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Volume 104, Issue 23, 15 June 1996

Efficient π electrons delocalization in α,α′‐dimethyl end‐capped oligothiophenes: A vibrational spectroscopic study
View Description Hide Descriptionα,α′‐dimethyl substituted oligothiophenes with increasing chain length (from the dimer up to the hexamer) were recently synthesized by chemical methods. In this paper we have investigated the vibrational Fourier transform‐IR and Fourier transform‐Ramanspectra of solid α,α′‐dimethyl substituted oligothiophenes in the neutral state. The data are consistent with the existence of a chain‐length dependent π electron delocalization: a large frequency dispersion with conjugation length is observed for some Raman and infrared active vibrational modes, particularly at the high‐energy side of the aromatic C=C stretching region. Vibrational assignments are proposed for the main vibrational features in the whole spectral range. This vibrational spectroscopicanalysis of the solid samples thus becomes a tool for deriving information on the structure of these neutral materials in solution and in the doped state.

A new class of collective excitations: Exciton strings
View Description Hide DescriptionOptical excitation in a strongly neutral quasi‐one‐dimensional mixed‐stack charge‐transfer solid results in an exciton state, in which the electron and the hole are bound by electrostatic Coulomb interactions that are large compared to the one‐electron hopping. We present a joint theoretical–experimental demonstration of a new class of collective excitations, multiexcitons or exciton strings, consisting of a string of several (more than two) bound excitons, in a prototype neutral charge‐transfer solid. The stability of the multiexciton states arise from the combined effects of one dimensionality and strong Coulomb interactions.Theoretically, we show that in narrow band one‐dimensional semiconductors with long range Coulomb interactions, the occurrence of stable 2‐exciton string (biexciton) necessarily implies stable higher multiexcitons. Experimentally, evidence for the multiexciton strings is demonstrated by femtosecond pump–probe spectroscopy of anthracene pyromellitic acid dianhydride. Excellent qualitative agreement is found between the calculated and the measured differential transmission spectra. Photoinduced absorptions to the 2‐exciton string at low pump intensity and to the 3‐exciton string at high pump intensity are observed, in agreement with the theory of excited state absorption. The 2‐exciton string is confirmed also by a direct two‐photon absorption measurement. The binding energies of the 2‐exciton and the 3‐exciton strings are obtained from the experimental data. The larger binding energy of the 3‐exciton is in agreement with theory.

Exciton‐to‐biexciton transition in quasi‐one‐dimensional organics
View Description Hide DescriptionIn the previous paper we demonstrated novel multiexcitons in a neutral mixed‐stack charge‐transfer solid. The lowest multiexciton, the biexciton, has recently been of interest also in the context of quasi‐one‐dimensional organic materials that are different from the mixed‐stack solids. The nature and strength of the optical transition from the exciton to the two‐exciton states is of importance in understanding photoinduced absorption as well as two‐photon absorption. We show that within the diverse theoretical models that describe these different classes of materials, the excited stateabsorption from the optical exciton to the two‐exciton states changes in a fundamental way upon the formation of the biexciton. The identical nature of the excitonabsorption within these models is a consequence of one dimensionality.

Octatetraene m ^{1} A _{ g } states: Two‐photon fluorescence excitation spectrum from 28 000 to 50 000 cm^{−1}
View Description Hide DescriptionThe 2‐photon fluorescence excitation spectra of all‐trans octatetraene in n‐hexane and n‐octane host crystals at 77 and 1.8 K have been recorded for the region 28 000 to 50 000 cm^{−1}. Measurements of the dependence of emission signal on excitation intensity and fluorescence lifetimes contributed to the assignment of the observed features. On the basis of their frequencies, intensities, and solvent shift behaviors all of the bands are seen in the region 28 000 to 44 000 cm^{−1} are assigned to vibronic bands of the 1 ^{1} A _{ g }–2 ^{1} A _{ g } transition. The unusual temperature dependence of one excitation feature is consistent with a near degeneracy of singlet and triplet levels. Above 44 000 cm^{−1} there are four broadbands, two of which must be assigned to 0–0 transitions from the 1 ^{1} A _{ g }ground state to higher lying m ^{1} A _{ g } states at 45 030 and 46 710 cm^{−1}, respectively. The other two bands at 48 000 and 49 860 cm^{−1} could be either vibronic additions to the 0–0 band at 46 710 cm^{−1} or 0–0 bands for new m ^{1} A _{ g } states.

