Volume 115, Issue 1, 01 July 2001
 ARTICLES

 Theoretical Methods and Algorithms

Selfconsistent solution of Dyson’s equation up to second order for atomic systems
View Description Hide DescriptionIn this paper, the singleparticle Green’s function approach is applied to the atomic manybody problem. We present the selfconsistent solution of the Dyson equation up to second order in the selfenergy for nonrelativistic spincompensated atoms. This Dyson secondorder scheme requires the solution of the Hartree–Fock integrodifferential equations as a preliminary step, which is performed in coordinate space (i.e., without an expansion in a basis set). To cope with the huge amount of poles generated in the iterative approach to tackle Dyson’s equation in second order, the BAGEL (BAsis GEnerated by Lanczos) algorithm is employed. The selfconsistent scheme is tested on the atomic systems He, Be, Ne, Mg, and Ar with spinsaturated ground state Predictions of the total binding energy, ionization energy, and singleparticle levels are compared with those of other computational schemes [density functional theory, Hartree–Fock (HF), postHF, and configuration interaction] and with experiment. The correlations included in the Dyson secondorder algorithm produce a shift of the Hartree–Fock singleparticle energies that allow for a close agreement with experiment.

Curing difficult cases in magnetic properties prediction with selfinteraction corrected density functional theory
View Description Hide DescriptionThe Perdew–Zunger selfinteraction correction (SIC) was implemented selfconsistently within a molecular density functional theory(DFT) program, using the Krieger–Li–Iafrate approximation to the optimized effective potential, and the Vosko–Wilk–Nusair (VWN) functional. The computationally efficient implementation relies on the fitting of orbital densities for the evaluation of orbital Coulomb potentials, and allows for routine applications to large molecules. Due to the use of the effective potential approach, the evaluation of the energy derivatives can be handled by standard Kohn–Sham DFT techniques in a straightforward way. The SICVWN technique is applied to the calculation of nuclear magnetic resonance(NMR) parameters in representative small molecules, containing C, H, N, O, and F. Removal of selfinteraction leads to a substantial improvement in the calculated isotropic chemical shifts for N, O, and F, where SICVWN holds an advantage over both local (VWN), and gradientcorrected functionals (Becke 88Perdew 86, BP86). For C and H isotropic chemical shifts, which are well described by the gradientcorrected functionals, SICVWN performs as well as BP86. SICVWN also improves the description of the absolute chemical shielding, and of the principal components of the NMR shielding tensors. The changes arise mainly from adjustments in the Kohn–Sham orbital energies, leading to a better description of the paramagnetic contribution to the shielding tensor. For spin–spin coupling constants, SICVWN improves the description of the paramagnetic contribution. At the same time, the magnitude of the Fermi contact term is underestimated, yielding mixed overall results. Slow convergence of the spinspin coupling results with the basis set size prevents a conclusive statistical evaluation for this property. The clear physical origin of the SICVWN effect in the prediction of magnetic properties opens the tantalizing possibility that this technique may be effective in solving problems often encountered in the calculations of NMR parameters of heavier nuclei.

Comparison of thermostatting mechanisms in NVT and NPT simulations of decane under shear
View Description Hide DescriptionNonequilibrium molecular dynamics (NEMD) simulations play a major role in characterizing the rheological properties of fluids undergoing shear flow. However, all previous studies of flows in molecular fluids either use an “atomic” thermostat which makes incorrect assumptions concerning the streaming velocity of atoms within their constituent molecules, or they employ a center of mass kinetic (COM) thermostat which only controls the temperature of relatively few degrees of freedom (3) in complex high molecular weight compounds. In the present paper we show how recently developed configurational expressions for the thermodynamic temperature can be used to develop thermostatting mechanisms which avoid both of these problems. We propose a thermostat based on a configurational expression for the temperature and apply it to NEMD simulations of decane undergoing Couette flow at constant volume and at constant pressure. The results so obtained are compared with those obtained using a COM kinetic thermostat. At equilibrium the properties of systems thermostatted in the two different ways are of course equivalent. However, we show that the two responses differ far from equilibrium. In particular, we show that the increase in the potential energy of the internal modes with increasing shear is only observed with a Gaussian isokinetic COM thermostat in both NVT and NPT simulations. There is no such increase with the configurational thermostat, which, unlike the Gaussian isokinetic COM thermostat, correctly accounts for the internal degrees of freedom of the molecular fluid.

