Dynamics and conformational sampling are essential for linking protein structure to biological function. While challenging to probe experimentally, computer simulations are widely used to describe protein dynamics, but at significant computational costs that continue to limit the systems that can be studied. Here, we demonstrate that machine learning can be trained with simulation data to directly generate physically realistic conformational ensembles of proteins without the need for any sampling and at negligible computational cost. As a proof-of-principle we train a generative adversarial network based on a transformer architecture with self-attention on coarse-grained simulations of intrinsically disordered peptides. The resulting model, idpGAN, can predict sequence-dependent coarse-grained ensembles for sequences that are not present in the training set demonstrating that transferability can be achieved beyond the limited training data. We also retrain idpGAN on atomistic simulation data to show that the approach can be extended in principle to higher-resolution conformational ensemble generation.

VL - 14 SN - 2041-1723 UR - https://doi.org/10.1038/s41467-023-36443-x IS - 1 JO - Nature Communications ER - TY - JOUR T1 - Development and evaluation of CO2 transport in MPAS-A v6.3 JF - Geoscientific Model Development Y1 - 2021 A1 - Zheng, T. A1 - Feng, S. A1 - Davis, K. J. A1 - Pal, S. A1 - Morguí, J.-A. AB -Chemistry transport models (CTMs) play an important role in understanding fluxes and atmospheric distribution of carbon dioxide (CO_{2}). They have been widely used for modeling CO_{2} transport through forward simulations and inferring fluxes through inversion systems. With the increasing availability of high-resolution observations, it has been become possible to estimate CO_{2} fluxes at higher spatial resolution. In this work, we implemented CO_{2} transport in the Model for Prediction Across Scales – Atmosphere (MPAS-A). The objective is to use the variable-resolution capability of MPAS-A to enable a high-resolution CO_{2} simulation in a limited region with a global model. Treating CO_{2} as an inert tracer, we implemented in MPAS-A (v6.3) the CO_{2} transport processes, including advection, vertical mixing by boundary layer scheme, and convective transport. We first evaluated the newly implemented model's tracer mass conservation and then its CO_{2} simulation accuracy. A 1-year (2014) MPAS-A simulation is evaluated at the global scale using CO_{2} measurements from 50 near-surface stations and 18 Total Carbon Column Observing Network (TCCON) stations. The simulation is also compared with two global models: National Oceanic and Atmospheric Administration (NOAA) CarbonTracker v2019 (CT2019) and European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS). A second set of simulation (2016–2018) is used to evaluate MPAS-A at regional scale using Atmospheric Carbon and Transport – America (ACT-America) aircraft CO_{2} measurements over the eastern United States. This simulation is also compared with CT2019 and a 27 km WRF-Chem simulation. The global-scale evaluations show that MPAS-A is capable of representing the spatial and temporal CO_{2} variation with a comparable level of accuracy as IFS of similar horizontal resolution. The regional-scale evaluations show that MPAS-A is capable of representing the observed atmospheric CO_{2} spatial structures related to the midlatitude synoptic weather system, including the warm versus cold sector distinction, boundary layer to free troposphere difference, and frontal boundary CO_{2} enhancement. MPAS-A's performance in representing these CO_{2} spatial structures is comparable to the global model CT2019 and regional model WRF-Chem.

Influenza fusion peptide is critical for mediating the fusion of viral and host cell membranes during viral entry. The interaction of monomeric influenza fusion peptide with membranes is studied with replica exchange molecular dynamics simulations using a new implicit membrane model to effectively reach microsecond to millisecond time scales. The conformational sampling of the fusion peptide was studied as a function of different N- and C-termini, including an experimental construct with an additional C-terminal tag, as well as a function of protonation of acidic residues. It is found that the influenza fusion peptide mostly adopts helical structures with a pronounced kink at residues 11−13 with both N-terminal and C-terminal helices oriented mostly parallel to the membrane surface. A charged C-terminus and the presence of a charge C-terminal tag significantly alters the conformational sampling of the fusion peptide and results in more diverse conformational ensembles that include obliquely inserted N-terminal peptide structures. Protonation of acidic residues also affects the conformational sampling, however, based on pKa shift estimates the overall effect of pH = 5 on the conformational sampling of the influenza fusion peptide appears to be only minor.

