Order Perturbation Corrections Research Articles

Restricted Open-Shell Cluster Mean-Field theory for Strongly Correlated Systems.

The cluster-based Mean Field method (cMF) and it is second order perturbative correction was introduced by Jiménez-Hoyos and Scuseria to reduce the cost of modeling strongly correlated systems by dividing an active space up into small clusters, which are individually solved in the mean-field presence of each other. In that work, clusters with unpaired electrons are treated by allowing the α and β orbitals to spin polarize. While that provided significant energetic stabilization, the resulting cMF wave function was spin-contaminated, making it difficult to use as a reference state for spin-pure post-cMF methods. In this work, we propose the Restricted Open-shell cMF (RO-cMF) method, extending the cMF approach to systems with open-shell clusters, while not permitting spin-polarization. While the resulting RO-cMF energies are necessarily higher in energy than the unrestricted orbital cMF, the new RO-cMF provides a simple reference state for post-cMF methods that recover the missing intercluster correlations. We provide a detailed explanation of the method, and report demonstrative calculations of exchange coupling constants for three systems: a di-iron complex, a dichromium complex, and a dimerized organic radical. We also report the first perturbatively corrected RO-cMF-PT2 results as well.

Enhancing the electron pair approximation with measurements on trapped-ion quantum computers

The electron pair approximation offers an efficient variational quantum eigensolver (VQE) approach for chemistry simulations on quantum computers. With the number of entangling gates scaling quadratically with system size and a constant measurement overhead, the orbital optimized unitary pair coupled cluster double (oo-upCCD) ansatz strikes a balance between accuracy and efficiency. However, the electron pair approximation prevents the method from achieving quantitative accuracy. To improve it, we explore the theory of second order perturbation (PT2) correction to oo-upCCD. PT2 accounts for the missing broken-pair contributions in oo-upCCD, while retaining its efficiencies. For molecular bond stretching and chemical reactions, the method significantly improves the predicted energy accuracy, reducing oo-upCCD’s error by up to 90%. On IonQ’s quantum computers, we find that the PT2 energy correction is highly noise-resilient. The predicted VQE-PT2 reaction energies are in excellent agreement with noise-free simulators after applying simple error mitigations solely on the VQE energies.

Weakly confined silicon nanodiscs as material system for THz absorption: analytical study

A weakly confined silicon based nano structure as a THz absorbing material is introduced. Using an effective mass approximation and 2D hydrogenic solution along with 1st order perturbation correction for truncated potential, we calculated inter-band and intra-band energy spectrum of weakly confined silicon nanodisc system. Variation of inter-band and intra-conduction-band absorption spectrum with the different sizes of the nanodisc are presented for various diameter from 10 nm to 32 nm and constant thickness of 4 nm. Inter-band and intra-band absorption spectrum are simulated using the oscillator strength. These calculation shows that intra-band absorption spectrum of the weakly confined nanodisc can cover a large THz (∼ 0.3–6.5 THz) spectrum range for these set of nanodiscs. The proposed silicon based THz absorbing material can be utilized for CMOS compatible THz technology if design on silicon-on-insulator system.

Pion valence-quark generalized parton distribution at physical pion mass

We present the first lattice-QCD x-dependent pion valence-quark generalized parton distribution (GPD) calculated directly at physical pion mass using the Large-Momentum Effective Theory (LaMET) with next-to-next-to-leading order perturbative matching correction. We use clover fermions for the valence action on 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, with lattice spacing a≈0.09 fm and box size L≈5.5 fm; the pion two-point measurements number up to O(106) with boost momentum 1.73 GeV. The pion valence distribution is renormalized in hybrid scheme with Wilson-line mass subtraction at large distances in coordinate space, followed by a procedure to match it to the MS‾ scheme. We focus on the zero-skewness limit, where the GPD has a probability-density interpretation in the longitudinal Bjorken x and the transverse impact-parameter distributions. We take the integral of our GPD functions to generate leading moment so that we can make comparisons with past lattice-QCD and experimental determinations of the pion form factors and found consistent agreement among them. We predict the higher GPD moments and reveal x-dependent tomography of the pion for the first time using lattice QCD.

Extension of selected configuration interaction for transcorrelated methods.

