Second-order Many-body Perturbation Theory Research Articles

Low scaling EOM-CCSD and EOM-MBPT(2) method with natural transition orbitals.

A low-scaling method is presented for the equation-of-motion coupled-cluster theory with single and double (EOM-CCSD) excitations and its second-order many-body perturbation theory [EOM-MBPT(2)] approximations. For a simple description of an excited state, the particular orbitals, and , are selected from the natural transition orbitals (NTOs, ), where and refer to NTO occupied and virtual orbital indices. They are chosen based on the largest eigenvalues of the transition density matrix. We expect the and pair to be dominant in representing excited states in EOM calculations. Therefore, the double excitation vector, R 2 which scale as ∼O 2 V 2, can be modified to keep only a few dominant excitations. Our work indicates that the most important contributions of the R 2 vector define smaller subspaces that scale as ∼OV, ∼O 2 V, and ∼OV 2, where O and V refer to the occupied and virtual orbitals in the NTO basis. Thus, the scaling for the EOM part becomes ∼M 5. The energy changes due to R 2 truncation are small (the mean average deviation from untruncated EOM-CCSD is ∼0.03 eV). We show that this approach works relatively well with various types of NTOs, ranging from configuration singles to time-dependent density functional theory making ∼M 5 scaling calculations possible with the use of MBPT(2) as the reference state.

Energy Levels, Transition Rates and Electron Impact Excitation Rates for the B-like Isoelectronic Sequence with Z = 24–30

Abstract We report calculations of spectroscopic accuracy for 513 states in the B-like ions with Z = 24–30. The energy levels and transition rates are calculated using the second-order many-body perturbation theory, while multiconfiguration Dirac–Hartree–Fock calculations are performed to support the former results. The present two sets of results agree excellently with each other, and can be used as benchmarks in the future. The electron-impact excitation (EIE) collision strengths are calculated based on independent processes and isolated resonances approximation using the distorted wave method. Based on the present atomic data, the spectral lines of these ions are simulated using a collisional radiative model. The amount of energy, transition data, and EIE collision strengths of high accuracy are significantly increased for several B-like ions of astrophysical interest, where experimental data are still very scarce. The results can be used in line identification, plasma modeling, and diagnostics of astrophysical plasmas.

Calculations with spectroscopic accuracy: Energies and transition parameters for lines of fusion interest in Mo XXXIX

We have performed high-accuracy calculations of energy levels, wavelengths, lifetimes, line strengths and radiative rates among the 250 lowest levels of the (1s2)2s2, (1s2)2s2p, (1s2)2p2, (1s2)2snl (n=3,4,5,6; l=0,1,2,3,4,5), and (1s2)2pnl (n=3,4,5,6; l=0,1,2,3,4,5) configurations of Mo XXXIX. The second-order relativistic many-body perturbation theory (MBPT) is adopted and data are provided for all electric/magnetic-dipole (E1/M1) and electric/magnetic-quadrupole (E2/M2) transitions. Similar data for the 98 lowest levels of the n ≤ 4 configurations are also determined using fully relativistic multi-configuration Dirac-Fock (MCDF) wave functions in the active space approximation with the inclusion of a finite nuclear size, the Breit interaction, self-energy, and vacuum polarization to assess the accuracy of the calculations. Based on direct comparisons between the results obtained from these two independent methods, MBPT and MCDF, as well as with the other available theoretical values and measurements, our energies are assessed to be accurate to better than 0.02%. The accuracy for strong radiative rates is estimated to be about 5%. For Mo XXXIX, only a few transition lines have been established experimentally. The present new results considerably expand the existing data sets for this ion, and should be beneficial in analysis of experimental spectra and useful for spectroscopic diagnostics and modeling of hot plasmas, in particular in fusion devices.

