Volume 114, Issue 22, 08 June 2001
 ARTICLES

 Theoretical Methods and Algorithms

On the crossing of electronic energy levels of diatomic molecules at the largeD limit
View Description Hide DescriptionAnalytical and numerical results are presented for the intersection of electronic energies of the same space symmetry for electrons in the field of two Coulomb centers in Ddimensions. We discuss why such crossings are allowed and may be less “exceptional” than one could think because even for a diatomic molecule there is more than one parameter in the electronic Hamiltonian. For a one electron diatomic molecule at the largeD limit, the electronic energies are shown analytically to diverge quadratically from the point of their intersection. The one electron two Coulomb centers problem allows a separation of variables even when the charges on the two centers are not equal. The case of two electrons, where their Coulombic repulsion precludes an exact symmetry, is therefore treated in the largeD limit. It is then found that, in addition to the quadratic intersection, there is also a curve crossing where the energies diverge linearly.

Explicitsolvent molecular dynamics simulation at constant Methodology and application to small amines
View Description Hide DescriptionA method is developed for performing classical explicitsolvent molecular dynamics (MD) simulations at constant where the protonation state of each ionizable (titratable) group in a simulated compound is allowed to fluctuate in time, depending on the instantaneous system configuration and the imposed In this method, each ionizable group is treated as a mixed state, i.e., the interactionfunction parameters for the group are a linear combination of those of the protonated state and those of the deprotonated state. Free protons are not handled explicitly. Instead, the extent of deprotonation of each group is relaxed towards its equilibrium value by weak coupling to a “proton bath.” The method relies on precalibrated empirical functions, one for each type of ionizable group present in the simulated compound, which are obtained through multiple MD simulations of monofunctional model compounds. In this study, the method is described in detail and its application illustrated by a series of constantMD simulations of small monofunctional amines. In particular, we investigate the influence of the relaxation time used in the weakcoupling scheme, the choice of appropriate model compounds for the calibration of the required empirical functions, and corrections for finitesize effects linked with the small size of the simulation box.

Trial wave functions for the calculation of vibrational states of molecules using quantum Monte Carlo
View Description Hide DescriptionIn this article we test three kinds of trial wave functions for the calculation of vibrational excited states of molecules using quantum Monte Carlo. We begin our study with the basis set originally used by Bernu and coworkers and further modified by Acioli and Soares Neto. The second set tested was the simplified Morse oscillatorlike with harmonic coupling (SMOLHC) proposed by Brown et al. to study the vibrational spectra of Finally we proposed a third basis set, based on the previous two. This basis set keeps the anharmonicity of the SMOLHC basis but with well conditioned Hamiltonian and overlap matrices. The calculations were performed in the and molecules. The results indicate that the basis sets proposed in this work yield more accurate results with a smaller number of basis functions.

Torsional diffusion Monte Carlo: A method for quantum simulations of proteins
View Description Hide DescriptionThe quantum diffusionMonte Carlo (DMC) method is extended to the treatment of coupled torsional motions in proteins. A general algorithm and computer program has been developed by interfacing this torsionalDMC method with allatom forcefields for proteins. The method gives the zeropoint energy and atomic coordinates averaged over the coupled torsional motions in the quantum ground state of the protein. Application of the new algorithm is made to the proteins gelsolin (356 atoms and 142 torsions) and gp41HIV (1101 atoms and 452 torsions). The results indicate that quantumdynamical effects are important for the energies and geometries of typical proteins such as these.

Why the anisotropic planar rotor model is nearly second order
View Description Hide DescriptionDespite extensive Monte Carlo(MC) simulations, the nature of the phase transition in the anisotropic planar rotor (APR) model remains elusive. The ground state is sixfold degenerate, which would naively suggest strongly firstorder Potts behavior. Extensive MC simulations indicate either a secondorder transition with Potts exponents, or a very weakly firstorder transition. We show that the APR model maps to a generalized sixstate Potts model, with a bond energy between pairs of Potts states q and mod 6 larger by a factor For there exists a tricritical point separating firstorder behavior (including Potts at from secondorder behavior (including Potts at large α). Thus the APR model is weakly first order because of the proximity to this tricritical point.

A mixed quantum classical rate theory for the collinear reaction
View Description Hide DescriptionA mixed quantum classical rate theory (MQCLT) is applied to the collinear hydrogen exchange reaction on the LSTH and PK II potential energy surfaces. Classical trajectories are combined with a numerically exact quantum Monte Carlo evaluation of the thermal flux operator to compute the thermal reaction rate. The MQCLT results are compared to quantum transition state theory (QTST) and centroid rate theory computations. The computed rates are found to bound the exact results from above for temperatures ranging from to As in previous studies, the mixed quantum classical theory gives better agreement with numerically exact computations, than the QTST computations, while the added numerical effort is not prohibitive. The MQCLT rate is almost exact at high temperature. At it is a factor of 2.8 (2.0) greater than the exact rate on the LSTH (PK II) potential energy surface, a significant improvement over the QTST overestimate of 3.7 (3.4). The mixed quantum classical results are comparable in accuracy to the centroid theory computations, except that the centroid theory is always lower than the exact result while MQCLT is always higher.

An efficient method for the coordinate transformation problem of massively threedimensional networks
View Description Hide DescriptionA new and efficient algorithm is presented for the coordinate transformation problem of massively threedimensional networks formed, e.g., by the atoms of crystal fragments or molecular clusters. The new algorithm is based on a divideandconquer technique to perform iterative coordinate transformation, applicable even for threedimensional networks, with linear scaling memory and near linear scaling CPU time requirements. The new algorithm proved to be very fast in the coordinate transformation problems and geometry optimization of diamond fragments, water clusters, globular proteins, and proteins in solvent.

Relations between parameters of density functional theories through exactly solvable manyfermion models
View Description Hide DescriptionBy considering exactly solvable manyfermion models in different spatial dimensions and with different interaction potentials, the chemical potential and Lagrange multiplier for the normalization requirement are identified with the energy of the last particle, and their relation to the average energy per particle is established.

Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals
View Description Hide DescriptionWe propose and implement an alternative approach to the original Car–Parrinello method where the density matrix elements (instead of the molecular orbitals) are propagated together with the nuclear degrees of freedom. Our new approach has the advantage of leading to an computational scheme in the large system limit. Our implementation is based on atomcentered Gaussian orbitals, which are especially suited to deal effectively with general molecular systems. The methodology is illustrated by applications to the threebody dissociation of triazine and to the dynamics of a cluster of a chloride ion with 25 water molecules.

A novel geometric embedding algorithm for efficiently generating dense polymer structures
View Description Hide DescriptionA new algorithm for generating starting polymer structures for molecular simulations (e.g., MD) in dense phase is presented. The algorithm yields structures that fulfill to a large extent rotational isomeric state (RIS) probabilities and avoid atomic overlap. The heuristic search bases on the new parallelrotation (ParRot) technique. We tested the performance of the algorithm on two polymeric systems: Atomistic polyethylene and polystyrene. The algorithm permits to tackle the problem of packing chains into large boxes of size up to 50 Å in a couple of hours on common workstations. Moreover, our packing algorithm is applicable for general polymer systems. The algorithm requires CPU effort scaling with a power 2.8 in the chain length, and with a power 1.5 in the number of chains.

