Volume 127, Issue 18, 14 November 2007
 ARTICLES

 Theoretical Methods and Algorithms

Statistical mechanics of time independent nondissipative nonequilibrium states
View Description Hide DescriptionWe examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent nondissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming that the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the interdomain population distribution. Assuming that these domains are robust with respect to small changes in thermodynamic state variables we derive a variety of fluctuation formulas for these systems. We verify our theoretical results using molecular dynamics simulations on a model glass forming system. Nonequilibrium transient fluctuation relations are derived for the fluctuations resulting from a sudden finite change to the system’s temperature or pressure and these are shown to be consistent with the simulation results. The necessary and sufficient conditions for these relations to be valid are that the domains are internally populated by Boltzmann statistics and that the domains are robust. The transient fluctuation relations thus provide an independent quantitative justification for the assumptions used in our statistical mechanical treatment of these systems.

On the calculation of velocitydependent properties in molecular dynamics simulations using the leapfrog integration algorithm
View Description Hide DescriptionWidely used programs for molecular dynamics simulation of (bio)molecular systems are the Verlet and leapfrog algorithms. In these algorithms, the particle velocities are less accurately propagated than the positions. Important quantities for the simulation such as the temperature and the pressure involve the squared velocities at full time steps. Here, we derive an expression for the squared particle velocity at full time step in the leapfrog scheme, which is more accurate than the standardly used one. In particular, this allows us to show that the full time step kinetic energy of a particle is more accurately computed as the average of the kinetic energies at previous and following half steps than as the square of the average velocity as implemented in various molecular dynamics codes. Use of the square of the average velocity introduces a systematic bias in the calculation of the instantaneous temperature and pressure of a molecular dynamics system. We show the consequences when the system is coupled to a thermostat and a barostat.

Density functional perturbational orbital theory of spin polarization in electronic systems. II. Transition metal dimer complexes
View Description Hide DescriptionWe present a theoretical scheme for a semiquantitative analysis of electronic structures of magnetic transition metal dimer complexes within spin density functionaltheory(DFT). Based on the spin polarization perturbational orbital theory [D.K. Seo, J. Chem. Phys.125, 154105 (2006)], explicit spindependent expressions of the spin orbital energies and coefficients are derived, which allows to understand how spin orbitals form and change their energies and shapes when two magnetic sites are coupled either ferromagnetically or antiferromagnetically. Upon employment of the concept of magnetic orbitals in the activeelectron approximation, a general mathematical formula is obtained for the magnetic coupling constant from the analytical expression for the electronic energy difference between lowspin brokensymmetry and highspin states. The origin of the potential exchange and kinetic exchange terms based on the oneelectron picture is also elucidated. In addition, we provide a general account of the DFT analysis of the magnetic exchange interactions in compounds for which the activeelectron approximation is not appropriate.

On the accuracy of densityfunctional theory exchangecorrelation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limit
View Description Hide DescriptionThe ability of several densityfunctional theory(DFT)exchangecorrelation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order MøllerPlesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.

WangLandau algorithm: A theoretical analysis of the saturation of the error
View Description Hide DescriptionIn this work we present a theoretical analysis of the convergence of the WangLandau algorithm [Phys. Rev. Lett.86, 2050 (2001)] which was introduced years ago to calculate the density of states in statistical models. We study the dynamical behavior of the error in the calculation of the density of states. We conclude that the source of the saturation of the error is due to the decreasing variations of the refinement parameter. To overcome this limitation, we present an analytical treatment in which the refinement parameter is scaled down as a power law instead of exponentially. An extension of the analysis to the fold way variation of the method is also discussed.

