Volume 113, Issue 15, 15 October 2000
 ARTICLES

 Theoretical Methods and Algorithms

The role of the localmultiplicative Kohn–Sham potential on the description of occupied and unoccupied orbitals
View Description Hide DescriptionThe optimum localmultiplicative exchange potential was found using as input the Hartree–Fock electron density, for the molecular systems: LiH, HF, CO, and The Zhao and Parr method was used to obtain the localmultiplicative potential where the kinetic energy is minimized using a constrainedsearch formulation of density functional theory. Two orbital sets were compared, those obtained with the nonlocal Hartree–Fock potential and those obtained with the localmultiplicative potential, both sets yielding the same electron density. As expected, the highest occupied molecular orbital (HOMO) energy was similar in both orbital sets. In contrast, the virtual orbital energies, and in particular the lowest unoccupied molecular orbital (LUMO), exhibited considerable differences. The Hartree–Fock LUMO energy goes to zero in a complete basis set limit and to nearly zero with reasonably large basis sets (e.g., augmented triple zeta) with sufficient diffuse functions added. The LUMO provided by the localmultiplicative potential using the same large basis set goes to a bounded energy not equal to zero. The nonlocal Hartree–Fock potential generates a large gap between the HOMO and LUMO energies; this difference is equal to the negative of the HOMO energy at the complete basis set limit. Contrary to this behavior, the gap obtained with the localmultiplicative potential is a reasonable approximation to the lowest experimental vertical excitation energy. For some of the molecules tested, the ordering of the orbitals corresponding to the HF and localmultiplicative potential are different.

Linear scaling density matrix search based on sign matrices
View Description Hide DescriptionThis paper presents a new approach to the linear scaling evaluation of density matrices in electronic structuretheory. The new approach is based on the iterative computation of a special matrix function, the sign of the matrix and its performance is compared to that of some other methods developed for similar purpose. One particular variant of the sign approach turned out to be very competitive with other linear scaling density matrix evaluation algorithms, in terms of computational time and accuracy. It is also shown that a special damping technique greatly improves the stability of selfconsistent field (SCF) calculations when using density matrix purification and sign methods.

Multidimensional replicaexchange method for freeenergy calculations
View Description Hide DescriptionWe have developed a new simulation algorithm for freeenergy calculations. The method is a multidimensional extension of the replicaexchange method. While pairs of replicas with different temperatures are exchanged during the simulation in the original replicaexchange method, pairs of replicas with different temperatures and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calculations of free energy in a wide temperature range from a single simulation run, using the weighted histogram analysis method.

Spincontamination of coupledcluster wave functions
View Description Hide DescriptionThe propensity of approximate solutions of the electronic Schrödinger equation to break spinsymmetry is directly related to the quality of the approximate wave function, and thus can be used as a diagnostic tool. The quasivariational nature of the (valence) optimized orbitals coupledcluster doubles methods, (V)OOCCD, enables a discussion of the stability of coupledclusterwave functions in terms of both spincontamination and a corresponding energy lowering relative to the pure spin solutions. The spincontamination of (V)OOCCD models has been studied for bondbreaking processes and diradicals. The main findings are: (i) The OOCCD method is stable for a relatively large range of nuclear distortions and is capable of eliminating even very large spincontamination of the unrestricted Hartree–Fock solution given that the molecular electronic configuration remains essentially singlereference. When a spincontaminated solution arises, the energy splitting rapidly becomes large and approaches the Hartree–Fock value; (ii) The VOOCCD method, which is designed to approximate a multireference model, remains stable over broader ranges; however, for pure diradicals it becomes unstable. In these cases, spincontamination is also very large, but the energy lowering for the spinunrestricted solutions is negligible; (iii) Higher order corrections described by perturbation theory lead to smaller energy splittings between restricted and unrestricted (V)OOCCD energies. However, in case of spincontaminated (V)OOCCD solutions, these corrections may lead to unphysical shapes of the potential energy surfaces. Thus, in order to quantitatively characterize the quality of the wave functions, both spincontamination and energy lowering due to the breaking of spinsymmetry must be considered.

Algebraic forcefield Hamiltonian expansion approach to linear polyatomic molecules
View Description Hide DescriptionThe algebraic forcefield Hamiltonian expansion recently proposed for vibrations of bent triatomic molecules [T. Sako, K. Yamanouchi, and F. Iachello, Chem. Phys. Lett. 299, 35 (1999)] is extended to linear polyatomic molecules by introducing operators constructed from the unitary algebra U(3). A comparison with the conventional forcefield method is made by fitting the experimental vibrationallevel energies of The results show that the algebraic Hamiltonian in local coordinates reproduces the levelenergies with a smaller rootmeansquare deviation and much faster convergence.

