Order Perturbation Theory Research Articles

Computational molecular structure analysis, electronic properties of sudan dye doped thioureabarium chloride crystals for nlo Applications

Pure thiourea barium chloride (TBC) crystals were grown by slow evaporation from aqueous solution and slow cooling (0.1oC/ day). The growth was carried out for 21 days by keeping the bath at a temperature of 39oC. Optimal molecular structures are explored by DFT / B3LYP method with 6-31G (d, p) based synthesis. Hyper conjugative interactions, charge delocalization and intra molecular hydrogen bonding have been analyzed using natural bond orbital (NBO) analysis. Moreover lower in the HOMO and LUMO energy gap explains the eventual charge transfer interactions taking place within the molecule, which influences the biological activity of the compound and also energy serves as a measure of the excitability of a compound, the smaller the energy gap, the more easily the compound will be excited. Electronic structures were discussed and the displacement of the electron density was determined. Second – order perturbation theory analysis of the intra molecular bonds of Methyl Orange doped TBC were derived.

Theoretical Investigations of Gyrating Ion Beam-Driven Ion-Acoustic Wave Instability in Plasma Using First Order Perturbation Theory

A Gyrating ion beam traveling through a plasma cylinder comprising of electrons, positive ions K + , and heavy C 7 F 14 − negative ions, through Cerenkov interaction, drive IAWs (ion-acoustic waves) to unstable mode. In this process, two ion-acoustic (IA) unstable wave modes: a fast K + mode and a slow C 7 F 14 − mode in the presence of positive and heavy negative ions are observed in the plasma. Numerical calculations of the sound wave phase velocity, unstable mode frequency, and the growth rates have been carried out. The calculations show that the growth rate and unstable wave frequencies for both the IA wave modes increase with the increase in the relative density of used heavy negative ions. Moreover, the growth rate is measured as 1/3rd of ion beam density power and the phase velocity rises with the concentration of heavy negative ions. There is a considerable effect of an increase in the magnetic field on the growth rate. The growth rate of the fast (K+) mode increases with the magnetic field more rapidly as compared to the slow ion mode C 7 F 14 − .

Memory-aware end-to-end learning of channel distortions in optical coherent communications.

We implement a new variant of the end-to-end learning approach for the performance improvement of an optical coherent-detection communication system. The proposed solution enables learning the joint probabilistic and geometric shaping of symbol sequences by using auxiliary channel model based on the perturbation theory and the refined symbol probabilities training procedure. Due to its structure, the auxiliary channel model based on the first order perturbation theory expansions allows us performing an efficient parallelizable model application, while, simultaneously, producing a remarkably accurate channel approximation. The learnt multi-symbol joint probabilistic and geometric shaping demonstrates a considerable bit-wise mutual information gain of 0.47 bits/2D-symbol over the conventional Maxwell-Boltzmann shaping for a single-channel 64 GBd transmission through the 170 km single-mode fiber link.

A non-perturbative study of the interplay between electron–phonon interaction and Coulomb interaction in undoped graphene

In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron–phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson–Schwinger (DS) integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the DS equation of full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized fermion velocity and show that its energy (momentum) dependence of renormalized fermion velocity is dominantly determined by the electron–phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.

Solvation Structure and Ion–Solvent Hydrogen Bonding of Hydrated Fluoride, Chloride and Bromide—A Comparative QM/MM MD Simulation Study

In this study, the correlated resolution-of-identity Møller–Plesset perturbation theory of second order (RIMP2) ab initio level of theory has been combined with the newly parameterised, flexible SPC-mTR2 water model to formulate an advanced QM/MM MD simulation protocol to study the solvation properties of the solutes F−, Cl− and Br− in aqueous solution. After the identification of suitable ion–water Lennard–Jones parameters for the QM/MM coupling, a total simulation period of 10 ps (equilibration) plus 25 ps (sampling) could be achieved for each target system at QM/MM conditions. The resulting simulation data enable an in-depth analysis of the respective hydration structure, the first shell ligand exchange characteristics and the impact of solute–solvent hydrogen bonding on the structural properties of first shell water molecules. While a rather unexpected tailing of the first shell ion–oxygen peak renders the identification of a suitable QM boundary region challenging, the presented simulation results provide a valuable primer for more advanced simulation approaches focused on the determination of single-ion thermodynamical properties.