A new approach to the problem of noniterative corrections within the coupledcluster framework
View Description Hide DescriptionNoniterative corrections to the coupledcluster (CC) method with singles and doubles (CCSD) due to triple and higher excitations in the cluster operator are investigated. The derivation is based on the standard procedure for evaluating contributions coming from higher excitation rank cluster operators into the CC equations for singles and doubles. The noniterative nature of the approach leads to a direct modification of the CCSD energy through a posteriori corrections, however, unlike previous derivations, we take into account the coupling between the energy and cluster amplitudes in the CC equations. The coupling is not present in the fully iterative CC schemes due to the linked diagram theorem which makes the cluster amplitude equations energy independent. We show, however, that if the problem of unlinked contributions is reexamined in the context of noniterative approaches, then their complete cancellation does not occur. This leads to a partial restoration of the energy dependence. The energy dependence then gives the cluster amplitudes more flexibility in adjusting to the energy changes within the noniterative approach which is especially important in quasidegenerate situations when the standard energy corrections become large. The resulting modifications introduce disconnected contributions to the energy so sizeextensivity is no longer preserved. This approach provides a new hierarchy of CC corrections in which the standard corrections, like CCSD[T] or CCSD(T), appear as a natural first step in the derivation. Some of the corrections can be easily identified as analogous to those recently proposed by Kowalski and Piecuch in the context of the method of moments of CC equations. We also suggest new approximations.

The ONIOMPCM method: Combining the hybrid molecular orbital method and the polarizable continuum model for solvation. Application to the geometry and properties of a merocyanine in solution
View Description Hide DescriptionWe present the ONIOMPCM method, which combines the ONIOM (our own nlayered integrated molecular orbital+molecular mechanics) method with the polarizable continuum model (PCM). Four versions of the method have been developed. These schemes differ mainly with respect to the level of coupling between the solute charge distribution and the continuum, which has important consequences for the computational efficiency. Any property that can be calculated by both ONIOM and PCM can also be calculated by the ONIOMPCM method. In the current paper we use this aspect for the calculation of the derivatives of the energy with respect to the nuclear coordinates to perform geometry optimizations, and the calculation of the nuclear magnetic resonance shielding for solvated molecules. To assess the various versions of the method, we performed ONIOM(B3LYP:Hartree–Fock)PCM calculations on a merocyanine, All four schemes yield results close to the target B3LYP (threeparameter Becke–Lee–Yang–Parr density functional)PCM, and the method appears to be a promising tool for accurate calculations on large molecules in solution.

Diffusionlimited reaction in one dimension: Paired and unpaired nucleation
View Description Hide DescriptionWe study the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and nucleation in pairs are considered. A new method of analysis permits exact calculation of the steadystate density and its time evolution in terms of the three parameters describing the microscopic dynamics: the nucleation rate, the initial separation of nucleated pairs, and the diffusivity of a particle. For paired nucleation at sufficiently small initial separation the nucleation rate is proportional to the square of the steadystate density. For unpaired nucleation, and for paired nucleation at sufficiently large initial separation, the nucleation rate is proportional to the cube of the steadystate density.

Symmetrybreaking and nearsymmetrybreaking in threeelectronbonded radical cations
View Description Hide DescriptionThe manifestations of the symmetrybreaking artifact in threeelectronbonded systems have been investigated at several computational levels including secondorder Møller–Plesset perturbation theory (MP2), coupled cluster (CC), and Brucknercoupled cluster (BCC) theories. The model systems, cover all types of threeelectron bonds that can possibly take place between atoms of the second and third rows of the Periodic Table. The critical interatomic distance beyond which symmetry breaking begins to take place at the Hartree–Fock and Møller–Plesset levels are determined for each model system. Their magnitude are found to obey regular tendencies which are related to the compactness of the orbitals involved in the threeelectron bonds. In all model systems, the onsets of symmetrybreaking at the MP2 level are greater or equal to the equilibrium bonding distance between the fragments. The symmetrybreaking artifact results in severe discontinuities in the dissociation curves at the MP2 level. The CC level pushes away the occurrence of the artifact to larger distances but do not remove the discontinuities. The artifact is practically cured at the BCC level with perturbative treatment of triple excitations. The onset of symmetrybreaking may in some cases be shortened by substituent effects, to the extent that it becomes shorter than the equilibrium bonding distance like in the and cation radicals that are found to be symmetryunstable even in their equilibrium geometries. The artifact carries over to unsymmetrical systems that display close functional resemblance to symmetrical systems, leading to convergence difficulties, erroneous geometries, and unphysical localization of the electronic charge. An economical alternative to the MP2 method, based on the average quadratic coupledclusters (AQCC), is proposed for such cases, or in cases some stretched threeelectronbonded systems or full dissociation curves are to be investigated.

