Center-of-mass problem in truncated configuration interaction and coupled-cluster calculations

The problem of center-of-mass (CM) contaminations in ab initio nuclear structure calculations using configuration interaction (CI) and coupled-cluster (CC) approaches is analyzed. A rigorous and quantitative scheme for diagnosing the CM contamination of intrinsic observables is proposed and applied to ground-state calculations for ⁴He and ¹⁶O. The CI and CC calculations for ¹⁶O based on model spaces defined via a truncation of the single-particle basis lead to sizable CM contaminations, while the importance-truncated no-core shell model based on the N_maxΩ space is virtually free of CM contaminations.     

Lifetimes and transition probabilities of Xe II: Experimental measurements and theoretical calculations

In this work we make an experimental and theoretical investigation of transition probabilities (A) and lifetimes of Xe II. Eighteen A_ij's corresponding to the 6p-6d array were measured using a Laser Produced Plasma (LPP) as the spectroscopic source. The ab initio (AI) and Least Square Fitting (LSF) approaches were used to calculate the atomic parameters. Relativistic corrections and Configuration Interaction (CI) effects have been taken into account using the HFR approach described by Cowan. Whereas the AI parameters corresponding to 6p levels are not very affected by CI effects, several of the 6d levels with J=1/2, 3/2and 5/2 making transitions to the fundamental levels 5p⁵ are affected by CI effects due to both, discrete nd and continuum states, modifying their lifetimes values. An extensive comparison with other measurements and calculations are made. In particular, concerned with branching ratio and forbidden transitions. Received 15 July 1999     

Analytic MRCI gradient for excited states: formalism and application to the n-π∗ valence- and n-(3s,3p) Rydberg states of formaldehyde

The previously developed formalism for the calculation of the analytic multireference (MR) CI energy gradient with respect to nuclear coordinates based on a single-state MCSCF calculation was extended to the case of state-averaged MCSCF. This extension is of particular importance for calculations of electronically excited states and enables automatic high-level geometry optimizations and saddle point searches on excited-state energy surfaces. Beyond MR-CI, the present analytic gradient method is also available for the MR-ACPF/AQCC methods including size-extensivity corrections for the multireference case. Full geometry optimizations for six electronic states of formaldehyde (valence and Rydberg states) are reported.     

Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.     

A Correction Function Method for Poisson problems with interface jump conditions

In this paper we present a method to treat interface jump conditions for constant coefficients Poisson problems that allows the use of standard “black box” solvers, without compromising accuracy. The basic idea of the new approach is similar to the Ghost Fluid Method (GFM). The GFM relies on corrections applied on nodes located across the interface for discretization stencils that straddle the interface. If the corrections are solution-independent, they can be moved to the right-hand-side (RHS) of the equations, producing a problem with the same linear system as if there were no jumps, only with a different RHS. However, achieving high accuracy is very hard (if not impossible) with the “standard” approaches used to compute the GFM correction terms.     

Applicability of medium-size basis sets in calculations of molecular dynamic polarisabilities

Static and dynamic average polarisabilities and polarisability anisotropies of seven linear non-polar and polar molecules are calculated within the CCS, CC2, and CC3 approximations using a range of medium-sized basis sets: the polarised LPol-n (n = ds, dl, fs, fl), the aug-pc-n (n = 1, 2), the def2-SVPD, and -TZVPD basis sets. Reference values are obtained using a hierarchy of Dunning's (d-)aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The results are discussed together with the available CCSD values in terms of basis set and correlation method errors, and their ratio. Detailed analysis shows that already the def2-SVPD basis set can be used in CCS polarisability calculations. When affordable, the slightly larger aug-pc-1 basis set is recommended, as it leads to significant reduction of basis set error. The def2-TZVPD, LPol-ds, and aug-pc-2 basis sets are optimal choice within the CC2 approximation, with the latter allowing to approach the CC2 basis set limit. The LPol-ds, -dl, and def2-TZVPD sets outperform the aug-cc-pVTZ set in average polarisability CCSD calculations, with the def2-TZVPD being competitive to other reduced-size sets also in determination of polarisability anisotropy. The aug-pc-2 basis is a particularly attractive choice for CCSD, giving the accuracy of aug-cc-pVQZ at a significantly reduced computational cost. The polarisability anisotropy is shown to be more computationally demanding than the average polarisability, in particular with respect to the accuracy of the correlation method and an accurate evaluation of this property requires at least the CCSD model.     

