Volume 122, Issue 16, 22 April 2005
 ARTICLES

 Theoretical Methods and Algorithms

Elimination of translational and rotational motions in nuclear orbital plus molecular orbital theory
View Description Hide DescriptionThe nuclear orbital plus molecular orbital (NOMO) theory was developed in order to determine the nonadiabatic nuclear and electronic wave functions. This study presents a formulation to remove the contamination of rotational motion as well as translational motion in the NOMO theory. We have formulated the translation and rotationfree (TRF)NOMO theory by introducing the TRF Hamiltonian. The principal moment of inertia, which is the denominator in the rotational Hamiltonian, is expanded in a Taylor series. The zerothorder of the Taylor expansion corresponds to a rigidbody rotator. The firstorder terms contribute the coupling between the vibration and the rotation. Hartree–Fock equations have been derived in the framework of the TRFNOMO theory. Numerical assessments, which were preformed for , , , (muon dimmer), and , confirmed the importance of the TRF treatment.

Selfconsistent solution of the Dyson equation for atoms and molecules within a conserving approximation
View Description Hide DescriptionWe have calculated the selfconsistent Green’s function for a number of atoms and diatomic molecules. This Green’s function is obtained from a conserving selfenergy approximation, which implies that the observables calculated from the Green’s functions agree with the macroscopic conservation laws for particle number, momentum, and energy. As a further consequence, the kinetic and potential energies agree with the virial theorem, and the many possible methods for calculating the total energy all give the same result. In these calculations we use the finite temperature formalism and calculate the Green’s function on the imaginary time axis. This allows for a simple extension to nonequilibrium systems. We have compared the energies from selfconsistent Green’s functions to those of nonselfconsistent schemes and also calculated ionization potentials from the Green’s functions by using the extended Koopmans’ theorem.

Multicanonical schemes for mapping out freeenergy landscapes of singlecomponent and multicomponent systems
View Description Hide DescriptionMulticanonical (MUCA) sampling is a powerful approach for simulating large domains of thermodynamic macrostate space that relies on mapping out either the density of states or a free energy of the system as a function of a suitable “order parameter.” The purpose of this study is to extend and apply to more complex systems the method introduced in a previous paper [M. K. Fenwick and F. A. Escobedo, J. Chem. Phys.120, 3066 (2004)] that uses Bennett’s acceptance ratio method for estimating MUCA free energies. Four types of MUCA schemes are considered according to what order parameter is adopted and how the macrostate space is traversed: a la grand canonical ensemble,a la semigrand canonical ensemble,a la semigrand isothermalisobaric ensemble, and a la isothermalisobaric ensemble. Two types of systems are studied, the first is a twocomponent LennardJones mixture that exhibits a vaporliquid transition, and the second is a hardcuboid containing system that exhibits an isotropicliquid crystalline transition. These systems are simulated with different MUCA schemes and the resulting freeenergy profiles are used to determine phasecoexistence conditions. For the LennardJones systems, it is also demonstrated that different types of MUCA simulations can be conveniently performed over different macrostate regions and the results can be subsequently pieced together into a continuous weighting function.

Multidimensional quantum trajectories: Applications of the derivative propagation method
View Description Hide DescriptionIn a previous publication [J. Chem. Phys.118, 9911 (2003)], the derivative propagation method (DPM) was introduced as a novel numerical scheme for solving the quantum hydrodynamicequations of motion (QHEM) and computing the time evolution of quantum mechanical wave packets. These equations are a set of coupled, nonlinear partial differential equations governing the time evolution of the realvalued functions and in the complex action, , where . Past numerical solutions to the QHEM were obtained via ensemble trajectory propagation, where the required first and secondorder spatial derivatives were evaluated using fitting techniques such as moving least squares. In the DPM, however, equations of motion are developed for the derivatives themselves, and a truncated set of these are integrated along quantum trajectories concurrently with the original QHEM equations for and . Using the DPM quantum effects can be included at various orders of approximation; no spatial fitting is involved; there is no basis set expansion; and single, uncoupled quantum trajectories can be propagated (in parallel) rather than in correlated ensembles. In this study, the DPM is extended from previous onedimensional (1D) results to calculate transmission probabilities for 2D and 3D wave packet evolution on coupled Eckart barrier/harmonic oscillator surfaces. In the 2D problem, the DPM results are compared to standard numerical integration of the timedependent Schrödinger equation. Also in this study, the practicality of implementing the DPM for systems with many more degrees of freedom is discussed.

Gear formalism of the always stable predictorcorrector method for molecular dynamics of polarizable molecules
View Description Hide DescriptionThe recently proposed always stable predictorcorrector method for molecular dynamics of polarizable molecules [J. Kolafa, J. Comput. Chem.25, 335 (2004)] is rewritten in the Gear formalism. This equivalent form simplifies an implementation if the Newton equations of motion are integrated by the Gear method and also enables a variable integration step. Algorithms are presented for both the original and new versions and tested on a pair of polarizable ions exhibiting anharmonic vibrations.

