Volume 113, Issue 10, 08 September 2000
 ARTICLES

 Theoretical Methods and Algorithms

The meaning of the irreducible memory function in stochastic theories of dynamics with detailed balance
View Description Hide DescriptionWe investigate the relationship between the memory functions that arise in stochastic theories of fluctuations at equilibrium and those appropriate for an underlying microscopic (deterministic) description. We consider the class of stochastic theories that are Markovian with transition rates that satisfy the detailed balance condition. This class includes, for example, Smoluchowski dynamics, kinetic lattice gas models, and kinetic Ising models. When a time autocorrelation function is calculated using stochastic and deterministic descriptions, and the projection operator method of Mori is used, first and second order memory functions arise in both descriptions. We find a close and simple relationship between the first order memory functions of the two descriptions but not for the second order memory functions. Instead, the second order memory function of the microscopic description is simply related to the socalled irreducible memory function of the stochastic description. The latter was introduced for Smoluchowski dynamics by Cichocki and Hess and generalized by Kawasaki. This explains the empirical findings that for stochastic dynamics the irreducible memory function, rather than the second order memory function, has a more fundamental physical interpretation and is more useful for constructing mode coupling theories.

Molecular engineering of push–pull dipolar and quadrupolar molecules for twophoton absorption: A multivalencebond states approach
View Description Hide DescriptionIn the search of organic molecules with large twophoton absorption crosssections, the push–pull dipolar and quadrupolar chromophores have both attracted major attention. In order to provide the basis of molecular engineering and comparison of these two families of molecules, we implement multivalencebond states models based on measurable parameters. The analytical expressions of the resonant twophoton absorption crosssections are derived for both families of molecules. Difference and likeness in a number of features are outlined by comparing the results obtained for these molecular systems. The multivalencebond states models provide useful guidelines for the design of push–pull dipolar and quadrupolar chromophores with enhanced twophoton absorption crosssections.

Proper construction of ab initio global potential surfaces with accurate longrange interactions
View Description Hide DescriptionAn efficient procedure based on the reproducing kernel Hilbert spaceinterpolation method is presented for constructing intermolecular potential energy surfaces (PES) using not only calculated ab initio data but also a priori information on longrange interactions. Explicitly, use of the reciprocal power reproducing kernel on the semiinfinite interval yields a set of exact linear relations between dispersion (multipolar) coefficients and PES data points at finite internuclear separations. Consequently, given a combined set of ab initio data and the values of dispersion (multipolar) coefficients, the potential interpolation problem subject to longrange interaction constraints can be solved to render globally smooth, asymptotically accurate ab initiopotential energy surfaces. Very good results have been obtained for the onedimensional He–He potential curve and the twodimensional Ne–CO PES. The construction of the Ne–CO PES was facilitated by invoking a new reproducing kernel for the angular coordinate based on the optimally stable and shapepreserving Bernstein basis functions.

Convergence of the multipole expansion for electrostatic potentials of finite topological atoms
View Description Hide DescriptionThe exact atomic electrostatic potential (AEP) and atomic multipole moments are calculated using the topological partitioning of the electron density. High rank spherical tensor multipole moments are used to examine the convergence properties of the multipole expansion. We vary independently the maximum multipole rank, and the radius of the spherical grid around an atom in a molecule where we measure the discrepancy between the exact AEP and the one obtained via multipole expansion. The root mean square values are between 0.1 and 1.6 kJ/mol for four atoms (C, N, O, S) on a spherical grid with the a.u. convergence radius and for Our calculations demonstrate that this fast convergence is due to the decay of the electron density. We show that multipole moments generated by finite atoms are adequate for use in the multipole expansion of the electrostatic potential, contrary to some claims made in the literature. Moreover they can be used to model intermolecular and in principle intramolecular interactions as well.

body density functional theory and the generalized hypernettedchain equation
View Description Hide DescriptionThe HNC (hypernettedchain) theory for twobody correlation in fluids is generalized so that up to Mbody correlation functions can be obtained selfconsistently. Our approach is based on the Mbody density functional theory and a generalized Percus idea where maximally particles are held fixed in space, leading to HNC equations for the correlation functions. These are supplemented with Ornstein–Zernike relations to give a closed set of equations. Due to the rather complicated structure of the coupled integral equations, we explicitly present the equations for the case which are compared with the HNC2 equations by Verlet. The theory is numerically solved for the case of a onedimensional liquid.

