bluuebunny/crossref_metadata_2025 huggingface dataset:
Quadratic response calculations of the electronic spin-orbit contribution to nuclear shielding tensors
Authors: Vaara Juha , Ruud Kenneth , Vahtras Olav , Ågren Hans , Jokisaari Jukka
Published: July 2002

The electronic spin-orbit contribution to nuclear magnetic shielding tensors, which causes the heavy-atom chemical shift of the shielding of light nuclei in the vicinity of heavy elements, is calculated as a sum of analytical quadratic response functions. We include both the one- and two-electron parts of the spin-orbit Hamiltonian and consider the interaction with both the Fermi contact and the spin-dipolar mechanisms. Ab initio calculations at the SCF and MCSCF levels are presented for the H1 and C13 shielding tensors in the hydrogen and methyl halides. The applicability of different approximations to the full spin-orbit correction is discussed, and the calculated results are compared with experimental data, where available.
Ab initio study of energy, structure and dynamics of the water–carbon dioxide complex
Authors: Sadlej Joanna , Makarewicz Jan , Chałasiński Grzegorz
Published: July 2002

The supermolecular Moller–Plesset perturbation theory (MPPT) is applied to calculate and analyze selected portions of the potential-energy surface (PES) of the H2O⋯CO2 complex. Two kinds of minima have been found. The global minimum, which corresponds to the T-shaped structure with the C atom bonded to the O atom, and the local minimum for the H-bonded arrangement OCO⋯HOH. The global minimum was estimated to be 920 cm−1 deep at the fourth order of MPPT combined with the extended spdf-quality basis set supplemented with bond functions. At the same level of theory the optimal H-bonded structure is 357 cm−1 higher in energy, and reveals a small 10° departure from the collinear arrangement OCO⋯H–O. Both the T-shaped and H-bonded forms are primarily bound by the electrostatic term, which is twice as large as the dispersion component. One-dimensional sections of the potential-energy surface were subsequently used to calculate vibrational energy levels for the wagging motion of the water moiety in the T-shaped and H-bonded forms. Two-dimensional cuts of the PES along the intermolecular Jacobi coordinates, r and θ, were employed to simulate the dynamics of the stretch–bend coupling close to the minima.
Molecule-interface coupling effects on electronic transport in molecular wires
Authors: Yaliraki Sophia N. , Ratner Mark A.
Published: July 2002

Transport studies of molecular wire circuits require a description of the molecule and the leads. Here we focus on the molecule–lead interaction. We extend a time-independent scattering formalism to include a more realistic description of the interface. This allows us to obtain the conductance as a function of dimensionality of contact and of electrode, number of contacts, and geometry between molecule and interface. We study conductance in adlayers of molecules by considering transport through two identical wires. Implications for experiments are discussed.
Noniterative local second order Mo/ller–Plesset theory: Convergence with local correlation space
Authors: Maslen P. E. , Head-Gordon M.
Published: July 2002

We extend our noniterative local correlation method [P. E. Maslen and M. Head-Gordon, Chem. Phys. Lett., 283, 102 (1998)] by defining a hierarchy of local spaces, ranging from small to large. The accuracy of the local method is then examined as a function of the size of the local space. A medium size local space recovers 98% of the MP2 correlation energy, and reproduces fine details of the potential energy surface such as rotational barriers with an RMS error of 0.2 kcal/mol and a maximum error of 0.4 kcal/mol. A large local space recovers 99.5% of the correlation energy and yields rotational barriers with a RMS error of 0.05 kcal/mol and a maximum error of 0.1 kcal/mol, at significantly increased computational cost.
Proton tunneling in benzoic acid crystals at intermediate temperatures: Nuclear magnetic resonance and neutron scattering studies
Authors: Neumann M. , Brougham D. F. , McGloin C. J. , Johnson M. R. , Horsewill A. J. , Trommsdorff H. P.
Published: July 2002

The dynamics of proton transfer along the hydrogen bonds of dimers of benzoic acid has been characterized in single crystals and powders at temperatures between 10 K and 110 K by quasi-elastic neutron scattering (QENS) and by proton spin-lattice relaxation using field-cycling NMR spectroscopy. These measurements define the geometry of the proton transfer, the energy difference between the two tautomers of benzoic acid corresponding to the two proton positions, as well as the proton correlation time. The proton jump vector agrees well with expectations from recent crystallographic data. The energy difference between tautomers of A/kB=86.5±1.5 K is in contradiction with the lower value of A/kB=50 K derived from older C13 NMR and infrared absorption measurements. NMR and QENS measurements provide mutually consistent values of the proton correlation time, τc, and an accurate characterization of the dynamics at temperatures where the onset of thermally activated processes is observed. Tunneling in an excited vibrational level, as well as multiphonon transitions between the lowest tunneling levels, are expected to contribute to these dynamics and are discussed. The inverse correlation time for the proton dynamics over the entire temperature range between 0 K and ambient temperature is well represented by the expression: 1/τc={1.72×108 coth(43/T)+1010 exp(−180/T)+6.3×1011 exp(−600/T)} s−1.
Temperature dependence of spin-spin and spin-lattice relaxation times of paramagnetic nitrogen defects in diamond
Authors: Reynhardt E. C. , High G. L. , van Wyk J. A.
Published: July 2002

