Accelerating Kohn‐Sham response theory using density fitting and the auxiliary‐density‐matrix method

An extension of the formulation of the atomic‐orbital‐based response theory of Larsen et al., JCP 113, 8909 (2000) is presented. This new framework has been implemented in LSDalton and allows for the use of Kohn‐Sham density‐functional theory with approximate treatment of the Coulomb and Exchange contributions to the response equations via the popular resolution‐of‐the‐identity approximation as well as the auxiliary‐density matrix method (ADMM). We present benchmark calculations of ground‐state energies as well as the linear and quadratic response properties: vertical excitation energies, polarizabilities, and hyperpolarizabilities. The quality of these approximations in a range of basis sets is assessed against reference calculations in a large aug‐pcseg‐4 basis. Our results confirm that density fitting of the Coulomb contribution can be used without hesitation for all the studied properties. The ADMM treatment of exchange is shown to yield high accuracy for ground‐state and excitation energies, whereas for polarizabilities and hyperpolarizabilities the performance gain comes at a cost of accuracy. Excitation energies of a tetrameric model consisting of units of the P700 special pigment of photosystem I have been studied to demonstrate the applicability of the code for a large system.

[1]  Chandan Kumar,et al.  Nuclei-selected atomic-orbital response-theory formulation for the calculation of NMR shielding tensors using density-fitting. , 2016, The Journal of chemical physics.

[2]  Jógvan Magnus Haugaard Olsen,et al.  Open-ended response theory with polarizable embedding: multiphoton absorption in biomolecular systems. , 2016, Physical chemistry chemical physics : PCCP.

[3]  Ville R. I. Kaila,et al.  Exploring the Light-Capturing Properties of Photosynthetic Chlorophyll Clusters Using Large-Scale Correlated Calculations. , 2016, Journal of chemical theory and computation.

[4]  C. Hättig,et al.  Excited state polarizabilities for CC2 using the resolution-of-the-identity approximation. , 2015, The Journal of chemical physics.

[5]  K. Ruud,et al.  Open-ended recursive calculation of single residues of response functions for perturbation-dependent basis sets. , 2015, Journal of chemical theory and computation.

[6]  Paul R. Horn,et al.  Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm. , 2015, The Journal of chemical physics.

[7]  Kenneth Ruud,et al.  Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements , 2015, Journal of chemical theory and computation.

[8]  Samuel F. Manzer,et al.  Efficient Implementation of the Pair Atomic Resolution of the Identity Approximation for Exact Exchange for Hybrid and Range-Separated Density Functionals , 2014, Journal of chemical theory and computation.

[9]  Patrick Merlot,et al.  Charge-constrained auxiliary-density-matrix methods for the Hartree-Fock exchange contribution. , 2014, The Journal of chemical physics.

[10]  Dan Jonsson,et al.  A general, recursive, and open‐ended response code , 2014, J. Comput. Chem..

[11]  C. Hättig,et al.  Optical rotation calculations on large molecules using the approximate coupled cluster model CC2 and the resolution-of-the-identity approximation. , 2014, Physical chemistry chemical physics : PCCP.

[12]  F. Jensen.  Unifying General and Segmented Contracted Basis Sets. Segmented Polarization Consistent Basis Sets. , 2014, Journal of chemical theory and computation.

[13]  Edward F. Valeev,et al.  Semi-exact concentric atomic density fitting: reduced cost and increased accuracy compared to standard density fitting. , 2014, The Journal of chemical physics.

[14]  E. Schlodder,et al.  Long-Wavelength Limit of Photochemical Energy Conversion in Photosystem I , 2014, Journal of the American Chemical Society.

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

[16]  Patrick Merlot,et al.  Attractive electron–electron interactions within robust local fitting approximations , 2013, J. Comput. Chem..

[17]  C. Hättig,et al.  Analytic Molecular Hessian Calculations for CC2 and MP2 Combined with the Resolution of Identity Approximation. , 2013, Journal of chemical theory and computation.

[18]  C. Hättig,et al.  Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolution-of-the-identity approximation. , 2012, The Journal of chemical physics.

[19]  Trygve Helgaker,et al.  Multi‐electron integrals , 2012 .

[20]  Kenneth Ruud,et al.  Calculation of two-photon absorption strengths with the approximate coupled cluster singles and doubles model CC2 using the resolution-of-identity approximation. , 2012, Physical chemistry chemical physics : PCCP.

[21]  Weitao Yang,et al.  Challenges for density functional theory. , 2012, Chemical reviews.

[22]  A. Tkatchenko,et al.  Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions , 2012, 1201.0655.

[23]  M. E. Casida,et al.  Progress in time-dependent density-functional theory. , 2011, Annual review of physical chemistry.

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

[25]  Trygve Helgaker,et al.  An efficient density-functional-theory force evaluation for large molecular systems. , 2010, The Journal of chemical physics.

[26]  Joost VandeVondele,et al.  Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations. , 2010, Journal of chemical theory and computation.

[27]  Julian Yarkony,et al.  Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration. , 2010, The Journal of chemical physics.

[28]  T. Renger,et al.  Structure-based calculations of optical spectra of photosystem I suggest an asymmetric light-harvesting process. , 2010, Journal of the American Chemical Society.

[29]  M. Schütz,et al.  Density fitted, local Hartree–Fock treatment of NMR chemical shifts using London atomic orbitals , 2010 .

[30]  Roland Lindh,et al.  Density fitting with auxiliary basis sets from Cholesky decompositions , 2009 .

[31]  Á. