Volume 117, Issue 12, 22 September 2002
 ARTICLES

 Theoretical Methods and Algorithms

Complex absorbing potentials in the framework of electron propagator theory. I. General formalism
View Description Hide DescriptionMetastable electronic states, ubiquitous in electron–molecule scattering and in ionization processes, still pose a serious challenge to theory. We suggest to make use of electron propagators and present a manyparticle theory that facilitates the direct computation of energy and decay width of electronic resonance states in molecular systems. A complex absorbing potential (CAP) is introduced to render resonancewave functions squareintegrable and, in this way, representable in standard basis sets. We perform a perturbative analysis, explicitly taking into account all diagrams up to third order, and then employ the algebraic diagrammatic construction (ADC) scheme to derive a numerically efficient and practical method for computing resonance parameters. We call this new method CAP/ADC.

Statistical sampling of semiclassical distributions: Calculating quantum mechanical effects using Metropolis Monte Carlo
View Description Hide DescriptionA statistical sampling method is proposed for computing oscillatory integrals associated with the semiclassical initial value representation. The semiclassical expression is rewritten as an integral over a phase distribution The phase distribution is obtained from Metropolis sampling of trajectories according to a properly chosen weight function. The averaging of oscillatory integrals is converted into a Monte Carlo algorithm where one diffuses through trajectory space. A histogram of phases is collect from importance sampling. Techniques of Metropolis Monte Carlo such as umbrella (or biased) sampling are generalized to the present context. From example calculations, phase distributions are seen to be multipeaked, thus clearly demonstrating the origin of quantum interference. Trajectories that are responsible for the interference patterns can be collected using this method.

From weak to strong interactions: A comprehensive analysis of the topological and energetic properties of the electron density distribution involving systems
View Description Hide DescriptionThe topological and energetic properties of the electron density distribution of the isolated pairwise interaction have been theoretically calculated at several geometries and represented against the corresponding internuclear distances. From long to short geometries, the results presented here lead to three characteristic regions, which correspond to three different interaction states. While the extreme regions are associated to pure closedshell (CS) and sharedshell (SS) interactions, the middle one has been related to the redistribution of between those electronic states. The analysis carried out with this system has permitted to associate the transit region between pure CS and SS interactions to internuclear geometries involved in the building of the H–F bonding molecular orbital. A comparative analysis between the formation of this orbital and the behavior of some characteristic properties has indicated their intrinsic correspondence, leading to the definition of a bond degree parameter and being the total electron energy density and the electron density value at the (3,−1) critical point]. Along with the isolated pairwise interaction, 79 (neutral, positively and negatively charged) complexes have been also theoretically considered and analyzed in terms of relevant topological and energetic properties of found at their critical points. In particular, the interaction energies of pure CS interactions have been estimated by using the bond degree parameter. On the other hand, the proton transfergeometry has been related to the local maximum of the electron kinetic energy density

Failure of densityfunctional theory and timedependent densityfunctional theory for large extended π systems
View Description Hide DescriptionDensityfunctional theory(DFT) is widely used for studying large systems such as metals, semiconductors, and large molecules, with timedependent densityfunctional theory becoming a very powerful tool for investigating molecular excited states. As part of a systematic study of both the intrinsic weaknesses of DFT and the weaknesses of present implementations, we consider its application to the one and twodimensional conjugated π systems: polyacetylene fragments and oligoporphyrins, respectively. Very poor results are obtained for the calculated spectra, and polyacetylene is predicted by all functionals considered, including gradientcorrected functionals, to have a triplet ground state. The cause of this is linked to known problems of existing density functionals concerning nonlocality and asymptotic behavior which result in the highestoccupied molecularorbital being too high in energy so that semiconductors and lowbandgap insulators are predicted to have metallike properties. The failure of modern density functionals to predict qualitatively realistic molecular hyperpolarizabilities for extended systems is closely related.

