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Perturbation Theory (perturbation + theory)
Kinds of Perturbation Theory Selected AbstractsOptimised Dirac operators on the lattice: construction, properties and applicationsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2 20082Article first published online: 29 NOV 200, W. Bietenholz Abstract We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p -regime and in the ,-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian , the chiral condensate and the pion decay constant , from QCD simulations with extremely light quarks. [source] Rydberg states of the helium atomINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 9 2009Jia Deng Abstract Using the recently introduced maximum overlap method and Hartree,Fock Perturbation Theory (HFPT), we compute Hartree,Fock (HF) wavefunctions for triplet 1s ns states of the helium atom. Comparison with near-exact results from Nakatsuji's free ICI method reveals that HF theory provides a simple route to accurate energies of these Rydberg states, especially for large n. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Calculation of the vibration frequencies of ,-quartz: The effect of Hamiltonian and basis setJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 15 2004C. M. Zicovich-Wilson Abstract The central-zone vibrational spectrum of ,-quartz (SiO2) is calculated by building the Hessian matrix numerically from the analytical gradients of the energy with respect to the atomic coordinates. The nonanalytical part is obtained with a finite field supercell approach for the high-frequency dielectric constant and a Wannier function scheme for the evaluation of Born charges. The results obtained with four different Hamiltonians, namely Hartree,Fock, DFT in its local (LDA) and nonlocal gradient corrected (PBE) approximation, and hybrid B3LYP, are discussed, showing that B3LYP performs far better than LDA and PBE, which in turn provide better results than HF, as the mean absolute difference from experimental frequencies is 6, 18, 21, and 44 cm,1, respectively, when a split valence basis set containing two sets of polarization functions is used. For the LDA results, comparison is possible with previous calculations based on the Density Functional Perturbation Theory and usage of a plane-wave basis set. The effects associated with the use of basis sets of increasing size are also investigated. It turns out that a split valence plus a single set of d polarization functions provides frequencies that differ from the ones obtained with a double set of d functions and a set of f functions on all atoms by on average less than 5 cm,1. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1873,1881, 2004 [source] Perturbation theory and excursion set estimates of the probability distribution function of dark matter, and a method for reconstructing the initial distribution functionMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2008Tsz Yan Lam ABSTRACT Non-linear evolution is sometimes modelled by assuming there is a deterministic mapping from initial to final values of the locally smoothed overdensity. However, if an underdense region is embedded in a denser one, then it is possible that its evolution is determined by its surroundings, so the mapping between initial and final overdensities is not as ,local' as one might have assumed. If this source of non-locality is not accounted for, then it appears as stochasticity in the mapping between initial and final densities. Perturbation theory methods ignore this ,cloud-in-cloud' effect, whereas methods based on the excursion set approach do account for it; as a result, one may expect the two approaches to provide different estimates of the shape of the non-linear counts in cells distribution. We show that, on scales where the rms fluctuation is small, this source of non-locality has only a small effect, so the predictions of the two approaches differ only on the small scales on which perturbation theory is no longer expected to be valid anyway. We illustrate our results by comparing the predictions of these approaches when the initial,final mapping is given by the spherical collapse model. Both are in reasonably good agreement with measurements in numerical simulations on scales where the rms fluctuation is of the order of unity or smaller. If the deterministic mapping from initial conditions to final density depends on quantities other than the initial density, then this will also manifest as stochasticity in the mapping from initial density to final. For example, the Zeldovich approximation and the ellipsoidal collapse model both assume that the initial shear field plays an important role in determining the evolution. We compare the predictions of these approximations with simulations, both before and after accounting for the ,cloud-in-cloud' effect. Our analysis accounts approximately for the fact that the shape of a cell at the present time is different from its initial shape; ignoring this makes a noticeable difference on scales where the rms fluctuation in a cell is of the order of unity or larger. On scales where the rms fluctuation is 2 or less, methods based on the spherical model are sufficiently accurate to permit a rather accurate reconstruction of the shape of the initial distribution from the non-linear one. This can be used as the basis for a method for constraining