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22 Sep 1995

Volume 103, Issue 12, pp. 4829-5169

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A stochastic theory of inhomogeneously broadened linewidths in solids

Ulrich Zürcher

J. Chem. Phys. 103, 4829 (1995); http://dx.doi.org/10.1063/1.470617 (5 pages) | Cited 1 time

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We investigate spectral diffusion decay using a model for solids that consists of two‐level‐systems (TLSs) interacting via strain fields. For the case when the rate of TLS flips vanishes, we find algebraic decay of correlation functions of the local field. We show that properties of equilibrium fluctuations are in agreement with the hierarchical picture proposed by Basché and Moerner: TLSs far away produce fast fluctuations that are small in magnitude, and close TLSs produce large fluctuations that are less frequent. © 1995 American Institute of Physics.
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
42.65.-k Nonlinear optics
63.20.Pw Localized modes

Structure of chemically synthesized nanophase GaAs studied by nuclear magnetic resonance and x‐ray diffraction

L. D. Potter, A. A. Guzelian, A. P. Alivisatos, and Y. Wu

J. Chem. Phys. 103, 4834 (1995); http://dx.doi.org/10.1063/1.470618 (7 pages) | Cited 4 times

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Nanophase GaAs produced by organometallic synthesis was studied by 71Ga, 69Ga, and 75As nuclear magnetic resonance (NMR) as well as x‐ray diffraction. The structure of the samples synthesized below 250 °C is predominantly amorphous. Raising the temperature of synthesis (or post‐synthesis annealing) above 280 °C improves significantly the crystallinity as evidenced by the appearance of a sharp bulklike 71Ga (and 69Ga) peak. In addition, a sharp peak shifted up‐field also appears. Other NMR features of this up‐field shifted peak are very similar to the bulklike peak including quadrupole interactions and spin–lattice and spin–spin relaxations. These results are consistent with the presence of stacking faults in nanocrystalline GaAs. © 1995 American Institute of Physics.
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33.25.+k Nuclear resonance and relaxation
61.05.cf X-ray scattering (including small-angle scattering)
61.05.cj X-ray absorption spectroscopy: EXAFS, NEXAFS, XANES, etc.
61.50.-f Structure of bulk crystals

Ab initio model potential study of the optical absorption spectrum of Mn2+‐doped CaF2

José Luis Pascual, Luis Seijo, and Zoila Barandiarán

J. Chem. Phys. 103, 4841 (1995); http://dx.doi.org/10.1063/1.470619 (6 pages) | Cited 6 times

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An ab initio calculation of the optical absorption spectrum of Mn2+‐doped CaF2 is performed in which electrostatic and quantum embedding effects originated by a relaxed and polarized CaF2 lattice on the ligand field ground and excited states of a MnF86− cluster have been considered. The theoretical spectrum is calculated by means of the complete active space self‐consistent‐field (CASSCF) and average coupled pair funtional (ACPF) methods, correlating up to 23 electrons. An excellent overall agreement with the experiments is found and a detailed analysis of the results is presented. The initial assignment of the 4A1g(4G) and 4Eg(4G) states, lately reversed, is supported. The wrong assignment of the 4T1g(4P) state is shown to be responsible for a recently proposed change of the value of the crystal field splitting paramenter initially accepted, 10Dq=4250 cm−1, which is in turn supported here. Also, new assignments for the absorptions to the 4T1g(4F) and 4T2g(4F) excited states are suggested. © 1995 American Institute of Physics.
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31.15.A- Ab initio calculations
33.20.Kf Visible spectra

A two‐color (1+1′)+1 multiphoton ionization study of CS2 in the 61 000–65 600 cm−1 energy region