Spin-lattice relaxation times of P1 centers in a suite of two natural type Ib, two synthetic type Ib, and one natural type Ia diamonds were measured at 9.6 GHz as a function of temperature in the range 300 K>T>4.2 K. An analysis of the results revealed that for three of the diamonds (two synthetic type Ib and the natural type Ia) spin-orbit phonon-induced tunneling is the main relaxation mechanism. In the case of the Ia diamond cross-relaxation takes place between P1 and P2 centers. In the natural type Ib samples a much more effective relaxation mechanism dominates at lower temperatures. Electron spin resonance spectra of the latter samples revealed the presence of N3 centers. It seems that the more effective relaxation mechanism is associated with the N3 centers and that the P1 centers relax via the N3 centers to the lattice at these temperatures.
The fluorescence depletion spectroscopy of CdCH3
Authors: Pushkarsky Michael B. , Barckholtz Timothy A. , Miller Terry A.
Published: July 2002

The fluorescence depletion spectroscopy (FDS) technique has been applied to the Ã 2E electronic state of the CdCH3 radical to investigate “dark” vibronic levels. The observed FDS spectrum complements the sparse laser-induced fluorescence and resonance-enhanced multiphoton ionization spectra. Both the upper and lower spin components of the vibrationless level as well as excitations involving the symmetric modes ν2 and ν3, and the antisymmetric mode ν6, as well as combinations involving these modes, were observed. A combined Jahn-Teller and spin-orbit coupling model was used to explain the vibronic structure in the Ã 2E electronic state as well as strong variations in the Coriolis coupling constants obtained from the resolved rotational K structure. Lifetimes for fluorescing levels have been determined from their temporal decay and those for some dark levels via lifetime broadening measurements. The selectivity of the radiationless decay channel and its possible attribution to an isomerization process are discussed.
Steady state simulation of planar elongation flow by nonequilibrium molecular dynamics
Authors: Baranyai András , Cummings Peter T.
Published: July 2002

We present a novel method for performing steady state nonequilibrium molecular dynamics simulation of planar elongation flow based on the studies of Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)]. These authors identified the orientation of the unit cell which leads to periodic behavior of the square lattice with the minimum period. This way the exponential deformation of the system periodically returns to a state where replacing some of the original particles with their images the initial state boundaries are recovered. We adopted their theoretical results to nonequilibrium molecular dynamics simulations and performed representative calculations for simple fluids. The new method solves the long-standing problem of simulating planar elongation flow in the steady state.
The PI4+ cation has an extremely large negative 31P nuclear magnetic resonance chemical shift, due to spin–orbit coupling: A quantum-chemical prediction and its confirmation by solid-state nuclear magnetic resonance spectroscopy
Authors: Kaupp Martin , Aubauer Christoph , Engelhardt Günter , Klapötke Thomas M. , Malkina Olga L.
Published: July 2002

We have used density-functional methods including explicit spin–orbit corrections, to calculate the 31P nuclear magnetic resonance (NMR) chemical shifts of the tetrahalophosphonium cations PX4+ (X=F, Cl, Br, I). The agreement between theory and experimental literature data for PF4+, PCl4+, and PBr4+ is good. For PI4+, the calculations predict an extremely negative (high-field) shift of approximately −520 ppm, due to particularly large spin–orbit contributions from the four heavy iodine substituents, transmitted to the phosphorus nucleus by a very effective Fermi-contact mechanism. No experimental data were available for PI4+. We have, therefore, prepared the compounds PI4AsF6, PI4SbF6, PI4AlI4, and PI4GaI4 and recorded their solid-state 31P NMR spectra, both with and without magic-angle spinning of the sample. Using the noncoordinating AsF6− and SbF6− anions, the measured isotropic shifts are −519 and −517 ppm, respectively, in good agreement with the predicted extreme value for the isolated cation. In contrast, δ31P values of only −304 and −295 ppm are found for PI4AlI4 and PI4GaI4, respectively. The large deviation from the isolated-cation limit in the latter two compounds is probably related to significant I⋯I secondary bonding interactions, as found in the solid-state structure of PI4AlI4. The observed solid-state shift tensors are discussed. The present results disagree clearly with previous claims for the synthesis of PI5.
Two-dimensional spectroscopy of electric birefringence relaxation in frequency domain: Measurement method for second-order nonlinear after-effect function
Authors: Hosokawa Kozo , Shimomura Takeshi , Frusawa Hiroshi , Kimura Yasuyuki , Ito Kohzo , Hayakawa Reinosuke
Published: July 2002