Relativistic density functional theory using Gaussian basis sets
View Description Hide DescriptionA fourcomponent formulation of relativistic density functional theory is presented together with the details of its implemention using a spinor basis set. The technical features of this approach are compared to those found in the nonrelativistic density functional theory of quantum chemistry which employ scalar basis sets of Gaussiantype functions. Numerical results of the spinor expansion method are presented for a sequence of closedshell atoms, and for a selection of relativistic density functionals, and are compared with finite difference benchmarks.

Deviations from the Boltzmann distribution in small microcanonical quantum systems: Two approximate oneparticle energy distributions
View Description Hide DescriptionThe Boltzmann distribution, which accurately describes the exponential energy dependence of the canonical ensemble, only describes the distribution of oneparticle energies for a microcanonical system in the large system limit. We present two distribution functions which closely approximate the distribution of allowed oneparticle energies in weakly coupled microcanonical quantum systems. One function is exact for a set of identical harmonic oscillators. The second function is a generalization of work by Andersen et al. [J. Chem. Phys. 114, 6518 (2001)] and is exact for a system with constant microcanonical heat capacity. We compare these two functions with enumerated probabilities for three model systems. The model system distributions and both approximate functions become exponential for large systems but differ from the Boltzmann distribution most dramatically at high energy, for which states can be considerably less populated than predicted by the Boltzmann distribution. Corrections to the Boltzmann distribution may be important in unimolecular reactions, fragmentation dynamics, and in the spectroscopy of nanoclusters.

Direct diabatization of electronic states by the fourfold way. II. Dynamical correlation and rearrangement processes
View Description Hide DescriptionDiabatic representation of coupled potential energy surfaces and their scalar couplings provides a compact and convenient starting point for dynamics calculations carried out in either the adiabatic or diabatic representation. In a previous paper we presented a general, pathindependent scheme, called the fourfold way, for calculating diabatic surfaces and their scalar couplings from adiabatic surfaces and electronic density matrices such that the manifold of diabatic states spans the variationally optimized space of a finite number of adiabatic states. In the present paper we extend that scheme in these ways: (1) We show how to include dynamical electronic correlation energy by multireference perturbation theory or configuration interaction based on a complete active reference space. (2) We present a more general strategy for treating rearrangements. (3) We present consistency criteria for testing the validity of the assumptions for a particular choice of reference geometries, diabatic molecular orbital (DMO) ordering, dominant configurationstatefunction lists, and choice(s) for reference DMO(s) for systems involving rearrangements. The first extension is illustrated by multiconfiguration quasidegenerate perturbation theory (MCQDPT) calculations on LiF, and all three extensions are illustrated by MCQDPT calculations on the reaction

Kramers–Fokker–Planck equation for polyatomic molecules
View Description Hide DescriptionStarting from the microscopic Hamiltonian of a whole solution system, we have derived a Kramers–Fokker–Planck (KFP) equation for polyatomic molecules by using Zubarev’s techinique of nonequilibrium statistical distribution function. For the purpose, a set of normal coordinates of a solute molecule is defined at a stationary point on the free energy surface. In the normal coordinate representation, the expression of the KFP equation includes not only the deformation originating in the Coriolis coupling but also the frictiontensor inducing a new type of coupling. For demonstration, two examples are examined. First, under the approximation of adiabatic elimination of fast variables, a onedimensional KFP equation is derived from the above KFP equation, which corresponds to the equation that Kramers first derived intuitively for onedimensional chemical reactionmodel in solution. Second, assuming a model system which describes simultaneously a couple of vibrational and rotational motions, a twodimensional KFP equation is solved numerically to investigate the role of the frictiontensor. It is found that the offdiagonal friction coupling reduces the diagonal friction influence.

