Volume 110, Issue 2, 08 January 1999
 THEORETICAL METHODS AND ALGORITHMS


Improving selfconsistent field convergence by varying occupation numbers
View Description Hide DescriptionOne problem commonly encountered in quantum chemistry calculations is the convergence of the selfconsistent field (SCF) iteration process. Numerous cases are known in which calculations (both Hartree–Fock and density functional theory), even when using extrapolation techniques, converge extremely slowly or do not converge at all. Many of these cases include molecules that contain transition metals. In this paper, we study two techniques that fractionally occupy orbitals around the Fermi energy during the SCF cycles. These methods use fractionally occupied orbitals to aid in the iterative process, but the occupations at convergence are forced to be ones and zeros. We show how using these fractionally occupied orbitals improves convergence for a number of difficult cases and that there is no significant overhead in the number of SCF cycles for molecules that easily converge with standard techniques.

Determining the molecular Aharonov–Bohm phase angle: A rigorous approach employing a molecular properties based adiabatic to diabatic states transformation
View Description Hide DescriptionRecently there has been considerable interest, not to mention controversy, concerning a key aspect of the molecular Aharonov–Bohm (MAB) effect: the construction of the phase angle, induced by geometric phase effect, whose gradient is the vector potential characteristic of MAB theory. In the past this angle was constructed from explicit knowledge of the locus of the seam of conical intersection. Here it is shown how a phase angle that satisfies the requirements of MAB theory can be determined without a priori knowledge of the locus of points of conical intersection. This approach has important implications for direct dynamics. It is a corollary of a recent analysis that showed that diagonalizing the matrix of virtually any symmetric (realvalued Hermitian) electronic property operator in the subspace of states that intersect conically generates a transformation that removes all of the singularity of the derivative coupling at a conical intersection. Key aspects of this method are illustrated by considering the dipole moment operator near a point on the seam of conical intersection in

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated ) multireference configuration interaction. III. Electron affinities of firstrow atoms
View Description Hide DescriptionThe computation of electron affinities of atoms and molecules is one of the most demanding tasks in quantum chemistry. This is because the electronic structures of neutral systems compared to their respective anions are qualitatively different and thus errors in the computed correlation energies, in general, do not cancel. Correlation energies obtained from traditional configuration interaction (CI) expansions, however, are known to converge notoriously slowly due to the presence of interelectronic cusps in the exact wave function. We compute the electron affinities of the firstrow atoms using the recently proposed (explicitly correlated) [multireference configuration interaction (single double) MRCI(SD)] and MRACPF (averaged coupledpair functional) methods which take care of the interelectronic cusps by means of terms being linear in the interelectronic distances The reference spaces and basis sets (which are further augmented with diffuse functions) are taken from our former study on neutral atoms and their respective positive ions [J. Chem. Phys. 109, 9795 (1998)]. The performance of MRACPF is validated by comparison with full CI. The computed electron affinities (corrected for relativistic effects and nuclear motion) deviate from experiment by: (H), (Li), (B, within experimental uncertainty), (C), −15 (O), and (F). Without relying on fortuitous error compensations, the electron affinities of B, C, O, and F can presently not be obtained in such an accuracy with traditional CI methods without extrapolation to the basis set limit.

Firstorder nonadiabatic coupling matrix elements using coupled cluster methods. I. Theory
View Description Hide DescriptionIt is shown how firstorder nonadiabatic coupling matrix elements can be calculated using coupled clusterelectronic structure methods. The formalism is consistent with the coupled cluster response theory approach for calculation of excitation energies and adiabatic transition properties. Expressions are derived that are in the limit of a complete coupled cluster expansion give results equivalent to the full configuration interaction results. Computational tractable expressions are given for the firstorder nonadiabatic coupling matrix in coupled clustertheory. The final expressions are quite similar to those employed in the implementation of the analytical calculation of molecular gradients.