A new measurement method for second-order nonlinear after-effect function has been developed. Theoretical calculation starting from a general time-evolution equation connects nonlinear responses in time domain and frequency domain and thus gives the nonlinear response to applied external field of arbitrary form. In addition, it turns out in the frequency domain that the dc component of a second-order nonlinear response function corresponds to a linear response function. For example, the dc component of the electric birefringence relaxation is equivalent to the dielectric relaxation. This simple relation indicates an advantage of a frequency-domain measurement for nonlinear responses. As an example, the electric birefringence relaxation is measured in two-dimensional frequency domain for aqueous solution of sodium poly(styrenesulfonate) to confirm the validity of the theoretical results.
Absorption and emission spectroscopy of perylene (C20H12) isolated in Ne, Ar, and N2 matrices
Authors: Joblin C. , Salama F. , Allamandola L.
Published: July 2002

The electronic absorption and emission spectra of perylene (C20H12) isolated in rare gas (Ne, Ar) and N2 matrices are presented. While the electronic band systems show, in all matrices, the same fundamental frequencies as those observed in gas-phase jet experiments, the spectra in Ar and N2 matrices exhibit much more spectral structure. The observed structure points to strong host–guest interactions and provides new insight into the low frequency modes of perylene. In particular, the spacing observed at 11 and 16 cm−1 in the S0 and S1 states, respectively, might be attributed to the gerade accordion mode of perylene. This mode, which has never been observed directly in jet experiments, could be induced into activity in solid matrices.
Uniform J-shifting approach for calculating reaction rate constant
Authors: Zhang D. H. , Zhang J. Z. H.
Published: July 2002

This paper presents a new uniform J-shifting approach for accurate calculation of rate constant in quantum dynamics study of chemical reaction. Instead of using a fixed shifting constant B in the standard J-shifting approach, the current method employs a temperature-dependent shifting constant which is obtained through an optimization procedure at a given temperature. By utilizing the calculated reaction probabilities at only a few total angular momentum values of J, the current approach automatically gives uniformly accurate rate constant across the entire range of temperature. Numerical studies of several benchmark reaction systems, including the H+H2, H2+OH and H2+CN reactions, show explicitly that the uniform J-shifting approach is far superior to the standard J-shifting approach and it provides a robust method for accurate and efficient calculation of reaction rate constant in rigorous quantum dynamics study of chemical reaction.
Structures and the vibrational relaxations of size-selected benzonitrile–(H2O)n=1–3 and –(CH3OH)n=1–3 clusters studied by fluorescence detected Raman and infrared spectroscopies
Authors: Ishikawa Seiichi , Ebata Takayuki , Mikami Naohiko
Published: July 2002

Vibrational spectroscopy of jet-cooled benzonitrile and its clusters, benzonitrile-(H2O)1–3, and benzonitrile–(CH3OH)1–3, has been carried out by using stimulated Raman-UV (ultraviolet) and IR-UV (infrared-ultraviolet) double resonance methods. CC stretching (ν12), CN stretching (νCN), CH stretching (νCH), and OH stretching (νOH) vibrations have been examined for each species, and characteristic frequency shifts were observed for νCN and νOH upon the cluster formation. The cluster structures were determined by comparing the observed spectra with those obtained by ab initio calculations with HF/SCF (Hartree–Fock self-consistent field) 6-31G(d,p) basis set. It was found that the stable structures of benzonitrile–(H2O)n and benzonitrile–(CH3OH)n are of the ring form, in which a linear chain of (H2O)n cluster or (CH3OH)n cluster is hydrogen bonded to the CN group and to the ortho hydrogen of benzonitrile. A size dependent transmutation of the hydrogen-bond structure between H2O or CH3OH and the CN group of benzonitrile was clearly identified for those clusters. In the small size cluster, the OH group of H2O or CH3OH is hydrogen-bonded perpendicularly to the CN triple bond (π-type hydrogen bond), while in the larger size clusters the OH group forms hydrogen bond linearly to the nitrogen atom of the CN group (σ-type hydrogen bond). The lifetimes and the relaxation of the vibrationally excited benzonitrile and its clusters were also investigated by the Raman pump and UV probe technique. The lifetimes of ν12 and νCN vibrations of bare benzonitrile were longer than 1 μs. For benzonitrile–H2O and benzonitrile–CH3OH, on the other hand, the lifetime of the ν12 level is less than 1 ns. The relaxation channels for benzonitrile–CH3OH have been characterized by observing the electronic transition from the relaxed levels or the transition of the dissociation product. It was concluded that the main relaxation channel after the ν12 excitation is the intracluster vibrational redistribution (IVR), while the νCN excitation is followed by the vibrational predissociation (VP).
On the origin and contribution of the diamagnetic term in four-component relativistic calculations of magnetic properties
Authors: Aucar G. A. , Saue T. , Visscher L. , Jensen H. J. Aa.
Published: July 2002

