Volume 120, Issue 6, 08 February 2004
 COMMUNICATIONS


Twodimensional optical spectroscopy: Twocolor photon echoes of electronically coupled phthalocyanine dimers
View Description Hide DescriptionTwocolor photon echo peak shift spectroscopy was used to study electronic coupling in a phthalocyanine homodimer. Two optical parametric amplifiers were used to produce pulses to excite the split lower states of The existence of a twocolor peak shift indicates the existence of correlation between these two dipoleallowed states. The nature of this correlation is discussed based on theoretical predictions of the interactions between exciton and charge resonance states.
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 ARTICLES

 Theoretical Methods and Algorithms

Atombond electronegativity equalization method fused into molecular mechanics. I. A sevensite fluctuating charge and flexible body water potential function for water clusters
View Description Hide DescriptionRecently, experimental and theoretical studies on the water system are very active and noticeable. A transferable intermolecular potential seven points approach including fluctuationcharges and flexible body (ABEEM7P) based on a combination of the atombond electronegativity equalization and molecular mechanics (ABEEM/MM), and its application to small water clusters are explored and tested in this paper. The consistent combination of ABEEM and molecular mechanics (MM) is to take the ABEEM charges of atoms, bonds, and lonepair electrons into the intermolecular electrostaticinteraction term in molecular mechanics. To examine the charge transfer we have used two models coming from the charge constraint types: one is a charge neutrality constraint on whole water system and the other is on each water molecule. Compared with previous water force fields, the ABEEM7P model has two characters: (1) the ABEEM7P model not only presents the electrostaticinteraction of atoms, bonds and lonepair electrons and their changing in respond to different ambient environment but also introduces “the hydrogen bondinteraction region” in which a new parameter is used to describe the electrostaticinteraction of the lonepair electron and the hydrogen atom which can form the hydrogen bond; (2) nonrigid but flexible water body permitting the vibration of the bond length and angle is allowed due to the combination of ABEEM and molecular mechanics, and for van der Waals interaction the ABEEM7P model takes an all atom–atom interaction, i.e., oxygen–oxygen, hydrogen–hydrogen, oxygen–hydrogen interaction into account. The ABEEM7P model based on ABEEM/MM gives quite accurate predictions for gasphase state properties of the small water clusters such as optimized geometries, monomer dipole moments, vibrational frequencies, and cluster interactionenergies. Due to its explicit description of charges and the hydrogen bond, the ABEEM7P model will be applied to discuss properties of liquid water, ice, aqueous solutions, and biological systems.

The role of fluctuations in both density functional and field theory of nanosystems
View Description Hide DescriptionThe role of fluctuations in both the density functional theory(DFT) and the field theory (FT) of nanosystems is studied. It turns out that although fluctuations are rigorously incorporated into the general formalism of DFT, they are often omitted in the choice of an approximate free energy functional that must be constructed in order to solve the basic integral equation appearing in DFT. Aside from the analytical discussion, it is demonstrated, in connection with a particular system (fluid in a nanopore) that the effects of fluctuation are missing when one of the most common functionals for this system is used. The demonstration involves a comparison of the results of Monte Carlo simulation with the predictions of DFT when this free energy functional is used. The applicability of FT and DFT in the context of the theory of nucleation is also discussed.

On the peculiarities of the diabatic framework: New insight
View Description Hide DescriptionIn this article we consider the electronic diabatic presentation of a twostate system with the aim of earning insight regarding the distribution of conical intersections in a given region. In this process we revealed explicit relationship between the diabatic potentials and the locations of conical intersections. The study is accompanied with numerical examples as worked out for a model and ab initiopotential energy surfaces of the system.

