Volume 111, Issue 8, 22 August 1999
 THEORETICAL METHODS AND ALGORITHMS


Correlated electron extracule densities in position and momentum spaces
View Description Hide DescriptionSpherically averaged extracule densities in position, and momentum, spaces have been calculated for the atoms helium to neon starting from explicitly correlated wave functions. Correlated values for the electron–electron counterbalance density in position, and in momentum, spaces, and also for the expectation values and are reported. A systematic study of the electronic correlation has been performed by comparing the correlated results with the corresponding Hartree–Fock ones.

A closure for the Ornstein–Zernike relation that gives rise to the thermodynamic consistency
View Description Hide DescriptionA closure is proposed for the direct correlation function in the grand canonical ensembletheory that gives rise to the thermodynamic consistency, by which it is meant that identical results are obtained when the equations of state are calculated via the virial and compressibility routes, respectively, and when the excess chemical potentials are calculated by means of the thermodynamic derivative and the statistical mechanical formula, respectively. The integral equation for the pair correlation function under the closure is analytically solved in the case of hard spheres. The equation of state for hard spheres turns out to have the same form as that in the scaled particle theory or the compressibility equation of state in the Percus–Yevick theory although the present closure is quite different from that of the Percus–Yevick theory. The excess chemical potential is also found in the same form as that in the scaled particle theory. It seems to suggest that the present closure produces an integral equationtheory equivalent to the scaled particle theory.

The Schrödinger formulation of the Feynman path centroid density
View Description Hide DescriptionWe present an analysis of the Feynman path centroid density that provides new insight into the correspondence between the path integral and the Schrödinger formulations of statistical mechanics. The path centroid density is a central concept for several approximations (centroid molecular dynamics, quantum transitionstate theory, and pure quantum selfconsistent harmonic approximation) that are used in path integral studies of thermodynamic and dynamical properties of quantum particles. The centroid density is related to the quasistatic response of the equilibrium system to an external force. The path centroid dispersion is the canonical correlation of the position operator, which measures the linear change in the mean position of a quantum particle upon the application of a constant external force. At low temperatures, this quantity provides an approximation to the excitation energy of the quantum system. In the zero temperature limit, the particle’s probability density obtained by fixed centroid path integrals corresponds to the probability density of minimum energy wave packets, whose average energy defines the Feynman effective classical potential.

Control of reaction rate by asymmetric twostate noise
View Description Hide DescriptionWe revisit the far from equilibrium escape problem across a fluctuating potential barrier that is driven by asymmetric, unbiased dichotomous noise. Our closed analytical solution for arbitrary noise strengths reveals new aspects of the socalled “resonantactivation” effect and leads to interesting implications regarding far from equilibrium or externally controlledchemical reaction processes. Specifically, a genuine asymmetryinduced variant of resonant activation within the constant intensity scaling scheme is discovered, and a new possibility to manipulate reaction rates and yields, as well as the balance between reactants and products, is put forward.

The accuracy of current density functionals for the calculation of electric field gradients: A comparison with ab initio methods for HCl and CuCl
View Description Hide DescriptionThe performance of current density functionals is analyzed in detail for the electric field gradients (EFG) of hydrogen chloride and copper chloride by comparison with ab initio methods and available experimental data. The range of density functionals applied shows good agreement with coupled cluster H and Cl field gradients for HCl, as has been demonstrated previously for other maingroup element containing compounds. However, the performance of most density functionals is very poor for the Cu EFG in CuCl (EFG for Cu 0.44 a.u. at the coupledcluster singles and doubles with perturbative triples [CCSD(T)] level, compared to, e.g., +0.54 a.u. at the BLYP level). Only the “halfandhalf” hybrid functionals give field gradients with the correct sign. The reason for the poor performance of the density functional theory is analyzed in detail comparing density functional with ab initio total electronic densities Due to the conservation of the number of particles, a change in the valence part of the electron density can lead to changes in the core part of the density. Errors in valence electronic properties like the dipole moment and in core properties like the Cu and Cl EFGs may therefore be connected. In fact the errors in both properties show a distinct linear relationship, indicating that if the dipole moment is correctly described by density functionals, the Cu and Cl EFGs may be accurate as well. Furthermore, at the atomic level, electric field gradients are described with reasonable accuracy by current density functionals as calculations for the excited state and the ground state show. A comparison between the different density functionals shows that the incorrect behavior of the electronic density appears to be mainly due to defects in the exchange part of the functional.