Fluctuationdissipation theorem densityfunctional theory
View Description Hide DescriptionUsing the fluctuationdissipation theorem (FDT) in the context of densityfunctional theory(DFT), one can derive an exact expression for the groundstatecorrelation energy in terms of the frequencydependent density response function. When combined with timedependent densityfunctional theory, a new class of density functionals results that use approximations to the exchangecorrelation kernel as input. This FDTDFT scheme holds promise to solve two of the most distressing problems of conventional Kohn–Sham DFT: (i) It leads to correlation energy functionals compatible with exact exchange, and (ii) it naturally includes dispersion. The price is a moderately expensive scaling of computational cost and a slower basis set convergence. These general features of FDTDFT have all been recognized previously. In this paper, we present the first benchmark results for a set of molecules using FDTDFT beyond the randomphase approximation (RPA)—that is, the first such results with . We show that kernels derived from the adiabatic localdensity approximation and other semilocal functionals suffer from an “ultraviolet catastrophe,” producing a pair density that diverges at small interparticle distance. Nevertheless, dispersion interactions can be treated accurately if hybrid functionals are employed, as is demonstrated for and HeNe. We outline constraints that future approximations to should satisfy and discuss the prospects of FDTDFT.

A coherent discrete variable representation method for multidimensional systems in physics
View Description Hide DescriptionA coherent discrete variable representation (ZDVR) is proposed for constructing a multidimensional potentialoptimized DVR basis. The multidimensional quadrature pivots are obtained by diagonalizing a complex coordinate operator matrix in a finite basis set, which is spanned by the lowest eigenstates of a twodimensional reference Hamiltonian. Here a norm condition is used in the diagonalization procedure. The orthonormal eigenvectors define a collocation matrix connecting the localized ZDVR basis functions and the finite basis set. The method is applied to two vibrational models for computing the lowest bound states. Results show that the ZDVR method provides exponential convergence and accurate energies. Finally, a zerothorder approximation method is also derived.

Topography of molecular scalar fields. II. An appraisal of the hierarchy principle for electron momentum densities
View Description Hide DescriptionThe previously observed hierarchy principle for nondegeneratecritical points (CPs) of the electron momentum density (EMD) of molecules [Kulkarni, Gadre, and Pathak, Phys. Rev. A.45, 4399 (1992)] is verified at a reliable level of theory. Application of Morse inequalities and the Poincaré–Hopf relation to EMD leads to some rigorous results viz (i) for total number of CPs, there must be either a or a CP at the center of symmetry, (ii) for there must be either a or a CP at the center of symmetry. A single directional maximum on every ray, starting from has been observed for all the test molecules and is suggested as a working topographical principle in space. This working principle is shown to satisfy the sufficiency condition for the hierarchy principle.

Partial averaging and the centroid virial estimator for stereographic projection pathintegral simulations in curved spaces
View Description Hide DescriptionWe develop and test three different partial averaging theories for the stereographic projection path integral in curved spaces. Additionally, we adapt and test the centroid virial estimator for the kinetic energy in curved spaces. We tested both a confining as well as a nonconfining potential for the particle in a ring. All three partial averaging theories are demonstrated to converge linearly in the asymptotic region with , the number of Fourier coefficients. We use an error estimator to determine the optimal parameters for an extrapolation to infinite . We verify that the centroid virial estimator (derived from the primitive DeWitt pathintegral formula) converges to the kinetic energy for both confining and nonconfining potentials.

Theory of solvent influence on reaction dynamics
View Description Hide DescriptionA generalization of the recently published quantumclassical approximation [A. A. Neufeld, J. Chem. Phys., 119, 2488 (2003)] for the purposes of reaction dynamics in condensed phase is presented. The obtained kinetic equations treat a solvent influence in a nonphenomenological way, account for the change of the free energy of the surrounding media, allow for different solvent dynamics in each reaction channel, and constitute a powerful framework for an accurate modeling of solvent effects, including ultrafast processes. The key features of the approach are its differential form, which considerably facilitates practical applications, and well defined wide applicability limits. The developed methodology fully accounts for an arbitrary long memory of the canonical bath and covers solventinduced processes from a subpicosecond time scale.

