Volume 121, Issue 22, 08 December 2004
 ARTICLES

 Theoretical Methods and Algorithms

Correlation energy extrapolation by intrinsic scaling. III. Compact wave functions
View Description Hide DescriptionThe information gained in the context of extrapolating the correlation energy by intrinsic scaling is used to shorten the full configurational expansions of electronic wave function without compromising their chemical accuracy. The truncations are accomplished by judiciously limiting the participation of the ranges of predetermined approximate sets of natural orbitals in the various excitation categories.

Globally convergent trustregion methods for selfconsistent field electronic structure calculations
View Description Hide DescriptionAs far as more complex systems are being accessible for quantum chemical calculations, the reliability of the algorithms used becomes increasingly important. Trustregion strategies comprise a large family of optimization algorithms that incorporates both robustness and applicability for a great variety of problems. The objective of this work is to provide a basic algorithm and an adequate theoretical framework for the application of globally convergent trustregion methods to electronic structure calculations. Closed shell restricted Hartree–Fock calculations are addressed as finitedimensional nonlinear programming problems with weighted orthogonality constraints. A Levenberg–Marquardtlike modification of a trustregion algorithm for constrained optimization is developed for solving this problem. It is proved that this algorithm is globally convergent. The subproblems that ensure global convergence are easytocompute projections and are dependent only on the structure of the constraints, thus being extendable to other problems. Numerical experiments are presented, which confirm the theoretical predictions. The structure of the algorithm is such that accelerations can be easily associated without affecting the convergence properties.

Variationally optimized basis orbitals for biological molecules
View Description Hide DescriptionNumerical atomic basis orbitals are variationally optimized for biological molecules such as proteins, polysaccharides, and deoxyribonucleic acid within a density functional theory. Based on a statistical treatment of results of a fully variational optimization of basis orbitals ( full optimized basis orbitals) for 43 biological model molecules, simple sets of preoptimized basis orbitals classified under the local chemical environment (simple preoptimized basis orbitals) are constructed for hydrogen, carbon, nitrogen, oxygen, phosphorous, and sulfur atoms, each of which contains double valence plus polarization basis function. For a wide variety of molecules we show that the simple preoptimized orbitals provide well convergent energy and physical quantities comparable to those calculated by the full optimized orbitals, which demonstrates that the simple preoptimized orbitals possess substantial transferability for biological molecules.

Lower and upper bounds for the absolute free energy by the hypothetical scanning Monte Carlo method: Application to liquid argon and water
View Description Hide DescriptionThe hypothetical scanning (HS) method is a general approach for calculating the absoluteentropyS and free energyF by analyzing Boltzmann samples obtained by Monte Carlo or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). At each step of the process the system is divided into two parts, the already treated molecules (the “past”), which are fixed, and the as yet unspecified (mobile) “future” molecules. Obtaining the TP exactly requires calculating partition functions over all positions of the future molecules in the presence of the frozen past, thus it is customary to invoke various approximations to best represent these quantities. In a recent publication [Proc. Natl. Acad. Sci. USA 101, 9235 (2004)] we developed a version of HS called complete HSMC, where each TP is calculated from an MC simulation involving all of the future molecules (the complete future); the method was applied very successfully to LennardJones systems (liquid argon) and a box of TIP3P water molecules. In its basic implementation the method provides lower and upper bounds for F, where the latter can be evaluated only for relatively small systems. Here we introduce a new expression for an upper bound, which can be evaluated for larger systems. We also propose a new exact expression for F and verify its effectiveness. These free energy functionals lead to significantly improved accuracy (as applied to the liquid systems above) which is comparable to our thermodynamic integration results. We formalize and discuss theoretical aspects of HSMC that have not been addressed in previous studies. Additionally, several functionals are developed and shown to provide the free energy through the analysis of a single configuration.

Correlation energy extrapolation by intrinsic scaling. I. Method and application to the neon atom
View Description Hide DescriptionRemarkably accurate scaling relations are shown to exist between the correlation energy contributions from various excitation levels of the configuration interaction approach, considered as functions of the size of the correlating orbital space. These relationships are used to develop a method for extrapolating a sequence of smaller configuration interaction calculations to the full configurationinteraction energy. Calculations of the neon atom ground state with the Dunning’s quadruple ζ basis set demonstrate the ability of the method to obtain benchmark quality results.

Correlation energy extrapolation by intrinsic scaling. II. The water and the nitrogen molecule
View Description Hide DescriptionThe extrapolation method for determining benchmark quality full configurationinteraction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules and As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configurationinteraction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configurationinteraction calculations to the full configurationinteraction energy and for constructing compact accurate configurationinteraction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as manybody perturbationtheory,coupledcluster theory, as well as with variational calculations wherever possible.

A natural linear scaling coupledcluster method
View Description Hide DescriptionIt is shown that using an appropriate localized molecular orbital (LMO) basis, one is able to calculate coupledcluster singles and doubles (CCSD) wave functions and energies for very large systems by performing full CCSD calculations on small subunits only. This leads to a natural linear scaling coupledcluster method (NLSCC), in which total correlation energies of extended systems are evaluated as the sum of correlation energy contributions from individual small subunits within that system. This is achieved by defining local occupied orbital correlation energies. These are quantities, which in the LMO basis become transferable between similar molecular fragments. Conventional small scale existing molecular CCSD codes are all that is needed, the local correlation effect being simply transmitted via the appropriate LMO basis. Linear scaling of electronic correlation energy calculations is thus naturally achieved using the NLSCC approach, which in principle can treat nonperiodic extended systems of infinite basis set size. Results are shown for alkanes and several polyglycine molecules and the latter compared to recent results obtained via an explicit large scale LCCSD calculation.

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas–Kroll–Hess transformation up to arbitrary order
View Description Hide DescriptionIn order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz–Sadlej–Snijders method) or a stepwise analytic approach (the Douglas–Kroll–Hess method) are possible. For the evaluation of Douglas–Kroll–Hess Hamiltonians up to a predefined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas–Kroll–Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas–Kroll–Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positiveenergy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalarrelativistic implementation of the symbolic operations for the evaluation of the positiveenergy part of the blockdiagonal Hamiltonian is presented, and its accuracy is tested for groundstate energies of oneelectron ions over the whole periodic table. Furthermore, the first manyelectron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.

Firstorder semidefinite programming for the direct determination of twoelectron reduced density matrices with application to manyelectron atoms and molecules
View Description Hide DescriptionDirect variational calculation of twoelectron reduced density matrices (2RDMs) for manyelectron atoms and molecules in nonminimal basis sets has recently been achieved through the use of firstorder semidefinite programming [D. A. Mazziotti, Phys. Rev. Lett. (in press)]. With semidefinite programming, the electronic groundstate energy of a molecule is minimized with respect to the 2RDM subject to Nrepresentability constraints known as positivity conditions. Here we present a detailed account of the firstorder algorithm for semidefinite programming and its comparison with the primaldual interiorpoint algorithms employed in earlier variational 2RDM calculations. The firstorder semidefiniteprogramming algorithm, computations show, offers an ordersofmagnitude reduction in floatingpoint operations and storage in comparison with previous implementations. We also examine the ability of the positivity conditions to treat strong correlation and multireference effects through an analysis of the Hamiltonians for which the conditions are exact. Calculations are performed in nonminimal basis sets for a variety of atoms and molecules and the potentialenergy curves for CO and

A canonical averaging in the secondorder quantized Hamilton dynamics
View Description Hide DescriptionQuantized Hamilton dynamics (QHD) is a simple and elegant extension of classical Hamilton dynamics that accurately includes zeropoint energy,tunneling,dephasing, and other quantum effects. Formulated as a hierarchy of approximations to exact quantum dynamics in the Heisenberg formulation, QHD has been used to study evolution of observables subject to a single initial condition. In present, we develop a practical solution for generating canonical ensembles in the secondorder QHD for position and momentum operators, which can be mapped onto classical phase space in doubled dimensionality and which in certain limits is equivalent to thawed Gaussian. We define a thermal distribution in the space of the QHD2 variables and show that the standard relationship becomes in the high temperature limit due to an overcounting of states in the extended phase space, and a more complicated function at low temperatures. The QHD thermal distribution is used to compute total energy, kinetic energy, heat capacity, and other canonical averages for a series of quartic potentials, showing good agreement with the quantum results.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Methane activation by nickel cluster cations, Reaction mechanisms and thermochemistry of cluster complexes
View Description Hide DescriptionThe kinetic energy dependences of the reactions of with are studied in a guided ion beam tandem mass spectrometer over the energy range of 0–10 eV. The main products are hydride formation dehydrogenation to form and double dehydrogenation yielding These primary products decompose at higher energies to form and and are not observed. In general, the efficiencies of the single and double dehydrogenation processes increase with cluster size. All reactions exhibit thresholds, and cross sections for the various primary and secondary reactions are analyzed to yield reaction thresholds from which bond energies for nickel cluster cations to C, CD, and are determined. The relative magnitudes of these bond energies are consistent with simple bond order considerations. Bond energies for larger clusters rapidly reach relatively constant values, which are used to estimate the chemisorption energies of the C, CD, and molecular fragments to nickel surfaces.

Quantum effect on the internal proton transfer and structural fluctuation in the cluster
View Description Hide DescriptionThe thermal equilibrium state of is investigated by means of an ab initio path integral molecular dynamics (PIMD) method, in which degrees of freedom of both nuclei and electrons at finite temperature are quantized within the adiabatic approximation. The secondorder MøllerPlesset force field has been employed for the present ab initio PIMD. At 5–200 K, is shown to have the structure that the proton is surrounded by the two units without any exchange of an atom between the central proton and the unit. At 5 K, the quantum tunneling of the central proton occurs more easily when the distance between the two units is shortened. At the high temperature of 200 K, the central proton is more delocalized in space between the two units, with less correlation with the stretching of the distance between the two units. As for the rotation of the units around the axis of the dihedral angle distribution is homogeneous at all temperatures, suggesting that the two units freely rotate around the axis, while this quantum effect on the rotation of the units becomes more weakened with increasing temperature. The influence of the structural fluctuation of on molecular orbital energies has been examined to conclude that the highest occupied molecular orbital–lowest unoccupied molecular orbital energy gap is largely reduced with the increase of temperature because of the spatial expansion of the whole cluster.

Multireference calculations of the phosphorescence and photodissociation of chlorobenzene
View Description Hide DescriptionMultireference complete active space selfconsistentfield (CASSCF) and multireference CASSF secondorder perturbation theory (MSCASPT2) calculations were performed on the ground state and a number of lowlying excited singlet and triplet states of chlorobenzene. The dual phosphorescence observed experimentally is clearly explained by the MSCASPT2 potentialenergy curves. Experimental findings regarding the dissociation channels of chlorobenzene at 193, 248, and 266 nm are clarified from extensive theoreticalinformation including all lowenergy potentialenergy curves.

Electronic structure, vibrational stability, and predicted infraredRaman spectra of the and clusters
View Description Hide DescriptionRecently an inorganic fullerinelike onion with nearperfect icosahedral symmetry in the crystalline phase was reported [M. J. Moses, J. C. Fettinger, and B. W. Eichhorn, Science 300, 778 (2003)]. This paper presents a detailed computational study in the framework of density functional theory on various aspects of this molecule. The electronic structure of the is investigated in its neutral as well as −3 charged state together with its subunits and by the all electron linear combination of Gaussiantype orbitals method. The bonding is studied by examining the integrated charge within atomic sphere, the electron localization function, changes in the electron density distribution, and from vibrational modes. We find that strong covalent AsAs bonds seen in isolated become weaker in the and strong covalent AsNi bonds are formed. The structural stability of all four clusters is examined by analyzing the energetics and by calculating the vibrational frequencies. Further, the infrared and Raman spectra is predicted for both the neutral and charged clusters. Finally, the energy barrier for removal of a single arsenic atom is calculated for the neutral cluster.

C–Cl bond fission dynamics and angular momentum recoupling in the 235 nm photodissociation of allyl chloride
View Description Hide DescriptionThe photodissociation dynamics of allyl chloride at 235 nm producing atomic fragments is investigated using a twodimensional photofragment velocity ion imaging technique. Detection of the and products by [2+1] resonance enhanced multiphoton ionization shows that primary C–Cl bond fission of allyl chloride generates 66.8% and 33.2% The fragments evidenced a bimodal translational energy distribution with a relative weight of low kinetic energy /high kinetic energy of 0.097/0.903. The minor dissociation channel for C–Cl bond fission, producing low kinetic energy chlorine atoms, formed only chlorine atoms in the spin–orbit state. The dominant C–Cl bond fission channel, attributed to an electronic predissociation that results in high kinetic energy Cl atoms, produced both and atomic fragments. The relative branching for this dissociation channel is The average fraction of available energy imparted into product recoil for the high kinetic energy products was found to be 59%, in qualitative agreement with that predicted by a rigid radical impulsive model. Both the spin–orbit ground and excited chlorine atom angular distributions were close to isotropic. We compare the observed ratio produced in the electronic predissociation channel of allyl chloride with a prior study of the chlorine atom spin–orbit states produced from HCl photodissociation, concluding that angular momentum recoupling in the exit channel at long interatomic distance determines the chlorine atom spin–orbit branching.

Anchoring the potential energy surface of the cyclic water trimer
View Description Hide DescriptionSix cyclic stationary points on the water trimer potential energy surface have been fully optimized at the MP2 level with the augccpVQZ basis set. In agreement with previous work, harmonic vibrational frequencies indicate that two structures are minima, three are transition states connecting minima on the surface while the remaining stationary point is a higherorder saddle point. The 1 and nparticle limits of the electronic energies of each of these six structures were estimated by systematically varying both the basis sets and theoretical methods. The former limit was approached with the and families of basis sets while MP2, CCSD(T), and BD(TQ) calculations helped examine the latter. Core correlation effects have also been assessed at the MP2 level with the series of basis sets These data have been combined to provide highly accurate relative energies and dissociation energies for these stationary points.

Action spectroscopy and temperature diagnostics of by chemical probing
View Description Hide DescriptionInfrared absorption spectroscopy of few hundred ions trapped in a 22pole ion trap is presented using chemical probing as a sensitive detection technique down to the single ion level. By exciting selected overtone transitions of the vibrational band using an external cavitydiode laser an accurate diagnosticsmeasurement of the effective translational and rotational temperatures of the trapped ions was performed. The absolute accuracy of the measured transition frequencies was improved by a factor of four compared to previous plasma spectroscopymeasurements using velocity modulation [Ventrudo et al., J. Chem. Phys. 100, 6263 (1994)]. The observed buffer gas cooling conditions in the ion trap indicate how to cool trapped ions into the lowest ortho and para rotational states. Future experiments will utilize such an internally cold ion ensemble for stateselected dissociative recombination experiments at the heavy ion storage ring Test Storage Ring (TSR).

Isotope branching and tunneling in reactions
View Description Hide DescriptionThe and reactions are studied using quantum scattering calculations and chemically accurate potential energy surfaces developed for the system by Rogers et al. [J. Phys. Chem. A 104, 2308 (2000)]. Cross sections and rate coefficients for OH and OD products are calculated using accurate quantum methods as well as the approximation. The approach is found to work remarkably well for both and collisions. The reactions are dominated by tunneling at low temperatures and for the reaction the hydrogen atom transfer leading to the OH product dominates at low temperatures. Our result for the OH/OD branching ratio is in close agreement with previous calculations over a wide range of temperatures. The computed OH/OD branching ratios are also in close agreement with experimental results of Robie et al. [Chem. Phys. Lett. 134, 579 (1987)] at temperatures above 400 K but the theoretical results do not reproduce the rapid rise in the experimental values of the branching ratio for temperatures lower than 350 K. We believe that new measurements could resolve the longstanding discrepancy between experiment and theory for this benchmark reaction.

van der Waals clusters revisited. I. New lowenergy isomeric structures for
View Description Hide DescriptionNew lowlying isomeric structures of clusters are reported for They were determined using simulated annealing and evolutionary programing, for pairwise additive intermolecular potential energy surfaces. New global minima were found for the clusters with 10, 11. The new lowestenergy structure of and several new local minima for 7 clusters have the HF bound on a threefold surface site, consistent with the recent spectroscopic data for clusters in helium nanodroplets. A new type of lowenergy local minima were determined for clusters.

Distributions of angular anisotropy and kinetic energy of products from the photodissociation of methanol at 157 nm
View Description Hide DescriptionWe investigated distributions of angularanisotropy parameter β and kinetic energy of fragments after photodissociation of methanol using timeofflight(TOF)mass spectrometry. Fragments, in particular and CO, were successfully detected using tunable radiation from a synchrotron for photoionization. Following O–H bond fission, a fragment with internal energy greater than 104 kJ mol^{−1} dissociates to Elimination of two accompanies formation of CO. The 〈β〉 value of hydroxyl hydrogen is −0.26 whereas that of methyl hydrogen is zero. has two distinct components in TOF spectra; these rapid and slow components have 〈β〉 values −0.30 and −0.18, respectively. The dissociation exhibits a highly anisotropicangular distribution with 〈β〉=−0.75. The β values of fragments from photolysis are addressed. From measurements of angularanisotropy parameters of various fragments, we surmise that the transition dipole moment μ is almost perpendicular to the C–O–H plane and that is the major photoexcited state at 157 nm.