Volume 112, Issue 17, 01 May 2000
 ARTICLES

 Theoretical Methods and Algorithms

Thermodynamic integration of the free energy along a reaction coordinate in Cartesian coordinates
View Description Hide DescriptionA generalized formulation of the thermodynamic integration (TI) method for calculating the free energy along a reaction coordinate is derived. Molecular dynamics simulations with a constrained reaction coordinate are used to sample conformations. These are then projected onto conformations with a higher value of the reaction coordinate by means of a vector field. The accompanying change in potential energy plus the divergence of the vector field constitute the derivative of the free energy. Any vector field meeting some simple requirements can be used as the basis of this TI expression. Two classes of vector fields are of particular interest here. The first recovers the conventional TI expression, with its cumbersome dependence on a full set of generalized coordinates. As the free energy is a function of the reaction coordinate only, it should in principle be possible to derive an expression depending exclusively on the definition of the reaction coordinate. This objective is met by the second class of vector fields to be discussed. The potential of mean constraint force (PMCF) method, after averaging over the unconstrained momenta, falls in this second class. The new method is illustrated by calculations on the isomerization of nbutane, and is compared with existing methods.

Including dispersion in configuration interactionsingles calculations for the spectroscopy of chromophores in solution
View Description Hide DescriptionIn this paper we prove that a configuration interactionelectronic structure calculation on a supermolecule that contains only single excitations includes dispersioninteractions between the two subsystems when energy differences are taken between the Hartree–Fock (molecular orbital) ground state and low energy excited states in which single excitations dominate. This theorem is proven up to second order in perturbation theory.

Evaluation of charge penetration between distributed multipolar expansions
View Description Hide DescriptionA formula to calculate the charge penetration energy that results when two charge densities overlap has been derived for molecules described by an effective fragment potential (EFP). The method has been compared with the ab initio charge penetration, taken to be the difference between the electrostatic energy from a Morokuma analysis and Stone’s Distributed Multipole Analysis. The average absolute difference between the EFP method and the ab initio charge penetration for dimers of methanol, acetonitrile, acetone, DMSO, and dichloromethane at their respective equilibrium geometries is 0.32 kcal mol^{−1}.

The mechanical strength of a covalent bond calculated by density functional theory
View Description Hide DescriptionThe rupture forces of covalent bonds in a polymer as a function of bond lifetime are calculated with an Arrhenius kinetics model based on highlevel density functional theory calculations. Relaxed potential energy surface scans of small model molecules yield potential functions that account for the deformations and hybridizations caused by the application of force. Morse potentials chosen to exhibit the same well depth and maximum force are used as an analytic representation of an individual bond in an infinitely long onedimensional polymer. Application of force deforms the potential, and the activation energy for the bond rupture event together with the frequency of an optical phonon in the onedimensional polymer are the two Arrhenius parameters. Rupture forces of the bonds C–C, C–N, C–O, Si–C, Si–N, Si–O, and Si–Si are reported as a function of the lifetime of the bond.

Inertial stochastic dynamics. I. Longtimestep methods for Langevin dynamics
View Description Hide DescriptionTwo algorithms are presented for integrating the Langevin dynamicsequation with long numerical time steps while treating the mass terms as finite. The development of these methods is motivated by the need for accurate methods for simulating slow processes in polymer systems such as twosite intermolecular distances in supercoiled DNA, which evolve over the time scale of milliseconds. Our new approaches refine the common Brownian dynamics (BD) scheme, which approximates the Langevin equation in the highly damped diffusive limit. Our LTID (“longtimestep inertial dynamics”) method is based on an eigenmode decomposition of the frictiontensor. The less costly integrator IBD (“inertial Brownian dynamics”) modifies the usual BD algorithm by the addition of a massdependent correction term. To validate the methods, we evaluate the accuracy of LTID and IBD and compare their behavior to that of BD for the simple example of a harmonic oscillator. We find that the LTID method produces the expected correlation structure for Langevin dynamics regardless of the level of damping. In fact, LTID is the only consistent method among the three, with error vanishing as the time step approaches zero. In contrast, BD is accurate only for highly overdamped systems. For cases of moderate overdamping, and for the appropriate choice of time step, IBD is significantly more accurate than BD. IBD is also less computationally expensive than LTID (though both are the same order of complexity as BD), and thus can be applied to simulate systems of size and time scale ranges previously accessible to only the usual BD approach. Such simulations are discussed in our companion paper, for long DNA molecules modeled as wormlike chains.

