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Volume 121, Issue 23, 15 December 2004
 ARTICLES

 Theoretical Methods and Algorithms

Using preconditioned adaptive step size RungeKutta methods for solving the timedependent Schrödinger equation
View Description Hide DescriptionIf the Hamiltonian is time dependent it is common to solve the timedependent Schrödinger equation by dividing the propagation interval into slices and using an (e.g., split operator, Chebyshev, Lanczos) approximate matrix exponential within each slice. We show that a preconditioned adaptive step size RungeKutta method can be much more efficient. For a chirped laser pulse designed to favor the dissociation of HF the preconditioned adaptive step size RungeKutta method is about an order of magnitude more efficient than the time sliced method.

Curvysteps approach to constraintfree extendedLagrangian ab initio molecular dynamics, using atomcentered basis functions: Convergence toward Born–Oppenheimer trajectories
View Description Hide DescriptionA dynamical extension of the “curvysteps” approach to linearscaling selfconsistent field calculations is presented, which yields an extendedLagrangian formulation of ab initiomolecular dynamics. An exponential parametrization of the oneelectron density matrix, expressed in terms of atomcentered Gaussian basis functions, facilitates propagation along the manifold of density matrices in a geometrically correct fashion that automatically enforces idempotency constraints. The extended Lagrangian itself is constraint free, thus neither density matrix purification nor expensive, iterative solution for Lagrange multipliers is required. Propagation is highly efficient, and time steps compare favorably to those used in Car–Parrinello molecular dynamics simulations. The behavior of the method, especially with regard to the maintenance of adiabatic decoupling of nuclei and electrons, is examined for a sequence of diatomic molecules, and comparison is made to trajectories propagated on the converged Born–Oppenheimer surface. Certain claims to the contrary notwithstanding, our results demonstrate that vibrational frequencies may depend on the value of the fictitious mass parameter, even in an atomcentered basis. Lightatom stretching frequencies can be significantly redshifted, even when the nuclear and electronic energy scales are well separated. With a sufficiently small fictitious mass and a short time step, accurate frequencies can be obtained; we characterize appropriate values of these parameters for a wide range of vibrational frequencies.

A ground state potential energy surface for using Monte Carlo methods
View Description Hide DescriptionUsing variational Monte Carlo and a simple explicitly correlated wave function we have computed the Born–Oppenheimer energy of the ground state at 24 internuclear distances. We have also calculated the diagonal correction to the Born–Oppenheimer approximation and the lowestorder relativistic corrections at each distance using variational Monte Carlo techniques. The nonadiabatic values are evaluated from numerical derivatives of the wave function with respect to the nuclear coordinates. With this potential energy surface we have computed several of the lowest vibrationalrotational energies for this system. Our results are in good agreement with the best values found in the literature.

The curvature of the conical intersection seam: An approximate secondorder analysis
View Description Hide DescriptionWe present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born–Oppenheimer potentialenergysurface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potentialenergysurface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first and secondorder degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of symmetry—presented here for the first time—is found to be the global minimum in the intersection space.

Semiclassical Liouville method for the simulation of electronic transitions: Single ensemble formulation
View Description Hide DescriptionIn this paper, we describe a single ensemble implementation of the semiclassical Liouville method for simulating quantum processes using classical trajectories. In this approach, one ensemble of trajectories supports the evolution of all semiclassical density matrix elements, rather than employing a distinct ensemble for each. The ensemble evolves classically under a single reference Hamiltonian, which is chosen based on physical grounds; for electronic relaxation of an initially excited state, the initially populated upper surface Hamiltonian is the natural choice. Classical trajectories evolving on the reference potential then represent the timedependent upper state population density and also the electronic coherence and the ground state density created by electronic transition. The error made in the classical motion of the trajectories for these latter distributions is compensated for by incorporating the difference between the correct and reference Liouville propagators into the calculation of the coefficients of the individual trajectories. This approach gives very accurate results for a number of model problems and cases describing ultrafast electronic relaxation dynamics.

