Multireference Many-body Perturbation Theory Research Articles

Bistability between π-diradical open-shell and closed-shell states in indeno[1,2-a]fluorene.

Indenofluorenes are non-benzenoid conjugated hydrocarbons that have received great interest owing to their unusual electronic structure and potential applications in nonlinear optics and photovoltaics. Here we report the generation of unsubstituted indeno[1,2-a]fluorene on various surfaces by the cleavage of two C-H bonds in 7,12-dihydroindeno[1,2-a]fluorene through voltage pulses applied by the tip of a combined scanning tunnelling microscope and atomic force microscope. On bilayer NaCl on Au(111), indeno[1,2-a]fluorene is in the neutral charge state, but it exhibits charge bistability between neutral and anionic states on the lower-workfunction surfaces of bilayer NaCl on Ag(111) and Cu(111). In the neutral state, indeno[1,2-a]fluorene exhibits one of two ground states: an open-shell π-diradical state, predicted to be a triplet by density functional and multireference many-body perturbation theory calculations, or a closed-shell state with a para-quinodimethane moiety in the as-indacene core. We observe switching between open- and closed-shell states of a single molecule by changing its adsorption site on NaCl.

Multi-reference many-body perturbation theory for nuclei

In spite of missing dynamical correlations, the projected generator coordinate method (PGCM) was recently shown to be a suitable method to tackle the low-lying spectroscopy of complex nuclei. Still, describing absolute binding energies and reaching high accuracy eventually requires the inclusion of dynamical correlations on top of the PGCM. In this context, the present work discusses the first realistic results of a novel multi-reference perturbation theory (PGCM-PT) that can do so within a symmetry-conserving scheme for both ground and low-lying excited states. First, proof-of-principle calculations in a small (\(e_{\mathrm {max}}=4\)) model space demonstrate that exact binding energies of closed- (\({}^{16}\mathrm {O}\)) and open-shell (\({}^{18}\mathrm {O}\), \({}^{20}\mathrm {Ne}\)) nuclei are reproduced within 0.5–\(1.5\%\) at second order, i.e. through PGCM-PT(2). Moreover, profiting from the pre-processing of the Hamiltonian via multi-reference in-medium similarity renormalization group transformations, PGCM-PT(2) can reach converged values within smaller model spaces than with an unevolved Hamiltonian. Doing so, dynamical correlations captured by PGCM-PT(2) are shown to bring essential corrections to low-lying excitation energies that become too dilated at leading order, i.e., at the strict PGCM level. The present work is laying the foundations for a better understanding of the optimal way to grasp static and dynamical correlations in a consistent fashion, with the aim of accurately describing ground and excited states of complex nuclei via ab initio many-body methods.

Multi-reference many-body perturbation theory for nuclei

The neon isotopic chain displays a rich phenomenology, ranging from clustering in the ground-state of the self-conjugate doubly open-shell stable $$^{20}$$ Ne isotope to the physics of the island of inversion around the neutron-rich $$^{30}$$ Ne isotope. This second (i.e. Paper II) of the present series proposes an extensive ab initio study of neon isotopes based on two complementary many-body methods, i.e. the quasi-exact in-medium no-core shell model (IM-NCSM) and the projected generator coordinate method (PGCM) that is ideally suited to capturing strong static correlations associated with shape deformation and fluctuations. Calculations employ a state-of-the-art generation of chiral effective field theory Hamiltonians and evaluate the associated systematic uncertainties. In spite of missing so-called dynamical correlations, which can be added via the multi-reference perturbation theory proposed in the first paper (i.e. Paper I) of the present series [1], the PGCM is shown to be a suitable method to tackle the low-lying spectroscopy of complex nuclei. Still, describing the physics of the island of inversion constitutes a challenge that seems to require the inclusion of dynamical correlations. This is addressed in the third paper (i.e. Paper III) of the present series [2].

Multi-reference many-body perturbation theory for nuclei

Multi-reference many-body perturbation theory for nuclei

Photoexcited tautomerization of vinyl alcohol to acetylaldehydevia a conical intersection from contracted Schrödinger theory

The photoexcited tautomerization of vinyl alcohol to acetylaldehyde via a conical intersection is analyzed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions to the anti-Hermitian contracted Schrödinger equation (ACSE). The study utilizes the recent generalization of the ACSE method for the treatment of excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A, 2009, 80, 022507]. We computed absolute energies of the critical points as well as various intermediate points along the ground- and excited-state potential energy surface of vinyl alcohol and acetylaldehyde. The ACSE, MCSCF, second-order multireference many-body perturbation theory (MRMP2), and various coupled cluster methods all demonstrate the existence of a family of pathways from vinyl alcohol to acetylaldehyde via a conical intersection that are monotonically decreasing in energy. The conical intersection, proposed for the first time in this paper, is both structurally and energetically similar to the ground-state transition state. We observe a relationship between conical intersections and transition states both in this paper and in our previous work on bicyclobutane's ring conical intersection [J. W. Snyder, Jr. and D. A. Mazziotti, J. Chem. Phys., 2011, 135, 024107]. To treat multireference correlation, we seeded the ACSE with an initial 2-RDM guess from a multiconfiguration self-consistent field (MCSCF) calculation. The ACSE recovers more single-reference correlation energy than MRMP2 and more multireference correlation energy than comparable single-reference wave function methods. The 2-RDMs from the ACSE nearly satisfy all necessary N-representability conditions.

