Volume 119, Issue 3, 15 July 2003
 ARTICLES

 Theoretical Methods and Algorithms

Multilayer formulation of the multiconfiguration timedependent Hartree theory
View Description Hide DescriptionA multilayer (ML) formulation of the multiconfiguration timedependent Hartree (MCTDH) theory is presented. In this new approach, the singleparticle (SP) functions in the original MCTDH method are further expressed employing a timedependent multiconfigurational expansion. The Dirac–Frenkel variational principle is then applied to optimally determine the equations of motion. Following this strategy, the SP groups are built in several layers, where each top layer SP can contain many more Cartesian degrees of freedom than in the previous formulation of the MCTDH method. As a result, the MLMCTDH method has the capability of treating substantially more physical degrees of freedom than the original MCTDH method, and thus significantly enhances the ability of carrying out quantum dynamical simulations for complex molecular systems. The efficiency of the new formulation is demonstrated by converged quantum dynamical simulations for systems with a few hundred to a thousand degrees of freedom.

Geometrical optimization for strictly localized structures
View Description Hide DescriptionRecently we proposed the block localized wavefunction (BLW) approach which takes the advantages of valence bond theory and molecular orbital theory and defines the wavefunctions for resonance structures based on the assumption that all electrons and orbitals are partitioned into a few subgroups. In this work, we implement the geometrical optimization of the BLW method based on the algorithm proposed by Gianinetti and coworkers. Thus, we can study the conjugation effect on not only the molecular stability, but also the molecular geometry. With this capability, the π conjugation effect in transpolyenes (n=2–5) as well as in formamide and its analogs are studied by optimizing their delocalized and strictly localized forms with the 631G(d) and 6311+G(d,p) basis sets. Although it has been well presumed that the π resonance shortens the single bonds and lengthens the double bonds with the delocalization of π electrons across the whole line in polyenes, our optimization of the strictly localized structures quantitatively shows that when the conjugation effect is “turned off,” the double bond lengths will be identical to the CC bond length in ethylene and the single bond length will be about 1.513–1.517 Å. In agreement with the classical Hückel theory, the resonance energies in polyenes are approximately in proportion to the number of double bonds. Similarly, resonance is responsible not only for the planarity of formamide, thioformamide, and selenoformamide, but also for the lengthening of the CX (X=O,S,Se) double bond and the shortening of the CN bonds. Although it is assumed that the CX bond polarization decreases in the order of O>S>Se, the π electronic delocalization increases in the opposite order, i.e., formamide<thioformamide<selenoformamide. All calculations with the 631G(d) and 6311+G(d,p) basis sets show that there is no noticeable basis set dependence for the results.

Linear scaling for the local energy in quantum Monte Carlo
View Description Hide DescriptionThe scaling of the diffusionquantum Monte Carlo method can be greatly improved when localized orbitals and shortrange correlation functions are employed as recently suggested by the authors. The local diffusionquantum Monte Carlo method is described in detail with a careful analysis of errors. The new method achieves near linear scaling in the calculation of the local energy. Results demonstrating the improved performance are presented.

Reaction paths based on mean firstpassage times
View Description Hide DescriptionFinding representative reaction pathways is important for understanding the mechanism of molecular processes. We propose a new approach for constructing reaction paths based on mean firstpassage times. This approach incorporates information about all possible reaction events as well as the effect of temperature. As an application of this method, we study representative pathways of excitation migration in a photosynthetic lightharvesting complex, photosystem I. The paths thus computed provide a complete, yet distilled, representation of the kinetic flow of excitation toward the reaction center, thereby succinctly characterizing the function of the system.

Explicitly correlated divideandconquertype electronic structure calculations based on twoelectron reduced density matrices
View Description Hide DescriptionA method for constructing a description of a large electron system from explicitly correlated calculations on overlapping subsystems is developed. One and twoelectron reduced density matrices for the system are constructed using the reduced density matrices obtained from explicitly correlated calculations on the subsystems. This “locally correlated reduced density matrix” method is closely related to divideandconquer treatments of meanfield and densityfunctional theory, and to wavefunctionbased treatments of correlation. Calculations on toy systems indicate that the method recovers a complete description of local correlation effects, is size extensive, and can be formally linear scaling.

Quantum instanton approximation for thermal rate constants of chemical reactions
View Description Hide DescriptionA quantum mechanical theory for chemical reaction rates is presented which is modeled after the [semiclassical (SC)] instanton approximation. It incorporates the desirable aspects of the instanton picture, which involves only properties of the (SC approximation to the) Boltzmann operator, but corrects its quantitative deficiencies by replacing the SC approximation for the Boltzmann operator by the quantum Boltzmann operator, Since a calculation of the quantum Boltzmann operator is feasible for quite complex molecular systems (by Monte Carlopath integral methods), having an accurate ratetheory that involves only the Boltzmann operator could be quite useful. The application of this quantum instanton approximation to several one and twodimensional model problems illustrates its potential; e.g., it is able to describe thermal rate constants accurately error) from high to low temperatures deep in the tunneling regime, and applies equally well to asymmetric and symmetric potentials.

Nuclear spin–spin coupling density functions and the Fermi hole
View Description Hide DescriptionNuclear spin–spin coupling density functions yield a threedimensional picture of the interaction between two nuclear dipole moments mediated by electron spin density. A physical interpretation of the Fermi contact coupling density maps can be readily arrived at on account of the Fermi correlation between samespin electrons as the mechanism whereby the spin polarization induced about one nucleus is transmitted to another nucleus coupled to it. It is shown that the Fermi hole density function, evaluated by an opportune choice of the reference electron, is characterized by morphological aspects very similar to those appearing in the plots of one and twobonds Fermi contact density functions. A comparison has been made for hydrogen fluoride, water, ammonia, and methane molecules at the Hartree–Fock level of theory. The results confirm the role of the Fermi correlation as the fundamental vehicle propagating nuclearspin/electronspin contact interaction, i.e., the process mainly responsible for nuclear spin–spin coupling. The plots of Fermi hole density show that the geminal H–H coupling would not be possible without the essential contribution of the spin density in the vicinity of the heavier nucleus. The combined use of Fermi contact density functions and Fermi hole distributions yields a very promising approach to the study of nuclear magnetic resonance coupling constants, and provides a sound physical basis for their interpretation.

Assessment of density functional methods for nuclear magnetic resonance shielding calculations
View Description Hide DescriptionSeveral different methods for calculating nuclear magnetic resonance shieldings in density functional theory are compared. All methods were implemented using gaugeincluding atomic orbitals to eliminate gauge dependence. The calculated shielding tensors are compared to accurate coupled cluster results with perturbative triples correction and to experimental data. We have implemented a simple method based on a uniform shift of virtual orbital energies and determined the optimum level shift in small molecules. Of the methods tested, the uniform level shift and procedure of Wilson, Amos, and Handy show the best performance. Malkin’s correction also gave good results. The optimized exchange functional of Cohen and Handy, in conjunction with the Lee–Yang–Parr (LYP) correlation functional, gives a marked improvement over the Becke exchange plus LYP.

Quantum initial value representations using approximate Bohmian trajectories
View Description Hide DescriptionQuantum trajectories, originating from the de Broglie–Bohm hydrodynamic description of quantum mechanics, are used to construct timecorrelation functions in an initial value representation. The formulation is fully quantum mechanical and the resulting equations for the correlation functions are similar in form to their semiclassical analogs but do not require the computation of the stability or monodromy matrix or conjugate points. We then move to a local trajectory description by evolving the cumulants of the wave function along each individual path. The resulting equations of motion are an infinite hierarchy, which we truncate at a given order. We show that timecorrelation functions computed using these approximate quantum trajectories can be used to accurately compute the eigenvalue spectrum for various potential systems.

Variational formulation for the electrostatic potential in dielectric continua
View Description Hide DescriptionThe thermodynamic potential for fixed charges in dielectric continua is given for arbitrary values of the polarization density. Minimization of the functional gives the equilibrium polarization density (equivalently image charges) and the electrostatic potential throughout the media. The functional, which in general involves volume integrals, for the case of piecewise uniform dielectrica is reduced to surface integrals of the constrained surface charge density at the dielectric discontinuities. A linear integral equation for the induced surface charge, which can be solved by iteration, is given. The conjugate thermodynamic force for the constrained surface charge is also given. The latter formulation is suitable for Car–Parrinello or Lagrangianmolecular dynamics in complex geometries.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

On the inversion of the and electronic states in α,ωdiphenylpolyenes
View Description Hide DescriptionAn alternative model to that of the inversion of the states and is proposed for interpreting the photophysics of the α,ωdiphenylpolyenes. This model is based upon the existence of two chemical structures with symmetry, which may be ascribed to the same excited electronic state One of the two chemical structures corresponds to the Franck–Condon structure with conjugated single and double bonds for the polyene chain, and another consists of a nearly equivalent series of partial double bonds along the polyene chain. The latter relaxed structure is consistent with the observation of high torsional energy barriers and low photoisomerization quantum yields for diphenylhexatriene in the singlet excited statemanifold. Interestingly, such a simple quantum model as that of the particle in a onedimensional box provides quite an accurate description of the absorptionspectroscopicproperties of these major compounds. This is partly the result of the most stable structures for these compounds being of the alltrans type; such structures increase in length as additional ethylene units are added, which makes them very similar to a onedimensional box becoming increasingly longer.

