Volume 114, Issue 23, 15 June 2001
 ARTICLES

 Theoretical Methods and Algorithms

Towards a molecular logic machine
View Description Hide DescriptionFinite state logic machines can be realized by pump–probe spectroscopic experiments on an isolated molecule. The most elaborate setup, a Turing machine, can be programmed to carry out a specific computation. We argue that a molecule can be similarly programmed, and provide examples using two photonspectroscopies. The states of the molecule serve as the possible states of the head of the Turing machine and the physics of the problem determines the possible instructions of the program. The tape is written in an alphabet that allows the listing of the different pump and probe signals that are applied in a given experiment. Different experiments using the same set of molecular levels correspond to different tapes that can be read and processed by the same head and program. The analogy to a Turing machine is not a mechanical one and is not completely molecular because the tape is not part of the molecular machine. We therefore also discuss molecular finite state machines, such as sequential devices, for which the tape is not part of the machine. Nonmolecular tapes allow for quite long input sequences with a rich alphabet (at the level of 7 bits) and laser pulse shaping experiments provide concrete examples. Single molecule spectroscopies show that a single molecule can be repeatedly cycled through a logical operation.

Diffusion into a pair of reactive spheres with firstorder reaction
View Description Hide DescriptionExact series solutions for the reaction rates of two identical spherical sinks immersed in an infinite medium are presented for both reactantimpenetrable and penetrable particles based on the method of twin spherical expansion. The reaction rates are explicitly expressed in terms of the interparticle distance from reaction to diffusionlimited conditions. The effect of the ratio of the diffusivities inside and outside the sink is investigated. The existence of the second particle influences the reaction rate most substantially for the external diffusionlimited condition. The exact solutions are used to evaluate the accuracy of simple, analytical approximations obtained by including the first few multipole contributions only. The result by keeping terms up to quadrupole level gives values in excellent agreement with the exact solution.

Introduction of nelectron valence states for multireference perturbation theory
View Description Hide DescriptionThe present work presents three secondorder perturbative developments from a complete active space (CAS) zeroorder wave function, which are strictly additive with respect to molecular dissociation and intruder state free. They differ by the degree of contraction of the outerspace perturbers. Two types of zeroorder Hamiltonians are proposed, both are bielectronic, incorporating the interactions between electrons in the active orbitals, therefore introducing a rational balance between the zeroorder wave function and the outerspace. The use of Dyall’s Hamiltonian, which puts the active electrons in a fixed core field, and of a partially contracted formalism seems a promising compromise. The formalism is generalizable to multireference spaces which are parts of a CAS. A few test applications of the simplest variant developed in this paper illustrate its potentialities.

Power series expansion of the roots of a secular equation containing symbolic elements: Computer algebra and Moseley’s law
View Description Hide DescriptionWe use computer algebra to expand the Pekeris secular determinant for twoelectron atoms symbolically, to produce an explicit polynomial in the energy parameter ε, with coefficients that are polynomials in the nuclear charge Z. Repeated differentiation of the polynomial, followed by a simple transformation, gives a series for ε in decreasing powers of Z. The leading term is linear, consistent with wellknown behavior that corresponds to the approximate quadratic dependence of ionization potential on atomic number (Moseley’s law). Evaluating the 12term series for individual Z gives the roots to a precision of 10 or more digits for This suggests the use of similar tactics to construct formulas for roots vs atomic, molecular, and variational parameters in other eigenvalue problems, in accordance with the general objectives of gradient theory. Matrix elements can be represented by symbols in the secular determinants, enabling the use of analytical expressions for the molecular integrals in the differentiation of the explicit polynomials. The mathematical and computational techniques include modular arithmetic to handle matrix and polynomial operations, and unrestricted precision arithmetic to overcome severe digital erosion. These are likely to find many further applications in computational chemistry.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Calculation of ion mobilities from electrospray ionization highfield asymmetric waveform ion mobility spectrometry mass spectrometry
View Description Hide DescriptionCareful analysis is made of the accuracies possible when gaseous ion mobilities are determined from data obtained by combining electrospray ionization (ESI), highfield asymmetric waveform ion mobility spectrometry (FAIMS) at atmospheric pressure and room temperature, and mass spectrometry(MS). New results are reported for the mobilities of positive and negative amino acid ions in air at elevated values of the ratio of the electric field strength to the gas number density.

Quantum Monte Carlo studies of the structure and spectroscopy of van der Waals complexes
View Description Hide DescriptionAdiabatic rigidbody diffusionMonte Carlo is used to study the structure and spectroscopy of complexes of with several neon atoms. Although the potential energy surfaces for these systems have many lowlying minima, the ground statewave functions are localized in the global minimum. This trend is found to persist in the first few vibrationally excited states of Lowlying vibrational states that are localized in the potential minimum that corresponds to the linear Ne–OH/D–Ne configuration of the complex are also found.

Photodissociation spectroscopy of –acetaldehyde
View Description Hide DescriptionWe have investigated the photodissociation spectroscopy of the –acetaldehyde bimolecular complex over the spectral range 220–400 nm. We find evidence for four distinct absorption bands in the near ultraviolet that correlate with based and acetaldehydebased transitions. Our results suggest that the centered and acetaldehydecentered transitions are mixed, and result in significant vibrational excitation in the complex leading to broad and unresolved absorption bands. In contrast, the predominantly based excitation bands, assigned as and each show prominent vibrational progressions identified with intermolecular wagging modes of the complex. These intermolecular wag progressions are short and anharmonic indicating low barriers to isomerization. In the band several higher frequency vibrational modes are also active and have been assigned to the intermolecular stretch, a CCO deformation mode, and the C–O stretch.

Relative stabilities of the two isomers of the methanolwater dimer: The effects of the internal rotations of the hydroxyl and methyl groups of methanol
View Description Hide DescriptionThe groundstate energies of the two isomers of the methanolwater dimer, with waterdonor (WM) and methanoldonor (MW) structures, have been calculated using the diffusionMonte Carlo (DMC) method with constraint dynamics. Unlike the rigidbody DMC, this method permits the internal rotations of the hydroxyl and methyl groups of methanol about the C–O bond. The DMC calculations were performed for the isotopomers and The calculations with the internal rotation of the methyl and hydroxyl groups of methanol included resulted in a much larger groundstateenergy gap between the WM and MW isomers than those in which these internal rotations were frozen. This result demonstrated the critical importance of including the internal hydroxyl and methyl rotations in the DMC calculations aimed at predicting accurately the relative stabilities of the two isomers of the methanolwater dimer.

Interaction of benzene (Bz) with Pt and A theoretical study on and clusters
View Description Hide DescriptionExtensive ab initio calculations have been carried out on benzene (Bz)–platinum complexes and using a variety of computational techniques. Both physisorbed structures and energetically lower chemisorbed species were found. Complete active space multiconfiguration selfconsistent field (CASMCSCF), multireference singles and doubles configurationinteraction (MRSDCI), density functional(DFT), and Møller–Plessett second order perturbation (MP2) calculations were employed to predict structures. While the DFT and MP2 calculations also consistent with the MRSDCI techniques predict chemisorbed structures to be lower, the CASMCSCF method seems to favor physisorbed structures. The effect of spinorbit coupling on the binding energies of complexes with the Pt atom and the dimer were considered. The computed dissociation energies are consistent with the relative abundance of these clusters found in the timeofflightmass spectra. The lowenergy staircase structures of and complexes found in this study could be electrically conducting.

Ultrafast spectroscopy of wavelengthdependent coherent photoionization cross sections of Li_{2} wave packets in the state: The role of Rydberg states
View Description Hide DescriptionThe significance of Rydberg states in the probing (via ionization) of wave packets has been studied through quantitativemeasurements of the relative coherent ionization cross sections in a twocolor pump–probe femtosecond experiment. Following the preparation of a single intermediate rovibronic state with a cw laser, a femtosecond pump pulse (around 800 nm) creates a single twostate rotational wave packet by coherent excitation of the and 29) states. The wave packet is then probed through ionization using timedelayed, wavelength tunable pulses (in the region 508–690 nm) while the total energy of the system is kept below the dissociation limit of The backgroundfree coherent ionization yield (for each probe wavelength) is measured as the relative oscillation amplitude of the single quantum beat timedependent signal. The experimental results closely follow a relatively simple theoretical model, which is based on the assumption that the coherent ionization predominantly takes place via the excitation of highn bound singly excited Rydberg states in the ionization continuum converging to the ground electronic state of The best interpretation is that the highnRydberg states (above undergo collisional ionization or autoionization and contribute to the measured coherent ionization signal, while the lownRydberg states undergo predissociation and do not contribute to the measured signal. An implication of the results is that the final states of the system, accessed by the above probe pulses, can be better approximated by a corresponding set of isolated discrete levels rather than by a continuum. This conclusion is important to experimental, as well as theoretical, coherent control and wave packet dynamics studies, in particular, when phase and amplitudeshaped pump and probe pulses are employed. This study is also the first to investigate ionization of lithium dimer slightly below the shelf region with visible light.

