Volume 114, Issue 17, 01 May 2001
 ARTICLES

 Theoretical Methods and Algorithms

Accuracy of freeenergy perturbation calculations in molecular simulation. I. Modeling
View Description Hide DescriptionWe examine issues involved in applying and interpreting freeenergy perturbation (FEP) calculations in molecular simulation. We focus in particular on the accuracy of these calculations, and how the accuracy differs when the FEP is performed in one or the other direction between two systems. We argue that the commonly applied heuristic, indicating a simple average of results taken for the two directions, is poorly conceived. Instead, we argue that the best way to proceed is to conduct the FEP calculation in one direction, namely that in which the entropy of the target is less than the entropy of the reference. We analyze the behavior of FEP calculations in terms of the perturbationenergy distribution functions, and present several routes to characterize the calculations in terms of these distributions. We also provide prescriptions for the selection of an appropriate multistage FEP scheme based on how the important phasespace regions of the target and reference systems overlap one another.

Quantum partition functions from classical distributions: Application to raregas clusters
View Description Hide DescriptionWe investigate the thermodynamic behavior of quantum manybody systems using several methods based on classical calculations. These approaches are compared for the melting of LennardJones (LJ) clusters, where pathintegral Monte Carlo (PIMC) results are also available. First, we examine two quasiclassical approaches where the classical potential is replaced by effective potentials accounting for quantum corrections of low order in ℏ. Of the Wigner–Kirkwood and Feynman–Hibbs effective potentials, only the latter is found to be in quantitative agreement with quantum simulations. However, both potentials fail to describe even qualitatively the lowtemperature regime, where quantum effects are strong. Our second approach is based on the harmonic superposition approximation, but with explicit quantum oscillators. In its basic form, this approach is in good qualitative agreement with PIMC results, and becomes more accurate at low temperatures. By including anharmonic corrections in the form of temperaturedependent frequency shifts, the agreement between the quantum superposition and the PIMC results becomes quantitative for the caloric curve of neon clusters. The superposition method is then applied to larger clusters to study the influence of quantum delocalization on the melting and premelting of and The quantum character strongly affects the thermodynamics via changes in the ground state structure due to increasing zeropoint energies. Finally, we focus on the lowest temperature range, and we estimate the Debye temperatures of argon clusters and their size variation. A strong sensitivity to the cluster structure is found, especially when many surface atoms reorganize as in the antiMackay/Mackay transition. In the large size regime, the Debye temperature smoothly rises to its bulk limit, but still depends slightly on the growth sequence considered.

Fastgrowth thermodynamic integration: Error and efficiency analysis
View Description Hide DescriptionEquilibrium free energy differences can be calculated accurately from repeated fastgrowth thermodynamic integration (TI) based on Jarzynski’s identity [Phys. Rev. Lett. 78, 2690 (1997)]. We derive expressions for the free energy differences. Error estimates allow us to quantify the relative efficiency of performing many fastgrowth vs few slowgrowth TIs for a given total computational cost. Fastgrowth TI is illustrated through the calculation of the potential of mean force between two methane molecules and compared to umbrella sampling analyzed by using the weighted histogram analysis method. Fastgrowth TI is well suited for parallel computer architectures, requiring only the simplest parallelism with repeated runs for different starting conditions.

Fourth order gradient symplectic integrator methods for solving the timedependent Schrödinger equation
View Description Hide DescriptionWe show that the method of splitting the operator to fourth order with purely positive coefficients produces excellent algorithms for solving the timedependent Schrödinger equation. These algorithms require knowing the potential and the gradient of the potential. One fourth order algorithm only requires four fast Fourier transformations per iteration. In a one dimensional scattering problem, the fourth order error coefficients of these new algorithms are roughly 500 times smaller than fourth order algorithms with negative coefficient, such as those based on the traditional Forest–Ruth symplectic integrator. These algorithms can produce converged results of conventional second or fourth order algorithms using time steps 5 to 10 times as large. Iterating these positive coefficient algorithms to sixth order also produced better converged algorithms than iterating the Forest–Ruth algorithm to sixth order or using Yoshida’s sixth order algorithm A directly.