Intermolecular potential and the equation of state of solid
View Description Hide DescriptionFirstprinciples totalenergy calculations are performed for the lowtemperature ordered phase of solid in the wide range of lattice parameter. The intermolecular potential obtained from these calculations is successfully modeled in terms of the interaction between carbon atoms on different molecules and the multipole Coulombic interaction between molecules. This model enables us to calculate structural and thermodynamic properties of both the orientationally ordered and disordered phases in a consistent manner. We find that the equation of state at finite temperature obtained for this potential is not in good agreement with experiments and the intermolecular potential is much shallower than that expected from the experimental heat of sublimation. These discrepancies are interpreted as arising from the limited capability of the densityfunctional calculations to appropriately incorporate the effect of electron correlations at large separation, which is responsible for the longrange behavior of the van der Waals interaction between molecules. In order to circumvent this difficulty we take an empirical approach to estimate the additional van der Waals interaction, which is not taken into account in the current densityfunctional calculations.

Photoinduced dynamics of the valence states of ethene: A sixdimensional potentialenergy surface of three electronic states with several conical intersections
View Description Hide DescriptionA sixdimensional analytic potentialenergysurface of the three valence states of ethene has been constructed on the basis of completeactivespace ab initio calculations and ab initio calculations with perturbation theory of second order based on a complete active reference space. The nuclear coordinate space is spanned by the torsion, the C–C stretch coordinate, the left and right pyramidalization and the symmetric and antisymmetric scissor coordinates. The C–H stretch coordinates and the rocking angles are kept frozen at their groundstate equilibrium value. A diabatic representation of the valence states of ethene has been constructed within the framework of a Hückeltype model. The diabatic potentialenergy elements are represented as analytic functions of the relevant coordinates. The parameters of the analytic functions have been determined by a leastsquares fit of the eigenvalues of the diabatic potentialenergy matrix to the ab initio data for onedimensional and twodimensional cuts of the sixdimensional surface. As a function of the torsion, the analytic potentialenergysurface describes the intersections of the and states for torsional angles near which are converted into conical intersections by the antisymmetric scissor mode. As a function of pyramidalization of perpendicular ethene, it describes the intersections of the diabatic and states, which are converted into conical intersections by displacements in the torsional mode. The analytic potentialenergysurfaces can provide the basis for a quantum wave packet description of the internal conversion of photoexcited ethene to the electronic ground state via conical intersections.

Calculation of electric properties using regular approximations to relativistic effects: The polarizabilities of and (Z=108)
View Description Hide DescriptionAnalytic expressions for the derivatives of the total molecular energy with respect to external electric field are derived within the regular approximation to the full fourcomponent relativistic Hamiltonian and presented in matrix form suitable for implementation in standard quantumchemical codes. Results of benchmark calculations using the infiniteorder regular approximation with modified metric method are presented and discussed. The static electric dipole polarizabilities of group VIII metal tetroxides for M=Ru, Os, Hs (Z=108) are studied with the help of secondorder Møller–Plesset perturbation theory using the infiniteorder regular approximation with modified metric Hamiltonian. The polarizabilities obtained vary in the sequence which is different from those obtained in other studies. However, it is in line with calculated excitation energies of the group VIII tetroxides, which provide a measure for the magnitude of their polarizabilities.

The bondforming reaction between and A computational and experimental study
View Description Hide DescriptionGroundstate stationary points on the potential energy surface of the reaction were calculated using the densityfunctional theory hybrid method B3LYP and the ab initio coupled cluster singles and doubles with perturbative triples [CCSD(T)] algorithm. The calculations reveal a reaction mechanism involving two transition states. The first transition state involves the migration of one hydrogen within the primary collision complex and the second corresponds to the loss of a proton. The neutral HF molecular product is formed in its stable ground state. Comparison of activation energies for the reactions of with and with calculated from Becke three parameter Lee–Yang–Parr (B3LYP) zeropoint energies, slightly favor the pathway by 0.04 and 0.07 eV for the first and second activations, respectively. Rate constant calculations using Rice–Ramsperger–Kassel–Marcus/quasiequilibrium theory also kinetically favor the pathway in comparison with the pathway. However, the magnitudes of the calculated rate constants are so large that the differences between the rates of reaction of with and with should not be distinguished by a crossedbeam timeofflight mass spectrometer experiment. Indeed, the ion yields reported in this paper from new collision experiments between and showed no isotope effect when compared with previous data from collisions of with