A class IV charge model for molecular excited states
View Description Hide DescriptionWe present a new parameterization for calculating class IV charges for molecules containing H, C, N, O, F, Si, P, S, Cl, Br, and I from wave functions calculated at the intermediateneglectofdifferentialoverlapforspectroscopy (INDO/S) level. First we readjust the oxygen parameters in INDO/S on the basis of electronic excitation energies; this yields a new set of parameters called INDO/S2. Then we parameterize the charge model. The new model, called charge model 2 for INDO/S2 (CM2/INDO/S2), is parameterized against the most accurate available data from both ab initio and experimental sources for dipole moments of ground and excited electronic states. For a training set containing 211 dipole moments of molecules in their ground states and 33 dipole moments of molecules in their first excited states, the CM2/INDO/S2 model leads to a rootmeansquare (rms) error in dipole moments of 0.26 D for ground states and 0.40 D for the excited states. The new model, INDO/S2 with CM2, systematically improves the excitation energies and the dipole moments of the excited states of carbonyl compounds. We also parameterized a CM2 model for the standard INDO/S model (CM2/INDO/S), which predicts quite accurate dipole moments for ground states with an rms error of 0.24 D.

Full configuration interaction benchmark calculations of firstorder oneelectron properties of BH and HF
View Description Hide DescriptionFull configuration interaction benchmark calculations have been carried out for the electric dipole and quadrupole moments and the electric field gradient at the nuclei of BH and HF. The accuracy of perturbation theory from second to fourth order and coupled clustertheory with up to triple excitations has been investigated. For all the properties the coupled cluster models outperform the perturbation series. The convergence of the series of coupled cluster models is significantly faster and more systematic than the one of the perturbation series, and only the coupled cluster series defines a hierarchy of models with well defined levels of accuracy. The CCSD(T) model is a good approximation to the full coupled cluster singles, doubles, and triples model. It recovers 80%–90% of the full effect of triple excitations, and the small error due to the approximate description of triple excitations is comparable in size to the error due to neglect of higherorder excitations. For accurate calculations, the CCSD(T) model is the preferred model for all the properties. Our estimates of the exact dipole moments and are in perfect agreement with the experimental values of and

Parametrizing a polarizable force field from ab initio data. I. The fluctuating point charge model
View Description Hide DescriptionWe have developed a polarizable force field for peptides, using allatom OPLS (OPLSAA) nonelectrostatic terms and electrostatics based on a fluctuating charge model and fit to ab initio calculations of polarization responses. We discuss the fitting procedure, and specific techniques we have developed that are necessary in order to obtain an accurate, stable model. Our model is comparable to the best existing molecular mechanics force fields in reproducing quantumchemical peptide energetics. It also accurately reproduces manybody effects in many cases. We believe that straightforward extensions of our linearresponse electrostatic model will significantly improve the accuracy for those cases that the present model does not adequately address.

Correlation energies obtained from symmetryadapted versus symmetrybroken Hartree–Fock solutions in a model delocalized onedimensional system
View Description Hide DescriptionSinglet instabilities of the Hartree–Fock (HF) solutions, leading to bondcentered or atomcentered chargedensitywaves, occur in extended onedimensional systems, such as a regular cyclic ring. These solutions are much less delocalized than the symmetryadapted one, as appears when comparing the equivalent localized molecular orbitals. The symmetrybroken solutions exhibit a finite gap at the Fermi level, whereas for the symmetryadapted solution the gap can be extrapolated with a law towards a zero asymptotic value. If one performs postHartree–Fock calculations, of Mo/ller–Plesset nth order or linearized coupled cluster type, one obtains a higher final energy from the symmetrybroken HF solutions than from the symmetryadapted HF wave function. A procedure is proposed to obtain directly symmetryadapted localized selfconsistent field orbitals in systems presenting HF instabilities.

A novel, general method of analyzing magnetic circular dichroism spectra and magnetization curves of highspin metal ions: Application to the protein oxidized rubredoxin, Desulfovibrio gigas
View Description Hide DescriptionWe have developed a general theoretical approach for analyzing the intensities of magnetic circular dichroism(MCD) spectra of paramagnetic species with in the nonlinear regions of temperature and magnetic field. The method takes full advantage of the irreducible tensor method in order to obtain maximum simplification from symmetry. The approach, which is based on a detailed treatment of spinorbit coupling and Zeemaninteraction in terms of the symmetry properties of basis sets of wave functions, factorizes contributions into bands with Gaussian and derivative shapes in order to extend earlier treatments based on the socalled linear field limit. The method is applied to analyze and fit the form of the MCD spectra and the MCD magnetization curves of pseudotetrahedral highspin Fe(III), in the protein rubredoxin from Desulfovibrio gigas, a representative of a family of iron–sulphur proteins. This treatment provides for the first time a satisfactory fit of these curves over a temperature range between 1.6 and 10 K and up to magnetic fields of 5 T. We show that the forms of the magnetization curves are strongly dependent on the polarizations of the optical transitions and on both the sign and magnitude of the ground state axial zerofield parameter. The sign and magnitude of is determined to be with a fixed value of obtained from an analysis of electron paramagnetic resonance data. This shows that earlier, simpler fitting procedures were inadequate.

Density functional study of the Fe–CO bond dissociation energies of
View Description Hide Description(n=1–5) complexes have been studied using density functional theory(DFT) methods. Several functionals have been used in the geometry optimizations, harmonic frequencies computation and calculation of the iron–carbonyl bonddissociation energies.Coupledcluster single double (triple) bonddissociation energies have also been computed for the smaller systems. The obtained results show that DFT methods yield reasonable geometries and vibrational frequencies. Regarding the bonddissociation energies, it is shown that the validity of the results depends on whether there is a change in the atomic state of the metal during the dissociation. When the atomic state is the same for both complexes, the bonddissociation energy computed using gradient corrected functionals is within the range of the experimental values, while when the atomic state changes, DFT methods overestimate the bonddissociation energy due to a poor description of the atomic multiplets.

The ab initio model potential method: Thirdseries transition metal elements
View Description Hide DescriptionIn this paper we present nonrelativistic and relativistic core ab initio model potentials (AIMPs) and valence basis sets for La and the thirdseries transition metal elements. The relativistic AIMPs are derived from atomic Cowan–Griffin calculations; they are made of a spinfree part and a oneelectron spinorbit operator according to Wood and Boring. The core potentials correspond to the 62electron core ]. The valence basis sets are optimized and spinorbit corrected. We present monitoring spinfree calculations on the atoms, singly ionized ions and monohydrides of the ten elements, which show a good performance overall. A spinfreestateshifted spinorbitconfiguration interaction calculation on Pt, which uses empirical spinfree data and which is expected to be essentially free from spinfree deficiencies, points out that the quality of the spinorbit operators is very good.

General methods for determining the droplet size distribution in emulsion systems
View Description Hide DescriptionWe present a general method that allows us to figure out the size distribution of an isolated collection of droplets of dilute emulsion system using nuclear magnetic resonance pulsed gradient spin echo measurements. We show that the expression to obtain the volume fraction distribution function is equivalent to a Fredholm integral equation of the first kind. We prove, using the Dirac notation, that a solution of this equation can be easily found if its kernel has a complete biorthogonal system of eigenvectors. Two numerical procedures are discussed. The first, termed indirect, is based on the expansion of the unknown distribution function in the eigenfunctions of the kernel. The second one, called direct, uses the properties of shifted Legendre polynomials to integrate numerically the integral equation and evaluates the unknown distribution by means of a constrained least square procedure. The computational limits are analyzed. To extract the distribution’s form directly by experimental data we have constructed a generating function using the shifted Jacobi polynomials. The procedures have been tested on simulated and experimental data and appear to be a powerful and flexible method to obtain the size distribution function directly by the experimental data.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Photodissociation spectroscopy and dynamics of the methylthio radical
View Description Hide DescriptionThe photodissociationspectroscopy and dynamics of the and radicals have been investigated using fast radical beam photofragment spectroscopy of the electronic band and an unstructured band near 45 600 cm^{−1}. At all energies, only one major channel, was observed. Photofragment yield spectra for the electronic band show resolved vibrational progressions extending well beyond those seen in laserinduced fluorescence studies of this band. Photofragment translational energy distributions yield the finestructure distribution for each vibrational level of the product. Photofragment angular distributions were found to be highly anisotropic ( to ) with increasing anisotropy at higher photon energies. The results yield a refined heat of formation for (1.346±0.018 eV) as well as the mechanism by which the state is predissociated. Results at 45 600 cm^{−1} imply that dissociation occurs on the repulsive state.

High level ab initio molecular orbital study of the structures and vibrational spectra of and
View Description Hide DescriptionThe equilibrium structures and harmonic vibrational frequencies for and have been determined using secondorder Mo/ller–Plesset perturbation theory (MP2), Becke’s three parameter hybrid method employing the LYP correction functional (B3LYP) [A. D. Becke, J. Chem. Phys. 98, 5648 (1993)], and coupledcluster theory with single and double excitations including perturbative corrections for the triple excitations CCSD(T) in conjunction with the triplezeta doublepolarized (TZ2P) and 6311++Gbasis sets. Our computational results predict a very nearly planar structure for the radical. At the CCSD(T)/6311++G level of theory bond lengths of 1.076 and 1.851 Å are predicted for the C–H and C–Br bonds, and a 124.6° for the H–C–H angle in the radical, which are in good agreement with the experimental values of 1.086 Å, 1.845 Å, and 124°, respectively. The calculated rotational constant value of at the same level is found to agree with experiment. Like and the C–Br bond length in the cation is found to be shorter than that of the neutral species, due to the reduction of repulsion between carbon and bromine atoms. The vibrational frequencies for the C–Br stretching are expected to increase by more than when the radical is ionized. The best estimate of the ionization potential for the radical is which agrees very well with the experimental value of

Pseudorotation tunneling in several water trimer isotopomers
View Description Hide DescriptionThe tunneling dynamics of several water trimer isotopomers is investigated by using an extension of the Hamiltonian that was previously derived for pure (more symmetric) trimers. This Hamiltonian takes into account the overall rotation of the trimer and three internal, torsional, or pseudorotational, motions of the monomers. Quantitative calculations of the torsional levels are presented, and the small effects of internal, i.e., hydrogen bonded, H/D substitutions and the much larger effects of external H/D substitutions are discussed. Transition line strengths are computed as well, and the assignment of most of the bands observed for the various water trimer isotopomers is confirmed. In one case we suggest a different assignment.

Energy partitioning following photodissociation of methyl iodide in the A band: A velocity mapping study
View Description Hide DescriptionTranslational and internal energy partitioning in the methyl and iodine fragments formed from photodissociation of methyl iodide in the Aband region is measured using velocity mapping. Stateselective detection combined with the very good image quality afforded by the twodimensional imaging technique allow a detailed analysis of the kinetic energy and angular distributions. Product vibrational energy is, as previously known, mainly partitioned into the umbrella mode of the methyl fragment, but a substantial fraction of molecules is also excited with one quantum of the symmetric C–H stretch, especially at higher dissociation energies. Preliminary evidence is also presented for excitation of several quanta of the asymmetric deformation mode. Rotational energy partitioning is similar for products formed in both the groundstate and the spin–orbit excited channel for photodissociation across the full Aband spectrum. Dissociation of vibrationally excited molecules plays an increasingly important role at longer dissociation wavelengths. Two modes remain populated in the pulsed beam expansion, the C–I stretch, and the methyl rock. Each reactant vibrational mode couples in a very specific manner into the I and dissociation channels. Trends in vibrational and rotational energy disposal are compared with recent theoretical predictions. Readjustment of many aspects of the ab initio multidimensional potential energy surfaces which have recently been calculated for appears to be necessary. The improved resolution offered by velocity mapping also allows a more accurate determination of the C–I bond energy. A dissociation energy of is found.

Local mode behavior in the acetylene bending system
View Description Hide DescriptionThe bending eigenfunctions of the acetylene state, as represented by our recently reported effective Hamiltonian [J. Chem. Phys. 109, 121 (1998)], are analyzed up to A transition from normal to local mode behavior is observed around 8000–10 000 such that above these energies, the eigenstates are better described in terms of local mode quantum numbers. The local mode behavior in the bend degrees of freedom of acetylene that is described here is in many ways analogous to the local mode behavior that has been observed in the stretching degrees of freedom of many ABA molecules. However, the local mode behavior in the acetylene bend degrees of freedom, because it involves two twodimensional rather than two onedimensional vibrational modes, encompasses a richer range of motions. Specifically, in the “local” limit, the bending eigenfunctions are describable in terms of a continuum of motions ranging from local bend (one hydrogen bending) to counterrotation (the two hydrogens executing rotations in opposite directions).

An ab initio study of and van der Waals complexes
View Description Hide DescriptionSingle and double excitation coupledcluster approach with noniterative perturbational treatment of triple excitations [CCSD(T)] has been used to calculate the ground statepotential energy surfaces for and van der Waals complexes. Calculations have been performed with the augmented correlation consistent triple zeta basis sets supplemented with an additional set of bond functions Single point calculations for approximate minima have also been performed with a larger quadruple zeta basis set For and the CCSD(T) results show that the linear configuration is lower in energy than the Tshaped one. For the CCSD(T) interaction energies of the two configurations are virtually the same. The linear configuration of each complex has been found to be much more sensitive than the Tshaped one to the changes of the F–F bond length with the interaction becoming weaker when the F–F bond length is shortened from its equilibrium value and stronger when it is lengthened. More detailed analysis shows that sensitivity of component energies such as exchange, dispersion, and induction is much greater than that of supermolecule results. Highorder correlation corrections have been found to play an important role in determining the relative stability of the linear and Tshaped configurations. The harmonic approximation zeropoint vibrational energy for exceeds the depth of both wells. For the zeropoint vibrational energy is greater for the linear configuration and, because of that, the complex has a Tshaped ground vibrational state. When the zeropoint vibrational energy is taken into account for the complex the linear and the Tshaped configurations are found to have nearly identical energies.

Timedependent quantum mechanical calculations on for total angular momentum II: On the importance of Coriolis coupling
View Description Hide DescriptionThe reaction has been studied for total angular momentum with a timedependent wave packet method using the Coriolis coupled method of Goldfield and Gray [E. M. Goldfield and S. K. Gray, Comp. Phys. Commun. 98, 1 (1996)] on parallel computers. Helicity conserving (HC) and coupled channel (CC) calculations were performed for and using two different embeddings for the body fixed coordinate system to investigate the importance of Coriolis coupling for this reactive system. If the distance is taken to be the z axis of the coordinate system, we find poor agreement between the HC and the CC calculations for When the bond is taken to be the z axis, we find good agreement between the CC and HC calculations at low J. For higher J the agreement gets progressively worse, especially at higher energies. We can explain these results using a classical model from a previous paper on [A. J. H. M. Meijer and E. M. Goldfield, J. Chem. Phys. 108, 5404 (1998)].

The permanent electric dipole moments of chromium and vanadium mononitride: CrN and VN
View Description Hide DescriptionThe branch feature of the (0,0) band system of was recorded as a function of an applied static electric field. The resultant Stark splitting and shifts were analyzed giving values of 3.07(7) D and 6.1(4) D for the and states, respectively, for the magnitude of the permanent electric dipole moment, μ. Similarly, the branch feature of the (0,0) band system of was recorded as a function of an applied static electric field and analyzed to produce μ values of 2.31(4) D and 5.42(2) D for the and states, respectively. In order to facilitate the dipole moment determinations for it was necessary to record and analyze the field free spectrum of the (0,0) subband system. A comparison of the dipole moments for the first row monoxides and mononitrides is made and trends are discussed with reference to a molecular orbital correlation scheme.