Theoretical determination of energies, wavelengths, and transition rates for the Y[formula omitted]–Y[formula omitted] spectra of fusion interest

We report a set of theoretical data for the energy levels, wavelengths, transition rates of electric/magnetic-dipole (E1/M1) and electric/magnetic-quadrupole (E2/M2) transitions for the L-shell charge states of Y30+, Y31+, Y32+, Y33+, Y34+, and Y36+ and the similar spectroscopic data of the 166 fine-structure levels arising from the 2s2, 2s2p, 2p2, 2snl (n=3,4,5; l=0,1,2,3,4), and 2pnl (n=3,4,5; l=0,1,2,3,4) configurations of Y35+, obtained using the second-order relativistic many-body perturbation theory (MBPT). The overall quality of the calculations is assessed by comparisons with the other available theoretical values and the measured spectra in the Electron Beam Ion Trap (EBIT) of the National Institute of Standards and Technology (NIST). For these yttrium ions, only a few levels have been experimentally established. The accuracy of our calculations is however high enough to facilitate identifications of observed lines. The present new data, fill in a gap in the available data of the extreme ultraviolet (EUV) transitions for these ions particularly important for fusion research where their spectra can provide diagnostic information on hot plasmas, in particular in fusion devices.

Electronic and Vibrational Hyperpolarizabilities of Lithium Substituted (Aza)benzenes and (Aza)naphthalenes

In this article we report results for the electronic and vibrational hyperpolarizabilities of ten molecules: Li@benzene, Li@pyridine, Li@pyrimidine, and Li@pyrazine; Li@naphthalene, Li@quinoline, Li@isoquinoline, Li@cinnolin, Li@quinazoline, and Li@quinoxaline. An electron correlation study shows that second-order many-body perturbation theory and density functional theory with CAM-B3LYP and M05-2X functionals give results for the electronic hyperpolarizabilities in good agreement with coupled cluster with single and doubles reference values. Static and dynamic vibrational corrections were computed through the perturbation theoretical method of Bishop and Kirtman and using a variational approach. In general, we obtained notable discrepancies between the results obtained by the two methods for the pure vibrational corrections because of the deficiency of the perturbation method to properly treat low-frequency normal modes present in the investigated systems. However, both methods give results similar to the zero-point vibrational average corrections.

Extended calculations of energy levels, radiative properties, AJ, BJ hyperfine interaction constants, and Landé gJ-factors for Nitrogen-like Se XXVIII

Employing two state-of-the-art methods, multiconfiguration Dirac–Fock and second-order many-body perturbation theory, highly accurate calculations are performed for the lowest 316 fine-structure levels arising from the 2s22p3, 2s2p4, 2p5, 2s22p23l, 2s2p33l, 2p43l, and 2s22p24l configurations in nitrogen-like Se XXVIII. Complete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors, and E1, E2, M1, M2 line strengths, oscillator strengths, and transition rates among these 316 levels are provided. Comparisons are made between the present two data sets, as well as with other available experimental and theoretical values. Previous measured lines of Se XXVIII are affected by large errors for some transitions, and should be remeasured. The present calculations provide a consistent and accurate data set for line identification and modeling purposes, which can also be considered as a benchmark for other calculations. The present data are accurate enough for identification and deblending of emission lines involving the n=3,4 levels, and are also useful for modeling and diagnosing fusion plasmas.

Coupled-cluster based basis sets for valence correlation calculations. New primitives, frozen atomic natural orbitals, and basis sets from double to hextuple zeta for atoms H, He, and B-Ne.

A series of new basis sets generated from coupled-cluster theory are presented. Sets of primitive Gaussians for angular momentum shells containing occupied orbitals are optimized and extended until the Hartree-Fock energy improvement per electron falls below 10 μH. This same energy threshold is applied to the energy from the coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) approximation and taken as a guide to the generation of sets of polarization functions, constructed at the level of second-order many-body perturbation theory, once it is shown that practically indistinguishable results are obtained if the more costly CCSD(T) approach is used. A variant of the usual atomic natural orbitals (ANOs) grounded on the frozen natural orbital idea is explored, leading to the frozen ANO (FANO) contraction scheme, whose truncation pattern and convergence capabilities are thoroughly tested. Due to its superior description of the single determinant solution, the FANOs are proposed as the recommended contraction approach. FANO basis sets of sizes ranging from double to hextuple zeta are provided for atoms H through Ne and examined in atomic and molecular calculations.