The approximation in density matrix functional and wave function theory
View Description Hide DescriptionVarious energyfunctionals applying the approximation which leads to twoindex twoelectron integrals instead of fourindex twoelectron integrals in the electron–electron interaction term of the electronic energy are presented. Numerical results of multiconfiguration selfconsistent field calculations for the best possible wave function are compared to those obtained from the pair excitation multiconfiguration selfconsistent (PEMCSCF) method and two versions of density matrix functionaltheory. One of these is derived making explicit use of some necessary conditions for N representability of the secondorder density matrix. It is shown that this method models the energyfunctional based on the best possible wave function with good accuracy. The calculations also indicate that only a minor fraction of the total correlationenergy is incorporated by approaches for larger molecules.

Multiresolution quantum chemistry: Basic theory and initial applications
View Description Hide DescriptionWe describe a multiresolution solver for the allelectron local density approximation KohnSham equations for general polyatomic molecules. The resulting solutions are obtained to a userspecified precision and the computational cost of applying all operators scales linearly with the number of parameters. The construction and use of separated forms for operators (here, the Green’s functions for the Poisson and boundstate Helmholtz equations) enable practical computation in three and higher dimensions. Initial applications include the alkaliearth atoms down to strontium and the water and benzene molecules.

HEAT: High accuracy extrapolated ab initio thermochemistry
View Description Hide DescriptionA theoretical model chemistry designed to achieve high accuracy for enthalpies of formation of atoms and small molecules is described. This approach is entirely independent of experimental data and contains no empirical scaling factors, and includes a treatment of electron correlation up to the full coupledcluster singles, doubles, triples and quadruples approach. Energies are further augmented by anharmonic zeropoint vibrational energies, a scalar relativistic correction, firstorder spin–orbit coupling, and the diagonal Born–Oppenheimer correction. The accuracy of the approach is assessed by several means. Enthalpies of formation (at 0 K) calculated for a test suite of 31 atoms and molecules via direct calculation of the corresponding elemental formationreactions are within 1 kJ mol^{−1} to experiment in all cases. Given the quite different bonding environments in the product and reactant sides of these reactions, the results strongly indicate that even greater accuracy may be expected in reactions that preserve (either exactly or approximately) the number and types of chemical bonds.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photochemistry of ethylene: A multireference configuration interaction investigation of the excitedstate energy surfaces
View Description Hide DescriptionMultireference configuration interaction with singles and doubles (MRCISD) calculations have been performed for the optimization of conical intersections and stationary points on the ethylene excitedstate energy surfaces using recently developed methods for the computation of analytic gradients and nonadiabatic coupling terms. Basis set dependence and the effect of various choices of reference spaces for the MRCISD calculations have been investigated. The crossing seam between the and states has been explored in detail. This seam connects all conical intersections presently known for ethylene. Major emphasis has been laid on the hydrogenmigration path. Starting in the state of twistedorthogonal ethylene, a barrierless path to ethylidene was found. The feasibility of ethylidene formation will be important for the explanation of the relative yield of cis and trans elimination.

Investigating the exciplexes, Density functional approach
View Description Hide DescriptionPotential curves for the ground and the first lowest excited states of the (where exciplexes are calculated using the density functional theory(DFT) formalism. Relativistic calculations are carried out with and without spinorbit (SO) coupling effect, using a zeroth order regular approximation (ZORA) approach. The depth and position parameters of the potential curves for the case without spinorbit effect are presented and compared with other works. Potential curves for LiHe, CsHe, and FrHe without spinorbit effect and CsHe with the spinorbit effect are shown. A bond analysis is presented too, since the central interest of the study of the exciplexes is the nature and the existence of the bonding states that are the origin of emission spectra observed experimentally for these systems.