Potential energy surface for and pure rotational spectra of isotopomeric Cl_{2}–Ar van der Waals complexes
View Description Hide DescriptionPure rotational spectra have been calculated for the three isotopomers of the Cl_{2}–Ar van der Waals complex formed by Cl_{2} in its ground electronic state. The potential energy surface involved is a sum of pairwise Morse atom–atom interactions, which are merged asymptotically into an anisotropic van der Waals form. The Morse atom–atom interactions have been refined by adjusting their parameters to obtain agreement with both excitation spectra and recent microwave transitions observed for the ^{35}Cl_{2}–Ar van der Waals complex, whereas the anisotropic long‐range part of the potential surface has been taken from ab initio results [Mol. Phys. 80, 533 (1993)]. The present model potential surface predicts a T‐shaped structure for the complex, in agreement with experiment. Excellent agreement has been found between the calculated and experimental microwave transition frequencies for the ^{35}Cl^{37}Cl–Ar complex. Good agreement has also been found between the experimentally determined bond energy, bond length, and average ‘‘bond angle’’ governing the overall geometry of the complex and the corresponding quantities determined from dynamical calculations based upon the present potential surface. The new potential surface has also been utilized to predict the microwave spectrum of the ^{37}Cl_{2}–Ar isotopomer.

Breaking symmetry with hydrogen bonds: Vibrational predissociation and isomerization dynamics in HF–DF and DF–HF isotopomers
View Description Hide DescriptionHigh‐resolution near‐IR spectra of jet‐cooled HF–DF and DF–HF isotopomers are presented and analyzed for fundamental excitation in the HF‐stretching region (3870 cm^{−1}–3960 cm^{−1}) and DF‐stretching region (2840 cm^{−1}–2880 cm^{−1}), based on direct absorption of tunable IR difference frequency radiation in a slit‐jet supersonic expansion (10 K). Spectra are obtained for excitation of all four stretching modes, *HF–DF, HF–*DF, *DF–HF, and DF–*HF (* denotes the vibrationally excited subunit), which probe both the hydrogen/deuterium bond donor and acceptor moieties in the complex. Vibrational redshifts and predissociation broadening measurements are compared with full 6D quantum calculations on theoretical HF dimer potential surfaces, which exhibit trends in qualitatively good agreement with experiment. Each of the three DF‐stretch‐excited bands are fit to spectroscopic precision (Δν≲0.0001 cm^{−1}) by conventional high‐resolution rotational analyses, whereas each of the four corresponding HF‐stretch‐excited bands appear extensively perturbed (Δν≊0.01 cm^{−1}). This H/D isotope effect is interpreted as vibrational state mixing of the HF‐stretch‐excited species with a dense manifold of combination band states built on DF‐stretch excitation, and therefore reflects intermolecular energy flow in the complex. Such vibrational state mixing is further corroborated by observation of ‘‘dark’’ state transitions that can be tentatively assigned to *HF–DF isomer interacting with the nearly isoenergetic DF–*HF isomer. This state mixing would correspond to a vibrationally promoted ‘‘isomerization’’ over the tunneling barrier, and yield a spectroscopic measure of the difference in hydrogen bond dissociation energies [ΔD _{0}=74.7(5) cm^{−1}] for the HF–DF and DF–HF isotopomers.