Formula omitted] electronic structure and strain-dependence of the crystal field splitting and inter-band transition energy of W–InN

In this paper, we study the electronic structure of wurtzite Indium Nitride (W–InN) using a k→∙π→ theory. Here π→ is the relativistic momentum operator. It is based on an eight-band model; three valence bands and one conduction band, each Kramers’ split by spin-orbit interaction. We diagonalize the k→∙π→ Hamiltonian following a two-band model, where each valence band is treated separately with the conduction band by using a suitable basis set in the presence of spin-orbit interaction. Effects of other valence bands on the dispersion of a given valence band are incorporated using second order perturbation theory. Valence band dispersions are plotted and compared with a previous calculation and our own results obtained by using a different method. Agreement is found to be satisfactory. Electronic and hole effective masses are calculated and compared with previously reported values, which are substantially different from each other. Fair agreement is noticed. Discrepancies are discussed. Effect of strain is calculated on the electronic structure by calculating the crystal field energy and transition energy for small variations of strain. Although results could not be compared with any previous calculation, due presumably to their absence in literature, trends and systematics are found to be in accord with the same found in case of other wurtzite semiconductors.

Geometric-arithmetic master equation in large and fast open quantum systems

Understanding nonsecular dynamics in open quantum systems is addressed here, with emphasis on systems with large numbers of Bohr frequencies, zero temperature, and fast driving. We employ the master equation, which replaces arithmetic averages of the decay rates in the open system, with their geometric averages, and find that it can improve the second order perturbation theory, known as the Redfield equation, while enforcing complete positivity on quantum dynamics. The characteristic frequency scale that governs the approximation is the minimax frequency: the minimum of the maximum system oscillation frequency and the bath relaxation rate; this needs to be larger than the dissipation rate for it to be valid. The concepts are illustrated on the Heisenberg ferromagnetic spin-chain model. To study the accuracy of the approximation, a Hamiltonian is drawn from the Gaussian unitary ensemble, for which we calculate the fourth order time-convolutionless master equation, in the Ohmic bath at zero temperature. Enforcing the geometric average, decreases the trace distance to the exact solution. Dynamical decoupling of a qubit is examined by applying the Redfield and the geometric-arithmetic master equations, in the interaction picture of the time dependent system Hamiltonian, and the results are compared to the exact path integral solution. The geometric-arithmetic approach is significantly simpler and can be super-exponentially faster compared to the Redfield approach.

Sudakov shoulder resummation for thrust and heavy jet mass

When the allowed range of an observable grows order-by-order in perturbation theory, its perturbative expansion can have discontinuities (as in the $C$ parameter) or discontinuities in its derivatives (as in thrust or heavy jet mass) called Sudakov shoulders. We explore the origin of these logarithms using both perturbation theory and effective field theory. We show that for thrust and heavy jet mass, the logarithms arise from kinematic configurations with narrow jets and deduce the next-to-leading logarithmic series. The left-shoulder logarithms in heavy jet mass ($\rho$) of the form $r\ \alpha_s^n \ln^{2n}r $ with $r=\frac{1}{3}-\rho$ are particularly dangerous, because they invalidate fixed order perturbation theory in regions traditionally used to extract $\alpha_s$. Although the factorization formula shows there are no non-global logarithms, we find Landau-pole like singularities in the resummed distribution associated with the cusp anomalous dimension, and that power corrections are exceptionally important.

Accurate property prediction by second order perturbation theory: The REMP and OO-REMP hybrids.