In this work, we present an extension of popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework. Although we used in this work the recently introduced one-parameter correlation factor [E. Giner, J. Chem. Phys. 154, 084119 (2021)], the theory presented here is valid for any correlation factor. Thanks to the formalization of the non-Hermitian TC eigenvalue problem as a search of stationary points for a specific functional depending on both left- and right-functions, we obtain a general framework, allowing for different choices for both the selection criterion in SCI and the second order perturbative correction to the energy. After numerical investigations on different second-row atomic and molecular systems in increasingly large basis sets, we found that taking into account the non-Hermitian character of the TC Hamiltonian in the selection criterion is mandatory to obtain a fast convergence of the TC energy. In addition, selection criteria based on either the first order coefficient or the second order energy lead to significantly different convergence rates, which is typically not the case in the usual Hermitian SCI. Regarding the convergence of the total second order perturbation energy, we find that the quality of the left-function used in the equations strongly affects the quality of the results. Within the near-optimal algorithm proposed here, we find that the SCI expansion in the TC framework converges faster than the usual SCI in terms of both the basis set and the number of Slater determinants.

Heavy-hole bilayer trions of transition metal dichalcogenides by analytical treatment to model He-isoelectronic ions upto dipole factor of Green’s function expansion of Coulomb interaction

Electronic structures of heavy-hole trions and He-isoelectronic ions show dependence on transitions among two-electron bound states constituted of hydrogenic orbitals for which Coulomb (exchange) interaction causes nontrivial secular divergence to Schrödinger equation (SE). Coulomb interaction between a pair of electrons triggers nonadiabatic transitions due conical intersections and larger vibrational amplitudes of nuclei. Therefore, existing state-of-art theories ubiquitously urge analytical integrals for multipoles of electrostatic Green’s function expansion. Born–Oppenheimer (BO) approximation separates the hamiltonian into electronic and nuclear coordinates at adiabatic limit. Employing associated Laguerre polynomial and Whittaker-M function basis sets of hydrogenic orbitals for the pair of electrons (electronic coordinate) furnishes analytical, terminable, simple and finitely summed integrals in terms of Lauricella functions. The exact integrals also remedy the difficulty arisen from different scaling factors of bound states for higher order perturbation calculations. Analytical perturbation calculations for monopole and dipole factors using singly and doubly excited states (|n2sn4s〉, |n2pn4p〉) with spherical and dumbbell symmetries show sufficient convergence of ground-state energy correction of He-isoelectronic series within 0.20–6.89% of reported results. Calculation of current-density with ground-state upto first order perturbation correction clearly shows that singly and doubly excited spherically symmetric states do not contribute to local current of He-isoelectronic series for monopole factor. Binding energies of heavy-hole trions of transition metal dichalcogenides (TMDCs) are found to be in good agreement with experimentally observed values.

Lattice QCD Determination of the Bjorken-x Dependence of Parton Distribution Functions at Next-to-Next-to-Leading Order.

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings a=0.04 and 0.06fm and valence pion mass m_{π}=300 MeV, at boost momentum as large as 2.42GeV. As a crucial step to control the systematics, we renormalize the pion valence quasidistribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the MS[over ¯] scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-x space yield a reliable determination of the valence quark distribution for 0.03≲x≲0.80 with 5%-20% uncertainties.

Three-Body Excitations in Fock-Space Coupled-Cluster: Fourth Order Perturbation Correction to Electron Affinity and Its Relation to Bondonic Formalism.

In this paper, we present a formulation of highly correlated Fock-space multi-reference coupled-cluster (FSMRCC) methods, including approximate triples on top of the FSMRCC with singles and doubles, which correct the electron affinities by at least at third and up to the fourth order in perturbation. We discuss various partial fourth-order schemes, which are reliable and yet computationally more efficient than the full fourth-order triples scheme. The third-order scheme is called MRCCSD+T*(3). We present two approximate fourth-order schemes, MRCCSD+T*−a(4) and MRCCSD+T*(4). The results that are presented allow one to choose an appropriate fourth-order scheme, which is less expensive and right for the problem. All these schemes are based on the effective Hamiltonian scheme, and provide a direct calculation of the vertical electron affinities. We apply these schemes to a prototype Li2 molecule, using four different basis sets, as well as BeO and CH+. We have calculated the vertical electron affinities of Li2 at the geometry of the neutral Li2 molecule. We also present the vertical ionization potentials of the Li2 anion at the geometry of the anion ground state. We have also shown how to calculate adiabatic electron affinity, though in that case we lose the advantages of direct calculation. BeO has been examined in two basis sets. For CH+, four different basis sets have been used. We have presented the partial fourth-order schemes to the EA in all the basis sets. The results are analyzed to illustrate the importance of triples, as well as highlight computationally efficient partial fourth-order schemes. The choice of the basis set on the electron affinity calculation is also emphasized. Comparisons with available experimental and theoretical results are presented. The general fourth-order schemes, which are conceptually equivalent with the Fock-space multi-reference coupled-cluster singles, doubles, and triplets (MRCCSD+T) methods, based on bondonic formalism, are also presented here in a composed way, for quantum electronic affinity.