Ultrafast quantum dynamics and resonance Raman spectroscopy of photoexcited I_{2}(B) in large argon and xenon clusters
View Description Hide DescriptionThe early quantum dynamics following the B(^{3}Π_{0u + })←Xphotoexcitation of I_{2} in large rare gas clusters is studied and the resonanceRaman spectrum of these systems is calculated by a novel time‐dependent quantum mechanical simulation approach. The method used is the classically based separable potential (CSP) approximation, in which classical molecular dynamics simulations are used in a first step to determine an effective time‐dependent separable potential for each mode, then followed by quantum wavepacket calculations using these potentials. In the simulations for I_{2}(Ar)_{ n } and I_{2}(Xe)_{ n }, with n=17, 47, all the modes are treated quantum mechanically. The Raman overtone intensities are computed from the multidimensional time‐dependent wavepacket for each system, and the results are compared with experimental data on I_{2} in Ar matrices and in liquid Xe. The main findings include: (i) Due to wavepacket dephasing effects the Raman spectra are determined well before the iodine atoms hit the rare gas ‘‘wall’’ at about 80 fs after photoexcitation. (ii) No recurrencies are found in the correlation functions for I_{2}(Ar)_{ n }. A very weak recurrence event is found for I_{2}(Xe)_{ n }. (iii) The simulations for I_{2}(Ar)_{17} (first solvation layer) and for I_{2}(Ar)_{47} (second solvation shell) show differences corresponding to moderate cluster size effects on the Raman spectra. (iv) It is estimated that coupling to the B″(^{1}Π_{1u }) state or to the a(1g) state have a small effect on the Raman intensities. (v) For I_{2}(Ar)_{47}, the results are in very good quantitative agreement with I_{2}/Ar matrix experiments. The I_{2}(Xe)_{ n } results are in qualitative agreement with experiments on I_{2} in liquid Xe. The reported calculations represent a first modeling of resonanceRaman spectra by quantum dynamical simulations that include all degrees of freedom in large systems, and they demonstrate the power of the CSP method in this respect.

One‐electron second‐order optical activity of a helix
View Description Hide DescriptionThe second‐order nonlinear‐optical response of a chiral molecule is calculated. We model the optical response classically using a single electron bound to a helical path. The helical motion of the electron causes optical activity in the second‐order response. The hyperpolarizability tensor of a single helix and the susceptibilitytensor for a thin film of helices are given. We examine the process of second‐harmonic generation from a chiral surface using the calculated susceptibilitytensor. The efficiency of the harmonic generation is different for left‐ and right‐hand circularly polarized fundamental light, which is ascribed to be a form of nonlinear optical activity. The roles of pitch and radius of the helix are readily seen in the microscopic and macroscopic second‐order optical responses and in the surface second‐harmonic generation, which may provide some insight for synthesizing new chiral compounds. Our results also allow us to draw conclusions about the relative strength and importance to second‐order optical activity of electric‐ and magnetic‐dipole transitions. For instance, we confirm that optical activity can occur in surface second‐harmonic generation from electric‐only response, but we find that magnetic response can make a similar contribution and thus should not be ignored.

Normal mode theory of two step relaxation in liquids: Polarizability dynamics in CS_{2}
View Description Hide DescriptionAn instantaneous normal mode (INM) theory is given for relaxation in liquids by a fast β process followed by a slow α process. The β process is harmonic dynamics in the wells of the N‐body potential, while the α process is structural relaxation coincident with barrier crossing to a neighbor well. The theory introduces a new parameter, the ‘‘harmonic fraction’’ denoted F _{ H }, which is the fraction of the mean‐square fluctuations of a dynamical variable capable of being relaxed by the harmonic β process. Theory and computer simulation are compared for the polarizabilitycorrelation function,PC(t), and the polarizability time derivative correlation function, DPC(t), in a model of CS_{2} including internal degrees of freedom. Agreement is good, with the INM theory clearly showing the ‘‘signature’’ time dependence of a correlation function undergoing αβ relaxation in a low temperature liquid; there are no adjustable parameters in the theory. The polarizability is calculated in the ‘‘point atomic polarizability approximation’’ (PAPA) which is sensitive to molecular vibrations, so a preliminary classical INM treatment of Raman scattering is obtained. The PAPA overestimates the derivative of the polarizability with respect to the internal coordinates, and in reality the vibrations behave quantum mechanically, so the Raman intensities are inaccurate, but otherwise a plausible description is obtained for several features of the spectrum. It is explained how an improved PAPA will be combined with a quantum INM theory in future Raman calculations.

