Symmetry-adapted many-body perturbation theory: use of the wave operator matrix elements

Pramana ◽  
1979 ◽  
Vol 13 (5) ◽  
pp. 535-544 ◽  
Author(s):  
Debashis Mukherjee ◽  
Dipan Bhattacharyya
Keyword(s):  
Perturbation Theory ◽  
Wave Operator ◽  
Operator Matrix ◽  
Matrix Elements ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Theory Use

Relativistic many-body calculations of atomic properties in Pd-like ions

2008 ◽  
Vol 86 (1) ◽  
pp. 131-149 ◽  
Author(s):  
U I Safronova ◽  
R Bista ◽  
R Bruch ◽  
H Merabet
Keyword(s):  
Perturbation Theory ◽  
Negative Energy ◽  
Second Order ◽  
Energy Splitting ◽  
Transition Rates ◽  
Matrix Elements ◽  
Many Body ◽  
Negative Energy States ◽  
Many Body Perturbation Theory ◽  
Energy States

Wavelengths, transition rates, and line strengths are calculated for the 85 possible multipole transitions between the excited 4p6 4d9 4f, 4p6 4d9 5l, 4p5 4d10 4f, and 4p5 4d10 5l states and the ground 4p6 4d10 state in Pd-like ions with the nuclear charges ranging from Z = 47 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in hole–particle systems. This method is based on the relativistic many-body perturbation theory, agrees with MCDF calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative energy states. The calculations start from a [Zn]4p64d10 Dirac–Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order multipole matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. Trends of the transitions rates for the selected multipole transitions as function of Z are illustrated graphically. The Z dependence of the energy splitting for all triplet terms of the 4p64d9 4f and 4p64d9 5l configurations are shown for Z = 47–100. PACS Nos.: 31.15.Ar, 31.15.Md, 32.70.Cs, 32.30.Rj, 31.25.Jf

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules

2019 ◽  
Author(s):  
Brian Nguyen ◽  
Guo P Chen ◽  
Matthew M. Agee ◽  
Asbjörn M. Burow ◽  
Matthew Tang ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
System Size ◽  
State Density ◽  
Second Order ◽  
Binding Energies ◽  
Basis Set ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Relative Errors ◽  
Ground State Density

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order Møller–Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFA), and the post-Kohn–Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5-10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 1‰ per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed which uses monomers at full coupling whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation–dissipation theorem, we obtain a nonperturbative “screened second-order” expression for the dispersion energy in terms of monomer quantities which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. Whereas the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series within MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete “electrodynamic” screening of the Coulomb interaction due to induced particle–hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust non-perturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.<br>

Investigations in Many-Body Perturbation Theory of Hyperfine Structure in Diatomic Molecules

1973 ◽  
Vol 7 (1) ◽  
pp. 51-59 ◽  
Author(s):  
James E. Rodgers ◽  
Taesul Lee ◽  
T. P. Das ◽  
Dennis Ikenberry
Keyword(s):  
Perturbation Theory ◽  
Hyperfine Structure ◽  
Diatomic Molecules ◽  
Many Body ◽  
Many Body Perturbation Theory

scholarly journals Many-Body Perturbation Theory Using the Density-Functional Concept: Beyond theGWApproximation

2005 ◽  
Vol 94 (18) ◽  
Author(s):  
Fabien Bruneval ◽  
Francesco Sottile ◽  
Valerio Olevano ◽  
Rodolfo Del Sole ◽  
Lucia Reining
Keyword(s):  
Perturbation Theory ◽  
Density Functional ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Functional Concept
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