Inertial stochastic dynamics. II. Influence of inertia on slow kinetic processes of supercoiled DNA
View Description Hide DescriptionWe apply our new algorithms presented in the companion paper (LTID: longtimestep inertial dynamics,IBD: inertial Brownian dynamics) for massdependent Langevin dynamics (LD) with hydrodynamics, as well as the standard Brownian dynamical (BD) propagator, to study the thermal fluctuations of supercoiled DNA minicircles. Our DNAmodel accounts for twisting, bending, and saltscreened electrostatic interactions. Though inertial relaxation times are on the order of picoseconds, much slower kinetic processes are affected by the Brownian (noninertial) approximation typically employed. By comparing results of LTID and IBD to those generated using the standard (BD) algorithm, we find that the equilibrium fluctuations in writhing number, Wr, and radius of gyration, are influenced by massdependent terms. The autocorrelation functions for these quantities differ between the BD simulations and the inertial LD simulations by as much as 10%. In contrast, when the nonequilibrium process of relaxation from a perturbed state is examined, all methods (inertial and diffusive) yield similar results with no detectable statistical differences between the mean folding pathways. Thus, while the evolution of an ensemble toward equilibrium is equally well described by the inertial and the noninertial methods, thermal fluctuations are influenced by inertia. Examination of such equilibrium fluctuations in a biologically relevant macroscopic property—namely the twosite intermolecular distance—reveals massdependent behavior: The rate of juxtaposition of linearly distant sites along a 1500base pair DNA plasmid, occurring over time scales of milliseconds and longer, is increased by about 8% when results from IBD are compared to those from BD. Since inertial modes that decay on the picosecond time scale in the absence of thermal forces exert an influence on slower fluctuations in macroscopic properties, we advocate that IBD be used for generating longtime trajectories of supercoiled DNA systems. IBD is a practical alternative since it requires modest computational overhead with respect to the standard BD method.

Manybody Green’sfunction calculations on the electronic excited states of extended systems
View Description Hide DescriptionElectron correlation corrections to the excitation energy of the lowestlying singlet exciton state of polyethylene are evaluated with the aid of the quasiparticleenergies obtained from secondorder manybody perturbationtheory and from the secondorder inverse Dyson equation. A simple approximation is proposed to avoid the evaluation of the quasiparticleenergies for high and lowlying energy bands, which is particularly problematic in extendedsystem calculations. The inclusion of both the electron correlation effects and diffuse basis functions is important for the proper description of the exciton state. The electron correlation corrections calculated by this method appear to be too large, probably due to the neglect of the screening effects of the quasiparticle interactions.

Simulation of nonadiabatic wave packet interferometry using classical trajectories
View Description Hide DescriptionIn this paper, we describe the application of our recently developed multistate semiclassical Liouville equation method for modelingmolecular dynamics on multiple coupled electronic states [C. C. Martens and J.Y. Fang, J. Chem. Phys. 106, 4918 (1997); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998)] to problems where electronic coherenceeffects play a dominant role. We consider a model problem involving the simultaneous evolution of wave packets on two coupled electronic states. We analyze the problem qualitatively from both quantum and semiclassical perspectives using perturbation theory, and identify the roles played by coupling strength and relative phase of the initial wave packets. We then perform trajectorybased simulations on a twostate onedimensional model problem and compare the results with those of exact quantum calculations. In marked contrast with most current methods for modelingnonadiabatic dynamics with classical trajectories, the semiclassical Liouville method is found to be capable of treating even dominant electronic coherenceeffects in a consistent and accurate manner.