UNO DMRG CASCI calculations of effective exchange integrals for m-phenylene-bis-methylene spin clusters

ABSTRACT

Theoretical examinations of the ferromagnetic coupling in the m-phenylene-bis-methylene molecule and its oligomer were carried out. These systems are good candidates for exchange-coupled systems to investigate strong electronic correlations. We studied effective exchange integrals (J), which indicated magnetic coupling between interacting spins in these species. First, theoretical calculations based on a broken-symmetry single-reference procedure, i.e. the UHF, UMP2, UMP4, UCCSD(T) and UB3LYP methods, were carried out with a GAUSSIAN program code under an SR wave function. From these results, the J value by the UHF method was largely positive because of the strong ferromagnetic spin polarisation effect. The J value by the UCCSD(T) and UB3LYP methods improved an overestimation problem by correcting the dynamical electronic correlation. Next, magnetic coupling among these spins was studied using the CAS-based method of the symmetry-adapted multireference methods procedure. Thus, the UNO DMRG CASCI (UNO, unrestricted natural orbital; DMRG, density matrix renormalised group; CASCI, complete active space configuration interaction) method was mainly employed with a combination of ORCA and BLOCK program codes. DMRG CASCI calculations in valence electron counting, which included all orbitals to full valence CI, provided the most reliable result, and support the UB3LYP method for extended systems.     

Computational modeling of MR flow imaging by the lattice Boltzmann method and Bloch equation

In this work, a computational model of magnetic resonance (MR) flow imaging is proposed. The first model component provides fluid dynamics maps by applying the lattice Boltzmann method. The second one uses the flow maps and couples MR imaging (MRI) modeling with a new magnetization transport algorithm based on the Eulerian coordinate approach. MRI modeling is based on the discrete time solution of the Bloch equation by analytical local magnetization transformations (exponential scaling and rotations).     

Size-consistent multireference configuration interaction method through the dressing of the norm of determinants

A new determinant-specific, effective change (‘dressing’) of the norm of the multireference configuration interaction (MRCI) wavefunction is proposed in order to achieve the size-consistency of the MRCI method. The new approach provides a unifying framework for analysis of size-consistent extensions of the MRCI method that are based on the coupled pair functional (CPF) strategy and lead to simplified computations of the analytical gradients. Using the new framework, a generalized multireference full coupled pair functional (MR-FCPF) method is introduced. The MR-FCPF method may be viewed as a functional counterpart of the recently proposed generalized (‘full’) coupled electron pair approximation (CEPA), referred to as the size-consistent self-consistent CI ((SC)²CI) method. A straightforward extension of the MR-FCPF method leads to a pseudo-functional form of the coupled cluster (CC) type formalisms. Therefore, the new approach may be used to introduce a simple alternative to existing CC-type gradient techniques. The new procedure is formally derived and compared with similar methods from the literature. Model systems calculations (H₂O, LiF, CH⁺ ₂) are further used to demonstrate the effect of various approximations and to elucidate the hierarchy of functional MR-CEPA schemes.     

Duality between QCD perturbative series and power corrections

We elaborate on the relation between perturbative and power-like corrections to short-distance sensitive QCD observables. We confront theoretical expectations with explicit perturbative calculations existing in literature. As is expected, the quadratic correction is dual to a long perturbative series and one should use one of them but not both. However, this might be true only for very long perturbative series, with number of terms needed in most cases exceeding the number of terms available. What has not been foreseen, the quartic corrections might also be dual to the perturbative series. If confirmed, this would imply a crucial modification of the dogma. We confront this quadratic correction against existing phenomenology (QCD (spectral) sum rules scales, determinations of light quark masses and of α_s from τ-decay). We find no contradiction and (to some extent) better agreement with the data and with recent lattice calculations.     