Calculations of energies, transition rates, and lifetimes for the fluorine-like isoelectronic sequence with [formula omitted

Employing two state-of-the-art methods, multiconfiguration Dirac–Hartree–Fock and second-order many-body perturbation theory, highly accurate calculations are performed for the lowest 200 fine-structure levels arising from the 2l7,2l63l′ and 2l64l′ configurations of the fluorine-like isoelectronic sequence with Z=31−35. Complete and consistent atomic data, including excitation energies, lifetimes, wavelengths, and E1, E2, M1, M2 line strengths, oscillator strengths, and transition rates among these 200 levels are provided. Comparisons are made between the present two data sets, as well as with other available experimental and theoretical values. The present data are accurate enough for identification and deblending of emission lines involving the n=3,4 levels, and are also useful for modeling and diagnosing fusion plasmas.

Determination of static dipole polarizabilities of Yb atom**Project supported by the National Natural Science Foundation of China (Grant Nos. 91536106 and U1332206), the Strategic Priority Research Program (Category B) of the Chinese Academy of Sciences (Grant No. 21030300), and the National Key Research and Development Program of China (Grant No. 2016YFA0302104).

We determine the static values of the scalar and tensor dipole polarizabilities of the ground, 6s6p , and 6s6p states of the Yb atom. These results can be useful in many experiments undertaken using this atom. We employed a combined configuration interaction (CI) method and a second-order many-body perturbation theory (MBPT) to evaluate energies and electric dipole (E1) matrix elements of many low-lying excited states of the above atom. These values are compared with the other available theoretical calculations and experimental values. By combining these E1 matrix elements with the experimental excitation energies, we estimate the dominant valence correlation contributions to the dipole polarizabilities of the above states. The core contribution is obtained from the finite field approach. We also compare these values with the other theoretical results as there are no precise experimental values that are available for these properties.

Comparison and combination of "direct" and fragment based local correlation methods: Cluster in molecules and domain based local pair natural orbital perturbation and coupled cluster theories.

Local correlation theories have been developed in two main flavors: (1) "direct" local correlation methods apply local approximation to the canonical equations and (2) fragment based methods reconstruct the correlation energy from a series of smaller calculations on subsystems. The present work serves two purposes. First, we investigate the relative efficiencies of the two approaches using the domain-based local pair natural orbital (DLPNO) approach as the "direct" method and the cluster in molecule (CIM) approach as the fragment based approach. Both approaches are applied in conjunction with second-order many-body perturbation theory (MP2) as well as coupled-cluster theory with single-, double- and perturbative triple excitations [CCSD(T)]. Second, we have investigated the possible merits of combining the two approaches by performing CIM calculations with DLPNO methods serving as the method of choice for performing the subsystem calculations. Our cluster-in-molecule approach is closely related to but slightly deviates from approaches in the literature since we have avoided real space cutoffs. Moreover, the neglected distant pair correlations in the previous CIM approach are considered approximately. Six very large molecules (503-2380 atoms) were studied. At both MP2 and CCSD(T) levels of theory, the CIM and DLPNO methods show similar efficiency. However, DLPNO methods are more accurate for 3-dimensional systems. While we have found only little incentive for the combination of CIM with DLPNO-MP2, the situation is different for CIM-DLPNO-CCSD(T). This combination is attractive because (1) the better parallelization opportunities offered by CIM; (2) the methodology is less memory intensive than the genuine DLPNO-CCSD(T) method and, hence, allows for large calculations on more modest hardware; and (3) the methodology is applicable and efficient in the frequently met cases, where the largest subsystem calculation is too large for the canonical CCSD(T) method.

High accuracy theoretical calculation of wavelengths and transition probabilities in Se- through Ga-like ions of tungsten

The Ab initio multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations of atomic parameters have been carried out with high accuracy for four highly charged tungsten ions from Se-like W40+ to Ga-like W43+. The second-order relativistic many-body perturbation theory (MBPT) was used to confirm the accuracy of the MCDHF calculations. Excitation energies, wavelengths and transition rates of E1, M1, E2, M2, E3 and lifetimes are presented. The core-valence electron correlation effects arising from deep subshells 3d and 3p, have been taken into account along with relativistic effects. The calculated wavelengths are in good agreement with available experimental results.