A novel parallelrotation algorithm for atomistic Monte Carlo simulation of dense polymer systems
View Description Hide DescriptionWe develop and test a new elementary Monte Carlo move for use in the offlattice simulation of polymer systems. This novel ParallelRotation algorithm (ParRot) permits moving very efficiently torsion angles that are deeply inside long chains in melts. The parallelrotation move is extremely simple and is also demonstrated to be computationally efficient and appropriate for Monte Carlo simulation. The ParRot move does not affect the orientation of those parts of the chain outside the moving unit. The move consists of a concerted rotation around four adjacent skeletal bonds. No assumption is made concerning the backbone geometry other than that bond lengths and bond angles are held constant during the elementary move. Properly weighted sampling techniques are needed for ensuring detailed balance because the new move involves a correlated change in four degrees of freedom along the chain backbone. The ParRot move is supplemented with the classical Metropolis Monte Carlo, the ContinuumConfigurationalBias, and Reptation techniques in an isothermal–isobaric Monte Carlo simulation of melts of short and long chains. Comparisons are made with the capabilities of other Monte Carlo techniques to move the torsion angles in the middle of the chains. We demonstrate that ParRot constitutes a highly promising Monte Carlo move for the treatment of long polymer chains in the offlattice simulation of realistic models of dense polymer systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electronic structure and bonding in metal phthalocyanines, Metal=Fe, Co, Ni, Cu, Zn, Mg
View Description Hide DescriptionElectronic structure and bonding in metal phthalocyanines is investigated in detail using a density functional method. The metal atoms are strongly bound to the phthalocyanine ring in each case, by as much as 10 eV. The calculated orbital energy levels and relative total energies of these structures indicate that Fe and Co phthalocyanines have and ground states, respectively, but that these states are changed upon interaction with strongfield axial ligands. The valence electronic structures of Fe and Co phthalocyanines differ significantly from those of the others. The HOMOs in Fe, Co, and Cu phthalocyanine are metal like, whereas in Ni and Zn phthalocyanines, the HOMO is localized on the phthalocyanine ring. The first ionization removes an electron from the phthalocyanine orbital in all cases, with very little sensitivity of the ionizationenergy to the identity of the metal. Whereas the first reduction in Fe and Co phthalocyanine occurs at the metal, it is the phthalocyanine that is reduced upon addition of an electron to the other systems. Fe, Ni, and Cu phthalocyanines have smaller HOMO–LUMO separations than do Zn and Co phthalocyanine. There is very little variation in atomic charges within the phthalocyanine from one metal to the next.

Geometry, electronic structure, and energetics of copperdoped aluminum clusters
View Description Hide DescriptionUsing density functional theory and generalized gradient approximation for exchangecorrelation potential, we have calculated the equilibrium geometries and energetics of neutral and negatively charged clusters. Unlike the alkali atomdoped aluminumclusters in the same size range, the copper atom resides inside the aluminumcluster cage. Furthermore, the and energy levels of Cu hybridize with the valence electrons of Al causing a redistribution of the molecular orbital energy levels of the clusters. However, this redistribution does not affect the magic numbers of clusters that could be derived by assuming that Cu donates one electron to the valence levels of clusters. This behavior, brought about by the smaller size and large ionization potential of the copper atom, contributes to the anomalous properties of anions: Unlike atom), the mass ion intensities of are similar to those of The calculated adiabatic electron affinities are also in very good agreement with experiment.

Multiphoton ionization and photoelectron spectroscopy of formaldehyde via its Rydberg states
View Description Hide DescriptionThe resonanceenhanced multiphoton ionization (REMPI) spectrum of formaldehyde, two photon resonant in the region of the and states, is reported. The state spectrum is dominated by the scissors), outofplane bending), asymmetric stretching), and rock) modes, with weaker bands observed for excitation of the (CO stretching) mode. Vibrational analysis of the spectrum provides many new frequencies for the state, not resolved or accessible in single photon spectroscopic measurements.Photoelectron spectroscopy is used to probe the nature of the vibronic levels associated with the intermediate state, to measure vibrational frequencies of the resulting cations, and to identify useful routes for preparing vibrational stateselected It is found that is a wellbehaved Rydberg state, generating cations in the same vibrational level that was populated in the intermediate. Cations with modeselective excitation of up to 0.62 eV can be produced. Ab initio calculations are used to help assign the cation vibrations. In contrast to the wellbehaved state, the and states are strongly mixed with each other and with valence states.

Pressure effects on bimolecular recombination and unimolecular dissociation reactions
View Description Hide DescriptionThe treatment of pressureeffects on bimolecular recombinations and unimolecular dissociations is discussed. The analysis of recombination and dissociation reactions is made by showing how the nonequilibrium energy (E) and angular momentum (J)dependent steadystate population distribution functions for the two reactions are related to each other and to the equilibrium population distribution function at the given E and J. As a special case a strong collision model is then used for the collisional rotational angular momentum transfer, and a ladder model for the collisional energy transfer. An analytical result is obtained for states below the dissociation threshold. The extension to recombinations with two exit channels is described, for application to ozone formation and isotopic effects.

Effects of π centers and symmetry on twophoton absorption cross sections of organic chromophores
View Description Hide DescriptionWe have theoretically examined a series of organic molecules that exhibit large twophoton absorption cross sections in the visible region and that have been synthesized in different laboratories. One and twophoton absorption cross sections of the four lowest excited states of each molecule have been calculated at the same theoretical level using ab initio response theory. It is found that the molecular length and the onephoton absorption intensity are quite strongly correlated factors, but that a corresponding correlation for the twophoton absorption is much weaker or is missing. In contrast, a most crucial role for large twophoton absorption is played by the π center. For molecules with a given π center a symmetrical structure with strong donor groups can result in a maximum twophoton absorption cross section. Our theoretical findings are consistent with some recent experimental observations. The chromophore based on dithienothiophene as π center attached with symmetrical N,Ndiphenylamine donors is found to have the largest twophoton cross section in the visible region among all known onedimensional twophoton organic materials that have been reported in the literature.

Branching ratios of products in the photodissociation of at 193 nm
View Description Hide DescriptionExperimental and theoretical results are combined to show that vibrationally excited radicals undergo photodissociation to produce radicals mainly in the state. Infrared (IR) emissions from the photolysis of acetylene with a focused and unfocused 193 nm excimer laser have been investigated using stepscan Fourier transform infrared (FTIR)emission spectroscopy at both low and high resolution. With an unfocused laser, the lowresolution infrared emission spectra from the radicals show a few new vibrational bands in addition to those previously reported. When the laser is focused, the only emissions observed in the 2800–5400 cm^{−1} region come from the electronic transitions of the radicals. Most of the emissions are the result of the transition of although there are some contributions from the Ballik–Ramsay bands A ratio of has been calculated from these results. High quality theoretical calculations have been carried out to determine what kind of ratio could be expected if the photodissociation products are formed solely by adiabatic dissociation from the excited states of To accomplish this, the geometries of different electronic states of and were optimized at the complete active space self consistent field [CASSCF(9,9)/6311G^{*} ^{*}] level. The calculated normal modes and vibrational frequencies were then used to compute Franck–Condon factors for a variety of vibronic transitions. In order to estimate the oscillator strengths for transitions from different initial vibronic states of transition dipole moments were computed at different geometries. The overall Franck–Condon factor for a particular excited electronic state of is defined as the sum of Franck–Condon factors originating from all the energetically accessible vibrational levels of states. The adiabatic excitation energies were calculated with the multireference configuration interaction/correlationconsistent polarized valence triple zeta [MRCI(9,9)/ccPVTZ] method. The overall Franck–Condon factors were then multiplied by the corresponding oscillator strengths to obtain the total absorption intensities characterizing the probabilities for the formation of different excited states. Then, the excited states of were adiabatically correlated to various electronic states of and to predict the photodissociation branching ratios from the different states of such as and For produced by 193 nm photodissociation of acetylene, the calculations gave the following branching ratios of 38:32:10:14:6. This means that the theoretical branching ratio for the is 2.7, which is in excellent agreement with experiment.