VL - 114 ER - TY - JOUR T1 - Conformational Sampling of S- and R-Warfarin in Polar Solvents: Implications for Stereoselective Complex Formation JF - Journal of Molecular Structure (Theochem) Y1 - 2010 A1 - Michael Feig A1 - K. Gebreyohannes A1 - V. McGuffin AB -Molecular dynamics simulations of the open side chain conformation of ionic and neutral S- and R-warfarin in aqueous solvent and acetonitrile are described. In all cases, warfarin is found to sample a broad conformational ensemble with major and minor states due to torsional degrees of freedom associated with its side chain. Thermodynamics and kinetics of transitions between these states are analyzed from the simulations and interpreted in the context of stereoselective interactions in biological and non-biological complexes.

VL - 949 IS - 1-3 ER - TY - JOUR T1 - Defect-induced rigidity enhancement in layered semiconductors JF - Solid State Communications Y1 - 2010 A1 - Rak, Zs. A1 - S. D. Mahanti A1 - Mandal, Krishna C A1 - Fernelius, N.C. VL - 150 IS - 27-28 ER - TY - JOUR T1 - Doping dependence of electronic and mechanical properties of GaSe_{1−x}Te_{x} and Ga_{1−x}In_{x}Se from first principles JF - Physical Review B Y1 - 2010 A1 - Rak, Zs. A1 - S. D. Mahanti A1 - Mandal, Krishna C A1 - Fernelius, N.C. VL - 82 IS - 15 ER - TY - JOUR T1 - Effect of membrane thickness on conformational sampling of phospholamban from computer simulations JF - Biophysical Journal Y1 - 2010 A1 - Sayadi, Maryam A1 - Seiichiro Tanizaki A1 - Michael Feig AB -The conformational sampling of monomeric, membrane-bound phospholamban is described from computer simulations. Phospholamban (PLB) plays a key role as a regulator of sarcoplasmic reticulum calcium ATPase. An implicit membrane model is used in conjunction with replica exchange molecular dynamics simulations to reach μs-ms timescales. The implicit membrane model was also used to study the effect of different membrane thicknesses by scaling the low-dielectric region. The conformational sampling with the membrane model mimicking dipalmitoylphosphatidylcholine bilayers is in good agreement overall with experimental measurements, but consists of a wide variety of different conformations including structures not described previously. The conformational ensemble shifts significantly in the presence of thinner or thicker membranes. This has implications for the structure and dynamics of PLB in physiological membranes and offers what we believe to be a new interpretation of previous experimental measurements of PLB in detergents and microsomal membrane.

VL - 98 IS - 5 ER - TY - JOUR T1 - On the Origin of the Highest Redshift Gamma-Ray Bursts JF - \apj Y1 - 2010 A1 - Belczynski, K. A1 - Holz, D. E. A1 - Fryer, C. L. A1 - Berger, E. A1 - Hartmann, D. H. A1 - O'Shea, B. W. KW - binaries: general KW - gamma rays: bursts KW - stars: formation VL - 708 ER - TY - JOUR T1 - PRIMO/PRIMONA: A coarse-grained model for proteins and nucleic acids that preserves near-atomistic accuracy JF - Proteins: Structure, Function, and Bioinformatics Y1 - 2010 A1 - Gopal, Srinivasa M. A1 - Mukherjee, Shayantani A1 - Cheng, Yi-Ming A1 - Michael Feig AB -The new coarse graining model PRIMO/PRIMONA for proteins and nucleic acids is proposed. This model combines one to several heavy atoms into coarse-grained sites that are chosen to allow an analytical, high-resolution reconstruction of all-atom models based on molecular bonding geometry constraints. The accuracy of proposed reconstruction method in terms of structure and energetics is tested and compared with other popular reconstruction methods for a variety of protein and nucleic acid test sets. Proteins 2010. © 2009 Wiley-Liss, Inc.

