Perturbation Theory Treatment Research Articles

Resonance width distribution in RMT: Weak-coupling regime beyond Porter-Thomas

We employ the random matrix theory (RMT) framework to revisit the distribution of resonance widths in quantum chaotic systems weakly coupled to the continuum via a finite number M of open channels. In contrast to the standard first-order perturbation theory treatment we do not a priori assume the resonance widths being small compared to the mean level spacing. We show that to the leading order in weak coupling the perturbative distribution of the resonance widths (in particular, the Porter-Thomas distribution at M = 1) should be corrected by a factor related to a certain average of the ratio of square roots of the characteristic polynomial (“spectral determinant”) of the underlying RMT Hamiltonian. A simple single-channel expression is obtained that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.

Most spin-1/2 transition-metal ions do have single ion anisotropy.

The cause for the preferred spin orientation in magnetic systems containing spin-1/2 transition-metal ions was explored by studying the origin of the easy-plane anisotropy of the spin-1/2 Cu(2+) ions in CuCl2·2H2O, LiCuVO4, CuCl2, and CuBr2 on the basis of density functional theory and magnetic dipole-dipole energy calculations as well as a perturbation theory treatment of the spin-orbit coupling. We find that the spin orientation observed for these spin-1/2 ions is not caused by their anisotropic spin exchange interactions, nor by their magnetic dipole-dipole interactions, but by the spin-orbit coupling associated with their crystal-field split d-states. Our study also predicts in-plane anisotropy for the Cu(2+) ions of Bi2CuO4 and Li2CuO2. The results of our investigations dispel the mistaken belief that magnetic systems with spin-1/2 ions have no magnetic anisotropy induced by spin-orbit coupling.

Transport properties of electron swarms in gaseous neon at low values of E/N

A detailed analysis of electron swarm transport through neon gas at applied reduced electric fields of E/N < 2 Td is presented. The root mean square difference of transport parameters calculated from a recent all-order many-body perturbation theory treatment (Cheng et al 2014 Phys. Rev. A 89 012701) with drift velocity measurements by the Australian National University group (Robertson 1972 J. Phys. B 5 648) is less than 1%. Differences of about 3% exist with characteristic energies, DT/μ, (Koizumi et al 1984 J. Phys. B 17 4387) indicating an incompatibility at the 3% level between drift velocity and transverse diffusion coefficient measurements. Multi-term solutions of the Boltzmann equation indicate that the two-term approximation gives transport parameters accurate to better than 0.01%. The diffusion constant at thermal energies is found to be sensitive to the numerical representation of the cross section. A recommended elastic momentum transfer cross section has been constructed that has a maximum difference of 0.5% with all ANU drift velocity data for E/N < 1.6 Td and a root mean square difference that is about a factor of 2 smaller.

One- and two-photon absorption in solution: the effects of a passive auxiliary beam.

The efficiencies of one- and two-photon absorption by chromophores in solution may be significantly modified by a sufficiently intense beam of off-resonant light. A molecular analysis based on quantum electrodynamics (QED) fully accounts for this phenomenon of laser-modified absorption. A time-dependent perturbation-theory treatment describes the process in terms of stimulated forward Rayleigh-scattering of the auxiliary beam occurring simultaneously with the absorption interaction(s). Our formulation accommodates media modifications to the basic character of light-matter interactions, taking into account the refractive and dispersive properties of a solution-phase environment. This introduces the bulk refractive index of the solvent directly into the QED framework. The measurable electronic response of molecules freely rotating in solution is defined by an average of all orientations. We explicitly derive fixed-orientation and rotationally averaged calculations for the Fermi-rule rate of laser-modified one- and two-photon absorption. For a given beam polarization geometry, the solution-phase molecular response is expressible as a set of natural invariant scalars. These results reveal details of the dependence on the beam polarisations and on the rotationally averaged molecular response: we illustrate the breadth of variation available via geometric manipulation of beam polarization, and raise new possibilities for quantum weak measurements of laser states.

Calculation of fundamental frequencies for small polyatomic molecules: a comparison between correlation consistent and atomic natural orbital basis sets

The performance of the NASA Ames atomic natural orbital (ANO) basis sets for calculating fundamental vibrational frequencies is examined, using the CCSD(T) treatment of electron correlation and second-order vibrational perturbation theory. Particular attention is paid to the performance of the small, cost-effective truncations ([3s 2p 1d] and [4s 3p 2d 1f] on second-row atoms) known as ANO0 and ANO1, as similarly sized basis sets must necessarily be used for high-level correlation treatment of ‘large’ molecules. It is found that the ANO0 and ANO1 basis sets – particularly the former – outperform comparably sized correlation consistent basis sets for the calculation of vibrational frequencies, suggesting that the ANO0 basis is a useful tool for this area of computational chemistry.