Study of the quasicanonical localized orbital method based on protein structures
View Description Hide DescriptionAn initial guess is one of the most important factors in solving selfconsistent field (SCF) molecular orbital calculations for large molecules. Recently, the authors reported that the quasicanonical localized orbital (QCLO) method was useful to prove the initial guess for allelectron calculations for proteins. This paper describes a new QCLO method that takes into account protein information derived from protein structures such as salt bridges and the secondary structure of the molecule. In several test calculations using typical models, the difference between the initial guess and final atomic charges was markedly decreased, and the number of SCF iterations was reduced. We suggest that the structurebased QCLO method improves the precision of the initial guess and achievement of automatic allelectron calculations for proteins.

Long time wave packet dynamics from energy eigenfunctions: Nonuniform energy resolution via adaptive bisection fast Fourier transformation
View Description Hide DescriptionThis article presents a new approach to long time wave packet propagation. The methodology relies on energy domain calculations and an onthesurface straightforward energy to time transformation to provide wave packet time evolution. The adaptive bisection fast Fourier transform method employs selective bisection to create a multiresolution energy grid, dense near resonances. To implement fast Fourier transforms on the nonuniform grid, the uniform grid corresponding to the finest resolution is reconstructed using an iterative interpolation process. By proper choice of the energy grid points, we are able to produce results equivalent to grids of the finest resolution, with far fewer grid points. We have seen savings 20fold in the number of eigenfunction calculations. Since the method requires computation of energy eigenfunctions, it is best suited for situations where many wave packet propagations are of interest at a fixed small set of points—as in time dependent flux computations. The fast Fourier transform (FFT) algorithm used is an adaptation of the DanielsonLanczos FFT algorithm to sparse input data. A specific advantage of the adaptive bisection FFT is the possibility of long time wave packet propagations showing slow resonant decay. A method is discussed for obtaining resonance parameters by least squares fitting of energy domain data. The key innovation presented is the means of separating out the smooth background from the sharp resonance structure.

Randomphaseapproximationbased correlation energy functionals: Benchmark results for atoms
View Description Hide DescriptionThe random phase approximation for the correlationenergy functional of the density functional theory has recently attracted renewed interest. Formulated in terms of the KohnSham orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as, for instance, their inability to account for dispersion forces. First results for atoms, however, indicate that the random phase approximation overestimates correlation effects as much as the orbitaldependent functional obtained by a second order perturbation expansion on the basis of the KohnSham Hamiltonian. In this contribution, three simple extensions of the random phase approximation are examined; (a) its augmentation by a local density approximation for shortrange correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlationenergies as well as the ionization potentials resulting from the extensions (a) and (c) for closed subshell atoms are clearly superior to those obtained with the unmodified random phase approximation. Quite some effort is made to ensure highly converged data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular, for the inherent frequency integration, should also be useful for applications of random phase approximationtype functionals to more complex systems.

Configuration selection as a route towards efficient vibrational configuration interaction calculations
View Description Hide DescriptionA configuration selective vibrational configuration interaction (CI) approach is presented that efficiently reduces the variational space and thus leads to significant speedups in comparison to standard vibrational CI implementations. Deviations with respect to reference calculations are well below the accuracy of the underlying electronic structure calculations for the potential and hence are essentially negligible. Parallel implementations of the presented configuration selective vibrational CI approaches lead to further significant time savings. Benchmark calculations based on potential energy surfaces of coupledcluster quality are presented for the fundamental modes of cis and transdifluoroethylene. The sizeconsistency error within the vibrational configuration interaction calculations of the difluoroethylene dimer has been studied in dependence on the excitation level.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Excited state dynamics of metastable phthalocyaninetetrasulfonate tetraanions probed by pump/probe photoelectron spectroscopy
View Description Hide DescriptionFemtosecond timeresolved pumpprobe photoelectron spectroscopy was used to study elementary relaxation processes occurring in isolated phthalocyaninetetrasulfonate tetraanions (, , and “freebase” ) following band excitation by onephoton absorption at . Whereas the Cu and Ni systems decay rapidly by means of internal conversion without electron loss, the freebase phthalocyanine primarily undergoes excited statetunneling electron emission. This reflects less efficient coupling to lower lying states within the corresponding spin manifold. Results are interpreted in terms of (timedependent) density functional theory calculations of ground and electronically excited states and kinetically modeled to yield the associated rates.