NonMarkovian evolution of the density operator in the presence of strong laser fields
View Description Hide DescriptionWe present an accurate, efficient, and flexible method for propagating spatially distributed density matrices in anharmonic potentials interacting with solvent and strong fields. The method is based on the Nakajima–Zwanzig projection operator formalism with a correlated reference state of the bath that takes memory effects and initial/final correlations to second order in the system–bath interaction into account. A key feature of the method proposed is a special parametrization of the bath spectral density leading to a set of coupled equations for primary and N auxiliary density matrices. These coupled master equations can be solved numerically by representing the density operator in eigenrepresentation or on a coordinate space grid, using the Fourier method to calculate the action of the kinetic and potential energy operators, and a combination of split operator and Cayley implicit method to compute the time evolution. The key advantages of the method are: (1) The system potential may consist of any number of electronic states, either bound or dissociative. (2) The cost for arbitrarily long solvent memories is equal to only times that of propagating a Markovian density matrix. (3) The method can treat explicitly timedependent system Hamiltonians nonperturbatively, making the method applicable to strong fieldspectroscopy,photodissociation, and coherent control in a solvent surrounding. (4) The method is not restricted to special forms of system–bath interactions. Choosing as an illustrative example the asymmetric twolevel system, we compare our numerical results with full pathintegral results and we show the importance of initial correlations and the effects of strong fields onto the relaxation. Contrary to a Markovian theory, our method incorporates memory effects, correlations in the initial and final state, and effects of strong fields onto the relaxation; and is yet much more effective than path integral calculations. It is thus wellsuited to study chemical systems interacting with femtosecond short laser pulses, where the conditions for a Markovian theory are often violated.

The generalized Heitler–London theory for the potential energy surface
View Description Hide DescriptionA systematic perturbation theory has been developed to analyze the terms contributing to the potential energy surface.Group theory is used to find the irreducible representations of the Hamiltonian matrix elements which then are decoupled to their simplest level. In the case of diatomic molecules, this approach leads naturally to the Generalized Heitler–London (GHL) theory derived previously [K. T. Tang and J. P. Toennies, J. Chem. Phys. 95, 5918 (1991)]. Many previous semiempirical potential surfaces for the triatomic system including the well known LEPS surface are examined in the light of the present results. In particular, the Cashion–Herschbach (or diatomicsinmolecules without overlap) surface is shown to encompass far more information than previously recognized. The new theory now contains all the terms needed for an exact perturbation calculation of the potential energy surface.

Calculating excess chemical potentials using dynamic simulations in the fourth dimension
View Description Hide DescriptionA general method for computing excess chemical potentials is presented. The excess chemical potential of a solute or ligand molecule is estimated from the potential of meanforce (PMF) calculated along a nonphysical fourth spatial dimension,w, into which the molecule is gradually inserted or from which it is gradually abstracted. According to this “4DPMF” (four dimensional) scheme, the free energy difference between two limiting states defines the excess chemical potential: At the molecule is not interacting with the rest of the system, whereas at it is fully interacting. Use of a fourth dimension avoids the numerical instability in the equations of motion encountered upon growing or shrinking solute atoms in conventional free energy perturbation simulations performed in three dimensions, while benefiting from the efficient sampling of configurational space afforded by PMF calculations. The applicability and usefulness of the method are illustrated with calculations of the hydration free energy of simple LennardJones (LJ) solutes, a water molecule, and camphor, using molecular dynamics simulations and umbrella sampling. Physical insight into the nature of the PMF profiles is gained from a continuum treatment of short and longrange interactions. The shortrange barrier for dissolution of a LJ solute in the added dimension provides an apparent surface tension of the solute. An approximation to the longrange behavior of the PMF profiles is made in terms of a continuum treatment of LJ dispersion and electrostatic interactions. Such an analysis saves the need for configurational sampling in the longrange limit of the fourth dimension. The 4DPMF method of calculating excess chemical potentials should be useful for neutral solute and ligand molecules with a wide range of sizes, shapes, and polarities.

Constraints upon natural spin orbital functionals imposed by properties of a homogeneous electron gas
View Description Hide DescriptionThe expression where are the occupation numbers of natural spin orbitals, and and are the corresponding Coulomb and exchange integrals, respectively, generalizes both the Hartree–Fock approximation for the electron–electron repulsion energy and the recently introduced Goedecker–Umrigar (GU) functional. Stringent constraints upon the form of the scaling function are imposed by the properties of a homogeneous electron gas. The stability and Nrepresentability of the 1matrix demand that for any homogeneous of degree β [i.e., In addition, the Lieb–Oxford bound for asserts that where for The GU functional, which corresponds to does not give rise to admissible solutions of the Euler equation describing a spinunpolarized homogeneous electron gas of any density. Inequalities valid for more general forms of are also derived.

