Volume 115, Issue 14, 08 October 2001
 ARTICLES

 Theoretical Methods and Algorithms

On the calculation of entropy from covariance matrices of the atomic fluctuations
View Description Hide DescriptionAn ad hoc method for calculating the entropy of a biomolecular system from the covariance matrix of the atomic fluctuations is analyzed. It is shown that its essential assumption can be eliminated by a quasiharmonic analysis. The computer time required for use of the latter is of the same order as that of the former.

Timedependent Hartree–Fock schemes for analytical evaluation of the Raman intensities
View Description Hide DescriptionUsing the timedependent Hartree–Fock method two analytical schemes are elaborated for determining the derivatives of frequencydependent polarizability with respect to atomic Cartesian coordinates. The first scheme is iterative and consists in determining the mixed derivatives of the density matrix with respect to atomic Cartesian coordinates and dynamic electrical fields. The second takes advantage of the rule to express the polarizability derivatives in terms of firstorder derivatives. Both schemes are implemented in the GAMESS program. They enable the fully analytical evaluation of the Raman intensities with inclusion of the frequency dispersion. The potential of these methods is illustrated by determining the polarizability derivatives and Raman intensities of small molecules.

Ground and excitedstate cusp conditions for the electron density
View Description Hide DescriptionHigherorder cusp relations are derived for the wave function and the electron density of the ground and the excited states of atoms, ions or molecules. The total energy is expressed in terms of the electronic potential and density terms defined at the nucleus. It is proved that the linear term of the spherical part in the expansion of the Kohn–Sham potential, the classical Coulomb and the exchange correlation potentials around a nucleus are all equal to zero. A relationship involving the values of the density and its second and third derivatives at the nucleus is derived.

Quantum relaxation dynamics using Bohmian trajectories
View Description Hide DescriptionWe present a new Bohmian trajectory based treatment of quantum dynamics suitable for dissipative systems. Writing the density matrix in complexpolar form, we derive and define quantum equations of motion for Liouvillespace trajectories for a generalized system coupled to a dissipative environment. Our theory includes a vector potential which mixes forward and backwards propagating components and pulls coherence amplitude away from the diagonal region of the density matrix. Quantum effects enter via a double quantum potential, which is a measure of the local curvature of the density amplitude. We discuss how decoherence can be thought of as a balancing between localization brought on by contact with a thermal environment which increases the local curvature of the density matrix and delocalization due to the internal pressure of the quantum force which seeks to minimize the local curvature. The quantum trajectories are then used to propagate an adaptive Lagrangian grid which carries the density matrix, and the action, thereby providing a complete hydrodynamiclike description of the dynamics.

Generalized Filinov transformation of the semiclassical initial value representation
View Description Hide DescriptionAn efficient method is proposed for the practical solution of the “sign” problem for integrals involved in the semiclassical initial value representation. It is based on a generalization of the conventional Filinov filtering procedure which has the (approximate) effect of incorporating complex initial conditions into the phase space average; it does this by including an explicit oscillatory term in the filtering function that partially cancels the oscillatory part of the original integrand. A systematic procedure is also described for making an optimal choice of the “smoothing parameters,” thus removing this arbitrariness in the overall approach. Tests on systems with chaotic dynamics demonstrate the accuracy and efficiency of the method.

Heats of formation of CCl and from ab initio quantum chemistry
View Description Hide DescriptionHigh level ab initioelectronic structure theory has been used to calculate the heats of formation of CCl and The calculations were done at the CCSD(T) level with new correlationconsistent basis sets up through augmented hextupleζ including tight d functions on the Cl and then extrapolated to the complete basis set limit. Additional corrections for core/valence correlation, relativistic effects both scalar and atomic spin–orbit, and zeropoint energies have been included. The heat of formation at 0 K of CCl is 103.1±0.4 kcal/mol and that of is 55.1±0.4 kcal/mol.