Light Meson Mass Spectra with Massive Quarks

We investigate light meson mass spectra with massive u, d, and s quarks and with a spin effect under a bound system in 3 + 1 dimensional QCD by using the first order perturbation correction. In the process of determining charged kaon and neutral kaonmasses, we obtain masses of u, d, and s quarks that are slightly smaller than the currently accepted values. Using these masses, we obtain light meson mass spectra that includes mass splitting of charged and neutral kaons and ρ mesons. The most interesting of our results is that the pion mass remains unchanged even though u, d, and s quarks become massive.

Quantum vacuum under mixed boundaryconditions: the case for curved spacetime

Influence of gravity on the quantum vacuum of a massless minimally coupled scalar field under Robin boundary conditions on parallel plates is investigated. We introduce the detailed calculation of the volume energy for the case the gravitational background is weak in its most general form for a static spacetime. It founds that the quantum vacuum usually reacts to the gravitational field by decreasing the Casimir energy. In addition, we find sufficient conditions under which the Casimir force increases. Interestingly, the first order perturbation corrections, are present in the obtained formula for the volume energy. We show that for some specific choices of parameters, the energy is independent of Robin coefficients. Consistency with the literature is shown in some limiting cases and well-known examples are presented for both an increase or decrease in the volume energy.

Distributions of the S-matrix poles in Woods–Saxon and cut-off Woods–Saxon potentials

The positions of the l=0S-matrix poles are calculated in generalized Woods–Saxon (GWS) potential and in cut-off generalized Woods–Saxon (CGWS) potential. The solutions of the radial equations are calculated numerically for the CGWS potential and analytically for GWS using the formalism of Gy. Bencze [1]. We calculate CGWS and GWS cases at small non-zero values of the diffuseness in order to approach the square well potential and to be able to separate effects of the radius parameter and the cut-off radius parameter. In the case of the GWS potential the wave functions are reflected at the nuclear radius therefore the distances of the resonant poles depend on the radius parameter of the potential. In CGWS potential the wave function can be reflected at larger distance where the potential is cut to zero and the derivative of the potential does not exist. The positions of most of the resonant poles do depend strongly on the cut-off radius of the potential, which is an unphysical parameter. Only the positions of the few narrow resonances in potentials with barrier are not sensitive to the cut-off distance. For the broad resonances the effect of the cut-off cannot be corrected by using a suggested analytical form of the first order perturbation correction.

Can Nonrelativistic QCD Explain the γγ^{*}→η_{c} Transition Form Factor Data?

Unlike the bewildering situation in the γγ^{*}→π form factor, a widespread view is that perturbative QCD can decently account for the recent BABAR measurement of the γγ^{*}→η_{c} transition form factor. The next-to-next-to-leading-order perturbative correction to the γγ^{*}→η_{c,b} form factor, is investigated in the nonrelativistic QCD (NRQCD) factorization framework for the first time. As a byproduct, we obtain, by far, the most precise order-α_{s}^{2} NRQCD matching coefficient for the η_{c,b}→γγ process. After including the substantial negative order-α_{s}^{2} correction, the good agreement between NRQCD prediction and the measured γγ^{*}→η_{c} form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of the NRQCD approach to hard exclusive reactions involving charmonium.

Self-force driven motion in curved spacetime

We adopt the Dirac–Detweiler–Whiting radiative and regular effective field in curved spacetime. Thereby, we derive straightforwardly the first order perturbative correction to the geodesic of the background in a covariant form, for the extreme mass ratio two-body problem. The correction contains the self-force contribution and a background metric-dependent term.

Orbital optimized double-hybrid density functionals

This paper advocates development of a new class of double-hybrid (DH) density functionals where the energy is fully orbital optimized (OO) in presence of all correlation, rather than using a final non-iterative second order perturbative correction. The resulting OO-DH functionals resolve a number of artifacts associated with conventional DH functionals, such as first derivative discontinuities. To illustrate the possibilities, two non-empirical OO-DH functionals are obtained from existing DH functionals based on PBE: OO-PBE0-DH and OO-PBE0-2. Both functionals share the same functional form, with parameters determined on the basis of different physical considerations. The new functionals are tested on a variety of bonded, non-bonded and symmetry-breaking problems.

A fully automated implementation of VPT2 Infrared intensities

In this contribution we present a fully automated implementation of the anharmonic second order perturbative correction to the infrared absorption intensities in the G aussian suite of programs. Several examples are discussed to show the possibilities of our program, as regards both the variety of treatable systems and eligible methods.

