A non-iterative perturbative triples correction for the spin-flipping equation- of-motion coupled-cluster methods with single and double substitutions Prashant Uday Manohar and Anna Krylov Department of Chemistry, University of Southern California, Los Angeles, CA Why non-iterative perturbative triples correction? Based on simple concepts of perturbation theory Start with CCSD Hamiltonian matrix as zeroth order approximation Triples contribution incorporated using diagonal part (only) of the triples-triples block of the EOM(2,3) Hamiltonian matrix as perturbation EOM-CC: SD, SDT and (2,3) methods EOM-CCSD: T=T 1 +T 2 EOM-CC(2,3): T=T 1 +T 2 EOM-CCSDT: T=T 1 +T 2 +T 3 Scaling: N 6 N 6 Scaling: N 8,N 8 Scaling: N 6,N 8  = exp(T) |  0 > In EOM-CC methods, the Hamiltonian matrix is formed over n-tuply excited configurations and diagonalised to obtain roots of exact states H0H0 V The non-iterative triples correction: Salient features Based on second order perturbation theory Start with CCSD Hamiltonian matrix and EOM-CCSD wavefunction as zeroth order approximation Triples contribution incorporated using diagonal part (only) of the triples-triples block of the EOM(2,3) Hamiltonian matrix as perturbation SF correction is size-intensive Non-SF correction identical to CR-CCSD(T) L Non-iterative method with N 7 scaling No storage of six-index tensors involved The methylene radical Deviation of excitation energies from FCI values (TZ2P basis set) c 1 A 1 a 1 A 1 b 1 B 1 Ortho-benzyneMeta-benzynePara-benzyne Benzynes SF-TDDFT/6-31G* optimized geometries as cc-pVTZ basis set (236 basis functions; the calculation requires approximately 6 hours per state) Expt. results: P.G. Wenthold, R.R. Squires and W.C. Linegerger, J. Am. Chem. Soc. 120, 5279 (1998) o-, m- and p- benzyne: Total energies (hartree) and adiabatic singlet-triplet gaps (eV) Methodo-benzynem-benzynep-benzyne SF-CCSD SF-CCSD(fT) SF-CCSD(dT) Expt.1.628± ± ±0.016  ZPE Expt-  ZPE ,3 Cyclobutadiene Orbital picture of cyclobutadiene at triplet and singlet geometries 1 3 A 2g geometryX 1 A g geometry Relative Energy levels in triplet(left) and singlet(right) geometries Adiabatic singlet-triplet gap ( 3 A 2g – 1 A g ) of cyclobutadiene (eV) calculated using cc-pVTZ basis set References P. Piecuch, M. Wloch, J.R. Gour and A. Kinal, Chem. Phys. Lett. 418, 463 (2005). P. Piecuch and M. Wloch, J. Chem. Phys. 123, (2005). M. Wloch, M. D. Lodriguito, Piecuch and J.R. Gour, Mol. Phys. 104, 10 (2006). J.F. Stanton and J. Gauss, Theor. Chim. Acta. 93, 303 (1996). T.D. Crawford and J.F. Stanton, Int. J. Quant. Chem. 70, 601 (1998). S.A. Kucharski and R.J. Bartlett, J. Chem. Phys. 108, 5243 (1998). S.R. Gwaltney, C.D. Sherrill, M. Head-Gordon and A.I. Krylov, J. Chem. Phys. 113, 3548 (2000). S.R. Gwaltney and M. Head-Gordon, J. Chem. Phys. 115, 2014 (2001). S. Hirata, M. Nooijen, I. Grabowski and R.J. Bartlett, J. Chem. Phys. 114, 3919 (2001). Y. Shao et. al. Phys. Chem. Chem. Phys. 8, 3172 (2006). P.U. Manohar and A.I. Krylov, J. Chem. Phys. (2008) communicated. Acknowledgements University of Southern California iOpenshell National Science Foundation