Vibrational structure of the N^{+} _{2} ground state observed by threshold photoelectron spectroscopy
View Description Hide DescriptionThe long vibrational progression of the ground state of N^{+} _{2} was observed in a high resolution threshold photoelectron spectrum obtained using the penetrating field technique and synchrotron radiation.Vibrational states were observed up to v′=67 for the first time and the final vibrational level was deduced to be v′=77 from extrapolation. The complete molecular constants of this state were obtained and the entire potential curve was then drawn.

Structure and vibrations of catechol and catechol⋅H_{2}O(D_{2}O) in the S _{0} and S _{1} state
View Description Hide DescriptionThe inter‐ and intramolecular vibrations in the S _{0} and S _{1} state of catechol, d2‐catechol, catechol(H_{2}O)_{1}, and d2‐catechol (D_{2}O)_{1} have been investigated experimentally by resonanttwo photonionization (R2PI), spectralhole burning (SHB), and dispersed fluorescence spectroscopy (DF). The experimental frequencies are compared to the vibrational frequencies obtained from ab initionormal mode calculations using the 6‐31G(d,p) basis set. In order to get a complete interpretation of the S _{0} state spectra of d2‐catechol the strong coupling of the two OD torsional motions has been taken into account. A two‐dimensional calculation of the torsional eigenvalues based on an ab initio potential [6‐31G(d,p) basis] obtained from single point calculations is presented. Due to these calculations all vibrations in the S _{0} state can be assigned. Furthermore a new assignment of the vibrations in the S _{1} state of d2‐catechol is given. In the case of catechol (H_{2}O)_{1} [d2‐catechol(D_{2}O)_{1}] different structural isomers are discussed. Using HF ab initio calculations (including MP2, BSSE, and ZPE corrections) a trans‐linear hydrogen bonding arrangement turns out to be more stable by an amount of 840 cm^{−1} compared to a cyclic structure which is also a minimum of the PES. Normal mode calculations have been carried out for both structures and anharmonic corrections are calculated for the τ and β_{2} mode of the trans‐linear arrangement. The prediction of the ab initio calculations is supported by the vibrational transitions observed in the spectra of the S _{0} and S _{1} state, which can be assigned on the basis of the vibrations calculated for the trans‐linear structure. The most important feature of the R2PI spectrum of catechol(H_{2}O)_{1} [d2‐catechol(D_{2}O)_{1}] is the occurrence of intermolecular vibrations of very low frequencies (14, 37 cm^{−1}). These vibrations and the low frequency torsional modes in the spectra of the S _{1} state of the catechol monomer strongly support the assumption that catechol is nonplanar in the S _{1} state with respect to the OH groups. Due to this nonplanarity a double minimum potential for the intermolecular ρ_{1} mode of catechol(H_{2}O)_{1} is postulated. Using this assumption the low frequency vibrations of the R2PI spectra as well as the vibrations observed in the spectra of the S _{0} state can be assigned.

Electronic structure of metal–rare gas dimers with sp configuration: Application to strong spin–orbit interaction in HgAr
View Description Hide DescriptionIn order to describe the electronic states of metal (M)–rare gas (Rg) van der Waals dimers having an sp configuration with a strong spin–orbit interaction, we derived an e/fparity adapted molecular Hamiltonian matrix by adopting a symmetry‐adapted atomic orbital approach. The molecular Hamiltonian was constructed by introducing (i) the interaction between the p electron and the attached rare gas atom, V _{Rg}, (ii) the exchange interaction between the s and p orbitals, e ^{2}/r _{ sp }, and (iii) the spin–orbit interaction for the p electron. As a basis set, twelve molecular electronic wave functions were derived by taking into account their e/fparities. We applied the derived molecular Hamiltonian matrix to the first excited 6s6p configuration of HgAr by performing a least‐squares fit to the spectroscopically determined term values for the v=0 levels of the a ^{3}Π_{0− }, A ^{3}Π_{0+ }, B ^{3}Π_{1}, b ^{3}Π_{2}, and C ^{1}Π_{1} states. From the results of the least‐squares fit, we clarified how the above interactions (i)–(iii) split twelve degenerate molecular wave functions into the eight electronic eigenstates; i.e., a ^{3}Π_{0− }, A ^{3}Π_{0+ }, B ^{3}Π_{1}, b ^{3}Π_{2}, c ^{3}Σ^{+} _{1}, d ^{3}Σ_{0− } ^{+}, C ^{1}Π_{1}, and D ^{1}Σ^{+} _{0}. On the basis of (i) a critical comparison between the atomic Hamiltonian matrix for Hg and the determined molecular Hamiltonian matrix and (ii) an examination of the mixing among the symmetry‐adapted molecular wave functions,characteristic features of the electronic structure arising from the formation of a van der Waals bond, were extracted.