Fulldimensional (15dimensional) quantumdynamical simulation of the protonated water dimer. I. Hamiltonian setup and analysis of the ground vibrational state
View Description Hide DescriptionQuantumdynamical fulldimensional (15D) calculations are reported for the protonated water dimer using the multiconfiguration timedependent Hartree (MCTDH) method. The dynamics is described by curvilinear coordinates. The expression of the kinetic energy operator in this set of coordinates is given and its derivation, following the polyspherical method, is discussed. The potentialenergy surface (PES) employed is that of Huang et al. [J. Chem. Phys.122, 044308 (2005)]. A scheme for the representation of the PES is discussed which is based on a highdimensional model representation scheme, but modified to take advantage of the modecombination representation of the vibrational wave function used in MCTDH. The convergence of the PES expansion used is quantified and evidence is provided that it correctly reproduces the reference PES at least for the range of energies of interest. The reported zero point energy of the system is converged with respect to the MCTDH expansion and in excellent agreement ( below) with the diffusion Monte Carlo result on the PES of Huang et al. The highly fluxional nature of the cation is accounted for through use of curvilinear coordinates. The system is found to interconvert between equivalent minima through wagging and internal rotation motions already when in the ground vibrational state, i.e., . It is shown that a converged quantumdynamical description of such a flexible, multiminima system is possible.

Full dimensional (15dimensional) quantumdynamical simulation of the protonated water dimer. II. Infrared spectrum and vibrational dynamics
View Description Hide DescriptionThe infrared absorptionspectrum of the protonated water dimer is simulated in full dimensionality (15 dimensional) in the spectral range of . The calculations are performed using the multiconfiguration timedependent Hartree (MCTDH) method for propagation of wavepackets. All the fundamentals and several overtones of the vibrational motion are computed. The spectrum of is shaped to a large extent by couplings of the protontransfer motion to large amplitude fluxional motions of the water molecules, water bending and waterwater stretch motions. These couplings are identified and discussed, and the corresponding spectral lines are assigned. The large couplings featured by do not hinder, however, to describe the coupled vibrational motion by well defined simple types of vibration (stretching, bending; etc.) based on well defined modes of vibration, in terms of which the spectral lines are assigned. Comparison of our results to recent experiments and calculations on the system is given. The reported MCTDH IR spectrum is in very good agreement to the recently measured spectrum by Hammer et al. [J. Chem. Phys.122, 244301 (2005)].

Laser induced fluorescence spectroscopy of the radical
View Description Hide DescriptionElectronic spectra of the radical have been observed for the first time in the near ultraviolet wavelength region by laser induced fluorescence(LIF) spectroscopy. Seventeen vibronic bands of the electronic transition system of were identified in LIFspectra of products in a discharge of . The origin of the state was determined to be from rovibrational analyses. It was found that observations of two types of vibronic levels, which have and symmetries originated from excitations of the transbending mode with a large RennerTeller (RT) interaction, and the cisbending mode with a small RennerTeller interaction, respectively. Vibronic levels, with excitations of the stretching mode, were also identified. The spinorbit interaction constant was determined to be from the RT analysis. In dispersed fluorescence spectra from , vibrational structures of the lowlying electronically excited state were clearly observed with a strong progression due to the mode, together with those of the state with weak intensities. The origin of , , and the vibrational frequencies, and for , and , , and for , were determined. Time profiles of fluorescence from have short and long decay components with quantum beats, indicating that there is a competition between radiative decay and the nonradiative internal conversion to vibrationally highly excited and .