Relativistic coupled-cluster-theory analysis of energies, hyperfine-structure constants, and dipole polarizabilities of Cd+

Roles of electron correlation effects in the determination of attachment energies, magnetic dipole hyperfine structure constants and electric dipole (E1) matrix elements of the low-lying states in the singly charged cadmium ion (Cd$^+$) have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation, second-order many-body perturbation theory and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation effects in this ion. Contributions from important RCC terms are also given to highlight importance of various correlation effects in the evaluation of these properties. At the end, we also determine E1 polarizabilities ($\alpha^{E1}$) of the ground and $5p \ ^2P_{1/2;3/2}$ states of Cd$^+$ in the {\it ab initio} approach. We estimate them again by replacing some of the E1 matrix elements and energies from the measurements to reduce their uncertainties so that they can be used in the high precision experiments of this ion.

Extended calculations of energy levels, radiative properties, AJ, BJ hyperfine interaction constants, and Landé gJ-factors for nitrogen-like Ge XXVI

Employing two state-of-the-art methods, multiconfiguration Dirac–Hartree–Fock and second-order many-body perturbation theory, highly accurate calculations are performed for the lowest 272 fine-structure levels arising from the 2s22p3, 2s2p4, 2p5, 2s22p23l (l=s,p,d), 2s2p33l (l=s,p,d), and 2p43l (l=s,p,d) configurations in nitrogen-like Ge XXVI. Complete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors, and E1, E2, M1, M2 line strengths, oscillator strengths, and transition rates among these 272 levels are provided. Comparisons are made between the present two data sets, as well as with other available experimental and theoretical values. The present data are accurate enough for identification and deblending of emission lines involving the n=3 levels, and are also useful for modeling and diagnosing fusion plasmas.

Theoretical energies, transition rates, lifetimes, hyperfine interaction constants and Land[formula omitted] gJ-factors for the Se XXVII spectrum of fusion interest

An extensive set of level energies, wavelengths, line strengths, oscillator strengths, lifetimes, hyperfine structures, Lande´ gJ-factors, electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) radiative transition rates among the lowest 318 states arising from the 2s22p4, 2s2p5, 2p6, 2s22p33l (l = 0, 1, 2), 2s2p43l (l = 0, 1, 2), 2p53l (l = 0, 1, 2), and 2s22p34l (l = 0, 1, 2, 3) configurations has been obtained for Se XXVII. These new data, calculated within the frameworks of the multi-configuration Dirac–Hartree–Fock method and the second-order many-body perturbation theory, fill in the gap existing in the atomic data needed for the diagnostic processes of tokamak plasmas. Using two methods allowed us to make an intercomparison and to estimate the uncertainties on the obtained data. The results arising in the two sets of calculations are quite close, suggesting that there is a high degree of convergence achieved in our work. i.e., our two sets of energies agree to better than 0.02%, and the lifetimes mostly agree to within 2%. Comparison is also made with the limited number of experimental data and previous computations to assess the accuracy of our calculations.

Extended calculations of energies, transition rates, and lifetimes for F-like Kr XXVIII

The excitation energies, lifetimes, wavelengths and E1, E2, M1 and M2 transition rates for the lowest 389 levels of the 2l7, 2l63l′, 2l64l′, and 2l65l′ configurations from second-order many-body perturbation theory (MBPT) calculations, and the results for the lowest 200 states of the 2l7, 2l63l′, and 2l64l′ configurations from multi-configuration Dirac-Hartree-Fock (MCDHF) calculations in F-like Kr XXVIII are presented in this work. The relative differences between our two sets of level energies are mostly within 0.005% for the lowest 200 levels. Comparisons are made with experimental and other available theoretical results to assess the reliability and accuracy of the present calculations. We believe them to be the most complete and accurate results for Kr XXVIII at present.