High pressure study on the Raman spectra of fluid nitrogen and nitrogen in helium
View Description Hide DescriptionA study on the Raman shift and width of nitrogen and nitrogen in helium has been performed as a function of pressure and temperature by means of experiments,molecular dynamics (MD) simulations and hard fluid (HF) theory. The experiments have been performed using Raman spectroscopy in a diamond anvil cell at pressures up to 10 GPa and temperatures between 250 and 400 K. Both the experimental shift and width results of pure nitrogen link up very well with accurate measurements at lower pressures and with less accurate measurements at higher pressures. For the first time the Raman shift and width have been determined as a function of temperature at an isobar, such that a sensitive test of theoretical models can be made. The MD calculations on the linewidth along an isobar show very good agreement with experiment. The influence on the linewidth of the bondlength dependence of the site–site interaction parameters (often called the attractive contribution) appears to be small, which indicates that this has a small anisotropy. For pure N_{2} the MD and the HF calculations of the repulsive contribution to the Raman shift are about the same. This shows that both ways of calculation are consistent. The experimental Raman shift of nitrogen diluted in helium appears to be much larger than that of pure nitrogen. In contrast, the linewidth is much smaller than that of pure nitrogen. HF calculations were also performed for the Raman shift of N_{2}, infinitely diluted in He. The results for the bondlength independent (repulsive) contribution give clearly smaller values than those of the experiment, which means that the effect of the change of the potential parameters at excitation must be positive. This implies that that part of the intermolecular potential, which is due to the overlap of the molecular charge distributions has a dependence on the bondlength, that results in a positive contribution to the Raman shift. It will be shown that for N_{2} the good agreement with experiment of earlier HF calculations with an attractive contribution, based on a purely dispersive model, is due to a cancellation of errors. For nondiluted mixtures of He–N_{2} under noncritical conditions the plot of experimental FWHM values as a function of the volume fraction shows a broad maximum, which is indicative for inhomogeneous broadening. This behavior is described with the help of the Knapp–Fischer model.

Reactions of Zn(4s4p ^{3} P _{1}) and Cd(5s5p ^{3} P _{1}) with SiH_{4}
View Description Hide DescriptionThe first nsnp ^{3} P _{1}excited states of Cd and Zn atoms are shown to readily activate Si–H bonds in SiH_{4}. The nascent quantum state distributions of the CdH(v;N) and ZnH(v;N) products in the reactions of Cd(^{3} P _{1}) and Zn(^{3} P _{1}) with SiH_{4} have been determined using the laser pump–probe technique. The results are discussed within the context of our current knowledge about the chemical interactions of valence M(nsnp ^{3} P) excited states with Si–H, H–H, and C–H bonds, where M=Mg, Zn, Cd, and Hg. It is proposed that the high reactivity of M(nsnp ^{3} P _{1}) states with H–H and Si–H bonds compared to C–H bonds is simply due to the lack of steric hindrance in the localized, side‐on, M(npπ)–XH(σ*) donor–acceptor molecular orbital interactions, since the Si–H bond‐length in SiH_{4} is ∼1.5 Å compared to C–H bond lengths of ∼1.1 Å.