Optimized effective potential method for polymers
View Description Hide DescriptionThe optimized effective potential (OEP) method allows for calculation of the local, effective single particle potential of density functional theory for explicitly orbitaldependent approximations to the exchangecorrelation energy functional. In the present work the OEP method is used together with the approximation due to Krieger, Li, and Iafrate (KLI). We present the first application of this method to polymers. KLI calculations have been performed for the insulating polyethylene and the results have been compared to those from other orbitaldependent potentials. Various properties of the band structure are also calculated. The singleparticle band gap strongly depends on the basis set with larger basis sets yielding narrow gaps. For certain physical quantities such as the total energy and the exchange energy, the various orbitaldependent Kohn–Sham exchangeonly and Hartree–Fock results differ only slightly. For the highest occupied orbital energy the difference is more significant than expected. In order to get the right band gap in OEP the exchange contribution to the derivative discontinuity is calculated and added to the Kohn–Sham gap. The corrected gap obtained by the KLI approach is 12.8 eV compared with the Hartree–Fock and experimental values of 16.6 and 8.8 eV, respectively. We observe, however, the strong dependence of the derivative discontinuity on the basis set.

Iterative determination of several interior eigenstates of large matrices: Application to the determination of lightinduced resonances in
View Description Hide DescriptionThe determination of several interior eigensolutions of large nonhermitian matrices is still an open problem for research. This paper brings significant improvements to the perturbative iterative methods. The theory is developed in the framework of Bloch formalism of wave operators and effective Hamiltonians. The progresses rely on two factors. First, the full Hilbert space is partitioned into three subspaces to improve the convergence and stability properties of the iterative processes. Second, the quasiquadratic algorithms are welldefined approximations of the exact quadratic Newton–Raphson solution. The addition of these two factors brings the computational efficiency far beyond standard perturbation theory. An application is presented to the determination of the Floquet resonances arising from the ten lowest vibrational states of the molecular ion for laser intensities up to These Floquet states provide the relevant basis of the dynamics of submitted to intense laser pulses.

Assessment of Gaussian3 and density functional theories for a larger experimental test set
View Description Hide DescriptionThe G2/97 test set [J. Chem. Phys. 106, 1063 (1997)] for assessing quantum chemical methods used to predict thermochemical data is expanded to include 75 additional enthalpies of formation of larger molecules. This new set, referred to as the G3/99 test set, includes enthalpies of formation,ionization potentials,electron affinities, and proton affinities in the G2/97 set and 75 new enthalpies of formation. The total number of energies in the G3/99 set is 376. Overall, G3 theory has a mean absolute deviation of 1.07 kcal/mol for the G3/99 test set and does about as well for the new hydrocarbons and substituted hydrocarbons as it does for those in the G2/97 test. However, G3 theory has large deviations for several of the new nonhydrogen systems in the G3/99 test set such as and Part of the source of error is traced to the inadequate geometries used in G3 theory for these molecules. Other variations of G3 theory are also assessed such as G3(MP2), G3(MP3), and the versions of G3 theory using scaled energy terms instead of the higher level correction. These variations also do well for the larger hydrocarbons and substituted hydrocarbons, but fail for the same nonhydrogen systems as G3 theory. The density functional methods assessed in this study, including the hybrid B3LYP method, all have much larger deviations from experiment for the new enthalpies of formation in the expanded test set; the mean absolute deviation more than doubles compared to that for the enthalpies in the G2/97 test set. This is due to a cumulative effect of the errors in the larger molecules in the density functional methods.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Rydberg states of propyne at 6.8–10.5 eV studied by twophoton resonant ionization spectroscopy and theoretical calculation
View Description Hide DescriptionThe vibronic spectra of jetcooled propyne at 6.8–10.5 eV have been observed using resonanceenhanced multiphoton ionization (REMPI) spectroscopy. The and Rydberg states of propyne have been identified, of which seven are newly discovered. The symmetries of the excited vibronic states have been determined directly from polarizationratio experiments applying linearly and circularly polarized lasers. Under a group, the observed Rydberg series are of symmetry and the Rydberg states belong to or Clear doublet splittings in the Rydberg states are observed for the first time. The splittings, at decrease with increasing The doublets of and symmetries, identified from the polarizationratio measurement, are that due to molecular geometry, rather than for the Rydberg states. The term values for the Rydberg series converge to an adiabatic ionization energy of with a quantum defect of Comparing with onephoton absorptionspectrum of propyne, the absence of and except Rydberg states in the REMPI spectra suggests a strong predissociation character for these states. Calculations for the vertical excitation energies of and Rydberg states of propyne were performed using timedependent density functional theory and ab initio methods to compare with experimental results and to test the computational accuracy.