Jacob Baker and Stelios Couris

J. Chem. Phys. 103, 4847 (1995); http://dx.doi.org/10.1063/1.470620 (8 pages) | Cited 11 times

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The (1+1′)+1 resonance enhanced multiphoton ionization (REMPI) spectrum of jet‐cooled CS2 has been recorded in the 61 000–65 600 cm−1 excitation energy range. Four prominent band groups are observed that can be assigned to Δν2=−1 and Δν2=1 sequences of the two‐photon electronically forbidden 4p 1,3Δu←math 1Σ+g transitions. Weak bands to higher energy appear to be associated with the 310, 230 and 110210 bands and corresponding sequence bands. The results show that the upper states are not 3d Rydberg states as has been previously supposed, and are consistent with a recent reinvestigation of the corresponding (3+1) REMPI spectrum. Further experimental information is obtained on the anomalous vibrational band structure of transitions to the 3Δu state. The 201 and 212 bands of the 4p 1Πu←math 1Σ+g transition are also observed, but are much weaker, suggesting that vibronic interactions are less important in this state compared to the 4p 1,3Δu states. © 1995 American Institute of Physics.
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33.20.Tp Vibrational analysis
33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)

van der Waals vibrations and isomers of 2,3‐dimethylnaphthalene⋅Ne: Experiment and quantum three‐dimensional calculations

Thierry Droz, Samuel Leutwyler, Margaret Mandziuk, and Zlatko Bačić

J. Chem. Phys. 103, 4855 (1995); http://dx.doi.org/10.1063/1.470621 (14 pages) | Cited 9 times

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We report a combined experimental and theoretical study of the van der Waals isomers and intermolecular vibrations of the 2,3‐dimethylnaphthalene⋅Ne complex in the S1 electronic state. The two‐color resonant two‐photon ionization spectrum exhibits eight bands within ≊40 cm−1 of the electronic origin. Theoretical considerations in combination with hole‐burning spectroscopic measurements show that the transition closest to the electronic origin (at 000+5 cm−1) arises from an isomer which is different from that responsible for the other seven bands in the spectrum. The latter involve excitations of the intermolecular vibrations of the main isomer of 2,3‐dimethylnaphthalene⋅Ne. Accurate three‐dimensional quantum calculations of the van der Waals vibrational levels of the complex were performed using a discrete variable representation method. Combination of theory and experiment led to a complete assignment as well as to a quantitative theoretical reproduction of the experimental intermolecular vibrational level structure, and a parametrization of the intermolecular potential energy surface, modeled as sum of atom–atom Lennard‐Jones pair potentials. This potential surface exhibits a global minimum above (and below) the aromatic ring plane of 2,3‐dimethylnaphthalene and a shallower local minimum at C2v geometry, on the C2 axis of the molecule, adjacent to the two methyl groups. The main and minor isomers identified experimentally are associated with the global and the local minimum, respectively. The quantum calculations were extended to ≊1000 van der Waals vibrational states, i.e., to energies up to 78% of D0. These include levels localized either in the global or local minima, as well as highly excited vibrational states delocalized over all three potential minima, providing comprehensive insight into the quantum dynamics of the high‐lying van der Waals states of an atom–large aromatic molecule complex. © 1995 American Institute of Physics.
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33.20.Tp Vibrational analysis
34.20.Gj Intermolecular and atom-molecule potentials and forces

Effects of magnetic field on the 15V 31 344.9 band of CS2 studied by sub‐Doppler high‐resolution spectroscopy

Hajime Katô, Atsushi Doi, Yoshikazu Taroura, and Saburo Nagakura

J. Chem. Phys. 103, 4869 (1995); http://dx.doi.org/10.1063/1.470622 (10 pages) | Cited 8 times

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Effects of an external magnetic field on the excitation spectrum of the 15V 31 344.9 band of the CS2 molecule are measured with sub‐Doppler resolution. New lines are observed to appear near the R(2) and P(4) lines when a magnetic field is applied. These lines are observed to be composed of five components both for the π pump and for the σ pump. From a theoretical analysis, we identify the new lines as transitions to the 3A2(A1−B1)(v−;12M) levels, which become allowed by Zeeman interaction with the V 1B2(v′;03M) level that is mixed with the 3A2(B2)(v;03M) level by spin–orbit interaction. Variations of energy shifts and intensities with the magnetic field strength are explained quantitatively by this analysis. M‐dependent perturbation and the quenching of fluorescence are observed. The reason why large Zeeman splittings are observed at many lines in the V system of CS2 can be attributed to the spin–orbit interaction between the V 1B2(v′;KJM) level and the 3A2(B2)(v;KJM) level combined with the rotational and/or the Zeeman interactions between 3A2(B2)(v;KJM) level and either 3A2(A1+B1)(v0;K±1JM) or 3A2(A1−B1)(v±; K±1J±1M) levels which are accidentally close in energy. © 1995 American Institute of Physics.
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33.50.Hv Radiationless transitions, quenching
33.57.+c Magneto-optical and electro-optical spectra and effects

