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.

1 aSayadi, Maryam1 aTanizaki, Seiichiro1 aFeig, Michael uhttps://icer.msu.edu/research/publications/effect-membrane-thickness-conformational-sampling-phospholamban-computer00680nas a2200157 4500008004100000245012900041210006900170653006000239100002100299700000500320700001900325700001800344700001800362700001700380856012500397 2010 eng d00aGalaxy Cluster Radio Relics in Adaptive Mesh Refinement Cosmological Simulations: Relic Properties and Scaling Relationships0 aGalaxy Cluster Radio Relics in Adaptive Mesh Refinement Cosmolog10aAstrophysics - Cosmology and Extragalactic Astrophysics1 aSkillman, S., W.1 a1 aO'Shea, B., W.1 aBurns, J., O.1 aSmith, B., D.1 aTurk, M., J. uhttps://icer.msu.edu/research/publications/galaxy-cluster-radio-relics-adaptive-mesh-refinement-cosmological-simulations01289nas a2200205 4500008004100000245006500041210006500106260001200171300001100183490000800194520066500202100001800867700001900885700002000904700001600924700001100940700001800951700002000969856009400989 2009 eng d00aConstraints on the Density Dependence of the Symmetry Energy0 aConstraints on the Density Dependence of the Symmetry Energy c03/2009 a1227010 v1023 aCollisions 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.

1 aTsang, M., B.1 aZhang, Yingxun1 aDanielewicz, P.1 aFamiano, M.1 aLi, Z.1 aLynch, W., G.1 aSteiner, A., W. uhttps://icer.msu.edu/research/publications/constraints-density-dependence-symmetry-energy00626nas a2200193 4500008004100000245005900041210005900100300001200159490000800171653002200179653001600201653001900217653002400236653002100260100001800281700001600299700001900315856009800334 2009 eng d00aDark Matter Annihilation and Primordial Star Formation0 aDark Matter Annihilation and Primordial Star Formation a574-5830 v69210acosmology: theory10adark matter10aearly universe10agalaxies: formation10astars: formation1 aNatarajan, A.1 aTan, J., C.1 aO'Shea, B., W. uhttps://icer.msu.edu/research/publications/dark-matter-annihilation-primordial-star-formation00505nas a2200133 4500008004100000245008200041210006900123300000900192490000800201100001700209700001300226700001900239856011300258 2009 eng d00aThe Formation of Population III Binaries from Cosmological Initial Conditions0 aFormation of Population III Binaries from Cosmological Initial C a601-0 v3251 aTurk, M., J.1 aAbel, T.1 aO'Shea, B., W. uhttps://icer.msu.edu/research/publications/formation-population-iii-binaries-cosmological-initial-conditions00607nas a2200181 4500008004100000245007300041210006900114260001100183490000700194100001400201700001300215700001500228700001800243700002000261700001900281700001600300856010900316 2009 eng d00aScanning tunneling microscopy study of the CeTe3 charge density wave0 aScanning tunneling microscopy study of the CeTe3 charge density c2/20090 v791 aTomic, A.1 aRak, Zs.1 aVeazey, J.1 aMalliakas, C.1 aMahanti, S., D.1 aKanatzidis, M.1 aTessmer, S. uhttps://icer.msu.edu/research/publications/scanning-tunneling-microscopy-study-cete3-charge-density-wave01591nas a2200217 4500008004100000245007600041210006900117260001200186300001100198490000800209520092200217100001801139700001501157700001501172700001601187700001401203700001201217700001801229700001501247856011101262 2009 eng d00aSurvey of Excited State Neutron Spectroscopic Factors for Z=8-28 Nuclei0 aSurvey of Excited State Neutron Spectroscopic Factors for Z828 N c01/2009 a0625010 v1023 aWe have extracted 565 neutron spectroscopic factors of sd and fp shell nuclei by systematically analyzing more than 2000 measured (d, p) angular distributions. We are able to compare 125 of the extracted spectroscopic factors to values predicted by large-basis shell-model calculations and evaluate the accuracies of spectroscopic factors predicted by different shell-model interactions in these regions. We find that the spectroscopic factors predicted for most excited states of sd-shell nuclei using the latest {USDA} or {USDB} interactions agree with the experimental values. For fp shell nuclei, the inability of the current models to account for the core excitation and fragmentation of the states leads to considerable discrepancies. In particular, the agreement between data and shell-model predictions for Ni isotopes is not better than a factor of 2 using either the {GXPF1A} or the {XT} interaction.