Photoexcited conversion of gauche-1,3-butadiene to bicyclobutane via a conical intersection: Energies and reduced density matrices from the anti-Hermitian contracted Schrödinger equation

The photoexcited reaction pathway from gauche-1,3-butadiene to bicyclobutane via a conical intersection is analyzed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions to the anti-Hermitian contracted Schrödinger equation (ACSE). The study utilizes the recent generalization of the ACSE method for the treatment of excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)]. We computed absolute energies of the critical points as well as various intermediate points along the ground-and excited-state potential energy surface of gauche-1,3-butadiene and bicyclobutane. To treat multi-reference correlation, we seeded the ACSE with an initial 2-RDM from a multi-configuration self-consistent field (MCSCF) calculation. The ACSE, MCSCF, and second-order multi-reference many-body perturbation theory (MRPT2) all demonstrate that there exists a family of pathways from gauche-1,3-butadiene to bicyclobutane via a conical intersection that are monotonically decreasing in energy, confirming a conjecture by Sicilia et al. [J. Phys. Chem. A 111, 2182 (2007)]. The ACSE recovers more single-reference correlation energy than MRPT2 and more multi-reference correlation energy than comparable single-reference wave function methods. The 2-RDMs from the ACSE nearly satisfy all necessary N-representability conditions.

Multi-reference many-body perturbation theory and coupled cluster developments

Multi-reference methods for the description of quasi-degenerate ground states and excited states of many-electron systems have been one of the main objectives of scientific activity at the Quantum Theory Project (QTP) University of Florida in Gainesville. The pioneering works by Dr. Per-Olov Löwdin on the partitioning technique, and important contributions to the development of multi-reference methods made by Dr. Monkhorst and Dr. Bartlett must be mentioned here. Dr. Bartlett, his group and its visitors have been especially active in this field. In this paper we describe some of the multi-reference developments, problems that have been faced and solved as well as those which still require solving. The focus is on multi-reference many-body perturbation theory and coupled-cluster approaches. We present recent advances and future perspectives in the development of these methods. Special attention is paid to two multi-reference approaches that seem very promising and have been either initiated or developed at QTP.

Conical intersections in triplet excited states of methylene from the anti-Hermitian contracted Schrödinger equation

A conical intersection in triplet excited states of methylene is computed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions of the anti-Hermitian contracted Schrodinger equation (ACSE). The study synthesizes recent extensions of the ACSE method for the treatment of excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary-spin states [A. E. Rothman, J. J. Foley, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]. We compute absolute energies of the 1 (3)B(1), 1 (3)A(2), and 2 (3)B(1) states of methylene (CH(2)) and the location of the conical intersection along the 1 (3)A(2)-2 (3)B(1) potential-energy surfaces. To treat multireference correlation, we seed the ACSE with an initial 2-RDM from a multiconfiguration self-consistent field (MCSCF) calculation. The ACSE produces energies that significantly improve upon those from MCSCF and second-order multireference many-body perturbation theory, and the 2-RDMs from the ACSE nearly satisfy necessary N-representability conditions. Comparison of the results from augmented double-zeta and triple-zeta basis sets demonstrates the importance of augmented (or diffuse) functions for determining the location of the conical intersection.

Relativistic multireference many-body perturbation theory for open-shell ions with multiple valence shell electrons: the transition rates and lifetimes of the excited levels in chlorinelike Fe X

A recently developed relativistic multireference many-body perturbation theory based on multireference configuration-interaction wavefunctions as zeroth-order wavefunctions is outlined. The perturbation theory employs a general class of configuration-interaction wavefunctions as reference functions, and thus is applicable to multiple open valence shell systems with near degeneracy of a manifold of strongly interacting configurations. Multireference many-body perturbation calculations are reported for the ground and excited states of chlorinelike Fe X in which the near degeneracy of a manifold of strongly interacting configurations mandates a multireference treatment. Term energies of a total of 83 excited levels arising from the 3s23p5, 3s3p6, 3s23p43d, 3s3p53d, and 3s23p33d2 configurations of the ion are evaluated to high accuracy. Transition rates associated with E1/M1/E2/M2/E3 radiative decays and lifetimes of a number of excited levels are calculated and compared with laboratory measurements to critically evaluate recent experiments.