Fragment charge difference method for estimating donor–acceptor electronic coupling: Application to DNA πstacks
View Description Hide DescriptionThe purpose of this communication is twofold. We introduce the fragment charge difference (FCD) method to estimate the electron transfer matrix element between a donor D and an acceptor A, and we apply this method to several aspects of hole transfer electronic couplings in πstacks of DNA, including systems with several donor–acceptor sites. Within the twostate model, our scheme can be simplified to recover a convenient estimate of the electron transfer matrix element based on the vertical excitation energy and the charge difference between donor and acceptor. For systems with strong charge separation, one should resort to the FCD method. As favorable feature, we demonstrate the stability of the FCD approach for systems which require an approach beyond the twostate model. On the basis of ab initio calculations of various DNA related systems, we compared three approaches for estimating the electronic coupling: the minimum splitting method, the generalized Mulliken–Hush (GMH) scheme, and the FCD approach. We studied the sensitivity of FCD and GMH couplings to the donor–acceptor energy gap and found both schemes to be quite robust; they are applicable also in cases where donor and acceptor states are off resonance. In the application to πstacks of DNA, we demonstrated for the Watson–Crick pair dimer [(GC),(GC)] how structural changes considerably affect the coupling strength of electron hole transfer. For models of three Watson–Crick pairs, we showed that the twostate model significantly overestimates the hole transfer coupling whereas simultaneous treatment of several states leads to satisfactory results.

Combining ab initio and density functional theories with semiempirical methods
View Description Hide DescriptionFor large reactive systems, the calculation of energies can be simplified by treating the active part with a highlevel quantum mechanical (QM) (ab initio or density functional) approach and the environment with a less sophisticated semiempirical (SE) approach, as an improvement over the widely used hybrid quantum mechanical/molecular mechanical (QM/MM) methods. An example is the interaction between an active region of an enzyme and its immediate environment. One such method is the original “OurownNlayer Integrated molecular Orbital+Molecular Mechanics (ONIOM)” approach. In this paper, the interaction between the QM and SE region is described explicitly by two different schemes. In the iterative QM/SE schemes (QM/SEI), the electrostatic interaction and polarization effects are introduced explicitly for both the QM and SE atoms by a selfconsistent procedure based on either polarizable point charges or the electron density. In the noniterative QM/SE scheme, based on the ONIOM model (QM/SEO), the exchange (Pauli repulsion) and charge transfer effects are taken into account at the SE level, in addition to the explicit electrostatic interaction and polarization between the two regions. Test calculations are made on a number of model systems (including small polar or charged molecules interacting with water and proton transfer reactions in the presence of polar molecules or an extended hydrogenbond network). The quantitative accuracy of the results depend on several parameters, such as the chargescaling/normalization factors for the SE charge and the QM/SE van der Waals parameters, which can be chosen to optimize the result. For the QM/SEO approach, the results are more sensitive to the quality of the SE level (e.g., selfconsistentcharge densityfunctionaltightbinding vs AM1) than the explicit interaction between QM and SE atoms.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Rubidium–xenon spin exchange and relaxation rates measured at high pressure and high magnetic field
View Description Hide DescriptionThe production of hyperpolarized Xe via spin exchange with optically pumped Rb atoms was studied at 47 000 G under highpressure conditions. From variable pressure and temperature studies, the spin exchange efficiency was found to be pressure dependent and lower than comparable lowfield measurements. Spin exchange due to short binary collisions is expected to be pressure independent, and the cross section was measured to be The pressure dependent component was attributed to the formation of Rb–Xe van der Waals (vdW) complexes. The rate constant for spin exchange in Rb–Xe vdW complexes was measured to be in He buffer gas. This value is comparable, though somewhat smaller than vdW rates measured previously for other buffer gases. While it is well known that spin exchange occurs readily in vdW complexes when vdW spin exchange at fields >10 000 G is not accounted for in current theories. Modulation of the hyperfine interaction during the vdW complex lifetime is proposed to account for these observations. Finally, relaxation by the walls of the pumping cell was found to increase with buffer gas pressure. These factors impact the equilibrium Xe polarization obtainable with highfield optical pumping.

