Volume 121, Issue 2, 08 July 2004
 COMMUNICATIONS


Evidence for a bound halo molecule by diffraction from a transmission grating
View Description Hide DescriptionThe van der Waals complex has been identified in a molecular beam produced by a cryogenic free jet expansion of a 1% mixture in 99% gas. The weakly bound complexes in the beam are identified via their first order diffraction angles after passing through a 100 nm period transmission grating. An electron impact mass spectrometeranalysis of the diffraction patterns is used to discriminate against ion fragments of the constituent gas clusters.

Exploring molecular complexity: Conical intersections and photodissociation
View Description Hide DescriptionThe role of conical intersections in the photodissociation of the state of is investigated using extended atomic basis sets and a configuration state function expansion of approximately 8.5 million terms. A previously unknown portion of the seam of conical intersections with only symmetry is located. This portion of the seam is readily accessible from the equilibrium geometry of the state. These conical intersections are expected to play a role in the competition between adiabatic and nonadiabatic pathways for photodissociation.

Tetrasulfur, Rotational spectrum, interchange tunneling, and geometrical structure
View Description Hide DescriptionThe rotational spectrum of has been observed for the first time in an electrical discharge through sulfur vapor. Two techniques have been used: Fourier transformmicrowave spectroscopy and longpath millimeterwave absorption spectroscopy. Small, but systematic shifts of the measured transition frequencies of the normal isotopic species indicate that has symmetry but with a lowlying transition state of symmetry, yielding interchange tunneling at 14.1(2) kHz in its ground vibrational state. From the rotational constants of the normal and the single isotopic species, an experimental structure has been derived: is a singlet planar trapezoid with a terminal bond length of 1.899(7) Å, a central bond of 2.173(32) Å, and an SSS angle of 103.9(8)°. Like thiozone is a candidate for detection in the atmosphere of the Jovian moon Io and in other astronomical sources.
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 ARTICLES

 Theoretical Methods and Algorithms

Higher order and infinite Trotternumber extrapolations in path integral Monte Carlo
View Description Hide DescriptionImprovements beyond the primitive approximation in the path integral Monte Carlo method are explored both in a model problem and in real systems. Two different strategies are studied: The Richardson extrapolation on top of the path integral Monte Carlo data and the TakahashiImada action. The Richardson extrapolation, mainly combined with the primitive action, always reduces the numberofbeads dependence, helps in determining the approach to the dominant power law behavior, and all without additional computational cost. The TakahashiImada action has been tested in two hardcore interacting quantum liquids at low temperature. The results obtained show that the fourthorder behavior near the asymptote is conserved, and that the use of this improved action reduces the computing time with respect to the primitive approximation.

Cumulative isomerization probability studied by various transition state wave packet methods including the MCTDH algorithm. Benchmark: isomerization
View Description Hide DescriptionThe 3D cumulative isomerization probability for the transfer of a light particle between two atoms is computed by one timeindependent and two timedependent versions of the transition state wave packet (TSWP) method. The timeindependent method is based on the direct expansion of the microcanonical projection operator on Chebyshev polynomials. In the timedependent TSWP methods, the propagations are carried out by the split operator scheme and the multiconfiguration timedependent Hartree (MCTDH) algorithm. This is the very first implementation of the TSWP method in the Heidelberg MCTDH package [G. W. Worth, M. H. Beck, A. Jäckle, and H.D. Meyer, The MCDTH package, Version 8.2 (2000); H.D Meyer, Version 8.3 (2002). See http://www.pci.uniheidelberg.de/tc/usr/mctdh/]. The benchmark is the isomerization for zero total angular momentum. Particular insights are given into the tunneling region. In larger systems, the timedependent version of TSWP making use of the MCTDH algorithm will permit to treat more and more modes quantum mechanically, for very accurate results. Therefore, it was important to calibrate the implementation. Besides, we also assess the efficiency of a reduced dimensionality approach by comparing the new exact 3D calculations of for the isomerization with results obtained via 1D or 2D active subspaces. This suggests that, it should be possible to take directly benefit of the present 3D approaches, adapted for triatomic Jacobi coordinates to compute for Htransfer in larger systems, via three active coordinates. The prerequisite is then the simplification of the reduced 3D kinetic energy operator with rigid constraint to take the form corresponding to a pseudo triatomic system in Jacobi coordinates with effective masses. This last step is checked in the methoxy radical and malonaldehyde. Finally, different ways to obtain reliable eigenvectors of the flux operator associated with a dividing surface are revisited.