Electron transfer reactions in a non‐Debye medium with frequency‐dependent friction
View Description Hide DescriptionA generalized Zusman equation and its formal solution for electron transferreactions in a non‐Debye medium with frequency‐dependent friction are presented. The derivation is based on the spin‐boson model, representing a two‐level system for a donor and an acceptor coupled to a non‐Debye polar solvent bath. An analytical expression for the electron transferrate constant will be derived using the Green’s function method. Because of the time retardation in such a non‐Markovian process, the initial electron‐transfer reaction is influenced more by the higher frequency components in the solvent relaxation, whereas the long‐time behavior is influenced more by the lower frequency components. Electron transfer processes in such a medium are therefore often nonexponential.

Keeping the shape but changing the charges: A simulation study of urea and its iso‐steric analogs
View Description Hide DescriptionAs a first step in simulating solvent denaturation, we compare two possible potentials for urea; one based directly on a parameterization for proteins and another generated from ab initio, quantum calculations. Our results, which are derived from numerous, 1 ns simulations, indicate that both potentials reproduce essentially the same observed water structure (as evident in radial distribution functions). However, even though the quantum potential better approximates dimer energies, it is unable to simulate the dynamic behavior of water (as evident in measurements of diffusion) as well as the potential based on protein parameters. To understand its behavior in aqueous solution, we compare the urea simulations with those of solute molecules that possess the same planar, Y‐shape as urea but are progressively more hydrophobic. We find that adding urea to a solution increases the number of hydrogen bonds, while adding any of the Y‐shaped analogs decreases the number of hydrogen bonds. Moreover, in contrast to the Y‐shaped analogs, which aggregate more as they become less polar, we find that urea mixes well in solution and has little tendency to aggregate. For our analysis of aggregation, we used a novel approach based on Voronoi polyhedra as well as the traditional method of radial distribution functions. In conclusion, we discuss how urea’s unique behavior in comparison to its Y‐shaped analogs has clear implications for models of urea solvation and mechanisms of urea protein denaturation.

Pressure tuning of solvent viscosity for the formation of twisted intramolecular charge‐transfer state in 4,4′‐diaminodiphenyl sulfone in alcohol solution
View Description Hide DescriptionThe effect of solvent shear viscosity on the formation of twisted intramolecular charge‐transfer (TICT) state in the excited state for 4,4′‐diaminodiphenyl sulfone (DAPS) in three linear alcohol solvents has been investigated by measuring the picosecond fluorescence lifetime as a function of pressure. At lower pressures the kinetics of the TICT‐state formation is controlled by solvent relaxation. While with increasing pressure, the reaction path shifts toward the ‘‘high viscosity regime’’ in which the reaction proceeds through the nonrelaxed path independent of solvent coordinate on the free energysurface of the S _{1}excited state. This behavior could be called as ‘‘pressure tuning effect’’ of solventviscosity. The power law parameter (α) is used as a measure of the viscosity dependence. For the high viscosity regime, α=0.2 can be attributed to the intrinsic viscosity dependence for barrier crossing.

Analytical energy derivatives for a realistic continuum model of solvation: Application to the analysis of solvent effects on reaction paths
View Description Hide DescriptionAnalytical expressions for the first and second derivatives of the Hartree–Fock energy have been derived in case of a solvated system simulated by a multipolar charge distribution embedded in a cavity of arbitrary shape and a solvent represented by a dielectric continuum. A computer code has been written on these bases. It allows geometry optimizations and more generally the determination of the critical points of the potential energy surface for a molecular system interacting with a solvent as easily as in the case of an isolated molecule. The use of this code is illustrated by the computation of the main features of the reaction path of a Menshutkin‐type reaction in various solvents. The results compare pretty well with those obtained by a full Monte Carlo simulation of the solvent by Gao. This agreement supports the idea that solvents, including water, can be safely modeled by a continuum. The advantage of such models rests in the fact that they allow refined computations on the solute at a minimum computational expense.