Photodissociation of HNO3 at 193 nm: Near‐infrared emission of NO detected by time‐resolved Fourier transform spectroscopy

Pey‐Shiun Yeh, Gen‐Hou Leu, Yuan‐Pern Lee, and I‐Chia Chen

J. Chem. Phys. 103, 4879 (1995); http://dx.doi.org/10.1063/1.470623 (8 pages) | Cited 21 times

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Rotationally resolved emission of NO, produced from photolysis of HNO3 at 193 nm, in the near infrared region (8900–9300 cm−1) was recorded with a step‐scan Fourier‐transform interferometer at a resolution of 0.1 cm−1. The emission is assigned as NO D 2Σ+−A 2Σ+ (v′,v″)=(0,0) band with rotational states N′=17–42. Emission from selective rotational states of NO D 2Σ+ was observed when HNO3 was photolyzed with an ArF excimer laser having a narrow bandwidth ≊0.01 nm. The experimental results indicate that the D 2Σ+ state of NO is formed via absorption of another 193 nm photon by NO (v″=1) in the ground electronic state. The measured distribution of intensity implies that NO is produced highly rotationally excited; the most likely mechanism for formation of NO is from the unstable NO2 fragment undergoing secondary dissociation. © 1995 American Institute of Physics.
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33.80.Gj Diffuse spectra; predissociation, photodissociation
82.50.Bc Processes caused by infrared radiation
82.50.Hp Processes caused by visible and UV light
42.30.Kq Fourier optics

Subpicosecond transient infrared spectroscopy of water: A theoretical description

S. Bratos and J‐Cl. Leicknam

J. Chem. Phys. 103, 4887 (1995); http://dx.doi.org/10.1063/1.470624 (7 pages) | Cited 20 times

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The pump–probe response of water in infrared is examined theoretically at time scales of the order of 100 fs; these times scales are characteristic of spectral diffusion. The theory is a statistical theory using correlation function description of the nonlinear optical processes involved. An analytical expression for the transient infrared signal is presented, and the corresponding time‐ and frequency‐resolved spectra are discussed. Real time shifts of spectral bands, preceded by a redistribution of their intensities, are predicted. Physical interpretation of these findings is proposed, corroborated by the help of simple models. The intrinsic interest of this time domain is emphasized. © 1995 American Institute of Physics.
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33.20.Ea Infrared spectra
82.30.Nr Association, addition, insertion, cluster formation

Vibronic coupling and energy transfer in bichromophoric molecules: The effect of symmetry

Niels A. van Dantzig, Donald H. Levy, Craig Vigo, and Piotr Piotrowiak

J. Chem. Phys. 103, 4894 (1995); http://dx.doi.org/10.1063/1.470625 (13 pages) | Cited 17 times

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The fluorescence spectra of a series of bichromophoric molecules consisting of covalently linked fluorene units were investigated in a supersonic jet. In three of the systems (spirobifluorene, d8h8‐spirobifluorene and 1‐methyl spirobifluorene) no electronic coupling and no corresponding exciton splitting were detected in the zero‐point level of the S1 state. Only 9,9′‐bifluorene exhibited an exciton splitting in the v=0 state. The lack of coupling was attributed to symmetry; in the spirobifluorenes the planes of the fluorene moieties and the S1←S0 transition moments are perpendicular. When low vibrational levels were excited, state mixing, and energy transfer between the chromophores was observed. This behavior is characteristic of the ‘‘small molecule’’ regime of radiationless transition theory. When higher vibrational levels were excited, the systems exhibited typical ‘‘large molecule’’ behavior. In this limit, both electronic energy transfer, as well as intramolecular vibrational relaxation contribute to the decay of the initially excited state. Intramolecular dispersive interactions were also investigated by comparing the bifluorenes with a series of reference compounds. © 1995 American Institute of Physics.
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31.50.Df Potential energy surfaces for excited electronic states
33.20.Wr Vibronic, rovibronic, and rotation-electron-spin interactions
33.50.Dq Fluorescence and phosphorescence spectra