Optical nonlinearities associated to applied electric fields in parabolic two-dimensional quantum rings

The linear and nonlinear optical absorption as well as the linear and nonlinear corrections to the refractive index are calculated in a disc shaped quantum dot under the effect of an external magnetic field and parabolic and inverse square confining potentials. The exact solutions for the two-dimensional motion of the conduction band electrons are used as the basis for a perturbation-theory treatment of the effect of a static applied electric field. In general terms, the variation of one of the different potential energy parameters – for a fixed configuration of the remaining ones – leads to either blueshifts or redshifts of the resonant peaks as well as to distinct rates of change for their amplitudes.

Macroscopic descriptions of non-linear electromagnetic interactions in many-electron systems

Reduced-density-matrix descriptions are developed for linear and non-linear (possibly coherent) electromagnetic interactions of many-electron systems. Applications of interest include pump-probe optical phenomena in warm atomic vapors, partially-ionized plasmas, and condensed matter. Collision processes are treated within the framework of environmental perturbations, giving rise to decoherence and relaxation phenomena, and externally applied magnetic fields are taken into account on an equal footing with the electromagnetic fields. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semi-classical perturbation-theory treatment of the electromagnetic interaction is adopted. However, it is emphasized that a quantized-electromagnetic-field approach will be necessary for a fully self-consistent quantum-mechanical formulation. The primary quantities of interest are the linear and the non-linear macroscopic electromagnetic-response tensors. Coherent initial electronic excitations and the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation can incorporated in the expressions for these macroscopic electromagnetic-response tensors. Collisional interactions can be treated in various approximations for the Liouville-space self-energy operator, and the influence of Zeeman coherences on the macroscopic electromagnetic response can be investigated.

Geometrical frustration of an argon monolayer adsorbed on the MgO (100) surface: An accurate periodicab initiostudy

We present an accurate first-principles method for calculating the energy of physisorption, based on a fully periodic local M\o{}ller-Plesset second order perturbation theory (LMP2) treatment. The LMP2 inter-surface-adsorbate interaction energy is scaled with a factor, obtained by comparing the method error of LMP2 versus coupled cluster singles doubles theory with perturbative triples at the basis set limit in small clusters mimicking the system under study. This method is applied to the investigation of geometrical frustration in argon monolayers adsorbed on the MgO (100) surface. It is found that several arrangements of the argon monolayer, i.e., $3\ifmmode\times\else\texttimes\fi{}2$, $4\ifmmode\times\else\texttimes\fi{}2$, optimal hexagonal, and $\ensuremath{\zeta}\ifmmode\times\else\texttimes\fi{}2$ 1D noncommensurate have very similar adsorption energies, which agrees with the experimental observations. Moreover, this study provides further insight in to the Ar-MgO adsorption process and sheds light on a controversy among different experiments. The calculated adsorption energy of 2.3 kcal/mol is in a very good agreement with the experimental values, which range from 2.0 to 2.3 kcal/mol, and provides a new benchmark for this system.

Between ethylene and polyenes - the non-adiabatic dynamics of cis-dienes

Using Ab Initio Multiple Spawning (AIMS) with a Multi-State Multi-Reference Perturbation theory (MS-MR-CASPT2) treatment of the electronic structure, we have simulated the non-adiabatic excited state dynamics of cyclopentadiene (CPD) and 1,2,3,4-tetramethyl-cyclopentadiene (Me4-CPD) following excitation to S1. It is observed that torsion around the carbon-carbon double bonds is essential in reaching a conical intersection seam connecting S1 and S0. We identify two timescales; the induction time from excitation to the onset of population transfer back to S0 (CPD: -25 fs, Me4-CPD: -71 fs) and the half-life of the subsequent population transfer (CPD: -28 fs, Me4-CPD: -48 fs). The longer timescales for Me4-CPD are a kinematic consequence of the inertia of the substituents impeding the essential out-of-plane motion that leads to the conical intersection seam. A bifurcation is observed on S1 leading to population transfer being attributable, in a 5 : 2 ratio for CPD and 7 : 2 ratio for Me4-CPD, to two closely related conical intersections. Calculated time-resolved photoelectron spectra are in excellent agreement with experimental spectra validating the simulation results.

The Absorption Spectrum of Cytosine Tautomers: Beyond the Static Approach.

The absorption spectrum of cytosine in water has been studied by combining Car-Parrinello molecular dynamics (MD) with a multiconfigurational perturbation theory treatment of the electronic structure. The MD simulations were performed for four different tautomeric forms of cytosine in a unit cell with 60 water molecules. The relative energies and transition dipole moments of a large number of excited states have been calculated on a representative sample of conformations along the MD trajectories. In this way, the broad experimental peaks can be decomposed, and the effect of the distortions on the nature of the excited states can be assessed. The loss of planarity of the molecule is significant, and hence, the excited states can no longer be defined as pure n → π* or π → π* excitations. We propose an analysis to assign the different transitions according to the main contribution. The keto N1H form turns out to be the most stable one, and the calculated spectra of this tautomer show good agreement with experimental measurements. The mixed nπ*/ππ* character of some states leads to a significant increase of intensity in spectral regions dominated by the dark nπ* transitions considering a planar structure.

Perturbation theory treatment of pseudorotation in cyclic-N3

A relatively simple treatment using perturbation theory is proposed to describe spectrum of pseudorotational states in cyclic-N(3). The purpose is to develop an analytical expression that could be used to fit the experimentally determined spectrum of cyclic-N(3), with purpose of identifying this molecule in the laboratory and deriving parameters of its potential energy surface directly from the experimental data. The perturbation theory expression derived in this work is used to fit the spectrum calculated numerically in the previous work [D. Babikov and B. Kendrick, J. Chem. Phys. 133, 174310 (2010)]. It is found that the second order of perturbation theory works well, giving a very good fit of the spectrum, with the rms deviation of only 0.26 cm(-1). Analysis reveals that important characteristics of the potential energy surface, such as equilibrium geometry and pseudorotation barriers, are directly related to the features of spectrum, such as splittings, and can be readily derived from experimental data, when those become available.

Electron Correlation Effects on the Femtosecond Dephasing Dynamics ofE22Excitons in (6,5) Carbon Nanotubes

Highly nonlinear pump fluence dependence was observed in the ultrafast one-color pump-probe responses excited by 38 fs pulses resonant with the E(22) transition in a room-temperature solution of (6,5) carbon nanotubes. The differential probe transmission (ΔT/T) at the peak of the pump-probe response (τ = 20 fs) was measured for pump fluences from ∼10(13) to 10(17) photons/pulse cm(2). The onset of saturation is observed at ∼2 × 10(15) photons/pulse cm(2) (∼8 × 10(5) excitons/cm). At pump fluences >4 × 10(16) photons/pulse cm(2) (∼1.6 × 10(6) excitons/cm), ΔT/T decreases as the pump fluence increases. Analogous signal saturation behavior was observed for all measured probe delays. Despite the high exciton density at saturation, no change in the E(22) population decay rate was observed at short times (<300 fs). The pump probe signal was modeled by a third-order perturbation theory treatment that includes the effects of inhomogeneous broadening. The observed ΔT/T signal is well-fit by a pump-fluence-dependent dephasing rate linearly dependent on the number of excitons created by the pump pulse. Therefore, the observed nonlinear pump intensity dependence is attributed to the effects of quasi-elastic exciton-exciton interactions on the dephasing rates of single carbon nanotubes. The low fluence total dephasing time is 36 fs, corresponding to a homogeneous width of 36 meV (290 cm(-1)), and the derived E(22) inhomogeneous width is 68 meV (545 cm(-1)). These results are contrasted with photon-echo-derived parameters for the E(11) transition.

A comprehensive theoretical investigation of the electronic states of Ca2 up to the Ca(4s2 S1)+Ca(4s5p P1) dissociation limit

A theoretical survey of the electronic structure of Ca(2) is presented using two-electron pseudopotentials complemented by core-polarization operators on Ca atoms and multireference configuration interaction/quasidegenerate perturbation theory (MRCI/QDPT) treatment of molecular excited states. The spectroscopic constants of 70 electronic states up to 30,000 cm(-1) above the ground state are determined. This implies all Ca(2) states dissociating up to the Ca(4s(2) (1)S) + Ca(4s5p (3,1)P) dissociation limits. All spin states (singlet, triplet, and quintet) are investigated. The work emphasizes the variety of interactions implying singly valence and lowest Rydberg excited states, doubly excited states generated by atom pairs (3)P(4s4p) + (3)P(4s4p), or (3)P(4s4p) + (3)D(4s3d), 4p3d double excitations asymptotically localized on a single-atom. Zwitterionic Ca(+) + Ca(-) configurations are evidenced and shown to induce specific electronic patterns in (1)Σ(g)(+), (3)Σ(g)(+), (1)Σ(u)(+), (3)Σ(u)(+), (1)Π(g), (3)Π(g), (1)Π(u), and (3)Π(u) symmetry manifolds. They also provide insight for qualitative features (barriers) found for the lower electronic states already investigated in previous publications by other authors.

Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory

We present an improved prescription for matter power spectrum in redshift space taking a proper account of both the non-linear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the non-linear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1~2%, and the growth rate parameter by ~5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription of redshift-space power spectrum including the non-linear corrections can be used as an accurate theoretical template for anisotropic BAOs.

High-resolution study ofK 3pphotoabsorption and resonant Auger decay in KF

High-resolution (K3p sigma and pi)->sigma absorption spectrum of KF in the photon energy range of 18.2-19.4 eV was measured at the new FINEST beamline branch on the I3 beamline on MAX III. The experimental spectrum is presented and interpreted using nonrelativistic ab initio molecular calculations corrected with perturbation theory treatment to account for spin-orbit interaction. Resonant Auger decay recorded at the strongest resonances is also presented and reproduced by theoretical calculations. Also a brief introduction to the FINEST beamline branch is presented.

Matrix element evaluation in the unitary group approach to the electron correlation problem

Computationally effective formulations are presented for the evaluation of matrix elements of unitary group generators and products of generators between Gelfand states. These matrix elements are the coefficients of the orbital integrals in the expressions for the Hamiltonian matrix elements in the Gelfand basis, and as such are the key elements in any application of the unitary group approach to wave-function calculations. The present formulations, which, like previous analyses, result in a simple factorization of the generator matrix elements, are based on a graphical representation of the Gelfand basis, and do not require orbital permutations or an interpretation of the Gelfand states in terms of Young tableaus. It is shown that the resulting formalism can lead to very efficient procedures for “direct” configuration-interaction calculations, and probably also for perturbation-theory treatments.

Third‐order generalized Van Vleck perturbation theory variant of multireference perturbation theory for electron correlation

AbstractA third‐order approximation to the generalized Van Vleck perturbation theory (GVVPT3) variant of multireference perturbation theory treatment of dynamic electron correlation is described. The approximation builds upon some aspects of the increasingly widely used GVVPT2, which we introduced previously (Khait et al., J Chem Phys 2002, 117, 4133). In addition, using formal relations obtained in connection with GVVPT3, a more thorough understanding of GVVPT2 is obtained, including a key diagnostic that assesses suitability of GVVPT2 for specific tasks. Computational aspects of the implementation of GVVPT3, especially the use of a macroconfiguration description of the model space, are described. The obtained GVVPT3 method can use both complete and incomplete model spaces efficiently. We demonstrate the new method on a series of model problems that demonstrate the applicability of the suggested approach. Among other tests, we show that GVVPT3 is capable of reproducing MRCISD results to within 0.01 eV for the problematic barrier height of the metastable N. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Logarithmic perturbation theory: Applications and limitations

The time independent, non-degenerate standard perturbation theory is compared the alternate treatment of perturbation theory called logarithmic perturbation theory (LPT). For determining the non-degenerate ground state the LPT is, in principle, easier to apply than standard perturbation theory. This is because, as opposed to the standard perturbation method which requires the knowledge of the complete set of eigenvalues and eigenfunctions of the unperturbed system, for the LPT one only needs to know the ground state wave function of the unperturbed system, the energy correction to the next lower order and some easily computable coupling constants. However, in reality, the LPT is a simpler method to apply when the ground state wavefunction is exponential in nature. But as shown here for trigonometric unperturbed wave function the LPT leads to integrals which have no analytical solutions thereby making LPT more difficult and less accurate method than the standard perturbation approach. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 595-600

Electrostatic interaction energies with overlap effects from a localized approach

An ab initio method is proposed for calculations of intermolecular forces which should be applicable to interactions of monomers containing several hundreds atoms and scale linearly with system size. This approach unifies asymptotic approximation to intermolecular forces with symmetry-adapted perturbation theory (SAPT) treatment. Inexpensive asymptotic formulas are applied to interactions of fragments of monomers which are far apart, whereas fairly expensive SAPT formulas are applied to fragments which are near each other, where overlap effects cannot be neglected. This Letter implements the method for the electrostatic interactions. The electrostatic energies are reproduced to 1% with about dozen or so atoms in near-range regions.

From primordial quantum fluctuations to the anisotropies of the cosmic microwave background radiation

These lecture notes cover mainly three connected topics. In the first part we give a detailed treatment of cosmological perturbation theory. The second part is devoted to cosmological inflation and the generation of primordial fluctuations. In part three it will be shown how these initial perturbation evolve and produce the temperature anisotropies of the cosmic microwave background radiation. Comparing the theoretical prediction for the angular power spectrum with the increasingly accurate observations provides important cosmological information (cosmological parameters, initial conditions).