Calculation of excitation energies from the CC2 linear response theory using Cholesky decomposition.

A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model is reported. It employs a Cholesky decomposition of the two-electron integrals that significantly reduces the computational cost and the storage requirements of the method compared to standard implementations. Our algorithm also exploits a partitioning form of the CC2 equations which reduces the dimension of the problem and avoids the storage of doubles amplitudes. We present calculation of excitation energies of benzene using a hierarchy of basis sets and compare the results with conventional CC2 calculations. The reduction of the scaling is evaluated as well as the effect of the Cholesky decomposition parameter on the quality of the results. The new algorithm is used to perform an extrapolation to complete basis set investigation on the spectroscopically interesting benzylallene conformers. A set of calculations on medium-sized molecules is carried out to check the dependence of the accuracy of the results on the decomposition thresholds. Moreover, CC2 singlet excitation energies of the free base porphin are also presented.

[1]  Peter Pulay,et al.  Orbital-invariant formulation and second-order gradient evaluation in Møller-Plesset perturbation theory , 1986 .

[2]  Peter Pulay,et al.  Fourth‐order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method , 1987 .

[3]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[4]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[5]  M. Jungen,et al.  Universal Gaussian basis sets for an optimum representation of Rydberg and continuum wavefunctions , 1989 .

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

[7]  David Feller,et al.  Application of systematic sequences of wave functions to the water dimer , 1992 .

[8]  Bernard Philippe,et al.  The Davidson Method , 1994, SIAM J. Sci. Comput..

[9]  A. Schäfer,et al.  Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr , 1994 .

[10]  Theoretical determination of the electronic spectrum of free base porphin , 1994 .

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

[12]  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 .

[13]  J. Olsen,et al.  Excitation energies of H2O, N2 and C2 in full configuration interaction and coupled cluster theory , 1996 .

[14]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[15]  Thomas Bondo Pedersen,et al.  Coupled cluster response functions revisited , 1997 .

[16]  Trygve Helgaker,et al.  The CC3 model: An iterative coupled cluster approach including connected triples , 1997 .

[17]  H. Koch,et al.  Integral-direct coupled cluster calculations of frequency-dependent polarizabilities, transition probabilities and excited-state properties , 1998 .

[18]  Rodney J. Bartlett,et al.  Coupled-cluster calculations of the electronic excitation spectrum of free base porphin in a polarized basis , 1998 .

[19]  Georg Hetzer,et al.  Low-order scaling local electron correlation methods. I. Linear scaling local MP2 , 1999 .

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

[21]  Keiji Morokuma,et al.  New challenges in quantum chemistry: quests for accurate calculations for large molecular systems , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[22]  Christof Hättig,et al.  Transition moments and excited-state first-order properties in the coupled-cluster model CC2 using the resolution-of-the-identity approximation , 2002 .

[23]  A. Köhn,et al.  First-order properties for triplet excited states in the approximated coupled cluster model CC2 using an explicitly spin coupled basis , 2002 .

[24]  Christof Hättig,et al.  Geometry optimizations with the coupled-cluster model CC2 using the resolution-of-the-identity approximation , 2003 .

[25]  Thomas Bondo Pedersen,et al.  Reduced scaling in electronic structure calculations using Cholesky decompositions , 2003 .

[26]  P. Schleyer,et al.  How Aromatic Are Large (4n + 2)π Annulenes? , 2003 .

[27]  Thomas Bondo Pedersen,et al.  Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using Cholesky decompositions. , 2004, The Journal of chemical physics.

[28]  Hans Lischka,et al.  Excited-state intramolecular proton transfer: a survey of TDDFT and RI-CC2 excited-state potential energy surfaces. , 2005, The journal of physical chemistry. A.

[29]  Roland Lindh,et al.  Unbiased auxiliary basis sets for accurate two-electron integral approximations. , 2007, The Journal of chemical physics.

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

[31]  Andreas W. Götz,et al.  Quantum Chemistry on Graphics Processing Units , 2010 .

[32]  L. Cederbaum,et al.  On the Cholesky decomposition for electron propagator methods: General aspects and application on C(60). , 2009, The Journal of chemical physics.

[33]  Klaus Schulten,et al.  GPU-accelerated molecular modeling coming of age. , 2010, Journal of molecular graphics & modelling.

[34]  Carl C. Wamser,et al.  Porphyrins and phthalocyanines in solar photovoltaic cells , 2010 .

[35]  Jonas Boström,et al.  Calibration of Cholesky Auxiliary Basis Sets for Multiconfigurational Perturbation Theory Calculations of Excitation Energies. , 2010, Journal of chemical theory and computation.

[36]  Tjerk P. Straatsma,et al.  NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations , 2010, Comput. Phys. Commun..

[37]  Roland Lindh,et al.  Cholesky Decomposition Techniques in Electronic Structure Theory , 2011 .

[38]  Poul Jørgensen,et al.  The divide-expand-consolidate family of coupled cluster methods: numerical illustrations using second order Møller-Plesset perturbation theory. , 2012, The Journal of chemical physics.

[39]  Trygve Helgaker,et al.  Recent advances in wave function-based methods of molecular-property calculations. , 2012, Chemical reviews.

[40]  R. McMahon,et al.  Photochemistry of benzylallene: ring-closing reactions to form naphthalene. , 2012, Journal of the American Chemical Society.

[41]  Reinhold Schneider,et al.  Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis , 2013, SIAM J. Sci. Comput..

[42]  A. Kerridge.  A RASSCF study of free base, magnesium and zinc porphyrins: accuracy versus efficiency. , 2013, Physical chemistry chemical physics : PCCP.