Can a local mode picture account for vibration–torsion coupling? Ab initio test based on torsional variation of methyl stretching and bending frequencies in methanol
View Description Hide DescriptionThe torsional dependence of the stretching and bending modes of methanol has been explored in terms of a local mode internal coordinate picture [X. Wang and D. S. Perry, J. Chem. Phys. 109, 10795 (1998)]. First, the torsional variations of the smallamplitude vibrational frequencies along the mass weighted intrinsic reaction coordinate from the top to the bottom of the torsional potential barrier were calculated by means of ab initio frequency projection utilizing GAUSSIAN 98. The resulting curves for the three C–H stretch ab initio frequencies as functions of the torsional angle cannot be reproduced by the original local mode model incorporating stretch–torsion and stretch–stretch couplings at lowestorder only, but are wellfitted if the model is extended to include higherorder coupling terms. For the CHbending modes, with internal coordinates chosen to give a high degree of localization, bend–torsion and bend–bend coupling parameters were determined from the ab initio projected frequencies, and were then used to predict torsional tunneling splittings. Just as observed for the C–H stretch modes, the two higherfrequency asymmetric CHbend modes are predicted to have inverted tunneling splittings with reduced amplitudes, while the splitting pattern for the lower frequency symmetricbend mode is predicted to be normal.

Evaluation of twoelectron integrals for explicit theories
View Description Hide DescriptionWe present a practical scheme for the evaluation of nonstandard twoelectron molecular integrals that appear in ab initio theories employing explicitly correlated wave functions with linear terms (“linear methods). In contrast with previous efforts, the target integrals are evaluated recursively via intermediates formulated solely in terms of Cartesian Gaussian functions. All working equations fit conveniently the framework of highly efficient HeadGordon and Pople method of evaluation of electron repulsion integrals. Thus, only straightforward modifications of existing codes that employ HGP or HGP–PRISM scheme are necessary to implement our approach. High potential of the pathway is realized in a robust practical implementation.

Approximate relativistic electronic structure methods based on the quaternion modified Dirac equation
View Description Hide DescriptionNew implementations of the Lévy–Leblond, zerothorder regular approach (ZORA) and spinfree Dirac equation are presented within the framework of the fourcomponent relativistic program system DIRAC. This implementation allows systematic incorporation of relativistic effects at different levels of theory and corresponding computational cost. One of the possibilities of the new code is to neglect the effect of spin–orbit coupling in the orbital optimization process and introduce it in a later stage of the calculation. This method is shown to be unstable despite the boundedness of the spin–orbit operator itself. © 2000 American Institute of Physics.

The relativistic scheme for eliminating small components Hamiltonian: Analysis of approximations
View Description Hide DescriptionThe derivation of the recently proposed onecomponent relativistic Hamiltonian, and the resulting relativistic scheme by eliminating small components (RESC) method of Nakajima and Hirao, are analyzed in terms of the Foldy–Wouthuysen transformation of the Dirac Hamiltonian. This approach reveals the meaning of different approximations used in the derivation of the RESC Hamiltonian and its close relation to approximate relativistic Hamiltonians resulting from the freeparticle Foldy–Wouthuysen transformation. Moreover, the present derivation combined with what is called the classical approximation in Nakajima and Hirao’s approach shows that there is a whole family of the RESCtype Hamiltonians. Some of them, including the original RESC Hamiltonian, are analyzed numerically. It is documented that neither of the RESCtype Hamiltonians offers variational stability. As a consequence the RESC methods may suffer from the variational collapse for heavier systems. On the other hand the energy differences (e.g., ionization potentials) computed within the RESC approach turn out to be close to the values obtained in the Douglas–Kroll scheme.

Simple accurate coupled cluster results for the linear pseudoJahn–Teller effect
View Description Hide DescriptionUsing the coupled cluster method (CCM), we present a simple accurate calculation for the energies of the ground and first excited states of the linear Jahn–Teller and pseudoJahn–Teller Hamiltonians. From the solution of a single transcendental equation, we obtain results with a maximal error of 1.2%. These results are notably better than previous results obtained both via the CCM and other manybody approximations.

Reduced density matrix and combined dynamics of electrons and nuclei
View Description Hide DescriptionNuclear dynamics is incorporated into an efficient density matrix formalism of electronic dynamics which has been applied to molecular systems containing thousands of atoms. The formalism for the combined dynamics of electrons and nuclei is derived from the Dirac–Frenkel variational principle. The single electron reduced density matrices and the Glauber coherent states are used for the electronic and nuclear degrees of freedom, respectively. The new formalism is applicable to simulate the dynamics of large molecular systems. As an illustration of its validity, the formalism is employed to calculate the electron and nuclei dynamics of hydrogen molecules.

Computing forces with quantum Monte Carlo
View Description Hide DescriptionWe present a simple and stable quantum Monte Carlo approach for computing forces between atoms in a molecule. In this approach we propose to use as Monte Carlo estimator of the force the standard Hellmann–Feynman expression (local force expressed as the derivative of the total potential energy with respect to the internuclear coordinates). Invoking a recently introduced zerovariance principle it is shown how the infinite variance associated with the Hellmann–Feynman estimator can be made finite by introducing some suitably renormalized expression for the force. Practical calculations for the molecules LiH, and illustrate the efficiency of the method.

Density functional study of intramolecular ferromagnetic interaction through mphenylene coupling unit (I): UBLYP, UB3LYP, and UHF calculations
View Description Hide DescriptionPolyradicals comprised of mphenylenebridged organic radicals are well known as building blocks of organic ferromagnets, in which radical groups are connected with each other at the meta position in the benzene ring, and the parallelspin configurations between radical sites are more stabilized than the antiparallel ones. Topological rules for spin alignments enable us to design organic highspin dendrimers and polymers with the ferromagneticground states by linking various radical species through an mphenylene unit. However, no systematic ab initio treatment of such spin dendrimers and magnetic polymers has been reported until now, though experimental studies on these materials have been performed extensively in the past ten years. As a first step to examine the possibilities of ferromagnetic dendrimers and polymers constructed of mphenylene units with organic radicals, we report density functional and molecular orbital calculations of six mphenylene biradical units with radical substituents and polycarbenes linked with an mphenylenetype network. The relative stability between the spin states and spin density population are estimated by BLYP or B3LYP and Hartree–Fock calculations in order to clarify their utility for constructions of large spin denderimers and periodic magnetic polymers, which are final targets in this series of papers. It is shown that neutral polyradicals with an mphenylene bridge are predicted as highspin groundstate molecules by the computations, while mphenylenebridged ionradical species formed by doping may have the lowspin ground states if zwitterionic configurations play significant roles to stabilize lowspin states. Ab initio computations also show an important role of conformations of polyradicals for stabilization of their highspin states. The computational results are applied to molecular design of highspin dendrimers and polymers. Implications of them are also discussed in relation to recent experimental results for highspin organic molecules.

An ab initio twocomponent relativistic method including spin–orbit coupling using the regular approximation
View Description Hide DescriptionIn this paper we present the implementation of the twocomponent scaled zerothorder regular approximation (ZORA) method in the molecular electronic structure package GAMESSUK. It is the first application of this method, which was earlier investigated in the context of density functional theory, in molecular ab initio basis set calculations. The performance of the method is tested in atomic calculations, which we can compare with numerical results, on xenon and radon and in molecular calculations on the molecules AgH, HI, AuH, TlH, and In calculations on the molecule we investigated the effect of the different approaches regarding the internal Coulomb matrix used in the ZORA method. For the remaining molecules we computed harmonic frequencies and bond lengths. It is shown that the scaled ZORA approach is a costeffective alternative to the Dirac–Fock method.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Theoretical study of kinetic isotope effects on rate constants for the reaction and its isotopic variants
View Description Hide DescriptionThermal rate constants have been calculated for the reaction (1) and its isotopic variants: (2); (3); (4); (5) using variational transition state theory with the multidimensional semiclassical tunneling correction. The geometries were optimized at the MP2(full)/ccpVTZ level and the potential energy curves for these reactions were calculated at the PMP4(SDTQ,full)/ccpVTZ and QCISD(T,full)/ccpVTZ levels. It was thus revealed that these reactions have “early” potential barriers. The calculated rate constants for reactions (1) and (5) were found to be comparable and the largest among these reactions. The calculated rate constants for reactions (1) and (4) showed good agreement with experiment at relatively low temperatures. The reactionpathcurvature effects and secondary kinetic isotope effects [the effects of change in zeropoint energies (ZPEs) along the reaction path relative to the reactant ZPEs] were predicted not to be so large in these reactions. Rather, the primary isotope effects (the effects of change in the effective mass for the reaction coordinate) were found to be the main contributions to tunneling. This is because these reactions have “early” characters.

Time and frequencyresolved spontaneous emission: Theory and application to the conical intersection
View Description Hide DescriptionWe present a theoretical scheme for the calculation of time and frequencyresolved spontaneous emissionspectra of nonstationary states prepared by a laser pulse, considering explicitly the effect of the frequency filter and the time gate of the measurement instrument. Our scheme treats in a perturbative manner the matterradiation interaction taking into account the states radiative lifetimes, and utilize the eigenstates of the molecular Hamiltonian up to the maximum excitation energy. We study the fluorescence of a nonstationary state of created by a Gaussian pulse mainly on the excited adiabatic potential, following an absorption from the ground adiabatic electronic state We analyze the conical intersection effects on the spectra and dynamics in a (excited) diabatic electronic representation. We have pointed out that the wave packet emits more strongly at times corresponding to partial recurrences, i.e., when it returns to the region of space where it was initially, and that the whole spectrum is redshifted. The nonadiabatic interactions between the electronic states bring the wave packet from the bright state to the quasidark one, and thus they quench the oscillations of the total emitted energy. Moreover, they cause the broadening of the part of the wave packet that remains on the upper diabatic surface, and this results in a further quenching of the emission. On the contrary, the nonadiabatic interactions have a negligible effects on the times at which the emission peaks occur. The striking effect of the duration of the interval in which the timegate is opened on the time and frequencyresolved emission is investigated and discussed.

Electronic properties of small neutral and charged beryllium clusters
View Description Hide DescriptionWe determine the atomic and electronic structures for neutral and singly positively chargedberyllium clusters containing from two to six atoms using density functional theory in the local spin density approximation. Ions are moved with a steepest descent method and the electronic wave functions optimized using a fictitious dynamics with simulated annealing, as conceived by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. Shelllike orbitals, filling angular momentum states in the order: are obtained. We employ a Mulliken population analysis using an atomic basis to examine how the shell orbitals arise from atomic orbitals. This analysis also allows us to associate the electron density distribution and, in the case of a charged cluster, the distribution of the hole with atomic sites and with regions of overlap between atom pairs. We show quantitatively that the contribution to the bonding density from delocalization of the state is hampered by the appearance of the antibonding state. In the case of charged clusters we observe the tendency of the hole to distribute itself near the most exterior atomic sites in geometries of high symmetry.

Experimental studies of the vapor phase nucleation of refractory compounds. V. The condensation of lithium
View Description Hide DescriptionLithiumnucleation was studied over the range of 830–1100 K in a gas evaporation apparatus yielding supersaturation ratios of approximately 300 to 7 over this temperature range, respectively, at an estimated flux of cm^{−3} s^{−1}. During runs we observed the same fluorescence phenomena due to atomic lithium vapor and the lithium dimer as noted by other researchers. The measured supersaturations are much higher than the values predicted by Classical Nucleation Theory. Modifications to Classical Nucleation Theory to account for the presence of dimers in the lithium vapor do not seem to account for this discrepancy. The data and Scaled Nucleation Theory agree fairly well at the lower temperature range, but at the higher end of the temperature range the data have a steeper drop in the supersaturation values than predicted by Scaled Nucleation Theory.

Thermochemistry of gas phase reactions: A density functional theory study
View Description Hide DescriptionEnthalpies of formation and enthalpies of reaction at 298 K for a set of fluorocarbon species derived from the pyrolysis of hexafluoropropylene oxide (HFPO) were computed using the B3LYP (Becke threeparameter Lee–Yang–Parr) density functional theory. Total energies were calculated at the level. Zeropoint energies and thermal corrections were calculated using vibrational frequencies scaled by a factor of 0.96. The average absolute deviation of enthalpies of formation and reaction were 2.33 and 1.42 kcal/mol, respectively. The pyrolysis of HFPO to produce difluorocarbene, and trifluoroacetyl fluoride, was predicted to be endothermic at 23.6 kcal/mol. The singlet state of was predicted to be more stable than its triplet state by 52.4 kcal/mol. polymerization through the addition of a singlet to an existing unterminated chain was calculated to be more favorable than through the addition of a singlet to an existing perfluoroalkene molecule. For the former pathway, a linear relationship was found between the enthalpy of formation of the chains and the number of chain carbons (n) for The reactionenthalpy for each successive extension was found to be −48.7 kcal/mol, and the carbon–carbon bond dissociation energy was found to be 75.5 kcal/mol. For the latter pathway, the stability of hindered chain polymerization but provided theoretical support to as a primary product in HFPO pyrolysis experiments.

Mass analyzed threshold ionization of the and isotopomers of pchloroaniline
View Description Hide DescriptionOnecolor, twocolor resonant twophotonionization (R2PI), and mass analyzed threshold ionization (MATI) spectroscopic methods have been used to study the electronic transition and the threshold ionization of the and isotopomers of pchloroaniline. The band origins of the electronic transitions of both species are found to be The ionization energies (IEs) of both isotopomers of pchloroaniline are determined to be by the twocolor R2PI spectroscopy and by the MATI spectroscopy.Analyses on the spectral features show that most of the active modes are related to the inplane ring vibrations in the state and cationic ground state. Isotope effect on the ring deformation vibrations 1, 6a, and 12 gives rise to a frequency shift of 1–3 cm^{−1} in the state and 3–9 cm^{−1} in the ion state. The experimental results are well supported by the computed ones on the basis of ab initio and density functional theory calculations.