Characterization of the CCCl radical in the state by Fouriertransform microwave spectroscopy and ab initio calculations
View Description Hide DescriptionPure rotational transitions of a new carbonchain radical, CCCl, a chlorine derivative of CCH, have been observed for the first time by Fouriertransform microwave spectroscopy. The radical has been produced in a supersonic free jet by a pulsed discharge in diluted to 0.3% with Ne. Transitions with spin splittings were observed for two isotopomers, and in the regions at 12.6 GHz for and 25.2 GHz for respectively. The radical shows a spectral pattern for a molecule with symmetry as is the case for CCH. Hyperfine splittings due to the Cl nucleus were also clearly resolved. The molecular constants have been precisely determined for the two isotopomers. Ab initio calculations at the MRCI level with the ccpVTZ basis set have revealed that the first excited electronic state corresponding to the state at linear geometry is very close to the ground electronic state, and the two states are more strongly interacting with each other than the case of CCH. Based on the results of the ab initio calculations and the determined hyperfine constants, it was found that a conical intersection exists due to a strong vibronic coupling in the vicinity of the ground state, and as a result the CCCl radical has a bent structure in the ground state.

Study of He flow properties to test He dimer potentials
View Description Hide DescriptionThe parameters which characterize the energy distribution of a supersonic helium beam are measured at different source parameters. The data are compared with the results of calculations based on three different He–He interatomic potentials in order to test their ability to describe the helium free jet expansion. This article follows a previous paper where calculations were performed at source temperatures between 20 and 80 K using the the LennardJones and the Tang–Toennies–Yiu potential [K. T. Tang, J. P. Toennies, and C. L. Yiu, Phys. Rev. Lett. 74, 1546 (1995)] but no satisfactory agreement was found. Here, calculations are presented also for a potential curve recently proposed by Hurly and Moldover [J. J. Hurly and M. R. Moldover, J. Res. Natl. Inst. Stand. Technol. 105, 667 (2000)]. The source temperature range where calculations are performed is extended between 6 and 300 K in order to compare the predictions of the three potentials with other measurements present in literature. Possible experimental limitations to the beam performances are discussed and in particular the skimmer interference is taken into account. As the considered potentials only partially describe the experiments, a phenomenological viscosity cross section is proposed which represents in a satisfactory way the He flow properties over the whole range of source temperatures.

Global geometry optimization of silicon clusters described by three empirical potentials
View Description Hide DescriptionThe “basichopping” global optimization technique developed by Wales and Doye is employed to study the global minima of silicon clusters with three empirical potentials: the Stillinger–Weber (SW), the modified Stillinger–Weber (MSW), and the Gong potentials. For the smallsized SW and Gong clusters it is found that the global minima obtained based on the basinhopping method are identical to those reported by using the genetic algorithm [Iwamatsu, J. Chem. Phys. 112, 10976 (2000)], as well as with those by using molecular dynamics and the steepestdescent quench (SDQ) method [Feuston, Kalia, and Vashishta, Phys. Rev. B 37, 6297 (1988)]. However, for the midsized SW clusters the global minima obtained differ from those based on the SDQ method, e.g., the appearance of the endohedral atom with fivefold coordination starting at as opposed to For larger SW clusters it is found that the “bulklike” endohedral atom with tetrahedral coordination starts at In particular, the overall structural features of SW and are nearly identical to the MSW counterparts. With the SW as the starting structure, a geometric optimization at the B3LYP/631G(d) level of densityfunctional theory yields an isomer similar to the groundstate isomer of reported by Pederson et al. [Phys. Rev. B 54, 2863 (1996)].

Amide I modes of tripeptides: Hessian matrix reconstruction and isotope effects
View Description Hide DescriptionFor seven representative tripeptide conformations, we carried out ab initio geometry optimizations and vibrational analyses. By using the Hessian matrix reconstruction method developed in the present paper, both the diagonal and offdiagonal coupling force constants of a given tripeptide were calculated and the relationship between the threedimensional conformation and local amide I mode frequency was discussed. Isotope labeling effects on both the amide I local and normal modes were elucidated. It was found that the C=O bond length of a given peptide, which represents the structural distortion induced by neighboring peptides, is linearly proportional to the local amide I mode frequency. A theoretical model for predicting the local amide I mode frequencies is discussed and compared with the ab initio calculation results.

Time delay as a tool to identify the signatures of reactive resonance: and reactions
View Description Hide DescriptionThe formalism of scattering time delay is investigated as a tool to identify the signatures of resonance in reactive molecular collisions. The concept of state and angle resolved time delay is reviewed and applied to model problems. Several numerical pathologies of the time delay formalism are discussed that potentially may obscure a resonance signature, or may lead to a false positive result. The time delay is computed explicitly for the and reactions using the results of full scattering calculations on the Stark–Werner potential energy surface. The reactive resonance known to exist for the reaction is clearly apparent both in the state resolved and angle resolved time delay functions. On the other hand, the analogous resonance in the reaction is masked in the state resolved time delay function through the influence of a nearby energetic threshold. However, the angle resolved time delay does provide a clear signature of the resonance, thus settling a controversy on the existence of a resonance for the system.