Is there any group additive rules in the calculation of electron correlation energies of long straight chain alkane molecules?
View Description Hide DescriptionAccording to the definition in the text, the correlationenergy of of carbon atoms, the primary and secondary C–H bonding electron pairs in some fragments and linear alkane molecules are calculated and analyzed. The transferability of the correlationenergies of these electron pairs in the linear alkanes is investigated. The results indicate that the correlationenergy of is perfectly transferable in the respective methyl and methylene groups, while the correlationenergies of the primary and secondary C–H bonding electron pairs are approximately transferable in methyl and methylene groups. The analysis of the results of group correlationenergy shows that both of the correlationenergies of methyl and methylene groups are transferable in these linear alkanes. The correlationenergies of methylene group in molecules are slightly decreasing showing a converging trend to a “standard” methylene group in linear alkanes. The excellent fitting relationship between the total correlationenergy and the number of methylene groups of the linear alkanes shows that the total correlationenergy is a linear function of the number of methylene groups, which means that the total correlationenergies of large linear alkanes can be reproduced and predicted by counting the numbers of methylene groups. In this way, total correlationenergy of large linear alkane molecule can be approximately calculated using this simple group additive scheme with substantial saving in computational time.

Coupledcluster singles and doubles for extended systems
View Description Hide DescriptionCoupledcluster theory with connected single and double excitation operators (CCSD) and related approximations, such as linearized CCSD, quadratic configuration interaction with single and double excitation operators, coupledcluster with connected double excitation operator (CCD), linearized CCD, approximate CCD, and second and thirdorder manybody perturbationtheories, are formulated and implemented for infinitely extended onedimensional systems(polymers), on the basis of the periodic boundary conditions and distancebased screening of integrals, density matrix elements, and excitation amplitudes. The variation of correlation energies with the truncation radii of short and longrange lattice sums and with the number of wave vector sampling points in the first Brillouin zone is examined for polyethylene, polyacetylene, and polyyne, and is shown to be a function of the degree of πelectron conjugation or the fundamental band gaps. The and amplitudes in the atomic orbital (AO) basis are obtained by first computing the amplitudes in the Blochorbital basis and subsequently backtransforming them into the AO basis. The plot of these AObased amplitudes as a function of unit cells also indicates that the amplitudes of polyacetylene and polyyne exhibit appreciably slower decay than those of polyethylene, although the asymptotic decay behavior is invariably The AObased amplitudes appear to correlate strongly with the electronic structure, and they decay seemingly exponentially for polyethylene whereas they stay at a constant magnitude across the seventh nearest neighbors of polyacetylene and polyyne, which attests to far reaching effects of nondynamical electron correlation mediated by orbital rotation. Nonetheless, the unit cell contributions to the correlation energies taper below hartree after 15 Å for all three polymers. The basis set dependence of the decay behavior of amplitudes is also examined for linear hydrogen fluoride polymer and linear beryllium polymer employing the STO3G, 631G, and basis sets, and proves to be rather small.

Analytical energy gradient of the symmetryadaptedcluster configurationinteraction general method for singlet to septet ground and excited states
View Description Hide DescriptionA method of calculating analytical energy gradients of the singlet and triplet excited states, ionized states, electronattached states, and highspin states from quartet to septet states by the symmetryadaptedcluster configurationinteraction general method is developed and implemented. This method is a powerful tool in the studies of geometries, dynamics, and properties of the states of molecules in which not only oneelectron processes but also two and multielectron processes are involved. The performance of the present method was confirmed by calculating the geometries and the spectroscopic constants of the diatomic and polyatomic molecules in various electronic states involving the ground state and the one to threeelectron excited states. The accurate descriptions were obtained for the equilibrium geometries, vibrational frequencies, and adiabatic excitation energies, which show the potential usefulness of the present method. The particularly interesting applications were to the state of acetylene, the and states of CNC and the and states of radical.

Semiclassical initial value treatment of correlation functions
View Description Hide DescriptionTwo semiclassical, initial value representation (IVR) treatments are presented for the correlation function where and are energy eigenfunctions of a “zeroorder” Hamiltonian describing an arbitrary, integrable, vibrational system. These wave functions are treated semiclassically so that quantum calculations and numerical integrations over these states are unnecessary. While one of the new approximations describes the correlation function as an integral over all phase space variables of the system, in a manner similar to most existing IVR treatments, the second approximation describes the correlation function as an integral over only half of the phase space variables (i.e., the angle variables for the initial system). The relationship of these treatments to the conventional HermanKluk approximation for correlation functions is discussed. The accuracy and convergence of these treatments are tested by calculations of absorption spectra for model systems having up to 18 degrees of freedom, using Monte Carlo techniques to perform the multidimensional phase space integrations. Both treatments are found to be capable of producing spectra of excited, anharmonic states that agree well with quantum results. Although generally less accurate than full phase space or HermanKluk treatments, the half phase space method is found to require far fewer trajectories to achieve convergence. In addition, this number is observed to increase much more slowly with the system size than it does for the former methods, making the halfphase space technique a very promising method for the treatment of large systems.

