Volume 113, Issue 17, 01 November 2000
 COMMUNICATIONS


Quasimicrowave spectroscopy of nonpolar diatomic molecules by using optical phaselocked lasers
View Description Hide DescriptionA new type of optical–optical double resonance (OODR) experiment using an optical phaselock loop was applied to a molecular system. The difference frequency between two singlemode lasers was locked to a tunable MW reference using an optical heterodyne technique. An OODR signal was observed in the subDoppler condition when three rovibronic levels in the transitions of the molecule interacted simultaneously with the two lasers. This optical phaselocked OODR spectroscopy achieves absolute frequency measurements of the rotational structure. It is especially advantageous to the ground state of nonpolar molecules because the resonance signal is free from the radiative lifetime of the electronic excited state, and then the accuracy would be as precise as that obtained by MW spectroscopy.
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 ARTICLES

 Theoretical Methods and Algorithms

Efficient free energy calculations by variationally optimized metric scaling: Concepts and applications to the volume dependence of cluster free energies and to solid–solid phase transitions
View Description Hide DescriptionFinitetime variational switching is an efficient method for obtaining converging upper and lower bounds to free energy changes by computer simulation. Over the course of the simulation, the Hamiltonian is changed continuously between the system of interest and a reference system for which the partition function has an analytic form. The bounds converge most rapidly when the system is kept close to equilibrium throughout the switching. In this paper we introduce the technique of metric scaling to improve adherence to equilibrium and thereby obtain more rapid convergence of the free energy bounds. The method involves scaling the coordinates of the particles, perhaps in a nonuniform way, so as to assist their natural characteristic evolution over the course of the switching. The scaling schedule can be variationally optimized to produce the best convergence of the bounds for a given Hamiltonian switching path. A correction due to the intrinsic work of scaling is made at the end of the calculation. The method is illustrated in a pedagogical onedimensional example, and is then applied to the volume dependence of cluster free energies, a property of direct relevance to vapor–liquid nucleationtheory. Orderofmagnitude improvements in efficiency are obtained in these simple examples. As a contrasting application, we use metric scaling to calculate directly the free energy difference between facecenteredcubic and bodycenteredcubic Yukawa crystals. A continuous distortion is applied to the lattice, avoiding the need for separate comparison of the two phases with an independent reference system.

Mixed quantumclassical molecular dynamics: Aspects of the multithreads algorithm
View Description Hide DescriptionThe mixed quantumclassical Liouville equation is derived from a semiclassical perspective starting from the full quantum Schrödinger equation. An asymptotic numerical scheme for solving the equation is discussed which relies on propagating swarms of interacting “threads” which represent the density matrix or other observable. It is demonstrated that this “multithreads” method performs extremely well on simple onedimensional model systems designed to test nonadiabaticmolecular dynamic methods, yielding essentially exact results for a variety of models.

Electronic and vibronic contributions to twophoton absorption of molecules with multibranched structures
View Description Hide DescriptionThe electronic and vibronic contributions to the twophoton absorption of a series molecules with multibranched structures have been studied using ab initio response theory. The results indicate that the electronic coupling between different branches alone cannot explain the experimental finding of a strong enhancement of the twophoton absorption cross section over the single branch structure, whereas it is predicted that vibronic contributions can play an important role in this respect. It is shown that for multibranched molecules the use of circularly polarized light can increase the twophoton absorption cross section by a factor of 1.5 over linearly polarized light excitation.

Chargetransfer correction for improved timedependent local density approximation excitedstate potential energy curves: Analysis within the twolevel model with illustration for and LiH
View Description Hide DescriptionTimedependent densityfunctional theory (TDDFT) is an increasingly popular approach for calculating molecular excitation energies. However, the TDDFT lowest triplet excitation energy, of a closedshell molecule often falls rapidly to zero and then becomes imaginary at large internuclear distances. We show that this unphysical behavior occurs because must become negative wherever symmetry breaking lowers the energy of the ground state solution below that of the symmetry unbroken solution. We use the fact that the ΔSCF method gives a qualitatively correct first triplet excited state to derive a “chargetransfer correction” (CTC) for the timedependent local density approximation (TDLDA) within the twolevel model and the TammDancoff approximation (TDA). Although this correction would not be needed for the exact exchange–correlation functional, it is evidently important for a correct description of molecular excited statepotential energy surfaces in the TDLDA. As a byproduct of our analysis, we show why TDLDA and LDA ΔSCF excitation energies are often very similar near the equilibrium geometries. The reasoning given here is fairly general and it is expected that similar corrections will be needed in the case of generalized gradient approximations and hybrid functionals.

Calculation of the twodimensional vibrational response function
View Description Hide DescriptionWe present a complete analytical expression of the twodimensional (2D) vibrational response function without invoking the factorization approximations based on the Wick’s theorem that have been used in most previously reported theories. Since the harmonic approximation to the vibrational degrees of freedom is not required in this new formulation, the vibrationallevel dependencies of the transition frequencies and the vibrational relaxation rates are fully incorporated in the obtained formula for the 2D vibrational response function. Furthermore, the nonMarkovian nature of the vibrational dephasing process in condensed phases is also fully taken into account by carrying out the resummation of the associated diagrams with the linked diagram theory. It is found that there exists an additional contribution to the 2D vibrational response function, which was completely ignored due to the approximations based on the Wick’s theorem.

Timedependent densityfunctional determination of arbitrary singlet and triplet excitedstate potential energy surfaces: Application to the water molecule
View Description Hide DescriptionOver the past few years a large number of densityfunctional schemes have been developed for molecular excited states, many of which have been shown to produce poor results for water. We apply the timedependent densityfunctional method using hybrid and asymptotically corrected functionals to evaluate the vertical excitation energies,relaxation energies and vibration frequencies, and dissociation pathways for up to eight singlet and six triplet excited states of water. The results are compared to experimental data as well as ab initio calculated data obtained using direct and equationsofmotion coupledcluster techniques, as well as multireference configurationinteraction techniques. For most properties, the asymptotically corrected densityfunctional method produces results of comparable quality to those produced by the ab initio methods. However, the timedependent methods produce very poor results for systems involving molecular dissociation. In fact, only the multireference approaches produce good descriptions of molecular dissociation, but in the regions of the minima of the potential energy surfaces singlereference techniques are found to be both more accurate and much more robust.

A simple method for deriving kinetic energy operators
View Description Hide DescriptionWe derive a general twovectorembedded rovibrational kinetic energy operator (KEO) for a molecule with N atoms. Our KEO is valid for any moleculefixed axis system attached to the two embedding vectors and any vibrational coordinates for the twovector part of the KEO. It can be used to build up KEOs for larger molecules from KEOs for smaller molecules.

Generalized variational density functional perturbation theory
View Description Hide DescriptionWe present an implementation of variational perturbation theory in the framework of density functional theory. We use an ab initio pseudopotential scheme with a plane wave basis set and expand the energy functional up to second order in the perturbation. The approach is fairly general and does not rely on the representativeness of the perturbation through a Hamiltonian operator and does not require the use of canonical orbitals. Instead, a functional formulation is used to characterize the perturbation. Several types of applications are presented which illustrate the variety of linear response phenomena that can be treated with our method (vibrational modes, Raman scattering, and nuclear magnetic resonancechemical shift computations). In combination with advanced gradient correction formulas, an accurate description of second order effects in periodic and isolated systems can be achieved.

The accuracy of the pseudopotential approximation. III. A comparison between pseudopotential and allelectron methods for Au and AuH
View Description Hide DescriptionThe quality of the pseudopotential approximation has been tested thoroughly by calculating spectroscopicproperties of the gold atom and ground state AuH for eight different effective core potentials using Hartree–Fock, secondorder Mo/ller–Plesset and coupled cluster methods. The pseudopotential valence basis set for Au was chosen to be identical for all pseudopotentials, a subset of the allelectron basis set and the condition was applied that all sets are of near basis set limit quality. The pseudopotential results are compared with data obtained from nonrelativistic, scalar relativistic Douglas–Kroll and fully relativistic fourcomponent allelectron calculations. The variation between the results obtained for all valence electron smallcore pseudopotentials and all electron Douglas–Kroll calculations is found to be small (for the Stuttgart pseudopotential Å, eV, D). Sizable differences to all electron results are only found for the 11 valence electron largecore pseudopotentials. The effects of the basis set superposition error on spectroscopic constants were investigated. Calculated coupled clusterelectron affinities and ionization potentials for gold and spectroscopicproperties for AuH were found to be in excellent agreement with available experimental data. The variation between the different smallcore pseudopotentials for one particular spectroscopicproperty is shown to be less than the error due to the incompleteness of electron correlation procedure or the basis set and approximately of the same size as the basis set superposition error. The results show that scalar relativistic effects for valence properties are perfectly described by the pseudopotential approximation.

Photodissociation of polarized diatomic molecules in the axial recoil limit: Control of atomic polarization
View Description Hide DescriptionA quantum mechanical treatment of the photofragment angular momentumpolarization following photodissociation of diatomic molecules is presented. This treatment extends that of Siebbeles et al. [J. Chem. Phys. 100, 3610 (1994)] by considering photodissociation of a molecule whose angular momentum is polarized in the laboratory frame, and also treats properly the angular momentum coupling between the two photofragments. The formalism treats coherent excitation of dissociative surfaces and the consequences of nonadiabatic coupling between surfaces. The possibility of exploiting the parent molecule polarization in order to control the photofragment polarization when both parallel and perpendiculartype dissociations are active is discussed. An example is given in which significant control over the molecular frame polarization of the fragments is achieved following photolysis of a parent molecule prepared by an electric dipole transition, which may be of use in the study of photoinitiated bimolecular reactions.

Environmentinduced corrections to the spin Hamiltonian as dynamic frequency shifts in nuclear magnetic resonance
View Description Hide DescriptionWe derive an expression for the correction to the spinsystem Hamiltonian that arises due to the system–bath interaction, starting both from the standard master equation for the spin density matrix and a perturbative diagonalization of the system–bath Hamiltonian to the second order in the interaction. We show that the dynamic frequency shifts observed in the evolution of the nuclear spin coherences are a result of these Hamiltonian corrections. We present a systematic decomposition of the relaxation superoperator into Hermitian and antiHermitian parts as opposed to the usual practice of partitioning it into real and imaginary parts. We point out that the relaxationinduced corrections to the coherent motion arise exclusively from the antiHermitian part and the dissipative effects, from the Hermitian part, both, in general, being complex. However, the secular terms of this correction are found to depend only on the imaginary and the real parts, respectively.

The initial implementation and applications of a general active space coupled cluster method
View Description Hide DescriptionA general coupled cluster method that allows arbitrary excitations from a single referencedeterminant is proposed and tested. The method is based on a generalization of the formalism of spinstrings and provides a unified method for the storage and manipulation of coupled cluster operators. An initial implementation of the method is discussed and used to study the convergence of the coupled cluster hierarchy for and at equilibrium geometry, employing up to eightfold excitations. The energy and wave function contributions of the various excitation levels are examined. The dissociation curve of HF is also studied. Using single and double excitations from a minimal active space, the coupled clusterdissociation curve for HF shows a largest deviation from full configuration interaction curve of which decreases by an order of magnitude up on the addition of triple excitations out of the active space.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Quantum yields and energy partitioning in the ultraviolet photodissociation of 1,2 dibromotetrafluoroethane (Halon2402)
View Description Hide DescriptionThe photodissociation of 1,2 dibromotetrafluoroethane (Halon2402) has been investigated at 193 nm using photofragment translational spectroscopy with vacuum ultraviolet ionization and at 193, 233, and 266 nm using stateselected translational spectroscopy with resonanceenhanced multiphoton ionization. The product branching ratios, angular distributions, and translational energy distributions were measured at these wavelengths, providing insight into the ultraviolet photodissociation dynamics of The total bromine atom quantum yields were found to be 1.9±0.1 at both 193 and 233 nm and 1.4±0.1 at 266 nm. The first C–Br bonddissociation energy was determined to be 69.3 kcal/mol from ab initio calculations. The second C–Br bonddissociation energy was determined to be 16±2 kcal/mol by modeling of the bromine quantum yield. In addition, variational Rice–Ramsperger–Kassel–Marcus theory was used to calculate the secondary dissociation rates for a range of dissociation energies above threshold. These results suggest that photofragments with sufficient internal energies will undergo secondary dissociation prior to collisional stabilization under atmospheric conditions. Based on the measured translational energy distributions and product branching ratios, a model is proposed to describe the wavelengthdependent bromine quantum yield and the implications of these results to atmospheric chemistry are discussed.

Quantum scattering calculations for the electronically nonadiabatic reaction
View Description Hide DescriptionThreedimensional quantum scattering calculations have been carried out for the electronically nonadiabaticreaction. The calculations have been done using two methods: the timeindependent hyperspherical closecoupling formalism for the total angular momentum quantum number and the generalized Rmatrix propagation method with negativeimaginary potentials which absorb the reactive flux for but employing the coupledstates approximation for The diabatic model, which was originally developed by Truhlar and coworkers, has been employed in the present calculations. The results calculated with the two methods agree very well with those obtained by Truhlar and coworkers, indicating that our results are numerically converged. Detailed analyses of the calculated probabilities show that the electronically nonadiabatic transitions from to effectively occur in the entrance region of the potential surface but that the contribution of the electronically nonadiabaticchemical reaction, is small.

Investigation of the vibrational dynamics of the HCN/CNH isomers through high order canonical perturbation theory
View Description Hide DescriptionMolecular vibrations of the molecule HCN/CNH are examined using a combination of a minimum energy path (MEP) Hamiltonian and high order canonical perturbation theory (CPT), as suggested in a recent work [D. Sugny and M. Joyeux, J. Chem. Phys. 112, 31 (2000)]. In addition, the quantum analog of the classical CPT is presented and results obtained therefrom are compared to the classical ones. The MEP Hamiltonian is shown to provide an accurate representation of the original potential energy surface and a convenient starting point for the CPT. The CPT results are subsequently used to elucidate the molecular dynamics: It appears that the isomerizationdynamics of HCN/CNH is very trivial, because the three vibrational modes remain largely decoupled up to and above the isomerization threshold. Therefore, the study of the threedimensional HCN/CNH system can be split into the study of several onedimensional bending subsystems, one for each value of the numbers and of quanta in the CH and CN stretches. In particular, application of high order CPT to the most precise available ab initio surface provides simple expressions (quadratic polynomials) for the calculation of the heights of the isomerization barrier and of the CNH minimum above the HCN minimum for each value of and

Raman spectra of rhodium trimers in argon matrices
View Description Hide DescriptionResonance Raman spectra of rhodium trimers in argon matrices have been obtained for the first time. Our samples are prepared by neutralizing a massfiltered beam of trimer ions. Although the absorptionspectrum of our optically thin samples failed to show any obvious transitions, a rich Raman spectrum was found for laser excitation wavelengths between 545 nm and 593 nm. Three fundamentals, corresponding to normal modes of a bent molecule can be assigned with up to four overtones in the symmetric stretch. Using standard techniques, we obtained for this mode with The resulting stretching force constant is Assuming a Morse potential governs the symmetric stretching normal coordinate, we obtain an atomization energy of The asymmetric stretch and bend are found at 259 cm^{−1} and 247.9(8) cm^{−1}, respectively. A line at 400 cm^{−1} is observed, which does not fit the normal mode scheme of the ground state. This is assigned as the origin of a low lying electronic state.

Quantum dynamics study of the reaction: Timedependent wave packet calculations
View Description Hide DescriptionThe quantum dynamics of the reaction has been studied by means of timedependent quantum wave packet calculations on the G3 and BW2 potential energy surfaces. Initial statespecific total reaction probabilities and integral cross sections are calculated, and the thermal rate constant is obtained. On the G3 surface, the effect of the reagent’s rotational excitation on the reactivity is negative, while on the BW2 surface, the rotation of reagent has positive effect on the reactivity. Comparison of the thermal rate constants on the G3 and BW2 surfaces with experimental measurement is shown.

Photoelectron spectroscopy of ammonia: Modedependent vibrational autoionization
View Description Hide DescriptionPhotoelectron spectroscopy was used to study the mode dependence of vibrational autoionization in highRydberg states of Twocolor, twophotonresonant, threephoton excitation via the intermediate state was used to populate selected autoionizing Rydberg states between the (1200) and (1300) ionization thresholds of the ground electronic state, and the ionic vibrational distributions were determined from the photoelectron spectra. Excitation of Rydberg states in which two different vibrational modes are excited allowed the direct comparison of the autoionization efficiencies for the two modes. Autoionization via the loss of one quantum of vibrational energy from the nontotally symmetric “umbrella” mode, was found to be the dominant autoionization process. Vibrational branching fractions obtained from the ionic vibrational distributions indicate that, for the Rydberg states accessed via the intermediate state, the mode is approximately 25 times more efficient at promoting autoionization than the totally symmetric stretching mode,

Binary nucleation of noctane and ioctane
View Description Hide DescriptionThe authors used a Wilson expansion cloud chamber to measure binary homogeneous nucleation rates for pure noctane, pure ioctane, and 3:1, 1:1, 1:3 (mole ratio) mixtures in a temperature range from 215 to 260 K. The nucleation rates range from approximately 100 to 50 000 Current binary nucleation theory is unable to predict the data for this nearly ideal system.