Assessment of the quality of orbital energies in resolutionoftheidentity Hartree–Fock calculations using deMon auxiliary basis sets
View Description Hide DescriptionThe Roothaan–Hartree–Fock (HF) method has been implemented in deMon–DynaRho within the resolutionoftheidentity (RI) auxiliaryfunction approximation. While previous studies have focused primarily upon the effect of the RI approximation on total energies, very little information has been available regarding the effect of the RI approximation on orbital energies, even though orbital energies play a central role in many theories of ionization and excitation. We fill this gap by testing the accuracy of the RI approximation against nonRIHF calculations using the same basis sets, for the occupied orbital energies and an equal number of unoccupied orbital energies of five small molecules, namely CO, and pyridine (in total 102 orbitals). These molecules have wellcharacterized excited states and so are commonly used to test and validate molecular excitation spectra computations. Of the deMon auxiliary basis sets tested, the best results are obtained with the (44) auxiliary basis sets, yielding orbital energies to within 0.05 eV, which is adequate for analyzing typical low resolution polyatomic molecule ionization and excitation spectra. Interestingly, we find that the error in orbital energies due to the RI approximation does not seem to increase with the number of electrons. The absolute RI error in the orbital energies is also roughly related to their absolute magnitude, being larger for the core orbitals where the magnitude of orbital energy is large and smallest where the molecular orbital energy is smallest. Two further approximations were also considered, namely uniterated (“zeroorder”) and singleiteration (“firstorder”) calculations of orbital energies beginning with a local density approximation initial guess. We find that zero and firstorder orbital energies are very similar for occupied but not for unoccupied orbitals, and that the firstorder orbital energies are fairly close to the corresponding fully converged values. Typical root mean square errors for firstorder calculations of orbital energies are about 0.5 eV for occupied and 0.05 eV for unoccupied orbitals. Also reported are a few tests of the effect of the RI approximation on total energies using deMon basis sets, although this was not the primary objective of the present work.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Fingerprints of the nodal structure of autoionizing vibrational wave functions in clusters: Interatomic Coulombic decay in Ne dimer
View Description Hide DescriptionThe removal of an innervalence electron from neutral neon clusters leads to autoionization and subsequent fragmentation of the cationic clusters in accordance with the interatomic Coulombic decay mechanism discovered recently. Using nonHermitian quantum scattering theory we investigate this process in detail for the Ne dimer. We show that a pronounced structure can be observed when measuring the autoionizing electron or the kinetic energy distributions. This phenomenon is associated with the properties of the vibrational autoionizing resonance states of the electronically excited cationic dimer. By suppressing coherence among the different vibrational autoionizing resonances, or by selectively exciting one of them, the structures in the kinetic energy distributions become more pronounced. It is demonstrated that these structures reflect the nodal structure of the wave functions of the autoionizing vibrational states most populated by the initial ionization of the neutral neon dimer. In a coherent decay we encounter substantial interference effects, but the nodal pattern of the corresponding wave functions is still present. The kinetic energy distributions are generally very sensitive to details of the potential energy curves of clusters.

Matrix isolation spectroscopy of propylbenzene conformers and trapping sites
View Description Hide DescriptionUltraviolet absorption and emission spectra of propylbenzene in an argon matrix are presented. The spectra are found to consist of several band series that are assigned to different trapping sites of the anti and gauche conformers of the molecule. Comparison with gas phase spectra and ab initio calculations allows the assignment of the vibronic bands of the emission spectrum. Some reassignments of the observed vibronic bands are proposed. The relatively small number of trapping sites found for this asymmetric molecule is compatible with molecular dynamic simulations that are found to produce a small number of preferred sites.

High resolution absorption spectrum of between 75 000 and 104 000 cm^{−1}
View Description Hide DescriptionThe absorptionspectrum of was photographed at a resolution limit of 0.0008 nm, from 134 nm to the ionization potential, at 96 nm. Ab initio calculations of the electronic energies and transition moments were carried out including spin–orbit interaction in the frozen core approximation. Rydberg states considered are those corresponding to and principal effective quantum number up to 5.5 and and terms), and three ionic cores and It is shown that in like in or terms are at lower energy than The strongest band of the lowresolution absorptionspectrum, at about 77 900 cm^{−1} is too broad and diffuse to be observed here. It is assigned to the origin of the transition. The most prominent bands in the 84 000–104 000 cm^{−1} interval are the electronic origins of the transitions, observed from to Previous lowresolution absorption and resonance enhanced multiphoton ionizationspectra are reviewed in the light of the present results.

Observation of collision induced statetostate energy transfer in electronically and highly rotationally excited
View Description Hide DescriptionStatetostate energy transfer of in its excited state is investigated with timeresolvedFourier transformemission spectroscopy. Originating from collisions with rovibrational energy transfer in with energy separations and in multiples of is observed. Based on the experimental determination of relative transition probabilities, absolute statetostate rate constants are derived. Collisional changes in the rotational quantum number range from −3 to +4. The analysis of the time dependence of the levels populated by rovibrational energy transfer shows that this variety is not the result of secondary collisions.

The electronic structure of and from anion photoelectron spectroscopy and ab initio calculations
View Description Hide DescriptionThe electronic structures of and Br) have been investigated in the gas phase by means of anion photodetachmentphotoelectron spectroscopy and ab initio theory. The photoelectron spectra of were recorded at two photon energies, 193 and 157 nm. Wellresolved and rich photodetachment features in the spectra provide unprecedented details for the lowlying electronic states of and The excitation energies for five lowlying electronic states of were determined, and they explain well the two previously observed optical absorption bands. The electron affinities for and were determined to be identical, within the experimental uncertainty. Both the anions and neutral species were calculated to be linear with only a slight bond length variation between the charged and neutral species. The calculated electron affinities and vertical excitation energies for the excited states agree well with the experimental values, yielding a definite assignment for the electronic states of and

Threecenter versus fourcenter elimination in photolysis of vinyl fluoride and vinyl bromide at 193 nm: Bimodal rotational distribution of HF and HBr detected with timeresolved Fourier transform spectroscopy
View Description Hide DescriptionFollowing photodissociation of vinyl fluoride and vinyl bromide at 193 nm, fully resolved vibration–rotational emission spectra of HF and HBr in spectral regions 3050–4900 and 2000–2900 respectively, are temporally resolved with a step–scan Fourier transform spectrometer. With a data acquisition window 0–5 μs suitable for spectra with satisfactory ratio of signaltonoise, emission from HX (with X = F or Br) up to is observed. All vibrational levels show bimodal rotational distributions. For these two components of HF have average rotational energies ∼2 and 23 and vibrational energies ∼83 and 78 respectively; the values are corrected for small quenching effects. For these two components of HBr correspond to average rotational energies ∼4 and 40 respectively, and similar vibrational energies ∼68 The separate statistical ensemble (SSE) model is suitable for threecenter (α, α) elimination of HX because of the loose transition state and a small exit barrier for this channel; predicted vibrational energy distributions of HX are consistent with those observed for the highJ component. An impulse model taking into account geometries and displacement vectors of transition states during bond breaking predicts substantial rotational excitation for threecenter elimination of HX but little rotational excitation for fourcenter (α, β) elimination; observed rotational energies of lowJ and highJ components are consistent with those predicted for fourcenter and threecenter elimination channels, respectively. The model also explains why observed rotational energy of HF produced via threecenter elimination of is smaller than that of HCl from Ratios of rate coefficients (0.66:0.34 and 0.88:0.12) predicted for threecenter or fourcenter elimination channels based on Rice–Ramsberger–Kassel–Marcus theory are consistent with estimated branching ratios ∼0.75:∼0.25 and ∼0.81:0.19 determined based on counting vibrational distribution of HF and HBr, respectively, to for highJ and lowJ components and considering possible quenching effects within 5 μs. Hence we conclude that, similar to photolysis of observed highJ and lowJ components correspond to HX produced from threecenter and fourcenter elimination channels, respectively. The results are compared with those from photolysis of vinyl chloride at 193 nm.

Electron collisions with octafluorocyclobutane,
View Description Hide DescriptionWe present calculated cross sections for elastic and inelastic collisions of lowenergy electrons with octafluorocyclobutane, The integral elastic cross section displays a rich resonance structure, which we analyze in terms of temporary trapping in virtual valence orbitals. The differential elastic cross sections compare well with recent measurements at energies where the approximations used in the calculations are expected to be valid. Integral and differential cross sections for electronimpact excitation of the lowest singlet and triplet excited states were obtained. We relate the small magnitude of the inelastic integral cross sections and the unusual form of the inelastic differential cross sections to the symmetries of the electronic states involved in the transition.

Ab initio and diatomics in molecule potentials for and
View Description Hide DescriptionThe electronic structure of the molecular anion and its photoproducts and were studied. Ab initio calculations were carried out using the multireference configuration interaction (MRCI) method for the valence electrons together with a relativistic effective core potential. The ab initiowave functions were also used to compute some spin–orbit coupling matrix elements, as well as approximate valence bondwave functions, used as guidelines in the construction of a 108state diatomics in molecule (DIM) description of the electronic structure of In the DIM model, spin–orbit coupling was introduced as a sum of atomic operators. For the ab initio and the DIM groundstate potentials show excellent agreement with the experimental results. The results for are also in very good agreement with experimental data. For the MRCI calculations give a very good description of the spectroscopic constants and agree with the vertical excitation energies, provided spin–orbit coupling is included. The DIM description fails both quantitively by leading to erroneous spectroscopic constants, and qualitatively by not even reproducing the MRCI ordering of the excitedstates. The failure of the DIM is attributed to the omission of ionic states. The overall qualitative picture of the excitedstate potentials shows a maze of dense avoided crossings which means that all energetically allowed photoproducts will be present in the experiment. The ground electronic state of was calculated to be a collinear and centrosymmetric The collinear state is stabilized by spin–orbit coupling relative to a bent configuration. Calculated vertical transition energies from the ground to lowlying excited states of the radical are in excellent agreement with the experimental data. The spin–orbit assignment of these states is provided.

The infraredultraviolet dispersed fluorescence spectrum of acetylene: New classes of bright states
View Description Hide DescriptionSingle rotational levels of ungerade vibrational levels, and (both with symmetry), in the electronically excited state of acetylene were excited by an IRUV double resonance scheme via the fundamental level in the state, and the rotationally resolved dispersed fluorescence (DF) spectra were recorded at 3.2–4.5 cm^{−1} resolution. The term values of the new ungerade levels were determined within an accuracy of 0.56 cm^{−1}(1σ) through careful calibration achieved by frequency standard atomic Fe and Hg lines. A total of 111 new ungerade vibrational levels with and symmetry below 10 000 cm^{−1} was identified in the highresolution IRUVDF spectra, which provide access to new classes of bright states: (i) and which are the Franck–Condon (FC) bright levels from the levels in the state; (ii) levels which appear through the aaxis Corioris interaction between and in the state; and (iii) and levels which gain transition intensity from the Duschinsky effect associated with the bentlinear transition. All observed ungerade term values and previously determined gerade and ungerade term values below 10 000 cm^{−1} were fitted by two effective model Hamiltonians, i.e., a purebend effective Hamiltonian and a stretch–bend effective Hamiltonian. The stretch–bend effective Hamiltonian is expressed in terms of 31 Dunham expansion parameters and 11 anharmonic resonance parameters associated with (i) five stretch–bend anharmonic resonances; (ii) one stretch–stretch and two bend–bend Darling–Dennison resonances; and (iii) one vibrational lresonance. The parameters in this Hamiltonian were determined from a leastsquares fit of 287 vibrational term values (111 new ungerade levels, 128 levels from absorption, 1 level from stimulated Raman, 13 levels from stimulated emission pumping (SEP), and 34 levels from UVDF spectroscopy) below 10 000 cm^{−1} with a standard deviation of The FC patterns for the ungerade levels, in the IRUVDF spectra were derived, and the nodes along the transbend mode were found at via the upper state, and at and 15 via the upper state, which is consistent with the dependence of the FC patterns observed in previous UVDF studies.

Ab initio electronic structure of and dipolebound anions and a description of electron loss upon tautomerization
View Description Hide DescriptionThe binding of an excess electron to HCN and HNC was studied at the coupled cluster level of theory with single, double, and noniterative triple excitations and with extended basis sets to accommodate the loosely bound excess electron. The HCN molecule, with a dipole moment of 3.05 Debye, binds an electron by 10 cm^{−1}, whereas the HNC tautomer possesses a similar dipole moment (3.08 Debye) and binds the electron by 43 cm^{−1}. The electronic stability of the anionic system along the minimum energy HCN→HNC tautomerization path has been investigated, and it was concluded that the excess electron autodetaches during the tautomerization. Unusually large electron correlation energy contributions to the total electron binding energy were found and are discussed.