1 aTsang, M., B.1 aLee, Jenny1 aSu, S., C.1 aDai, J., Y.1 aHoroi, M.1 aLiu, H.1 aLynch, W., G.1 aWarren, S. uhttps://icer.msu.edu/research/publications/survey-excited-state-neutron-spectroscopic-factors-z8-28-nuclei02667nas a2200157 4500008004100000245008500041210006900126260001200195300001400207490000800221520211000229100001902339700001302358700001802371856012002389 2009 eng d00aThermochemical Kinetics for Multi-reference Systems: Addition Reactions of Ozone0 aThermochemical Kinetics for Multireference Systems Addition Reac c04/2009 a5786-57990 v1133 aThe 1,3-dipolar cycloadditions of ozone to ethyne and ethene provide extreme examples of multireference singlet-state chemistry, and they are examined here to test the applicability of several approaches to thermochemical kinetics of systems with large static correlation. Four different multireference diagnostics are applied to measure the multireference characters of the reactants, products, and transition states; all diagnostics indicate significant multireference character in the reactant portion of the potential energy surfaces. We make a more complete estimation of the effect of quadruple excitations than was previously available, and we use this with CCSDT/CBS estimation of Wheeler et al. (Wheeler, S. E.; Ess, D. H.; Houk, K. N. J. Phys. Chem. A 2008, 112, 1798.) to make new best estimates of the van der Waals association energy, the barrier height, and the reaction energy to form the cycloadduct for both reactions. Comparing with these best estimates, we present comprehensive mean unsigned errors for a variety of coupled cluster, multilevel, and density functional methods. Several computational aspects of multireference reactions are considered: (i) the applicability of multilevel theory, (ii) the convergence of coupled cluster theory for reaction barrier heights, (iii) the applicability of completely renormalized coupled cluster methods to multireference systems, (iv) the treatment by density functional theory, (v) the multireference perturbation theory for multireference reactions, and (vi) the relative accuracy of scaling-type multilevel methods as compared with additive ones. It is found that scaling-type multilevel methods do not perform better than the additive-type multilevel methods. Among the 48 tested density functionals, only M05 reproduces the best estimates within their uncertainty. Multireference perturbation theory based on the complete-active-space reference wave functions constructed using a small number of reaction-specific active orbitals gives accurate forward barrier heights; however, it significantly underestimates reaction energies.

1 aPiecuch, Piotr1 aZhao, Y.1 aTruhlar, D.G. uhttps://icer.msu.edu/research/publications/thermochemical-kinetics-multi-reference-systems-addition-reactions-ozone00639nas a2200193 4500008004100000245007100041210006900112260000800181300001200189490000800201653001900209653002100228100001800249700001700267700001900284700001900303700001900322856010400341 2009 eng d00aThree Modes of Metal-Enriched Star Formation in the Early Universe0 aThree Modes of MetalEnriched Star Formation in the Early Univers cjan a441-4510 v69110aearly universe10astars: formation1 aSmith, B., D.1 aTurk, M., J.1 aSigurdsson, S.1 aO'Shea, B., W.1 aNorman, M., L. uhttps://icer.msu.edu/research/publications/three-modes-metal-enriched-star-formation-early-universe02100nas a2200181 4500008004100000245008800041210006900129300001000198490000800208520148500216100001401701700001601715700001501731700001401746700001901760700001801779856012101797 2008 eng d00aApplication of Renormalized Coupled- Cluster Methods to Potential Function of Water0 aApplication of Renormalized Coupled Cluster Methods to Potential a59-780 v1203 aThe goal of this paper is to examine the performance of the conventional and renormalized single-reference coupled-cluster (CC) methods in calculations of the potential energy surface of the water molecule. A comparison with the results of the internally contracted multi-reference configuration interaction calculations including the quasi-degenerate Davidson correction (MRCI(Q)) and the spectroscopically accurate potential energy surface of water resulting from the use of the energy switching (ES) approach indicates that the relatively inexpensive completely renormalized (CR) CC methods with singles (S), doubles (D), and a non-iterative treatment of triples (T) or triples and quadruples (TQ), such as CR-CCSD(T), CR-CCSD(TQ), and the recently developed rigorously size extensive extension of CR-CCSD(T), termed CR-CC(2,3), provide substantial improvements in the results of conventional CCSD(T) and CCSD(TQ) calculations at larger internuclear separations. It is shown that the CR-CC(2,3) results corrected for the effect of quadruply excited clusters through the CR-CC(2,3)+Q approach can compete with the highly accurate MRCI(Q) data. The excellent agreement between the CR-CC(2,3)+Q and MRCI(Q) results suggests ways of improving the global potential energy surface of water resulting from the use of the ES approach in the regions of intermediate bond stretches and intermediate energies connecting the region of the global minimum with the asymptotic regions.

