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Volume 105, Issue 4, 22 July 1996

Determination of the conduction band energy minimum in fluid argon by means of field ionization
View Description Hide DescriptionThe evolution of the ionization potential of H_{2}S doped in argon for argon densities between the dilute gas and the triple point liquid was obtained by means of field ionization. The field ionization spectra of H_{2}S in argon were simulated by convoluting the spectrum obtained in pure H_{2}S with the calculated polarization energy distribution between the H_{2}S ion and the medium. The density dependence of the conduction band energy minimum V _{0}(ρ) (relative to vacuum) was obtained from the energy difference between the experimental spectra and the simulations. Excellent agreement was found between these values and those obtained using a larger molecule, CH_{3}I. The values of V _{0}(ρ) are compared to recent theoretical calculations.

A general and efficient filter‐diagonalization method without time propagation
View Description Hide DescriptionA general and efficient filter‐diagonalization method is proposed to solve the quantum mechanical eigenvalue/eigenstate problem in a pre‐specified energy range. This method is in similar spirit to the original filter‐diagonalization approach, but it eliminates the time propagation by expanding the filter operator directly in the energy space in terms of Chebychev polynomials. Our approach is more efficient than the existing methods because neither time propagation nor time‐to‐energy transformation is needed. It also allows the choice of the most efficient filter operator for the system of interest. This method is tested for a one‐dimensional Morse oscillator and for the two‐dimensional Henon–Heiles system. The results show excellent convergence and accuracy.

Spectroscopy of F_{2} in Ne matrices
View Description Hide DescriptionThe excited states of free and matrix‐isolated F_{2} were investigated in the windowless VUV region by absorption and excitation spectroscopy. In emission the f ^{3}Π_{ g }→a ^{3}Π_{ u } laser band of F_{2} at 7.72 eV with a radiative lifetime of 2 ns and a weaker and broader band at 7.47 eV attributed to emission of F_{2} aggregates are observed in an Ne matrix independent on excitation energy. The Franck–Condon envelope of the charge transfer state C ^{1}Σ^{+} _{ u } extends further to the blue by more than 1 eV in Ne (12 to 14 eV) compared to the gas phase due to a blueshift of the avoided crossing with the Rydberg 3pπ_{ u }(^{1}Σ^{+} _{ u }) state. The H ^{1}Π_{ u }Rydberg state remains unperturbed in the Ne matrix but is blueshifted by 1.24 eV and significantly broadened due to electron–phonon coupling. A previously unreported broad absorption is observed both in the gas phase and in the matrix around 15 eV and is assigned to a strongly perturbed charge transfer state with Σ symmetry corresponding to F ^{+}*(^{1} S) and F ^{−}(^{1} S) ions in the dissociation limit. This charge transfer state is strongly perturbed in the gas phase by the high density of npπ_{ u }(^{1}Σ^{+} _{ u }) Rydberg states (n≥4) while in Ne matrix it is mixed mainly with the low‐lying 4pπ_{ u }(^{1}Σ^{+} _{ u }) state. The analogy of the resulting two separated groups of bands with irregular vibrational progressions to the Cl_{2} case is shown. Further npπ_{ u } and npσ_{ u }Rydberg progressions and the repulsive ^{3}Σ^{+} _{ u } valence state are treated. The utility of matrix‐isolated F_{2} for a solid state laser is discussed.

The B(1/2 ^{2} P _{3/2})→X(1/2 ^{2}Σ^{+}) transition in XeI
View Description Hide DescriptionThe B(1/2 ^{2} P _{3/2})→X(1/2 ^{2}Σ^{+}) transition in XeI (2385–2490 Å) is recorded at high resolution for the single isotopomer ^{136}Xe^{127}I, using a Tesla discharge source and a CCD array detector. The high signal‐to‐noise capabilities of the detector make it possible to measure the discrete vibrational structure in this system for the first time. The assignments consist of 86 v′–v″ bands spanning 15 upper‐state levels (assigned as v′=3–17) and 17 lower‐state levels (tentatively assigned as v″=0–16). A vibrational analysis yields the following spectroscopic constants (cm^{−1}): ΔT _{ e }=40 047.8, ω_{ e } ^{′}=110.6, ω_{ ex } _{ e } ^{′}=0.217, ω_{ e } ^{″}=24.0, ω_{ ex } _{ e } ^{″}=0.66. From a near‐dissociation analysis, the X state has a dissociation energy (D_{ e }) of 267±5 cm^{−1} and supports 28 bound vibrational levels. However, it is likely that our lowest observed v″ level is not v″=0, so these values should be considered lower limits. The potential energy curves are modeled by a Morse–RKR function for the X state and a Rittner function for the B state. Trial‐and‐error Franck–Condon calculations are used to locate the B‐ and X‐state potential curves relative to each other, fixing the X‐state internuclear distance R _{ e } at a value ∼0.7 Å larger than that for the B state. Bound–free simulations of the low‐resolution spectrum indicate that the X potential must be significantly steeper in the Franck–Condon region than found from previous scattering studies.

High‐resolution laser spectroscopy of the X ^{1}Σ^{+} and (1)^{3}Σ^{+} states of ^{23}Na^{85}Rb molecule
View Description Hide DescriptionHigh‐resolution spectra of the B ^{1}Π→X ^{1}Σ^{+} transition of ^{23}Na^{85}Rb molecule are measured by the technique of the Doppler‐free optical–optical double resonance polarizationspectroscopy (OODRPS). The molecular constants of the X ^{1}Σ^{+}(v ^{″}=5−30) levels are determined, and the potential energy curve is constructed up to v ^{″}=30 by the RKR method. The time‐resolved fluorescence intensity following the excitation to the B ^{1}Π(v ^{′}=5,J ^{′}= around 20) level is measured, and the lifetime of the B ^{1}Π(v ^{′}=5) level in collisionless limit is determined to be 17.8 ns. The absolute value of the electric dipole moment of the B ^{1}Π−X ^{1}Σ^{+} transition is determined to be 7.0 D in the region of 3.73 Å<R<4.98 Å. Transition lines to the (1)^{3}Σ^{+} state from the B ^{1}Π(v′=8,J′=15) level, which is perturbed by the (1)^{3}Π_{1}(v ^{0},N=J=15) level, are measured by the Doppler‐free OODRPS. The energy spacing between the F _{1} and F _{3} components of the (1)^{3}Σ^{+}(v=4,N=15) level is observed to be smaller than 0.001 cm^{−1}. The hyperfine splittings, which are described by Hund’s case (b _{βS }), are observed, and the hyperfine constants A _{Na} and A _{Rb} of the (1)^{3}Σ^{+}(v=4) level are determined to be 0.0293 and 0.0336 cm^{−1}, respectively. The hyperfine splittings are identified as originating from the Fermi contact interaction. From the analysis, it is concluded that the electron spins in the (1)^{3}Σ^{+} state are almost equally populated to the 5s ^{Rb} and 3s ^{Na} orbitals.

Theory of odd torsional transitions in the V−N resonance Raman spectrum of ethylene
View Description Hide DescriptionThe V−N resonance Raman spectrum of ethylene shows a long progression in even quanta of the ground‐state torsional mode ν_{4} ^{″}(a _{ u }). Bands approximately midway between the even quanta have been assigned to transitions to odd quanta of ν_{4} ^{″}, although such transitions are forbidden according to the usual g↔/u selection rule of Raman spectroscopy. We consider the theory of the intensity of such transitions allowing for the fact that the excited state is twisted by 90° at equilibrium, using Hougen’s double group theory for the separation of the torsional and a‐rotational motions. From approximate one‐dimensional torsional potentials of the V and N electronic states, it is shown that qualitative agreement between observed and calculated intensities is obtained. The electronic transition moment is assumed to be proportional to cos2γ, where 2γ is the torsional angle, but the calculated relative intensities are not sensitive to the precise torsional dependence. More detailed theory will require inclusion of the CC‐stretching and CH_{2}‐scissoring degrees of freedom and consideration of an avoided crossing affecting the V state.

The vibrational energy pattern in ^{12}C_{2}H_{2}(II): Vibrational clustering and rotational structure
View Description Hide DescriptionWe achieve a systematic modeling of all rovibrational levels in the ^{12}C_{2}H_{2} (X̃ ^{1}Σ^{+} _{ g }) molecule, which is tested up to the near infrared range. It is based on the cluster picture, which was demonstrated to block diagonalize the full vibrational energy matrix, and to allow unraveling the vibrational energy pattern in ^{12}C_{2}H_{2}, up to 12 000 cm^{−1} [see M. Abbouti Temsamani and M. Herman, J. Chem. Phys. 102, 6371 (1995)]. Each of those clusters, which are called here V‐clusters, is made of pure vibrational type diagonal and off‐diagonal matrix elements. That model is extended to take care of the rotational structure, defining the V/l/C‐cluster model. In a first step J‐dependent terms are included in the diagonal elements of the V‐clusters, and rotational l resonance off‐diagonal matrix elements are included, leading to couple specific V‐cluster matrices, resulting into so‐called V/l‐clusters. This extension is quantitatively demonstrated to reproduce the reported effective principal rotational constant and effective higher order distortion constants, for four selected clusters of levels: those containing V _{1}+V _{3}, V _{1}+V _{2}+V _{3}, 3V _{3} and V _{2}+3V _{3}. In the case of the 3ν_{3} range, new FTIR spectra recorded around 9700 cm^{−1} are used. The related experimental conditions and new observed spectral features are briefly presented. A further extension of the model is then accomplished to include Coriolis‐type interaction, by coupling V/l‐clusters using a systematic mechanism. That step, defining the model of V/l/C‐clusters, allows to suggest assignment for extra rovibrational lines observed around 3ν_{3}. Those various steps are supported by a consistent picture involving constants of the motion, starting with three pseudoquantum numbers in the case of V‐ cluster, {n _{ s },n _{ r },k}, from which two, {n _{ s },n _{ r }} and then one {n _{ r }} remain when defining respectively the V/l‐cluster and V/l/C‐cluster matrices.

The dynamics of predissociating high Rydberg states of NO
View Description Hide DescriptionIn this paper we present a theoretical study of the predissociation dynamics of the nf(N ^{+}=2) (with the principal quantum numbers n=40–95) and the np(N ^{+}=0) (n=70–125) Rydberg series of NO, which exhibit a marked lifetime dilution (lengthening) at n≳65 for the f series and at n≳116 for the p series [M.J.J. Vrakking and Y. T. Lee, J. Chem. Phys. 102, 8818 (1995)]. The multichannel effective Hamiltonian with several doorway (for excitation) and escape (for decay) states was constructed using experimental information on the quantum defects and on the decay width constants incorporating both intramolecular coupling and exterior electric field coupling between high Rydbergs. The analysis of the intramolecular Rydberg electron–core dipole long range coupling (H _{R‐D}) in conjunction with the energy gaps between proximal pairs of energy levels, which are subjected to appropriate selection rules, reveals that (i) for low l(≤3) core‐penetrating Rydbergs only a small number of accidental near‐resonances are exhibited, and (ii) for high l(≳3) nonpenetrating Rydbergs the electron‐core dipole coupling decreases fast with increasing l, i.e., (H _{R‐D})∝l ^{−7}. The general characteristics of the high l(≳3) manifold establish a bottleneck effect, which precludes intramolecular l mixing, implying that high Rydberg lifetime dilution effects can be induced only by exterior electric field coupling (H _{STARK}). Parameter‐free multichannel effective Hamiltonian calculations were conducted under narrow‐band excitation conditions, which interrogate the electric field induced mixing in the energetic vicinity of the doorway state. The electric field induced l mixing model accounts semiquantitatively for the electric field dependence of the energy‐resolved line shapes of the nf(N ^{+}=2) series and for the n and electric field dependence of the lifetimes of the nf(N ^{+}=2) and the np(N ^{+}=0) series. Accidental near‐resonant simultaneous intramolecular and electric field coupling np(N ^{+}=0)↔^{ H } _{R‐D} n′d(N ^{+}=1)↔^{ H } _{STARK} n′ l(≥3)(N ^{+}=1) for two sets of proximal states n=92, n′=80 and n=95, n′=82, result in mediated‐sequential mixing, which is manifested by slow decay times below the onset of effective electric field mixing by weak (F _{0}≂0.04–0.08 V/cm) stray electric fields.

Collisional deactivation of highly vibrationally excited pyrazine
View Description Hide DescriptionThe collisional deactivation of vibrationally excited pyrazine (C_{4}N_{2}H_{4}) in the electronic ground state by 19 collider gases was studied using the time‐resolved infrared fluorescence (IRF) technique. The pyrazine was photoexcited with a 308 nm laser and its vibrational deactivation was monitored following rapid radiationless transitions to produce vibrationally excited molecules in the electronic ground state. The IRF data were analyzed by a simple approximate inversion method, as well as with full collisional master equation simulations. The average energies transferred in deactivating collisions (〈ΔE〉_{ d }) exhibit a near‐linear dependence on vibrational energy at lower energies and less dependence at higher energies. The deactivation of ground state pyrazine was found to be similar to that of ground state benzene [J. R. Barker and B. M. Toselli, Int. Rev. Phys. Chem. 12, 305 (1990)], but it is strikingly different from the deactivation of triplet state pyrazine [T. J. Bevilacqua and R. B. Weisman, J. Chem. Phys. 98, 6316 (1993)].

A quasiclassical trajectory calculation for the Penning ionization H_{2}O+He*(2^{3} S)→H_{2}O^{+}+He+e ^{−}: Rotational cooling effects
View Description Hide DescriptionA quasiclassical trajectory calculation is performed for the Penning ionization system H_{2}O+He*(2^{3} S)→H_{2}O^{+}(^{2} B _{2},^{2} A _{1},^{2} B _{2})+He+e ^{−} at H_{2}O rotational temperatures of 300, 200, 100, and 25 K. The resonance potential and the widths for the three ionized states are fitted to analytical functions on the previous ab initio points [J. Chem. Phys. 102, 4169 (1995)]. The calculational results are compared with experimental measurements. The total and partial ionization cross sections are calculated in the energy range 0.05–1.0 eV. As the rotational temperature is lowered, the following results are predicted: the total cross section decreases with collision energy, and the dominant ionization into the ^{2} A _{1} state is more enhanced. These results are due to the increasing drawing of trajectories into the attractive H_{2}O lone pair region with decreasing rotation frequency. Opacity functions and total and partial ionization probabilities for each trajectory are analyzed to interpret the results obtained for the cross sections.

Particle simulation of chemical chaos
View Description Hide DescriptionA microscopic computer experiment is set up to investigate the statistical properties of a homogeneous chemical system undergoing chaos at the macroscopic level. A specific model, the Willamowski–Rössler having a well‐defined microscopic counterpart is used. Quantitative comparison with both the prediction of the deterministic description based on the rate equations and the results of the stochastic analysis is carried out. Dynamical and static properties obtained from these three procedures are in very good agreement and confirm the robustness of the underlying deterministic attractor even when microscopic aspects are taken into account.

Investigation on the reflection and transmission properties of complex absorbing potentials
View Description Hide DescriptionThe reflection and transmission properties of different complex absorbing potentials (CAPs) are studied using WKB and scaling procedures which make the results transferable to any mass and kinetic energy. Explicit formulas are obtained which describe the reflection and transmission properties of monomial CAPs −iηx ^{ n } with high accuracy. These properties are now well understood. The approximate results are compared to exact analytical results available for quadratic CAPs, and to numerical results obtained by wave packet propagation followed by an energy resolved analysis. The approximate, but accurate, description of the action of the CAP is finally used to determine optimal CAP parameters. CAP length, strength, and order can now be chosen in such a way that the sum of reflection and transmission is minimized. Optimal parameters are compiled for different energies and energy intervals.

Collisional deactivation of N_{2}O(00^{0}1) studied by time‐resolved infrared fluorescence
View Description Hide DescriptionThe time‐resolved infrared fluorescence (IRF) technique has been used to study the vibrational deactivation of excited N_{2}O by large polyatomic colliders at ambient temperature (295±2 K). N_{2}O(00^{0}1) molecules were prepared by direct pumping with the P(18) line of a pulsed CO_{2} laser at 9.536 μm. The bimolecular rate constant for self‐deactivation was determined to be (0.763±0.006)×10^{3} Torr^{−1} s^{−1}, in very good agreement with previous work. The rate constants for deactivation by Ar and H_{2} were found to be (0.103±0.003) and (4.89±0.52)×10^{3} Torr^{−1} s^{−1}, respectively. The deactivation rate constants for the large polyatomic molecules, c‐C_{6}H_{10}, c‐C_{6}H_{12}, C_{6}H_{6}, C_{6}D_{6}, C_{7}H_{8}, C_{7}D_{8}, C_{6}H_{5}F, p‐C_{6}H_{4}F_{2}, C_{6}HF_{5} and C_{6}F_{6}, were found to be (176±10), (153±22), (115±4), (201±2), (127±11), (407±52), (144±14), (173±13), (129±8), and (48±9)×10^{3} Torr^{−1} s^{−1}, respectively. Experimental deactivation probabilities and average energies removed per collision are calculated and compared. There is little difference in deactivation probabilities between the acyclic ring compounds and their aromatic analogues and the partially‐fluorinated benzenes but the perfluorinated compound, C_{6}F_{6} is much less efficient than the other species. The perdeuterated species, C_{6}D_{6} and C_{7}D_{8}, especially the latter, show enhanced deactivation relative to the other species, probably as a result of near‐resonant intermolecular V–Venergy transfer. The results are compared with our recent work on the deactivation of CO_{2}(00^{0}1) by the same group of large polyatomic colliders [K. L. Poel, Z. T. Alwahabi, and K. D. King, Chem. Phys. 201, 263 (1995)].

Molecular dynamics with multiple time scales: The selection of efficient reference system propagators
View Description Hide DescriptionSeveral heuristic rules are developed to assist in the implementation of the reversible reference system propagator algorithm (rRESPA). This is done through the use of examples, illustrating the use of properly chosen rRESPA splits of various types, as well as the dangers associated with improperly chosen ones. It is concluded that a particle‐based rRESPA split should be used only when there is a great disparity in particle masses, and that a force‐based split should be used only when there is no persisting opposition between forces in the system which are integrated with different time steps.

Ab initio computation of semiempirical π‐electron methods. V. Geometry dependence of H ^{ν} π‐electron effective integrals
View Description Hide DescriptionThe ab initio effective valence shell Hamiltonian (H^{ν}) provides ab initio analogs of the correlated π‐electron integrals which should appear in the traditional Pariser–Parr–Pople (PPP) semiempirical π‐electron theory. In our continuing studies of the ab initio basis of an improved PPP theory, we examine the geometry dependence of the correlated H^{ν} π‐electron effective integrals (also called parameters) for the linear polyenes, ethylene, the allyl radical, trans‐butadiene, and hexatriene, and the cyclic polyenes, cyclobutadiene and benzene. We find particularly interesting features for each of the true π‐electron parameters corresponding to the PPP α_{ i }, β_{ i,j }, and γ_{ i,j } integrals. First, the one‐electron, two‐center resonance integrals β_{ i,j } differ from the so‐called ‘‘theoretical’’ values by roughly a constant shift of 0.3–0.4 eV for nearest neighbors i and j and not at all for more distant neighbors. Second, the correlated α_{ i } parameters conform to the standard point charge model fairly well, except the slopes and intercepts lack the transferability typically ascribed to them. A more accurate PPP model therefore must model the one‐center, one‐electron interactions more carefully. Finally, the effective Coloumb interactions γ_{ i,j } follow the standard Mataga–Nishimoto distance dependence quite well for the linear polyenes, although there is a small breakdown of transferability due to long range correlation effects. For instance, the hexatriene γ_{1,2} is 0.5 eV smaller than the ethylene γ_{1,2} even when the C1=C2 bond lengths are identical. Additionally, the set of γ_{ i,j } for the cyclic polyenes is not even a single function of R _{ i,j }, a feature reflecting the subtle contributions of electron correlation to the ab initio γ_{ i,j }. However, plots of γ^{−1} _{ i,j } vs R _{ i,j } display some unforeseen regularity which may prove useful in improving current semiempirical models for cyclic polyenes.

Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies
View Description Hide DescriptionThe contributions from various excitation levels to excitation energies calculated within a coupled cluster framework are analyzed in terms of order in the fluctuation potential. In particular, the role of triple excitations is considered, focusing on their importance for describing excitations of single and double replacement dominated character. Several noniterative triples corrections to the coupled cluster singles and doubles (CCSD) excitation energies are proposed. In the CCSDR(3) approach, which is a noniterative analog to the recently proposed iterative CC3 model, single replacement dominated excitations are correct through third order in the fluctuation potential, and double replacement dominated excitations are correct through second order. The performance of CCSDR(3) is compared to other noniterative and iterative triples models in benchmark calculations on CH^{+}, Ne, BH, and CH_{2}.

Coupled Hartree–Fock calculations of molecular magnetic properties annihilating the transverse paramagnetic current density
View Description Hide DescriptionThe reliability of the continuous transformations of origin of the current density method, which makes the transverse paramagnetic current vanish (CTOCD‐PZ), for the prediction of nearly gauge‐origin independent molecular magnetic susceptibility and gauge‐origin independent nuclear magnetic shielding, is proved on the basis of a fairly large number of calculations. It is shown that, within the computational scheme provided by the coupled Hartree–Fock perturbation theory (CHF), convergence towards the presumed Hartree–Fock limit, for magnetic susceptibility and protonmagnetic shielding, is systematically reached using basis sets which are smaller than those required by conventional common origin and CTOCD‐DZ techniques. For second‐row nuclear magnetic shieldings a variant of the CTOCD‐PZ method, which shifts the origin of the current towards the nearest nucleus for points close to nuclei, as suggested originally by Keith and Bader with the CSDGT method [T. A. Keith and R. F. W. Bader, Chem. Phys. Lett. 210, 223 (1993)], gives likewise good results with affordable basis sets.

New operators for electronic density calculation. I. Derivations and formal analysis
View Description Hide DescriptionThe electronic charge and spin density at any point in space are reexpressed in terms of the expectation values of any member of a general class of global operators. For practical use with approximate wave functions, two particular choices of operator are made that should provide advantages for the difficult case of density evaluation at a nucleus. Formal properties of these operators are derived and discussed in detail. Certain serious difficulties known for the behavior of the global operator previously introduced by Hiller, Sucher, and Feinberg are ameliorated in the new formulations.

New operators for electronic density calculation. II. Application to hydrogen, first‐row atoms, and first‐row diatomic hydrides
View Description Hide DescriptionThe first practical calculations using two new operators specifically designed for determination of electronic spin and charge density at nuclei are reported. Applications are given for hydrogen, first‐row atoms, and first‐row diatomic hydrides. Numerical grid methods that simulate complete basis set results confirm a number of relations previously derived formally for the new operators. They also serve as benchmarks for testing the practical utility of the new operators in calculations with small to large Gaussian basis sets. In this connection, the new operators are generally found to have performance superior to the usual delta function formulation and to an alternative one based on the Hiller–Sucher–Feinberg identity.

A pseudopotential hole‐particle treatment of neutral rare gas excimer systems. I. Formalism
View Description Hide DescriptionA pseudopotential hole‐particle formalism is developed for the treatment of rare‐gas excimers and excited rare‐gas clusters. The formalism relies on the definition of a model Hamiltonian on the basis of single hole‐particle excitations (from the neutral closed shell ground state) involving localized np hole orbitals and any orthogonal molecular orbital (MO) basis set for the excited particle. Hole contributions in the Hamiltonian matrix elements are taken into account via distance‐ and orientation‐dependent transfer integrals (hole delocalization) and repulsion integrals like in diatomic in molecules treatments of rare gas ions, while the contribution of the excited particle is included through an explicit quantal treatment via one‐electron e‐Rg and averaged e‐Rg^{+} pseudopotentials. Core‐polarization pseudopotentials are also added to account for core‐polarization and core‐Rydberg correlation effects. Some approximated core‐Rydberg two‐electron integrals needed for adequate space and spin multiplicity of the excited states are also included. The possible applications and extensions of this formalism are discussed.