Adiabatic Corrections Research Articles

Ground-state potential and dipole moment of carbon monoxide: Contributions from electronic correlation, relativistic effects, QED, adiabatic correction, and nonadiabatic correction

Ground-state potential and dipole moment of carbon monoxide: Contributions from electronic correlation, relativistic effects, QED, adiabatic correction, and nonadiabatic correction

The ground electronic state of ClF: Updated molecular constants and potential curves for 35ClF and 37ClF

A comprehensive assessment of available literature spectroscopic data and molecular constants for the X 1Σ+ ground electronic states of isotopologues 35ClF and 37ClF is undertaken. Three different approaches are employed in the analysis of the available information. The first approach involves merging molecular constants from various studies to yield an optimized set of Dunham coefficients {Y01, Y02, Y03, Y10, Y11, Y21, Y02 and Y12}. Utilizing these updated constants, vibrational energies (Gυ) and rotational constants (Bυ) for υ = 0–9 are calculated, and RKR potentials are determined for both isotopologues. The second approach involves calculating synthetic spectroscopic line positions using literature molecular constants, with normally distributed random errors added on, and subjecting these to a modern direct-potential-fit analysis. This analysis produces a precise analytical potential energy function for 35ClF, and Born-Oppenheimer breakdown functions that characterize adiabatic and non-adiabatic corrections. The third approach involves fitting the synthetic spectroscopic data directly to Dunham coefficients. The results of the three approaches are compared and discussed.

The effect of the adiabatic assumption on asteroseismic scaling relations for luminous red giants

ABSTRACT Although stellar radii from asteroseismic scaling relations agree at the per cent level with independent estimates for main sequence and most first-ascent red giant branch (RGB) stars, the scaling relations over-predict radii at the tens of per cent level for the most luminous stars ($R \gtrsim 30 \, \mathrm{R}_{\odot }$). These evolved stars have significantly superadiabatic envelopes, and the extent of these regions increase with increasing radius. However, adiabaticity is assumed in the theoretical derivation of the scaling relations as well as in corrections to the large frequency separation. Here, we show that a part of the scaling relation radius inflation may arise from this assumption of adiabaticity. With a new reduction of Kepler asteroseismic data, we find that scaling relation radii and Gaia radii agree to within at least 2 per cent for stars with $R \lesssim 30\, \mathrm{R}_{\odot }$, when treated under the adiabatic assumption. The accuracy of scaling relation radii for stars with $50\, \mathrm{R}_{\odot }\lesssim R \lesssim 100\, \mathrm{R}_{\odot }$, however, is not better than $10~{{\ \rm per \, cent}}-15~{{\ \rm per \, cent}}$ using adiabatic large frequency separation corrections. We find that up to one third of this disagreement for stars with $R \approx 100\, \mathrm{R}_{\odot }$ could be caused by the adiabatic assumption, and that this adiabatic error increases with radius to reach 10 per cent at the tip of the RGB. We demonstrate that, unlike the solar case, the superadiabatic gradient remains large very deep in luminous stars. A large fraction of the acoustic cavity is also in the optically thin atmosphere. The observed discrepancies may therefore reflect the simplified treatment of convection and atmospheres.

Time-dependent Aharonov–Casher effect on noncommutative space

In this paper, we study the time-dependent Aharonov–Casher effect and its corrections due to spatial noncommutativity. Given that the charge of the infinite line in the Aharonov–Casher effect can adiabatically vary with time, we show that the original Aharonov–Casher phase receives an adiabatic correction, which is characterized by the time-dependent charge density. Based on Seiberg–Witten map, we show that noncommutative corrections to the time-dependent Aharonov–Casher phase contains not only an adiabatic term but also a constant contribution depending on the frequency of the varying electric field.

Efimov physics implications at p -wave fermionic unitarity

Efimov physics at $p$-wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long-range interaction potential energy, but without producing a true Efimov effect. This analysis treats the total orbital angular momenta and parities, ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+},{1}^{+},{1}^{\ensuremath{-}}$, and ${2}^{\ensuremath{-}}$, for either three spin-polarized fermions ($\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$) or two spin-up and one spin-down fermion ($\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$). Our results for the long-range interaction in some of those cases agree with previous work by Werner and Castin and by Blume et al., namely, in cases where the $s$-wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the $p$-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.