Low lying vibrational excitation energies from equilibrium path integral simulations
View Description Hide DescriptionThe centroid density is a function defined for quantum systems in thermodynamic equilibrium that is readily obtained by path integral simulations. The physical information provided by the centroid density is a static response of the system under isothermal conditions, namely, the change in the expectation value of the position operator of the quantum particles upon application of constant external forces. An interesting application of this function is the study of vibrational properties of atomic nuclei in molecules and solids. In particular, the analysis of the tensor defined by the second cumulants of the centroid density (i.e., the static isothermal susceptibility tensor) leads to the definition of the linear response vibrational modes, which are characterized by a response of the quantum system parallel to the applied force. The eigenvalues of the susceptibility tensor provide the linear response of the system. This response function is the basis for the formulation of two approximations to evaluate vibrational frequencies. The capability of these approximations is tested in the study of the tunneling frequency of a particle in a doublewell potential, the anharmonic shift in the vibrational frequencies of molecules and HOCl), and the anharmonic shifts of phonon frequencies in diamond.

Compton scattering and the character of the hydrogen bond in ice
View Description Hide DescriptionCompton scattering is an experimental technique which probes the electron momentum density. Here we present a method which allows the calculation of the Compton profile using the formalism of the maximally localized Wannier functions. We applied this method to analyze recent experimental measurements of the anisotropy component of the Compton profile which have been interpreted as the signature of the partial covalent character of the hydrogen bond in ice We are able to reproduce well the experimental results, however we do not find evidence of a covalent nature of the hydrogen bond. In fact our analysis shows that, although the wave functions in ice have a quantummechanical, multicenter character, this gives rise to an antibonding, repulsive interaction between neighboring water molecules. Application to our technique to other, nonhydrogen bonded systems, and analysis of the corresponding Compton scattering profile anisotropy, gives further support to our interpretation.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Vibrational and collisional energy effects in the reaction of ammonia ions with methylamine
View Description Hide DescriptionWe have investigated the reactions of vibrationally stateselected ammonia ions with methylamine over the centerofmass collisional energy range of 0.5 to 10.0 eV and for ammonia ion vibrational states ranging from Under these conditions, five major products appear: and The cross section for each product is a decreasing function of collision energy and also a decreasing function of energy in the mode of the ammonia ion, except for that shows about a twofold enhancement with increasing internal energy, most notably at lowcollision energies. Examination of the velocity scattering profiles shows that the mechanism for formation of each major product does not involve complex formation in this energy range. Branching ratios for each product are measured, and a comparison is presented for and arising from reactions with ammonia ions prepared in two nearly isoenergetic states. One state has no quanta in the symmetric stretch and five quanta in the umbrella bending mode and the other has one quantum in the symmetric stretch and two quanta in the umbrella bending mode Comparison indicates that this reaction is vibrationally mode selective, although the extent of mode selectivity is small.

Torsional analyses of trans2butene and propene cations: A comparative investigation of two prototypical ions with different degrees of symmetry
View Description Hide DescriptionThe mass analyzed threshold ionizationspectra of trans2butene and propene have been obtained using singlestep vacuum ultraviolet excitation. The ionization potential for trans2butene is while for propene it is Both species have progressions of the low frequency, torsional, normal modes. Using the torsional normal mode and first overtone from a trans2butene cation the torsional barrier is determined to be approximately 453 cm^{−1}, assuming a sinusoidal potential. Normal modeanalysis indicates that all low frequency normal modes of the propene cation involve substantial internal motion of the vinyl component, and the spectrum shows a very anharmonic torsional mode progression. These factors complicate direct torsional barrier analysis from the experimental lines, but through the use of various ab initio methods the propene torsional barrier is determined to be approximately 429 cm^{−1}. Due to the anharmonicity found in propene, the correlation corrected vibrational selfconsistent field method in GAMESS was used to verify the assignments of the experimental lines. The torsional barriers for both cations are found to lie approximately 275–300 cm^{−1} below the barrier heights of the neutral species.

