INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2009: (ICCMSE 2009)
 PLENARY AND INVITED SPEAKERS


Variational definitions of orbital energies
View Description Hide DescriptionA formulation of Koopmans' theorem is derived for highspin halffilled open shells in the restricted openshell HartreeFock (ROHF) method based on a variational treatment of both the initial (nonionized) openshell system X with spin S and the corresponding ions having a hole or an extra electron in the closed, open and virtual shells respectively. The six processes for forming ions with spin S±1/2 require two different definitions for canonical orbitals within each shell. These processes may be treated equivalently within a restricted CI using arbitrary noncanonical linear transforms of the ROHF orbitals optimal for the initial system. Canonical UHF orbitals also obey a variational principle for the ion energies, but they provide less appropriate estimates for actual states of the ion. Canonical spinunrestricted KohnSham orbitals with common exchangecorrelation functionals suffer from all of the UHF problems and from selfinteraction error. They generally are not useful estimates for ion energies.

Rate of convergence of basis expansions in quantum chemistry
View Description Hide DescriptionTraditional expansions in an orthonormal basis of the type of a Fourier series are very sensitive to the singularities of the function to be expanded. Exponential convergence is only possible, if the basis functions describe the singularities of the expanded functions correctly. Otherwise only an inversepowerlaw convergence is realized, which is usually slow. An example is the slow convergence of the CI expansion due to the correlation cusp. An improved convergence can be achieved, if one augments the basis by functions that describe the singularities of the wave function correctly, like in the R12 method. An alternative approach towards an improved convergence is possible in terms of a discretized integral transformation. This is realized in the conventional BoysHuzinagaRuedenberg expansion of wave functions in a Gaussian basis. Such expansions are surprisingly insensitive to singularities of the wave function to be expanded (e.g. the nuclear cusp). The rate of convergence is of an unconventional type, with an error estimate , if n is the basis size.

Nanoparticles and theory
View Description Hide DescriptionThis article provides an overview of recent work in the Schatz group concerned with using the discrete dipole approximation (DDA) to study the optical properties of silver and gold nanoparticles and other nanostructures, with emphasis on the determination of extinction and surface enhanced Raman scattering (SERS) spectra, and on nearfield imaging. Computational electromagnetic methods provide an immensely useful approach for interpreting a wide range of nanoscience experiments, including the capability to describe optical properties of particles and other nanostructures up to several hundred nm in dimension, allowing for arbitrary particle structures and a complex dielectric environment. While there are many different methods for doing computational electromagnetics, the DDA method is one of the most useful, due to its ability to describe particles in three dimensions with modest computational resources. After a brief description of the method, we show its utility through applications to a variety of nanostructures, including triangular bifrustums, rods, gapped rods with roughened surfaces, rodsheath structures and rings, including new results for many of the rodstructures.

Molecular modeling and the violation of linear scaling principles
View Description Hide DescriptionMost molecular modeling methods involve some simplifying assumptions which are often based on certain molecular properties where linear scaling features with molecular size are assumed. In this study we show that at least one contribution to the inherent inaccuracies of most molecular modeling methods is due to the inevitable violation of the principle of linear scaling. This violation can be interpreted both classically and quantum mechanically. Whereas some of the popular molecular modeling approaches use only classical or semiclassical analogies and do not directly rely on any quantum chemical treatment, nevertheless, the inherent violation of linear scaling principles equally apply to those methods as well.

Calculation of the vibrational contribution to electronic properties
View Description Hide DescriptionApart from zeropoint averaging, there are vibrational contributions to second and higherorder 'electronic' properties that can be related to the shift in equilibrium geometry induced by a perturbing field. These contributions often exceed the pure electronic term in systems of technological interest. Their computation by means of the finite fieldnuclear relaxation (FFNR) method, and its several extensions, is described using the example of static and dynamic nonlinear optical properties. Mechanical and other anharmonicities, dependent upon the property, may be quite important. We discuss the evolving treatment of systems where such is the case. Special handling for electric (and/or orbital magnetic) properties is required for polymers, surfaces and solids when they are modeled as periodic in one or more dimensions. The current status of developments in this area is included along with speculation regarding ultimate application to nanosystems.