Reactivity Sites in Dopamine Depend on its Intramolecular Hydrogen Bond

In this work, three conformers of dopamine were theoretically analyzed, two of them forming an intramolecular hydrogen bond between OH groups in the catechol moiety, the third one without this interaction. The used theoretical method was based on the Kohn-Sham method within the hybrid exchange-correlation functionals without empirical parameters, PBE0. The molecular geometry obtained by this method was contrasted with that obtained from the second-order many-body perturbation theory (MP2) method and the 6-31+G(d), 6-311+G(d) and 6-311++G(d,p) basis sets. Global reactivity descriptors were predicted by using only the PBE0/6-311++G(d,p) method. This method revealed that dopamine is not a good acceptor of electrons. Thus, in one charge transfer process, this compound prefers donating electrons, as observed experimentally. All global chemical predictors do not show important changes regardless of the presence of an intramolecular hydrogen bond. However, in the case of local reactivity predictors, oxygen atoms of the catechol moiety exhibit changes when this contact is present. This conclusion was confirmed when 8 catechol derivatives were analyzed with the same procedure applied over the dopamine. Additionally, the carbon atoms opposite to the carbon atoms linked to oxygen atoms, in the catechol moiety, present the biggest changes when these systems donate one electron. Consequently, the electron involved during the charge transfer process of these systems will be detached from the region defined between these two carbon atoms.

Calculations for energies, transition rates, and lifetimes in Al-like Kr XXIV

Using the second-order many-body perturbation theory (MBPT) method, a complete and accurate data set of excitation energies, lifetimes, wavelengths, and electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) line strengths, transition rates, and oscillator strengths for the lowest 880 levels arising from the 3l3 (0≤l≤2), 3l24l′ (0≤l≤2, 0≤l′≤3), 3s25l (0≤l≤4), 3p25l (0≤l≤1), and 3s3p5l (0≤l≤4) configurations in Al-like Kr XXIV is provided. Comparisons are made with available experimental and theoretical results. Our calculated energies are expected to be accurate enough to facilitate identifications of observed lines involving the n=4,5 levels. The complete data set is also useful for modeling and diagnosing fusion plasma.

Extended Calculations of Spectroscopic Data: Energy Levels, Lifetimes, and Transition Rates for O-like Ions from Cr xvii to Zn xxiii

Abstract Employing two state-of-the-art methods, multiconfiguration Dirac–Hartree–Fock and second-order many-body perturbation theory, the excitation energies and lifetimes for the lowest 200 states of the , , , , , , , , and configurations, and multipole (electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2)) transition rates, line strengths, and oscillator strengths among these states are calculated for each O-like ion, from Cr xvii to Zn xxiii. Our two data sets are compared with the National Institute of Standards and Technology and CHIANTI compiled values, and previous calculations. The data are accurate enough for identification and deblending of new emission lines from the Sun and other astrophysical sources. The amount of high-accuracy data is significantly increased for the n = 3 states of several O-like ions of astrophysical interest, where experimental data are very scarce.

Responsivity calibration of the extreme ultraviolet spectrometer in the range of 175-435 Å

We reported the relative responsivity calibration of the grazing-incidence flat-field EUV spectrometer between 175 and 435 Å by means of two methods. The first method is implemented by measuring the diffraction efficiency of the grating with synchrotron radiation light source. Considering the transmission efficiency and quantum efficiency of the other optical components in the spectrometer, the total responsivity was then obtained. The second one was carried out by measuring line emissions from C3+, N4+ and O3+ ions at Shanghai high temperature super conductor electron beam ion trap (SH-HtscEBIT). The EUV spectra were also simulated theoretically via a collisional radiative model. In the calculation, the second-order relativistic many-body perturbation theory approach based on the flexible atomic code was used to calculate the energy levels and transition rates; the close-coupling R-matrix approach and relativistic distorted wave method were utilized to calculate the collision strength of electron impact excitation. In comparison with the spectroscopic measurements at EBIT device, the differences between the measured and simulated relative line intensities were obtained. The responsivity calibration for the spectrometer was then achieved by a 3rd degree polynomial function fitting. Our measurement shows that the responsivity between 175 and 435 Å varies by factor of ∼ 46. The two results of calibration demonstrated a consistency within an average deviation of 24%. In addition, an evaluation of our calculations on C iv, N v and O iv line emissions in this wavelength region was given.

Full QM Calculation of RNA Energy Using Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps Method.

In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree-Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol.