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Volume 104, Issue 16, 22 April 1996

Perturbation theory and dynamic reaction path analysis of intramolecular vibration mixing: An application to the case of H_{2}O
View Description Hide DescriptionA perturbational method in terms of cubic force constants was proposed to predict how intramolecular vibration mixing among normal modes occurs through the anharmonicity of the potential energy. The method was applied to H_{2}O and it was predicted that symmetric and antisymmetric stretching normal modes having similar frequencies should couple strongly with each other, even at the equilibrium point moiety, as the antisymmetric normal vibration develops. Dynamic reaction path calculations were also performed for H_{2}O, and the strong vibration coupling between those predicted normal vibration pair was confirmed.

Third‐order nonlinear time domain probes of solvation dynamics
View Description Hide DescriptionSeveral closely related third‐order nonlinear time‐resolved spectroscopic techniques, pump/probe transient absorption, transient grating, and three pulse stimulated photon echo peak shift measurements, are investigated theoretically and experimentally. It is shown in detail, through the consideration of response functions and numerical simulations including both finite pulse durations and detuning from exact resonance, how the solvation dynamics are manifested in these third‐order nonlinear time‐resolved spectroscopies. It is shown that the three pulse stimulated photon echo peak shift measurement and the transient grating measurement can give accurate dynamical information, whereas transient absorption may not be a reliable technique for a study of solvation dynamics in some cases. The contribution of very slow or static (inhomogeneous) components to the dynamics, however, can only be obtained from the three pulse echo peak shift measurements. Comprehensive experimental measurements are presented to illustrate and corroborate the calculations. We show that it is possible to separate the intramolecular vibrational and solvent contributions to the dephasing (or optical lineshape). Furthermore it is shown that the solvation of polar solutes in polar protic solvents has rather universal characteristics. The initial ultrafast process, usually identified as an inertial response of solvent molecules, occurs on a ∼100 fs time scale, and is essentially identical in methanol, ethanol, and butanol. The amplitude of this ultrafast component does, however, decrease with increasing alcohol size in 1‐alkanols. The diffusive (≳0.5 ps) regime of the solvation process shows a strong solvent dependence, and may be described satisfactorily by dielectric relaxation theories.

Electronic absorption spectra of molecules and aggregates with interatomic charge transfer using a normal mode treatment of the atomic monopole–dipole interaction model
View Description Hide DescriptionThe theory of the atom monopole–dipole interaction model for electronic polarizability is extended to the case of complex frequency‐dependent atom polarizabilities, allowing the prediction of absorption spectra in terms of a set of electronic normal modes. The charge constraints on the system are taken into account using Lagrangian and penalty function methods. Expressions are obtained for the complex polarizability of an aggregate of molecules in which intermolecular charge transfer is precluded. The results are illustrated by calculations for naphthalene using atom polarizability parameters which give an approximate fit to the experimentally observed absorptionspectrum. We also treat helical stacked aggregates of naphthalene molecules and predict intensity shifts analogous to those observed in the stacked aromatic bases of helical nucleic acids.

Resonance enhanced multiphoton ionization spectroscopy of carbon disulphide
View Description Hide DescriptionRydbergexcited states of the CS_{2} molecule in the energy range 56 000–81 000 cm^{−1} have been further investigated via the two and three photon resonance enhancements they provide in the mass resolved multiphoton ionization (MPI) spectrum of a jet‐cooled sample of the parent molecule. Spectral interpretation has been aided by parallel measurements of the kinetic energies of the photoelectrons that accompany the various MPI resonances. Thus we have been able to extend, and clarify, previous analyses of the tangled spin–orbit split vibronic structure associated with the ^{3}Π_{ u } and ^{1}Π_{ u } states derived from the configuration [^{2}Π_{ g }]4pσ_{ u } and the ^{3}Δ_{ u }, ^{1}Δ_{ u }, and ^{1}Σ^{+} _{ u } states resulting from the configuration [^{2}Π_{ g }]4pπ_{ u }, and to deduce an approximate wave number for the origin of the hitherto unidentified ^{3}Σ^{+} _{ u } state derived from this same configuration. Moving to higher energies we are able to locate, unambiguously, the origins of the next (n=5) members of four of these [^{2}Π_{ g }]npRydberg series, and to identify extensive series based on the presumed Rydberg configurations [^{2}Π_{ g }]nsσ_{ g } and [^{2}Π_{ g }]nfλ_{ u } with, in both cases, n≤10. We also identify MPI resonances attributable to CS(a ^{3}Π) fragments, to ground state C atoms, and to S atoms in both their ground (^{3} P) and excited (^{1} S) electronic states. Analysis of the former resonances indicates that the CS(a ^{3}Π) fragments resulting from two photon dissociation of CS_{2} at excitation wavelengths around 300 nm are formed with substantial rovibrational excitation.

