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Atomic, Chemical, and Nuclear Developments in Coupled Cluster Methods
(INT program June 23  July 25, 2008)
Reported by Rod Bartlett, David Dean, Walter Johnson, and Achim Schwenk
Date posted December 2, 2008
Today, Coupled Cluster (CC) theory is widely recognized as often offering the most accurate description available for a wealth of important problems in physics and chemistry, ranging from the structure of nuclei, to relativistic CC theory of atoms, to spectra and properties of molecules. The powerful exponential ansatz for the CC wave function, Ψ = exp(T) Φ_{0}, was proposed for nuclear manybody problems by Coester and Kuemmel 50 years ago. T=T1+T2+T3+... corresponds to the sum over particlehole excitation operators and Φ_{0} is a meanfield reference state. Detailed equations for the electronic structure of atoms and molecules were presented by Cizek 40 years ago, with initial applications and further developments by Paldus. In solving directly for the cluster operators, T1, T2,... , CC theory provides a nonperturbative method that extends abinitio approaches to important manybody systems with on the order of 100 particles. This positions CC theory as key to developing abinitio density functional theory and a unified description for all nuclei or atoms and molecules. The equations for the cluster operators, truncated at the CCSD[exp(T1+T2)], CCSDT[exp(T1+T2+T3)], or higher level, are always in closed form and lead to sizeextensive solutions. In addition, equationofmotion and Fock space extensions are used to study excitation energies in CC theory. At the 50th anniversary of CC theory, the INT program brought together nuclear physicists, atomic physicists, and quantum chemists to discuss the current status of CC efforts in these three fields; to identify and discuss new directions that may be of common interest; and to share common experiences in understanding and applying the CC methods to various problems of interest. As part of the program, we organized a threeday symposium on "50 Years of CoupledCluster Theory". In attendance celebrating this anniversary were the founders of CC theory: Profs. Hermann Kuemmel, Jiri Cizek, and Joe Paldus; Fritz Coester had planned to attend, but could unfortunately not be present. The program and symposium attracted 50 scientists from 15 countries, and the talks are available on the INT website. This provides a unique set of overviews and stateoftheart on CC theory for atoms, molecules and nuclei. CC methods for atoms, molecules and nuclei employ different symmetries and basis functions and have different objectives, but all three fields are connected by the underlying formalism.
In nuclear physics, CC theory connects key frontiers. CC theory tests nuclear forces based on effective field theory and the renormalization group, advances abinitio methods to mediummass nuclei, can provide benchmarks for developing a universal density functional from microscopic interactions, and takes advantage of largescale computing resources. Recent CC highlights in nuclear physics are shown in Figs. 1 and 2. The discussions at the program and the symposium focused on including threenucleon interactions and studying looselybound neutronrich nuclei in CC theory, on using CC theory to validate nuclear density functional theory (see also the SciDAC UNEDF project), and on ideas to derive nonperturbative shell model interactions using CC methods. Future CC milestones will be set by the first abinitio calculation with threenucleon interactions for mediummass nuclei, for the Helium and Oxygen chain, by advancing spherical CC theory to heavier nuclei, such as 100Sn and 208Pb, and an abinitio calculation of the neutron radius of 208Pb. Recent significant advances in developing coupledcluster theory have occurred in quantum chemistry. CC methods for ground, excited, closedshell, and openshell, nondegenerate and quasidegenerate states of atoms and molecules and molecular properties have been developed and were discussed in the program and the symposium. In quantum chemistry, CC theory is used to develop an abinitio density functional theory for electronic systems and there was much interest on these topics. Other main and crossdiscipline areas of discussion were applications to openshell systems, multireference CC theory, and alternative approaches for excited states. The focus of the atomic physics part of the program was on highprecision calculations of energy levels, transition moments, hyperfine constants, and other properties of atoms and ions with high nuclear charge. For neutral systems, highprecision calculations are needed to extract the weakcharge and nuclear anapole moment from experiments on atomic parity nonconservation at a level where significant tests of the Standard Model and theories of weak nuclear forces can be tested. Other important applications include atomic clocks, blackbody radiation shifts, and design of optical traps for quantum computer experiments. For highlycharged atoms, precision manybody calculations, when compared with measurements, are used to test strongfield corrections to quantum electrodynamics. From the point of view of chemistry, precise manybody calculations are needed to predict chemical properties of superheavy elements where direct chemical experiments are not yet possible. This INT program and symposium attracted many of the researchers who have been instrumental in working with CC theory and related methods for atoms, molecules, and nuclei. By all accounts, the workshop was a great success: The participants found the topics and discussions very useful for their future research. They planted the seeds for many ideas and showed a vibrant field for crossfertilization between the three areas! We gratefully acknowledge additional financial support from ORNL and TRIUMF.