Transient photoelectron spectroscopy of the dissociative state
View Description Hide DescriptionPhotodissociation of bromine on the state is probed with ultrafast extreme ultraviolet singlephoton ionization. Timeresolved photoelectron spectra show simultaneously the depletion of ground state bromine molecules as well as the rise of products due to photolysis. A partial photoionization crosssection ratio of atomic versus molecular bromine is obtained. Transient photoelectron spectra of a dissociative wave packet on the excited state are presented in the limit of lowpowerdensity, singlephoton excitation to the dissociative state. Transient binding energy shifts of “atomiclike” photoelectron peaks are observed and interpreted as photoionization of nearly separated Br atom pairs on the state to repulsive dissociativeionization states.

Microwave spectra and ab initio studies of Arpropane and Nepropane complexes: Structure and dynamics
View Description Hide DescriptionMicrowave spectra in the region have been measured for the van der Waals complexes, , , , and . Both  and type transitions are observed for the Arpropane complex. The type transitions are much stronger indicating that the small dipole moment of the propane is aligned perpendicular to the van der Waals bond axis. While the 42 transition lines observed for the primary argon complex are well fitted to a semirigid rotor Hamiltonian, the neon complexes exhibit splittings in the rotational transitions which we attribute to an internal rotation of the propane around its inertial axis. Only type transitions are observed for both neon complexes, and these are found to occur between the tunneling states, indicating that internal motion involves an inversion of the dipole moment of the propane. The difference in energy between the two tunneling states within the ground vibrational state is for and for . The Kraitchman substitution coordinates of the complexes show that the rare gas is oriented above the plane of the propanecarbons, but shifted away from the methylene carbon, more so in Ne propane than in Ar propane. The distance between the rare gas atom and the center of mass of the propane,, is for Arpropane and for Nepropane. Ab initio calculations are done to map out segments of the intermolecular potential. The global minimum has the rare gas almost directly above the center of mass of the propane, and there are three local minima with the rare gas in the plane of the carbon atoms. Barriers between the minima are also calculated and support the experimental results which suggest that the tunneling path involves a rotation of the propane subunit. The path with the lowest effective barrier is through a symmetric configuration in which the methyl groups are oriented toward the rare gas. Calculating the potential curve for this onedimensional model and then calculating the energy levels for this potential roughly reproduces the spectral splittings in Nepropane and explains the lack of splittings in Arpropane.

Modeling the photodissociation dynamics through a nonadiabatic wave packet study of the complex
View Description Hide DescriptionThe nonadiabaticphotodissociation dynamics of is simulated by applying a wave packet approach which starts from the complex (where denotes the excited electronic state) produced after the photodissociation of the first HI moiety within . In the model, two excited electronic potential surfaces corresponding to and , which interact through spinrotation coupling, are considered. The simulations show that upon photodissociation of HI within , the dissociating H fragment undergoes intracluster collisions with the atom. Some of these collisional events induce an electronically nonadiabatic transition which causes the deactivation of to the I ground electronic state. The probability of such nonadiabatic process is found to be 0.37%. Most of the photodissociation process takes place in the upper excited electronic surface [that of the complex], where H dissociation is found to be mainly direct or involving weak intracluster collisions. These weak collisions with high collisional angular momentum, and therefore high collisional impact parameters associated, are responsible for most of the probability of nonadiabatic transitions found. The type of collisions leading to nonadiabatic transitions appears to be closely related to the nature of the spinrotation coupling between the two excited electronic states involved.