Study of ab initio molecular data for inelastic and reactive collisions involving the quasimolecule
View Description Hide DescriptionThe lowest two ab initiopotential energy surfaces (PES), and the corresponding nonadiabatic couplings between them, have been obtained for the system; the molecular data are compared to those calculated with the diatomic in molecules (DIM) method. The form of the couplings is discussed in terms of the topology of the molecular structure of the triatomic. The method of Baer is employed to generate “diabatic” states and the residual nonadiabatic couplings are calculated. The ab initio results for these are markedly different from the corresponding DIM data, and show the need to consider the third PES.

Zeeman effect in
View Description Hide DescriptionThe Zeeman effect in the excited state of CaF is measured and analyzed over a wide range of magnetic fields. It is found that the splitting of the Zeeman levels is largely determined by the coupling between different rotational states and there are no lowfield seeking states in the manifold of Zeeman levels at high magnetic fields. A model of the Zeemanspectrum based on the ligandfield theory of CaF is shown to be accurate in the interval of magnetic fields 0–5 Tesla. This demonstrates that the magnetic moment of the molecule is effectively determined by the spin angular momentum of a single electron and the orbital motion of the valence electron around the core. An analysis of the Zeemanspectrum as a function of the molecular rotational constant indicates that molecules should have significant rotational constants (at least as large as twice the rotational constant of CaF) to be amenable to magnetic trapping in high fields.

Photodissociation of laboratory oriented molecules: Revealing molecular frame properties of nonaxial recoil
View Description Hide DescriptionWe report the photodissociation of laboratory oriented OCS molecules. A molecular beam of OCS molecules is hexapole stateselected and spatially oriented in the electric field of a velocity map imaging lens. The oriented OCS molecules are dissociated at 230 nm with the linear polarization set at 45° to the orientation direction of the OCS molecules. The photofragments are quantum stateselectively ionized by the same 230 nm pulse and the angular distribution is measured using the velocity map imaging technique. The observed images are strongly asymmetric and the degree of asymmetry varies with the CO rotational state J. From the observed asymmetry in the laboratory frame we can directly extract the molecular frame angles between the final photofragment recoil velocity and the permanent dipole moment and the transition dipole moment. The data for CO fragments with high rotational excitation reveal that the dissociation dynamics is highly nonaxial, even though conventional wisdom suggests that the nearly limiting β parameter results from fast axial recoil dynamics. From our data we can extract the relative contribution of parallel and perpendicular transitions at 230 nm excitation.

Absolute electronimpact total ionization cross sections of chlorofluoromethanes
View Description Hide DescriptionAn experimental study is reported on the electronimpact total ionization cross sections (TICSs) of and molecules. The kinetic energy of the colliding electrons was in the 10–85 eV range. TICSs were obtained as the sum of the partial ionization cross sections of all fragment ions, measured and identified in a linear double focusing timeofflightmass spectrometer. The resulting TICS profiles—as a function of the electronimpact energy—have been compared both with those computed by ab initio and (semi)empirical methods and with the available experimental data. The computational methods used include the binaryencounterBethe (BEB) modified to include atoms with principal quantum numbers the Deutsch and Märk (DM) formalism, and the modified additivity rule (MAR). It is concluded that both modified BEB and DM methods fit the experimental TICS for and to a high accuracy, in contrast with the poor accord of the MAR method. A discussion on the factors influencing the discrepancies of the fittings is presented.

A density functional study on nitrogendoped carbon clusters
View Description Hide DescriptionUsing molecular graphics software, we designed numerous models of Geometry optimization and calculation on vibration frequency were carried out by the B3LYP density functional method. After comparison of structure stability, we found that the structures of groundstate and are bent chains with a nitrogen atom at either end, whereas when the groundstateclusters show three branches, each with a nitrogen atom located at the end. When the longest branch of is polyacetylenelike. When or 7, the longest branch is connected to the central carbon in a nonlinear manner. The with an even number of carbon atoms are more stable than those with odd numbers, matching the peak pattern observed in laserinduced mass spectra of The trend of such odd/even alternation is explained based on concepts of bonding characteristics, electron affinities, and incremental binding energies.