Dust acoustic dressed soliton with dust charge fluctuations

Modeling of dust acoustic solitons observed in dusty plasma experiment [Bandyopadhyay et al., Phys. Rev. Lett. 101, 065006 (2008)] using the Korteweg–de Vries (KdV) equation showed significant discrepancies in the regime of large amplitudes (or high soliton speed). In this paper, higher order perturbation corrections to the standard KdV soliton are proposed and the resulting dressed soliton is shown to describe the experimental data better, in particular, at high soliton speed. The effects of dust charge fluctuations on the dust acoustic dressed soliton in a dusty plasma system are also investigated. The KdV equation and a linear inhomogeneous equation, governing the evolution of first and second order potentials, respectively, are derived for the system by using reductive perturbation technique. Renormalization procedure is used to obtain nonsecular solutions of these coupled equations. The characteristics of dust acoustic dressed solitons with and without dust charge fluctuations are discussed.

Spin Foam Perturbation Theory for Three-Dimensional Quantum Gravity

We formulate the spin foam perturbation theory for three-dimensional Euclidean Quantum Gravity with a cosmological constant. We analyse the perturbative expansion of the partition function in the dilute-gas limit and we argue that the Baez conjecture stating that the number of possible distinct topological classes of perturbative configurations is finite for the set of all triangulations of a manifold, is not true. However, the conjecture is true for a special class of triangulations which are based on subdivisions of certain 3-manifold cubulations. In this case we calculate the partition function and show that the dilute-gas correction vanishes for the simplest choice of the volume operator. By slightly modifying the dilute-gas limit, we obtain a nonvanishing correction which is related to the second order perturbative correction. By assuming that the dilute-gas limit coupling constant is a function of the cosmological constant, we obtain a value for the partition function which is independent of the choice of the volume operator.

Absolutely Local Excited Orbitals in the Higher Order Perturbation Expansion for the Molecular Interaction

Based on the locally projected molecular orbitals, the third and fourth order perturbation corrections for the molecular interaction within the single excitations are evaluated, and the calculated interaction energies are compared with the counterpoise (CP) corrected interaction energy of the Hartree-Fock level of theory. It is demonstrated that the third order calculation is a practical and powerful method to obtain the binding energy almost equal to the CP corrected energy. It requires only one more two-electron integral handling after the LP MO calculation, which is faster than a usual supermolecule HF calculation. For the perturbation expansion, the absolutely local excited orbitals are determined. For small basis sets, it is shown that the partial delocalization of the absolutely local excited orbitals is a compromizing technique to take into account the charge-transfer contribution without reintroducing a large basis set superposition error.

Dipole excitation of ions in linear radio frequency quadrupole ion traps with added multipole fields

Ion motion with auxiliary dipole excitation and collisional damping in a linear radiofrequency quadrupole ion trap incorporating small amounts of even higher order multipoles is studied analytically. The ion motion is modeled in a pseudopotential that is mostly quadratic with small amounts of higher spatial harmonics. Ion motion along x and y axes is characterized by two uncoupled forced and damped anharmonic oscillator equations. A multiple time scales method is used to solve the equations of motion of ions with a first order perturbation correction. Analytical relations between the oscillation amplitudes at steady state (the stationary amplitudes) and excitation frequency are calculated. The frequency response curves show that in some cases bistable behavior might be obtained, i.e., there are two stable stationary amplitudes for a given excitation frequency.

Quasidegenerate scaled opposite spin second order perturbation corrections to single excitation configuration interaction

Scaled opposite spin (SOS) second order perturbative corrections to single excitation configuration interaction (CIS) are extended to correctly treat quasidegeneracies between excited states. Two viable methods, termed as SOS-CIS(D(0)) and SOS-CIS(D(1)), are defined, implemented, and tested. Each involves one empirical parameter (plus a second for the SOS-MP2 ground state), has computational cost that scales with the fourth power of molecule size, and has storage requirements that are cubic, with only quantities of the rank of single excitations produced and stored during iterations. Tests on a set of low-lying adiabatic valence excitation energies and vertical Rydberg excitations of organic and inorganic molecules show that the empirical parameter can be acceptably transferred from the corresponding nondegenerate perturbation theories without any further fitting. Further tests on higher excited states show that the new methods correctly perform for surface crossings for which nondegenerate approaches fail. Numerical results show that SOS-CIS(D(0)) appears to treat Rydberg excitations in a more balanced way than SOS-CIS(D(1)) and is, therefore, likely to be the preferred approach. It should be useful for exploring excited state geometries, transition structures, and conical intersections for states of medium to large organic molecules that are dominated by single excitations.