On the low‐lying Rydberg states of azabenzenes

C. F. Dion and E. R. Bernstein

J. Chem. Phys. 103, 4907 (1995); http://dx.doi.org/10.1063/1.470626 (7 pages) | Cited 7 times

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Mass resolved excitation spectra of supersonic expansion cooled mono‐ and diazabenzenes are reported for the low lying Rydberg states. Transitions are located for pyridine, pyrazine, and pyridazine, but not pyrimidine. The Rydberg state lifetimes of these molecules are estimated, based on a Lorentzian line shape analysis, to be ca. 500 fs. Ab initio calculations for pyrazine at the complete active space self‐consistent‐field (CASSCF) and CASSCF many‐body second‐order perturbation theory (CASSCF/MBPT2) levels show that extensive configuration interaction and dynamic electron correlation are necessary to account for the excited states of these systems. © 1995 American Institute of Physics.
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31.15.xp Perturbation theory
31.15.xr Self-consistent-field methods
33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)
79.60.Fr Polymers; organic compounds

The quasi‐minimal residual algorithm applied to complex symmetric linear systems in quantum reactive scattering

Hans O. Karlsson

J. Chem. Phys. 103, 4914 (1995); http://dx.doi.org/10.1063/1.470627 (6 pages) | Cited 16 times

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The solution of systems of linear equations Ax=b with complex symmetric coefficient matrix A of size N, typically appearing in quantum‐reactive scattering problems, is discussed. The quasiminimal residual (QMR) method is introduced to solve the complex symmetric linear system and is compared to the generalized minimal residual (GMRES) method. The methods are applied to two different chemical problems: the initial state‐selected reaction probability for the H2+OH→H +H2O reaction, and the cumulative reaction probability for the isomerization of ketene, both with N≳104. It is shown that the QMR method behaves more favorably, i.e., converges faster, than the GMRES for large N, especially when high accuracy is needed. © 1995 American Institute of Physics.
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34.50.Lf Chemical reactions
82.30.-b Specific chemical reactions; reaction mechanisms

Critical scaling behavior in the activated barrier crossing problem. II. Power‐law potential

Surjit Singh and G. Wilse Robinson

J. Chem. Phys. 103, 4920 (1995); http://dx.doi.org/10.1063/1.470628 (10 pages) | Cited 2 times

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Using the Pollak–Grabert–Hänggi (PGH) weak‐coupling approximation, the activated barrier crossing (ABC) problem is studied with a general memory friction kernel and for a general power‐law potential added to a parabolic barrier. We focus on the recently discovered critical behavior of the rate for large memory friction correlation times. All the relevant critical exponents in different regimes of the strength of the friction are determined, and explicit expressions for the scaling function are obtained. We verify that the universality of exponents and amplitudes is applicable for this model within the PGH approximation. The results are compared with the results for canonical variational transition state theory (CVTST) recently obtained by us. © 1995 American Institute of Physics.
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64.60.F- Equilibrium properties near critical points, critical exponents
82.20.-w Chemical kinetics and dynamics

Characterization of the minimum energy path for the reaction of singlet methylene with N2: The role of singlet methylene in prompt NO

Stephen P. Walch

J. Chem. Phys. 103, 4930 (1995); http://dx.doi.org/10.1063/1.470629 (7 pages) | Cited 9 times

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We report calculations of the minimum energy pathways connecting 1CH2+N2 to diazomethane and diazirine, for the rearrangement of diazirine to diazomethane, for the dissociation of diazirine to HCN2+H, and of diazomethane to CH2N+N. The calculations use complete active space self‐consistent field (CASSCF) derivative methods to characterize the stationary points and internally contracted configuration interaction (ICCI) to determine the energetics. The calculations suggest a potential new source of prompt NO from the reaction of 1CH2 with N2 to give diazirine, and subsequent reaction of diazirine with hydrogen abstracters to form doublet HCN2, which leads to HCN+N(4S) on the previously studied CH+N2 surface. The calculations also predict accurate 0 K heats of formation of 77.7 kcal/mol and 68.0 kcal/mol for diazirine and diazomethane, respectively. © 1995 American Institute of Physics.
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31.15.vq Electron correlation calculations for polyatomic molecules
31.15.xr Self-consistent-field methods
33.15.Fm Bond strengths, dissociation energies