The 1550–1460 Å region of CS_{2}
View Description Hide DescriptionThe 1550–1460 Å region of CS_{2} has been investigated by both (1+1′)+1 and (3+1) resonance enhanced multiphoton ionization and the spectra obtained compared to previous one photon and electron impact studies. The results of this study indicate that the main feature in this region is due to an optically allowed transition to either a ^{1}Π_{ u } valence state or a ^{1}Σ^{+} _{ u } Rydberg‐valence type state and that this state is strongly predissociated. There is also evidence of gerade valence states in this region but there is no evidence of gerade Rydberg states.

Solvation dynamics study of 4‐amino‐N‐methyl‐phthalimide in n‐alcohol solutions
View Description Hide DescriptionWe have studied the solvation dynamics of 4‐amino‐N‐methyl‐phthalimide (4‐ANMP) in n‐butanol and n‐decanol solutions. Solvation time correlation functions were evaluated from wavelength‐dependent fluorescence lifetime distributions at two temperatures for the two solvents. Solvation dynamics of 4‐ANMP was strongly temperature dependent in n‐butanol, which is a more polar and less viscoussolvent than n‐decanol. A smaller effect was observed in n‐decanol solution. We also measured the rotational correlation times of 4‐ANMP in the same solutions and resolved two components indicative of a nonspherical structure of the molecule. The solvation times with relation to the dielectric relaxation times τ_{ L } and τ_{D} for linear alcohols are discussed.

Destruction cross sections for low energy collisions of H^{+} _{3} and D^{+} _{3} with rare gas atoms
View Description Hide DescriptionAbsolute total cross sections for collisional dissociation and charge transfer have been measured for collisions of H^{+} _{3} and D^{+} _{3} with He, Ar, and Xe for projectile energies ranging from 15 to 400 eV. The cross sections for collision‐induced dissociation of H^{+} _{3} into H^{+}+H_{2} or H+H^{+} _{2} are a few Å^{2} and exhibit a weak target dependence. It is suggested that the charge transfer cross sections, which vary markedly with target species, are due primarily to proton transfer to the rare gas target rather than electron transfer from the target. At the lower collision energies,proton abstraction is favored over deuteron abstraction for the He and Ar targets.

Quantum scattering calculations on the NH_{3}+OH→NH_{2}+H_{2}O reaction
View Description Hide DescriptionQuantum scattering calculations on the NH_{3}+OH→NH_{2}+H_{2}O reaction have been performed at energies up to 0.8 eV. The rotating bond approximation is used, treating NH_{2} as a pseudoatom. The OH rotation and a reactive N–H stretch of NH_{3} are treated explicitly as well as the bending motion and one OH local stretch vibration of H_{2}O. A reduced dimensionality potential energy surface is developed. It has accurate reactant and product rovibrational energy levels for the modes explicitly treated in the scattering calculations and incorporates the zero point energy of the other modes. Quantized transition states gating the flux are found and mode selectivity is observed. Reactants in their ground rovibrational states produce mainly ground state H_{2}O and vibrationally excited NH_{3} produces mainly vibrationally excited H_{2}O. Rate constants are obtained using an adiabatic approach to account for all degrees of freedom not explicitly treated in the scattering calculations. Tunneling makes a dominant contribution to the rate constants, which are in reasonable agreement with previous theoretical and experimental work.

A theory for adiabatic electron transfer processes across the semiconductor/electrolyte interface
View Description Hide DescriptionA theory for adiabatic electron transfer between a semiconductorelectrode and an electron acceptor species in a polar electrolyte is developed by extending the Anderson–Newns model as adapted for metal/electrolyte interfaces. It is shown that perturbations of the electrode electronic spectrum can lead to qualitative changes in Marcus free energy curves and thus in the electron transfer kinetics. In particular, the adiabatic solventfree energy curve may exhibit a triple well structure even when the linear response model is used to describe the solventpolarization fluctuations.