The triplet state of cytosine and its derivatives: Electron impact and quantum chemical study
View Description Hide DescriptionThe excitation of the lowest electronic states and vibrational excitation of cytosine (C) have been studied using electron energy loss spectroscopy(EELS, 0–100 eV) with angular analysis. The singlet states have been found to be in good agreement with UVVIS absorption results on sublimed films, slightly blueshifted by about 0.1 eV. The EEL spectra recorded at residual energy below 2 eV show clear shoulders at energy losses of 3.50 and 4.25 eV (±0.1 eV). They are assigned to the lowest triplet electronic states of cytosine. Energies and molecular structures of the lowestlying triplet state of C and its methylated and halogenated and substituted derivatives F, Cl, and Br) have been studied using quantum chemical calculations with both molecular orbital and density functional methods, in conjunction with the and augccpVTZ basis sets. The tripletsinglet energy gap obtained using coupledcluster theory [CCSD(T)] and density functional theory(DFT) methods agrees well with those derived from EELS study. The first C’s vertical triplet state is located at 3.6 eV, in good agreement with experiment. The weak band observed at 4.25 eV is tentatively assigned to the second C’s vertical triplet excitation. For the substituted cytosines considered, the vertical triplet state is consistently centered at 3.0–3.2 eV above the corresponding singlet ground state but about 1.0 eV below the first excited singlet state. Geometrical relaxation involving outofplane distortions of hydrogen atoms leads to a stabilization of 0.6–1.0 eV in favor of the equilibrium triplet. The lowestlying adiabatic triplet states are located at 2.3–3.0 eV. Halogen substitution at both C(5) and C(6) positions tends to reduce the tripletsinglet separations whereas methylation tends to enlarge it. The vibrational modes of triplet cytosine and the ionization energies of substituted derivatives were also evaluated.

Lifetime of reactive scattering resonances: Qmatrix analysis and angular momentum dependence for the reaction by the hyperquantization algorithm
View Description Hide DescriptionWe report a study on the behavior with total angular momentumJ of several resonances occurring at collision energies below or slightly above the reaction barrier in the reaction.Resonance positions and widths are extracted from exact timeindependent quantum mechanical calculations using the hyperquantization algorithm and Smith’s Qmatrix formalism which exploits complete Smatrix information. The results confirm previous work but provide much greater insight. Identification of quasibound states responsible for the resonances based on adiabatic models for the longrange atom–molecule interactions both in the entrance and exit channels, is successful except for the feature occurring at the lowest energy, which is found to overlap with an exitchannel resonance for The two features are analyzed as overlapping resonances and their excellent Lorentzian fits, with wellbehaved Jdependences of positions and widths, support the interpretation of the lowenergy feature as a resonance to be associated to the triatomic transition state of the reaction.Resonance role on the reactive observables (integral cross sections and angular distributions) is investigated. The mechanism leading to forward scattering in the reactive differential cross section is commented, while the effects on rate constants, as well as the sensitivity of the resonancepattern to modification of the potential energy surface, are fully discussed elsewhere.