Asymptotic correction of the exchange–correlation kernel of timedependent density functional theory for longrange chargetransfer excitations
View Description Hide DescriptionTimedependent density functional theory (TDDFT) calculations of chargetransferexcitation energies are significantly in error when the adiabatic local density approximation (ALDA) is employed for the exchange–correlation kernel We relate the error to the physical meaning of the orbital energy of the Kohn–Sham lowest unoccupied molecular orbital (LUMO). The LUMO orbital energy in Kohn–Sham DFT—in contrast to the Hartree–Fock model—approximates an excited electron, which is correct for excitations in compact molecules. In CT transitions the energy of the LUMO of the acceptor molecule should instead describe an added electron, i.e., approximate the electron affinity. To obtain a contribution that compensates for the difference, a specific divergence of is required in rigorous TDDFT, and a suitable asymptotically correct form of the kernel is proposed. The importance of the asymptotic correction of is demonstrated with the calculation of for the prototype diatomic system HeBe at various separations The TDDFT–ALDA curve roughly resembles the benchmark ab initio curve of a configuration interaction calculation with single and double excitations in the region where a sizable He–Be interaction exists, but exhibits the wrong behavior at large R. The TDDFT curve obtained with however approaches closely in the region Then, the adequate rigorous TDDFT approach should interpolate between the LDA/GGA ALDA xc kernel for excitations in compact systems and for weakly interacting fragments and suitable interpolation expressions are considered.

Dissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin and harmonic baths
View Description Hide DescriptionThe dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the surrogate Hamiltonian approach. This method is based on constructing a system–bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results are compared to calculations that include a finite number of harmonic modes carried out by using the multiconfiguration timedependent Hartree method of Nest and Meyer [J. Chem. Phys. 119, 24 (2003)]. In the weak coupling regime, at zero temperature and for small excitations of the primary system, both methods converge to the Markovian limit. When initially the primary system is significantly excited, the spin bath can saturate restricting the energy acceptance. An interaction term between bath modes that spreads the excitation eliminates the saturation. The loss of phase between two cat states has been analyzed and the results for the spin and harmonic baths are almost identical. For stronger couplings, the dynamics induced by the two types of baths deviate. The accumulation and degree of entanglement between the bath modes have been characterized. Only in the spin bath the dynamics generate entanglement between the bath modes.

Classical spin and quantummechanical descriptions of geometric spin frustration
View Description Hide DescriptionGeometric spin frustration (GSF) in isolated plaquettes with local spin s, i.e., an equilateraltriangle spin trimer and a regulartetrahedron spin tetramer, was examined on the basis of classical spin and quantummechanical descriptions to clarify their differences and similarities. An analytical proof was given for how the state degeneracy and the total spin S of their ground states depend on the local spin s. The quantummechanical conditions for the occurrence of GSF in isolated plaquettes were clarified, and their implications were explored. Corner sharing between plaquettes and how it affects GSF in the resulting spin systems was examined.

Efficient and reliable numerical integration of exchangecorrelation energies and potentials
View Description Hide DescriptionAn adaptive numerical integrator for the exchangecorrelation energy and potential is presented. It uses the diagonal elements of the exchangecorrelation potential matrix as a grid generating function. The only input parameter is the requested grid tolerance. In combination with a defined cell function the adaptive grid generation scales almost linear with the number of basis functions in a system. With the adaptive numerical integrator the selfconsistent field energy error, which is due to the numerical integration of the exchangecorrelation energy, converges with increasing adaptive grid size to a reference value. The performance of the adaptive numerical integration is analyzed using molecules with first, second, and third row elements. Especially for transition metal systems the adaptive numerical integrator shows considerably improved performance and reliability.

Potential energy surface discontinuities in local correlation methods
View Description Hide DescriptionWe have examined the occurence of discontinuities in bondbreaking potential energy surfaces given by local correlation methods based on the Pulay–Saebø orbital domain approach. Our analysis focuses on three prototypical dissociating systems: the CF bond in fluoromethane, the CC bond in singlet, ketene, and the central CC bond in propadienone. We find that such discontinuities do not occur in cases of homolytic bond cleavage due to the inability of the Pipek–Mezey orbital localization method to separate singletcoupled charges on distant fragments. However, for heterolytic bond cleavage, such as that observed in singlet ketene and propadienone, discontinuities occur both at stretched geometries and near equilibrium. These discontinuities are usually small, but may be of the same order of magnitude as the localization error in some cases.

