Volume 118, Issue 20, 22 May 2003
 ARTICLES

 Theoretical Methods and Algorithms

A spincomplete version of the spinflip approach to bond breaking: What is the impact of obtaining spin eigenfunctions?
View Description Hide DescriptionSpincomplete versions of the spinflip configurationinteractionsingles (SFCIS) approach have been investigated to determine the impact of making the wave function an eigenfunction of The method has been implemented within an extended restricted active space configuration interaction formalism. Spincomplete results are presented for excitation energies, equilibrium geometries, and potential energy curves for dissociation of a single bond in several small molecules. The effect of different orbital choices has also been investigated. The spincomplete results are compared both to results using the original spinflip method and to more computationally expensive benchmarks. Using spin eigenfunctions dramatically improves upon the accuracy of the SFCIS approach.

Improved secondorder Møller–Plesset perturbation theory by separate scaling of parallel and antiparallelspin pair correlation energies
View Description Hide DescriptionA simple modification of secondorder Møller–Plesset perturbation theory (MP2) to improve the description of molecular ground state energies is proposed. The total MP2 correlation energy is partitioned into parallel and antiparallelspin components which are separately scaled. The two parameters (scaling factors), whose values can be justified by basic theoretical arguments, have been optimized on a benchmark set of 51 reaction energies composed of 74 firstrow molecules. It is found, that the new method performs significantly better than standard MP2: the rms [mean absolute error (MAE)] deviation drops from 4.6 (3.3) to 2.3 (1.8) kcal/mol. The maximum error is reduced from 13.3 to 5.1 kcal/mol. Significant improvements are especially observed for cases which are usually known as MP2 pitfalls while cases already described well with MP2 remain almost unchanged. Even for 11 atomization energies not considered in the fit, uniform improvements [MAE: 8.1 kcal/mol (MP2) versus 3.2 kcal/mol (new)] are found. The results are furthermore compared with those from density functional theory (DFT/B3LYP) and quadratic configuration interaction [QCISD/QCISD(T)] calculations. Also for difficult systems including strong (nondynamical) correlation effects, the improved MP2 method clearly outperforms DFT/B3LYP and yields results of QCISD or sometimes QCISD(T) quality. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for ten diatomic molecules also show consistent enhancements. The uniformity with which the new method improves upon MP2, thereby rectifying many of its problems, indicates significant robustness and suggests it as a valuable quantum chemical method of general use.

Trajectorydependent cellularized frozen Gaussians, a new approach for semiclassical dynamics: Theory and application to He–naphtalene eigenvalues
View Description Hide DescriptionA semiclassical cellular method is proposed. Signals generated by semiclassical techniques generally deteriorate over time as trajectories become chaotic. One approach to remedy this problem has been to have each trajectory weighted by an entire cell of nearby trajectories (Filinov transform). But even in this approach the exponential part of the propagator typically becomes large and positive over time. Here the cellularization (Filinov) parameter is subject to constraints which make it time dependent and trajectory dependent. It also depends on dimensionality, so it ends up as a matrix. Physically, the Filinov transform is done differently in different directions associated with the stability matrix for the phase—essentially a more confined integration in directions where the matrix diverges and a wider integration in other directions. This squelches the contribution from any part of a trajectory that becomes excessively chaotic. A trajectorydependent cellurized frozen Gaussian is applied here within the Herman–Kluk semiclassical approach. It is tested by looking at a singleparticle threedimensional problem, He attached to a rigid immovable naphtalene, where it is shown to be more accurate than the original HK approach, without the divergence of the correlation function common in the usual cellular dynamics (HK) formulation, and is able to separate a lowlying excited state from the ground state.

Microscopic derivation of hydrodynamic equations for phaseseparating fluid mixtures
View Description Hide DescriptionThe hydrodynamicequations of a phaseseparating fluid mixture are derived from the underlying microscopic dynamics of the system. A projection operator method is used in the GENERIC form [H. C. Öttinger, Phys. Rev. E 57, 1416 (1998)]. In this way, the thermodynamic consistency of the final equations is apparent. The microscopic potential is separated into short and longrange parts, in the spirit of the original work of van der Waals. Explicit expressions for surface tension terms in the hydrodynamicequations are obtained. These terms describe diffuse interfaces in the system. Miscible–immiscible and gas–liquid phase transitions are possible, nonisothermal situations can be studied, and explicit account of cross effects is taken.

Linear scaling computation of the Fock matrix. VI. Data parallel computation of the exchangecorrelation matrix
View Description Hide DescriptionRecently, early onset linear scaling computation of the exchangecorrelation matrix has been achieved using hierarchical cubature [J. Chem. Phys. 113, 10037 (2000)]. Hierarchical cubature differs from other methods in that the integration grid is adaptive and purely Cartesian, which allows for a straightforward domain decomposition in parallel computations; the volume enclosing the entire grid may be simply divided into a number of nonoverlapping boxes. In our data parallel approach, each box requires only a fraction of the total density to perform the necessary numerical integrations due to the finite extent of Gaussianorbital basis sets. This inherent data locality may be exploited to reduce communications between processors as well as to avoid memory and copy overheads associated with data replication. Although the hierarchical cubature grid is Cartesian, naive boxing leads to irregular work loads due to strong spatial variations of the grid and the electron density. In this paper we describe equal time partitioning, which employs time measurement of the smallest subvolumes (corresponding to the primitive cubature rule) to load balance gridwork for the next selfconsistentfield iteration. After startup from a heuristic center of mass partitioning, equal time partitioning exploits smooth variation of the density and grid between iterations to achieve load balance. With the 321G basis set and a medium quality grid, equal time partitioning applied to taxol (62 heavy atoms) attained a speedup of 61 out of 64 processors, while for a 110 molecule watercluster at standard density it achieved a speedup of 113 out of 128. The efficiency of equal time partitioning applied to hierarchical cubature improves as the grid work per processor increases. With a fine grid and the 6311G(df,p) basis set, calculations on the 26 atom molecule αpinene achieved a parallel efficiency better than 99% with 64 processors. For more coarse grained calculations, superlinear speedups are found to result from reduced computational complexity associated with data parallelism.

Fast evaluation of the Coulomb potential for electron densities using multipole accelerated resolution of identity approximation
View Description Hide DescriptionA new computational approach is presented that allows for an accurate and efficient treatment of the electronic Coulomb term in density functional methods. This multipole accelerated resolution of identity for method partitions the Coulomb interactions into the near and farfield parts. The calculation of the farfield part is performed by a straightforward application of the multipole expansions and the nearfield part is evaluated employing expansion of molecular electron densities in atomcentered auxiliary basis sets approximation). Compared to full calculations, up to 6.5fold CPU time savings are reported for systems with about 1000 atoms without any significant loss of accuracy. Other multipolebased methods are compared with regard to reduction of the CPU times versus the conventional treatment of the Coulomb term. The approach compares favorably and offers speedups approaching two orders of magnitude for molecules with about 400 atoms and more than 5000 basis functions. Our new method shows scalings as favorable as where is the number of basis functions, for a variety of systems including dense threedimensional molecules. Calculations on molecules with up to 1000 atoms and 7000 to 14 000 basis functions, depending on symmetry, can now be easily performed on single processor work stations. Details of the method implementation in the quantum chemical program TURBOMOLE are discussed.

A novel method for the solution of the Schrödinger equation in the presence of exchange terms
View Description Hide DescriptionIn the Hartree–Fock approximation the Pauli exclusion principle leads to a Schrödinger equation of an integrodifferential form. We describe the extension of a new spectral noniterative method (SIEM), previously developed for solving the Lippmann–Schwinger integral equation with local potentials, so as to include the exchange nonlocality. We apply it to the restricted case of electronhydrogen scattering in which the bound electron remains in the ground state and the incident electron has zero angular momentum, and we compare the acuracy and economy of the new method to two other methods. One is a noniterative solution of the integral equation as described by Sams and Kouri in 1969. Another is an iterative method introduced by Kim and Udagawa in 1990 for nuclear physics applications, which makes an expansion of the solution into an especially favorable basis obtained by a method of moments. The SIEM method turns out to be more accurate than the two comparison methods by many orders of magnitude for the same number of mesh points.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Structural study of the hydrogenbonded cluster
View Description Hide DescriptionThe structure of the cluster was investigated by rotational coherencespectroscopy (RCS), mass selective one and twocolor resonant twophotonionization (R2PI) experiments and ab initio calculations. RCS measurements yielded rotational constants of as and as well as those for several isotopomers. The counterpoisecorrected secondorder Møller–Plesset perturbation theory (MP2) method predicts two isomers A and B. Both structures have hydrogen bonded chains, with the second bent above the proximal aromatic ring and pointing towards the πelectron system and have nearly the same binding energy. The experimental rotational constants agree better with those calculated for structure B. The B3LYP and PW91 density functional methods also predict two isomers A, B with the rotational constants of B in acceptable agreement with experiment. Based on twocolor R2PI experiments using low ionization frequency to suppress cluster fragmentation, the electronic origin region of the cluster series was reassigned, in agreement with the work of DedonderLardeux et al. [Phys. Chem. Chem. Phys. 3, 4316 (2001)]. In onecolor experiments, the cluster fragments with nearly 100% efficiency into the mass channel.

Polarization propagator calculations of the polarizability tensor at imaginary frequencies and longrange interactions for the noble gases and nalkanes
View Description Hide DescriptionThe linear polarization propagator has been computed at imaginary frequencies for He, Ne, Ar, and Kr as well as for the alkanes including heptane and its smaller members. It is shown that an effective and direct evaluation of the polarization propagator using standard electronic structure first principle methods can be achieved on the whole imaginary axis without expanding the polarizability in a series of the Cauchy moments. The linear response equation will be complex in this case, but an effective algorithm can be constructed so that the computational cost parallels that of the real propagator. Calculations of the polarizabilitytensor are used to determine the Casimir–Polder interaction potentials for the molecules under consideration. Theoretical results for the dispersion coefficient are compared with accurate experimental data, and it is shown that results for the extended alkanes obtained with density functional theory and the hybrid B3LYP exchange correlation functional are in excellent agreement with experiment. At the same level of theory, on the other hand, there are significant discrepancies for the noble gas atoms. The electron correlation contribution to is less than 9% for the alkanes and decreases with the size of the system.

Ab initio potentialenergy surfaces for the and states of the molecular ion
View Description Hide DescriptionMultireference configuration interaction calculations with the ccpVQZ basis set are reported for the potentialenergysurfaces of the and states of Seams of intersection between the states have been characterized and the conical intersection between the and states has been located. Optimized geometries and vertical and adiabatic ionization energies are in good agreement with the available experimental data. The state is strongly bound with an equilibrium geometry very similar to that of groundstate The equilibrium bond angle for the state is 126.4°. The dissociation of this state to is interpreted in terms of an initial increase in bond angle on formation and a transition to the surface at linearity. As the bond angle decreases the intersection with the state is reached and a nonadiabatic transition to this state results in dissociation. It is suggested that the dissociation of the state to occurs via asymmetric stretching followed by a nonadiabatic transition to the dissociativesurface.

Studies on the photodissociation and symmetry of
View Description Hide DescriptionWith the preparing of by multiphoton ionization of the neutral molecules at 380.85 nm, the photodissociation process and the symmetry of the excited states of molecular ions has been investigated by measuring the photofragment excitation (PHOFEX) spectrum in ultraviolet (282–332 nm) and in visible (562–664 nm) wavelength ranges, respectively. The transitions of were assigned in the PHOFEX spectrum in the UV range. By comparing the discernible PHOFEX spectrum in UV range with the continuous PHOFEX spectrum in visible range, it is deduced that (i) around there exists a repulsive state converging to the dissociation limit of (ii) the coupling between and leads to the dissociation to (iii) the symmetry of state is

Photoelectron imaging of carbonyl sulfide cluster anions: Isomer coexistence and competition of excitedstate decay mechanisms
View Description Hide DescriptionWe investigate the structure and decay of cluster ions using photoelectron imaging spectroscopy. The results indicate the coexistence of isomers with and covalently bound cluster cores. A severalfold decrease in the relative abundance of the dimerbased species is observed for and 4 compared to The cluster ions undergo direct photodetachment similar to while exhibits both direct electron detachment and cluster decomposition via ionic fragmentation and autodetachment. The autodetachment originates from either the excited states of the parent cluster or internally excited anionic fragments. It is described using a statistical model of thermionic emission, which assumes rapid thermalization of the excitation energy. A decrease in the relative autodetachment yield in the trimer and tetramer cluster ions, compared to the covalent dimer, is attributed to competition with ionic fragmentation.

On the electronic structure of by allelectron Dirac–Hartree–Fock calculations
View Description Hide DescriptionAllelectron Dirac–Hartree–Fock calculations were performed to investigate the electronic structure of curium fluoride molecules The curium–fluorine distances, atomization energies, and Mulliken populations were all evaluated. The bonding was found to be of ionic type with the electron delocalization primarily from F to Cm where the formal configurations of Cm were for respectively. The – delocalization is significant in the tetrafluoride. For comparison, the isovalent gadolinium fluorides were also studied. exists but does not, reflecting the fact that in is less stable than in

Singlepulse coherent antiStokes Raman spectroscopy in the fingerprint spectral region
View Description Hide DescriptionQuantum coherent control techniques are applied to achieve high spectral resolution nonlinear vibrational spectroscopy using a single ultrashort laser source. By controlling the spectral phase of pulses, we are able to obtain detailed coherent antiStokes Raman (CARS)spectra in the important fingerprint spectral region, which reflects the structural chemical information. A full theoretical analysis and an experimental demonstration of two alternative schemes leading to spectral resolution two orders of magnitude better than the pulse bandwidth are presented. The first involves selective excitation of vibrational levels within the pulse bandwidth by periodic modulation of the spectral phase of the pulse. In the second scheme an effective narrow probing of the vibrational level has been achieved by phase shifting of a narrow spectral band. Singlepulse CARS offers an attractive alternative to conventional multibeam nonlinear vibrational spectroscopy techniques.

A dynamical definition of quasibound molecular clusters
View Description Hide DescriptionMolecular configurations which count as snapshots of a quasibound cluster are identified through a retrospective dynamical definition. The trajectory of a molecular cluster is followed, and a clear evaporation event is considered to have occurred when a molecule moves a very long distance away from the others. The cluster is judged to have broken before this condition is satisfied, however, at the instant that the energy of the departing molecule in the center of mass frame becomes positive. The decay of a cluster is therefore defined dynamically as the production of a molecule with positive energy on a separating trajectory. Not all positive energy molecules created by the system follow such a trajectory, hence the need to examine the subsequent behavior in molecular dynamics. We simulate a sequence of decays by repairing broken clusters as they occur. This approach enables us to calculate mean decay rates of isolated LennardJones clusters in what promises to be a physically realistic fashion.

Theoretical studies of the firstrow transition metal phosphides
View Description Hide DescriptionThe electronic structures and spectroscopic parameters of the ground and some lowlying excited states of the firstrow transition metal phosphides have been calculated with the density functional theory using the Becke threeparameter hybrid exchange functional with the Lee–Yang–Parr correlation functional (B3LYP). The ground states of the transition metal phosphides are found to be (ScP), (TiP), (VP), (CrP), (MnP), (FeP), (CoP), (NiP), and (CuP). The B3LYP functional predicts an increase in covalent character in the bonds between the metal and the phosphorus across the transition metal series. The energies of the lowlying excited states relative to the ground state for TiP, FeP, and CoP have been found to be so small that many lowlying states are possible candidates to be the ground state.

Rydberg–valence interactions in photodissociation: Dependence of absorption probability on ground state vibrational excitation
View Description Hide DescriptionA strong enhancement of absorption to the lowest state is observed for vibrationally excited chloromethyl radicals. It is demonstrated that this enhancement is due to a significant increase in both electronic and vibrational Franck–Condon factors. Electronic structure calculations of potential energy surfaces (PESs) and transition dipole moments for the ground and the two lowest excited states of symmetry, the valence and Rydberg states, reveal the origin of this effect. The shelflike shape of the PES in the Franck–Condon region and the strong dependence of the electronic transition dipole moment on C–Cl distance are responsible for the enhancement. Analysis of the shape of the electron density distribution demonstrates that Rydberg–valence interaction in the two lowest excited states causes the changes in the shape of PESs and transition dipoles with C–Cl distance.

Born–Oppenheimer potential hypersurfaces
View Description Hide DescriptionThe full Born–Oppenheimer potential energy hypersurfaces of the system have been explored by the local spindensity scheme using an analytic potential. Our calculated physical properties, such as dissociation energies and barriers to isomerization, compare well with the available highlevel configuration interaction calculations and experiments at the equilibrium geometry. Despite its simplicity, the analytic potential provides an excellent description of the neutral trimer system for silver and the other transition metals.

Dispersed fluorescence spectroscopy of AlNi, NiAu, and PtCu
View Description Hide DescriptionDispersed fluorescence studies of AlNi, NiAu, and PtCu have been performed, providing spectroscopic information about the ground and lowlying excited electronic states. Vibrational frequencies are reported for the ground state of all three molecules. In the case of AlNi, fluorescence to all five of the states originating from the manifold has been observed. For both NiAu and PtCu, fluorescence to two lowlying excited states in addition to the ground state was observed. Relative energies, vibrational constants, and, when possible, Ω values of these states are reported. Comparisons of the measured electronic states to the predictions of a ligandfield plus spin–orbit model are also provided, along with a comparison of the electronic structure of PtCu to that of PtH.

Density functional and Monte Carlo studies of sulfur. I. Structure and bonding in rings and chains
View Description Hide DescriptionDensity functional calculations have been performed for ring isomers of sulfur with up to 18 atoms, and for chains with up to ten atoms. There are many isomers of both types, and the calculations predict the existence of new forms. Larger rings and chains are very flexible, with numerous local energy minima. Apart from a small, but consistent overestimate in the bond lengths, the results reproduce experimental structures where known. Calculations are also performed on the energy surfaces of rings, on the interaction between a pair of such rings, and the reaction between one ring and the triplet diradical chain. The results for potential energies, vibrational frequencies, and reaction mechanisms in sulfur rings and chains provide essential ingredients for Monte Carlo simulations of the liquid–liquid phase transition. The results of these simulations will be presented in Part II.