Dissipation-enabled resonant adiabatic quantum state transfer: Entanglement generation and quantum cloning

Resonant dissipation-enabled adiabatic quantum state transfer processes between the polarization degrees of freedom of a single photon wave packet and quantum emitters are discussed. These investigations generalize previous work [N. Trautmann and G. Alber, Phys. Rev. A 93, 053807 (2015)] by taking into account the properties of the spontaneously emitted photon wave packet and of non adiabatic corrections. It is demonstrated that the photonic degrees of freedoms of these adiabatic one-photon quantum state transfer processes can be used for the passive, heralded and deterministic preparation of Bell states of two material quantum emitters and for realizing a large family of symmetric and asymmetric quantum cloning processes. Although these theoretical investigations concentrate on waveguide scenarios they are expected to be relevant also for other scenarios as long as the processes involved are adiabatic so that the Fourier-limited bandwidth of the single photon wave packet involved is small in comparison with the relevant dissipative rates.

Ionization Energies and Dyson Orbitals of the Iso-electronic SO2, O3, and S3 Molecules from Electron Propagator Calculations.

Adiabatic and vertical ionization energies corresponding to the X̃ , à , and B̃ final states of SO2+, O3+, and S3+ have been calculated with a variety of electron-propagator and coupled-cluster methods. The BD-T1 electron-propagator method for vertical ionization energies and coupled-cluster adiabatic and zero-point corrections yield agreement with experiment to within 0.1 eV in all cases but one. The remaining discrepancies for the à state of SO2+ indicate a need for higher levels of theory in determining cationic minima and their accompanying vibrational frequencies. Predictions for the still unobserved à and B̃ final states of S3+ are included. To account for increased biradical character in O3 and S3, highly correlated reference states are required to produce the correct order of final states. Electron correlation plays a subtle role in determining the contours of the Dyson orbitals obtained with BD-T1 and NR2 electron-propagator calculations.

Potential-energy curve for the a3Σu+ state of a lithium dimer with Slater-type orbitals

We report state-of-the-art ab initio calculations of the potential energy curve for the $a^3\Sigma_u^+$ state of the lithium dimer conducted to achieve spectroscopic accuracy ($<$1cm$^{-1}$) without any prior adjustment to fit the corresponding experimental data. The nonrelativistic clamped-nuclei component of the interaction energy is calculated with a composite method involving six-electron coupled cluster and full configuration interaction theories combined with basis sets of Slater-type orbitals ranging in quality from double- to sextuple-zeta. To go beyond the nonrelativistic Born-Oppenheimer picture we include both the leading-order relativistic and adiabatic corrections, and find both of these effects to be non-negligible within the present accuracy standards. The potential energy curve developed by us allowed to calculate molecular parameters ($D_e$, $D_0$, $\omega_e$ etc.) for this system, as well as the corresponding vibrational energy levels, with an error of only a few tenths of a wavenumber ($0.2-0.4\,$cm$^{-1}$). We also report an ab initio value for the scattering length of two $^2S$ lithium atoms which determines the stability of the related Bose-Einstein condensate.