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r 12-)MR-CI IV. The helium dimer (He 2)

The helium dimer interaction potential is computed using the recently proposed (explicitly correlated) r ₁₂-MR-ACPF (averaged coupled-pair functional) method and a [11s8p6d5f4g] basis set. With an MR-ACPF ansatz that contains 121 references we obtain interaction energies that are close to full CI. In a smaller reference space containing 9 functions, however, even by successively adding [3h] and [2i] functions to the basis set mentioned above, the basis set limit could not be reached. While convergence to the basis set limit is slow, it nevertheless is monotonic and therefore allows for extrapolation to the limit. We obtain basis set corrections at R = 4 a ₀ and 5.6 a ₀ which we further extend to all distances and which we apply to the potential energy curve mentioned above. From our calculations, we conclude that a very recent potential which has been calculated using the SAPT (symmetry adapted perturbation theory) method, and which previously was assumed to be the most accurate available, is insufficiently repulsive at short distances. We correct our extrapolated potential for retardation and finally calculate the expectation value of the interatomic distance (?R?) and dissociation energy (D ₀) by solving the Schrödinger equation of the vibrating ⁴He₂. Our results (?R? = 41 ± 13 Å and D ₀ = 2.2 ± 1.0 mK) are in acceptable agreement with very recent calculations in the literature, but they disagree with a recent experiment.     

Pre-roughening dynamics on Si(100) stepped surfaces: a study by molecular dynamics

The thermal evolution of steps on Si(100) is well studied and experiment indicates that at temperatures below the roughening transition (i.e. T? 1000 K) the displacements of atoms at the step-edge are the basic factor of this evolution. However the evaluation of the nature and participants of these displacements is beyond experimental observations and a theoretical approach is therefore needed. The problem addressed by this study is the identification of the properties of atomic motions of step-edge atoms and this investigation is performed applying an isothermal Molecular Dynamics simulation method to simple stepped configurations on Si(100). The calculations describe the functional dependence of the motions of step-edge atoms on the step type, size and temperature and on the nature of the interatomic forces. Possible mechanisms of kink formations are suggested. Received 15 February 2002 Published online 13 August 2002     

Variational-integral perturbation corrections of some lower excited states for hydrogen atoms in magnetic fields

A variational-integral perturbation method(VIPM) is established by combining the variational perturbation with the integral perturbation.The first-order corrected wave functions are constructed,and the second-order energy corrections for the ground state and several lower excited states are calculated by applying the VIPM to the hydrogen atom in a strong uniform magnetic field.Our calculations demonstrated that the energy calculated by the VIPM only shows a negative value,which indicates that the VIPM method is more accurate than the other methods.Our study indicated that the VIPM can not only increase the accuracy of the results but also keep the convergence of the wave functions.     

Application of perceptual difference model on regularization techniques of parallel MR imaging

Parallel magnetic resonance imaging through sensitivity encoding using multiple receiver coils has emerged as an effective tool to reduce imaging time or to improve image SNR. The quality of reconstructed images is limited by the inaccurate estimation of the sensitivity map, noise in the acquired k-space data and the ill-conditioned nature of the coefficient matrix. Tikhonov regularization is a popular method to reduce or eliminate the ill-conditioned nature of the problem. In this approach, selection of the regularization map and the regularization parameter is very important. Perceptual difference model (PDM) is a quantitative image quality evaluation tool that has been successfully applied to varieties of MR applications. High correlation between the human rating and PDM score shows that PDM should be suitable to evaluate image quality in parallel MR imaging. By applying PDM, we compared four methods of selecting the regularization map and four methods of selecting the regularization parameter. We found that a regularization map obtained using generalized series (GS) together with a spatially adaptive regularization parameter gave the best reconstructions. PDM was also used as an objective function for optimizing two important parameters in the spatially adaptive method. We conclude that PDM enables one to do comprehensive experiments and that it is an effective tool for designing and optimizing reconstruction methods in parallel MR imaging.     