Theory of solutions in the energetic representation. I. Formulation
View Description Hide DescriptionThe energetic representation of the molecular configuration in a dilute solution is introduced to express the solvent distribution around the solute over a onedimensional coordinate specifying the solute–solvent interaction energy. In this representation, the correspondence is shown to be onetoone between the set of solute–solvent interaction potentials and the set of solventdistribution functions around the solute. On the basis of the onetoone correspondence, the Percus–Yevick and hypernettedchain integral equations are formulated over the energetic coordinate through the method of functional expansion. It is then found that the Percus–Yevick, hypernettedchain, and superposition approximations in the energetic representation determine the solventdistribution functions correctly to firstorder with respect to the solute–solvent interaction potential and to the solvent density. The expressions for the chemical potential of the solute are also presented in closed form under these approximations and are shown to be exact to secondorder in the solute–solvent interaction potential and in the solvent density.

Ab initio group model potentials including electron correlation effects
View Description Hide DescriptionA method for determination of ab initio group model potentials, with the intention of describing the effects of a whole molecule or a chemical group within a density functional theory framework, is reported. The oneelectron part of the Kohn–Sham equations is modified by incorporation of a Coulomb operator, which accounts for the classical electron interaction arising from the group. Exchange and correlation effects are introduced by a suitable modification of the exchangecorrelation functionals. The strong orthogonality condition, usually required by the theory of separability of many electron systems, is written in terms of first order reduced density matrices. In order to check the method a group model potential for (environment) was obtained and employed in the calculation of and complexes using several functionals. Equilibrium intergroup distances and binding energies are compared with allelectron calculations.

NonHermitian formulation of interference effect in scattering experiments
View Description Hide DescriptionNonHermitian quantum mechanics allows one to calculate a physical observable, e.g., scattering cross section, as a sum over a finite number of discrete resonance states. The coefficients in the sum can get complex and negative values even in cases where conventional scattering theory predicts real positive coefficients only. Consequently, structure (or absence of structure) in scattering cross section can be obtained as a result of interference between a small number of discrete resonance states; whereas, conventional scattering theory would require integration over the continuum of scattering states and therefore it is a heavy numerical task. We show here that in electron scattering experiments the interference between overlapping broad resonances leads to oscillations in the phase of transition probability amplitude and to enhancement of the transition state lifetime due to nuclear motion.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

From small to large behavior: The transition from the aromatic to the Peierls regime in carbon rings
View Description Hide DescriptionResults of local density approximation(LDA) and Hartree–Fock (HF) calculations for even numbered monocyclic rings are reported. Small rings satisfying show aromatic stability with equal bondlength structures, whereas rings of size show antiaromatic destabilization with bondlength alternation. For large rings a transition, the Peierls transition, from aromatic and antiaromatic to nonaromatic behavior, takes place. Above the Peierls transition, both and rings show bondlength alternation and no differences in stability. The critical size for the transition to nonaromatic behavior depends on the electronphonon coupling strength and therefore depends on the choice of ab initio method. HF predicts nonaromatic behavior for ring sizes and above. Fully optimized LDA results are presented up to which still has a cumulenic structure. Calculations based on periodic infinite ring systems show that within LDA the onset of nonaromatic behavior does not occur until Experimental results suggest that aromatic behavior exists in these ring systems to at least The force constant for inplane angle bending may also be estimated from these calculations and was found to be 0.022 kcal mol^{−1} deg^{−2} per atom, not a strong function of size beyond and in good agreement with experimental estimates.

Photodissociation of at 193 nm by translational spectroscopy
View Description Hide DescriptionThe photodissociation of at 193 nm has been studied by product translational spectroscopy. Results show that the molecule undergoes competing dissociation into three pairs of products: (1) (2) and (3) with a relative yield of 1.0:∼0.1:1.4. When photolyzed with polarized laser light, reactions (1) and (3) were detected with fragments recoiling anisotropically, indicating that dissociation occurs primarily on the excited potential energy surface. From the maximum kinetic energy derived for reactions (2) and (3), a upper limit of 110 and 90 kcal/mol was determined for the C–F bond and the C–Cl bond dissociation energy, respectively. In addition to these primary dissociation channels, we have observed the secondary products, and from the primary fragment by absorbing an additional photon.

Applying diatomic in molecules in excited electronic state calculations for flexible polyatomic molecules. The molecule
View Description Hide DescriptionIn this paper we calculate the 64 potential energy surfaces of the manifold of states of that dissociate to three ground state iodine radicals as functions of bend and stretching coordinates. We describe the set of quantum rotations necessary to generate the full Hamiltonian matrix using only experimental energies and describe the formal connection between this approach and the usual diatomic in molecules Hamiltonian formulation. The excited statesurfaces calculated in this way are used to compute various excited state features in the photoelectron spectrum of and we use these results to interpret the recently measured spectrum.

Ab initio investigations of
View Description Hide DescriptionAb initio investigations at the coupledcluster single double (triple) [CCSD(T)] and MRCISD level with augmented triple and quadruple zeta basis sets have identified various stationary points on the hypersurfaces. The electrostatic complexes, are very weakly bound with respect to loss) and interactions play a contributing role in determining the equilibrium structures within the electrostatic constraint of a linear or nearlinear orientation. The covalent molecular ion, is found to have a linear centrosymmetric structure and to be bound with respect to in agreement with previous calculations. The interaction of with additional is purely electrostatic but with a larger than those of the complexes. is found to have a linear equilibrium structure and is found to have two almost isoenergetic structures: linear with an on either end of the and with both on the same end of the Of particular interest is the dramatic change in the nature of the transition state for production depending on the number of molecules present. For the reaction proceeds through a conical intersection between the lowest energy and electronic surfaces in symmetry. For the reaction occurs on a single surface in a pericyclic mechanism through a transition state consisting of a planar fivemember ring where simultaneously two bonds are broken while two LiH bonds and one new bond are formed. For the reaction proceeds by direct insertion of into one of the molecules with the two additional molecules providing substantial stabilization of the transition state by taking on part of the negative charge in a weakly covalent interaction. The results are discussed in comparison to the isoelectronic systems where significant sigma bond activation through a cooperative interaction mechanism has been identified recently.

Controlling molecular alignment rephasing through interference of Ramaninduced rotational coherence
View Description Hide DescriptionQuantum control over molecular alignment rephasing is experimentally investigated in gaseous The control process is achieved by illuminating the medium with a pair of pumppulses separated in time by approximately an integer value of where is the rotational constant. Through a Ramantype process, each pulse alone produces rotational coherence leading to a periodic orientational anisotropy. It is the combination of the two pulses that yields to quantum interference, resulting in a modification of this anisotropy probed by a third delayed pulse. The effect is accurately analyzed for different time delays between the two pulses. A theoretical analysis supplies a clear understanding of the role played by the different rotational motions involved in the overall process. The relative orientation of the electric field vector for the two pulses is discussed in terms of an additional control parameter.

A molecular orbital study on H and elimination pathways from methane, ethane, and propane
View Description Hide DescriptionDecomposition pathways for propane, as well as methane and ethane for comparison, in its ground electronic state were studied using density functional and high accuracy ab initio calculations. The reaction pathways were characterized by locating the transition states and following the intrinsic reaction coordinate. Atomic hydrogen as well as molecular hydrogen elimination pathways were investigated, including three deuterated propane species for comparison with experiment. The methyl and ethyl groups in propane are found to stabilize transition states and radical/biradical intermediates along the reaction pathways. For propane, 2,2elimination of an hydrogen molecule is found to be the dominant molecular elimination pathway, in agreement with recent photochemical experiments. We find 1,1elimination to be the next important molecular elimination pathway, followed by 1,2elimination, which disagrees with the experimental result favoring 1,2 over 1,1elimination.

Direct ab initio dynamics studies of reaction
View Description Hide DescriptionKinetics of the reaction have been studied using a direct ab initio dynamics method. Potential energy surface for low electronic states have been explored at the QCISD/ccpVDZ level of theory. We found the groundstatereaction is Thermal rate constants for this reaction were calculated using the microcanonical variational transition state theory.Reaction path information was calculated at the QCISD/ccpVDZ level of theory. Energies along the minimum energy path (MEP) were then refined at the QCISD(TQ)/ccpVTZ level of theory. The forward and reverse barriers of the groundstatereaction are predicted to be 29.60 and 0.53 kcal/mol, respectively. The calculated rate constants for both forward and reverse reactions are in good agreement with available experimental data. They can be expressed as for the forward reaction and for the reverse reaction in the temperature range 400–2500 K.

Positron and positronium chemistry by quantum Monte Carlo. V. The ground state potential energy curve of
View Description Hide DescriptionThe potential energy curve of has been computed by means of diffusion Monte Carlo using explicitly correlated trial wave functions. This curve allows us to compute the adiabatic total and binding energies and the vibrational spectrum of and the adiabatic positron affinity of LiH. Using these results, we discuss the possibility to detect spectroscopically in the gas phase, in order to have the first direct observation of a positroncontaining system.

Structures, vibrational frequencies, and infrared spectra of the hexahydrated benzene clusters
View Description Hide DescriptionThe water hexamer is known to have a number of isoenergetic structures. The first experimental identification of the O–H stretching vibrational spectra of the water hexamer was done in the presence of benzene. It was followed by the identification of the pure water hexamer structure by vibrationrotational tunneling (VRT) spectroscopy. Although both experiments seem to have located only the Cage structure, the structure of the benzene–water hexamer complex is not clearly known, and the effect of benzene in the water hexamer is unclear. In particular, it is not obvious how the energy difference between nearly isoenergetic water hexamer conformers changes in the presence of benzene. Thus, we have compared the benzene complexes with four lowlying isoenergetic water hexamers, Ring, Book, Cage, and Prism structures, using ab initio calculations. We also investigated the effects of the presence of benzene on the structures, harmonic vibrational frequencies, and infrared (IR) intensities for the four lowlying energy conformers. There is little change in the structure of the water hexamer upon its interaction with the benzene molecule. Hence the deformation energies are very small. The dominant contribution to the benzene–water cluster interaction mainly comes from the π–H interactions between benzene and a single water molecule. As a result of this π–H interaction, bond length increases and the corresponding stretching vibrational frequencies are redshifted. The IR spectral features of both and are quite similar. From both the energetics and the comparison of calculated and experimental spectra of the the water structure in these complexes is found to have the Cage form. In particular, among the four different Cage structures, only one conformer matches the experimental O–H vibrational frequencies.

Transition probability of Cu I, Ag I, and Au I from weakest bound electron potential model theory
View Description Hide DescriptionIn this paper, the weakest bound electron potential model (WBEPM) theory is employed to study the transition probability of manyvalenceelectron systems Cu I, Ag I, and Au I. According to this theory, a coupled equation is used to obtain the parameters and which are needed in the calculation of transition probability. In the calculation, spectral fine structure is taken into consideration, and node numbers of silver and gold are adjusted. Compared with the accepted values, the results reported here are fairly good, and agreement is within the uncertainty of the accepted values. In our discussion, we give the explanation of node number adjustment from the view of WBEPM theory.

On the ultraviolet photofragmentation of hydrogen iodide
View Description Hide DescriptionAn ab initioconfiguration interaction (CI) study including spinorbit coupling is carried out for the ground and lowlying excited states of the HI molecule by employing a relativistic effective core potential for the iodine atom. The computed spectroscopic constants for the ground and Rydberg states are in good agreement with available experimental data, as are the vertical excitation energies for the repulsive and states of the A band. The state is found to possess a shallow minimum of 600 cm^{−1} depth outside the Franck–Condon region, at The electricdipole moments have also been calculated for transitions from the ground to the A band states. Contrary to what is usually assumed, the transition moments are found to depend strongly on internuclear distance. Employing the computed potential energy and transition moment data, partial and total absorption spectra for the A band are calculated and the quantum yields, are determined as a function of excitation energy. The maximal values are calculated to be 0.55–0.59 and lie at 39 000–40 000 cm^{−1}, which agrees well with experimental results. The influence of the state and of the nonadiabatic effects on the values is found to be negligible in the essential part of the A band. Finally, it is shown that significantly higher quantum yield values (up to 0.8–0.9) may be achieved when vibrationally hot HI molecules are excited in the appropriate spectral range.

Quantum scattering calculations of the reaction using a new ab initio potential and extensions of Jshifting
View Description Hide DescriptionWe report results of quantum wave packet calculations of the reactions for zero and nonzero total angular momentum,J, (using the centrifugal sudden approximation), and using a new fit to extensive ab initio calculations of a global potential [K. A. Peterson, S. Skokov, and J. M. Bowman, J. Chem. Phys. 111, 2445 (1999)]. Initial stateselected and cumulative reaction probabilities to form each set of products for are calculated by a direct summation of the initial stateselected reaction probabilities. We propose and test a simple energyshifting approximation that relates the initial stateselected reaction probability for arbitrary j to the one for Extensions of standard J and Kshifting methods are suggested and applied to both reaction channels. In doing this extension the adiabatic rotation approximation is used to determine the rotational barriers in the entrance and exit channels. The energy dependence of the reaction cross sections to form the two products is calculated for using J and Kshifting and compared at two translational energies to results of quasiclassical trajectory calculations. The thermal rate constants for the two reaction channels are calculated from 200 to 400 K and compared to experiment.