Comparison of zero‐point energy constrained and quantum anharmonic Rice–Ramsperger–Kassel–Marcus and phase space theory rate constants for Al_{3} dissociation
View Description Hide DescriptionThe ZPE constrained trajectory model is found to retain the ergodicity and intrinsic Rice–Ramsperger–Kassel–Marcus (RRKM) behavior observed previously [J. Chem. Phys. 101, 8535 (1994)] in unconstrained trajectories of Al_{3} decomposition. Microcanonical unimolecular rate constants for Al_{3} decomposition are calculated from the ZPE constrained trajectories and compared with the predictions of the vibrator and flexible transition state models of RRKM theory, phase space theory, and the orbiting transition state model of phase space theory (OTS/PST). Quantum anharmonic Al_{3} vibrational densities of state, determined by a semiclassical approach, are used to calculate these statistical rate constants. Anharmonicity increases the density of states threefold for total energies 1–2 kcal/mol above the classical product asymptotic limit, but has a negligible effect on the Al_{2}‐‐‐Al transition state sum of states. The ZPE constrained trajectory unimolecular rate constants are in poor agreement with the quantum anharmonic OTS/PST and flexible RRKM rate constants. This is because the ZPE constraint is too restrictive and some of the ZPE constrained trajectories are temporarily trapped in the ZPE forbidden region of phase space. The ZPE constrained trajectory rate constants are smaller than their purely classical counterparts, since Al_{2} is not formed without its ZPE and thus the effective dissociation threshold is larger for the ZPE constrained trajectories. ZPE constrained sums and densities are calculated by including the ZPE constraint when solving the classical phase integral. RRKM rate constants calculated from these ZPE constrained sums and densities are in much better agreement with the quantum anharmonic OTS/PST and flexible RRKM rate constants, than are those calculated from the ZPE constrained trajectories. The difference between the ZPE constrained RRKM and quantum flexible RRKM rate constants becomes small and much less than the anharmonic correction, for energies slightly in excess of the Al_{2}+Al classical asymptotic limit. This is because the number of real frequencies in the instantaneous normal mode analysis decreases as the total energy is increased, which makes the ZPE constrained RRKM rate constant more accurate. Product energy partitioning from the ZPE constrained trajectories is in good agreement with the predictions of quantum phase space theories, except that the product diatom is formed too rotationally excited. The ZPE constraint scheme retains a spurious frequency and zero‐point energy for the Al_{2}‐‐‐Al bending motion at large separations, which increases the Al_{2} product rotational energy. The work reported here supports the proposal that a ZPE constraint model, based on an instantaneous normal mode analysis, may be a valid approach for including zero‐point energy effects in trajectory simulations of ergodic anharmonic coupled systems. However, additional work needs to be done to remove some of the numerical problems with the current ZPE constraint model and to make the model less restrictive.

Gauge transformations of electron group functions
View Description Hide DescriptionWithin the scope of the electron group functions (EGF) theory, the concept of gauge transformations (GT) of EGFs is introduced as such transformations that leave the state of the entire system invariant. The variational equations for EGFs should contain additional terms representing the Pauli repulsion part of the pseudopotential and being consistent with the choice of EGFs (the requirement of gauge consistency). The GTs present a natural way of ab initio defining the generalized many‐electron pseudopotentials produced by an internally correlated subsystem. Some specific, but rather general forms of GTs are proposed. One of the form is defined using properties of group functions with odd number of electrons. The GTs belonging to another class are defined using properties of antisymmetrically annulling (ASA) functions introduced in our earlier work and studied further in the present work. In particular, we introduce the ASA kernel basis set for a given group function and show that any function ASA the given group function can be expanded in terms of this set. The algebraic properties of GTs and of their sets are studied, both general ones and specific for the mentioned forms. In general case, the proposed GTs depend on a set of parameters which are functions rather than numbers, that can provide improved transferability of pseudopotentials. The linear transformations of one‐electron functions of a determinant as well as the procedures of strong orthogonalization of a group function to a determinant (by Fock, Veselov, and Petrashen’, and by Szasz) are shown to be special cases of the GTs considered.