Optimal generalized internal vibrational coordinates and potential energy surface for the ground electronic state of
View Description Hide DescriptionAn optimization of generalized internal vibrational coordinates for the electronic ground state of the molecule is carried out. These coordinates are given by the magnitudes and the angle formed by two vectors expressed as linear combinations of the internal valence vectors, and depend on two external parameters which can be optimized so as to reduce the vibrational coupling of the molecule as much as possible. The optimal values of the parameters are found by minimizing a set of unconverged vibrational energies which are computed variationally using a small basis function set. It is shown that the optimal internal coordinates obtained for are superior to both valence and Radau coordinates, as well as to a set of normal coordinates previously derived by proper rotation of the Jacobi coordinates. These optimal internal coordinates are then applied to calculate the vibrational energies of the molecule using an ab initio force field expressed as a Morsecosine expansion, and then to refine it by nonlinear leastsquares fitting to the observed vibrational frequencies.

Spectroscopy and photodissociation of ClF in rare gas solids
View Description Hide DescriptionVibrational progressions in the fluorescence of ClF in Ar and Kr matrices with are observed in the spectral range from 600 to 900 nm with lifetimes of 141 ms.Twophoton excitation leads to emission from the ionic state to the 2 and 2 valence states in the range from 390 to 470 nm with 50 ns lifetime. Ground state parameters and as well as values for the and states are derived. Matrix and Stokes shifts are observed and the large linewidth of the emission is related to the strong coupling of the ionic state to the lattice. Dissociation quantum efficiencies of 5% and 4.8% are determined for kinetic energies of the F fragment of 0.92 eV and 0.39 eV in Ar (19 K), respectively.

Exponentially correlated Gaussian functions in variational calculations. Momentum space properties of the ground state helium dimer
View Description Hide DescriptionMicrohartree accuracy wave functions composed of exponentially correlated Gaussians were transformed in closed form to momentum space representation and applied to compute various isotropic momentum space properties of helium dimer in the ground state. The set of properties includes electron momentum density distribution, expectation values of powers of the electronic momentum operator, and the Compton profile. Calculations were performed at many internuclear separations including the united atom (beryllium) and the separated atoms (helium) limits.

The infrared spectra of and trapped in solid neon
View Description Hide DescriptionWhen a Ne:OCS sample was codeposited at approximately 5 K with a beam of neon atoms that were excited in a microwavedischarge, the infrared spectrum of the resulting deposit included absorptions which can be assigned to and one or more dimer ions. Detailed isotopic substitution studies support the assignments offered for and The CO and CSstretching absorptions observed for isolated in a neon matrix lie close to the corresponding gasphase band centers. The CO and CSstretching fundamentals of isolated in solid neon were observed for the first time at 1646.4 and 718.2 cm^{−1}, respectively. These frequencies are in good agreement with values previously calculated using ab initio and density functional methods. The leastsquares force constant fit to the data obtained in isotopic substitution experiments supports the proposed assignment. Dimer ions were also stabilized, but infrared data for these species were insufficient to provide definitive assignments.

Ab initio potentialenergy surfaces for the reactions
View Description Hide DescriptionAccurate global ab initiosurfaces are presented for the title reactions and competing exchange processes. The ab initio calculations were based on the quadratic configuration interaction treatment with all single and double excitations and perturbative account for triple excitations together with a 6311++G(3df,2pd) basis, the multireference configuration interaction method with the Davidson correction procedure together with an augccpVTZ basis, and the unrestricted coupledcluster treatment with all single and double excitations and perturbative account for triple excitations together with an augccpVQZ basis. The surfaces are interpolations of ab initio data for energies, energy gradients, and second derivatives at configurations scattered throughout the relevant configuration space.