Seven dimensional quantum dynamics study of the reaction
View Description Hide DescriptionInitial stateselected timedependent wave packet dynamics calculations have been performed for the reaction using a seven dimensional model on an analytical potential energy surface based on the one developed by Corchado and EspinosaGarcía [J. Chem. Phys.106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values and nonreactive group keeps symmetry and the rotationvibration coupling in is neglected. The total reaction probabilities are calculated when the two reactants are initially at their ground states, when the bending mode is excited, and when is on its first vibrational excited state, with total angular momentum . The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants and equilibrium constants are calculated for the temperature range of and compared with transition state theory results and the available experimental data. The study shows that (a) the reaction is dominated by groundstate reactivity and the main contribution to the thermal rate constants is thought to come from this state, (b) the excitation energy of was used to enhance reactivity while the excitation of the bending mode hampers the reaction, (c) the calculated thermal rate constants are very close to the experimental data and transition state theory results at high and middle temperature, while they are ten times higher than that of transition state theory at low temperature , and (d) the equilibrium constants results indicate that the approximations applied may have different roles in the forward and reverse reactions.

Intermolecular potential energy surface of Ar–NO
View Description Hide DescriptionRotational spectra of an openshell complex, Ar–NO, in the electronic ground state have been analyzed by employing an analysis using a freerotor model, where previously observed data by Mills et al. [J. Phys. Chem.90, 3331 (1986); 90, 4961 (1986)] and additional transitions observed by Fouriertransform microwave spectroscopy in the present study are simultaneously analyzed with a standard deviation of the leastsquares fit to be . A twodimensional intermolecular potential energy surface for Ar–NO has been determined from the analysis. The determined potential energy surface is compared with those of Ar–OH and Ar–SH, which are also complexes containing an openshell species with the ground electronic state.

NH stretching vibrations of pyrrole clusters studied by infrared cavity ringdown spectroscopy
View Description Hide DescriptionThe IR spectra for various sizes of pyrrole clusters were measured in the NH stretching vibration region by infrared cavity ringdown spectroscopy. The hydrogenbonded structures and normal modes of the pyrrole clusters were analyzed by a density functional theory calculation of the level. Two types of pulsed nozzles, a slit and a large pinhole, were used to generate different cluster size distributions in a supersonic jet. A rotational contour analysis of the NH stretching vibration for the monomer revealed that the slit nozzle provides a warmer jet condition than the pinhole one. The IR spectra,measured under the warmer condition, showed the intense bands at 3444, 3392, and , which were assigned to hydrogenbonded NH stretching vibrations due to the dimer, the trimer, and the tetramer, respectively. On the other hand, the IR spectrameasured under a lower temperature condition by a pinhole nozzle showed a broad absorption feature in addition to sharp bands. This broad absorption was reproduced by the sum of two Gaussians peaks at 3400 and with widths of 30 and (FWHM), respectively. Compared with the spectra of the condensed phase, two bands at 3400 and were assigned to hydrogenbonded NH stretching vibrations of larger clusters having liquidlike and solidlike structures, respectively.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Unique role of hydrophilic ionic liquid in modifying properties of aqueous Triton X100
View Description Hide DescriptionModification of important physicochemical properties of aqueous surfactantsolutions can be achieved by addition of environmentally benign room temperature ionic liquids (ILs). While low aqueous solubility of “hydrophobic” ILs limits the amount of IL that may be added to achieve desired changes in the physicochemical properties, hydrophilic ILs do not have such restrictions associated to them. Alterations in the key physicochemical properties of aqueous solutions of a common nonionic surfactant Triton X100 (TX100) on addition of up to hydrophilic IL 1butyl3methylimidazolium tetrafluoroborate are reported. The presence of micellar aggregates in as high as added aqueous TX100 solutions is established by dynamic light scattering and fluorescence probe behavior. Increasing the concentration of results in decrease in average micellar size and aggregation number and increase in critical micelle concentration, indicating an overall unfavorable aggregation process. Increase in the dipolarity and the microfluidity of the probe cybotactic region within the palisade layer of the micellar phase upon addition implies increased water penetration and the possibility of TX100 interactions. While the changes in some of the physicochemical properties indicate the role of to be similar to a cosurfactant, the IL acts like a cosolvent as far as changes in other properties are concerned. Effectiveness of IL in modifying physicochemical properties of aqueous TX100 is demonstrated.