Elastic scattering, muon transfer, bound states and resonances in the three-body mesic molecular systems in the reduced adiabatic hyperspherical approach

The uniform method of numerical investigation of bound states and scattering processes 2→ 2 (including resonance states) in the Coulomb three-body (CTB) systems is developed. It is based on the adiabatic hyperspherical approach (AHSA) and includes the numerical realization and applications to the three-body mesic atomic systems. The results of calculations of bound states of these systems (including the local characteristics of the wave functions) and the scattering processes 2→ 2 (including the characteristics of the resonance states) are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electroweak corrections to the observables of W-boson production at RHIC

The processes of the single W-production in hadron-hadron collisions are suggested for investigation of the nucleon spin. An approach is proposed for the determination of quark spin densities at low x. The lowest order electroweak radiative corrections to the observable quantities are calculated. The numerical calculations of the cross sections and the single spin asymmetries taking into consideration the electroweak corrections at RHIC energies have been made.     

Construction and solution of a Wannier-functions based Hamiltonian in the pseudopotential plane-wave framework for strongly correlated materials

Ab initio determination of model Hamiltonian parameters for strongly correlated materials is a key issue in applying many-particle theoretical tools to real narrow-band materials. We propose a selfcontained calculation scheme to construct, with an ab initio approach, and solve such a Hamiltonian. The scheme uses a Wannier-function-basis set, with the Coulomb interaction parameter U obtained specifically for theseWannier functions via constrained Density functional theory (DFT) calculations. The Hamiltonian is solved by Dynamical Mean-Field Theory (DMFT) with the effective impurity problem treated by the Quantum Monte Carlo (QMC) method. Our scheme is based on the pseudopotential plane-wave method, which makes it suitable for developments addressing the challenging problem of crystal structural relaxations and transformations due to correlation effects. We have applied our scheme to the “charge transfer insulator” material nickel oxide and demonstrate a good agreement with the experimental photoemission spectra.     

Second-order eikonal corrections for

The first-order eikonal approximation is frequently adopted in interpreting the results of A(e,e^′p) measurements. Glauber calculations, for example, typically adopt the first-order eikonal approximation. We present an extension of the relativistic eikonal approach to A(e,e^′p) which accounts for second-order eikonal corrections. The numerical calculations are performed within the relativistic optical model eikonal approximation. The nuclear transparency results indicate that the effect of the second-order eikonal corrections is rather modest, even at Q²≈0.2 (GeV/c)². The same applies to polarization observables, left–right asymmetries, and differential cross sections at low missing momenta. At high missing momenta, however, the second-order eikonal corrections are significant and bring the calculations in closer agreement with the data and/or the exact results from models adopting partial-wave expansions.     

Comparison of quantum, semiclassical and classical methods in hydrogen broadening of nitrogen lines

We use an accurate N₂-H₂ab initio potential energy surface (PES) in order to inter-compare various methods commonly employed to calculate pressure broadening coefficients. Close-coupling (CC) calculations of the collisional linewidths of the isotropic Raman lines of N₂ perturbed by H₂ are performed for temperatures between 77 and 2000 K. The CC results compare well with available experimental values. Three less exact methods of calculation are also used: the full classical (FC) model of Gordon, the semiclassical (SC) formalism of Robert and Bonamy and the quantum dynamical coupled states (CS) method. The CS method provides good agreement with CC calculations for all studied temperatures, FC calculations can be considered as accurate above room temperature while the SC method gives overestimated values by about 20-30% in all cases. The temperature dependences of pressure broadening coefficients provided by each method are very similar at elevated (above room) temperatures.     

A posteriori Brillouin—Wigner correction of limited multireference configuration interaction: analysis for an (H2)4 cluster model

An a posteriori Brillouin—Wigner correction is applied to a limited multireference configuration interaction study of a simple model problem consisting of four H₂ molecules arranged in a distorted octagonal conformation in which the degree of quasidegeneracy depends on a single parameter designated a. Double reference configuration interaction calculations are performed as a function of the parameter a. A posteriori Brillouin—Wigner corrections are applied and compared with a generalization of the Davidson correction for multireference applications. The calculated total energies for the ground state are compared with full configuration interaction studies carried out within the same basis set of Gaussian-type functions. The basis set dependence of the problem is explored by performing calculations in two small Gaussian basis sets: one of minimum basis set quality and the other of ‘double ζ’ type.