The prediction of molecular properties such as equilibrium structures or vibrational wavenumbers is a routine task in computational chemistry. If very high accuracy is required, however, the use of computationally demanding ab initio wavefunction methods is mandatory. We present property calculations utilizing Retaining the Excitation Degree - Møller-Plesset (REMP) and Orbital Optimized REMP (OO-REMP) hybrid perturbation theories, showing that with the latter approach, very accurate results are obtained at second order in perturbation theory. Specifically, equilibrium structures and harmonic vibrational wavenumbers and dipole moments of closed and open shell molecules were calculated and compared to the best available experimental results or very accurate calculations. OO-REMP is capable of predicting bond lengths of small closed and open shell molecules with an accuracy of 0.2 and 0.5pm, respectively, often within the range of experimental uncertainty. Equilibrium harmonic vibrational wavenumbers are predicted with an accuracy better than 20cm-1. Dipole moments of small closed and open shell molecules are reproduced with a relative error of less than 3%. Across all investigated properties, it turns out that a 20%:80% Møller-Plesset:Retaining the Excitation Degree mixing ratio consistently provides the best results. This is in line with our previous findings, featuring closed and open shell reaction energies.

Analytic gradients for compressed multistate pair-density functional theory

Photochemical reactions often involve states that are closely coupled due to near degeneracies, for example by proximity to conical intersections. Therefore, a multistate method is used to accurately describe these states; for example, ordinary perturbation theory is replaced by quasidegenerate perturbation theory. Multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to approximate the full dynamical correlation energy of strongly correlated systems, and we recently proposed compressed multistate pair-density functional theory (CMS-PDFT) to treat closely coupled states. In the present paper, we report the implementation of analytic gradients for CMS-PDFT in both OpenMolcas and PySCF, and we illustrate the use of these gradients by applying the method to the excited states of formaldehyde and phenol.

Non-iterative method for constructing valence antibonding molecular orbitals and a molecule-adapted minimum basis.

While bonding molecular orbitals exhibit constructive interference relative to atomic orbitals, antibonding orbitals show destructive interference. When full localization of occupied orbitals into bonds is possible, bonding and antibonding orbitals exist in 1:1 correspondence with each other. Antibonding orbitals play an important role in chemistry because they are frontier orbitals that determine orbital interactions, as well as much of the response of the bonding orbital to perturbations. In this work, we present an efficient method to construct antibonding orbitals by finding the orbital that yields the maximum opposite spin pair correlation amplitude in second order perturbation theory (AB2) and compare it with other techniques with increasing basis set size. We conclude the AB2 antibonding orbitals are a more robust alternative to the Sano orbitals as initial guesses for valence bond calculations due to having a useful basis set limit. The AB2 orbitals are also useful for efficiently constructing an active space, and they work as good initial guesses for valence excited states. In addition, when combined with the localized occupied orbitals, and relocalized, the result is a set of molecule-adapted minimal basis functions that is built without any reference to atomic orbitals of the free atom. As examples, they are applied to the population analysis of halogenated methane derivatives, H-Be-Cl, and SF6, where they show some advantages relative to good alternative methods.

The many-body expansion for metals. I. The alkaline earth metals Be, Mg, and Ca

We examine the many-body expansion (MBE) for alkaline earth metal clusters, Ben, Mgn, Can (n = 4, 5, 6), at the Møller–Plesset second order perturbation theory, coupled-cluster singles and doubles with perturbative triples, multi-reference perturbation theory, and multi-reference configuration interaction levels of theory. The magnitude of each term in the MBE is evaluated for several geometrical configurations. We find that the behavior of the MBE for these clusters depends strongly on the geometrical arrangement and, to a lesser extent, on the level of theory used. Another factor that affects the MBE is the in situ (ground or excited) electronic state of the individual atoms in the cluster. For most geometries, the three-body term is the largest, followed by a steady decrease in absolute energy for subsequent terms. Though these systems exhibit non-negligible multi-reference effects, there was little qualitative difference in the MBE when employing single vs multi-reference methods. Useful insights into the connectivity and stability of these clusters have been drawn from the respective potential energy surfaces and quasi-atomic orbitals for the various dimers, trimers, and tetramers. Through these analyses, we investigate the similarities and differences in the binding energies of different-sized clusters for these metals.