Cumulative reaction probability via transition state wave packets
View Description Hide DescriptionA new time‐dependent approach to the cumulative reaction probability, N(E), has been developed based on the famous formulation given by Miller and co‐workers [J. Chem. Phys. 79, 4889 (1983)], N(E)=[(2π)^{2}/2] tr[δ(E−H)Fδ(E−H)F]. Taking advantage of the fact that the flux operator has only two nonzero eigenvalues, we evaluate the trace efficiently in a direct product basis of the first flux operator eigenstates and the Hamiltonian eigenstates on the dividing surface (internal states). Because the microcanonical density operator, δ(E−H), will eliminate contributions to N(E) from an internal state with the energy much higher than the total energy E, we can minimize the number of internal states required by choosing a dividing surface with the lowest density of internal states. If the dividing surface is located in an asymptotic region, one just needs to include all the open channels, i.e., with internal energy lower than the total energy. Utilizing the Fourier transform for δ(E−H), we can obtain the information for all the energies desired by propagating these wave packets once. Thus the present approach will be much more efficient than the initial state selected wave packet (ISSWP) approach to N(E) for systems with many rotation degrees of freedom because the density of states in asymptotic region for such systems is much higher than that in the transition state region. With the present method one can also calculate the cumulative reaction probability from an initial state (or to a final state) by locating the second flux operator in the corresponding asymptotic region. This provides an alternative to the ISSWP approach which may be more efficient if the reaction probabilities from a large number of initial states are desired. The method is applied to the 3D H + H_{2} (even rotation) reaction for J=0 by locating the first dividing surface in the transition state region. The demonstration also shows an aspect less than ideal; the contribution to N(E) from a wave packet may be slightly larger than 1 or slightly smaller than 0, making it improper to interpret the contribution as a probability.

Complex scaling of ab initio molecular potential surfaces
View Description Hide DescriptionThe energies and lifetimes (i.e., inverse decay rates) of resonance (quasibound) states in chemical reactions are associated with the complex eigenvalues of the complex scaled Hamiltonian. The corresponding eigenfunctions are square integrable and are compact, localized functions in the coordinate space. Complex scaling is applicable when the potential, V(x), is dilation analytic. Ab initio potentials, however, are given on a grid, V _{ n }=V(x _{ n }). Starting from the theoretical work of Moiseyev and Hirschfelder [J. Chem. Phys. 88, 1063 (1988)], we propose an efficient numerical method of calculating V(x _{ n } exp(iθ)) by acting on the unscaled potential with a grid represented scaling operator Ŝ.

Temperature dependence of vibrational relaxation of N_{2} by O_{2} in liquid N_{2} along the coexistence curve
View Description Hide DescriptionThe temperature dependence of vibrational relaxation rates of N_{2}(υ=1) by O_{2} in liquid N_{2} has been studied at several temperatures along the coexistence curve between 80 and 120 K. A small amount of CO was added to the N_{2}–O_{2} mixture as a pump and a probe. A CO laser was used to excite CO in solution and its fluorescence was monitored to obtain the rate of vibrational energy transfer. The liquid‐phase rate constants k ^{ l } were compared with the gas‐phase constants k ^{ g } at the same temperatures and found to be essentially equal. This result is in reasonable agreement with the predictions of the isolated binary collision model.

Kinetic‐energy release in the dissociation of CO_{2} ^{2+}
View Description Hide DescriptionThe kinetic‐energy release distributions (KERDs) of the fragment ion pairs (O^{+}+CO^{+} and C^{+}+O^{+}) produced in dissociative double photoionization of carbon dioxide have been determined by analyzing the photoion–photoion coincidence spectra measured in the region hν=40–100 eV by use of a time‐of‐flight mass spectrometer and synchrotron radiation. The mechanism of the three‐body dissociation (CO^{2+} _{2}→C^{+}+O^{+}+O) has been examined to take place sequentially via CO^{+} by a triple photoelectron–photoion–photoion coincidence experiment. The KERD observed for the O^{+}+CO^{+} and C^{+}+O^{+} channels at low excitation energies cannot be explained by a simple framework whereby a doubly charged molecular ion (AB ^{2+}) is directly produced on single photon absorption followed by the dissociation of AB ^{2+} into two ionic fragments. Some of the ion pairs are produced through indirect processes in which highly excited CO_{2} ^{*+} and CO_{2} ^{**} (double Rydberg) states converging to the high‐lying CO^{2+} _{2} electronic states autoionize before and after dissociation. From the observed KERDs for the O^{+}+CO^{+} and C^{+}+O^{+} channels of CO^{2+} _{2}, the range of the intercharge distances of two positive holes is estimated by assuming that the KER is given purely by Coulomb repulsion.