Timedependent quantum wave packet study of the H+DCN→HD+CN reaction
View Description Hide DescriptionTimedependent wave packet calculation for the reaction H+DCN→HD+CN is carried out using the semirigid vibrating rotor target model [J. Z. H. Zhang, J. Chem. Phys. 111, 3929 (1999)] on the TSH3 potential energy surface [J. Chem. Phys. 105, 558 (1996)]. Reaction probabilities are calculated from various initial rovibrational states of the reagent. Reaction cross sections and rate constants are calculated and are compared with the previous results for the isotopic reaction H+HCN on the same potential energy surface.

The nucleation behavior of supercooled water vapor in helium
View Description Hide DescriptionThe nucleation behavior of supersaturated water vapor in helium is experimentally investigated in the temperature range of 200–240 K. The experiments are performed using a pulse expansion wave tube. The experimental results show a sharp transition in the nucleation rates at 207 K. We suggest that the transition is due to the transition of vapor/liquid to vapor/solid nucleation (ordered with decreasing temperature). A qualitative theoretical explanation is given based on the classical nucleation theory and the surface energy of ice.

Reactions of with and their isotopic variants: Rate constants and the production yields of H(D) atoms
View Description Hide DescriptionThe reactions of with and their isotopic variants were examined. was produced by energy transfer from while was produced by twophoton excitation of ground state The rate constant for the deactivation of can be determined by measuring the decay profiles of under the conditions that equilibration between and can be assumed. The detection of was accomplished by a laserinduced fluorescence technique by utilizing the state as an upper state. The rate constants for the quenching of by and were determined to be and respectively. H(D) atoms were identified as reaction products by a twophotonlaserinduced fluorescence technique. The yields for the production of H(D) atoms from and were both determined to be under the assumption that the only exit for is the production of two H(D) atoms. No preferential production of H or D atoms was observed in the reaction with suggesting that the reaction proceeds via bound intermediate complexes.

A connection between quantum critical points and classical separatracies of electronic states
View Description Hide DescriptionWave functions for oneelectron diatomic molecules such as and are analyzed by Bader’s atoms in molecules method. The locations of the degenerate axial critical points in the electron density generated from states arising from the united atom manifolds are shown to correspond well with the boundaries of domains obtained solely from a classical description of the electron motion. The relationship clarifies the connection between the atomic and molecular regimes of classical trajectories and the quantum description of the states. In particular, the classical transition from atomic to molecular character roughly corresponds to the appearance of a critical point in the electron density located on the internuclear axis between the nuclei. The global aspects of the relationship between the classical and quantum descriptions helps to demonstrate the classical framework of the quantum picture.

Fourier transform microwave spectroscopy of the radical
View Description Hide DescriptionThe hyperfine resolved rotational spectrum of the radical in the ground electronic state has been observed for the first time using a Fourier transformmicrowave spectrometer in combination with a pulsed discharge nozzle. The radical was produced by discharging a mixture of and diluted in either Ar or Ne. A total of 25 hyperfine components of the and transitions have been measured which enabled us to precisely determine hyperfine coupling constants for both phosphorus and hydrogen nuclei. Spin densities on the phosphorus and βcarbon atoms, estimated from the hyperfine coupling constants, suggest that the radical forms an allenic structure (CP double bond) that is modified by a phosphoryl structure (CP triple bond), which is consistent with the theoretical estimation obtained previously by an ab initio calculation. The nature of the CP chemical bond in the radical is investigated in comparison with the corresponding nitrogen bearing counterparts.