Ground and excited states of HNC, NH, and transients: Ab initio geometries, electronic structures, and molecular properties
View Description Hide DescriptionGeometrical and vibrational characterization of and hitherto experimentally unreported systems is reported by taking different sets of active electrons/orbitals in complete active space self consistent field (CASSCF) calculations. Employing CASSCF optimized geometries, the excitation energies,electric field gradients, and dipole moments for these systems have been computed at complete active space secondorder perturbation (CASPT2) and multireference singles and doubles configuration interaction (MRDCI) levels of theory. Computed field gradients are very similar at CASSCF and CASPT2 levels, but differ significantly with those obtained at MRDCI level. The outcome of present numerical experiment is that the inclusion of excitations higher than singles and doubles and use of a very large CI space employing iterative natural orbitals is necessary to account for the anisotropy of the molecular charge distribution around any nucleus in a molecule.

A quantum and semiclassical study of dynamical resonances in the reaction
View Description Hide DescriptionAccurate quantum mechanical reactive scattering calculations were performed for the collinear C+NO→CN+O reaction using a polynomialmodified London Eyring Polanyi Sato (PQLEPS) potential energy surface (PES), which has a 4.26 eV deep well in the strong interaction region, and a reference LEPS PES, which has no well in that region. The reaction probabilities obtained for both PESs show signatures for resonances. These resonances were characterized by calculating the eigenvalues and eigenvectors of the collision lifetime matrix as a function of energy. Many resonances were found for scattering on both PESs, indicating that the potential well in the PQLEPS PES does not play the sole role in producing resonances in this relatively heavy atom system and that Feshbach processes occur for both PESs. However, the well in the PQLEPS PES is responsible for the differences in the energies, lifetimes, and compositions of the corresponding resonance states. These resonances are also interpreted in terms of simple periodic orbits supported by both PESs (using the WKB formalism), to further illustrate the role played by that potential well on the dynamics of this reaction. The existence of the resonances is associated with the dynamics of the longlived CNO complex, which is much different than that of systems having an activation barrier. Although these results were obtained for a collinear model of the reaction, its collinearlydominated nature suggests that related resonant behavior may occur in the real world.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Theory of time dependent optical linewidths in supercooled liquids
View Description Hide DescriptionThe time resolved inhomogeneous broadened line shape is derived from analytical theory for a liquid which exhibits spatial heterogeneity regarding the solvent response times. The results demonstrate that it is the heterogeneous nature of supercooled liquids which gives rise to asymmetric lines and to a maximum in the linewidth as a function of time while the average emission energy experiences a redshift. The time dependence of the calculated and of the observed linewidths agree quantitatively, but differ significantly from the behavior expected for systems with homogeneous dynamics.

Structure and electronic properties of carbon onions
View Description Hide DescriptionSpherical and polyhedral carbon onions prepared from diamondnanoparticles are investigated by highresolution transmission electron microscopy(HRTEM),Raman spectroscopy, and electron spin resonance(ESR).HRTEM and Raman studies show that, as a result of thermal annealing, diamondnanoparticles are transformed into spherical onions, and finally into polyhedral onions by the progress of graphitization. ESR spectra for spherical onions show only a narrow signal corresponding to dangling bond spins associated with structural defects. In contrast, for polyhedral onions, an additional broad signal due to conduction electron spins emerges. These results combined with previous results of electron energyloss spectroscopy suggest that the spherical onions consist of small domains of the graphitic sheets with dangling bond defects in the peripheries. π electrons in spherical onions are thus localized in the small domains and do not act as conduction electrons. In the polyhedral onions, the graphitization proceeds further, resulting in the decrease in the number of dangling bonds and the delocalization of π electrons.

Reliability theory for receptor–ligand bond dissociation
View Description Hide DescriptionCell adhesion in the presence of hydrodynamic forces is a critical factor in inflammation, cancermetastasis, and blood clotting. A number of assays have recently been developed to apply forces to small numbers of the receptor–ligand bonds responsible for adhesion. Examples include assays using hydrodynamic shear in flow chambers or elastic probe deflection assays such as the atomic force microscope or the biomembrane force probe. One wishes to use the data on the time distribution of dissociation from these assays to derive information on the force dependence of reaction rates, an important determinant of cell adhesive behavior. The dissociation process can be described using the theory developed for reliability engineering of electronic components and networks. We use this framework along with the Bell model for the reverse reaction rate where f is the applied force and and are Bell model parameters) to write closed form expressions for the probability distribution of breakup with multiple independent or interacting bonds. These expressions show that the average lifetime of nbonds scales with the harmonic number multiplied by the lifetime of a single bond. Results from calculation and simulations are used to describe the effect of experimental procedures in forced unbinding assays on the estimation of parameters for the force dependence of reverse reaction rates.