Bridge‐assisted electron transfer driven by dichotomically fluctuating tunneling coupling

I. A. Goychuk, E. G. Petrov, and V. May

J. Chem. Phys. 103, 4937 (1995); http://dx.doi.org/10.1063/1.470630 (8 pages) | Cited 41 times

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The influence of dichotomically fluctuating tunneling coupling on long‐range electron transfer is studied theoretically. Within an approach similar to the noninteracting blip approximation known from the spin‐boson model a set of coupled integrodifferential kinetic equations is derived. These equations describe the time development of the electronic populations difference between the donor and acceptor states averaged with respect to the stochastic process and the quantum fluctuations of the bath. Furthermore, they contain the correlator between the level population difference and the fluctuating tunneling matrix element. A detailed analysis is carried out for the case of a strong coupling of the transferred electron to a single soft reaction coordinate. Within a Markovian approximation and an adiabatic removing of the correlator, the balance type kinetic equations can be derived which contain effective transfer rates. These rates depend strongly on the correlation time of fluctuations and can exhibit a resonancelike behavior. © 1995 American Institute of Physics.
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34.70.+e Charge transfer
82.20.Fd Collision theories; trajectory models
82.30.Fi Ion-molecule, ion-ion, and charge-transfer reactions

Orbital alignment during cage‐exit of open‐shell photofragments: F in solid Ar and Kr

K. S. Kizer and V. A. Apkarian

J. Chem. Phys. 103, 4945 (1995); http://dx.doi.org/10.1063/1.470631 (8 pages) | Cited 9 times

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The statistical theory for sudden cage‐exit [J. Zoval and V. A. Apkarian, J. Phys. Chem. 98, 7945 (1994)] is extended to orbitally degenerate photofragments, specifically treating the case of F atoms in solid Ar and Kr. It is shown that the experimental energy‐dependent quantum yields of photodissociation of F2 are only compatible with the p hole on the F atom being completely aligned parallel to the cage wall during the sudden exit. Although relative quantum yields and energy thresholds are well predicted, the calculated absolute quantum yields are a factor of ∼2 smaller than the experimental values. © 1995 American Institute of Physics.
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33.80.Gj Diffuse spectra; predissociation, photodissociation
82.50.Bc Processes caused by infrared radiation
82.50.Hp Processes caused by visible and UV light

Vibrational energy transfer in shock‐heated norbornene

John R. Barker and Keith D. King

J. Chem. Phys. 103, 4953 (1995); http://dx.doi.org/10.1063/1.470581 (14 pages) | Cited 11 times

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Recently, Kiefer et al. [J. H. Kiefer, S. S. Kumaran, and S. Sundaram, J. Chem. Phys. 99, 3531 (1993)] studied shock‐heated norbornene (NB) in krypton bath gas using the laser‐schlieren technique and observed vibrational relaxation, unimolecular dissociation (to 1,3‐cyclopentadiene and ethylene), and dissociation incubation times. Other workers have obtained an extensive body of high‐pressure limit unimolecular reaction rate data at lower temperatures using conventional static and flow reactors. In the present work, we have developed a vibrational energy transfer‐unimolecular reaction model based on steady‐state RRKM calculations and time‐dependent master equation calculations to satisfactorily describe all of the NB data (incubation times, vibrational relaxation times, and unimolecular rate coefficients). The results cover the temperature range from ∼300 to 1500 K and the excitation energy range from ∼1 000 to 18 000 cm−1. Three different models (based on the exponential step‐size distribution) for the average downward energy transferred per collision, 〈ΔE〉down were investigated. The experimental data are too limited to enable the identification of a preferred model and it was not possible to determine whether the average 〈ΔE〉down is temperature dependent. However, all three 〈ΔE〉down models depend linearly on vibrational energy and it is concluded that standard unimolecular reaction rate codes must be revised to include energy‐dependent microcanonical energy transfer parameters. The choice of energy transfer model affects the deduced reaction critical energy by more than 2 kcal mol−1, however, which shows the importance of energy transfer in determining thermochemistry from unimolecular reaction fall‐off data. It is shown that a single set of Arrhenius parameters gives a good fit of all the low temperature data and the shock‐tube data extrapolated to the high pressure limit, obviating the need to invoke a change in reaction mechanism from concerted to diradical for high temperature conditions. Some possible future experiments are suggested. © 1995 American Institute of Physics.
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82.20.Pm Rate constants, reaction cross sections, and activation energies
82.20.Rp State to state energy transfer
82.30.Lp Decomposition reactions (pyrolysis, dissociation, and fragmentation)
82.40.Fp Shock wave initiated reactions, high-pressure chemistry