Interfacial Sensitivity Enhancement in Optical Microfiber Functionalized With Gold Nanorods Through Tunable LSPR Coupling Strategy

The nanointerface-sensitized optical microfiber is shown with ultrahigh sensing sensitivity to the small variation of the external refractive index. By optimizing localized surface plasmon resonance (LSPR), we theoretically and experimentally investigated the extinction characteristics of three gold nanorods with different aspect ratios. A simple self-assembly method through electrostatic attraction was used to immobilize gold nanorods with different aspect ratios on optical microfiber. By tuning the LSPR to be consistent with operation wavelengths of the microfiber, the optimized nanointerface-sensitized optical microfiber shows the highest sensing sensitivity of 3146 nm/RIU, which is about 2-fold better than that of the silica optical microfiber, and about 3-fold and 4-fold better than that of the nanointerface-sensitized plastic-clad silica multimode optical fiber. For better understanding of the enhancement mechanism, a FDTD method was used to simulate the near-field mapping of the different nanointerfaces for comparison, and a first order perturbation theory was employed to detailed illustrate the interacting between the electric field overlap integral and the shift of the wavelength. Thus, this work can open up a significant way for developing the ultrasensitive optical microfiber sensing probe.

Methodology for Determining Parameters of Ozone-Safe Fire Extinguishing Substances

In this work, the objects of research are individual chemical substances and multicomponent mixtures (gaseous and liquid) used in extinguishing fires.The design of automatic gas fire extinguishing installations is associated with the solution of many scientific and technical issues and is based on the calculation and forecasting of such important data as the thermophysical properties of individual substances and mixtures consisting of them. Phase equilibria parameters data are of particular interest. Also, such data are necessary for scientific and practical research in the creation of the latest, more progressive fire extinguishing agents. It is often difficult or simply impossible to obtain experimentally thermophysical characteristics and parameters of phase equilibria for a wide range of states. Moreover, experimental information is expensive and time-consuming.The work is dedicated to the development of theoretical methods for determining the parameters of phase equilibria of both individual chemicals used to extinguish fires and multicomponent fire-extinguishing mixtures. The use of the proposed techniques makes it possible to obtain numerical values of the required characteristics of fire extinguishing agents by calculation with the required accuracy using a minimum of initial data.The method of mathematical modeling makes it possible to obtain a mathematical model of phase equilibria based on thermodynamic perturbation theory in order to determine the basic functions of the state in the absence of empirical parameters.The proposed method for calculating the parameters of phase diagrams for multi component fire-extinguishing mixtures was used to determine the thermodynamic parameters of the ozone-safe fire-extinguishing composition.

Multireference Approach to Normal and Resonant Auger Spectra Based on the One-Center Approximation.

A methodology to calculate the decay rates of normal and resonant Auger processes in atoms and molecules based on the One-Center Approximation (OCA), using atomic radial Auger integrals, is implemented within the restricted-active-space self-consistent-field (RASSCF) and the multistate restricted-active-space perturbation theory of second order (MS-RASPT2) frameworks, as part of the OpenMolcas project. To ensure an unbiased description of the correlation and relaxation effects on the initial core excited/ionized states and the final cationic states, their wave functions are optimized independently, whereas the Auger matrix elements are computed with a biorthonormalized set of molecular orbitals within the state-interaction (SI) approach. As a decay of an isolated resonance, the computation of Auger intensities involves matrix elements with one electron in the continuum. However, treating ionization and autoionization problems can be overwhelmingly complicated for nonexperts, because of many peculiarities, in comparison to bound-state electronic structure theory. One of the advantages of our approach is that by projecting the intensities on the atomic center bearing the core hole and using precalculated atomic radial two-electron integrals, the Auger decay rates can be easily obtained directly with OpenMolcas, avoiding the need to interface it with external programs to compute matrix elements with the photoelectron wave function. The implementation is tested on the Ne atom, for which numerous theoretical and experimental results are available for comparison, as well as on a set of prototype closed- and open-shell molecules, namely, CO, N2, HNCO, H2O, NO2, and C4N2H4 (pyrimidine).