Topology of electron–electron interactions in atoms and molecules. III. Morphology of electron intracule density in two states of the hydrogen molecule
View Description Hide DescriptionThe differences in electronic structures of two states of the hydrogen molecule are vividly reflected in their intracule densities The groundstatewave function of is associated with two distinct topologies of (one of which pertains to the united atom limit), whereas no fewer than 11 unequivalent sets of critical entities are found for of the EF state that involves multiple electronic configurations. These sets and the catastrophes that interrelate them, which arise from conflicts between topological features of pertinent to different configurations, are characterized in detail. The usefulness of topological analysis of in the detection and characterization of various types of electron correlation is demonstrated.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Multidimensional tunneling dynamics on HSiOH cistrans isomerization with interpolated potential energy surface
View Description Hide DescriptionThe ab initiopotential energy surface (PES) for the HSiOH cistransisomerization was generated by the modified Shepard interpolation method at the computational level of the complete active space selfconsistent field (CASSCF) method. This isomerization has three reaction paths, i.e., one inplane and two outofplane paths, so the reactionpath PES (RPPES) has first been generated by setting reference points on these paths for the interpolation. In this RPPES, there is an artifact of potential ridges between the inplane and outofplane paths. By adding molecular configurations around potential ridges as reference points, the global PES has been much improved (the potential ridges have disappeared). Following trajectory simulations on this fulldimensional PES, the energy level shift of vibrational ground states due to tunneling was estimated by the semiclassical method. It is verified that there is a relatively large tunneling effect in this reaction, which is consistent with the experimental observations.

Structure and potential energy surface for
View Description Hide DescriptionAttention is focused on the complex as part of a study of containing complexes, which have been implicated in the formation of sporadic sodium layers in the upper atmosphere. The equilibrium structure is found to be linear, in agreement with previous studies. A potential energy hypersurface is calculated at the CCSD(T)/augccpVTZ level of theory, where the moiety is held fixed, but a wide range of Jacobi bond lengths and bond angles are sampled. This hypersurface is fitted to an analytic form and from this anharmonic vibrational separations are calculated, and compared to harmonic values. Rovibrational energy levels are also calculated from the fitted hypersurface. The best estimate of the interaction energy, is and

Solvent mediated vibrational relaxation: Superfluid helium droplet spectroscopy of HCN dimer
View Description Hide DescriptionRotationally resolved infrared spectra are reported for the HCN dimer, grown and solvated in liquid heliumdroplets. This is the first study for which two different vibrational modes within the same liquid helium solvated molecule have been observed, namely those associated with the “free” and the “hydrogenbonded” C–H stretching vibrations. Comparing the line broadening in these two bands, we conclude that the heliumsolvent plays an important role in the vibrational relaxation dynamics of the dimer. The rotational constants obtained from these spectra indicate that the dimer rotates more slowly in the liquid than in the gas phase.

Photoionization of methanol dimer using a tunable vacuum ultraviolet laser
View Description Hide DescriptionMethanol dimer ion–molecule reaction is initialized by VUV (vacuum ultraviolet) laser photoionization. The proton and deuteron transfers are the dominant reactions. The relative probabilities of deuteron transfer from the methyl group and proton from the hydroxyl group were measured as a function of VUVphotonenergy between 10.91 to 10.49 eV. According to those results, the probability of proton transfer from the hydroxyl group increases with the VUVphotonenergy. Isotopic scrambling is not complete before dissociation of the ion complex in the photonenergy used. In addition, ab initio calculations are performed and four stable structures of the methanol dimer ion are found. One of these structures is an unreported complex, which has a very unusual type of hydrogen bond. This complex plays a significant role in the deuteron transfer reaction in the range of excitation energies used in this study.

Photodissociation dynamics of the propargyl radical
View Description Hide DescriptionThe photochemistry and photodissociation dynamics of the propargyl radical, upon UV excitation is investigated by time and frequencyresolved detection of hydrogen atoms. From a statistical analysis of the data, we conclude that formation of cyclopropenylidene, is the dominant reaction channel. Around 22% of the excess energy is released into the translational degrees of freedom. By varying the excitation energy between 265 and 240 nm, microcanonical rates for the loss of a hydrogen atom can be obtained as a function of excess energy. The experimental rates, on the order of several are in good agreement with Rice–Ramsperger–Kassel–Marcus (RRKM) calculations, provided a scaling factor is used for the vibrational frequencies, to account for the effects of anharmonicity. The interpretation is confirmed in experiments using monodeuterated propargyl radicals, indicating a mechanism that proceeds via an initial [1,2] Hshift, followed by cyclization.