Statistical theory of nonadiabatic transitions
View Description Hide DescriptionBased on results of the preceding paper, and assuming fast equilibration in phase space to the temperature of the surrounding media compared to the time scale of a reaction, we formulate a statistical theory of intramolecular nonadiabatictransitions. A classical mechanics description of phase space dynamics allows for an ab initio treatment of multidimensional reaction coordinates and easy combination with any standard molecular dynamics (MD) method. The presented approach has several features that distinguishes it from existing methodologies. First, the applicability limits of the approach are well defined. Second, the nonadiabatictransitions are treated dynamically, with full account of detailed balance, including zeropoint energy, quantum coherence effects, arbitrarily long memory, and change of the free energy of the bath. Compared to popular trajectory surface hopping schemes, our MDbased algorithm is more efficient computationally, and does not use artificial ad hoc constructions like a “fewest switching” algorithm, and rescaling of velocities to conserve total energy. The enhanced capabilities of the new method are demonstrated considering a model of two coupled harmonic oscillators. We show that in the rate regime and at moderate friction the approach precisely reproduces the freeenergygap law. It also predicts a general trend of the reaction dynamics in the low friction limit, and is valid beyond the rate regime.

Simulation of electronic and geometric degrees of freedom using a kinkbased path integral formulation: Application to molecular systems
View Description Hide DescriptionA kinkbased path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. The results for , , and demonstrate this method to be accurate for both geometries and energies. A comparison with density functional theory(DFT) and secondorder Moller–Plesset (MP2) level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

A pulsedfield ionization photoelectron secondary ion coincidence study of the proton transfer reaction
View Description Hide DescriptionThe endothermic proton transferreaction,, is investigated over a broad range of reactant vibrational levels using highresolution vacuum ultraviolet to prepare reactant ions either through excitation of autoionization resonances, or using the pulsedfield ionizationphotoelectronsecondary ion coincidence (PFIPESICO) approach. In the former case, the translational energy dependence of the integral reaction cross sections are measured for with high signaltonoise using the guidedion beam technique. PFIPESICO cross sections are reported for and at centerofmass collision energies of 0.6 and , respectively. All ion reactant states selected by the PFIPESICO scheme are in the rotational level. The experimental cross sections are complemented with quasiclassical trajectory(QCT) calculations performed on the ab initiopotential energy surface provided by Palmieri et al. [Mol. Phys.98, 1839 (2000)]. The QCT cross sections are significantly lower than the experimental results near threshold, consistent with important contributions due to resonances observed in quantum scattering studies. At total energies above , the QCT calculations are in excellent agreement with the present results. PFIPESICO timeofflight (TOF) measurements are also reported for and 4 at a collision energy of . The velocity inverted TOF spectra are consistent with the prevalence of a spectatorstripping mechanism.

NonBorn–Oppenheimer variational calculations of bound states with zero angular momentum
View Description Hide DescriptionWe report fully nonadiabatic calculations of all rotationless bound states of molecular ion carried out in the framework of the variational method. We show that, in all the states, except the two highest ones, the bond in the system can be described as covalent. In the highest two states the bond becomes essentially ionic and can be described as a complex. The wave function of the system was expanded in terms of spherically symmetric, explicitly correlated Gaussian functions with preexponential multipliers consisting of powers of the internuclear distance. Apart from the total energies of the states, we have calculated the expectation values of the , , and interparticle distances, their squares, and the nucleusnucleus correlation functions.

The role of relativity in the optical response of gold within the timedependent currentdensityfunctional theory
View Description Hide DescriptionWe included relativistic effects in the formulation of the timedependent currentdensityfunctional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalarrelativistic effects using the zerothorder regular approximation in the groundstate densityfunctional theory calculations, as well as in the timedependent response calculations. The results for the dielectric function of gold calculated in the spectral range of are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around , obtained in a nonrelativistic calculation, to around when relativity is included. With the inclusion of the scalarrelativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorptionspectrum are not well reproduced, but can be explained in terms of spinorbit couplingeffects. The remaining deviations are attributed to the underestimation of the interband gap ( band gap) in the localdensity approximation and to the use of the adiabatic localdensity approximation in the response calculation.

IR/UV and UV/UV doubleresonance study of guaiacol and eugenol dimers
View Description Hide DescriptionGuaiacol (2methoxyphenol) and eugenol (4allyl2methoxyphenol) molecules are biologically active phenol derivatives with an intramolecular hydrogen bond (H bond). Pulsed supersonic expansions of mixtures of either of the two molecules with He yield weakly bound homodimers as well as other higherorder complexes. A number of complementary and powerful laser spectroscopic techniques, including UVUV and IRUV double resonances, have been employed to interrogate the species formed in the expansion in order to get information on their structures and spectroscopic properties. The interpretation of the spectra of eugenol dimer is complex and required a previous investigation on a similar but simpler molecule both to gain insight into the possible structures and support the conclusions. Guaiacol (2methoxyphenol) has been used for that purpose. The combination of the broad laser study combined with ab initio calculations at the Becke 3 Lee–Yang–Parr/ level has provided the isomer structures, the potentialenergy wells, and shed light on the inter and intramolecular interactions involved. Guaiacol homodimer has been shown to have a single isomer whereas eugenol dimer has at least two. The comparison between the computed geometries of the dimers, their respective energies, and the vibrational normal modes permits the identification of the spectra.

Search for global minimum geometries for medium sized germanium clusters:
View Description Hide DescriptionWe have performed an unbiased search for the global minimum geometries of smalltomedium sized germanium clusters as well as a biased search (using seeding method) for . We employed the basinhopping algorithm coupled with the planewave pseudopotential density functional calculations. For each size, we started the unbiased search with using several structurally very different initial clusters, or we started the biased search with three different seeds. Irrespective of the initial structures of clusters we found that the obtained lowestenergy clusters of the size and 18 are the same. Among them, the predicted global minima of are identical to those reported previously [Shvartsburg et al., Phys. Rev. Lett.83, 167 (1999)]. For , we have identified two or three nearly isoenergetic lowlying isomers (for each size) that compete for the global minimum. Nearly all the lowlying clusters in the size range of contain the tricaped trigonal prism motif and are all prolate in geometry, in agreement with the experiment.

Comparative studies of the spectroscopy of : DFT versus standard ab initio approaches
View Description Hide DescriptionThe , , , transitions on have been studied using several exchangecorrelation functionals from the various types of density functional theory(DFT) approaches like local density approximation (LDA), generalized gradient approximation (GGA), hybrid and metaGGA. The results are compared with the experience and with those coming from the most sophisticated nondynamic and dynamic electronic correlation treatments using the same relativistic effective core potentials and especially developed basis sets to study the electronic structure of the five lowest states and the corresponding vertical and adiabatic transition energies. The calculated transition energies for three of the hybrid functionals (B3LYP, B972, and PBE0) are in very good agreement with the benchmark ab initio results and experimental figures. All of the other functionals largely overestimate the and transition energies, many of them even placing the ligand field state above the charge transfer and states. The relative weight of the HartreeFock exchange in the definition of the functional used appears to play a key role in the accurate description of the density defined by the orientation of the hole (, , or ) on Cu in the field of both chlorine atoms, but no simple connection of this weight with the quality of the spectra has been found. Mulliken charges and spin densities are carefully analyzed; a possible link between the extent of spin density on the metal for the state and the performance of the various functionals was observed, suggesting that those that lead to the largest values (close to 0.65) are the ones that best reproduce these four transitions. Most functionals lead to a remarkably low ionicity for the three ligand field states even for the best performing functionals, compared to the complete active space (SCF) (21, 14) ab initio values. These findings show that not only large variational ab initio calculations can produce reliable spectroscopic results for extremely complex systems where delicate electronic correlation effects have to be carefully dealt with. However, those functionals that were recently shown to perform best for a series of molecular properties [J. Chem. Phys.1213405 (2004)] are not the ones that produce the best transition energies for this complex case.

Penning ionization of molecules by and metastable atoms: A crossed beam study
View Description Hide DescriptionThe energetics of autoionizing collision complexes (where or ) and their dynamical evolution have been studied in a crossed beam apparatus, respectively, by Penning ionization electron spectroscopy (PIES) and by mass spectrometry (MS) techniques in the thermal energy range. The PIES spectra, detected by an electron energy analyzer, were recorded for both complexes at four different collision energies. Such spectra allowed the determination of the energy shifts for Penning electron energy distributions, and the branching ratios for the population of different electronic states and for the vibrational population in the molecular nascent ions. For the collision complex it was found, by MS, that the autoionization leads to the formation of , , , and product ions whose total and partial cross sections were measured in the collision energy range between 0.03 and . The results are analyzed exploiting current models for the Penning ionization process: the observed collision energy dependence in the PIES spectra as well as in the cross sections are correlated with the nature of the molecule orbitals involved in the ionization and are discussed in term of the interaction potentials, which are estimated by using a semiempirical method developed in our laboratory.

Penning ionization of molecules by and metastable atoms: Theoretical considerations about the intermolecular interactions
View Description Hide DescriptionA theoretical investigation of the intermolecular interaction, operative in collision complexes of , , and with , is carried out to explain the main results of the experimental study reported in the preceding paper. The analysis is carried out by means of a semiempirical method based on the identification, modeling, and combination of the leading interaction components, including the effect of the selective polarization of the more external electronic cloud of the metastable atom in the intermolecular electric field. These and other crucial aspects of our approach have been quantitatively verified by ab initio calculations. The proposed method permits to evaluate the interaction at any configuration of the complexes and provides a useful and inexpensive representation of the intermolecular potential energy for dynamics studies. The main experimental findings can be rationalized taking into account the critical balancing between molecular orientation effects in the intermolecular interaction field and the ionization probability. These orientation effects tend to become less pronounced with increasing collision energy.