratio of All of the and radicals were found to dissociate spontaneously to produce Cl or respectively. The angular distributions of these secondary products were found to be anisotropic. These fast secondary reactions are discussed on the basis of the calculated dissociation rates and rotational frequencies.