The relativistic Dirac Hamiltonian that describes the motion of electrons in a magnetic field contains only paramagnetic terms (i.e., terms linear in the vector potential A) while the corresponding nonrelativistic Schrödinger Hamiltonian also contains diamagnetic terms (i.e., those from an A2 operator). We demonstrate that all diamagnetic terms relativistically arise from second-order perturbation theory and that they correspond to a “redressing” of the electrons by the magnetic field. If the nonrelativistic limit is taken with a fixed no-pair Hamiltonian (no redressing), the diamagnetic term is missing. The Schrödinger equation is normally obtained by taking the nonrelativistic limit of the Dirac one-electron equation, we show why nonrelativistic use of the A2 operator is also correct in the many-electron case. In nonrelativistic approaches, diamagnetic terms are usually considered in first-order perturbation theory because they can be evaluated as an expectation value over the ground state wave function. The possibility of also using an expectation value expression, instead of a second-order expression, in the relativistic case is investigated. We also introduce and discuss the concept of “magnetically balanced” basis sets in relativistic calculations.
The (X 2Πg) nsσg 1,3Πg Rydberg states of O2: Spectra, structures, and interactions
Authors: Morrill J. S. , Ginter M. L. , Lewis B. R. , Gibson S. T.
Published: July 2002

The results of a critical reexamination of previous experimental observations of the (X 2Πg) nsσg 1,3Πg Rydberg states of O2 are employed to optimize a coupled-channel Schrödinger-equation (CSE) model describing rovibronic interactions among a number of Πg1,3 Rydberg and valence states. The results of calculations using this CSE model are compared with the experimental energy-level and predissociation linewidth data base. As a result of the optimization process, relevant potential-energy curves and Rydberg–valence, Rydberg–Rydberg, and valence–valence interactions are characterized for Πg1,3 states in the ∼6.5–9.5 eV region above the ground state of O2. The precision of these characterizations and the interpretation of the experimental observations are found to be limited by the quality of the existing data, which exhibit a number of inconsistencies that cannot be reconciled without new, well-characterized experimental studies. In spite of these difficulties, the present CSE model, as currently parametrized, represents a significant improvement over previous work, enabling identification of a number of previously unassigned spectral features associated with perturbation of the 3sσg d 1Πg state by the II 1Πg valence state and an anomalous J sensitivity in predissociation branching ratios for the d(v=1) level. In addition, the electronic structure and predissociation of the nsσg states for n⩾4 are found to be strongly influenced by nsσg−(n−1)dσg Rydberg–Rydberg interactions.
Non-Markovian evolution of the density operator in the presence of strong laser fields
Authors: Meier Christoph , Tannor David J.
Published: July 2002

We 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 N+1 times that of propagating a Markovian density matrix. (3) The method can treat explicitly time-dependent system Hamiltonians nonperturbatively, making the method applicable to strong field spectroscopy, 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 two-level system, we compare our numerical results with full path-integral 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 well-suited to study chemical systems interacting with femtosecond short laser pulses, where the conditions for a Markovian theory are often violated.
A new ab initio potential energy curve for the helium dimer
Authors: van Mourik Tanja , Dunning Thom H.
Published: July 2002

The He2 interaction potential has been computed employing augmented correlation-consistent basis sets and several methods beyond those commonly used to recover electron correlation, namely fifth-order Mo/ller–Plesset perturbation theory (MP5), coupled cluster theory with full triple excitations (CCSDT), and full configuration interaction (FCI). Calculations employing the largest basis sets were not feasible for the most sophisticated methods (MP5, CCSDT, and FCI). Nonetheless, because of the rapid convergence of the calculated interaction energy differences with basis set, it was possible to obtain reliable estimates of the complete basis set MP5, CCSDT, and FCI results. The MP5 method is predicted to yield a well depth of 10.67±0.03 K at the complete basis set (CBS) limit. Thus, the accuracy of the MP5 method is comparable to that of the CCSD(T) method which yields a De of 10.68±0.02 K. The CCSDT method yields an estimated well depth of 10.98±0.03 K. Thus, the full effect of connected triple excitations on the He2 well depth is 1.74 K (CCSDT-CCSD). Comparing the basis set dependence of the CCSDT and FCI well depths, the effect of connected quadruple excitations on the well depth is estimated to be just 0.015–0.020 K. Thus, the current calculations predict the FCI He2 well depth to be 11.00±0.03 K, in excellent agreement with the recent quantum Monte Carlo calculations of Anderson et al. [J. Chem. Phys. 99, 345 (1993)]. Taking advantage of the rapid convergence of the full triples and quadruples correlation corrections to the CCSD(T) interaction energy with basis set, an estimated FCI/CBS potential energy curve has been constructed for He2 from 3.5 to 15.0 a0. The resulting curve lies between the HFD-B3-FCI1 and SAPT2 semi-empirical potentials of Aziz et al., being closer to the SAPT2 potential.
Orbital-free molecular dynamics simulations of melting in Na8 and Na20: Melting in steps
Authors: Aguado Andrés , López José M. , Alonso Julio A. , Stott Malcolm J.
Published: July 2002

