Volume 121, Issue 5, 01 August 2004
 COMMUNICATIONS


Isomer abundance of small carbon clusters formed in buffer He gas
View Description Hide DescriptionWe calculated the isomer spectrum of carbonclusters of 3–36 atoms, and performed molecular dynamics simulations of the cluster growth in buffer helium gas, showing that the isomers with potentials higher than those of the most stable clusters form with considerable probabilities under common experimental conditions.
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 ARTICLES

 Theoretical Methods and Algorithms

Bounds to average interelectronic angles in HartreeFock theory of atoms
View Description Hide DescriptionThe average interelectronic angle is the expectation value of the angle subtended by the position vectors and of a pair of electrons i and j. In the HartreeFock theory of atoms, we point out that the angle and its subshellpair components are bounded from above and below, where n and l are the principal and azimuthal quantum numbers. The upper bounds for with are 9π/16 (=101.25°), 135π/256 (≅94.922°), 265π/512 (≅93.164°), and 129π/256 (≅90.703°) for and pairs, respectively, while they are π/2 (=90°) for the other pairs, independent of n and A weighted sum of these subshellpair bounds gives an upper bound to The lower bounds are π/2 in all the cases.

Fewstates models for threephoton absorption
View Description Hide DescriptionFewstates models are derived for the calculation of threephoton absorption matrix elements. Together with earlier derived fewstates models for twophoton absorption, the models are evaluated against results from response theory calculations that provide the full sumoverstates values. It is demonstrated that not even for systems with chargetransfer character, where fewstates models for twophoton absorption are in excellent agreement with response theory, do the models provide a quantitatively correct description for threephoton absorption. The convergence behavior, merits, and shortcomings of the models are elucidated in some detail. The role of various characteristics of the electronic structure, such as symmetry, charge transfer, and conjugation—important for the formation of a large threephoton cross section—is analyzed. As for twophoton absorption cross sections, it is essential to consider generalized fewstates models also for threephoton absorption, that is, to account for dipolar directions and laser beampolarization. Despite their poor quantitative performance, it is argued that fewstates models at times can be useful for interpretation purposes when applied to threephoton absorption.

Conjugategradient optimization method for orbitalfree density functional calculations
View Description Hide DescriptionOrbitalfree density functional theory as an extension of traditional ThomasFermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugategradient method for the numerical solution of spindependent extended ThomasFermi equation by incorporating techniques previously used in KohnSham calculations. The key ingredient of the method is an approximate linesearch scheme and a collective treatment of two spin densities in the case of spindependent extended ThomasFermi problem. Test calculations for a quartic twodimensional quantum dot system and a threedimensional sodium cluster with a local pseudopotential demonstrate that the method is accurate and efficient.

Exact decoupling of the Dirac Hamiltonian. I. General theory
View Description Hide DescriptionExact decoupling of positive and negativeenergy states in relativistic quantum chemistry is discussed in the framework of unitary transformation techniques. The obscure situation that each scheme of decoupling transformations relies on different, but very special parametrizations of the employed unitary matrices is critically analyzed. By applying the most general power series ansatz for the parametrization of the unitary matrices it is shown that all transformation protocols for decoupling the Dirac Hamiltonian have necessarily to start with an initial freeparticle Foldy–Wouthuysen step. The purely numerical iteration scheme applying operator techniques to the Barysz–Sadlej–Snijders (BSS) Hamiltonian is compared to the analytical schemes of the Foldy–Wouthuysen (FW) and Douglas–Kroll–Hess (DKH) approaches. Relying on an illegal expansion of the Dirac Hamiltonian around the nonrelativistic limit, any higherorder FW transformation is in principle ill defined and doomed to fail, irrespective of the specific features of the external potential. It is shown that the DKH method is the only valid analytic unitary transformation scheme for the Dirac Hamiltonian. Its exact infiniteorder version can be realized purely numerically by the BSS scheme, which is only able to yield matrix representations of the decoupled Hamiltonian but no analytic expressions for this operator. It is explained why a straightforward numerical iterative extension of the DKH procedure to arbitrary order employing matrix representations is not feasible within standard onecomponent electronic structure programs. A more sophisticated ansatz based on a symbolical evaluation of the DKH operators via a suitable parser routine is needed instead and introduced in Part II of this work.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Thermal decomposition of peroxy acetyl nitrate
View Description Hide DescriptionThe thermal decomposition of peroxy acetyl nitrate (PAN) is investigated by low pressure flash thermolysis of PAN highly diluted in noble gases and subsequent isolation of the products in noble gas matrices at low temperatures and by density functional computations. The IR spectroscopically observed formation of and (ketene) besides and HOO implies a unimolecular decay pathway for the thermal decomposition of PAN. The major decomposition reaction of PAN is bond fission of the ON single bond yielding the peroxy radical. The OO bond fission pathway is a minor route. In the latter case the primary reaction products undergo secondary reactions whose products are spectroscopically identified. No evidence for rearrangement processes as the formation of methyl nitrate is observed. A detailed mapping of the reaction pathways for primary and secondary reactions using quantum chemical calculations is in good agreement with the experiment and predicts homolytic ON and OO bond fissions within the PAN molecule as the lowest energetic primary processes. In addition, the first IR spectroscopic characterization of two rotameric forms for the radical is given.

Classical trajectory calculations of intramolecular vibrational energy redistribution. I. Methanolwater complex
View Description Hide DescriptionIntramolecular vibrational energy redistributions of the OH stretching vibration for the methanol monomer and its water complex, the methanolwater dimer, are investigated by using ab initio fulldimensional classical trajectory calculations. For the methanol monomer, in the highenergy regime of the overtone, the time dependence of the normalmode energies indicates that energy flowed from the initial excited OH stretching mode to the CH stretching mode. This result confirms the experimental observation of energy redistribution between the OH and CH stretching vibrations [L. Lubich et al., Faraday Discuss. 102, 167 (1995)]. Furthermore, a lot of dynamical information in the time domain is contained in the power spectra, whose density is given by the Fourier transformation of the total momentum obtained from trajectory calculations. For the methanolwater hydrogenbonded complex, at the highenergy level of the overtone, the calculated power spectrum shows considerable splitting and broadening, indicating significant energy redistribution through strong coupling between the OH stretching vibration and other vibrations. It is thus clear that the AH⋯B hydrogenbond formation facilitates energy redistribution subsequent to the vibrational excitation of the hydrogenbonded AH stretching mode.

Classical trajectory calculations of intramolecular vibrational energy redistribution. II. Phenolwater complex
View Description Hide DescriptionAb initio classical trajectory calculations have been applied to the intramolecular vibrational energy redistribution process of an OH stretching vibration for phenol cation, and its hydrogenbonded water complex, In phenol cation, a single narrow peak in the power spectrum, obtained by Fourier transformation of the autocorrelation function of its total momentum, indicates that the initial energy given to the OH stretching oscillator of the phenol moiety is conserved and no energy flow occurs. On the other hand, for phenolwater cation, the calculated broadened power spectrum implies that the initial energy is not conserved and the energy flow causes an energy redistribution among various vibrational modes.

Calculation of converged rovibrational energies and partition function for methane using vibrational–rotational configuration interaction
View Description Hide DescriptionThe rovibration partition function of was calculated in the temperature range of 100–1000 K using wellconverged energy levels that were calculated by vibrational–rotational configuration interaction using the Watson Hamiltonian for total angular momenta and the MULTIMODEcomputer program. The configuration state functions are products of groundstate occupied and virtual modals obtained using the vibrational selfconsistent field method. The Gilbert and Jordan potential energy surface was used for the calculations. The resulting partition function was used to test the harmonic oscillator approximation and the separablerotation approximation. The harmonic oscillator, rigidrotator approximation is in error by a factor of 2.3 at 300 K, but we also propose a separablerotation approximation that is accurate within 2% from 100 to 1000 K.

Isomeric interconversion in the linear anion complex
View Description Hide DescriptionThe rotationally resolved infrared photodissociationspectrum of is measured in the HD stretch region. Two ΣΣ bands are observed, corresponding to transitions from the ground state [the level] and first excited intermolecular bend state [the level]. The and states are predominantly associated with the linear and geometries, respectively. The spectrum is complicated by perturbative interactions between levels of the and rotational manifolds and between levels of the and rotational manifolds. A global fit to the transition frequencies, taking the lower and upper state perturbations into account, yields zeroorder rotational and centrifugal distortion constants and allows us to establish that the level lies 13.7 cm^{−1} above the level. Rovibrational energy level calculations performed using a recent ab initiopotential energy surface confirm the picture emerging from the experimental data and provide good agreement with measured molecular parameters. The results emphasize the importance of quantum mechanical interconversion between two isomeric structures of a simple anion complex.

Replacement equivalence of and argon in small clusters from optimized structure calculations
View Description Hide DescriptionThe structural properties of some of the smaller ionic clusters of argon atoms containing the atomic impurity with n from 2 up to 7, are examined using different modeling for the interactions within each cluster and by employing different theoretical treatments, both classical and quantum, for the energetics. The same calculations are also carried out for the corresponding neutral homogeneous clusters The results of the calculations, the physical reliability of the interactions modeling, and the similarities and the difference between the anionic and the neutral complexes are discussed in some detail. The emerging picture shows that, due to specific features of the employed atomatom potentials, the and clusters present very similar structures, where the dopant substitutes for one of the outer Ar atoms but does not undergo as yet solvation within such small clusters.

Excited state electronic structures and dynamics of NOCl: A new potential function set, absorption spectrum, and photodissociation mechanism
View Description Hide DescriptionA set of analytical potential energy surfaces (PESs) for six singlet excited states of NOCl are constructed based on multireference configuration interaction calculations. The total absorption cross section at the energy range of 2–7 eV is calculated by quantum dynamics calculations with the present PESs and transition dipole moments. The calculated absorptionspectrum agrees well with the experiment. It is also found that the A band with the absorption maximum at 6.3 eV is attributed to the transition to the state, though the excitations to the and states contribute to the spectrum at the energy range between 4 and 5 eV. The spinforbidden transitions are concluded to be negligibly weak. The mechanism of photodissociation reaction at the energy region corresponding to the A band is examined. The nonadiabatic transition rates from the state to lower singlet and triplet states are estimated by Fermi’s golden rule, and the transitions to the and states induced by vibronic coupling are found to be the predominant dissociation pathways. The experimentally observed energy dependence of the recoil anisotropy of the fragments is discussed based on the calculated nonadiabatic transition rates.

Preparation and resolution of molecular states by coherent sequences of phaselocked ultrashort laser pulses
View Description Hide DescriptionWe study the application of nonlinear wave packet interferometry to the preparation and resolution of the overlaps of nonstationary nuclear wave functions evolving in an excited electronic state of a diatomic molecule. It is shown that possible experiments with two phaselocked ultrashort pulsepairs can be used to determine a specific vibrational wave packet state in terms of coherent states of the ground electronic state. We apply this scheme to an idealized molecule with harmonic potential energy surfaces and to the transition states of the iodine molecule. Our results indicate that this scheme is very promising as a potential tool to quantum control.

First principles simulation of the UV absorption spectrum of ethylene using the vertical FranckCondon approach
View Description Hide DescriptionA new method which we refer to as vertical FranckCondon is proposed to calculate electronic absorption spectra of polyatomic molecules. In accord with the shorttime picture of spectroscopy, the excitedstatepotential energy surface is expanded at the groundstate equilibrium geometry and the focus of the approach is more on the overall shape of the spectrum and the positions of the band maxima, rather than the precise position of the 00 lines. The BornOppenheimer approximation and the separability of the excitedstatepotential energy surface along the excitedstatenormal mode coordinates are assumed. However, the potential surface is not necessarily approximated as harmonic oscillator potentials along the individual normal modes. Instead, depending upon the nature of the potential surface along a particular normal mode, it is treated either in the harmonic approximation or the full onedimensional potential is considered along this mode. The vertical FranckCondon approach is applicable therefore even in cases where the excited statepotential energy surface is highly anharmonic and the conventional harmonic FranckCondon approach is inadequate. As an application of the method, the ultraviolet spectrum of ethylene between 6.2 eV (50 000 cm^{−1}) and 8.7 eV (70 000 cm^{−1}) is simulated, using the Similarity Transformed Equation of Motion CoupledCluster method to describe the required features of the potential energy surfaces. The spectrum is shown to be a result of sharp doublet structures stemming from the (Rydberg) state superimposed on top of a broad band resulting from the π→π^{*} (valence) state. For the Rydberg state, the symmetric C=C stretch and the torsion mode contribute to the spectrum, while the broad valence band results from excitation into the C=C stretch, scissors, and the torsion mode. For both states, the potential along the torsion mode is highly anharmonic and the full treatment of the potential along this mode in the vertical FranckCondon method is required.

Highresolution kinetic energy release distributions and dissociation energies for fullerene ions
View Description Hide DescriptionWe have measured the kinetic energy released in the unimolecular dissociation of fullerene ions, for sizes A threesectorfield mass spectrometer equipped with two electric sectors has been used in order to ensure that contributions from isotopomers of different masses do not distort the experimental kinetic energy release distributions. We apply the concept of microcanonical temperature to derive from these data the dissociation energies of fullerene cations. They are converted to dissociation energies of neutral fullerenes with help of published adiabatic ionization energies. The results are compared with literature values.

Density functional investigations of the properties and thermochemistry of and using valenceelectron and allelectron approaches
View Description Hide DescriptionThe structural properties and thermochemistry of and have been investigated using both HartreeFock and density functional theory(DFT) approximations. Within the latter approach, the local spindensity approximation, the generalized gradient approximation, and hybrid density functionals were considered. To describe the uranium atom we employed smallcore (60 electrons) and largecore (78 electrons) relativistic effective core potentials (RECPs), as well as the allelectron approximation based on the twocomponent thirdorder DouglasKrollHess Hamiltonian. For structural properties, we obtained very good agreement with experiment with DFT and both large and smallcore RECPs. The best match with experiment is given by the hybrid functionals with the smallcore RECP. The bond dissociation energy (BDE) was obtained from the relative energies of the fragments corrected for zeropoint energy and spinorbit interaction. Very good agreement was found between the BDE obtained from allelectron calculations and those calculated with the smallcore RECP, while those from the largecore RECP are off by more than 50%. In order to obtain good agreement with experiment in the BDE it is imperative to work with hybrid density functionals and a smallcore RECP.

The Xe shielding surfaces for Xe interacting with linear molecules and spherical tops
View Description Hide DescriptionThe nuclear magnetic resonancespectrum of xenon in gas mixtures of Xe with other molecules provides a test of the ab initiosurfaces for the intermolecular shielding of Xe in the presence of the other molecule. We examine the electron correlation contributions to the Xe–CO, and shielding surfaces and test the calculations against the experimental temperature dependence of the density coefficients of the Xe chemical shift in the gas mixtures at infinite dilution in Xe. Comparisons with the gas phase data permit the refinement of site–site potential functions for Xe–CO, and especially for atomXe distances in the range 3.5–6 Å. With the atom–atom shielding surfaces and potential parameters obtained in the present work, construction of shielding surfaces and potentials for applications such as molecular dynamics averaging of Xe chemical shifts in liquid solvents containing and groups is possible.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Vibrational and rotational dynamics of cyanoferrates in solution
View Description Hide DescriptionUltrafast infrared spectroscopy has been used to measure vibrational energy relaxation (VER) and reorientation times for the high frequency vibrational bands of potassium ferrocyanide and ferricyanide (CN stretches), and sodium nitroprusside (SNP, CN, and NO stretches) in water and several other solvents. Relatively short VER times (4–43 ps) are determined for the hexacyano species and for the NO band of SNP, but the CN band of SNP relaxes much more slowly (55–365 ps). The solvent dependence of the VER times is similar for all the solutes and resembles what has been previously observed for triatomic molecular ions [Li et al., J. Chem. Phys. 98, 5499 (1993)]. Anisotropy decay times are also measured from the polarization dependence of the transient absorptions. The times determined for SNP are different for the different vibrational bands; for the nondegenerate NO mode of nitroprusside (SNP) they are much longer (>15 ps), correlate with solvent viscosity, and are attributed to overall molecular rotation. The short (<10 ps) times for the CN band in SNP and for the hexacyanoferrates are due to dipole orientational relaxation in which the transition moment rapidly redistributes among the degenerate modes. There is no evidence of intramolecular vibrational relaxation (IVR) to other high frequency modes. VER times measured for hexacarbonyls and SNP in methanol are similar, which suggests that the generally faster VER for the latter is in part because they are soluble in more strongly interacting polar solvents. The results are compared to those for small ions and metal carbonyls and are discussed in terms of the importance of solute charge and symmetry on VER.

Phase behavior of nalkanes in supercritical solution: A Monte Carlo study
View Description Hide DescriptionWe present a coarsegrained model for nalkanes in a supercritical solution, which is exemplified by a mixture of hexadecane and For pure hexadecane, the Monte Carlo simulations of the coarsegrained model reproduce the experimental phase diagram and the interfacial tension with good accuracy. For the mixture, the phase behavior sensitively depends on the compatibility of the polymer with the solvent. We present a global phase diagram with critical lines, which is in semiquantitative agreement with experiments. In this context we developed two computational schemes: The first adopts WangLandau sampling to the offlattice grand canonical ensemble, the second combines umbrella sampling with an extrapolation scheme to determine the weight function. Additionally, we use Wertheim’s theory (TPT1) to obtain the equation of state for our coarsegrained model of supercritical mixtures and discuss the behavior for longer alkanes.

A KirkwoodBuff derived force field for the simulation of aqueous guanidinium chloride solutions
View Description Hide DescriptionA force field for the simulation of aqueous guanidinium chloride solutions is presented. The force field was parametrized to reproduce the experimental density and KirkwoodBuff integrals as a function of composition. Consequently, a reasonable description of the salt activity is obtained. The model also performs well for other properties such as the relative permittivity and enthalpy of mixing.