Study of the electronic structure of the actinide tetrabromides and using ultraviolet photoelectron spectroscopy and density functional calculations
View Description Hide DescriptionUltraviolet photoelectron spectra of and have been recorded in the gasphase and interpreted using relativistic density functional calculations. For eight bands were observed which are interpreted as ionization from the five symmetry orbitals of a unit in symmetry, with three of the bands [the and ionizations] each being split into two by spin–orbit interaction. The observed splittings are rationalized in terms of the and contributions to the orbitals and by comparison with the known ultraviolet photoelectron spectra of and The first vertical ionization energy (VIE) of was measured as (10.92±0.03) eV. shows a very similar photoelectron spectrum with an extra band at (9.65±0.02) eV VIE. This is associated with a ionization. Supporting matrix isolation infrared experiments were also carried out under very similar vaporization conditions to those used in the photoelectron spectroscopy experiments to check the composition of the vapor beams used. In these experiments, the stretching modes of and have been measured as 230±2 and 239±2 cm^{−1}, respectively. Both the photoelectron and infrared matrix isolation spectra are consistent with an effective tetrahedral geometry for and

Highresolution photoelectron spectroscopic study of the first electronic states of
View Description Hide DescriptionThe pulsedfieldionization zerokineticenergy (PFIZEKE) photoelectron spectrum of has been recorded between 103 500 cm^{−1} and 118 000 cm^{−1}. Photoelectronic transitions to four [the and states] of the first six electronic states of have been observed. The photoelectronic transition to the ground state consists of a long progression of vibrational bands, starting at From the resolved isotopic substructure of vibrational levels with the absolute numbering of the vibrational quantum number could be determined. The analysis of the spectrum has led to improved values of the adiabatic ionization potential the dissociation energy and to the determination of an analytical potential energy curve that reproduces the experimental data from to beyond 81% of the dissociation energy. The transitions to vibrational levels of the state with and have vanishing Franck–Condon factors for direct ionization from the ground neutral state and gain intensity from transitions to low Rydberg states that belong to series converging on excited electronic states of In the region immediately below the first dissociation limit of a second progression was observed and assigned to a photoelectronic transition to the state. The adiabatic ionization potential the dissociation energy and vibrational constants could be extracted for this state. Two further progressions were observed below the second dissociation limit of and assigned to transitions to the and states. The adiabatic ionization potentials and the dissociation energies were determined for these two ionic states. In the region just below the ionic dissociation limits, artifact lines are observed in the PFIZEKE photoelectron spectra at the position of transitions to Rydberg states of the krypton monomer. At the lowest threshold, collisional and associative ionization of the long lived atomic Rydberg states leads to the formation of ZEKE electrons; at the upper threshold, the rapid autoionization of the atomic Rydberg states forms high ion concentrations, and the electrons that remain trapped in the ion cloud are released by the delayed pulsed field used to produce and extract the PFIZEKE electrons.

Two channel vapor nucleation in the vicinity of the triple point
View Description Hide DescriptionConsidering the topology of semiempiricalnucleation rate surfaces originate from lines describing the appropriate phase equilibria, there will be two nucleation rate surfaces that exist for the different physical states of the critical embryo phases that are formed near the triple point. Each rate surface is independently related to a nucleation channel and is described by individual equations for nucleation rates. Because of the differences in the sticking probability of vapor molecules when they collide with a physical surface (in this case, with the surface of the nucleation embryos) in the different phases, the growth rates of the different phase clusters will be different. As a result of this difference, one expects to find different sized particles for two cluster phases in the vicinity of the triple point for first order phase transitions. In the present study, particle size distributions were measured near glycerin triple point. A clearly bimodal size distribution was observed. This result suggests that there are two independent nucleation channels that exist near the triple point. This experimental system has the ability to discern particles produced through the two separate nucleation channels so that the nucleation rates can be measured for each channel.