Free energy simulations: Use of reverse cumulative averaging to determine the equilibrated region and the time required for convergence
View Description Hide DescriptionA method is proposed for improving the accuracy and efficiency of free energy simulations. The essential idea is that the convergence of the relevant measure (e.g., the free energy derivative in thermodynamic integration) is monitored in the reverse direction starting from the last frame of the trajectory, instead of the usual approach, which begins with the first frame and goes in the forward direction. This simple change in the use of the simulation data makes it straightforward to eliminate the contamination of the averages by contributions from the equilibrating region. A statistical criterion is introduced for distinguishing the equilibrated (production) region from the equilibrating region. The proposed method, called reverse cumulative averaging, is illustrated by its application to the wellstudied case of the alchemical free energy simulation of ethane to methanol.

Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimalbasis orbitals
View Description Hide DescriptionA method is presented for expressing the occupied selfconsistentfield (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic minimalbasisset orbitals that deviate as little as possible from freeatom SCF minimalbasis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the freeatom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed “quasiatomic minimalbasissets” is independent of the calculational atomic orbital basis used. The resulting resolution of molecular orbitals in terms of quasiatomic minimal basis set orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimalbasis orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn–Sham density functional theory orbitals and is easily generalized to valence MCSCF orbitals.

Molecule intrinsic minimal basis sets. II. Bonding analyses for and to
View Description Hide DescriptionThe method, introduced in the preceding paper, for recasting molecular selfconsistent field (SCF) or density functional theory(DFT) orbitals in terms of intrinsic minimal bases of quasiatomic orbitals, which differ only little from the optimal freeatom minimalbasis orbitals, is used to elucidate the bonding in several silicon clusters. The applications show that the quasiatomic orbitals deviate from the minimalbasis SCF orbitals of the free atoms by only very small deformations and that the latter arise mainly from bonded neighbor atoms. The Mulliken population analysis in terms of the quasiatomic minimalbasis orbitals leads to a quantum mechanical interpretation of smallring strain in terms of antibonding encroachments of localized molecularorbitals and identifies the origin of the bondstretch isomerization in In the virtual SCF/DFT orbital space, the method places the qualitative notion of virtual valence orbitals on a firm basis and provides an unambiguous ab initio identification of the frontier orbitals.

Estimating entropies from molecular dynamics simulations
View Description Hide DescriptionWhile the determination of freeenergy differences by MD simulation has become a standard procedure for which many techniques have been developed, total entropies and entropy differences are still hardly ever computed. An overview of techniques to determine entropy differences is given, and the accuracy and convergence behavior of five methods based on thermodynamic integration and perturbation techniques was evaluated using liquid water as a test system. Reasonably accurate entropy differences are obtained through thermodynamic integration in which many copies of a solute are desolvated. When only one solute molecule is involved, only two methods seem to yield useful results, the calculation of solute–solvent entropy through thermodynamic integration, and the calculation of solvation entropy through the temperature derivative of the corresponding freeenergy difference. Onestep perturbation methods seem unsuitable to obtain entropy estimates.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Laserinduced fluorescence spectroscopy of
View Description Hide DescriptionIn a discharged supersonic jet of acetonitrile and carbon disulfide, we have for the first time observed an electronic transition of the radical using laserinduced fluorescence(LIF)spectroscopy. A progression originating from the C–S stretching mode of the upper electronic state appears in the excitation spectrum. Each band of the progression has a polyad structure due to anharmonic resonances with even overtones of bending modes. Rotationally resolved spectra have been observed by highresolution laser scans, and the electronic transition is assigned to For the vibronic origin band, the position and the effective rotational constant of the upper level have been determined to be 21 553.874(1) and 0.046 689(4) cm^{−1}, respectively. The dispersed fluorescencespectrum from the zero vibrational level of has also been observed; its vibrational structure is similar to that of the LIF excitation spectrum, showing a prominent C–S stretching progression with polyad structures. The vibrational frequencies of the C–S stretching mode in the ground and excited electronic states are determined to be 550 and 520 cm^{−1}, respectively. Fluorescence decay profiles have been measured for several vibronic levels of the state.