the statistical properties of the initial fluctuation field from the present-day field, under the hypothesis that the evolution was purely gravitational. We illustrate by showing how the highly non-Gaussian non-linear density field in a numerical simulation can be transformed to provide an accurate estimate of the initial Gaussian distribution from which it evolved. [source] Convergence radii of the polarization expansion of intermolecular potentialsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009William H. Adams Abstract A new method is presented to evaluate convergence radii of the polarization expansion of interaction energies for pairs of atoms or molecules. The method is based on an analysis of the variation of the perturbed state vector as a function of the coupling constant , and does not require a calculation of perturbation corrections to high order. The convergence radii at infinite interatomic/intermolecular distances R, as well as a remarkably accurate representation of the R dependence of the convergence radii are obtained from simple calculations involving only monomer wave functions. For the interaction of the lithium and hydrogen atoms, the obtained convergence radii agree well with those obtained previously from the large-order calculations of Patkowski et al. (Patkowski et al., J Chem Phys, 2002, 117, 5124), but are expected to be considerably more accurate. Rigorous upper bounds and reasonable approximations to the convergence radii at R = , are obtained for the pairs of lithium, beryllium, boron, neon, and sodium atoms, as well as for the dimer consisting of two LiH molecules. For all the systems studied, the convergence radii are significantly smaller than the unity and rapidly decrease with the increase of the nuclear charge. It is hoped that the results of this investigation will help to analyze and eventually to compute the convergence radii of the symmetry-adapted perturbation theories which utilize the same partitioning of the Hamiltonian as the polarization expansion. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Structure, reactivity and spectroscopic properties of minerals from lateritic soils: insights from ab initio calculationsEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 4 2007E. Balan Summary We review here some recent applications of ab initio calculations to the modelling of spectroscopic and energetic properties of minerals, which are key components of lateritic soils or govern their geochemical properties. Quantum mechanical ab initio calculations are based on density functional theory and density functional perturbation theory. Among the minerals investigated, zircon is a typical resistant primary mineral. Its resistance to weathering is at the origin of the peculiar geochemical behaviour of Zr, an element often used in mass balance calculations of continental weathering. Numerical modelling gives a unique picture of the origin of the chemical durability and radiation-induced amorphization of zircon. We also present several applications of ab initio calculations to the description of properties of secondary minerals, such as kaolinite-group minerals and gibbsite. Special attention is given to the calculation of infrared and Raman spectra. Surface properties and particle shape are major properties of finely-divided materials such as clay minerals. We show how theoretical modelling of infrared spectroscopic data provides information on natural samples at both the microscopic (atomic structure) and macroscopic (particle shape) length-scale. The systematic comparison of experimental and theoretical data significantly improves our understanding of mineral transformations during soil formation and evolution in lateritic environments. [source] Membranes, strings and integrabilityFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-7 2009C. Krishnan Abstract In the first half of this note, after briefly motivating and reviewing membrane field theories, we discuss their BPS funnel solutions. We discuss some aspects of embedding M-theory fuzzy funnels in these theories. In the second half, we focus on ABJM theory and discuss a test of AdS4/CFT3 based on integrability. We discuss a numerical mismatch at one loop in worldsheet perturbation theory and its possible resolutions. [source] Optimised Dirac operators on the lattice: construction, properties and applicationsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2 20082Article first published online: 29 NOV 200, W. Bietenholz Abstract We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p -regime and in the ,-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian , the chiral condensate and the pion decay constant , from QCD simulations with extremely light quarks. [source] Generalizations of the AdS/CFT correspondence,FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 8 2004I. Kirsch Abstract We consider generalizations of the AdS/CFT correspondence in which probe branes are embedded in gravity backgrounds dual to either conformal or confining gauge theories. These correspond to defect conformal field theories (dCFT) or QCD-like theories with fundamental matter, respectively. Moreover, starting from the dCFT we discuss the deconstruction of intersecting M5-branes and M-theory. We obtain the following results: i) Holography of defect conformal field theories. We consider holography for a general