Predissociation of HONO upon excitation into the S _{1} state: An ab initio and dynamics study
View Description Hide DescriptionWe have investigated the vibrational predissociation of nitrous acid in the first excited singlet state, HONO (S _{1}) → OH (X̃ ^{2}Π) + NO (X̃ ^{2}Π), by calculating the potential energy surface as a function of the pertinent coordinates. Of the ab initio methods tested in this context, the multiconfigurational second‐order perturbation theory (CASPT2) was found to deliver the best trade‐off between accuracy and expense of computer time. We solved the nuclear dynamics for a three dimensional model system treating the OH group as a pseudo atom and obtained the absorptionspectrum, the lifetimes and the partial cross sections of the NO fragment state distributions. The OH rotational state distribution was assessed with a model treating the NO group as a pseudo atom and keeping the OH bond frozen. Special attention was given to the mechanistic features of the decay such as the coupling effects among the degrees of freedom and the state specific lifetimes, and the assignment of the S _{0}→S _{1}absorptionspectrum of anti‐ and syn‐HONO.

Probing hydrogen bond potentials via combination band spectroscopy: A near infrared study of the geared bend/van der Waals stretch intermolecular modes in (HF)_{2}
View Description Hide DescriptionHigh resolution near infrared spectra of the two lowest frequency intermolecular modes in HF‐stretch excited states of (HF)_{2} have been characterized using a slit‐jet infrared spectrometer. In the spectral region surveyed, ten vibration–rotation–tunneling (VRT) bands are observed and assigned to the low frequency ‘‘van der Waals stretch’’ (ν_{4}) and ‘‘geared bend’’ (ν_{5}) intermolecular modes, in combination with either the hydrogen bond acceptor (ν_{1}) or donor (ν_{2}) high‐frequency intramolecular HF stretches. Analysis of the rotationally resolved spectra provide intermolecular frequencies, rotational constants, tunneling splittings, and predissociation rates for the ν_{4}/ν_{5} intermolecular excited states. The intermolecular vibrational frequencies in the combination states display a systematic dependence on intramolecular redshift that allows far‐IR intermolecular frequencies to be reliably extrapolated from the near‐IR data. Approximately tenfold increases in the hydrogen bond interconversion tunneling splittings with either ν_{4} or ν_{5} excitation indicate that both intermolecular modes correlate strongly to the tunneling coordinate. The high resolution VRT line shapes reveal mode specific predissociation broadening sensitive predominantly to intramolecular excitation, with weaker but significant additional effects due to low frequency intermolecular excitation. Analysis of the high resolution spectroscopic data for these ν_{4} and ν_{5} combination bands suggests strong state mixing between what has previously been considered van der Waals stretch and geared bend degrees of freedom.

Theoretical study of the valence π→π* excited states of polyacenes: Benzene and naphthalene
View Description Hide DescriptionMultireference perturbation theory with complete active space self‐consistent field (CASSCF) reference functions was applied to the study of the valence π→π* excited states of benzene and naphthalene. The eigenvectors and eigenvalues of CASSCF with valence π active orbitals satisfy pairing properties for the alternant hydrocarbons to a good approximation. The excited states of polyacenes are classified into the covalent minus states and ionic plus states with the use of the alternancy symmetry. The present theory satisfactorily describes the ordering of low‐lying valence π→π* excited states. The overall accuracy of the present approach is surprisingly high. We were able to predict the valence excitation energies with an accuracy of 0.27 eV for singlet u states and of 0.52 eV or better for singlet g states of naphthalene. Our predicted triplet states spectrum provides a consistent assignment of the triplet–triplet absorptionspectrum of naphthalene. For benzene we were able to predict the valence excitation energy with an accuracy of about 0.29 eV. The covalent minus states and ionic plus states exhibit different behavior as far as the electron correlation is concerned. The ionic plus states are dominated by the single excitations but covalent minus states include a large fraction of doubly excited configurations. The covalent minus states always give lower energy than the corresponding ionic plus states. This is true for triplet states. The dynamic σ–π polarization effects introduced by perturbation theory are significant for the ionic plus states while those on covalent excited states are usually of the same order as in the covalent ground state. The enlargement of the active space of the reference functions represents a great improvement of the description of the ionic states. The present approach with the pairing properties has proved to be of great value in understanding and predicting the experimental data of the alternant hydrocarbons.

