LoFEx - A local framework for calculating excitation energies: Illustrations using RI-CC2 linear response theory.

We present a local framework for the calculation of coupled cluster excitation energies of large molecules (LoFEx). The method utilizes time-dependent Hartree-Fock information about the transitions of interest through the concept of natural transition orbitals (NTOs). The NTOs are used in combination with localized occupied and virtual Hartree-Fock orbitals to generate a reduced excitation orbital space (XOS) specific to each transition where a standard coupled cluster calculation is carried out. Each XOS is optimized to ensure that the excitation energies are determined to a predefined precision. We apply LoFEx in combination with the RI-CC2 model to calculate the lowest excitation energies of a set of medium-sized organic molecules. The results demonstrate the black-box nature of the LoFEx approach and show that significant computational savings can be gained without affecting the accuracy of CC2 excitation energies.

[1]  Richard L. Martin.  NATURAL TRANSITION ORBITALS , 2003 .

[2]  Pablo Baudin,et al.  Calculation of excitation energies from the CC2 linear response theory using Cholesky decomposition. , 2014, The Journal of chemical physics.

[3]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[4]  P. Jørgensen,et al.  Orbital spaces in the divide-expand-consolidate coupled cluster method. , 2016, The Journal of chemical physics.

[5]  E. Davidson.  The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .

[6]  T. Etienne.  Transition matrices and orbitals from reduced density matrix theory. , 2015, The Journal of chemical physics.

[7]  Trygve Helgaker,et al.  Molecular Electronic-Structure Theory: Helgaker/Molecular Electronic-Structure Theory , 2000 .

[8]  P. Jørgensen,et al.  Characterization and Generation of Local Occupied and Virtual Hartree-Fock Orbitals. , 2016, Chemical reviews.

[9]  Jeppe Olsen,et al.  Excitation energies of BH, CH2 and Ne in full configuration interaction and the hierarchy CCS, CC2, CCSD and CC3 of coupled cluster models , 1995 .

[10]  C. Hättig,et al.  A pair natural orbital implementation of the coupled cluster model CC2 for excitation energies. , 2013, The Journal of chemical physics.

[11]  P. Jørgensen,et al.  Orbital localization using fourth central moment minimization. , 2012, The Journal of chemical physics.

[12]  H. Koch,et al.  Multi-level coupled cluster theory. , 2014, The Journal of chemical physics.

[13]  Martin W. Feyereisen,et al.  Use of approximate integrals in ab initio theory. An application in MP2 energy calculations , 1993 .

[14]  Stinne Høst,et al.  Local orbitals by minimizing powers of the orbital variance. , 2011, The Journal of chemical physics.

[15]  F. Weigend,et al.  Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations , 2002 .

[16]  S. F. Boys.  Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another , 1960 .

[17]  Thomas Kjærgaard,et al.  Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide-expand-consolidate RI-MP2 model. , 2016, The Journal of chemical physics.

[18]  Poul Jørgensen,et al.  The second-order approximate coupled cluster singles and doubles model CC2 , 1995 .

[19]  Tatiana Korona,et al.  Local CC2 electronic excitation energies for large molecules with density fitting. , 2006, The Journal of chemical physics.

[20]  H. Werner,et al.  Local treatment of electron excitations in the EOM-CCSD method , 2003 .

[21]  H. Koch,et al.  The extended CC2 model ECC2 , 2013 .

[22]  Jógvan Magnus Haugaard Olsen,et al.  PERI-CC2: A Polarizable Embedded RI-CC2 Method. , 2012, Journal of chemical theory and computation.

[23]  W. Thiel,et al.  Basis set effects on coupled cluster benchmarks of electronically excited states: CC3, CCSDR(3) and CC2 , 2010 .

[24]  Ville R. I. Kaila,et al.  Benchmarking the Approximate Second-Order Coupled-Cluster Method on Biochromophores. , 2011, Journal of chemical theory and computation.

[25]  Martin Schütz,et al.  A multistate local coupled cluster CC2 response method based on the Laplace transform. , 2009, The Journal of chemical physics.

[26]  E. Davidson,et al.  Improved Algorithms for the Lowest Few Eigenvalues and Associated Eigenvectors of Large Matrices , 1992 .

[27]  Ernest R. Davidson,et al.  Super-matrix methods , 1989 .

[28]  S. F. Boys,et al.  Canonical Configurational Interaction Procedure , 1960 .

[29]  Frank Neese,et al.  The ORCA program system , 2012 .

[30]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[31]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

[32]  Trygve Helgaker,et al.  Excitation energies from the coupled cluster singles and doubles linear response function (CCSDLR). Applications to Be, CH+, CO, and H2O , 1990 .

[33]  Christof Hättig,et al.  CC2 excitation energy calculations on large molecules using the resolution of the identity approximation , 2000 .

[34]  Ove Christiansen,et al.  Response functions in the CC3 iterative triple excitation model , 1995 .

[35]  Luca Frediani,et al.  The Dalton quantum chemistry program system , 2013, Wiley interdisciplinary reviews. Computational molecular science.

[36]  Jacob Kongsted,et al.  The polarizable embedding coupled cluster method. , 2011, Journal of Chemical Physics.

[37]  R. Mata,et al.  An incremental correlation approach to excited state energies based on natural transition/localized orbitals. , 2011, The Journal of chemical physics.

[38]  Conrad C. Huang,et al.  UCSF Chimera—A visualization system for exploratory research and analysis , 2004, J. Comput. Chem..