1 aZheng, J.1 aGour, J., R1 aLutz, J.J.1 aWloch, M.1 aPiecuch, Piotr1 aTruhlar, D.G. uhttps://icer.msu.edu/research/publications/application-renormalized-coupled-cluster-methods-potential-function-water02156nas a2200181 4500008004100000245022700041210006900268260001200337490000800349520139600357100001401753700001601767700001501783700001401798700001901812700001801831856012501849 2008 eng d00aA Comparative Assessment of the Perturbative and Renormalized Coupled Cluster Theories with a Non-iterative Treatment of Triple Excitations for Thermochemical Kinetics, Including a Study of Basis Set and Core Correlation E0 aComparative Assessment of the Perturbative and Renormalized Coup c01/20080 v1283 aThe CCSD, CCSD(T), and CR-CC(2,3) coupled cluster methods, combined with five triple-zeta basis sets, namely, MG3S, aug-cc-pVTZ, aug-cc-pV(T+d)Z, aug-cc-pCVTZ, and aug-cc-pCV(T+d)Z, are tested against the DBH24 database of diverse reaction barrier heights. The calculations confirm that the inclusion of connected triple excitations is essential to achieving high accuracy for thermochemical kinetics. They show that various noniterative ways of incorporating connected triple excitations in coupled cluster theory, including the CCSD(T) approach, the full CR-CC(2,3) method, and approximate variants of CR-CC(2,3) similar to the triples corrections of the CCSD(2) approaches, are all about equally accurate for describing the effects of connected triply excited clusters in studies of activation barriers. The effect of freezing core electrons on the results of the CCSD, CCSD(T), and CR-CC(2,3) calculations for barrier heights is also examined. It is demonstrated that to include core correlation most reliably, a basis set including functions that correlate the core and that can treat core-valence correlation is required. On the other hand, the frozen-core approximation using valence-optimized basis sets that lead to relatively small computational costs of CCSD(T) and CR-CC(2,3) calculations can achieve almost as high accuracy as the analogous fully correlated calculations.

1 aZheng, J.1 aGour, J., R1 aLutz, J.J.1 aWloch, M.1 aPiecuch, Piotr1 aTruhlar, D.G. uhttps://icer.msu.edu/research/publications/comparative-assessment-perturbative-renormalized-coupled-cluster-theories-non01478nas a2200193 4500008004100000245010300041210006900144260001200213300001400225490000800239520081400247100001901061700002001080700001601100700001101116700001801127700001801145856012101163 2008 eng d00aThe influence of cluster emission and the symmetry energy on neutron-proton spectral double ratios0 ainfluence of cluster emission and the symmetry energy on neutron c02/2008 a145–1480 v6643 aThe 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.

1 aZhang, Yingxun1 aDanielewicz, P.1 aFamiano, M.1 aLi, Z.1 aLynch, W., G.1 aTsang, M., B. uhttps://icer.msu.edu/research/publications/influence-cluster-emission-symmetry-energy-neutron-proton-spectral-double01816nas a2200217 4500008004100000245009100041210006900132260001200201490000700213520109300220653002301313653001901336100001401355700001801369700001601387700001201403700002001415700001801435700001901453856012601472 2008 eng d00aTransport Model Simulations of Projectile Fragmentation Reactions at 140 {MeV/nucleon}0 aTransport Model Simulations of Projectile Fragmentation Reaction c08/20080 v783 aThe collisions in four different reaction systems using {\$ˆ{40,48}\$Ca} and {\$ˆ{58,64}\$Ni} isotope beams and a Be target have been simulated using the Heavy Ion Phase Space Exploration and the Antisymmetrized Molecular Dynamics models. The present study mainly focuses on the model predictions for the excitation energies of the hot fragments and the cross sections of the final fragments produced in these reactions. The effects of various factors influencing the final fragment cross sections, such as the choice of the statistical decay code and its parameters have been explored. The predicted fragment cross sections are compared to the projectile fragmentation cross sections measured with the A1900 mass separator. At {\$E/A=140\$} {MeV,} reaction dynamics can significantly modify the detection efficiencies for the fragments and make them different from the efficiencies applied to the measured data reported in the previous work. The effects of efficiency corrections on the validation of event generator codes are discussed in the context of the two models.