D3-Dp brane intersection in type IIB string theory (p , {3,5,7}). The corresponding near-horizon geometry is given by a probe AdS-brane in AdS5 × S5. The dual defect conformal field theory describes ,, = 4 super Yang-Mills degrees of freedom coupled to fundamental matter on a lower-dimensional space-time defect. We derive the spectrum of fluctuations about the brane embedding and determine the behaviour of correlation functions involving defect operators. We also study the dual conformal field theory in the case of intersecting D3-branes. To this end, we develop a convenient superspace approach in which both two- and four-dimensional fields are described in a two-dimensional (2,2) superspace. We show that quantum corrections vanish to all orders in perturbation theory, such that the theory remains a (defect) conformal field theory when quantized. ii) Flavour in generalized AdS/CFT dualities. We present a holographic non-perturbative description of QCD-like theories with a large number of colours by embedding D7-brane probes into two non-supersymmetric gravity backgrounds. Both backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the quark condensate and meson spectrum associated with these backgrounds. In the first background, we find some numerical evidence for a first order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the second, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson. iii) Deconstruction of extra dimensions. We apply the deconstruction method to the dCFT of intersecting D3-branes to obtain a field theory description for intersecting M5-branes. The resulting theory corresponds to two six-dimensional (2,0) superconformal field theories which we show to have tensionless strings on their four-dimensional intersection. Moreover, we argue that the SU(2)L R-symmetry of the dCFT matches the manifest SU(2) R-symmetry of the M5-M5 intersection. We finally explore the fascinating idea of deconstructing M-theory itself. We give arguments for an equivalence of M-theory on a certain background with the Higgs branch of a four-dimensional non-supersymmetric (quiver) gauge theory: in addition to a string theoretical motivation, we find wrapped M2-branes in the mass spectrum of the quiver theory at low energies. [source] Field theory on a non-commutative plane: a non-perturbative studyFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5 2004F. Hofheinz Abstract The 2d gauge theory on the lattice is equivalent to the twisted Eguchi,Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. The large N double scaling limit corresponds to the continuum limit of non-commutative gauge theory, so the observed large N scaling demonstrates the non-perturbative renormalizability of this non-commutative field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter. Next we investigate the 3d ,,4 model with two non-commutative coordinates and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d = 4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns. We further present results for the correlators and the dispersion relation. In non-commutative field theory the Lorentz invariance is explicitly broken, which leads to a deformation of the dispersion relation. In one loop perturbation theory this deformation involves an additional infrared divergent term. Our data agree with this perturbative result. We also confirm the recent observation by Ambjø rn and Catterall that stripes occur even in d = 2, although they imply the spontaneous breaking of the translation symmetry. [source] Non-commutative field theories beyond perturbation theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003W. Bietenholz We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we measure Wilson loops in 2d NC gauge theory of rank 1. It turns out that they are non-perturbatively renormalizable, and the phase follows an Aharonov-Bohm effect if we identify , = 1/B. Next we study the 3d , ,4 model with two NC coordinates, where we present new results for the correlators and the dispersion relation. We further reveal the explicit phase diagram. The ordered regime splits into a uniform and a striped phase, as it was qualitatively conjectured before. We also confirm the recent observation by Ambjø rn and Catterall that such stripes occur even in d = 2, although they imply the spontaneous breaking of translation symmetry. However, in d = 3 and d = 2 we observe only patterns of two stripes to be stable in the range of parameters investigated. [source] On the absence of large-order divergences in superstring theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 1 2003S. Davis The genus-dependence of multi-loop superstring amplitudes is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string perturbation theory, a result which is based only on the supersymmetric generalization of the Polyakov measure and not the gauge group of the string model. [source] Body waves in a weakly anisotropic medium,II.GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2001P waves from a centre of rotation, S waves from a centre of expansion Summary A perturbation theory is presented, providing a simple description of the S wave from a centre of expansion and the P wave from a centre of rotation. The relationships between the directivities of these waves and polarization anomalies of plane waves are established. The effect of anisotropy on the generation of