A comparison of two approaches to perturbation triple excitation corrections to the coupled‐cluster singles and doubles method for high‐spin open‐shell systems
View Description Hide DescriptionAn analysis of molecular properties is presented for several first‐row diatomic molecules as determined at the CCSD(T) level of theory. In particular, a comparison of spectroscopic constants predicted by the ROHF‐CCSD(T) methods of Scuseria vs Gauss et al. is given. Accurate determination of the values of equilibrium bond lengths, dissociation energies, harmonic vibrational frequencies, anharmonic constants, vibration–rotation coupling constants, and centrifugal distortion constants show only small differences between the two methods. In particular, we show that the average absolute differences between the two methods for the equilibrium bond length, harmonic vibrational frequency, and the dissociation energy are 0.000 09 Å, 0.8 cm^{−1} and 0.1 kcal/mol, respectively.

Phase space path integrals in Monte Carlo quantum dynamics
View Description Hide DescriptionIn this article we present two phase space path integrals in terms of coherent states. The first one is derived in a standard fashion but using a nonstandard resolution of the identity in terms of coherent states with different width parameters. The second path integral emerges from a novel phase space representation in terms of coherent states distributed on n‐dimensional manifolds embedded in the 2n‐dimensional phase space of an n‐degree‐of‐freedom system. These states are shown to form locally complete basis sets since we show that fairly smooth and localized functions can be expanded in terms of them in a unique way. In this representation the time evolution operator can be cast in the form of a phase space path integral. Both path integrals can be evaluated by straightforward implementation of Monte Carlo methods. In both cases the probability amplitude between two phase points turns out to be proportional to the average of the phase, e ^{ i } h∫(p dq−H dt), over a Markov process of phase space paths consisting of classical trajectories interrupted at intervals by Gaussian ‘‘quantum jumps.’’ The numerical evaluation of these expressions through importance sampling is demonstrated.

A generator coordinate version of the closed‐shell Dirac–Fock equations
View Description Hide DescriptionA generator coordinate version of the Dirac–Fock equations for relativistic closed‐shell atoms is presented. The integration of the Dirac–Fock equations is performed through the integral discretization technique so as to preserve the continuous character of the generator coordinate formalism. With the new formalism we generate a universal Gaussian basis set for relativistic closed‐shell atoms with d and f orbitals (zinc up to nobelium). The results obtained with the universal Gaussian basis set for Dirac–Fock–Coulomb self‐consistent‐field energies are compared with numerical‐finite‐difference results and Dirac–Fock–Coulomb energies obtained by using other Gaussian basis sets. The excellent performance of our universal Gaussian basis set is attributed to the integral discretization technique of the generator coordinate Dirac–Fock method, as with it we are capable of generating Gaussian‐type function exponents that are able to represent properly the relativistic kinematics of an electron inside the nucleus.

Local treatment of electron correlation in coupled cluster theory
View Description Hide DescriptionThe closed‐shell coupled clustertheory restricted to single and double excitation operators (CCSD) is formulated in a basis of nonorthogonal local correlation functions. Excitations are made from localized molecular orbitals into subspaces (domains) of the local basis, which strongly reduces the number of amplitudes to be optimized. Furthermore, the correlation of distant electrons can be treated in a simplified way (e.g., by MP2) or entirely neglected. It is demonstrated for 20 molecules that the local correlation treatment recovers 98%–99% of the correlation energy obtained in the corresponding full CCSD calculation. Singles‐doubles configuration interac‐ tion (CISD), quadratic configuration interaction (QCISD), and Mo/ller–Plesset perturbation theory [MP2, MP3, MP4(SDQ)] are treated as special cases.