On the Padé method for sequence acceleration and calculation of Madelung constants

An iterative variant of Padé approximants (PA) is presented and employed to accelerate convergence of sequences. Pilot calculations on partial lattice sums for NaCl and CsCl crystals have been explicitly shown to offer accurate estimates of their Madelung constants.     

Padé approximation for the polynomial representation of the correlation energy density functional

Polynomials in the one-third power of the density were recently proposed to represent approximately the correlation energy density functional [S. Liu and R.G. Parr, Phys. Rev. A 53 (1996) 2211]. Studied in the present work is a Padé-approximant in that same variable which overcomes weaknesses in the polynomial form. Numerical results for atoms and molecules show that Padé forms fairly reproduce the experimental values, and are comparable in accuracy with other commonly used local functionals for the correlation energy.     

Static and dynamic first- and second-order properties by variational wave functions

The problem of the evaluation of first- and second-order energies by the use of arbitrary variational wave functions is examined in detail for time-independent perturbations as well as for time-dependent perturbations. By using a compact formalism the general formulae to be used for the case of a fully optimized set of variational parameters are readily obtained and the most prominent features are examined. The generality of the approach is tested by showing how some widely used methods are obtained by using particular types of variational wave functions. The case of incompletely optimized sets of variational parameters is examined examined extensively and several approaches at different levels of approximation are proposed. Emphasis is put upon the importance of considering, in the calculation of higher-order energies, the variational parameters which may be of negligible importance, and thus often neglected, in the absence of perturbations.     

Quadratic Padé approximants and the intruder state problem of multireference perturbation methods

Simple and quadratic Padé resummation methods are applied to high‐order series from multireference many‐body perturbation theory (MR‐MBPT) calculations using various partitioning schemes (Møller–Plesset, Epstein–Nesbet, and forced degeneracy) to determine their efficacy in resumming slowly convergent or divergent series. The calculations are performed for the ground and low‐lying excited states of (i) CH₂, (ii) BeH₂ at three geometries, and (iii) Be, for which full configuration interaction (CI) calculations are available for comparison. The 49 perturbation series that are analyzed include those with oscillatory and monotonic divergence and convergence, including divergences that arise from either frontdoor or backdoor intruder states. Both the simple and quadratic Padé approximations are found to speed the convergence of slowly convergent or divergent series. However, the quadratic Padé method generally outperforms the simple Padé resummation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Influence of cylindrical submicrometer confinement on the static and dynamic properties in nonyloxycyanobiphenyl (9OCB)

Broadband dielectric spectroscopy (10(2)-1.9 x 10(9) Hz) and specific heat measurements have been performed on nonyloxycyanobiphenyl (9OCB) in the isotropic (I), nematic (N), and smectic A (SmA) phases confined to 200 nm diameter parallel cylindrical pores of Anopore membranes. Untreated and HTBA-treated membranes have been found to obtain axial and radial confinements, respectively. However, structural or configurational transitions in untreated membranes have been reported to exist in the SmA-mesophase of 9OCB. Both confinements clearly affect the N-I and SmA-N phase transitions. In the axial confinement, the analysis of the specific heat and static dielectric permittivity data leads to a second order SmA-N phase transition, which is known to be weakly first order for bulk 9OCB. Dynamic dielectric measurements have accounted for the different molecular motions in both confinements. On both mesophases, either N or SmA, the relaxation processes in axial configuration are faster than in the bulk. However, in radial confinement, they are either equal or slower than in the bulk. Additionally, there are no differences in the energy barrier hindering the molecular motions between the axial and radial confinements and even in relation to bulk. Likewise, dielectric results suggest that the extension inside the pores of the surface pinned molecular layer (proved to be temperature-dependent) persists at high enough temperature as a residual-thin layer adjacent to the pore wall.     

Theoretical study of static second-order nonlinear optical properties of push–pull heteroquinonoid dimers

The static first-hyperpolarizabilities (β) of a number of donor–acceptor substituted heteroquinonoid dimers has been calculated analytically by using the time-dependent Hartree Fock (TDHF) method and split-valence basis sets. The evolution pattern of β of mono-substituted quinoid rings has been found to mirror the pattern of variation of β of the corresponding polyenes. The charge transfer (CT) characteristics of the chosen quinonoid chromophores have been studied in terms of effective CT parameters which have been found to fairly correlate with the calculated β of mono-substituted quinonoids. The relative trend in β of quinonoid dimers has been rationalized on the basis of calculated hardness parameter η and which exhibit linear relationships with the ZINDO-S/CI calculated vertical transition energy corresponding to HOMO→LUMO excitation. The analytically evaluated response property, β correlates fairly with the corresponding two-state calculated β₀ and relevant spectroscopic quantities. The general qualitative trend in β obtained for 3-21G and 6-31G** basis sets has been found to be same. The aromatic factor does not play any significant role in the evolution of second-order NLO responses in heteroquinonoid compounds.     

Fast Padé transform for optimal quantification of time signals from magnetic resonance spectroscopy

The fast Padé transform (FPT) is both a parametric and a nonparametric estimator that is capable of quantifying the input raw time signals without any fitting. The FPT simultaneously interpolates as well as extrapolates, and this is expected to mitigate truncation artifacts. To assess performance, it is necessary to compare the main features of the FPT with the characteristics of other parametric estimators, as well as with the fast Fourier transform (FFT), which can yield only shape spectra. The FPT can also give the shape of a spectrum, but accomplishes this in two totally different ways, with and without computing the spectral parameters (complex frequencies and amplitudes). A number of other parametric estimators used in signal processing are unable to yield shape spectra without prior extraction of the fundamental frequencies and the corresponding amplitudes. The primary goal of the present study is to assess the accuracy, robustness, and efficiency of the FPT for parametric and nonparametric estimations of experimentally measured time signals from in vivo magnetic resonance spectroscopy (MRS). Robustness and steadiness of the FPT are assessed relative to the FFT by monitoring the convergence rates of these two processors through a systematic and gradual decrease of the truncation level of the full signal length. Accuracy of the FPT is verified by performing error analysis of proven validity, using a gold standard, if available. Alternatively, comparison is made between the two complementary variants of the FPT that converge inside and outside the unit circle. Efficiency of the FPT is checked with respect to the FFT for estimation of the shape of a spectrum, as well as relative to other parametric processors, in the case of quantifications. To establish the accuracy, robustness, and efficiency of the FPT within the outlined multi‐level strategy, we use a time signal encoded via MRS at 4T from the brain of a healthy volunteer. We also assess the overall usefulness of the FPT for signal processing of data acquired from patients, in light of the emerging appreciation that spectroscopy of the tissue metabolites offers a number of vital advantages over the corresponding anatomical imaging in diagnostics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Divergence of the R−1 expansion for the second-order H–H interaction

The conventional R^?1 expansion of the second-order intermolecular interaction energy (R = intermolecular distance) is shown to diverge for all R in the prototype case of two 1s hydrogen atoms.     

The calculation of second-order molecular properties at the CI level of accuracy. The magnetisability of LiH

The perturbation theory approach to the calculation of second-order molecular properties is amended for the case when the perturbation is a magnetic field. It is therefore possible to calculate reliably the CI contributions to molecular magnetisabilities and large basis results are presented for LiH.     

Toward a general protocol for the study of static and dynamic properties of hydrogen-bonded systems

We report a critical assessment of the building blocks constituting a general protocol for the study of the structure, strength, and kinetics of hydrogen bridges in large biological systems. The potentialities of self-consistent hybrid approaches for computing reliable potential energy surfaces are described and validated for a number of model systems. Combined discrete-continuum models for studying environmental effects are introduced and applied to some case studies. Finally, some aspects about the role of tunneling are discussed. © 1997 John Wiley & Sons, Inc.     

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H(2)O and NH(3). The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined.     

Efficient polarized basis sets for evaluation of static and dynamic molecular electric properties

New medium size Gaussian‐type basis set R‐ORP for evaluation of static and dynamic electric properties in molecular systems is presented. It is obtained in a close resemblance to the original ORP basis set, from the source basis set through addition of two first‐order polarization functions whose exponent values are optimized with respect to the finite field restricted open‐shell Hartree–Fock (ROHF) atomic polarizabilities. As the source set the VTZ basis set of Ahlrichs and coworkers, augmented with additional diffuse functions and contracted to the form [6s/3s] for hydrogen and [11s7p/4s3p] for carbon through fluorine, is chosen. The resulting basis set is of the form [6s2p/3s2p] for hydrogen and [11s7p2d/4s3p2d] for other atoms. Presented basis set is next tested in the CCSD static and dynamic molecular polarizability and hyperpolarizability calculations for a set of ten and four test molecules, respectively, for which very accurate reference data exist. Additionally, the recently developed ORP basis set is employed in the calculations to examine the limits of its applicability. Results are compared to the literature data obtained in both, large and diffuse, as well as reduced‐size basis sets. In the case of polarizability calculations, the aug‐pc‐1 and R‐ORP are the optimal choices among the investigated smaller basis sets, with the overall performance of the aug‐pc‐1 set being better. Among the larger sets, the ORP performs better in the case of average polarizability, while the RMSE values for polarizability anisotropy are practically identical for d‐aug‐cc‐pVDZ and ORP sets. Finally, the R‐ORP and ORP basis sets compete other small bases in the evaluation of the first hyperpolarizability in investigated systems. © 2016 Wiley Periodicals, Inc.     

Polarized basis sets for accurate calculations of static and dynamic electric properties of molecules

We report on the development and testing of large polarized basis sets (LPolX, where X is the element symbol) for accurate calculations of linear and nonlinear electric properties of molecules. The method used to generate LPolX sets is based on our studies of the analytic dependence of Gaussian functions on external time‐independent and time‐dependent electric fields. At variance with the earlier investigations of small, highly compact (ZPolX) basis sets for moderately accurate calculations of electric properties of large molecules, the present goal is to obtain basis sets that are nearly saturated with respect to the selected class of electric properties and can be used for accurate studies of interaction‐induced properties. This saturation makes the LPolX sets also useful in calculations of optical properties for chiral molecules. In this article, the LPolX sets are generated for X = H, C, N, O, and F, and examined in calculations of linear and nonlinear electric properties of four standard test systems: HF, N₂, CO, and HCN. The study of the performance of LPolX basis sets has been carried out at different levels of approximation ranging from the SCF HF method to highly correlated CCSD(T) approach. The results obtained in this study compare favorably with accurate reference data and show a high level of saturation of LPolX basis sets with respect to the polarization effect due to external electric fields. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Parallel computation of the Moller–Plesset second-order contribution to the electronic correlation energy

We report herein, the implementation of a second-order Moller–Plesset perturbation theory (MP2) program on the IBM LCAP parallel supercomputers. The LCAP systems comprise IBM 308X hosts and 10 FPS-X64 attached processing units (APs). The APs are interconnected by a 512 Mbyte shared memory which allows rapid interprocessor communication. All the computationally demanding steps of the MP2 procedure execute efficiently in parallel. Parallel computation of two-electron integrals is accomplished by distributing the loop over shell blocks among the APs. Parallel Fock matrix formation is achieved by having each AP evaluate the contribution of its own integral sublist to the total Fock matrix. The contributions are added together on the host, and the sum diagonalized either on the host or on a single AP. The parallel implementations of the integral transformation and the MP2 calculation are less straightforward. In each case, the use of the shared memory is essential for an efficient implementation. Details of the implementations and performance data are given.     

Investigation of excited‐state properties of fluorene–thiophene oligomers by the SAC‐CI theoretical approach

Excited states of fluorene‐ethylenedioxythiophene (FEDOT) and fluorene‐S,S‐dioxide‐thiophene (FTSO2) monomers and dimers were studied by the symmetry‐adapted cluster (SAC)‐configuration interaction (CI) method. The absorption and emission peaks observed in the experimental spectra were theoretically assigned. The first three excited states of the optimized conformers, and the conformers of several torsional angles, were computed by SAC‐CI/D95(d). Accurate absorption spectra were simulated by taking the thermal average for the conformers of torsional angles from 0° to 90°. The conformers of torsional angles 0°, 15°, and 30° mainly contributed to the absorption spectra. The full width at half‐maximum of the FEDOT absorption band is 0.60 eV (4839 cm^?1), which agrees very well with the experimental value of 0.61 eV (4900 cm^?1). The maximum absorption wavelength is located at 303 nm, which is close to those of the experimental band (327 nm). The calculated absorption spectrum of FTSO2 showed two bands in the range of 225–450 nm. This agrees very well with the available experimental spectrum of a polymer of FTSO2, where two bands are detected. The excited‐state geometries were investigated by CIS/6‐31G(d). These showed a quinoid‐type structure which exhibited a shortening of the inter‐ring distance (0.06 Å for FEDOT and 0.04 Å for FTSO2). The calculated emission energy of FEDOT is 3.43 eV, which agrees very well with the available experimental data (3.46 eV). The fwhm_E is about 0.49 eV (3952 cm^?1), while the experimental fwhm is 0.43 eV (3500 cm^?1). For FTSO2, two bands were also found in the emission spectrum. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Generalization of the superoperator algorithm for large-scale configuration interaction

A new version of the superoperator algorithm for large-scale configuration interaction (CI), taking into account singly and doubly excited configurations, has been obtained from the covariant CI equations by going to a mixed representation for the variational operators. The rule for operation of the Hamiltonian matrix on the configuration coefficient vector in this representation is reduced to the operations of Coulomb and exchange interaction, without requiring transformations of the molecular integrals. The proposed algorithm saves time in calculation for large basis sets, when the number of vacant orbitals approaches the square of the number of occupied orbitals. An advantage of the proposed approach to the problem of optimization of the geometry, taking into account electron correlation effects, is illustrated by a nonempirical calculation for the H₃O⁺ ion.Report given at the Fourth All-Union Conference on study of the Structure of Molecules in the Gas Phase (Ivanovo, 1987).Translated from Teoretischeskaya i Éksperimental'naya Khimiya, Vol. 26, No. 5, pp. 536–5A3, September–October, 1990.We acknowledge G. E. Vaiman, who directed out attention to the work of Meyer [5], and A. V. Luzanov for help with the work.