these waves is compared with that of a smooth inhomogeneity. [source] Ab Initio Structure/Reactivity Investigations of Illudin-Based Antitumor Agents: A Model for Reaction in vivoHELVETICA CHIMICA ACTA, Issue 12 2003Laura (Hydroxymethyl)acylfulvene (HMAF, irofulven; 4), a third-generation derivative of a natural product extracted from the mushroom Omphalotus illudens, is selectively toxic towards certain forms of malignant tumors. Conversion of HMAF and cognates to stable aromatic derivatives is triggered by thiol attack in vitro and in vivo. Quantum-chemical methods predict well the structure for several functionalized derivatives of irofulven as compared to known X-ray crystallographic structures. Computational reaction profiles for thiol attack and aromatic rearrangement of irofulven and illudin S, a toxin from which irofulven is derived, provide insight into HMAF's selectivity and toxicity. Methods used include hybrid density-functional theory (HDFT), HartreeFock (HF), and MøllerPlesset second-order perturbation theory (MP2). Solvent effects have been explored by means of the new continuum-solvation method, COSab, presented in an accompanying paper. [source] Computing eigenvalue bounds of structures with uncertain-but-non-random parameters by a method based on perturbation theoryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2007Huinan Leng Abstract In this paper, an eigenvalue problem that involves uncertain-but-non-random parameters is discussed. A new method is developed to evaluate the reliable upper and lower bounds on frequencies of structures for these problems. In this method the matrix in the deviation amplitude interval is considered to be a perturbation around the nominal value of the interval matrix, and the upper and lower bounds to the maximum and minimum eigenvalues of this perturbation matrix are computed, respectively. Then based on the matrix perturbation theory, the eigenvalue bounds of the original interval eigenvalue problem can be obtained. Finally, two numerical examples are provided and the results show that the proposed method is reliable and efficient. Copyright © 2006 John Wiley & Sons, Ltd. [source] A two-dimensional stochastic algorithm for the solution of the non-linear Poisson,Boltzmann equation: validation with finite-difference benchmarks,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2006Kausik Chatterjee Abstract This paper presents a two-dimensional floating random walk (FRW) algorithm for the solution of the non-linear Poisson,Boltzmann (NPB) equation. In the past, the FRW method has not been applied to the solution of the NPB equation which can be attributed to the absence of analytical expressions for volumetric Green's functions. Previous studies using the FRW method have examined only the linearized Poisson,Boltzmann equation. No such linearization is needed for the present approach. Approximate volumetric Green's functions have been derived with the help of perturbation theory, and these expressions have been incorporated within the FRW framework. A unique advantage of this algorithm is that it requires no discretization of either the volume or the surface of the problem domains. Furthermore, each random walk is independent, so that the computational procedure is highly parallelizable. In our previous work, we have presented preliminary calculations for one-dimensional and quasi-one-dimensional benchmark problems. In this paper, we present the detailed formulation of a two-dimensional algorithm, along with extensive finite-difference validation on fully two-dimensional benchmark problems. The solution of the NPB equation has many interesting applications, including the modelling of plasma discharges, semiconductor device modelling and the modelling of biomolecular structures and dynamics. Copyright © 2005 John Wiley & Sons, Ltd. [source] Self-propulsion of oscillating wings in incompressible flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2008A. Carabineanu Abstract In this paper, we show that the oscillatory motion of an airfoil (wing) in an ideal fluid can determine the apparition of thrust. In the framework of the linearized perturbation theory, the pressure jump over the oscillating wing is the solution of a two-dimensional hypersingular integral equation. Using appropriate quadrature formulas, we discretize the oscillatory lifting surface integral equation in order to obtain the jump of the pressure across the surface. Integrating numerically, we obtain the drag coefficient. For some oscillatory motions, if the frequency of the oscillations surpasses a certain value, the drag coefficient becomes negative, i.e. there appears a propulsive force. Copyright © 2007 John Wiley & Sons, Ltd. [source] How many-body perturbation theory (MBPT) has changed quantum chemistryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009Werner KutzelniggArticle first published online: 26 AUG 200 Abstract The history of many-body perturbation theory (MBPT) and its impact on Quantum Chemistry is reviewed, starting with Brueckner's conjecture of a linked-cluster expansion and the time-dependent derivation by Goldstone of such an expansion. A central part of this article is the time-independent formulation of quantum chemistry in Fock space and its diagrammatic representation including the particle-hole picture and the inversion of a commutator. The results of the time-independent