Mode dependent vibrational autoionization of Rydberg states of II. Comparing the symmetric stretching and bending vibrations
View Description Hide DescriptionTripleresonance excitation and highresolution photoelectron spectroscopy are combined to characterize the mode selectivity of vibrational autoionization of the high Rydberg states of Photoelectron spectra and vibrational branching fractions are reported for autoionizing Rydberg states converging to the state, that is, with one quantum in the symmetric stretch, and one quantum in the bending vibration, These results indicate that autoionization proceeds most efficiently through the loss of one quantum from the symmetric stretch rather than from the bending vibration. The implications of this result are discussed in terms of the autoionization mechanism.

Combined experimental/theoretical investigation of the He+ICl interactions. I. Rovibronic spectrum of He⋯ICl complexes in the 3–0 region
View Description Hide DescriptionTransitions of two different stereoisomers of the weakly bound complex, one with a Tshaped orientation and another that is most likely linear, have been observed in laserinduced fluorescence experiments performed in the region [Bradke and Loomis, J. Chem. Phys. 118, 7233 (2003)]. Here we present experimental and theoretical results aimed at confirming the previous assignments and at gaining additional insights into the He+ICl interactions. High resolution action spectra were recorded in the same region to identify those features that could be attributed to transitions of the isomers and not to higherorder complexes, where or containing species. Calculations of the rovibronic spectra of the complexes in the 2–0 and 3–0 regions were performed using an ab initiopotential energy surface for the ground state [Prosmiti et al., J. Chem. Phys. 117, 7017 (2002)] and two different pairwise additive potentials for the excited states [Waterland et al., J. Chem. Phys. 89, 7277 (1988); Gray and Wozny, J. Chem. Phys. 94, 2817 (1991)]. The rotationvibration energies and wave functions for the complexes were obtained for all bound states with total angular momentum using both of these potentials. Electronic spectra were generated using these results, assuming that the transition moment lies along the ICl bond and is not perturbed by the presence of the helium atom. The calculations qualitatively reproduce the action spectrum and strongly support the previous assignments. The calculations also indicate that some of the spectral congestion observed near the linear band may be attributed to transitions of the linear isomer to multiple intermolecular levels in the excited state. Coriolis coupling strongly mixes states with rotational excitation, making simulations and assignments of the linear band observed in the experimental spectrum difficult.

High resolution measurements of kinetic energy release distributions of neon, argon, and krypton cluster ions using a three sector field mass spectrometer
View Description Hide DescriptionUsing a newly constructed three sector field mass spectrometer (resulting in a BE1E2 field configuration) we have measured the kinetic energy release distributions of neon, argon, and krypton cluster ions. In the present study we used the first two sectors, B and E1, constituting a high resolution mass spectrometer, to select the parent ions in terms of mass, charge, and energy, and studied the decay of those ions in the third field free region. Due to the improved mass resolution we were able to extend earlier studies carried out with a two sector field machine, where an upper size limit arose from the fact that several isotopomers contribute to a decaying parent ion beam when the cluster size exceeds a certain value. Furthermore we developed a new data analysis. It allows us to model also fragment ion peaks that are a superposition of different decay reactions and thus we can determine the average kinetic energy release for all decay reactions of a given cluster ion. In a further step we used these results to determine the binding energies of cluster ions by applying finite heat bath theory. The smaller sizes have not been included in this analysis, because the validity of finite heat bath theory becomes questionable below The present average kinetic energy releases and binding energies are compared with other experiments and various calculations.