Theory of chemical bonds in metalloenzymes  Manganese oxides clusters in the oxygen evolution center 
View Description Hide DescriptionIn early 1980 we have initiated brokensymmetry (BS) MO theoretical calculations of transitionmetal oxo species ( ) to elucidate the nature of dσpσ and dπpπ bonds. It has been concluded that highvalent species such as and exhibit electrophilic property in a sharp contrast with nucleophilic character of lowvalent bonds: , and closedshell dπpπ bonds of highvalent species often suffer the tripletinstability, giving rise to openshell (BS) configurations with significant metaldiradical (MDR) character: •MO•: note that these bonds are therefore regarded as typical examples of strongly correlated electron systems. Because of the MDR character, 1,4metal diradical mechanism was indeed preferable to fourcentered mechanism in the case of addition reaction of naked to ethylene. Recently the manganeseoxo species have been receiving renewed interest in relation to catalytic cycle of oxygen evolution from water molecules in the photosynthesis II (PSII) system. Accumulated experimental results indicate that this process is catalyzed with four manganese oxide clusters coordinated with calcium ion ( ). Past decade we have performed BS MO theoretical investigations of manganese oxide clusters related to . These calculations have elucidated that highvalent ( ) bonds exhibit intermediate MDR character (y=4060%) in the case of total lowspin (LS) configuration but the MDR character decreases with coordination of and water molecules. While the MDR character of the Mnoxo bonds becomes very high at the highspin (HS) configuration. Our computational results enabled us to propose two possible mechanisms on the theoretical ground: (A) electrophilic (EP) mechanism and (B) radical coupling (RC) mechanism. The theoretical results indicate that the EP mechanism is preferable for the lowspin (LS) state in polar media like in the protein environments (native OEC), whereas the RC mechanism is feasible at the state without such environmental stabilization: local singlet and local triplet diradical mechanisms are proposed for the OO coupling process. Possibilities of EP and RC mechanisms are examined in comparison with a lot of experimental results accumulated and theoretical results with several groups.

Efficient quantum chemical valenceonly treatments of lanthanide and actinide systems
View Description Hide DescriptionRecent progress in the development of lanthanide and actinide relativistic energyconsistent ab initio pseudopotentials is reported. Lanthanide 4fincore and actinide 5fincore pseudopotentials form an efficient tool for quantum chemical ab initio and firstprinciples calculations on larger systems, whenever the detailed electronic structure of the f shell is not of primary interest. The reliability of the 4fincore approximation is demonstrated for molecular lanthanide trihalides by comparison of calculated structural data with recommended experimental values. Due to the scarceness of experimental reference data the calibration of the 5fincore approximation is performed with respect to results from other more rigorous calculations. Lanthanide 4finvalence and actinide 5finvalence pseudopotentials allow the study of individual electronic states arising from a given f occupancy in a system. Recent progress to develop highly accurate smallcore pseudopotentials which model allelectron calculations using the DiracCoulombBreit Hamiltonian is summarized and first applications are outlined.

Rangedependent adiabatic connections
View Description Hide DescriptionRecently, we have implemented a scheme for the calculation of the adiabatic connection linking the KohnSham system to the physical, interacting system. This scheme uses a generalized Lieb functional, in which the electronicinteraction strength is varied in a simple linear fashion, keeping the potential or the density fixed in the process. In the present work, we generalize this scheme further to accommodate arbitrary twoelectron operators, allowing the calculation of adiabatic connections following alternative paths as outlined by Yang [J. Chem. Phys. 109, 10107 (1998)]. Specifically, we examine the errorfunction and Gaussianattenuated errorfunction adiabatic connections. We explore the highdensity and strong staticcorrelation regimes for twoelectron systems. The resulting adiabatic connections give an alternative view of the exchange correlation problem and their utility for the development of new exchangecorrelation functionals in KohnSham and rangeseparated hybrid schemes is discussed.