A direct approach to one photon interference contributions in the coherent control of photodissociation
View Description Hide DescriptionFormally exact quantum mechanical expressions for cumulative transition matrix elements central to one photoncoherent control scenarios of photodissociation, are derived. The resultant approach bypasses the need for solving the complete statetostate quantum mechanical reactive scattering problem to obtain control results. These exact expressions are implemented both quantum mechanically and via a semiclassical initial value representation method to investigate coherent control in the generic photodissociation of a triatomic into more than one product. The semiclassical approach is shown to provide an accurate description of bimolecular control in this system.

Laserinduced fluorescence of nascent CH from ultraviolet photodissociation of HCCO and the absolute rate coefficient of the reaction over the range
View Description Hide DescriptionThe absolute rate coefficient of the gasphase reaction was determined over the temperature range 296–839 K and at a pressure helium. The experiments were performed in a slowflow kinetic apparatus employing pulsed photolysis of at 193 nm as a source of HCCO radicals. Reaction time profiles of [HCCO] were constructed using a newly developed, sensitive spectroscopic technique in the visible spectral region to detect this radical: laser—induced fluorescence of nascent photofragments following HCCO photodissociation at 266 nm. Photodissociation of HCCO at this wavelength was found to produce rotationally excited populated to The rate coefficient for the title reaction was found to be described by (2σ errors). The absorption cross section of HCCO at 266 nm, was also determined relative to that of at 193 nm as

Capture rates for collisions of C and Ge with unsaturated hydrocarbons
View Description Hide DescriptionWe have calculated the capture rate coefficients for collisions of C and Ge with unsaturated hydrocarbons and compared them with the experiments of Husain and coworkers [Clary, Haider, Husain, and Kabir, Astrophys. J. 422, 416 (1994); Husain, Ioannou, and Kabir, Z. Phys. Chemie 203, 213 (1998)]. Our findings indicate (i) that all nine electronic surfaces for the C reactions must contribute to the observed reaction rate coefficients, (ii) a central multipole approach is inappropriate for calculating the capture rate coefficients involving the larger hydrocarbons, (iii) the trends observed in the measured rate coefficients for the Ge and C reactions can simply be understood in terms of the physical size of the hydrocarbons, and (iv) the electrostatic interaction plays a significant role in the determination of capture rate coefficients for reactions involving C and highly polar species as well as acetylene.

Electronic and infrared spectra of and cyclic in neon matrices
View Description Hide DescriptionThe electronic transition of the propargyl cation with the origin band at 267.8(2) nm has been identified in a neon matrix at 5 K. The frequencies of the two modes excited in the upper state are 667(50) and 1629(50) cm^{−1} and imply a reduction of symmetry from in the ground state to in the excited state. The most intense IR mode of the propargyl cation is observed at 2079.9(1.0) cm^{−1} and for the cyclopropenyl cation at 3130.4(1.0) cm^{−1}. Ab initio calculations on the excited states of the two isomer cations support the assignment and explain why the electronic transition could not be observed for the cyclic species; it lies below 200 nm. The and absorptions of the neutral propargyl radical have also been observed with origin bands at 351.9(2) and 343.0(2) nm, respectively. These results provide the basis for the study of these astrophysically interesting species in the gas phase.