VL - 78 IS - 5 ER - TY - JOUR T1 - Constraints on the Density Dependence of the Symmetry Energy JF - Physical Review Letters Y1 - 2009 A1 - M. B. Tsang A1 - Yingxun Zhang A1 - P. Danielewicz A1 - M. Famiano A1 - Li, Z. A1 - W. G. Lynch A1 - A. W. Steiner AB -Collisions involving {112Sn} and {124Sn} nuclei have been simulated with the improved quantum molecular dynamics transport model. The results of the calculations reproduce isospin diffusion data from two different observables and the ratios of neutron and proton spectra. By comparing these data to calculations performed over a range of symmetry energies at saturation density and different representations of the density dependence of the symmetry energy, constraints on the density dependence of the symmetry energy at subnormal density are obtained. The results from the present work are compared to constraints put forward in other recent analyses.

VL - 102 N1 - Copyright {(C)} 2010 The American Physical Society; Please report any problems to prola@aps.org ER - TY - JOUR T1 - Electronic structure of substitutional defects and vacancies in GaSe JF - Journal of Physics and Chemistry of Solids Y1 - 2009 A1 - Rak, Zs. A1 - S. D. Mahanti A1 - Mandal, Krishna C A1 - Fernelius, N.C. VL - 70 IS - 2 ER - TY - JOUR T1 - Strategies for Online Communities JF - Strategic Management Journal Y1 - 2009 A1 - Miller, K. D. A1 - Fabian, F. H. A1 - Lin, S. VL - 51 ER - TY - JOUR T1 - Theoretical studies of defect states in GaTe JF - Journal of Physics: Condensed Matter Y1 - 2009 A1 - Rak, Zs A1 - S. D. Mahanti A1 - Mandal, Krishna C A1 - Fernelius, N.C. AB -Using first principle electronic structure calculations within density functional theory and the supercell model, we have investigated the nature and formation energies of defect states associated with Ga and Te vacancies and Ge and Sn substitutional impurities in GaTe. We have also calculated the band structure of pure GaTe for comparison with systems with defects and also to find out the importance of spin–orbit interaction (SOI) on its band structure. We find that the top valence band at the Γ-point shifts up in energy by 0.1 eV due to the mixing of Te p x –p y and p z bands, this splitting being considerably smaller than in atoms where it is 0.8 eV. From an analysis of charge densities and band structures associated with the defect states, we find that most of them are strongly localized and lie deep in the band gap region. The calculated binding energy of the deep defect state and the ε(−1 / −2) transition level associated with the Ga vacancy appears to be in good agreement with experiment. Formation energy calculations suggest that V Ga is the preferred intrinsic defect in GaTe.

VL - 21 ER - TY - JOUR T1 - The influence of cluster emission and the symmetry energy on neutron-proton spectral double ratios JF - Physics Letters B Y1 - 2008 A1 - Yingxun Zhang A1 - P. Danielewicz A1 - M. Famiano A1 - Li, Z. A1 - W. G. Lynch A1 - M. B. Tsang AB -The emissions of neutrons, protons and bound clusters from central {124Sn} + {124Sn} and {112Sn} + {112Sn} collisions are simulated using the Improved Quantum Molecular Dynamics model for two different density-dependent symmetry-energy functions. The calculated neutron-proton spectral double ratios for these two systems are sensitive to the density dependence of the symmetry energy, consistent with previous work. Cluster emission increases the double ratios in the low energy region relative to values calculated in a coalescence-invariant approach. To circumvent uncertainties in cluster production and secondary decays, it is important to have more accurate measurements of the neutron-proton ratios at higher energies in the center of mass system, where the influence of such effects is reduced.

VL - 664 ER - TY - JOUR T1 - Theoretical studies of defect states in GaTe JF - Journal of Physics: Condensed Matter Y1 - 2008 A1 - Rak, Zs A1 - S. D. Mahanti A1 - Mandal, Krishna C A1 - Fernelius, N.C. VL - 21 IS - 1 ER - TY - CHAP T1 - New Alternatives for Accurate Electronic Structure Calculations of Potential Energy Surfaces Involving Bond Breaking T2 - Electron Correlation Methodology Y1 - 2007 A1 - Piotr Piecuch A1 - I. S. O. Pimienta A1 - P.-D. Fan A1 - K. Kowalski AB -The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches.