A multireference many-body perturbation theory study of Be + H2 → BeH2

A multireference many-body perturbation theory (MR-MBPT) is discussed and illustrated by the model problem of the vertical insertion pathways of Be into H2. The results are compared with full CI and previous coupled-cluster results. The comparison of MR-MBPT results reveals good qualitative agreement. It is suggested that a more extensive reference space is necessary even for this small problem in order to achieve quantitative results. The paper discusses the question of orbital choice in MR-MBPT methods.

Relativistic many-body calculations of excited-state energies and transition wavelengths for six-valence-electron sulfurlike ions

Relativistic multireference many-body perturbation theory calculations have been performed on sulfurlike ions as benchmarks for high-accuracy treatment of multiple open-shell ions with as many as six valence shell electrons. Term energies of the 46 excited states arising from the $3{s}^{2}3{p}^{4}$, $3s3{p}^{5}$, and $3{s}^{2}3{p}^{3}3d$ configurations in ions of the sulfur isoelectronic sequence $(Z=26--32)$ are evaluated to high accuracy. Transition wavelengths associated with electric dipole radiative decays were calculated with an accuracy on the order of $0.01\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ and compared with high-resolution laboratory and solar wavelength measurements to critically evaluate the line identifications.

RelativisticR-matrix close-coupling method based on the effective many-body Hamiltonian: Benchmarks on the electron-impact excitations of theKr6+ion

A relativistic $R$-matrix close-coupling method based on effective many-body Hamiltonians is employed to calculate the electron-impact excitations of intercombination transitions in the ${\text{Kr}}^{6+}$ ion as benchmarks in the quest for accurate representation of the target and collisional states in multivalence-electron ions. The effective Hamiltonian in relativistic multireference many-body perturbation theory accurately accounts for short-range many-body interactions unaccounted for by limited configuration-interaction representations of the basis states. The $R$-matrix method is successfully applied to the near-threshold electron impact excitation of the $4{s}^{2}\text{ }^{1}S\ensuremath{\rightarrow}4s4p\text{ }^{3}P$ intercombination transition in the zinclike krypton $({\text{Kr}}^{6+})$ ion, where the observed disagreement between the experimental absolute total cross sections dominated by dielectronic resonances and those predicted by using the Breit-Pauli and Dirac $R$-matrix methods reveals an inadequacy of the extant $R$-matrix close-coupling calculations in compact configuration-interaction representation of target states.

Relativistic many-body Møller–Plesset perturbation theory calculations of the energy levels and transition rates in Na-like to P-like Xe ions

Relativistic multireference many-body perturbation theory calculations have been performed for Xe 43+ to Xe 39+ ions, resulting in energy levels, electric dipole transition rates, and level lifetimes. The second-order many-body perturbation theory calculation of energy levels included mass shifts, the frequency-dependent Breit correction, and Lamb shifts. The calculated transition energies and E1 transition rates are used to present synthetic spectra in the extreme ultraviolet range for some of the Xe ions.

RelativisticR-matrix close-coupling method based on the effective Hamiltonian in many-body perturbation theory

A relativistic $R$-matrix close-coupling method is developed and implemented based on effective many-body Hamiltonians for accurate representation of the target and collisional states in multielectron ions. The effective Hamiltonian in relativistic multireference many-body perturbation theory accurately accounts for short-range many-body interactions unaccounted for in the extant nonrelativistic and Breit-Pauli $R$-matrix methods. The method is successfully applied to the near-threshold electron impact excitation of the $3{s}^{2}$ $^{1}S\ensuremath{\rightarrow}3s3p$ $^{3}P$ transition in Mg-like argon $({\mathrm{Ar}}^{6+})$ ion where the observed disagreement between the experimental absolute total cross sections and those predicted by using the Breit-Pauli $R$-matrix method reveals an inadequacy of the $R$-matrix methods based on the configuration-interaction representation of the basis states.

Relativistic multireference many-body perturbation theory calculations on Au64+ - Au69+ ions

Many-body perturbation theory (MBPT) calculations are an adequate tool for the description of the structure of highly charged multi-electron ions and for the analysis of their spectra. We demonstrate this by way of a re-investigation of n=3, Δn=0 transitions in the EUV spectra of Na-, Mg-, Al-like, and Si-like ions of Au that have been obtained previously by heavy-ion accelerator based beam-foil spectroscopy. We discuss the evidence and propose several revisions on the basis of our multi-reference many-body perturbation theory calculations of Ne- through P-like ions of Au.

Non-iterative coupled-cluster methods employing multi-reference perturbation theory wave functions

A new class of non-iterative coupled-cluster (CC) methods, which improve the results of standard CC and equation-of-motion (EOM) CC calculations for ground and excited-state potential energy surfaces along bond breaking coordinates and for excited states dominated by two-electron transitions, is explored. The proposed approaches combine the method of moments of coupled-cluster equations (MMCC), in which the a posteriori corrections due to higher-order correlations are added to standard CC/EOMCC energies, with the multi-reference many-body perturbation theory (MRMBPT), which provides information about the most essential non-dynamic and dynamic correlation effects that are relevant to electronic quasi-degeneracies. The performance of the basic MRMBPT-corrected MMCC approximation, in which inexpensive non-iterative corrections due to triple excitations are added to ground- and excited-state energies obtained with the CC/EOMCC singles and doubles approach, is illustrated by the results of a few test calculations, including bond breaking in HF and H 2O, and excited states of CH +.

Quadratic Padé approximants and the intruder state problem of multireference perturbation methods

Simple and quadratic Pade resummation methods are applied to high-order series from multireference many-body perturbation theory (MR-MBPT) calculations using various partitioning schemes (Moller–Plesset, Epstein–Nesbet, and forced degeneracy) to determine their efficacy in resumming slowly convergent or divergent series. The calculations are performed for the ground and low-lying excited states of (i) CH2, (ii) BeH2 at three geometries, and (iii) Be, for which full configuration interaction (CI) calculations are available for comparison. The 49 perturbation series that are analyzed include those with oscillatory and monotonic divergence and convergence, including divergences that arise from either frontdoor or backdoor intruder states. Both the simple and quadratic Pade approximations are found to speed the convergence of slowly convergent or divergent series. However, the quadratic Pade method generally outperforms the simple Pade resummation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Relativistic Many-Body Perturbation Calculations of Boron-Like Silicon, Si X

Relativistic multireference many-body perturbation theory has been employed to calculate the energies of levels in the 2sn12pn23l (l = 0–2) and 2sn12pn24l (l = 0–3) configurations of boron-like silicon (Si X) to high accuracy. Synthetic spectra based on theoretical electric dipole transition probabilities and wavelengths are compared with laboratory spectra in order to identify EUV and soft-x-ray spectral lines.

New classes of non-iterative energy corrections to multi-reference coupled-cluster energies

Two new classes of non-iterative corrections to the ground- and excited-state energies obtained in the state-universal multi-reference coupled-cluster (SUMRCC) calculations have been developed using the multi-reference extension of the method of moments of coupled-cluster equations (MMCC) [KOWALSKI, K., and PIECUCH, P., 2001, J. molec. Struct. (THEOCHEM), 547, 191]. In the first class of the configuration interaction (CI) corrected multi-reference MMCC (MRMMCC) approximations, the non-iterative corrections due to triply or triply and quadruply excited clusters are constructed with the help of multi-reference CI (MRCI) calculations employing the same active space as used in the SUMRCC calculations. In the second class of the completely renormalized (CR) SUMRCC methods, which can be viewed as the multi-reference extensions of the single-reference CR-CCSD(T) theory [KOWALSKI, K., and PIECUCH, P., 2000, J. chem. Phys., 113, 18], the non-iterative corrections due to triply excited clusters are constructed with the help of the multi-reference many-body perturbation theory. In both cases, the non-iterative corrections due to higher-order clusters are added to the energies obtained with the SUMRCC method with singles and doubles. It is demonstrated that the newly developed corrections, including the CR-SUMRCC methods, offer considerable improvements in the SUMRCCSD results, reducing, in particular, the large errors in the SUMRCCSD results due to intruders.

Relativistic multireference many-body perturbation theory calculations on ions of the phosphorus isoelectronic sequence

Term energies of the ground and excited states arising from the 3s23p3, 3s3p4, 3s23p23d and 3s3p33d configurations in ions of the phosphorus isoelectronic sequence (Z = 26–32) are evaluated in relativistic multireference many-body perturbation theory calculations. Theory deviates from experiment on the order of 0.01% for the majority of the experimentally identified levels. The term energies of the 12 hitherto unidentified 3s23p23d levels are determined with 0.01% accuracy. Theoretical photon wavelengths of the electric-dipole (E1) decays from the 3s23p23d and 3s3p33d levels are compared with laboratory and solar lines to critically evaluate previous line identifications. A number of new solar line identifications are given on the basis of theoretical wavelengths and transition probabilities. Theoretical lifetimes of 39 levels arising from the 3s3p4, 3s23p23d and 3s3p33d configurations are evaluated. For the 3s23p23d 4F7/2, 4D7/2 and 4G7/2 levels in Fe XII, Co XIII and Ni XIV, theoretical lifetimes exhibit significant deviation from those obtained in a recent fast-beam spectroscopy experiment.