Fullerene Are there still more isomers?
View Description Hide DescriptionA theoretical investigation of fullerene using density functional theory is presented. Following the isolated pentagon rule (IPR), seven different topologies are considered. Calculated energy differences are less than 30 kJ/mol except for topology which is more unstable. Isomers of and topology are found to have singlet ground states. Calculated nuclear magnetic resonance and electronic absorption spectra allow to identify the two known isomers as and in agreement with previous assignments. The absolute configuration of the chiral isomer is predicted by means of the calculated electronic circular dichroism spectrum. The results further suggest that the isomer might be accessible from soots. All other IPR isomers are either diradicals or have nearly zero singlet–triplet splittings. These species are expected to polymerize, forming insoluble solids. The classification of fullerenes according to their gap is analyzed, and computational methods for treating small gap cases are discussed.

and atom formation dynamics of allyl bromide and chloride at 234 nm
View Description Hide DescriptionThe photodissociation dynamics of allyl bromide and chloride have been investigated at 234 nm using a twodimensional photofragment ion imaging technique coupled with a resonanceenhanced multiphoton ionization scheme. After absorbing a photon, allyl bromide dissociates into exclusively via the repulsive surfaces. The enhanced contribution of the singlet state to the initial transition is attributed to intensity borrowing from the nearby state. Trimodal translational energy distributions of have been observed after the photolysis of allyl chloride. Lowvelocity components with Boltzmann shapes are produced via internal conversion between the initially pumped state and the vibrationally excited ground state. Middlevelocity components with Gaussian shapes originated from curve crossing between the bound state and the dissociative state. Highvelocity components are produced via curve crossing from the state to the state. The enhanced curve crossings in exit channels are attributed to the nonplanar geometry of the parent molecule and torsional torque induced by the initial transition. The location of the curve crossing between the state and the state has been estimated to be based on the localized available energy.

Spectroscopic constants and potential energy curves of and
View Description Hide DescriptionPotential energy curves and spectroscopic constants for 45 lowlying electronic states of 18 electronic states of and 2 lowlying states of have been computed using the complete active space multiconfiguration selfconsistent field followed by the multireference configuration interaction calculations that included up to 17 million configurations. The equilibrium distances vibrational frequencies and energy separations are reported. We have also computed the properties of the two lowest electronic states of Possible assignments are suggested for the recently observed fragmentation spectra and threephoton fragmentation spectra of as well as the spectra of The dissociation energies and ionization potentials of and as well as electron affinities of are computed. The nature of bonding is discussed using the wave function composition and Mulliken population analysis.

Nuclear quadrupole moments for and derived from fourcomponent molecular coupled cluster calculations
View Description Hide DescriptionIn this work we investigate different approaches for calculating electric field gradients in order to provide accurate theoretical values for the nuclear quadrupole moments (NQM) for aluminum and gallium. Electron correlation is included in a fully fourcomponent framework at the CCSD(T) level. The resulting NQM for is in good agreement with earlier work, while the value for is higher than suggested on basis of previous molecular calculations.

Ab initio calculation of predissociation linewidths in the Schumann–Runge bands of the oxygen molecule
View Description Hide DescriptionAb initio multireference single and doubleexcitation configuration interaction calculations have been carried out for potential curves of the and electronic states of the molecule. Spinorbit interaction matrix elements among the above states and rotational interaction matrix elements between the and the states have been evaluated in order to investigate the observed line broadening in the Schumann–Runge bands. Predissociationlinewidths of rovibrational levels of the state are determined by using the complex rotation method in conjunction with the Gauss–Hermite quadrature procedure. It has been found that the and states play dominant roles in the predissociation of the state. The calculated linewidths for rovibrational levels of of the finestructure components of the state are in very good agreement with experimental results. Isotopic effects in the predissociation of the state are studied by means of calculations for and and the theoretical results are found to be in good agreement with the observed average predissociationlinewidths in each case.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Diffusion in phase space with molecular friction: A numerical study for undercooled liquids
View Description Hide DescriptionWe present a molecular dynamic simulation (MD) to study relaxations in a LennardJones liquid with an additional molecular friction term. To avoid crystallization the atomic size is varied. The simulation is done for a fixed density. The problems of MDsimulations in undercooled systems with a Newtonian friction term and under conservation of the total momentum are overcome by our analysis. The origin of friction terms in a more microscopical approach is discussed. We calculate trajectories connecting the minima in the phase space of the total system. It is shown that both structural relaxations and vibrations of atoms around their fixed positions can be analyzed by those socalled pseudotrajectories used here. The size of cooperatively rearranging regions and the length of jumps between neighbored structures are studied.