Ab initioproperties of the NaLi molecule in thea3Σ+electronic state

Ultracold polar and magnetic ${}^{23}$Na${}^6$Li molecules in the rovibrational ground state of the lowest triplet $a^3\Sigma^+$ electronic state have been recently produced. Here, we calculate the electronic and rovibrational structure of these 14-electron molecules with spectroscopic accuracy ($<0.5\,$cm$^{-1}$) using state-of-the-art ab initio methods of quantum chemistry. We employ the hierarchy of the coupled-cluster wave functions and Gaussian basis sets extrapolated to the complete basis set limit. We show that the inclusion of higher-level excitations, core-electron correlation, relativistic, QED, and adiabatic corrections is necessary to reproduce accurately scattering and spectroscopic properties of alkali-metal systems. We obtain the well depth, $D_e=229.9(5)\,$cm$^{-1}$, the dissociation energy, $D_0=208.2(5)\,$cm$^{-1}$, and the scattering length, $a_s=-84^{+25}_{-41}\,$bohr, in good agreement with recent experimental measurements. We predict the permanent electric dipole moment in the rovibrational ground state, $d_0=$0.167(1)$\,$debye. These values are obtained without any adjustment to experimental data, showing that quantum chemistry methods are capable of predicting scattering properties of many-electron systems, provided relatively weak interaction and small reduced mass of the system.

Understanding Hot Workability and Flow Stress Prediction through Processing Map with Microstructural Correlation for HY85 Steel

Abstract In this study, the hot compression tests of HY85 steel have been experimented by using thermomechanical simulator Gleeble 3800 in hot compression temperature range of 750°C–1,100°C under strain rates between 0.001–10 s−1 up to true strain 0.7. It is worth noticing from the results that the flow stresses are dependent on the combination of temperature and strain rate. Adiabatic heating corrections of experimental flow stress data were carried out and were used to model stress-strain curves. The predictability of these stress-strain curves was confirmed from experimental results. True stress-true strain curves show the peak stresses followed by softening probability because of the existence of dynamic recrystallization (DRX). The apparent activation energy is calculated to be 360 KJ/mol using the sinh type constitutive equation, and it is observed that its value decreases with increasing strain. Hot compression of HY85 steel is controlled by dislocation climb and glide (n = 6.3). The processing maps are plotted based on different dynamic materials modeled with strain rate versus temperatures. The flow localization is one of the primary factors with resulting instability, which is revealed from the microstructure. Moreover, the partial DRX was noticed besides the grain boundaries and compression bands. Workability regions were identified using processing maps in the domain of strain rate and temperature and verified with microstructures.

Hartree-Fock instabilities and the diagonal Born-Oppenheimer correction

The NO and NO radicals are used to demonstrate how instabilities in Hartree-Fock wavefunctions can result in unsatisfactory, or even unphysical, values of the diagonal Born-Oppenheimer correction (DBOC). For NO, an avoided crossing between two UHF solutions of symmetry results in a nearly 1 kJ/mol (80 cm) defect in the SCF-level DBOC just beyond the equilibrium bond distance. In that case, CCSD is able to recover essentially correct behaviour. For ground-state () NO, a second-order CPHF pole is observed in the dependence of the DBOC on the bending angle at a geometry rather far from the true conical intersection between the and states, an artifact that cannot be completely ameliorated by any method short of full CI. These effects arise from well-known problems associated with (near) instabilities of Hartree-Fock solutions, though there is little in the literature about this in the current context. The goal of this paper is to raise awareness of these potential problems, as the DBOC (adiabatic correction) is now an essential part of many modern protocols for high-accuracy calculations, and to provide some comments of the causes of these phenomena.

Analysis of QED and non-adiabaticity effects on the rovibrational spectrum of H3 + using geometry-dependent effective nuclear masses.

The influence of QED effects (including one- and two-electron Lamb-shift, Araki-Sucher term, one-loop self-energy, and finite nuclear size correction) together with non-adiabatic effects on the rovibrational bound states of H3 + has been investigated. Non-adiabaticity is modeled by using geometry-dependent effective nuclear masses together with only one single potential energy surface. In conclusion, for rovibrational states below 20 000 cm-1, QED and relativistic effects do nearly compensate, and a potential energy surface based on Born-Oppenheimer energies and diagonal adiabatic corrections has nearly the same quality as the one including relativity with QED; the deviations between the two approaches for individual rovibrational states are mostly below 0.02 cm-1. The inclusion of non-adiabatic effects is important, and it reduces deviations from experiments mostly below 0.1 cm-1.

Non-Born–Oppenheimer study of the muonic molecule ion 4He μ+**Project supported by the National Natural Science Foundation of China (Grant No. 11704399), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030300), and the National Key Research and Development Program of China (Grant No. 2017YFA0304402).