A comprehensive thermodynamic theory of the Soret effect in a multicomponent gas, liquid, or solid
View Description Hide DescriptionA comprehensive theory for the Soret effect (also called thermal diffusion) is presented which incorporates both the thermodynamic contribution from selective attraction/repulsion and the kinetic contribution from selective collision interaction between the components. The new theory is an extension of a theory presented earlier in which the thermodynamic contribution only was modeled. The single assumption of the theory is that the Soret effect in the steady state is the macroscopic state accomplished by a maximum number of microstates with respect to the ideal gas state. As a result, the Soret effect in a multicomponent mixture can be calculated by using input from an equationofstate of the mixture and kinetic gas theory without the use of matching parameters. The theory is not limited to systems with a small temperature difference and/or a small concentration difference. The methodology of the new theory can be used to model other crosseffects in irreversible thermodynamics. A test of the theory against the measured Soret effect in 18 mixtures shows agreement within a factor of 2 over four decades. Closer agreement cannot be expected since it appears that the calculation of the Soret effect is extremely sensitive to the accuracy of input from the equationofstate. The present equationsofstate, even those that are calibrated for use in the chemical and petroleum industry, require modification for the calculation of the Soret effect, because of a higher demand in accuracy. In addition, it is also important to examine which frame of reference (centerofvolume or centerofmass) applies to a particular measurement or practical application, because the frame of reference determines which mathematical expression for the Soret effect must be used.

A comprehensive thermodynamic theory of the crosseffect in isothermal diffusion (“Hertz effect”) in a multicomponent gas, liquid, or solid
View Description Hide DescriptionThe crosseffect between diffusion fluxes in a nonuniform, multicomponent mixture is the cause of diffusion of a component against its own concentration gradient. Gustav Hertz was the first to use this crosseffect for the separation of isotopes. The calculation of the magnitude of the crosseffect, which we call Hertz effect, is possible if all coefficients of the diffusiontensor of the mixture are known. For dilute gases, kinetic gas theory enables the calculation of the diffusiontensor, but calculation methods for dense gases, liquids, and solids require input of measured binary or tracer diffusion coefficients. This paper presents for the first time a calculation method for the magnitude of the Hertz effect without using input of any measured diffusion coefficient. Input is required from the equationofstate of the mixture and from kinetic gas theory. The theory is based on the principle of a maximum number of possible microstates in the stationary, nonequilibrium state. The theory has been compared with all measured diffusion data of mixtures that can be represented by our phasebehavior package. There is fair to good agreement between measurement and theory, but the Hertz effect in these mixtures is small. A test against diffusion data of highly nonideal mixtures is therefore recommended.

Estimate of the cutoff errors in the Ewald summation for dipolar systems
View Description Hide DescriptionTheoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The applicability of the estimates is tested and confirmed in several numerical examples. We demonstrate that these estimates can be used easily in determining the optimal parameters of the dipolar Ewald summation in the sense that they minimize the computation time for a predefined, user set, accuracy.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Intrinsic bond strengths of multiple gallium–gallium bonds: A compliance matrix study using multiconfiguration selfconsistent field wave functions and hybrid density functionals
View Description Hide DescriptionInverted matrices of force constants (compliance matrices) are used to reassign the bond order of the Ga–Ga bond in a recently synthesized compound The results of multiconfiguration wave functions using the complete active space selfconsistent field method are compared to hybrid density functionals and Hartree–Fock wave functions.

Potential energy curves and dipole transition moments for electronic states of ArHe and HeNe
View Description Hide DescriptionRelativistic corepotential calculations have been carried out on the ground and excited Ω states of ArHe and HeNe correlating with the atomic limits and respectively, and with groundstate He atoms. The potential energy curves of the excited states of ArHe are repulsive. The potential energy curves of the 1(I) and states of HeNe show a local Rydberg minimum at 2.8 bohr and a barrier at 4.0 bohr, while the other excited state potentials of HeNe are repulsive. For both ArHe and HeNe, large dipole transition moments are calculated connecting the ground state with states dissociating to atomic limits from which radiative transitions to the atomic ground state are allowed. Small but nonzero dipole transition moments are obtained for short internuclear distances for the transitions from the 1(I) state, which correlates with the metastable state of Ar (in ArHe) or Ne (in HeNe). The radiative lifetime of the 1(I) state of HeNe (estimated from the vertical transition at 2.8 bohr) is 18 μs.