Effects of solvation on chemical bonding: An electron‐flow analysis

Jerzy Cioslowski and Martin Martinov

J. Chem. Phys. 103, 4967 (1995); http://dx.doi.org/10.1063/1.470582 (8 pages) | Cited 5 times

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Effects of nonspecific solvation on chemical bonding, described with a simple self‐consistent reaction field model, are rigorously analyzed in terms of electron flow and electronegativity equalization between two molecular fragments A and B. In most (but not all) systems AB, the energy‐lowering rise in the dipole moment that accompanies solvation is the result of an enhanced charge transfer between A and B, the enhancement stemming from both the increased electronegativity difference ΔχAB and the decreased bond hardness κAB. In systems, such as H⋅Cl, H⋅CN, and CH3⋅CN, that ensue from interactions between charged closed‐shell fragments (H++Cl−, H++CN−, CH+3+CN−, etc.) the energy‐stabilizing effect of solvation is a trade‐off between the energy lowering due to the enhanced charge‐transfer component of bonding and destabilization due to diminished covalent bonding. On the other hand, interactions between electrically neutral fragments (NH3+SO3, etc.) produce systems, such as the zwitterion of sulfamic acid (+H3N⋅SO−3), in which charge‐transfer and covalent components of bonding are strengthened in tandem by solvation. The aforementioned phenomena account for the experimentally observed solvation‐induced changes in the A–B bonds, namely their lengthening (or even a complete dissociation) in the former systems and shortening in the latter ones. © 1995 American Institute of Physics.
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31.70.Ks Molecular solids
31.15.A- Ab initio calculations
31.15.E- Density-functional theory
31.10.+z Theory of electronic structure, electronic transitions, and chemical binding

Characterization of the minimum energy paths and energetics for the reaction of vinylidene with acetylene

Stephen P. Walch and Peter R. Taylor

J. Chem. Phys. 103, 4975 (1995); http://dx.doi.org/10.1063/1.470583 (5 pages) | Cited 6 times

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The reaction of vinylidene (CH2C) with acetylene may be an initiating reaction in soot formation. We report minimum energy paths and accurate energetics for a pathway leading to vinylacetylene and for a number of isomers of C4H4. The calculations use complete active space self‐consistent field (CASSCF) derivative methods to characterize the stationary points and internally contacted configuration interaction (ICCI) and/or coupled cluster singles and doubles with a perturbational estimate of triple excitations [CCSD(T)] to determine the energetics. We find an entrance channel barrier of about 5 kcal/mol for the addition of vinylidene to acetylene, but no barriers above reactants for the reaction pathway leading to vinylacetylene. © 1995 American Institute of Physics.
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31.15.bw Coupled-cluster theory
31.15.xr Self-consistent-field methods
82.30.Cf Atom and radical reactions; chain reactions; molecule-molecule reactions
82.33.Vx Reactions in flames, combustion, and explosions

Theoretical investigation of the Kerr effect for CH4

David M. Bishop and Janusz Pipin

J. Chem. Phys. 103, 4980 (1995); http://dx.doi.org/10.1063/1.470584 (5 pages) | Cited 13 times

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The vibrational contributions to the Kerr effect and to electric‐field‐induced second‐harmonic generation (ESHG) are calculated for methane for a number of optical frequencies. The latter results, together with the experimental ESHG values of the total mean second hyperpolarizability, allow for the determination of the ω2L‐dispersion curve for the mean electronic hyperpolarizability. Since this curve is identical, to fourth order, for both processes, we are able to combine it with the calculated Kerr vibrational hyperpolarizabilities and predict the total Kerr hyperpolarizabilities for CH4 for several laser frequencies. © 1995 American Institute of Physics.
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42.65.An Optical susceptibility, hyperpolarizability
42.65.Ky Frequency conversion; harmonic generation, including higher-order harmonic generation