The melting-like transitions of Na8 and Na20 are investigated by ab initio constant energy molecular dynamics simulations using a variant of the Car–Parrinello method which employs an explicit electronic kinetic energy functional of the density, thus avoiding the use of one-particle orbitals. Several melting indicators are evaluated in order to determine the nature of the various transitions, and are compared with other simulations. Both Na8 and Na20 melt over a wide temperature range. For Na8, a transition is observed to begin at ∼110 K, between a rigid phase and a phase involving isomerizations among the different permutational isomers of the ground state structure. The “liquid” phase is completely established at ∼220 K. For Na20, two transitions are observed: the first, at ∼110 K, is associated with isomerization transitions among those permutational isomers of the ground state structure which are obtained by interchanging the positions of the surface-like atoms; the second, at ∼160 K, involves a structural transition from the ground state isomer to a new set of isomers with the surface molten. The cluster is completely liquid at ∼220 K.
On the conduction mechanism in ionic glasses
Authors: Baranovskii S. D. , Cordes H.
Published: July 2002

Conduction mechanism in ionic glasses is still considered one of the great challenges in physics and chemistry of glasses [A. Bunde, K. Funke, and M. Ingram, Solid State Ionics 105, 1 (1998)]. We show that consequent application of the routine percolation theory leads to the consistent description of most puzzling conduction effects for both direct current (dc) and alternating current (ac) conductivity. Moreover, comparison of the theoretical results with experimental data reveals the well-known random-energy model suggested a few decades ago for ionic transport in glasses as a very plausible model. The results provide a general basis for the study of transport phenomena in ionic glasses.
Perturbation theory of three-body exchange nonadditivity and application to helium trimer
Authors: Lotrich Victor F. , Szalewicz Krzysztof
Published: July 2002

The many-body symmetry-adapted perturbation theory (SAPT) of intermolecular interactions has been applied to the nonadditivity of the trimer first-order exchange energy. The orbital expressions including intramonomer correlation effects up to the second order have been derived. These expressions, together with other many-body SAPT terms developed earlier, have been used to compute the nonadditivity of the helium trimer. The computed points have been fitted by a global potential function.
The microwave spectra and structures of Ar–AgX (X=F,Cl,Br)
Authors: Evans Corey J. , Gerry Michael C. L.
Published: July 2002

The rotational spectra of the complexes Ar–AgF, Ar–AgCl, and Ar–AgBr have been observed in the frequency range 6–20 GHz using a pulsed jet cavity Fourier transform microwave spectrometer. All the complexes are linear and rather rigid in the ground vibrational state, with the Ar–Ag stretching frequency estimated as ∼140 cm−1. Isotopic data have been used to calculate an r0 structure for Ar–AgF, while for Ar–AgCl and Ar–AgBr partial substitution structures have also been obtained. To reduce zero-point vibrational effects a double substitution method (rd) was employed to calculate the structures of Ar–AgCl and Ar–AgBr. The Ar–Ag bond distance has been found to be rather short and to range from 2.56 Å in Ar–AgF to 2.64 Å in Ar–AgBr. Ab initio MP2 and density functional theory calculations for Ar–AgF and Ar–AgCl model the geometries and stretching frequency well, and predict an Ar–Ag bond energy in Ar–AgF of ∼23 kJ mol−1. These results indicate that the Ar–AgX complexes are more strongly bound than typical van der Waals complexes. Analysis of the halogen nuclear quadrupole coupling constants was unable to confirm whether extensive electron rearrangement occurs upon formation of the complexes.
The electronic structure of polyhex carbon tori
Authors: Ceulemans A. , Chibotaru L. F. , Bovin S. A. , Fowler P. W.
Published: July 2002

The π-orbital electronic structure of polyhex carbon tori constructed from bent individual single-wall nanotubes is investigated within the tight-binding approach. Analytical solutions for tori from nanotubes of arbitrary radius, length, chirality, and twisting angle are derived using simple geometrical and band-structure arguments. Vanishing of the gap between highest occupied and lowest unoccupied molecular orbitals for a torus imposes divisibility by 3 on the indices of chiral and twisting vectors, which translates into one graph-theoretical condition: a metallic polyhex torus is constructible as a leapfrog transformation of a smaller polyhex torus.
Line of triple points for the hard-core Yukawa model: A computer simulation study
Authors: El Azhar Fouad , Baus Marc , Ryckaert Jean-Paul , Meijer Evert Jan
Published: July 2002

A computer simulation method is devised whereby the change in location of a triple point is followed as one of the parameters of the interaction potential is modified. The method, a two-dimensional Clapeyron integration, is illustrated here for the case of a hard-core plus repulsive Yukawa potential of variable range. The latter is a crude model for charge-stabilized colloids. It is shown that the body-centered-cubic (bcc) phase becomes metastable when the range of the Yukawa term is smaller than, approximately, one-sixth of the hard-core diameter.
The performance of density-functional theory in challenging cases: Halogen oxides
Authors: Alcami M. , Mó O. , Yáñez M. , Cooper I. L.
Published: July 2002