Parallel iterative reaction path optimization in ab initio quantum mechanical/molecular mechanical modeling of enzyme reactions
View Description Hide DescriptionThe determination of reaction paths for enzyme systems remains a great challenge for current computational methods. In this paper we present an efficient method for the determination of minimum energy reaction paths with the ab initio quantum mechanical/molecular mechanical approach. Our method is based on an adaptation of the path optimization procedure by Ayala and Schlegel for small molecules in gas phase, the iterative quantum mechanical/molecular mechanical (QM/MM) optimization method developed earlier in our laboratory and the introduction of a new metric defining the distance between different structures in the configuration space. In this method we represent the reaction path by a discrete set of structures. For each structure we partition the atoms into a core set that usually includes the QM subsystem and an environment set that usually includes the MM subsystem. These two sets are optimized iteratively: the core set is optimized to approximate the reaction path while the environment set is optimized to the corresponding energy minimum. In the optimization of the core set of atoms for the reaction path, we introduce a new metric to define the distances between the points on the reaction path, which excludes the soft degrees of freedom from the environment set and includes extra weights on coordinates describing chemical changes. Because the reaction path is represented by discrete structures and the optimization for each can be performed individually with very limited coupling, our method can be executed in a natural and efficient parallelization, with each processor handling one of the structures. We demonstrate the applicability and efficiency of our method by testing it on two systems previously studied by our group, triosephosphate isomerase and 4oxalocrotonate tautomerase. In both cases the minimum energy paths for both enzymes agree with the previously reported paths.

Quantumclassical dynamics of scattering processes in adiabatic and diabatic representations
View Description Hide DescriptionWe demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantumclassical approach, for simulating scattering processes on a quasiJahn–Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The timedependent Schrödinger equation and classical equations of motion are solved selfconsistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantumclassical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive statetostate transition probabilities, along with calculations on an adiabatic surface with ordinary Born–Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations.

NonHermitian quantum mechanics: Wave packet propagation on autoionizing potential energy surfaces
View Description Hide DescriptionThe correspondence between the timedependent and timeindependent molecular dynamic formalisms is shown for autoionizing processes. We demonstrate that the definition of the inner product in nonHermitian quantum mechanics plays a key role in the proof. When the final state of the process is dissociative, it is technically favorable to introduce a complex absorbing potential into the calculations. The conditions which this potential should fulfill are briefly discussed. An illustrative numerical example is presented involving three potential energy surfaces.

A multidimensional discrete variable representation basis obtained by simultaneous diagonalization
View Description Hide DescriptionDirect product basis functions are frequently used in quantum dynamics calculations, but they are poor in the sense that many such functions are required to converge a spectrum, compute a rate constant, etc. Much better, contracted, basis functions, that account for coupling between coordinates, can be obtained by diagonalizing reduced dimension Hamiltonians. If a direct product basis is used, it is advantageous to use discrete variable representation (DVR) basis functions because matrix representations of functions of coordinates are diagonal in the DVR. By diagonalizing matrices representing coordinates it is straightforward to obtain the DVR that corresponds to any direct product basis. Because contracted basis functions are eigenfunctions of reduced dimension Hamiltonians that include coupling terms they are not direct product functions. The advantages of contracted basis functions and the advantages of the DVR therefore appear to be mutually exclusive. A DVR that corresponds to contracted functions is unknown. In this paper we propose such a DVR. It spans the same space as a contracted basis, but in it matrix representations of coordinates are diagonal. The DVR basis functions are chosen to achieve maximal diagonality of coordinate matrices. We assess the accuracy of this DVR by applying it to model fourdimensional problems.

Analytical energy gradients for local secondorder Møller–Plesset perturbation theory using density fitting approximations
View Description Hide DescriptionAn efficient method to compute analytical energy derivatives for local secondorder Møller–Plesset perturbation energy is presented. Density fitting approximations are employed for all 4index integrals and their derivatives. Using local fitting approximations, quadratic scaling with molecular size and cubic scaling with basis set size for a given molecule is achieved. The density fitting approximations have a negligible effect on the accuracy of optimized equilibrium structures or computed energy differences. The method can be applied to much larger molecules and basis sets than any previous secondorder Møller–Plesset gradient program. The efficiency and accuracy of the method is demonstrated for a number of organic molecules as well as for molecular clusters. Examples of geometry optimizations for molecules with 100 atoms and over 2000 basis functions without symmetry are presented.