Comparison of nearthreshold reactivity of groundstate and spinorbit excited chlorine atoms with methane
View Description Hide DescriptionA 4:1 mixture of and BrCl diluted in He are coexpanded into a vacuum chamber and the reaction of methane with atomic chlorine is initiated by photolysis of BrCl. Near 420 nm, the resulting mixture of ground and excitedstate chlorine atoms have spatial anisotropies of for the channel and for the channel. The speeddependent spatial anisotropy of the reaction product is detected by resonanceenhanced multiphoton ionization. Our results indicate that the reaction is unimportant in the nearthreshold collision energy range of 0.13–0.16 eV, whereas the reaction with groundstate Cl atoms with excited with one quantum in the (torsion) or (bending) mode is dominant.

Configuration interaction study of singlet excited state of thiophene and its cyano derivative oligomers
View Description Hide DescriptionUsing the singles configuration interaction(CIS)theoretical approach, we investigated the nature of the geometric conformations and electronic transitions in πconjugated oligo(thiophene)s, and their cyano derivatives. Geometryoptimizations were carried at the restricted Hartree–Fock (RHF/321G^{*}) level for the groundstate configurations, which were followed by calculations of first (lowest) singlet excitation energies using the CIS (CIS/321G^{*}) method. In agreement with several previous theoretical/experimental studies, this investigation indicates that the cyano substituted thiophene polymer has a considerably smaller intrinsic band gap than its parent polymer.CIS calculations produce singlet excitation energies in excellent agreement with the experimental values (∼0.1–0.5 eV). They also show that delocalized first singlet excited states(CIS) are accompanied by a strong geometry relaxation in comparison to their groundstate (HF) geometries. The shape and the location of the relaxation depends on the oligomer length.

Ab initio study of the reaction: Kinetics, mechanism and product branching probabilities
View Description Hide DescriptionThe reaction of radical with molecular has been investigated by ab initio molecular orbital theory and variational transition state theory calculations. The detailed potential energy surfaces, including the crossing seams between the PES, located by means of the intrinsic reaction coordinate approach are presented. The rate constants for the association and product formation channels have been calculated and compared with the experimental data. Under the atmospheric pressure condition, the association reaction (a) producing dominates reaction below 1500 K. The branching probabilities for channels (b) and (c) producing and respectively, have been calculated and compared; channel (b) is predicted to be dominant below 2000 K with the rate constant Over 2000 K, channel (c) becomes competitive; its rate constant could be represented by in the temperature range of 1000–3000 K. In addition, the most exothermic products, were found to be kinetically inaccessible because of the large barrier, 47.4 kcal/mol above the reactants.

Photodissociating methyl vinyl ether to calibrate product branching and to test propensity rules for product channel electronic accessibility
View Description Hide DescriptionThese experiments investigate the photodissociation of methyl vinyl ether at 193 nm in a crossed lasermolecular beam apparatus. We observe two C–O bond fission channels, a minor channel producing and the major channel yielding Some of the neutral state vinoxy product undergoes secondary dissociation to produce These experiments on the photodissociation of methyl vinyl ether, which produce nascent vinoxy and methyl radicals cleanly in a onetoone ratio, serve two purposes. First, using the measured photofragment velocities and product branching we calibrate the relative sensitivity of mass spectrometric detection to the methyl and vinoxy polyatomic radical products at the daughter ion, taking into account the loss of neutral vinoxy to formation. This relative mass spectrometric sensitivity calibration factor is determined to be Knowledge of this factor allows us to extract the product branching ratio between the two major competing primary product channels from the reaction, a branching ratio that has been much disputed in the literature. Our results give a product branching ratio of corresponding to 38% (±5%) branching to the channel. Second, we use the result that the channel producing state vinoxy dominates over the formation of groundstate vinoxy to test propensity rules being developed to help predict what product channels may be suppressed by electronically nonadiabatic effects in chemical reactions. These propensity rules discriminate between channels that are “electronically facile” and “electronically difficult/prohibitive.” We find that a qualitative analysis of the changes in electronic configuration along the reaction coordinates for the photodissociation of methyl vinyl ether correctly predicts the dominant channel to be the production of excited state vinoxy, the electronically facile channel.