Halogen dioxides (FOO, ClOO, BrOO, OClO, OBrO), their cationic and anionic derivatives and two isomers of ClO3 have been studied by means of density-functional theory (DFT) and the results compared with those from high level ab initio molecular orbital calculations. Three different density functionals (SVWN, B3LYP, and G96LYP) combined with a 6-311+G(2df ) basis set were used to obtain geometries and vibrational frequencies, which were then compared with MP2 (second-order Moller–Plesset), QCISD, and CCSD(T) (coupled-cluster single double triple) results. The B3LYP/6-311+G(2df ) calculations generally give geometries and frequencies in excellent agreement with those calculated from high level ab initio calculations such as CCSD(T). Exceptions, such as ClOO and BrOO, arise when high spin contamination at B3LYP level produces spurious results. Atomisation enthalpies evaluated at B3LYP/6-311+G(3df ) level of theory are observed to be in good agreement with the experimental values. In some particular cases this agreement is better than that obtained at CCSD(T)/6-311+G(3df ) level. For ionization enthalpies the CCSD(T) calculations seem to be superior to the DFT ones. Wave function instabilities [with respect to the UHF (unrestricted Hartree–Fock) transformation in the case of the cations and internal symmetry breaking in the case of the OXO (X=Cl, Br) compounds and the C3v isomer of ClO3] are observed less frequently when DFT methods are used.
Simulation study of the phase behavior of a primitive model for thermotropic liquid crystals: Rodlike molecules with terminal dipoles and flexible tails
Authors: van Duijneveldt Jeroen S. , Gil-Villegas Alejandro , Jackson George , Allen Michael P.
Published: July 2002

A primitive model for small mesogenic molecules is proposed, consisting of three elements: (i) a rigid rodlike core, modeled as a hard spherocylinder of length/diameter ratio L/D=5; (ii) a flexible end group, consisting of five segments of length D, which is “ideal” in the sense that it has no volume; (iii) a terminal dipole, located in the end cap opposite the flexible tail. This model is studied using Monte Carlo computer simulation, and the dipolar interactions are evaluated using the reaction field method. The hard spherocylinder model displays four phases: isotropic, nematic, smectic-A and crystal. Previously, it was found that the addition of the terminal dipole to hard spherocylinders without tails greatly enhances the range of stability of the nematic phase, at the expense of the smectic-A phase [McGrother et al., J. Phys.: Condens. Matter 8, 9649 (1996)]. Conversely, adding the flexible tail to hard spherocylinders without dipoles is found to suppress the nematic phase, whereas the smectic-A and crystal phase are little affected. Combining the effects of the terminal dipole and the flexible tail, all four phases survive. Because of the dipoles, the particles prefer to adopt a staggered antiparallel arrangement. In the smectic-A and crystal phases, this gives rise to interdigitation of the smectic layers. In the crystal phase a tendency towards columnar ordering is observed. The results are compared with experimental observations.
Potential energy surface, thermal, and state-selected rate coefficients, and kinetic isotope effects for Cl+CH4→HCl+CH3
Authors: Corchado J. C. , Truhlar D. G. , Espinosa-Garcı́a J.
Published: July 2002

A new potential energy surface is reported for the gas-phase reaction Cl+CH4→HCl+CH3. It is based on the analytical function of Jordan and Gilbert for the analog reaction H+CH4→H2+CH3, and it is calibrated by using the experimental thermal rate coefficients and kinetic isotope effects. The forward and reverse thermal rate coefficients were calculated using variational transition state theory with semiclassical transmission coefficients over a wide temperature range, 200–2500 K. This surface is also used to analyze dynamical features, such as reaction-path curvature, the coupling between the reaction coordinate and vibrational modes, and the effect of vibrational excitation on the rate coefficients. We find that excitation of C–H stretching modes and Cl–H stretching modes enhances the rate of both the forward and the reverse reactions, and excitation of the lowest frequency bending mode in the CH4 reactant also enhances the rate coefficient for the forward reaction. However, the vibrational excitation of the CH3 umbrella mode (lowest frequency mode in products) slows the reaction at temperatures below 1000 K, while above 1000 K it also accelerates the reaction.
Two-dimensional vibrational spectroscopy. VI. Higher-order contributions to the two-dimensional vibrational response functions
Authors: Park Kisam , Cho Minhaeng
Published: July 2002

The temperature-dependent first-order quantum correction contributions to the two-dimensional vibrational response functions, that are linearly proportional to ℏ, are theoretically investigated. By carrying out the semiclassical expansion of the nonlinear response function in the limit of weak anharmonicity of the potential-energy surface, seventy nine quantum correction terms are obtained. Although it is the cubic anharmonic couplings that were found to be important at the level of classical calculation of the associated nonlinear response functions, it is found that the quartic anharmonic terms can play a role as the quantum contributions. For a three-Brownian-oscillator model system, various numerical calculations of the 2D (two-dimensional) spectra are carried out to show how these quantum correction terms depend on temperature as well as on relative amplitudes of the quartic and cubic anharmonic coupling constants.
The third- and fifth-order nonlinear Raman response of liquid CS2 calculated using a finite field nonequilibrium molecular dynamics method
Authors: Jansen Thomas l. C. , Snijders Jaap G. , Duppen Koos
Published: July 2002