Density functional theory study of H and interacting with NiAl(110)
View Description Hide DescriptionWe present results of extensive density functional theory(DFT) calculations for H and interacting with NiAl(110). Continuous representations of the full dimensional potential energy surface (PES) for the H/NiAl(110) and systems are obtained by interpolation of the DFT results using the corrugation reducing procedure. We find a minimum activation energy barrier of ∼300 meV for dissociativeadsorption of which is consistent with the energy threshold obtained in molecular beam experiments for (ν=0). We explain vibrational enhancement observed in experiments as the consequence of vibrational softening in the entrance channel over the most reactive surface site. The PES shows a high surface site selectivity: for energies up to 0.1 eV above threshold, adsorption can only take place around topNi sites (within a circle of radius ∼0.3 Å). A strong energetic corrugation is observed: energy barriers for dissociation vary by more than 1 eV between the most and the least reactive sites. In contrast, geometric corrugation is much less pronounced and comparable to that of low index single metal surfaces like Cu or Pt.

A simple model for NMR relaxation in the presence of internal motions with dynamical coupling
View Description Hide DescriptionIn this paper some effects of dynamical coupling between two interactioncarrying vectors on the internal auto and crosscorrelation functions are investigated in the limit of small amplitude motions. A linearized Langevin approach allows the derivation of explicit expressions for these correlation functions and for the corresponding order parameters.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Selective infrared photodissociation of protonated parafluorophenol isomers: Substitution effects in oxonium and fluoronium ions
View Description Hide DescriptionIsomerselective infrared photodissociation (IRPD) spectra are obtained for the first time for protonated polyfunctional aromatic molecules isolated in the gas phase. IRPD spectra of the oxonium and fluoronium isomers of protonated parafluorophenol were separately obtained by monitoring resonant photoinduced and HF loss, respectively. Analysis of the F–H, O–H, and C–H stretch wave numbers provides valuable spectroscopic information on the chemical properties of these reactive intermediates, in particular on the substitution effects of functional groups.

Free energy perturbation study of water dimer dissociation kinetics
View Description Hide DescriptionAn efficient approach is described for using accurate ab initio calculations to determine the rates of elementary condensation and evaporation processes that lead to nucleation of aqueous aerosols. The feasibility of the method is demonstrated in an application to evaporation rates of water dimer at 230 K. The method, known as ABCFEP (ab initio/classical free energyperturbation), begins with a calculation of the potential of mean force for the dissociation (evaporation) of small water clusters using a molecular dynamics (MD) simulation with a model potential. The free energyperturbation is used to calculate how changing from the model potential to a potential calculated from ab initio methods would alter the potential of mean force. The difference in free energy is the Boltzmannweighted average of the difference between the ab initio and classical potential energies, with the average taken over a sample of configurations from the MD simulation. In principle, the method does not require a highly accurate model potential, though more accurate potentials require fewer configurations to achieve a small sampling error in the free energyperturbation step. To test the feasibility of obtaining accurate potentials of mean force from ab initio calculations at a modest number of configurations, the free energyperturbation method has been used to correct the errors when some standard models for bulk water (SPC, TIP4P, and are applied to water dimer. To allow a thorough exploration of sampling issues, a highly accurate fit to results of accurate ab initio calculations, known as SAPT5s, as been used a proxy for the ab initio calculations. It is shown that accurate values for a point on the potential of mean force can be obtained from any of the water models using ab initio calculations at only 50 configurations. Thus, this method allows accurate simulations of small clusters without the need to develop water models specifically for clusters.

On the interconversion pathway of
View Description Hide DescriptionThe potential energy surfaces have been constructed for the and states of HBO by using the multireference perturbation theory with the basis set ccpVTZ Two stationary points and a transition state have been characterized on all the three surfaces, which are in good agreement with available experiments and previous calculations. The interconversion pathways from metastable boron hydroxide BOH to the considerably more stable HBO are expounded based on the nature of the surfaces.