Volume 114, Issue 15, 15 April 2001
 COMMUNICATIONS


Gas phase ligand field photofragmentation spectroscopy
View Description Hide DescriptionLigand field spectra have been recorded in the gas phase for the two complexes and Both spectra compare favorably with analogous condensed phase measurements; however, for the results differ in interpretation. The Ag(II) data are attributed to a ligandtometal charge transfer process, and the Cu(II) data (spectral region and extinction coefficient) match the characteristics of a d–d transition.

Crystal lattice transition of behenic acid monolayer on pure water surface observed by polarization modulation infrared spectroscopy
View Description Hide DescriptionThe crystal lattice of (behenic acid)monolayer on pure water subphase was investigated in situ by polarization modulation infrared reflection absorption spectroscopy. Two kinds of centered rectangular unit cells were found: rectangular parallel and orthorhombic packing of the trans zigzag planar––chain. In the former cell the chain was tilted on the water surface and the C–C–C plane at the rectangle center was parallel to that at the corner. In the latter cell the chain was normal to the water surface and the C–C–C plane at the rectangle center was perpendicular to that at the corner. A rectangular paralleltoorthorhombic transition was discovered for two kinks from 0.260 to 0.220 along the surface pressurearea isotherm at 283 K, evidenced by splitting of the scissoring mode. By holding the barrier at 0.240 and cyclically varying the monolayer temperature, a partially reversible transition from rectangular parallel to orthorhombic unit cells was observed.
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 ARTICLES

 Theoretical Methods and Algorithms

A transversing connection between density functionals
View Description Hide DescriptionWe identified a transversing physical connection between kinetic, exchange, and correlation functionals by using parameterfree (Pfree) exchange and oneparameter progressive (OP) correlation. On the basis of this connection, we investigated how the calculated energies and chemical properties depend on the shape of the functional in the Kohn–Sham scheme. We found that the fundamental conditions of the functionals are connected through Pfree and OP functionals with the exception of a rapidly varying density limit. We also found that the calculated properties are highly affected by the exchange functional shape in particular regions of

On the determination of orientational configurational temperature from computer simulation
View Description Hide DescriptionA straightforward derivation for the configurational temperature associated with the orientational portion of the configurational phase space of the molecules in an open system is presented. Explicit relationships are given for determining the configurational temperatures in classical simulations of molecular liquids, such as water, and their forms and their evaluation discussed.

On the concept of temperature for a small isolated system
View Description Hide DescriptionThe microcanonical temperature is shown to be a useful concept in calculations of the decay of a small isolated system with well defined energy. A simpler and more transparent description is obtained than in Klots’ formulation of finiteheatbath theory, where the system is represented by a canonical ensemble. As a further illustration of the utility of the microcanonical temperature concept, we discuss a formula derived by Dunbar for the probabilities for excitation of a single oscillator in a collection of harmonic oscillators with well defined total energy. This formula expresses the excitation probabilities in terms of the temperature for a canonical ensemble with mean energy equal to the energy of the system. However, a much improved accuracy is obtained if the canonical temperature and heat capacity are replaced by their microcanonical values. We justify this replacement through a modified derivation, in which the microcanonical temperature appears as the canonical temperature of a fictitious system with level density the derivative of the level density of the collection of oscillators.

A new computational scheme for the Dirac–Hartree–Fock method employing an efficient integral algorithm
View Description Hide DescriptionA highly efficient computational scheme for fourcomponent relativistic ab initio molecular orbital (MO) calculations over generally contracted spherical harmonic Gaussiantype spinors (GTSs) is presented. Benchmark calculations for the ground states of the group IB hydrides, MH, and dimers, Ag, and Au), by the Dirac–Hartree–Fock (DHF) method were performed with a new fourcomponent relativistic ab initio MO program package oriented toward contracted GTSs. The relativistic electron repulsion integrals (ERIs), the major bottleneck in routine DHF calculations, are calculated efficiently employing the fast ERI routine SPHERICA, exploiting the general contraction scheme, and the accompanying coordinate expansion method developed by Ishida. Illustrative calculations clearly show the efficiency of our computational scheme.

Atom–atom partitioning of intramolecular and intermolecular Coulomb energy
View Description Hide DescriptionAn atom–atom partitioning of the (super)molecular Coulomb energy is proposed on the basis of the topological partitioning of the electron density. Atom–atom contributions to the molecular intra and intermolecular Coulomb energy are computed exactly, i.e., via a double integration over atomic basins, and by means of the spherical tensor multipole expansion, up to rank The convergence of the multipole expansion is able to reproduce the exact interaction energy with an accuracy of 0.1–2.3 kJ/mol at for atom pairs, each atom belonging to a different molecule constituting a van der Waals complex, and for nonbonded atom–atom interactions in single molecules. The atom–atom contributions do not show a significant basis set dependence (3%) provided electron correlation and polarization basis functions are included. The proposed atom–atom Coulomb interaction energy can be used both with postHartree–Fock wave functions and experimental charge densities in principle. The Coulomb interaction energy between two molecules in a van der Waals complex can be computed by summing the additive atom–atom contributions between the molecules. Our method is able to extract from the supermoleculewave function an estimate of the molecular interaction energy in a complex, without invoking the reference state of free noninteracting molecules. We provide computational details of this method and apply it to butane; 1,3,5hexatriene; acrolein and urocanic acid, thereby covering a cross section of hydrogen bonds, and covalent bonds with and without charge transfer.

The accurate determination of molecular equilibrium structures
View Description Hide DescriptionEquilibrium structures have been determined for 19 molecules using leastsquares fits involving rotational constants from experiment and vibrational corrections from highlevel electronicstructure calculations. Equilibrium structures obtained by this procedure have a uniformly high quality. Indeed, the accuracy of the results reported here likely surpasses that reported in most experimental determinations. In addition, the accuracy of equilibrium structures obtained by energy minimization has been calibrated for the following standard models of ab initio theory: Hartree–Fock, MP2, CCSD, and CCSD(T). In accordance with previous observations, CCSD(T) is significantly more accurate than the other models; the mean and maximum absolute errors for bond distances of the 19 molecules are 0.09 and 0.59 pm, respectively, in CCSD(T)/ccpCVQZ calculations. The maximum error is obtained for in and is so large compared with the mean absolute error that an experimental reinvestigation of this molecule is warranted.

An assumptionviolating application of the Lawrance–Knight deconvolution procedure: A retrieval of electronic coupling mechanisms underlying complex spectra
View Description Hide DescriptionThe Lawrance–Knight (L–K) deconvolution method is a spectral inversion scheme which allows one to relate an absorption or a fluorescencespectrum to the energies and couplings of the zeroorder states via analytical expressions. In order to obtain accurate results, the L–K method can only be applied to spectra that arise from one precisely defined zeroorder picture. Namely, a single bright state must be coupled directly to a background of noninteractingdark states, the “direct coupling model.” In most situations, the zeroorder picture that gives rise to a particular absorption or a fluorescencespectrum is not known a priori. Nonetheless, it is typically assumed that the zeroorder circumstances governing the spectral intensities are as described above, and the L–K method has been applied indiscriminantly to the spectra of a variety of systems such as pyrazine, acetylene, and naphthalene to extract zeroorder parameters. We show here that if the L–K algorithm is applied to spectra where the underlying zeroorder picture departs from the direct coupling limit, the resulting output has characteristic qualitative and quantitative features that reflect this situation. By applying the L–K method to a series of simulated spectra, we recover from a pattern of patterns new information about the couplings among the dark states. We have specifically considered the alternative picture of a single bright state coupled to a background of noninteracting states by a doorwaymediated mechanism. We demonstrate here that the L–K algorithm can be employed to distinguish between the contrasting doorwaymediated and direct coupling schemes, and also to obtain coupling matrix elements.

Phase space optimization of quantum representations: Threebody systems and the bound states of HCO
View Description Hide DescriptionIn an earlier paper [J. Chem. Phys. 111, 4869 (1999)] we introduced a quasiclassical phase space approach for generating a nearly optimal directproduct basis for representing an arbitrary quantum Hamiltonian within a given energy range of interest. From a few reduceddimensional integrals, the method determines the optimal onedimensional marginal Hamiltonians, whose eigenstates comprise the directproduct basis. In this paper the method is applied to threebody vibrational systems expressed in radial and angular coordinates. Numerical results are obtained for the bound state eigenenergies of the nonrotating HCO molecule, determined to ∼0.01 cm^{−1} accuracy using a phase space optimized directproduct basis of 1972 functions. This represents a computational reduction of several orders of magnitude, in comparison with previous calculations.

Efficient evaluation of the Coulomb force in densityfunctional theory calculations
View Description Hide DescriptionThe Coulomb force in densityfunctional theory calculations is efficiently evaluated based on a partitioning into nearfield (NF) and farfield (FF) interactions. For the NF contributions, a J force engine method is developed based on our previous J matrix engine methods, and offers a significant speedup over derivative electron repulsion integral evaluation, without any approximation. In test calculations on water clusters and linear alkanes, the computer time for the NF force is reduced by a factor of 5–7 with a 321G basis set and 6–8 with a 631G^{*} ^{*} basis set. The FF force is treated by a generalization of the continuous fast multipole method, and the FF computational cost is found to be comparable to that of an energy evaluation.

Multigrid methods for classical molecular dynamics simulations of biomolecules
View Description Hide DescriptionWe present an multigridbased method for the efficient calculation of the longrange electrostatic forces needed for biomolecular simulations, that is suitable for implementation on massively parallel architectures. Along general lines, the method consists of: (i) a charge assignment scheme, which both interpolates and smoothly assigns the charges onto a grid; (ii) the solution of Poisson’s equation on the grid via multigrid methods; and (iii) the back interpolation of the forces and energy from the grid to the particle space. Careful approaches for the charge assignment and the force interpolation, and a Hermitian approximation of Poisson’s equation on the grid allow for the generation of the highaccuracy solutions required for highquality molecular dynamics simulations. Parallel versions of the method scale linearly with the number of particles for a fixed number of processors, and with the number of processors, for a fixed number of particles.

A harmonic adiabatic approximation to calculate highly excited vibrational levels of “floppy molecules”
View Description Hide DescriptionThe harmonic adiabatic approximation (HADA), an efficient and accurate quantum method to calculate highly excited vibrational levels of molecular systems, is presented. It is wellsuited to applications to “floppy molecules” with a rather large number of atoms A clever choice of internal coordinates naturally suggests their separation into active, slow, or large amplitude coordinates and inactive, fast, or small amplitude coordinates which leads to an adiabatic (or Born–Oppenheimertype) approximation (ADA), i.e., the total wave function is expressed as a product of active and inactive total wave functions. However, within the framework of the ADA, potential energy data concerning the inactive coordinates are required. To reduce this need, a minimum energy domain (MED) is defined by minimizing the potential energy surface (PES) for each value of the active variables and a quadratic or harmonic expansion of the PES, based on the MED, is used (MED harmonic potential). In other words, the overall picture is that of a harmonic valley about the MED. In the case of only one active variable, we have a minimum energy path (MEP) and a MEP harmonic potential. The combination of the MED harmonic potential and the adiabatic approximation (harmonic adiabatic approximation: HADA) greatly reduces the size of the numerical computations, so that rather large molecules can be studied. In the present article however, the HADA is applied to our benchmark molecule HCN/CNH, to test the validity of the method. Thus, the HADA vibrational energy levels are compared and are in excellent agreement with the ADA calculations (adiabatic approximation with the full PES) of Light and Bačić [J. Chem. Phys. 87, 4008 (1987)]. Furthermore, the exact harmonic results (exact calculations without the adiabatic approximation but with the MEP harmonic potential) are compared to the exact calculations (without any sort of approximation). In addition, we compare the densities of the bending motion during the HCN/CNH isomerization, computed with the HADA and the exact wave function.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Vector correlations in dissociative photoionization of in the 20–28 eV range. I. Electronion kinetic energy correlations
View Description Hide DescriptionImaging and time resolved coincidence techniques are combined to determine ionelectron velocity vector correlations in dissociativephotoionization (DPI) of the molecule induced by linearly polarized synchrotron radiation (P). The ionelectron kinetic energycorrelations identify each DPI process by its reaction pathway, intermediate molecular state and dissociation limit. The 4π collection of ions and electrons provides their branching ratios. Up to 12 DPI processes are identified in the 20–28 eV range. Photoionization into the in the Franck–Condon (FC) region populating the limit is the dominant process. In the 22.3–24 eV region excitation of the Rydberg series, followed by dissociation and atomic autoionization to the limit reaches about 10% of the DPI flux. A new DPI process is identified in the same energy range, which populates the limit. At higher energies the relative weight of the four distinct processes which correspond to ionization into the and states in the FC region and population of distinct excited limits is evaluated. The spatial analysis of the vector correlation for selected processes will be discussed in a companion paper.

Multiphoton ionization and photoelectron spectroscopy of 1,3transbutadiene via its Rydberg state
View Description Hide DescriptionResonanceenhanced multiphoton ionization (REMPI) and photoelectron spectroscopy (PES), have been used to study the Rydberg state of 1,3transbutadiene in the two photon energy range from 61 000 to 66 400 cm^{−1}. The spectrum is dominated by the and vibrational modes, with some excitation of the mode, as well. Photoelectron spectroscopy shows that the dominant ionization pathways are diagonal, i.e., they produce cations in the same vibrational level that was populated in the Rydberg state. Weaker offdiagonal ionization is also observed, with excitation of the and modes. The relative intensities of diagonal and offdiagonal PES bands are observed to be strongly dependent on the angle between the laser polarization and the detection axis. It is possible to use REMPI to generate stateselected cations, however, the nascent ions are quite efficiently photodissociated by the REMPI laser.

Statespecific reactions at low collisional energies
View Description Hide DescriptionStatespecific ionmolecule reactions of Hatom transfer between the HBr and molecules with were studied in a free jet flow reactor. The selected spinorbit and vibrational states of the ion were prepared by resonanceenhancedmultiphoton ionization. All of the reactant and product ions were monitored using a timeofflightmass spectrometer. Rate coefficients of the reaction vary from for the lowest spinorbitvibrational state to for the highest. Rates for the reaction are independent of the internal state of the ion.

Resonance Raman spectroscopy in the dissociative A band of nitrosyl chloride
View Description Hide DescriptionResonance Raman spectra measured for ClNO photoexcited at 212.5, 219, and 222 nm produce evidence that the strong transition at the vacuum ultraviolet end of the merged A band system dominates to wavelengths as long as 222 nm. The spectral resolution is sufficient to enable definitive assignments of excited vibrational levels in the ground electronic state, several of which have not been previously observed. A curvilinear coordinate model of the ground statepotential surface around the Franck–Condon region has been constructed. This model yields vibrational eigenvalues in excellent agreement with all known transitions.

Quantum dressed classical mechanics
View Description Hide DescriptionWe have formulated a new way of making quantum corrections to classical mechanics. The method is based on a timedependent discrete variable representation (DVR) of the wave function with grid points defined by the Hermite part of a basis set, the Gauss–Hermite basis set. The formulation introduces a set of grid points which follow the classical trajectory in space. With enough trajectories (DVRpoints) the method approaches the exact quantum formulation. With just a single grid point in each dimension, we recover classical mechanics.

Rotationalstate and velocitysubgroup dependence of the rotational alignment of drifted in
View Description Hide DescriptionExperimental results are presented for the rotational alignment of as a function of both rotational state and component Doppler velocity. A singlefrequency ring dye laser is used to probe the alignment of drifted in helium in a flowdrift apparatus by the technique of polarized laserinduced fluorescence. The collisioninduced quadrupole rotational alignment parameter is determined as a function of the field direction component of subDoppler laboratory velocity at a fixed field strength of 12 Td for five rotational states. A dramatic difference in velocityselected alignment as a function of rotational state is observed, with the higher rotational states exhibiting a greater degree of alignment than the lower rotational states. Additionally, for sufficiently low rotational state changes sign across the Doppler profile, a behavior that has not previously been reported in the literature. A companion theoretical paper presents molecular dynamics calculations that are in excellent agreement with these experimental observations.

Molecular dynamics study of the collisioninduced rotational alignment of drifting in helium
View Description Hide DescriptionThe full velocityangular momentum distribution function for gasphase drifting in helium is calculated using a molecular dynamics method, and utilized to examine collisioninduced rotational alignment in detail. These results are also compared with experimental measurements, most especially those of Anthony et al. [J. Chem. Phys. 112, 10269 (2000)] and those appearing in the preceding article [Anthony et al., J. Chem. Phys. 114, 6654 (2001)]. Both the calculations and experiments show a number of interesting features including, drift velocities which depend upon rotational state, and quadrupolar alignment parameters which change from negative at high velocities to positive at low velocities.