Towards a pair natural orbital coupled cluster method for excited states.

The use of back-transformed pair natural orbitals in the calculation of excited state energies, ionization potentials, and electron affinities is investigated within the framework of equation of motion coupled cluster theory and its similarity transformed variant. Possible approaches to a more optimal use of pair natural orbitals in these methods are indicated.

[1]  Achintya Kumar Dutta,et al.  EOMIP-CCSD(2)*: an efficient method for the calculation of ionization potentials. , 2015, Journal of chemical theory and computation.

[2]  Frank Neese,et al.  An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix , 2003, J. Comput. Chem..

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

[4]  C. David Sherrill,et al.  Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction. , 2014, The Journal of chemical physics.

[5]  P Pulay,et al.  Local Treatment of Electron Correlation , 1993 .

[6]  F. Neese,et al.  Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange , 2009 .

[7]  Frank Neese,et al.  Natural triple excitations in local coupled cluster calculations with pair natural orbitals. , 2013, The Journal of chemical physics.

[8]  H. Lischka,et al.  PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. II. The molecules BeH2, BH, BH3, CH4, CH−3, NH3 (planar and pyramidal), H2O, OH+3, HF and the Ne atom , 1975 .

[9]  C. Hättig,et al.  A pair natural orbital based implementation of ADC(2)-x: Perspectives and challenges for response methods for singly and doubly excited states in large molecules , 2014 .

[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]  L. H. Andersen,et al.  S1 and S2 excited States of gas-phase Schiff-base retinal chromophores. , 2006, Physical review letters.

[12]  Frederick R Manby,et al.  The orbital-specific virtual local triples correction: OSV-L(T). , 2013, 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]  T. Martínez,et al.  Tensor hypercontraction equation-of-motion second-order approximate coupled cluster: electronic excitation energies in O(N4) time. , 2013, The journal of physical chemistry. B.

[15]  Robert M Parrish,et al.  Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions. , 2012, The Journal of chemical physics.

[16]  Manoj K. Kesharwani,et al.  Exploring the Accuracy Limits of Local Pair Natural Orbital Coupled-Cluster Theory. , 2015, Journal of chemical theory and computation.

[17]  John F. Stanton,et al.  Perturbative treatment of the similarity transformed Hamiltonian in equation‐of‐motion coupled‐cluster approximations , 1995 .

[18]  Frank Neese,et al.  Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals. , 2015, The Journal of chemical physics.

[19]  Marcel Nooijen,et al.  Second order many-body perturbation approximations to the Coupled Cluster Green's Function. , 1995 .

[20]  Frank Neese,et al.  An efficient and near linear scaling pair natural orbital based local coupled cluster method. , 2013, The Journal of chemical physics.

[21]  Robert M Parrish,et al.  Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory. , 2012, The Journal of chemical physics.

[22]  J. Gauss,et al.  Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method , 1994 .

[23]  Achintya Kumar Dutta,et al.  Partitioned EOMEA-MBPT(2): An Efficient N(5) Scaling Method for Calculation of Electron Affinities. , 2014, Journal of chemical theory and computation.

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

[25]  Henrik Koch,et al.  Coupled cluster response functions , 1990 .

[26]  M. Krauss,et al.  Pseudonatural Orbitals as a Basis for the Superposition of Configurations. I. He2 , 1966 .

[27]  Evgeny Epifanovsky,et al.  General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: theory and benchmarks. , 2013, The Journal of chemical physics.

[28]  Wilfried Meyer,et al.  Ionization energies of water from PNO‐CI calculations , 2009 .

[29]  Walter Thiel,et al.  Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. , 2008, The Journal of chemical physics.

[30]  Holger Patzelt,et al.  RI-MP2: optimized auxiliary basis sets and demonstration of efficiency , 1998 .

[31]  H. Koch,et al.  Calculation of size‐intensive transition moments from the coupled cluster singles and doubles linear response function , 1994 .

[32]  Fock space multi-reference coupled-cluster method for energies and energy derivatives , 2010 .

[33]  Dimitrios G Liakos,et al.  Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis. , 2009, The Journal of chemical physics.

[34]  F. Neese,et al.  Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method. , 2009, The Journal of chemical physics.

[35]  Frederick R Manby,et al.  The orbital-specific-virtual local coupled cluster singles and doubles method. , 2012, The Journal of chemical physics.

[36]  Christof Hättig,et al.  Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation , 2003 .

[37]  Rodney J. Bartlett,et al.  Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons , 1997 .

[38]  Rodney J. Bartlett,et al.  Equation of motion coupled cluster method for electron attachment , 1995 .

[39]  F. Neese,et al.  Speeding up equation of motion coupled cluster theory with the chain of spheres approximation. , 2016, The Journal of chemical physics.

[40]  W. Kutzelnigg.  Die Lösung des quantenmechanischen Zwei-Elektronenproblems durch unmittelbare Bestimmung der natürlichen Einelektronenfunktionen , 1963 .

[41]  John F. Stanton,et al.  The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties , 1993 .

[42]  R. Bartlett,et al.  Simplified methods for equation-of-motion coupled-cluster excited state calculations , 1996 .

[43]  Robert M Parrish,et al.  Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2. , 2013, The Journal of chemical physics.

[44]  J. Almlöf,et al.  Integral approximations for LCAO-SCF calculations , 1993 .

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

[46]  S. Pal,et al.  Performance of the EOMIP-CCSD(2) Method for Determining the Structure and Properties of Doublet Radicals: A Benchmark Investigation. , 2013, Journal of chemical theory and computation.

[47]  K. Emrich,et al.  An extension of the coupled cluster formalism to excited states (I) , 1981 .

[48]  Florian Weigend,et al.  Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods. , 2009, The Journal of chemical physics.

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

[50]  F. Neese,et al.  Efficient and accurate local single reference correlation methods for high-spin open-shell molecules using pair natural orbitals. , 2011, The Journal of chemical physics.

[51]  Frank Neese,et al.  Sparse maps--A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory. , 2016, The Journal of chemical physics.

[52]  Debashree Ghosh,et al.  Perturbative approximations to single and double spin flip equation of motion coupled cluster singles doubles methods. , 2013, The Journal of chemical physics.

[53]  M. Head‐Gordon,et al.  Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange , 2003 .

[54]  T. Daniel Crawford,et al.  Locally correlated equation-of-motion coupled cluster theory for the excited states of large molecules , 2002 .

[55]  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 .

[56]  Frank Neese,et al.  An overlap fitted chain of spheres exchange method. , 2011, The Journal of chemical physics.

[57]  Christof Hättig,et al.  Local pair natural orbitals for excited states. , 2011, The Journal of chemical physics.