derivation of MBPT are compared with those of Goldstone. It is analyzed which ingredients of Goldstone's approach are decisive. The connected diagram theorem is derived both in a constructive way based on a Lie-algebraic formulation and a nonconstructive way making use of the separation theorem. It is discussed why the Goldstone derivation starting from a unitary time-evolution operator, ends up with a wave operator in intermediate normalization. The Møller,Plesset perturbation expansions of Bartlett and Pople are compared. Examples of complete summations of certain classes of diagrams are discussed, for example, that which leads to the Bethe-Goldstone expansion. MBPT for energy differences is analyzed. The paper ends with recent developments and challenges, such as the generalization of normal ordering to arbitrary reference states, contracted Schrödinger k -particle equations and Brillouin conditions, and finally the Nakatsuji theorem and the Nooijen conjecture. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Chiral discrimination in hydrogen-bonded complexes of 2-methylol oxirane with hydrogen peroxideINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2009Guiqiu Zhang Abstract A systematic quantum chemical study reveals the effects of chirality on the intermolecular interactions between two chiral molecules bound by hydrogen bonds. The methods used are second-order Møller,Plesset perturbation theory (MP2) with the 6-311++g(d,p) basis set. Complexes via the OH···O hydrogen bond formed between the chiral 2-methylol oxirane (S) and chiral HOOH (P and M) molecules have been investigated, which lead to four diastereomeric complexes. The nomenclature of the complexes used in this article is enantiomeric configuration sign corresponding to English letters. Such as: sm, sp. The relative positions of the methylol group and the hydrogen peroxide are designated as syn (same side) and anti (opposite side). The largest chirodiastaltic energy was ,Echir = ,1.329 kcal mol,1 [9% of the counterpoise correct average binding energy De(corr)] between the sm-syn and sp-anti in favor of sm-syn. The largest diastereofacial energy was ,1.428 kcal mol,1 between sm-syn and sm-anti in favor of sm-syn. To take into account solvents effect, the polarizable continuum model (PCM) method has been used to evaluate the chirodiastaltic energies, and diastereofacial energies of the 2-methylol oxirane···HOOH complexes. The chiral 2,3-dimethylol oxirane (S, S) is C2 symmetry which offers two identical faces. Hence, the chirodiastaltic energy is identical to the diastereomeric energy, and is ,Echir = 0.563 kcal mol,1 or 5.3% of the De(corr) in favor of s,s-p. The optimized structures, interaction energies, and chirodiastaltic energies for various isomers were estimated. The harmonic frequencies, IR intensities, rotational constants, and dipole moments were also reported. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Theoretical studies on structures and electronic spectra of linear carbon chains C2nH+ (n = 1,5)INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2009Jinglai Zhang Abstract The density functional theory (DFT) and the complete active space self-consistent-field (CASSCF) method have been used for full geometry optimization of carbon chains C2nH+ (n = 1,5) in their ground states and selected excited states, respectively. Calculations show that C2nH+ (n = 1,5) have stable linear structures with the ground state of X3, for C2H+ or X3,, for other species. The excited-state properties of C2nH+ have been investigated by the multiconfigurational second-order perturbation theory (CASPT2), and predicted vertical excitation energies show good agreement with the available experimental values. On the basis of our calculations, the unsolved observed bands in previous experiments have been interpreted. CASSCF/CASPT2 calculations also have been used to explore the vertical emission energy of selected low-lying states in C2nH+ (n = 1,5). Present results indicate that the predicted vertical excitation and emission energies of C2nH+ have similar size dependences, and they gradually decrease as the chain size increases. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Comparison of second-order orbital-dependent DFT correlation functionalsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 12 2008Ireneusz Grabowski Abstract The choice of the orbital-dependent second-order correlation functional plays the prime role in the description of the correlation effects in orbital-dependent DFT calculations. Using second-order perturbation theory we were able to derive the simplest orbital-dependent correlation functional, but even at this lowest correlation level, we had several possibilities to define it. Applications of different second-order correlation functionals for the atomic as well as molecular systems are presented. The ab initio DFT-type OEP2 functionals based on Møller-Plesset or semicanonical partitioning (OEP2-sc) are compared with those based on Epstein-Nesbet type partitioning, showing that the latter ones can fail in more difficult molecular problems, e.g., the Be dimer potential curve. We show that currently the best performing orbital-dependent second-order correlation functional is the OEP2-sc one. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Algebraic modifications to second quantization for non-Hermitian complex scaled hamiltonians with application to a quadratically convergent multiconfigurational self-consistent field methodINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2005Danny L. Yeager Abstract The algebraic structure for creation and annihilation operators defined on orthogonal orbitals is generalized to permit easy development of bound-state techniques involving the use of non-Hermitian Hamiltonians arising from the use of complex-scaling or complex-absorbing potentials in the treatment of electron scattering resonances. These extensions are made possible by an orthogonal transformation of complex biorthogonal orbitals and states as opposed to the customary unitary transformation of real orthogonal orbitals and states and preserve all other formal and numerical simplicities of existing bound-state methods. The ease of application is demonstrated by deriving the modified equations for implementation of a quadratically convergent multiconfigurational self-consistent field (MCSCF) method for complex-scaled Hamiltonians but the generalizations are equally applicable for the extension of other techniques such as single and multireference coupled cluster (CC) and many-body perturbation theory (MBPT) methods for their use in the treatment of resonances. This extends the domain of applicability of MCSCF, CC, MBPT, and methods based on MCSCF states to an accurate treatment of resonances while still using L2 real basis sets. Modification of all other bound-state methods and codes should be similarly straightforward. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Logarithmic perturbation theory for a spiked oscillator and sum rulesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005S. K. Bandyopadhyay Abstract We show that logarithmic perturbation theory nicely yields the wavefunction correction terms in closed forms for the spiked perturbation ,/x2 on the first excited state of the harmonic oscillator, where the conventional Rayleigh-Schrödinger scheme is known to encounter serious problems. The study also provides a direct route to obtain several sum rules, some of which appear to be new. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Computation of STM images of carbon nanotubesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2003P. Lambin Abstract Scanning tunneling microscopy (STM) is the only probing technique that allows for the investigation of both the topography and the electronic structure of carbon nanosystems at a subnanometer resolution. The interpretation of the STM images of carbon nanostructures involves complications that are normally absent in the study of planar crystalline surfaces. The complications typically appear from a number of quantum effects responsible for distortions in the microscope image of a nano-object. Because of these difficulties, computer simulation plays an extremely important role in the analysis of experimental data. In the current article, we report on two theoretical approaches developed for aiding in the interpretation and understanding of the formation of the STM image of a nanotube: first, the quantum mechanical dynamics of a wave packet, which allows for the modeling of the flow of the tunneling current between a tip and a nanotube supported by a substrate; and, second, a tight-binding perturbation theory that allows for the explicit calculation of realistic STM images and scanning tunneling spectra of carbon nanostructures. An atlas of computed STM images is provided for a series of 27 single-wall nanotubes with diameter around 1.3 nm. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003 [source] A posteriori corrections to multireference limited configuration interaction based on a Brillouin,Wigner perturbative analysisINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2002I. Hubac Abstract A new a posteriori correction to the method of limited configuration interaction is described that attempts to restore a linear scaling with particle number. The corrections are based on an analysis of the limited configuration interaction method in terms of the Brillouin,Wigner perturbation theory using a Lippmann,Schwinger-like equation. The new correction procedure is general and, in this work, the application to the limited multireference configuration interaction approximation is considered in some detail. An illustrative application to the rigid rotation of the diimine molecule is presented and the results are compared with those obtained by employing Davidson-like corrections and the corresponding full configuration interaction energies. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] BSSE-free description of the formamide dimersINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2001A. Bende Abstract The different configurations (linear, zig-zag, and cyclic) of formamide dimers have been studied at the level of both Hartree,Fock (HF) and second order Møller,Plesset perturbation theory (MP2). The widely used a posteriori Boys,Bernardi "counterpoise" (CP) correction scheme has been compared with our a priori methods utilizing the "chemical Hamiltonian approach" (CHA). The appropriate interaction energies have been calculated in six different basis sets (6-31G, 6-31G**, DZV, DZP, TZV, and cc-pVDZ). © 2001 John Wiley & Sons, Inc. Int J Quant Chem, 2001 [source] Rotationally symmetric FDTD for wideband performance prediction of TM01 DR filtersINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 3 2002Andrew R. Weily Abstract The generalized perfectly matched layer (GPML) coupled with rotationally symmetric (RS)-FDTD method has been utilized to extract the S-parameters for several probe-coupled TM01 dielectric resonator (DR) filters to directly obtain the theoretical wideband spurious performance. The computationally efficient (RS)-FDTD method has also been used to obtain accurate filter parameters for TE01 and TM01 dielectric resonators loaded in cylindrical cavities. The RS-FDTD method combined with digital filtering and the Matrix Pencil technique are used to analyze the resonant frequencies, inter-resonator coupling, and external Q values. When perturbation theory is used with RS-FDTD, accurate values of unloaded Q are obtained. © 2002 Wiley Periodicals, Inc. Int J RF and Microwave CAE 12: 259,271, 2002. [source] MOLCAS 7: The Next GenerationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2010Francesco Aquilante Abstract Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented in this report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two-electron integrals and in the generation of so-called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self-consistent field, density functional theory, 2nd order perturbation theory, complete-active space self-consistent field multiconfigurational reference 2nd order perturbation theory, and coupled-cluster methods. The report further elaborates on the implementation of a restricted-active space self-consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas-Kroll-Hess transformation for one-component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so-called picture-change-free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010 [source] Relativistic and electron-correlation effects on magnetizabilities investigated by the Douglas-Kroll-Hess method and the second-order Møller-Plesset perturbation theoryJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 15 2009Terutaka Yoshizawa Abstract Isotropic and anisotropic magnetizabilities for noble gas atoms and a series of singlet and triplet molecules were calculated using the second-order Douglas-Kroll-Hess (DKH2) Hamiltonian containing the vector potential A and in part using second-order generalized unrestricted Møller-Plesset (GUMP2) theory. The DKH2 Hamiltonian was resolved into three parts (spin-free terms, spin-dependent terms, and magnetic perturbation terms), and the magnetizabilities were decomposed into diamagnetic and paramagnetic terms to investigate the relativistic and electron-correlation effects in detail. For Ne, Kr, and Xe, the calculated magnetizabilities approached the experimental values, once relativistic and electron-correlation effects were included. For the IF molecule, the magnetizability was strongly affected by the spin-orbit interaction, and the total relativistic contribution amounted to 22%. For group 17, 16, 15, and 14 hydrides, the calculated relativistic effects were small (less than 3%), and trends were observed in relativistic and electron-correlation effects across groups and periods. The magnetizability anisotropies of triplet molecules were generally larger than those of similar singlet molecules. The so-called relativistic-correlation interference for the magnetizabilities computed using the relativistic GUMP2 method can be neglected for the molecules evaluated, with exception of triplet SbH. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Molecular dynamics simulations of fluid methane properties using ab initio intermolecular interaction potentialsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 12 2009Shih-Wei Chao Abstract Intermolecular interaction energy data for the methane dimer have been calculated at a spectroscopic accuracy and employed to construct an ab initio potential energy surface (PES) for molecular dynamics (MD) simulations of fluid methane properties. The full potential curves of the methane dimer at 12 symmetric conformations were calculated by the supermolecule counterpoise-corrected second-order Møller-Plesset (MP2) perturbation theory. Single-point coupled cluster with single and double and perturbative triple excitations [CCSD(T)] calculations were also carried out to calibrate the MP2 potentials. We employed Pople's medium size basis sets [up to 6-311++G(3df, 3pd)] and Dunning's correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q). For each conformer, the intermolecular carbon,carbon separation was sampled in a step 0.1 Å for a range of 3,9 Å, resulting in a total of 732 configuration points calculated. The MP2 binding curves display significant anisotropy with respect to the relative orientations of the dimer. The potential curves at the complete basis set (CBS) limit were estimated using well-established analytical extrapolation schemes. A 4-site potential model with sites located at the hydrogen atoms was used to fit the ab initio potential data. This model stems from a hydrogen,hydrogen repulsion mechanism to explain the stability of the dimer structure. MD simulations using the ab initio PES show quantitative agreements on both the atom-wise radial distribution functions and the self-diffusion coefficients over a wide range of experimental conditions. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009 [source] | ||||||||||||||||||||||||||||||||||