Novel adiabatic invariant for the three‐body Coulomb problem

Jörg Müller, Joachim Burgdörfer, and Donald W. Noid

J. Chem. Phys. 103, 4985 (1995); http://dx.doi.org/10.1063/1.470585 (5 pages) | Cited 11 times

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The two‐(fixed) center Coulomb problem possesses in nonrelativistic mechanics, besides the ‘‘classical’’ constants of motion, an additional constant of motion associated with dynamical symmetry and separability of the problem. When the motion of the nuclei is taken into account the constant of motion is destroyed but reappears as an adiabatic invariant. We have identified this novel adiabatic invariant for the unrestricted three‐body problem in the limit of two heavy particles and one light particle. Unlike all other known adiabatic invariants, it is globally conserved to order δ=m/M in the light‐ to heavy‐mass ratio. The significance of this invariant for the semiclassical description of the chemical bond and for diatomic molecules beyond the Born–Oppenheimer approximation is discussed. © 1995 American Institute of Physics.
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03.65.Sq Semiclassical theories and applications
31.15.vn Electron correlation calculations for diatomic molecules
31.50.Df Potential energy surfaces for excited electronic states

Applications of multireference perturbation theory to potential energy surfaces by optimal partitioning of H: Intruder states avoidance and convergence enhancement

James P. Finley, Rajat K. Chaudhuri, and Karl F. Freed

J. Chem. Phys. 103, 4990 (1995); http://dx.doi.org/10.1063/1.470586 (21 pages) | Cited 67 times

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The minimum basis set hydrogen rectangular system (HRS), consisting of four hydrogen atoms arranged in a rectangle, is examined using a variety of partitionings of the Hamiltonian H for high order single and double reference perturbation computations. The potential energy surface is mapped out over a range of geometries in which the length L of one side of the rectangle is varied. Several criteria are derived governing the necessary conditions for perturbative convergence of two‐state systems, and these criteria are useful in explaining the behavior of the HRS for the range of geometries and partitioning methods investigated. The divergence caused by intruder states, observed by Zarrabian and Paldus [Int. J Quantum Chem. 38, 761 (1990)] for the nondegenerate, double reference space perturbation expansions at L=3.0 a.u. with traditional partitioning methods, is shown to correspond to avoided crossings with negative real values of the perturbation parameter—backdoor intruder states. These intruder state induced divergences result from too small zeroth order energy differences between the high lying reference space state and an orthogonal space intruder state whose identity depends on the partitioning method. Forcing the valence orbitals to be degenerate enlarges these zeroth order energy differences and, thus, yields a convergent perturbative expansion for L=3.0 a.u.
The convergent or divergent behavior of all the partitioning method computations and the locations of their avoided crossings are accurately predicted by using two‐state models composed of the high lying reference space state and the intruder state. A partitioning method is introduced in which the zeroth order state energies are selected to optimize the convergence in low orders of the perturbation expansion. This optimization method yields perturbative convergence which is both rapid and free of intruder state for geometries between L=2.0 and 3.0 a.u. The divergent behavior for various partitioning methods at L=5.0 a.u., also observed by Zarrabian and Paldus, is caused by one or more orthogonal space states and the high lying reference space state that are strongly coupled and have close expectation values of H. The two‐state model illustrates why no partitioning choice with a double reference space can yield a satisfactory rate of perturbative convergence for L=5.0. Therefore, the entire potential energy surface is treated using more than one reference space: a double reference space for L≤3.0 a.u. and a single reference space for L≳3.0 a.u. The entire potential surface of interest, which is generated with the optimized partitioning method and the two different reference spaces, is very accurate by third order, with eigenvalues for all geometries considered differing from the FCI by no more than 1 kcal/mol. © 1995 American Institute of Physics.
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31.15.xp Perturbation theory
34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions

Direct numerical solution of the Ornstein–Zernike integral equation and spatial distribution of water around hydrophobic molecules