The Soft Anomalous Dimension at four loops in the Regge Limit

The soft anomalous dimension governs the infrared divergences of scattering amplitudes in general kinematics to all orders in perturbation theory. By comparing the recent Regge-limit results for 2\to22→2 scattering (through Next-to-Next-to-Leading Logarithms) in full colour to a general form for the soft anomalous dimension at four loops we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.

Perturbative Quantum MonteCarlo Method for Nuclear Physics.

While first order perturbation theory is routinely used in quantum MonteCarlo (QMC) calculations, higher-order terms present significant numerical challenges. We present a new approach for computing perturbative corrections in projection QMC calculations. We demonstrate the method by computing nuclear ground state energies up to second order for a realistic chiral interaction. We calculate the binding energies of several light nuclei up to ^{16}O by expanding the Hamiltonian around the Wigner SU(4) limit and find good agreement with data. In contrast to the natural ordering of the perturbative series, we find remarkably large second-order energy corrections. This occurs because the perturbing interactions break the symmetries of the unperturbed Hamiltonian. Our method is free from the sign problem and can be applied to QMC calculations for many-body systems in nuclear physics, condensed matter physics, ultracold atoms, and quantum chemistry.

Exact tricritical point from next-to-leading-order stability analysis

In the massive chiral Gross-Neveu model, a phase boundary separates a homogeneous from an inhomogeneous phase. It consists of two parts, a second order line and a first order line, joined at a tricritical point. Whereas the first order phase boundary requires a full, numerical Hartree-Fock calculation, the second order phase boundary can be determined exactly and with less effort by a perturbative stability analysis. We extend this stability analysis to higher order perturbation theory. This enables us to locate the tricritical point exactly, without need to perform a Hartree-Fock calculation. Divergencies due to the emergence of spectral gaps in a spatially periodic perturbation are handled using well established tools from many body theory.

A Minimum Quantum Chemistry CCSD(T)/CBS Data Set of Dimeric Interaction Energies for Small Organic Functional Groups: Heterodimers.

We extend our previous quantum chemistry calculations of interaction energies for 31 homodimers of small organic functional groups (the SOFG-31 data set) by including 239 heterodimers with monomers selected within the SOFG-31 data set, thus resulting in the SOFG-31+239 data set. The minimum-level theoretical scheme contains (1) the basis set superposition error corrected supermolecule (BSSE-SM) approach for intermolecular interactions; (2) the second-order Møller–Plesset perturbation theory (MP2) with the Dunning’s aug-cc-pVXZ (X = D, T, Q) basis sets for the geometry optimization and correlation energy calculations; and (3) the single-point energy calculations with the coupled cluster with single, double, and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS] using the well-tested extrapolation methods for the MP2 energy calibrations. In addition, we have performed a parallel series of energy decomposition calculations based on the symmetry adapted perturbation theory (SAPT) in order to gain chemical insights. That the above procedure cannot be further reduced has been proven to be very crucial for constructing reliable data sets of interaction energies. The calculated CCSD(T)/CBS interaction energy data can serve as a benchmark for testing or training less accurate but more efficient calculation methods, such as the electronic density functional theory. As an application, we employ a segmental SAPT model previously developed for the SOFG-31 data set to predict binding energies of large heterodimer complexes. These model energy “quanta” can be used in coarse-grained molecular dynamics simulations by avoiding large-scale calculations.

Fragmentation and Emergent Integrable Transport in the Weakly Tilted Ising Chain.

We investigate emergent quantum dynamics of the tilted Ising chain in the regime of a weak transverse field. Within the leading order perturbation theory, the Hilbert space is fragmented into exponentially many decoupled sectors. We find that the sector made of isolated magnons is integrable with dynamics being governed by a constrained version of the XXZ spin Hamiltonian. As a consequence, when initiated in this sector, the Ising chain exhibits ballistic transport on unexpectedly long timescales. We quantitatively describe its rich phenomenology employing exact integrable techniques such as generalized hydrodynamics. Finally, we initiate studies of integrability-breaking magnon clusters whose leading-order transport is activated by scattering with surrounding isolated magnons.