10aNuclear Experiment10aNuclear Theory1 aMocko, M.1 aTsang, M., B.1 aLacroix, D.1 aOno, A.1 aDanielewicz, P.1 aLynch, W., G.1 aCharity, R., J uhttps://icer.msu.edu/research/publications/transport-model-simulations-projectile-fragmentation-reactions-140-mev-nucleon01096nas a2200385 4500008004100000245011100041210006900152260001200221490000700233100001400240700001700254700001400271700001800285700001800303700001900321700001600340700001500356700001600371700001300387700001600400700001900416700002600435700001400461700001500475700001600490700002000506700001700526700001700543700001400560700001600574700001400590700001900604700001600623856007100639 2007 eng d00aZ = 0 Shell Gap near 100Sn from Intermediate-Energy Coulomb Excitations ￼in Even-Mass 106-112Sn Isotopes0 aZ 0 Shell Gap near 100Sn from IntermediateEnergy Coulomb Excitat c10/20070 v991 aVaman, C.1 aAndreoiu, C.1 aBazin, D.1 aBeccerril, A.1 aBrown, B., A.1 aCampbell, C.M.1 aChester, A.1 aCook, J.M.1 aDinca, D.C.1 aGade, A.1 aGalaviz, D.1 aGlasmacher, T.1 aHjorth-Jensen}, M., {1 aHoroi, M.1 aMiller, D.1 aMoeller, V.1 aMueller, W., F.1 aSchiller, A.1 aStarosta, K.1 aStolz, A.1 aTerry, J.R.1 aVolya, A.1 aZelevinsky, V.1 aZwahlen, H. uhttp://journals.aps.org/prl/abstract/10.1103/PhysRevLett.99.16250102232nas a2200253 4500008004100000245008800041210006900129260001100198300001400209490000800223520146400231100001901695700001601714700001401730700001701744700001501761700001801776700001401794700001701808700001401825700001801839700001501857856010601872 2006 eng d00aExperimental and Theoretical UV Characterizations of Acetyloacetone and its Isomers0 aExperimental and Theoretical UV Characterizations of Acetyloacet c2/2006 a3920-39260 v1103 aCryogenic 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.

1 aPiecuch, Piotr1 aCoussan, S.1 aFerro, Y.1 aTrivella, A.1 aRoubin, P.1 aWieczorek, R.1 aManca, C.1 aKowalski, K.1 aWloch, M.1 aKucharski, S.1 aMusial, M. uhttps://icer.msu.edu/experimental-and-theoretical-uv-characterizations-acetyloacetone-and-its-isomers01358nas a2200301 4500008004100000245003200041210003100073260001200104300001100116490000700127520059800134100002000732700002000752700001800772700002200790700001900812700001400831700002400845700001900869700002000888700001400908700001500922700001400937700001800951700001900969700001800988856005001006 2006 eng d00aHalf-life and spin of 60Mng0 aHalflife and spin of 60Mng c04/2006 a0443220 v733 aA value of 0.28±0.02 s has been deduced for the half-life of the ground state of {60Mn,} in sharp contrast to the previously adopted value of 51±6 s. Access to the low-spin {60Mn} ground state was accomplished via β decay of the 0+ {60Cr} parent nuclide. New low-energy states in {60Mn} have been identified from β-delayed γ-ray spectroscopy. The new, shorter half-life of {60Mng} is not suggestive of isospin-forbidden β decay, and new spin and parity assignments of 1+ and 4+ have been adopted for the ground and isomeric β-decaying states, respectively, of {60Mn.}