Fluorescence lifetimes and predissociation processes in the state of CCH
View Description Hide DescriptionFluorescence lifetimes have been measured under supersonic jet conditions for various N, Krotational levels of three vibrational levels (T, and of the state of CCH. It was found that the lifetimes of levels and are significantly shorter than that of level T. Furthermore, the lifetimes vary in a complicated way from one rovibronic level to another, indicating the presence of local perturbations. The previously reported CC–H bond energy ranges from 95.6 to 116.3 kcal/mol, which leads to a large uncertainty in assigning the onset of the dissociation process, CCH In this work, fluorescence excitation spectra of photofragment via and have been recorded to determine the predissociation processes of the state. Assuming no barrier is present in the dissociation process of the and states, the upper bound of was estimated as Hence, the lifetime quenching phenomenon observed in the state is primarily due to predissociation via the dissociative continuum of either the or the state of CCH.

Tunnelling lifetimes of metastable and binding properties of stable covalent dianions
View Description Hide DescriptionMixed berylliumcarbon dianions and have been examined using ab initio methods. The dianionic systems have been investigated in detail with respect to electron autodetachment as well as with respect to fragmentation. Only linear isomers have been found to represent geometrically stable isomers, i.e., are minima on the corresponding potential energy surfaces. While a linear isomer of the dianions lies on the verge of electronic stability, a linear isomer of the dianions, better referred to as is the smallest free stable Be–C dianion. To estimate the lifetime of the system we have calculated the repulsive Coulomb barrier following ab initio approaches introduced in this work and used this potential to compute the tunnel probability with the help of Wentzel–Kramer–Brioullin theory. The tunnel probability makes the lifetime of the system directly accessible, when the electron detachment energy (EDE) is known. All calculated EDEs yield lifetimes markedly longer than 5 μs, which is the lower limit for experimental observation in a mass spectrometer.

Theoretical study on ammonia cluster ions: Nature of kinetic magic number
View Description Hide DescriptionWe theoretically investigated collision cross sections due to the attractive forces between and We found that the dependence of the collision cross sections on collision energy and cluster size are comparable to those of measured fusion cross sections. The kinetic magic number, is related to the structure of the pentamer. Namely, the center ion in the pentamer is surrounded by firstshell ammonia molecules.

Comparison of direct and resonant scattering for Collisional energy transfer versus predissociation of complexes
View Description Hide DescriptionElectronic predissociation of was examined by characterizing action spectra and product state distributions. Both spinorbit and internal conversion decay channels were observed. For comparison with the predissociation data, collisional energy transfer was examined at temperatures near 10 K. The product state distributions resulting from collisions showed symmetry preferences that were not evident in the distributions resulting from predissociation. It is argued that the lack of symmetry preferences in the predissociationdynamics is indicative of a resonant scattering process. Qualitative differences in the predissociation and collisional transfer dynamics can be explained by considering the symmetry properties of the intermolecular potential energy surfaces, and the regions of these surfaces that are sampled by each type of event. Most predissociation data was recorded for ortho complexes. A new spectral feature of the complex, tentatively assigned to para was observed in this study. The predissociationdynamics of this state were significantly different from those of the ortho complex.