Dispersion corrections to density functionals for water aromatic interactions
View Description Hide DescriptionWe investigate recently published methods for extending density functional theory to the description of longrange dispersive interactions. In all schemes an empirical correction consisting of a term is introduced that is damped at short range. The coefficient is calculated either from average molecular or atomic polarizabilities. We calculate geometrydependent interactionenergy profiles for the water benzene cluster and compare the results with secondorder Møller–Plesset calculations. Our results indicate that the use of the B3LYP functional in combination with an appropriate mixing rule and damping function is recommended for the interaction of water with aromatics.

Quantummechanical calculations on pressure and temperature dependence of threebody recombination reactions: Application to ozone formation rates
View Description Hide DescriptionA quantummechanical model is designed for the calculation of termolecular association reaction rate coefficients in the lowpressure falloff regime. The dynamics is set up within the energy transfer mechanism and the kinetic scheme is the steadystate approximation. We applied this model to the formation of ozone for making use of semiquantitative potential energy surfaces. The stabilization process is treated by means of the vibrational closecoupling infinite order sudden scattering theory. Major approximations include the neglect of the vibrational bending mode and rovibrational couplings. We calculated individual isotopespecific rate constants and rate constant ratios over the temperature range 10–1000 K and the pressure falloff region The present results show a qualitative and semiquantitative agreement with available experiments, particularly in the temperature region of atmospheric interest.

Raman under nitrogen. The highresolution Raman spectroscopy of crystalline uranocene, thorocene, and ferrocene
View Description Hide DescriptionThe utility of recording Raman spectroscopy under liquid nitrogen, a technique we call Raman under nitrogen (RUN), is demonstrated for ferrocene, uranocene, and thorocene. Using RUN, lowtemperature (liquid nitrogen cooled) Raman spectra for these compounds exhibit higher resolution than previous studies, and new vibrational features are reported. The first Raman spectra of crystalline uranocene at 77 K are reported using excitation from argon (5145 Å) and krypton (6764 Å) ion lasers. The spectra obtained showed bands corresponding to vibrational transitions at 212, 236, 259, 379, 753, 897, 1500, and 3042 cm^{−1}, assigned to ring–metal–ring stretching, ring–metal tilting, outofplane CCC bending, inplane CCC bending, ringbreathing, C–H bending, CC stretching and CH stretching, respectively. The assigned vibrational bands are compared to those of uranocene in THF, and thorocene. All vibrational frequencies of the ligands, except the 259 cm^{−1} outofplane CCC bending mode, were found to increase upon coordination. A broad, polarizable band centered about ∼460 cm^{−1} was also observed. The 460 cm^{−1} band is greatly enhanced relative to the vibrational Raman transitions with excitations from the krypton ion laser, which is indicative of an electronic resonance Raman process as has been shown previously. The electronic resonance Raman band is observed to split into three distinct bands at 450, 461, and 474 cm^{−1} with 6764 Å excitation. Relativistic density functional theory is used to provide theoretical interpretations of the measured spectra.

Spinlocking of halfinteger quadrupolar nuclei in nuclear magnetic resonance of solids: Creation and evolution of coherences
View Description Hide DescriptionSpinlocking of halfinteger quadrupolar nuclei, such as and is of renewed interest owing to the development of variants of the multiplequantum and satellitetransition magic angle spinning (MAS) nuclear magnetic resonance experiments that either utilize spinlocking directly or offer the possibility that spinlocked states may arise. However, the large magnitude and, under MAS, the time dependence of the quadrupolar interaction often result in complex spinlocking phenomena that are not widely understood. Here we show that, following the application of a spinlocking pulse, a variety of coherence transfer processes occur on a time scale of before the spin system settles down into a spinlocked state which may itself be time dependent if MAS is performed. We show theoretically for both spin and 5/2 nuclei that the spinlocked state created by this initial rapid dephasing typically consists of a variety of single and multiplequantum coherences and nonequilibrium population states and we discuss the subsequent evolution of these under MAS. In contrast to previous work, we consider spinlocking using a wide range of radio frequency field strengths, i.e., a range that covers both the “strongfield” and “weakfield” limits. Single and multiplequantum filtered spinlocking experiments on and under both static and MAS conditions, are used to illustrate and confirm the results of the theoretical discussion.