Deprotonation energy of Basis set limit energies
View Description Hide DescriptionThe deprotonation energy of radical has been accurately determined using ab initiocoupled cluster methods.Basis sets up to augccpVQZ quality have been used, and an extrapolation for further basis set incompleteness has been applied. The best computed deprotonation energy for is

Structure and dynamics of Monte Carlo and molecular dynamics simulations
View Description Hide DescriptionThe structures and relaxation dynamics of embedded in clusters of molecules are studied by Monte Carlo and molecular dynamics simulations. The equilibrium structures of clusters are obtained as a function of cluster size and the closing of the first solvation shell is found to occur at consistent with experimental observation. By comparing with the previous studies with different types of solvent molecules, it is found that differences in solvent polarity lead to noticeable changes in equilibrium structures and caging dynamics of clusters. clusters tend to form more symmetric, spreadout solvent configurations, resulting in a weaker solventelectric field being exerted on the solute. The localization of the charge distribution for large internuclear separations happens for longer bond length and much more rapidly in than in clusters. Molecular dynamics simulations showed that vibrational relaxation is very rapid, losing almost 90% of its internal energy within 1 ps of recombination. It is suggested that the change of charge distribution provides an efficient mechanism for energy transfer from the anion to the surrounding solvents. The solvent with permanent dipole moment exhibits a slightly shorter relaxation time than the nonpolar solvent. The electrostatic interactions are found to be major driving forces for the compression of the solute throughout the relaxation processes. The effects of solvent flexibility on the relaxation dynamics are investigated for embedded in clusters of flexible solvents. It is found that including the flexibility of the molecules has minimal effect on the vibrational relaxation dynamics of clusters.

Spinorbit branching in the collisioninduced dissociation reaction of
View Description Hide DescriptionThe collisioninduced dissociation process, has been studied using a threedimensional semiclassical coupled wave packet method with a focus on electronically nonadiabatic transitions induced by spinorbit interaction. The radial motion is described by classical mechanics and the other degrees of freedom are treated quantum mechanically. The diabatic potential energy surfaces have been constructed with the diatomicsinmolecule approach. The diatomic potential energy curves for the ground and excited states are obtained from the ab initio electronic structure calculations at the multireference configuration interaction level. The calculated spinorbit branching fraction depends only weakly on the initial vibrational quantum number of HF and on the total angular momentum. This implies that the branching fraction is determined mainly in the large regions where the spinorbit interaction of the F atom is dominant. We also found that the electronic anisotropy interaction between the He atom and the F atom in HF plays a less important role in collisioninduced dissociation processes.

Rotationally resolved infrared spectrum of the anion complex
View Description Hide DescriptionThe midinfrared spectrum of the anion complex is measured in the stretch region by monitoring the production of photofragments in a tandem mass spectrometer. The rotationally resolved spectrum comprises two overlapping Σ−Σ subbands, redshifted by ≈85 cm^{−1} from the free vibrational frequency. These subbands are assigned to absorptions by complexes containing para and ortho forms of the molecule. The complex is deduced to possess a linear equilibrium geometry, although the zeropoint bending excursion is expected to be substantial. The rotational constants are consistent with vibrationally averaged intermolecular separations between the anion and center of mass of 3.414(4) Å for and 3.413(1) Å for The intermolecular bond contracts by 0.076 Å following vibrational excitation of the diatomic molecule. Effective onedimensional radial potential energy curves are developed through Rydberg–Klein–Rees inversion of the spectroscopic data and consideration of the longrange electrostatic and induction interaction between the molecule and a point charge. On the basis of these potential energy curves the binding energies of and are estimated as 364 and 418 cm^{−1}, respectively.

Ring closure in dioxin formation process: An ab initio molecular dynamics study
View Description Hide DescriptionThe four possible mechanisms of ring closure in dioxin formation from chlorophenols are studied using ab initiomolecular dynamics, within generalized gradient approximation.Free energy barriers, derived as the potential of mean constraint force, directly lead to a static approximation for the transition rates. We show, however, that the static approximation overestimates the actual rates by 33%–345%, depending on the intermediate/temperature. Comparing our results with the available experimental data, we conclude that, contrary to what is widely assumed, the pathways starting from two chlorophenols are not among the most dominant pathways in the formation of highly toxic dioxins, at least in the gas phase. This signifies the role of catalysts and/or other precursors.

Hydrogen bonding and collective proton modes in clusters and periodic layers of squaric acid: A density functional study
View Description Hide DescriptionHydrogen bonding in clusters and extended layers of squaric acid molecules has been investigated by density functional computations. Equilibrium geometries, harmonic vibrational frequencies, and energy barriers for proton transfer along hydrogen bonds have been determined using the Car–Parrinello method. The results provide crucial parameters for a first principles modeling of the potential energy surface, and highlight the role of collective modes in the lowenergy proton dynamics. The importance of quantum effects in condensed squaric acid systems has been investigated, and shown to be negligible for the lowestenergy collective proton modes. This information provides a quantitative basis for improved atomistic models of the order–disorder and displacive transitions undergone by squaric acid crystals as a function of temperature and pressure.

Dynamics of vibrationally mediated photodissociation of
View Description Hide DescriptionThe ∼235 nm photodissociation of preexcited to three, four, and five quanta of C–H methyl stretches was studied to investigate the effect of internal parent excitation on the dynamics of two and threebody photofragmentation. The ∼235 nm photons also tagged spinorbit ground [Cl] and excited [Cl^{*}] state photofragments, via (2+1) resonantly enhanced multiphoton ionization in a timeofflightmass spectrometer. Monitoring the shapes of and timeofarrival profiles revealed their energies and angular distributions and showed broad and unstructured fragment kinetic energy distributions. Although a significant amount (∼50%) of the available energy is transferred into internal energy of the fragment, the spatial Cl distribution is characterized by a nonvanishing anisotropy parameter, β, which indicates at a fast dissociation of the parent molecule along the C–Cl dissociation coordinate. Moreover, β for Cl changes from a slightly positive value to a negative value, while that for Cl^{*} increases when the preexcitation is increased from three to five quanta of C–H methyl stretches. This is attributed to the promotion of one of the nonbonding electrons located on the Cl atoms to the σ^{*} antibonding C–Cl orbital and involvement of several upper states with different symmetry properties.

Detailed study of pyridine at the C 1s and N 1s ionization thresholds: The influence of the vibrational fine structure
View Description Hide DescriptionHigh resolution, vibrationally resolved, nearedge xray absorption fine structure(NEXAFS)spectra at the C 1s and N 1sionization thresholds of pyridine and deuterated pyridine in the gas phase have been recorded. The high resolution of 65 meV (150 meV) at the C s (N 1s) ionization thresholds reveals vibrational structures in the spectra. Detailed ab initio and density functional theory(DFT) calculations were performed to interpret the experimental spectra and to assign the observed peaks. In particular we focused on the previously unexplained intensity ratio for the two components of the C 1s→1π^{*} transition. For this transition the vibrational structure is included through a linear coupling model in the DFT calculations and leads to the experimentally observed ∼2:3 intensity ratio between the two π^{*} components in the C 1s spectrum rather than the ∼3:2 ratio obtained without vibrational effects. After inclusion of relaxation effects in the excited states, in addition to the vibrational effects, both theoretical methods yield almost perfect agreement with experiment.

Dipoleallowed excited states of Potential energy curves, vibrational analysis, and absorption intensities
View Description Hide DescriptionThe three lowest adiabatic potential energy curves for each of the two dipoleallowed symmetries, and are calculated in the multireference configuration–interaction framework. Diabatic potentials and corresponding coupling elements are obtained by diagonalizing the electronic operator which serves to discriminate Rydberg and valence type states. A large basis set and judiciously chosen active orbital and configuration spaces furnish smooth and reliable potential curves. However, a vibrational analysis of the coupled systems in diabatic representation still shows some disappointing deviations from the experimental interference patterns of overlapping absorption bands that are highly sensitive to potential energy differences. Starting from the calculated curves, a fitting procedure accounting also for empirical information yields potential energy curves and diabatic coupling elements that reproduce all details of the experiment very well. These recommended results also serve to identify residual defects in the ab initio curves mainly as vertical shifts. The performance of other commonly used ab initio methods for the calculation of excited states is briefly discussed.