Accurate non-Born–Oppenheimer variational calculations of all bound states of the positive muon molecular ion 4Heμ+ have been performed using explicitly correlated Gaussian functions in conjunction with the global vectors. All the energies obtained are accurate in the order of 10−6 Hartree (1 Hartree = 27.2114 eV). Compared with the binding energies obtained from calculations based on the Born–Oppenheimer potential with the mass-weighted adiabatic corrections (Chem. Phys. Lett. 110 487 (1984)), the largest relative deviation is up to 15%. By analyzing the average interparticle distances and possibility distributions of interparticle distances of this system, it is confirmed that the Born–Oppenheimer approximation is reasonable for this system and that 4He μ+ can be regarded as a system of positive muon bound to a slightly distorted helium atom.

Spin Lock Adiabatic Correction (SLAC) for B1-insensitive pulse design at 7T.

A new framework for B1 insensitive adiabatic pulse design is proposed, denoted Spin Lock Adiabatic Correction (SLAC), which counteracts deviations from ideal behaviour through inclusion of an additional correction component during pulse design. SLAC pulses are theoretically derived, then applied to the design of enhanced BIR-4 and hyperbolic secant pulses to demonstrate practical utility of the new pulses. At 7T, SLAC pulses are shown to improve the flip angle homogeneity compared to a standard adiabatic pulse with validation in both simulations and phantom experiments, under SAR equivalent experimental conditions. The SLAC framework can be applied to any arbitrary adiabatic pulse to deliver excitation with increased B1 insensitivity.

Benchmark Rovibrational Linelists and Einstein A-coefficients for the Primordial Molecules and Isotopologues

Abstract Complete benchmark rovibrational energy linelists calculated for the primordial polar molecules of the universe, namely HD+, HD, and the HeH+ isotopologues, with accuracy up to 10−2 cm−1 for low-lying states, are presented. To allow for these calculations to be performed, new high-accuracy potential energy curves, which include the diagonal Born–Oppenheimer adiabatic corrections and the leading relativistic corrections, are determined. Also, a new approach for calculating non-adiabatic corrections involving an effective vibrational nuclear mass obtained based on the atoms-in-molecules theory is employed. The vibrational and rotational masses are taken as being different and dependent on the nuclear distance. Accurate dipole moment curves are calculated and used to generate lists of Einstein A-coefficients. The energy linelists and the sets of Einstein A-coefficients for HD are upgrades of previous calculations including quasibound states, while for HD+ and HeH+ and its isotopologues the present results represent significant improvement over the previous calculations. The results obtained here suggest that, with the inclusion of the non-adiabatic corrections, the accuracy limit at least for low-lying states might have been reached. Thus, further progress should involve accounting for even smaller effects such as the quantum-electrodynamics corrections. The present results represent the state-of-the-art of theoretical spectroscopy of the primordial polar molecules.

An accurate ab initio electronic structure calculation for interstellar argonium

A high level electronic structure calculation of the Born–Oppenheimer (BO) potential, scalar-relativistic effect and adiabatic correction is performed for the X1Σ+ ground state of astronomically important isotopologues of the ArH+ cation. Particular attention is paid to both short and long distances, where experimental spectroscopic data is not yet available. The BO energy is obtained over a wide range of interatomic distances (R ∈ [0.5, 20] Å) in the framework of multi-reference coupled pair functional (MR-ACPF) and single-reference coupled-cluster (CCSD(T)) methods. The all-electrons basis sets of the def2-nZVPP (n=3,4) and nZaPa-NR, aug-cc-pCVnZ (n=3−6) quality are used to monitor energy convergence. The BO energies are corrected for the basis set superposition error (BSSE) via the counterpoise method and are reduced to the complete basis set (CBS) limit using alternative extrapolating schemes. The permanent dipole moment d(R) and static dipole polarizability α(R) are calculated using a finite-field method. The molecular structure parameters coincide with their empirical counterparts for low vibrational levels to within 0.1%. Implementation of the ab initio results to circumscribe our understanding of the chemical networks in interstellar space is discussed.

Theoretical study of the LiNa molecule beyond the Born–Oppenheimer approximation: adiabatic and diabatic potential energy curves, radial coupling, adiabatic correction, dipole moments and vibrational levels

ABSTRACTThe adiabatic potential energy curves for ground and many excited states of 1, 3Σ+, 1,3Π, 1,3Δ symmetries of the LiNa molecule have been performed. We have used an ab initio approach based on non-empirical pseudopotentials, parameterised l-dependent polarisation potentials and full configuration interaction calculations. In addition, the adiabatic potential energy curves determined in our previous work [Mabrouk and Berriche, J. Phys. B: At. Mol. Opt. Phys. 41, 155101 (2008).] are corrected by using a diabatisation procedure, based on the effective Hamiltonian theory and an effective metric. The diabatic permanent moments for first 10 1Σ+ electronic states show linear behaviours, especially at intermediate and large distance. The transition dipole moment between neighbour states has revealed many peaks located around the avoided crossing positions. The radial coupling between the adiabatic states was calculated using the Hellmann-Feynman formula and numerical differentiation of the rotation matrix. The first and the second derivatives revealed many peaks, associated to neutral-neutral and ionic-neutral crossings. Furthermore, the radial coupling is used to evaluate the adiabatic correction, which is found to be of an order of tens and hundreds of cm−1, especially of higher excited states. In addition, we have determined the vibrational level spacing for all studied states.

EStokTP: Electronic Structure to Temperature- and Pressure-Dependent Rate Constants-A Code for Automatically Predicting the Thermal Kinetics of Reactions.

A priori rate predictions for gas phase reactions have undergone a gradual but dramatic transformation, with current predictions often rivaling the accuracy of the best available experimental data. The utility of such kinetic predictions would be greatly magnified if they could more readily be implemented for large numbers of systems. Here, we report the development of a new computational environment, namely, EStokTP, that reduces the human effort involved in the rate prediction for single channel reactions essentially to the specification of the methodology to be employed. The code can also be used to obtain all the necessary master equation building blocks for more complex reactions. In general, the prediction of rate constants involves two steps, with the first consisting of a set of electronic structure calculations and the second in the application of some form of kinetic solver, such as a transition state theory (TST)-based master equation solver. EStokTP provides a fully integrated treatment of both steps through calls to external codes to perform first the electronic structure and then the master equation calculations. It focuses on generating, extracting, and organizing the necessary structural properties from a sequence of calls to electronic structure codes, with robust automatic failure recovery options to limit human intervention. The code implements one or multidimensional hindered rotor treatments of internal torsional modes (with automated projection from the Hessian and with optional vibrationally adiabatic corrections), Eckart and multidimensional tunneling models (such as small curvature theory), and variational treatments (based on intrinsic reaction coordinate following). This focus on a robust implementation of high-level TST methods allows the code to be used in high accuracy studies of large sets of reactions, as illustrated here through sample studies of a few hundred reactions. At present, the following reaction types are implemented in EStokTP: abstraction, addition, isomerization, and beta-decomposition. Preliminary protocols for treating barrierless reactions and multiple-well and/or multiple-channel potential energy surfaces are also illustrated.

Influence of the deformation heating on the flow behavior of 6063 alloy during compression at medium strain rates

Abstract

Perturbation approximations for bathymetrically controlled ocean acoustic mode coupling

A perturbation approximation of mode coupling equations for acoustic propagation in a submarine canyon environment is presented. The vertical modes and mode coefficients are represented by nearly adiabatic dominant mode functions and correction terms that are sensitive to the horizontal gradient of the variable bathymetry. This approach allows for a more accurate representation of the bottom boundary condition, and eliminates computationally expensive implicit equations for the mode coefficients, replacing them with explicit equations for the nearly adiabatic contributions and the bathymetrically sensitive corrections. The presented method is applied to sloping bottom environments based on real bathymetric data to examine in detail the role of bottom variations in coupled mode propagation scenarios. [Work supported by the ONR.]