Fourier transform emission spectroscopy and ab initio calculations on OsN
View Description Hide DescriptionThe emission spectrum of OsN has been recorded in the 3000–13 000 cm^{−1} region using a Fourier transform spectrometer. OsN molecules were excited in an osmium hollow cathode lamp operated with neon gas and a trace of nitrogen. Six bands observed in the 8000–12 200 cm^{−1} region have been classified into three transitions, and with the 0–0 band origins near 8381.7, 11 147.9, and 12 127.2 cm^{−1}, respectively. A rotational analysis of these bands provides the following equilibrium constants for the ground electronic state: and Ab initio calculations have been performed on OsN and the spectroscopicproperties of the lowlying electronic states have been calculated. Our assignments are supported by these calculations. The ground state of OsN has been identified as a state consistent with the observations for the isoelectronic IrC molecule [Jansson et al., Chem. Phys. Lett. 4, 188 (1969); J. Mol. Spectrosc. 36, 248 (1970)]. The electron configuration has been proposed for the ground state and the configurations for the other lowlying electronic states have also been discussed. This work represents the first experimental or theoretical investigation of the electronic spectra of OsN.

A coupledcluster study of the mechanism for the CHF+H reaction
View Description Hide DescriptionThe reaction of atomic hydrogen with the CHF radical has been examined using coupledclusterab initio methods. The heats of formation for both CHF and radicals have been examined using isodesmic reaction schemes. The best estimate of the heats of formation are 36.5±3 and −4.5±3 kcal mol^{−1}, respectively. For the CHF+H reaction, there are two pathways for the formation of each of the products (CH+HF and The lowest energetic pathway appears to proceed by an association–elimination mechanism, which is consistent with results from experiments. The reaction channels leading to the products (CH+HF and via the intermediate proceed without a barrier relative to the CHF+H reactants.

A coupledcluster study of the molecular structure, vibrational frequencies, and energetics of and cations
View Description Hide DescriptionThe structural and energetic properties of and are examined using the singles and doubles coupledcluster method that includes a perturbational estimation of the effects of connected triples excitation (coupledcluster single double triple CCSD (T)). Of the two isomers, the lowest energy isomer is the species. It is stable to dissociation into and by 140.9 and 111.6 kcal mol^{−1}, respectively. Moreover, it is 74.6 kcal mol^{−1} below the isomer. Harmonic vibrational frequencies, as well as charge distributions and dipole moments for and are presented.

Inner shell excitation spectroscopy of transient molecules: HBS, HBO, and
View Description Hide DescriptionInner shell electron energyspectroscopy (ISEELS) was used to study HBS, HBO, and reactive, transient species generated in situ. The reaction of with crystalline boron in a quartz tube was used to produce thioborine (HBS) at ∼1100 °C, and borine (HBO) at ∼1200 °C. The reaction of vapor with crystalline boron in a quartz tube at ∼1200 °C was used to produce boroxine These species were identified from their inner shell excitation spectra and mass spectrometry. The and ISEEL spectra of HBS, and the and spectra of HBO and are reported and analyzed with the help of GSCF3 ab initio calculations. A reaction scheme is proposed for the generation of HBO from the reaction of and boron in a heated quartz tube.

The structure and electronic state of photoexcited fullerene linked with a nitroxide radical based on an analysis of a twodimensional electron paramagnetic resonance nutation spectrum
View Description Hide DescriptionAn electron paramagnetic resonance(EPR) study of 3,4fulleropyrrolidine2spiro4^{′}[2^{′},2^{′},6^{′},6^{′}tetramethyl]piperidine1^{′}oxyl (1) was performed on the photoexcited quartet state in toluene glass. The spectrum of the transitions was observed selectively by using a twodimensional (2D) nutation method and analyzed with a spectral simulation in a randomly oriented system. A position of the nitroxide moiety was determined with respect to the zerofield splitting (zfs) axes of excited triplet fullerene by taking into account of the dipolar–dipolar interaction between the radical and the hyperfine coupling, the anisotropicgvalue of the nitroxide radical, and the zfs of the moiety. It was found that none of the zfs axes of the moiety coincide with the local axis of the molecule which is defined by the position of addition. A symmetry of the electronic structure in is discussed on the basis of the result.