A finite field molecular dynamics (MD) method has been developed to calculate the off-resonant Raman response of liquids. The method has been used to calculate the third- and fifth-order optical responses of CS2. From the third-order response, the intensity of third-order cascading processes has been estimated. The calculated ratio between the fifth-order intensity and the intensity of the third-order cascading processes supports experimental observations, claiming that two-dimensional Raman spectra are dominated by third-order cascading processes. © 2000 American Institute of Physics.
The vibrations of H2O2, studied by “multimode,” with a large amplitude motion
Authors: Carter Stuart , Handy Nicholas C.
Published: July 2002

Recently Carter and Bowman [J. Chem. Phys. 108, 4397 (1998)] have introduced a variational scheme (“multimode”) for the calculation of rovibrational energy levels of polyatomic molecules using normal coordinates with the Watson Hamiltonian [Mol. Phys. 15, 479 (1968)]. The key to their algorithm is that at most four-mode coupling is allowed in matrix element evaluation. However nearly all larger molecules have one or more “large amplitude” motions, which are not treatable using normal coordinates. Here we extend multimode to include one large amplitude motion, using the theory of the reaction path Hamiltonian [J. Chem. Phys. 72, 99 (1980)], which is an almost identical problem. Essentially exact variational calculations are possible, and the approach is applied to the vibrations and tunneling motion of hydrogen peroxide.
Extension of the Genkin and Mednis treatment for dynamic polarizabilities and hyperpolarizabilities of infinite periodic systems. I. Coupled perturbed Hartree–Fock theory
Authors: Kirtman Bernard , Gu Feng Long , Bishop David M.
Published: July 2002

The uncoupled theory of Genkin and Mednis [Sov. Phys. JETP 27, 609 (1968)] for the nonlinear optical properties of infinite periodic systems has been extended to yield a fully analytical coupled perturbed Hartree–Fock treatment. Similarities and differences from other approaches to the same problem are analyzed. Future addition of electron correlation and vibrational contributions is discussed.
Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. I. Velocity-dependent mappings of second-order differential equations
Authors: Katzin Gerald H. , Levine Jack
Published: July 2002

The primary purpose of this paper is to show that infinitesimal velocity-dependent symmetry mappings [(a) x̄i =xi +δxi, δxi  ≡ ξi(ẋ,x,t)δa with associated change in path parameter (b) t̄=t+δt, δt ≡ ξ0(ẋ,x,t)] of classical (including relativistic) particle systems (c) Ei(ẍ,ẋ,x,t) =0 are expressible in a form with a characteristic functional structure which is the same for all dynamical systems (c) and is manifestly dependent upon constants of motion of the system. In this characteristic form the symmetry mappings are determined by (d) ξi =Zi(ẋ,x,t) +ẋiξ0,ξ0 arbitrary; the functions Zi appearing in (d) have the form (e) Zi =BAgiA(C1,...,Cr; t), 0≤r≤2n, A=1,...,2n, where the BA are arbitrary constants of motion and the C’s appearing in the functions giA are specified constants of motion.

A procedure is given to determine the giA. For Lagrangian systems it follows that velocity-dependent Noether mappings are a subclass of the above-mentioned general symmetry mappings of the form (a)–(e). An analysis of velocity-dependent Noether mapping theory is included in order to compare for Lagrangian systems the procedure for obtaining the characteristic form (e) of the general mappings with the procedure for obtaining the well-known formula (f) ZiN =Hij(ẋ,x,t)∂Z/∂ẋ j (Z ≡  constant of motion), characteristic of velocity-dependent Noether mappings. It is shown how any given velocity-dependent symmetry mapping function Zi(ẋ,x,t) (including Noether mappings) can be expressed in the form (e). A collection of variational formulas and identities is derived in order to develop from first principles the velocity-dependent symmetry mapping theory. Throughout, comparisons are made between velocity-dependent and velocity-independent symmetry theory.
Eulerian parametrization of Wigner’s little groups and gauge transformations in terms of rotations in two-component spinors
Authors: Han D. , Kim Y. S. , Son D.
Published: July 2002

A set of rotations and Lorentz boosts is presented for studying the three-parameter little groups of the Poincaré group. This set constitutes a Lorentz generalization of the Euler angles for the description of classical rigid bodies. The concept of Lorentz-generalized Euler rotations is then extended to the parametrization of the E(2)-like little group and the O(2,1)-like little group for massless and imaginary-mass particles, respectively. It is shown that the E(2)-like little group for massless particles is a limiting case of the O(3)-like or O(2,1)-like little group. A detailed analysis is carried out for the two-component SL(2,c) spinors. It is shown that the gauge degrees of freedom associated with the translationlike transformation of the E(2)-like little group can be traced to the SL(2,c) spins that fail to align themselves to their respective momenta in the limit of large momentum and/or vanishing mass.
The Hirota conditions
Authors: Newell Alan C. , Yunbo Zeng
Published: July 2002