Steric asymmetry and lambdadoublet propensities in statetostate rotationally inelastic scattering of with He
View Description Hide DescriptionRelative integrated cross sections are measured for rotationally inelastic scattering of hexapole selected in the upper Λdoublet level of the ground rotational state in collisions with He at a nominal energy of 514 cm^{−1}. Application of a static electric fieldE in the scattering region, directed parallel or antiparallel to the relative velocity vector v, allows the stateselected NO molecule to be oriented with either the N end or the O end towards the incoming He atom. Laserinduced fluorescence detection of the final state of the NO molecule is used to determine the experimental steric asymmetry, which is equal to within a factor of (−1) to the molecular steric effect, The dependence of the integral inelastic cross section on the incoming Λdoublet component is also observed as a function of the final rotational spinorbit (Ω^{′}), and Λdoublet (ε^{′}) state. The measured steric asymmetries are significantly larger than previously observed for NOAr scattering, supporting earlier proposals that the repulsive part of the interaction potential is responsible for the steric asymmetry. In contrast to the case of scattering with Ar, the steric asymmetry of NOHe collisions is not very sensitive to the value of Ω^{′}. However, the Λdoublet propensities are very different for and transitions. Spinorbit manifold conserving collisions exhibit a propensity for parity conservation at low but spinorbit manifold changing collisions do not show this propensity. In conjunction with the experiments, statetostate cross sections for scattering of oriented molecules with He atoms are predicted from closecoupling calculations on restricted coupledcluster methods including single, double, and noniterated triple excitations [J. Klos, G. Chalasinski, M. T. Berry, R. Bukowski, and S. M. Cybulski, J. Chem. Phys. 112, 2195 (2000)] and correlated electronpair approximation [M. Yang and M. H. Alexander, J. Chem. Phys. 103, 6973 (1995)] potential energy surfaces. The calculated steric asymmetry of the inelastic cross sections at is in reasonable agreement with that derived from the present experimental measurements for both spinmanifold conserving and spinmanifold changing collisions, except that the overall sign of the effect is opposite. Additionally, calculated fieldfree integral cross sections for collisions at are compared to the experimental data of Joswig et al. [J. Chem. Phys. 85, 1904 (1986)]. Finally, the calculated differential cross section for collision energy is compared to experimental data of Westley et al. [J. Chem. Phys. 114, 2669 (2001)] for the spinorbit conserving transition

Crossed beams and theoretical studies of the dynamics of hyperthermal collisions between Ar and ethane
View Description Hide DescriptionCrossed molecular beams experiments and classical trajectory calculations have been used to study the dynamics of collisions at hyperthermal collision energies. Experimental timeofflight and angular distributions of ethane molecules that scatter into the backward hemisphere (with respect to their original direction in the centerofmass frame) have been collected. Translational energy distributions, derived from the timeofflight distributions, reveal that a substantial fraction of the collisions transfer abnormally large amounts of energy to internal excitation of ethane. The flux of the scattered ethane molecules increased only slightly from directly backward scattering to sideways scattering.Theoretical calculations show angular and translational energy distributions which are in reasonable agreement with the experimental results. These calculations have been used to examine the microscopic mechanism for large energy transfer collisions (“supercollisions”). Collinear (“headon”) or perpendicular (“sideon”) approaches of Ar to the C–C axis of ethane do not promote energy transfer as much as bent approaches, and collisions in which the H atom is “sandwiched” in a bent configuration lead to the largest energy transfer. The sensitivity of collisional energy transfer to the intramolecular potential energy of ethane has also been examined.

The rotational spectrum and dynamical structure of LiOH and LiOD: A combined laboratory and ab initio study
View Description Hide DescriptionMillimeter waverotational spectroscopy and ab initio calculations are used to explore the potential energy surface of LiOH and LiOD with particular emphasis on the bending states and bending potential. New measurements extend the observed rotational lines to for LiOH and for LiOD for all bendingvibrational states up to Rotationvibration energy levels, geometric expectation values, and dipole moments are calculated using extensive highlevel ab initio threedimensional potential energy and dipole momentsurfaces. Agreement between calculation and experiment is superb, with predicted values typically within 0.3%, D values within 0.2%, values within 0.7%, and dipole moments within 0.9% of experiment. Shifts in values with vibration and isotopic substitution are also well predicted. A combined theoretical and experimental structural analysis establishes the linear equilibrium structure with and Predicted fundamental vibrational frequencies are and for LiOH and and for LiOD. The molecule is extremely nonrigid with respect to angular deformation; the calculated deviation from linearity for the vibrationally averaged structure is 19.0° in the (000) state and 41.9° in the state. The calculation not only predicts, in agreement with previous work [P. R. Bunker, P. Jensen, A. Karpfen, and H. Lischka, J. Mol. Spectrosc. 135, 89 (1989)], a change from a linear to a bent minimum energy configuration at elongated Li–O distances, but also a similar change from linear to bent at elongated O–H distances.