Collisioninduced dipoles and polarizabilities of pairs of hydrogen molecules: Ab initio calculations and results from spherical tensor analysis
View Description Hide DescriptionNew ab initio results are reported for the interactioninduced changes in the dipole moments and polarizabilities of pairs of hydrogen molecules, computed using finitefield coupledcluster methods in MOLPRO 2000 and GAMESS, with an augccpV5Z (spdf) basis set. Earlier work by X. Li, C. Ahuja, J. F. Harrison, and K. L. C. Hunt, J. Chem. Phys. 126, 214302 (2007), on collisioninduced polarizabilities Δα has been extended with 170 additional geometrical configurations of the pairs. In calculations of Δα, we have used a "random field" technique, with up to 120 different field strengths, having components that range from 0.001 to 0.01 a.u. Numerical tests show that the pair dipoles Δμ can be obtained accurately from calculations limited to 6 values of the field in each direction, so this approach has been used to compute Δμ by X. Li, K. L. C. Hunt, F. Wang, M. Abel, and L. Frommhold, Int. J. Spectroscopy 2010, 371201 (2010). We have evaluated the collisioninduced dipoles of pairs for 28 combinations of bond lengths (ranging from 0.942 a.u. to 2.801 a.u.), 7 intermolecular separations R, and 17 different relative orientations. In our work on Δα, the bond lengths are fixed at 1.449 a.u. Our results agree well with the previous ab initio work of W. Meyer, A. Borysow, and L. Frommhold, Phys. Rev. A 40, 6931 (1989), and of Y. Fu, C. G. Zheng and A. Borysow, J. Quant. Spectroscopy and Rad. Transfer, 67, 303 (2000)where those data existfor Δμ of pairs. For Δα, our results agree well with the CCSD(T) results obtained by G. Maroulis, J. Phys. Chem. A 104, 4772 (2000) for two pair orientations and fixed R. The pair polarizability anisotropies also agree well with the smallbasis selfconsistent field results of D. G. Bounds, Mol. Phys. 38, 2099 (1979), although the trace of the polarizability differs by factors of 2 or more from Bounds' results. We have determined the expansion coefficients for Δμ and Δα, expressed as series in the spherical harmonics of the orientation angles of the intermolecular vector and of unit vectors along the molecular axes. The leading coefficients converge at long range to the predictions from perturbation theory, derived by J. E. Bohr and K. L. C. Hunt, J. Chem. Phys. 87, 3821 (1987); T. Bancewicz, W. G.az, and S. Kielich, Chem. Phys. 128, 321 (1988); and X. Li and K. L. C. Hunt, J. Chem. Phys. 100, 7875 (1994); ibid, 9276 (1994). Based on our results for Δμ, we find excellent agreement for the binary rototranslational absorption spectrum of at 297.5 K as calculated by X. Li, K. L. C. Hunt, F. Wang, M. Abel, and L. Frommhold, Int. J. Spectroscopy 2010, 371201 (2010) and as determined experimentally by G. Bachet, E. R. Cohen, P. Dore, and G. Birnbaum, Can. J. Phys. 61, 591 (1983), out to ∼1500 cm^{−1}. We have also calculated the vibrational spectra out to 20,000 cm^{−1}, at T = 600 K, 1000 K, and 2000 K, for which there are no experimental data. We are currently working to extend the temperature range in the calculations to 7000 K, for application in modeling the spectra of cool white dwarf stars. We have used the results for Δα to calculate collisioninduced rototranslational Raman spectra for pairs [M. Gustafsson, L. Frommhold, X. Li, and K. L. C. Hunt, J. Chem. Phys. 130, 164314 (2009)]. Experimental results for the Raman spectra have been reported by U. Bafile, M. Zoppi, F. Barocchi, M. S. Brown, and L. Frommhold, Phys. Rev. A 40, 1654 (1989); U. Bafile, L. Ulivi, M. Zoppi, F. Barocchi, M. Moraldi, and A. Borysow, Phys. Rev. A 42, 6916 (1990); and M. S. Brown, S.K. Wang, and L. Frommhold, Phys. Rev. A 40, 2276 (1989). Agreement between our calculations and experiment is good for both the polarized and depolarized spectra, with the remaining discrepancies probably attributable to the difference between the static (calculated) and frequencydependent (experimental) values of Δα.

One and twophoton absorptions in openshell singlet systems
View Description Hide DescriptionOne and twophoton absorption cross sections of symmetric openshell singlet molecular systems are investigated using a valence configuration interaction scheme. It is found for onephoton absorption (OPA) that the peak intensity decreases and the peak position moves to the low energy region as increasing the diradical character of the system. In contrast, a significant enhancement of twophoton absorption (TPA) peak is predicted for openshell singlet systems with intermediate diradical character as compared to the closedshell and pure diradical systems. It is revealed that the largest TPA peak intensities occur for openshell singlet diradicals having a ferromagneticallycoupled ground state and strongly depends on the ratio between damping factors of the excited states.

HartreeFock via variational coupled cluster theory: An alternative way to diagonalization free algorithm
View Description Hide DescriptionIt is shown that the nonterminating expansions of the wave function within the variational coupled cluster singles (VCCS) can be exactly treated by summing up the oneparticle density matrix elements in the occupied block using simple recurrence relation. At the same time, this leads to an extremely simple 'a priori' diagonalization free algorithm for the solution of the HartreeFock equations. This treatment corresponds to a nonunitary transformation of orbitals, however, preserving the norm and idempotency of the density matrix. The resulting algorithm enables a HartreeFock solution with 'a priori' localized orbitals. Similar approach can be applied within the KohnSham theory. Analysis of the VCCS expansion in terms of the generalized perturbation theory is also presented. Numerical results are presented for model systems , , , but also for a larger Uracile molecule and an interaction of four Guanine molecules.

Vibrational treatment from a variationperturbation scheme: The VCIP method. Application to the glycolaldehyde
View Description Hide DescriptionAn iterative variationperturbation algorithm allowing a anharmonic vibrational treatment of polyatomic molecules is proposed. This state specific process consists on an iterative construction of small 3N5 Vibrational Configuration Interation (VCI) matrixes (N being the number of atoms) with the most pertinent couplings and includes a perturbative treatment of the weakest contributions. Thus, this scheme allow to massively reduce the size of the CI matrixes with a minimum loss of correlation energy. Through the example of , the results stemmed from the VCIP process are compared to their full VCI counterpart. Moreover, the computations of anharmonic intensities are also implemented. As illustration, the modelization of the medium infrared (MIR) spectrum of the glycolaldehyde is reported.

Analysis of the structure, bonding, aromaticity and existence of possible bondstretch isomerism in trigonal anionic metal clusters,
View Description Hide DescriptionA detailed study of the structure and bonding pattern of the trigonal alkaline earth, metal clusters at the B3LYP/6311+G(d) level is carried out. The stability aspects of these clusters are correlated with their aromaticity criterion calculated in terms of NICS measures. Further stabilization of such anionic metal clusters upon complexation with suitable counter cations is predicted. The existence of the phenomenon of "bond stretch isomerism" among such anionic metal systems is also explored.

Elongation method for linear scaling
View Description Hide DescriptionIn this work, we present a review of the elongation method, focusing on the linearscaling implementation, which speeds up HartreeFock (HF) selfconsistent field (SCF) calculations. The two important aspects of the elongation method for linear scaling are described. One is the socalled cutoff technique, which avoids the bottleneck of the conventional HF scheme, i.e., the number of 2eintegrals and the dimension of diagonalization. The other one is the QFMM method to finally achieve the linear scaling. Some test calculations show its good linear scaling for the elongation method.

Can longrange collisioninduced properties be modeled semiclassically?
View Description Hide DescriptionThe collisioninduced (CI) dipole moment, the CI polarizability and the CI hyperpolarizability are discussed for the pair and the one. The symmetryadapted components of these CI properties are calculated and discussed. Analytical, multipolar longrange behavior of these CI properties is considered as well. In the long range comparison has been made between abinitio symmetryadapted data and the model semianalytical ones. In general good agreement has been observed.

On the chemical enhancement in SERS
View Description Hide DescriptionIn Surfaceenhanced Raman scattering (SERS), the Raman signal of a molecule adsorbed on a metal surface is enhanced by many orders of magnitude. This provides a "fingerprint" of molecules which can be used in ultrasensitive sensing devises. Here we present a timedependent density functional theory (TDDFT) study of the moleculesurface chemical coupling in SERS. A systematic study of the chemical enhancement (CHEM) of metaand parasubstituted pyridines interacting with a small silver cluster ( ) is presented. We find that the magnitude of chemical enhancement is governed to a large extent by the energy difference between the highest occupied energy level (HOMO) of the metal and the lowest unoccupied energy level (LUMO) of the molecule. A twostate approximation shows that the enhancement scales roughly as , where is an average excitation energy between the HOMO of the metal and the LUMO of the molecule and wX the HOMOLUMO gap of the free molecule. Furthermore, we demonstrate that it is possible to control the CHEM enhancement by switching a dithienylethene photoswitch from its closed form to its open form. The open form of the photoswitch is found to be the strongest Raman scatterer when adsorbed on the surface whereas the opposite is found for the free molecule. This trend is explained using the simple twostate approximation.

Overview of finite difference HartreeFock method algorithm, implementation and application
View Description Hide DescriptionTwodimensional, finite difference HartreeFock method has been in constant usage and development over the last two decades. The method has proved stable and efficient enough to be applied to dozens of diatomic molecules, even to systems as large as the thorium fluoride. Its latest version is presented and the dependence of its accuracy on the grid size and efficiency on the overrelaxation parameters are discussed. The method has been mainly used to develop and calibrate sequences of universal eventempered and polarizationconsistent basis sets and assess basis set truncation and superposition errors. Its modified version has proved useful in testing various exchangecorrelation potentials within the density functional theory. The method has turned out to be a valuable source of reference values of total energies, multipole moments, static polarizabilities and hyperpolarizabilities (α_{zz}, β_{zzz}, γ_{zzzz}, A_{z,zz} and B_{zz,zz}) for atoms, diatomic molecules and their ions. Recently, it has been modified to allow to calculate the electrical properties of homonuclear molecules and the results for the , , and systems are presented. Electrical properties of the AlF, CS, KCl diatomics and of highly ionized krypton atom ( ) are reported as well. Accuracy of both the matrix HartreeFock employing universal eventempered basis sets and the finite difference HartreeFock methods is discussed and the basis set superposition errors of the dipole polarizability and the first hyperpolarizability of the FH molecule is reexamined. Basis set superposition errors are also discussed in case of the dipole polarizability and the second hyperpolarizability of the system.

Atomic calculations for future technology and study of fundamental problems
View Description Hide DescriptionSelected modern applications of the atomic calculations ranging from the study of fundamental interactions to applications of atomic physics to future technological developments are reviewed. The coupledcluster approach to highprecision calculation of various atomic properties of monovalent systems is discussed. The computational challenges in the implementation of the allorder approaches including the development of the computer programs capable of performing complicated symbolic calculations, automatic generation of the computer codes are discussed. Novel approach to calculation of the atomic properties of more complicated systems that combines configuration interaction and allorder methods is discussed and preliminary results are presented.