JF - Electron Correlation Methodology T3 - ACS Symposium Series PB - American Chemical Sociegy CY - Washington, DC VL - 958 SN - ISBN13: 9780841238435 ER - TY - JOUR T1 - Automated derivation and parallel computer implementation of renormalized and active-space coupled-cluster methods JF - International Journal of Quantum Chemistry Y1 - 2006 A1 - Piotr Piecuch A1 - So Hirata A1 - K. Kowalski A1 - P.-D. Fan A1 - Theresa L. Windus AB -Our recent efforts that have led to an automated derivation and computer implementation of the renormalized and active-space coupled-cluster {(CC)} methods with Tensor Contraction Engine {(TCE)} are summarized. The {TCE-generated} renormalized and active-space {CC} computer codes are parallel and applicable to closed- and open-shell references, enabling accurate calculations of potential energy surfaces along bond-breaking coordinates and excited states displaying a significant multi-reference character. The effectiveness of the new codes in describing electronic quasi-degeneracies is illustrated by the renormalized {CC} calculations of the potential energy curve of {HCl} and the active-space {CC} calculations for the low-lying excited states of the Be3 system. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

VL - 106 IS - 1 ER - TY - JOUR T1 - Balancing an accurate representation of the molecular surface in generalized born formalisms with integrator stability in molecular dynamics simulations JF - Journal of Computational Chemistry Y1 - 2006 A1 - Jana Chocholouscaronová A1 - Michael Feig AB -Different integrator time steps in {NVT} and {NVE} simulations of protein and nucleic acid systems are tested with the {GBMV} {(Generalized} Born using Molecular Volume) and {GBSW} {(Generalized} Born with simple {SWitching)} methods. The simulation stability and energy conservation is investigated in relation to the agreement with the Poisson theory. It is found that very close agreement between generalized Born methods and the Poisson theory based on the commonly used sharp molecular surface definition results in energy drift and simulation artifacts in molecular dynamics simulation protocols with standard 2-fs time steps. New parameters are proposed for the {GBMV} method, which maintains very good agreement with the Poisson theory while providing energy conservation and stable simulations at time steps of 1 to 1.5 fs. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 719-729, 2006

VL - 27 IS - 6 ER - TY - JOUR T1 - Experimental and Theoretical UV Characterizations of Acetyloacetone and its Isomers JF - The Journal of Physical Chemistry A Y1 - 2006 A1 - Piotr Piecuch A1 - S. Coussan A1 - Y. Ferro A1 - A. Trivella A1 - P. Roubin A1 - R. Wieczorek A1 - C. Manca A1 - K. Kowalski A1 - M. Wloch A1 - S. Kucharski A1 - M. Musial AB -Cryogenic matrix isolation experiments have allowed the measurement of the UV absorption spectra of the high-energy non-chelated isomers of acetylacetone, these isomers being produced by UV irradiation of the stable chelated form. Their identification has been done by coupling selective UV-induced isomerization, infrared spectroscopy, and harmonic vibrational frequency calculations using density functional theory. The relative energies of the chelated and non-chelated forms of acetylacetone in the S0 state have been obtained using density functional theory and coupled-cluster methods. For each isomer of acetylacetone, we have calculated the UV transition energies and dipole oscillator strengths using the excited-state coupled-cluster methods, including EOMCCSD (equation-of-motion coupled-cluster method with singles and doubles) and CR-EOMCCSD(T) (the completely renormalized EOMCC approach with singles, doubles, and non-iterative triples). For dipole-allowed transition energies, there is a very good agreement between experiment and theory. In particular, the CR-EOMCCSD(T) approach explains the blue shift in the electronic spectrum due to the formation of the non-chelated species after the UV irradiation of the chelated form of acetylacetone. Both experiment and CR-EOMCCSD(T) theory identify two among the seven non-chelated forms to be characterized by red-shifted UV transitions relative to the remaining five non-chelated isomers.