The condition on the polynomial P for a Hirota equation Pτ ⋅ τ=0 to have an N-soliton solution for arbitrary N is examined and simplified.
Time-ordering techniques and solution of differential difference equation appearing in quantum optics
Authors: Dattoli G. , Gallardo J. , Torre A.
Published: July 2002

Time-ordering techniques based on the Magnus expansion and the Wei–Norman algebraic procedure are discussed and their relevance and usefulness to quantum optics are stressed.
A bimodular representation of ten-dimensional fermions
Authors: Davies A. J. , Joshi G. C.
Published: July 2002

The fermionic and supersymmetric octonionic bimodular representations are constructed. It is shown that an octonionic formulation of the fermion leads to an intrinsically ten-dimensional world with two independent representations. Consistency conditions for an octonionic supersymmetric algebra are also discussed.
Electromagnetic scattering of an arbitrary plane wave from a spherical shell with a circular aperture
Authors: Ziolkowski Richard W. , Johnson William A.
Published: July 2002

The problem of the scattering of an electromagnetic plane wave with arbitrary polarization and angle of incidence from a perfectly conducting spherical shell with a circular aperture is solved with a generalized dual series approach. This canonical problem encompasses coupling to an open spherical cavity and scattering from a spherical reflector. In contrast to the closed sphere problem, the electromagnetic boundary conditions couple the TE and TM modes. A pseudodecoupling of the resultant dual series equations system into dual series problems for the TE and TM modal coefficients is accomplished by introducing terms that are proportional to the associated Legendre functions P−m0. The solutions of the TE and TM dual series problems require the further introduction of terms proportional to P−mn, where 0≤n<m. These functions effectively complete the standard spherical harmonic basis set when an aperture is present and guarantee the satisfaction of Meixner’s edge conditions. Having generated the modal coefficients, all desired electromagnetic quantities follow immediately. Numerical results for the currents induced on the open spherical shell and for the energy density of the field at its center are presented for the case of normal incidence.
The energy levels and the corresponding normalized wave functions for a model of a compressed atom. II
Authors: Yngve Staffan
Published: July 2002

Recently Fröman et al. [J. Math. Phys. 28, 1813 (1987)] obtained a simple formula for the energy shift due to the compression of an atom. In the model considered the usual condition (associated with the corresponding uncompressed atom) that the wave function must vanish at r=∞ is replaced by the boundary condition that the wave function must have a node at the finite distance r=a. The treatment of the problem of obtaining the energy shift due to the compression is based on the phase-integral method developed by Fröman and Fröman. In the present work the formula for the energy shift is generalized to a possible additional choice of the base function in the phase-integral treatment. The normalized wave function close to the origin is also obtained. As an application, the resulting general formula for the energy shift is particularized to the case of a hydrogenic atom and a numerical illustration of the accuracy of the formula for the two alternative choices of the base function is given.
Generalized Luneburg canonical varieties and vector fields on quasicaustics
Authors: Janeczko S.
Published: July 2002

Some aspects of a particular class of bifurcation varieties which are provided by simple and unimodal boundary singularities are studied. Their correspondence to diffraction theory is established. The generic caustics by diffraction on apertures are derived and their generating families for the corresponding Lagrangian varieties are calculated. It is proved that the quasicaustics associated to simple singularities are smooth hypersurfaces or Whitney’s cross-caps. The procedure for calculating the modules of logarithmic vector fields is given, and the minimal sets of the corresponding generators are explicitly calculated. The general boundary singularities are constructed and the structure of quasicaustics defined by parabolic singularities is investigated.
A systematic approach to self-similarity in Newtonian space-time
Authors: Carter B. , Henriksen R. N.
Published: July 2002

After an introductory mathematical review of the general concept of self-similarity with respect to a given rescaling algebra, attention is focused on the case of Newtonian systems in Galilean space-time, whose self-similarity transformations will form subgroups of the maximal self-similarity group of the Galilean space-time structure itself. As a prerequisite for a systematic general investigation of self-similarity in such Newtonian systems, it is shown how an appropriately adapted similarity transporting coordinate system can be constructed explicitly for an arbitrary generator of the 12 parameter Galilean self-similarity group. A concrete application is provided by the case of the Keplerian disk, which is kinematically self-similar under the action of a three parameter subgroup. It is shown in the explicit example of a Eulerian fluid system how the generic self-similarity problem can be formulated as an effective stationarity problem.
Nonclassical symmetry solutions and the methods of Bluman–Cole and Clarkson–Kruskal
Authors: Arrigo D. J. , Broadbridge P. , Hill J. M.
Published: July 2002

Nonclassical symmetry solutions of physically relevant partial differential equations are considered via the reduction methods of Bluman and Cole and Clarkson and Kruskal. Consistency conditions will be provided to show that, if satisfied, these two methods are equivalent in the sense that they lead to the same symmetry solutions. The Boussinesq equation and Burgers’ equation are used as illustrative examples. Exact solutions, one of which is new, will be presented for Burgers’ equation obtained from the Bluman and Cole method, yet not obtainable by Clarkson and Kruskal’s method.