Vibrational interactions of acetonitrile: Doubly vibrationally resonant IR–IR–visible fourwavemixing spectroscopy
View Description Hide DescriptionThe origin of the vibrational coupling that was observed between the CC and CN stretching modes of acetonitrile by doubly vibrationally enhanced (DOVE) IR–IR–Vis fourwavemixing (IIVFWM) spectroscopy is investigated by various ab initio calculations including DFT(B3LYP), HF, and MP2 methods with the same baisis set, The linear and nonlinear susceptibilities of the combination bands and cross peaks are numerically calculated and compared with the experimental values, and the agreement between ab initio results and experiments are quantitative. By separately analyzing the contributions from each coherence pathway to the vibrational coupling of the CC and CN stretching modes, a quantitative understanding of the DOVE IIVFWM signals is possible. Although the direct coupling of the CC and CN stretching modes by mechanical and electric anharmonicity coupling is sizable, the CH bending and CH stretching modes are also involved in the vibrational coupling between CC and CN stretching modes as promoting modes. The numerically simulated twodimensional (2D) DOVE spectrum for a sample is presented and compared with experiment. It is found that the interference among distinctive pathways plays a central role in describing the distorted, asymmetric shape of the 2D DOVE spectrum. In addition, the IIVFWM cross peak associated with the vibrational coupling between the CH and CN stretching mode is also calculated and its magnitude is compared with that of the CC and CN stretching modes.

The rotational spectra of oxirane⋯xenon isotopomers): Bond energy and dynamics of Xe
View Description Hide DescriptionThe pulsed jet millimeter wave spectra of five isotopomers of the weakly bonded oxirane⋯Xe complex have been measured. Information on the equilibrium conformation,dynamics and dissociation energy have been deduced. The equilibrium distance of Xe with respect to the centerofmass of the molecules is 3.82 Å, with Xe tilted 15° from the perpendicular to the centerofmass of the ring toward the oxygen atom. The dissociation energy is estimated, from the centrifugal distortion constant to be ≈3.9 kJ/mol.

The dynamics of formation of HCl products from the reaction of Cl atoms with methanol, ethanol, and dimethyl ether
View Description Hide DescriptionThe dynamics of ground stateatom reactions with methanol, methanolethanol, and dimethyl ether have been studied both experimentally and theoretically. The reactions were photoinitiated by 355 nm photolysis of to produce monoenergetic atoms that react with ground electronic state organic molecules under single collision conditions. The rotational quantum state population distributions of the nascent products were probed by resonanceenhanced multiphoton ionization in a timeofflight mass spectrometer. Nascent products from reaction of Cl atoms with methanol, methanol ethanol, and dimethyl ether, at mean collision energies in the range of 5.6–6.7 kcal/mol, exhibit distributions of population over rotational levels that all peak at The average rotational energies of the products for the respective reactions are and (1σ uncertainties). Ab initio calculations were performed in order to examine the mechanisms of Cl atom abstraction of hydrogen from the alcohols and ether. Optimized geometrical structures and vibrational frequencies of molecular complexes and transition states on the reaction pathways were obtained at the MP2/6311G(d,p) level and their energies were further refined at the G2 level of theory. Comparisons are drawn between the mechanisms and energetic pathways of the various reactions. The degree of rotational excitation of the HCl, which is significantly greater than for Cl atom abstraction of an H atom from alkanes, is attributed to a dipole–dipole interaction between the HCl and RCHOR^{′} (R, or moieties in the products’ region of the potential energy surface.

Classical trajectory calculations for collisionenergy/electronenergy resolved twodimensional Penning ionization electron spectra of CO, and with metastable atoms
View Description Hide DescriptionCollisionenergy/electronenergy resolved twodimensional Penning ionization electron spectra (2DPIES) of CO, and with metastable atoms are measured, and classical trajectory calculations with anisotropic entrance and exit potential energy surfaces are performed for these systems. Numerical qualities of the entrance potential surfaces are decisively important to understand the collisional ionizationdynamics as well as to reproduce observed 2DPIES, whereas the exit potential surfaces are less sensitive to the collisional ionizationdynamics and the electron spectra except for special cases in which a deep potential well is relevant in the entrance potential surface.Ab initio calculations of both entrance and exit potentials as well as ionization widths are found to be reliable in obtaining their anisotropy and radial dependence with good quantitative accuracy.