VL - 110 IS - 11 ER - TY - JOUR T1 - Intriguing Accuracies of the Exponential Wave Function Expansions Exploiting Finite Two-Body Correlation Operators in Calculations for Many-Electron Systems JF - Journal of Molecular Structure: THEOCHEM Y1 - 2006 A1 - P.-D. Fan A1 - P. Piecuch KW - xact many-electron wave functions; Generalized coupled-cluster methods; Two-body correlation operators; Nooijen's conjecture; Variational calculations; Multi-determinantal reference states; Excited states AB -Following the ideas laid down by Nooijen and Nakatsuji, several authors have considered an intriguing possibility of representing the exact many-electron wave functions by the exponential cluster expansions involving two-body correlation operators. In particular, inspired by the symmetric form of the Horn–Weinstein exact energy formula, and exploiting the variational principle and numerical analysis, we have demonstrated that one can obtain nearly exact ground-state wave functions for a few many-electron systems using the exponential cluster expansion involving a finite two-body operator acting on the Hartree–Fock determinant [P. Piecuch et al., Phys. Rev. Lett. 90 (2003) 113001]. After summarizing these earlier findings and making some additional comments on the nature of the exponential cluster expansions involving two-body correlation operators, we examine the following issues: (i) the improvements in the accuracy and convergence toward the full configuration interaction (CI) limit offered by cluster operators containing two-body as well as one-body components, (ii) the improvements in the accuracy resulting from the use of multi-determinantal reference states, and (iii) the potential accuracy of the exponential wave function expansions involving finite one- and two-body cluster operators in excited-state calculations. All calculations are performed for an eight electron model system, which is simple enough to allow for the exact, full CI, and other electronic structure calculations, which has fewer independent parameters in the Hamiltonian than the dimension of the corresponding full CI problem, and which enables one to examine ground and excited states with a varying degree of configurational quasi-degeneracy by simple changes in the corresponding nuclear geometry.

VL - 768 IS - 1-3 ER - TY - JOUR T1 - Molecular Dynamics Simulations of Large Integral Membrane Proteins with an Implicit Membrane Model JF - The Journal of Physical Chemistry B Y1 - 2006 A1 - Seiichiro Tanizaki A1 - Michael Feig AB -The heterogeneous dielectric generalized Born {(HDGB)} methodology is an the extension of the {GBMV} model for the simulation of integral membrane proteins with an implicit membrane environment. Three large integral membrane proteins, the bacteriorhodopsin monomer and trimer and the {BtuCD} protein, were simulated with the {HDGB} model in order to evaluate how well thermodynamic and dynamic properties are reproduced. Effects of the truncation of electrostatic interactions were examined. For all proteins, the {HDGB} model was able to generate stable trajectories that remained close to the starting experimental structures, in excellent agreement with explicit membrane simulations. Dynamic properties evaluated through a comparison of B-factors are also in good agreement with experiment and explicit membrane simulations. However, overall flexibility was slightly underestimated with the {HDGB} model unless a very large electrostatic cutoff is employed. Results with the {HDGB} model are further compared with equivalent simulations in implicit aqueous solvent, demonstrating that the membrane environment leads to more realistic simulations.

VL - 110 ER - TY - JOUR T1 - The Usefulness of Exponential Wave Function Expansions Employing One- and Two-Body Cluster Operators in Electronic Structure Theory: The Extended and Generalized Coupled-Cluster Methods JF - Advances in Quantum Chemistry Y1 - 2006 A1 - P.-D. Fan A1 - Piotr Piecuch AB -In this paper, the applicability of exponential cluster expansions involving one- and two-body operators in high accuracy ab initio electronic structure calculations is examined. First, the extended coupled-cluster method with singles and doubles (ECCSD) is tested in the demanding studies of systems with strong quasi-degeneracies, including potential energy surfaces involving multiple bond breaking. The numerical results show that the single-reference ECCSD method is capable of providing a qualitatively correct description of quasi-degenerate electronic states and potential energy surfaces involving bond breaking, eliminating, in particular, the failures and the unphysical behavior of standard coupled-cluster methods in similar cases. It is also demonstrated that one can obtain entire potential energy surfaces with millihartree accuracies by combining the ECCSD theory with the non-iterative a posteriori corrections obtained by using the generalized variant of the method of moments of coupled-cluster equations. This is one of the first instances where the relatively simple single-reference formalism, employing only one- and two-body clusters in the design of the relevant energy expressions, provides a highly accurate description of the dynamic and significant non-dynamic correlation effects characterizing quasi-degenerate and multiply bonded systems. Second, an evidence is presented that one may be able to represent the virtually exact ground- and excited-state wave functions of many-electron systems by exponential cluster expansions employing general two-body or one- and two-body operators. Calculations for small many-electron model systems indicate the existence of finite two-body parameters that produce the numerically exact wave functions for ground and excited states. This finding may have a significant impact on future quantum calculations for many-electron systems, since normally one needs triply excited, quadruply excited, and other higher-than-doubly excited Slater determinants, in addition to all singly and doubly excited determinants, to obtain the exact or virtually exact wave functions.