1 aLiddick, S., N.1 aMantica, P., F.1 aBrown, B., A.1 aCarpenter, M., P.1 aDavies, A., D.1 aHoroi, M.1 aJanssens, R., V. F.1 aMorton, A., C.1 aMueller, W., F.1 aPavan, J.1 aSchatz, H.1 aStolz, A.1 aTabor, S., L.1 aTomlin, B., E.1 aWiedeking, M. uhttps://icer.msu.edu/half-life-and-spin-60mng00743nas a2200277 4500008004100000245003200041210003100073260001200104490000700116100002000123700002000143700001800163700002200181700001900203700001400222700002400236700001900260700002000279700001400299700001500313700001400328700001800342700001900360700001800379856006800397 2006 eng d00aHalf-life and spin of 60Mng0 aHalflife and spin of 60Mng c04/20060 v731 aLiddick, S., N.1 aMantica, P., F.1 aBrown, B., A.1 aCarpenter, M., P.1 aDavies, A., D.1 aHoroi, M.1 aJanssens, R., V. F.1 aMorton, A., C.1 aMueller, W., F.1 aPavan, J.1 aSchatz, H.1 aStolz, A.1 aTabor, S., L.1 aTomlin, B., E.1 aWiedeking, M. uhttp://journals.aps.org/prc/abstract/10.1103/PhysRevC.73.04432201686nas a2200133 4500008004100000245010300041210006900144300001400213490000800227520116200235100002401397700001801421856011301439 2006 eng d00aMolecular Dynamics Simulations of Large Integral Membrane Proteins with an Implicit Membrane Model0 aMolecular Dynamics Simulations of Large Integral Membrane Protei a548–5560 v1103 aThe 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.

1 aTanizaki, Seiichiro1 aFeig, Michael uhttps://icer.msu.edu/molecular-dynamics-simulations-large-integral-membrane-proteins-implicit-membrane-model01552nas a2200169 4500008004100000245026000041210006900301260001200370300001600382490000800398520078000406100001901186700001501205700001801220700002301238856012101261 2005 eng d00aCan a Single-Reference Approach Provide a Balanced Description of Ground and Excited States? A Comparison of the Completely Renormalized Equation-of-the-Motion Coupled-Cluster Method with Multi-Reference Quasi-Degenerate Perturbation Theory Near a Conical0 aCan a SingleReference Approach Provide a Balanced Description of c11/2005 a11643-116460 v1093 aWe calculated the two lowest electronically adiabatic potential energy surfaces of ammonia in the region of the conical intersection and at a sequence of geometries along which one of the N-H bonds is broken. We employed both a multireference (MR) method and a single-reference (SR) method. The MR calculations are based on multiconfiguration quasidegenerate perturbation theory (MC-QDPT) with a 6-311+G(3df,3pd) basis set. The SR calculations, carried out with the same basis, employ the completely renormalized equation-ofmotion coupled-cluster method with singles and doubles, and a noniterative treatment of triples, denoted CR-EOMCCSD(T). At 91 geometries used for comparison, including geometries near a conical intersection, the surfaces agree to 7% on average.

1 aPiecuch, Piotr1 aNangia, S.1 aTruhlar, D.G.1 aMcGuire}, M., J. { uhttps://icer.msu.edu/research/publications/can-single-reference-approach-provide-balanced-description-ground-excited01534nas a2200265 4500008004100000245007500041210006900116260001500185300001200200490000800212520073300220100001900953700002000972700001600992700001301008700001701021700001401038700002201052700001801074700001401092700001701106700001301123700001701136856011501153 2005 eng d00aComparison of Low-Order Multireference Many-Body Perturbation Theories0 aComparison of LowOrder Multireference ManyBody Perturbation Theo c04/01/2005 a9 pages0 v1223 aTests 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.

1 aPiecuch, Piotr1 aChaudhuri, R.K.1 aFreed, K.F.1 aHose, G.1 aKowalski, K.1 aWloch, M.1 aChattopadhyay, S.1 aMukherjee, D.1 aRolik, R.1 aSzabados, A.1 aToth, G.1 aSurjan, P.R. uhttps://icer.msu.edu/research/publications/comparison-low-order-multireference-many-body-perturbation-theories