# Methods & Acronyms

**RJB and the Bartlett Group are responsible for developing a number of methods widely used by theoretical chemists today. Below is a list of methods and pertinent paper(s) by RJB and his group.**

#### Many Body Perturbation Theory

MBPT | R.J. Bartlett and D.M. Silver, "Pair-correlation energies in sodium hydride with many-body perturbation theory," Phys. Rev. A 10, 1927-1931 (1974). |

R. J. Bartlett and D. M. Silver, “Many-body perturbation theory applied to hydrogen fluoride,” Chem. Phys. Lett. 29, 199-203 (1974). | |

R. J. Bartlett and D. M. Silver, “Many-body perturbation theory applied to electron pair correlation energies. I. Closed-shell first-row diatomic hydrides,” J. Chem. Phys. 62, 3258-3268 (1975). | |

MR-MBPT | S.A. Kucharshi and R.J. Bartlett, “Multireference many-body perturbation theory,” Int. J. Quant. Chem. Symp 22, 383-405 (1988). |

#### Coupled Cluster Theory

CCD, MBPT4, LCCD | R.J. Bartlett and G.D. Purvis, “Many-body perturbation theory, coupled-pair many-electron theory and the importance of quadruple excitations for the correlation problem,” Proceedings of the American Theoretical Chemistry Conference, Boulder, CO, Int. J. Quant. Chem. 14, 561-581 (1978). |

R. J. Bartlett and G. D. Purvis III, “Molecular applications of coupled cluster and many-body perturbation methods,” Proceedings of the Nobel Symposium on Many-Body Theory, Lerum, Sweden, Physica Scripta 21, 255-265 (1980). | |

CCSD | G.D. Purvis, III and R.J. Bartlett, “A full coupled-cluster singles and doubles method: The inclusion of disconnected triples,” J. Chem. Phys. 76, 1910-1918 (1982). |

CCSDT | J. Noga and R. J. Bartlett, “The full CCSDT model for molecular electronic structure,” J. Chem. Phys. 86, 7041-7050 (1987). Erratum: J. Chem. Phys. 89, 3401 (1988). |

CCSDTQ | S. A. Kucharski and R. J. Bartlett, “The coupled-cluster single, double, triple and quadruple excitation method,” J. Chem. Phys. 97, 4282-4288 (1992). |

CCSDT-1 | Y.S. Lee, S.A. Kucharski and R.J. Bartltt, "A coupled cluster approach with triple excitations,” J. Chem. Phys. 81, 5906-5912 (1984). |

CCSD[T] | Fourth order triples with CCSD amplitudes. M. Urban, J. Noga, S. J.Cole and R. J. Bartlett, “Towards a full CCSDT model for electron correlation,” J. Chem. Phys. 83, 4041-4046 (1985). [T] is the only fourth-order term using a HF reference. Raghavachari, Trucks, Head-Gordon and Pople added the fifth-order singles to get CCSD(T). This was facilitated by the Purvis Bartlett CCSD program, the only one in existence at the time, that was made available by Gary Trucks, a former Bartlett graduate student. In the next paper, we derive the most general form, which then properly counts the singles and the new, non-HF term as fourth-order subject to non-HF corrections. We also have to make a semi-canonical transformation to keep CCSD(T) non-iterative for the general case. |

CCSD(T) | General reference like Brueckner, ROHF, KS, etc. J. D. Watts, J. Gauss and R. J. Bartlett, “Coupled-cluster methods with noniterative triple excitations for restricted open-shell Hartree-Fock and other general single determinant reference functions. Energies and analytical gradients,” J. Chem. Phys. 98, 8718-8733 (1993). |

CCSDT-n | J. Noga, R. J. Bartlett and M. Urban, “Towards a full CCSDT model for electron correlation. CCSDT-n models,” Chem. Phys. Lett. 134, 126-132 (1987). |

ROHF-CCSD | M. Rittby and R. J. Bartlett, “An open-shell spin-restricted coupled cluster method: Application to ionization potentials in N2,” J. Phys. Chem. 92, 3033-3036 (1988). |

#### Reduced Space Methods

OVOS | L. Adamowicz and R.J. Bartlett, "Optimized virtual orbital space for high-level correlated calculations," J. Chem. Phys. 86, 6314-6324 (1987). |

FNO | A. Taube and R.J. Bartlett, "Frozen natural orbitals: Systematic basis set truncation for coupled-cluster theory," Coll. Czech. Chem. Commun. 70, 837-850 (2005). A. Taube and R.J. Bartlett,"Frozen natural orbital cooupled-cluster theory: Forces and applications to decomposition of nitroethane," J. Chem. Phys. 128, 164101/1-17 (2008). |

#### Analytical Gradients

ANALYTICAL GRADIENTS FOR MBPT/CC | L. Adamowicz, W. D. Laidig and R. J. Bartlett, “Analytical gradients for the coupled-cluster method,” Int. J. Quantum Chem. Symp. 18, 245-254 (1984). Critical idea for non-variational method. |

R. J. Bartlett, “Analytical evaluation of gradients in coupled-cluster and many-body perturbation theory” in Geometrical Derivatives of Energy Surfaces and Molecular Properties (P. Jørgensen and J. Simons, editors). Reidel, Dordrecht, The Netherlands, 35-61 (1986). Amplification and lambda operator | |

E. A. Salter, G. W. Trucks and R. J. Bartlett, “Analytic energy derivatives in many-body methods. I. First derivatives,” J. Chem. Phys. 90, 1752-1766 (1989). |

#### Equation-of-Motion

EOM-CC | J.F. Stanton and R. J. Bartlett, “The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties,” J. Chem. Phys. 98, 7029-7039 (1993). |

The first paper: Sekino and RJB, Int. J. Quantum Chem. Symp. 18, 255-265 (1984). | |

The second paper: (J. Geertsen, M. Rittby and R. J. Bartlett, “The equation-of-motion coupled-cluster method: Excitation energies of Be and CO,” Chem. Phys. Lett. 164, 57-62 (1989). | |

STEOM-CC | M. Nooijen and R. J. Bartlett, “Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons,” J. Chem. Phys. 107, 6812-6830 (1997). |

#### Multi-reference C-C Theory

SU-MR-CCSD | First formulation: S. A. Kucharski and R. J. Bartlett, “Hilbert space multireference coupled-cluster methods. I. The single and double excitation model,” J. Chem. Phys. 95, 8227-8238 (1991). |

Balkova, S. A. Kucharski, L. Meissner and R. J. Bartlett, “The multireference coupled-cluster method in Hilbert space: An incomplete model space application to the LiH molecule,” J. Chem. Phys. 95, 4311-4316 (1991). | |

A. Balkova, S. A. Kucharski, L. Meissner and R. J. Bartlett, “A Hilbert space multi-reference coupled-cluster study of the H4 model system,” Theor. Chim. Acta 80, 335-348 (1991). | |

Fock Space MR-CCSD | S. Pal, M. Rittby, R. J. Bartlett, D. Sinha and D. Mukherjee, “Multireference coupled-cluster methods using an incomplete model space: Application to ionization potentials and excitation energies of formaldehyde,” Chem. Phys. Lett. 137, 273-278 (1987). |

M. Rittby, S. Pal and R.J. Bartlett, “Multireference coupled-cluster method: Ionization potentials and excitation energies for ketene and diazomethane,” J. Chem. Phys. 90, 3214-3320 (1989). | |

M. L. Rittby and R. J. Bartlett, “Multireference coupled cluster theory in Fock space with an application to s-tetrazine,” Theor. Chim. Acta 80, 469-482 (1991). | |

TD-CCSD | A.Balkova and R.J. Bartlett, “Coupled-cluster method for open-shell singlet states,” Chem. Phys. Lett. 193, 364-372 (1992). |

MR-AQCC | P. G. Szalay and R. J. Bartlett, “Multi-reference averaged quadratic coupled-cluster method: A size-extensive modification of multi-reference CI,” Chem. Phys. Lett. 214, 481-488 (1993). This hybrid CI-CC MR method most often offeres the comparison numbers for the new MR-CC developments. It is in COLUMBUS and MOLPRO. |

#### Effective One-Particle Theories

AB INITIO DFT | R.J. Bartlett, V. F. Lotrich and I.V. Schweigert, “Ab initio DFT: The best of both worlds?” J. Chem. Phys. 123, 062205/1-062205/21 (2005). P. Verma, A. Perera, and R.J. Bartlett, "Increasing the applicability of DFT. I. Non-variational correlation corrections from Hartree-Fock DFT for predicting transition states," Chem. Phys. Letts. 524, 10-15 (2012). P. Verma and R.J. Bartlett, "Increasing the applicability of density functional theory. II. Correlation potentials from the random phase approximation and beyond," J. Chem. Phys. 136 (4), 044105/1-8 (2012). P. Varma and R.J. Bartlett, "Increasing the applicability of density functional theory. III. Do consistent Kohn_Sham density functional mthods exist?" J. Chem. Phys. 137, 134102/1-12 (2012). P. Varma and R.J. Bartlett, "Increasing the applicability of DFT. IV. Consequences of ionization-potential improved exchange-correlation potentials," J. Chem. Phys. 140 18A534/1-11 (2014). |

CORRELATED ORBITAL THEORY | R. J. Bartlett, “Towards an exact correlated orbital theory for electrons,” Frontiers Article, Chem. Phys. Lett. 484, 1-9 (2009). |

#### Reviews

R. J. Bartlett, “Many-body perturbation theory and coupled cluster theory for electron correlation in molecules” in Annual Reviews of Physical Chemistry, Volume 32, 359-401 (1981). | |

R. J. Bartlett and M. Musial, “Coupled-cluster theory in quantum chemistry”, Revs. of Modern Phys. 79, 291-352 (2007). |

#### Applications

1ST APPLICATION TO A POLYMER | S. Hirata, R. Podeszwa, M. Tobita and R. J. Bartlett, “Coupled-cluster singles and doubles for extended systems,” J. Chem. Phys. 120, 2581-2592 (2004). |

NMR COUPLING CONSTANTS | S. A. Perera, H. Sekino and R. J. Bartlett, “Coupled-cluster calculations of indirect nuclear coupling constants: The importance of non-Fermi contact contributions,” J. Chem. Phys. 101, 2186-2191 (1994). First theory to get these right. Now can even do it with DFT! |

METASTABLE MOLECULES | W. J. Lauderdale, J. F. Stanton and R. J. Bartlett, “Stability and energetics of metastable molecules: tetraazatetrahedrane (N4), hexaazabenzene (N6), and octaazacubane (N8),” J. Phys. Chem. 96, 1173-1178 (1992). This is another high visibility application area that RJB group has started and are still persuing. |