Mitsunori Ikeguchi and Junta Doi

J. Chem. Phys. 103, 5011 (1995); http://dx.doi.org/10.1063/1.470587 (7 pages) | Cited 49 times

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The Ornstein–Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid‐spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso‐value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α‐cholest‐2‐ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed. © 1995 American Institute of Physics.
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31.15.xv Molecular dynamics and other numerical methods
64.75.-g Phase equilibria

On the Feynman path centroid density as a phase space distribution in quantum statistical mechanics

Rigoberto Hernandez, Jianshu Cao, and Gregory A. Voth

J. Chem. Phys. 103, 5018 (1995); http://dx.doi.org/10.1063/1.470588 (9 pages) | Cited 5 times

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The phase space formulation of quantum statistical mechanics using the Feynman path centroid density offers an alternative perspective to the standard Wigner prescription for the classical‐like evaluation of equilibrium and/or dynamical quantities of statistical systems. The use of this formulation has been implicit in recent work on quantum rate theories, for example, in which the centroid density distribution replaces the classical Boltzmann distribution. In order to further understand the approximations involved in this and similar transcriptions, the present work elaborates and clarifies the issue of operator ordering in a rigorous centroid‐based formulation. In particular, through the use of the Weyl correspondence, a precise definition of the centroid symbol of operators and their products is presented. Though we fall short of finding the algebraic structure tantamount to that found in the Weyl symbols—of which the Wigner distribution is an example— the resulting expressions have internal consistency and are amenable to approximate evaluation through cumulant expansions. © 1995 American Institute of Physics.
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05.30.-d Quantum statistical mechanics
31.15.xk Path-integral methods

Equation of state for classical hard‐particlelike fluids

U. F. Edgal, A. Boukahil, and D. L. Huber

J. Chem. Phys. 103, 5027 (1995); http://dx.doi.org/10.1063/1.470589 (4 pages) | Cited 1 time

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We extend earlier studies of the equation of state of classical hard‐particle fluids to potentials where there is an attractive tail in addition to a repulsive hard core. Like the earlier work, the approach is based on the arbitrary point, nearest‐neighbor probability density function. In the high temperature (hard‐particle) limit, a parametrization of the integrated distribution is introduced. By matching the parameters against the coefficients in a seven‐term virial expansion, we obtain an equation of state that is in excellent agreement with the results from Monte Carlo, molecular dynamics calculations in both two and three dimensions. The theory is extended to finite temperatures by treating deviations from the hard‐particle limit as small corrections that can be evaluated using hard‐particle distribution functions. A comparison is made with the results from a five‐term finite temperature virial expansion for a three‐dimensional hard‐particle system with a square well attractive potential. © 1995 American Institute of Physics.
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61.20.Gy Theory and models of liquid structure
61.25.Em Molecular liquids
64.30.-t Equations of state of specific substances

First‐principles molecular‐dynamics simulation of liquid CsPb

G. A. de Wijs, G. Pastore, A. Selloni, and W. van der Lugt

J. Chem. Phys. 103, 5031 (1995); http://dx.doi.org/10.1063/1.470590 (10 pages) | Cited 20 times

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Many alkali–post‐transition group IV alloy systems exhibit clearly defined equiatomic compounds together with a pronounced intermediate range ordering, indicated by a first sharp diffraction peak at ≊0.9 Å−1. These phenomena have been explained assuming that tetrahedral group IV anions, ‘‘Zintl’’ ions, survive in the liquid state. As a prototype system we considered liquid CsPb, for which several experimental results are available, and studied it by means of first‐principles molecular‐dynamics. Agreement with experiment is satisfactory, provided the 5s and 5p electrons of cesium are explicitly taken into account in the computation of the electronic valence charge density. In particular, our calculations reproduce the structure factor prepeak reasonably well. The local liquid structure however is quite complex. This can be described as a disordered network, which still has many features in common with the ‘‘Zintl’’ ion model. For instance, the average Pb‐Pb coordination is close to 3, the value for perfect tetrahedra, but the coordination distribution of Pb around Pb shows a broad range of values. The calculated electronic density of states shows a minimum at the Fermi level indicating compound formation. © 1995 American Institute of Physics.
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61.20.Ja Computer simulation of liquid structure
61.25.Mv Liquid metals and alloys
71.22.+i Electronic structure of liquid metals and semiconductors and their alloys
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