Spectroscopic constants and potential energy curves of tungsten carbide
View Description Hide DescriptionSpectroscopic constants and potential energy curves for 40 lowlying electronic states of the diatomic tungstencarbide (WC) were obtained using the complete active space multiconfiguration selfconsistent field followed by the multireference configuration interaction and full first and secondorder configuration interaction calculations that included up to 6.4 mil configurations. Spin–orbit effects were included through the enhanced relativistic configuration interaction method described here for 28 electronic states of WC lying below ∼20 000 cm^{−1}. The spin–orbit splitting of the ground state of WC was found to be very large (4394 cm^{−1}). The ground and excited electronic states of the W atom were also computed and were found to be in good agreement with the experimental data. The nature of bonding was analyzed through the composition of orbitals, leading configurations, Mulliken populations, and dipole moments. The dissociation energy of WC was computed including spin–orbit and electron correlationeffects. The recent photoelectron spectra of were assigned on the basis of our computed results.

A theoretical study of ion dissociation of
View Description Hide DescriptionIon dissociation of following the radiationless decay of coreexcited is studied theoretically. The detailed mechanisms of the ion dissociation are discussed by using potential energy diagrams for various electronic states of depicted as a function of the internuclear distance of OH and the bending angle of HOH. The dynamics of the ion dissociation is categorized into three types depending on the site where positive holes of are found. The three types are as follows. (i) One or more positive holes are found on the bonding orbital between O and H. (ii) Two positive holes localize on the oxygen orbital (i.e., the lonepaired electrons on the oxygen atom are ejected). (iii) Two positive holes are present on the oxygen orbital and one more hole appears by shakeup excitation. In the case of (i), easily dissociates by the force of Coulomb repulsion between and A few lowest electronic states of belong to the type (ii). These lowlying potential curves are less steep than those of the type (i) because Coulomb repulsion does not work. Moreover, such potential energy curves have a shallow well. Reflecting these characteristic features, the ion dissociation is relatively depressed. These results are qualitatively in good accord with the experimental observation. In the case of (iii), it is found that a new twostep ion dissociation process of following possibly occurs.

Atomization enthalpies and enthalpies of formation of the germanium clusters, and by Knudsen effusion mass spectrometry
View Description Hide DescriptionThe hightemperature mass spectrometric method was employed to measure the equilibrium partial pressures of small germanium clusters above liquid germanium contained in a graphite Knudsen cell. These data were combined with new thermal functions, calculated from recent theoretical and spectroscopic molecular parameters, to evaluate the atomization enthalpies and enthalpies of formation of Mass spectrometric equilibrium data available in literature were also reevaluated. The following atomization enthalpies, and enthalpies of formation in kJ mol^{−1}, have been obtained: and and and and The atomization energies are compared with available theoretical values.

Bondbreaking in quantum state selected clusters: Inelastic and nonadiabatic intracluster collision dynamics in
View Description Hide DescriptionHighresolution vibrationally mediated photodissociation methods are used to investigate the dynamics of H–OH bond breaking in quantum state selected and van der Waal complexes prepared in a slit supersonic jet expansion. This capability is based on the following strategy: (i) Specific rovibrational quantum states of the dimer and monomer are optically selected in the second overtone region with an injection seeded, Fourier transform limited optical parametric oscillator. (ii) Selective H–OH bond cleavage of the vibrationally excited subunit in the cluster is achieved by 248 nm or 222 nm UVphotolysis. (iii) Multibody collision dynamics between the H, OH, and Ar photofragments are probed via laser induced fluorescence(LIF) on the asymptotic OH rotational, lambdadoublet and spin–orbit distributions. Comparison between cluster and monomer data explicitly samples the influence of the Ar “solvent” on the UVphotolysisdynamics and in particular highlights the dominant role of intracluster collisions as the fragments recoil. Most importantly, the OH fine structure distributions are found to be dramatically different for vs photolysis, indicating the major contribution of nonadiabatic events in the photofragmentation dynamics.