VL - 51 ER - TY - JOUR T1 - Comparison of Low-Order Multireference Many-Body Perturbation Theories JF - Journal of Chemical Physics Y1 - 2005 A1 - Piotr Piecuch A1 - R.K. Chaudhuri A1 - K.F. Freed A1 - G. Hose A1 - K. Kowalski A1 - M. Wloch A1 - S. Chattopadhyay A1 - D. Mukherjee A1 - R. Rolik A1 - A. Szabados A1 - G. Toth A1 - P.R. Surjan AB -Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.

VL - 122 IS - 13 ER - TY - JOUR T1 - Noniterative Corrections to Extended Coupled-Cluster Energies Employing the Generalized Method of Moments of Coupled-Cluster Equations JF - Molecular Physics Y1 - 2005 A1 - Piotr Piecuch A1 - {P.-D.} Fan A1 - K. Kowalski AB -It is shown that the extended coupled-cluster method with singles and doubles (ECCSD) does not suffer from the non-variational collapse observed in the standard CCSD calculations when multiple bond breaking is examined. This interesting feature of the single-reference ECCSD theory is used to design the non-iterative CC methods with singles, doubles and non-iterative triples and quadruples, which provide a highly accurate and variational description of potential energy surfaces involving multiple bond breaking with computational steps that scale as with the system size. This is accomplished with the help of the generalized version of the method of moments of coupled-cluster equations (GMMCC), which can be used to correct the results of non-standard CC calculations, such as ECCSD. The theoretical considerations are illustrated by the preliminary results of the ECCSD-based GMMCC calculations for triple bond breaking in N2. Keywords: Coupled-cluster theory; Extended coupled-cluster method; Method of moments of coupled-cluster equations; Non-iterative coupled-cluster approaches; Bond breaking

VL - 103 IS - 15 & 16 ER - TY - JOUR T1 - Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states JF - Theoretical Chemistry Accounts: Theory, Computation, and Modeling Y1 - 2004 A1 - Piotr Piecuch A1 - K. Kowalski A1 - I. S. O. Pimienta A1 - P.-D. Fan A1 - M.D. Lodriguito A1 - M. J. {McGuire} A1 - S. A. Kucharski A1 - T. Kuś A1 - M. Musial KW - Coupled-cluster theory - Method of moments of coupled-cluster equations - Renormalized coupled-cluster methods - extended coupled cluster theory - Potential energy surfaces AB -The method of moments of coupled-cluster equations {(MMCC),} which provides a systematic way of improving the results of the standard coupled-cluster {(CC)} and equation-of-motion {CC} {(EOMCC)} calculations for the ground- and excited-state energies of atomic and molecular systems, is described. The {MMCC} theory and its generalized {MMCC} {(GMMCC)} extension that enables one to use the cluster operators resulting from the standard as well as nonstandard {CC} calculations, including those obtained with the extended {CC} {(ECC)} approaches, are based on rigorous mathematical relationships that define the many-body structure of the differences between the full configuration interaction {(CI)} and {CC} or {EOMCC} energies. These relationships can be used to design the noniterative corrections to the {CC/EOMCC} energies that work for chemical bond breaking and potential energy surfaces of excited electronic states, including excited states dominated by double excitations, where the standard single-reference {CC/EOMCC} methods fail. Several {MMCC} and {GMMCC} approximations are discussed, including the renormalized and completely renormalized {CC/EOMCC} methods for closed- and open-shell states, the quadratic {MMCC} approaches, the {CI-corrected} {MMCC} methods, and the {GMMCC} approaches for multiple bond breaking based on the {ECC} cluster amplitudes.

VL - 112 ER -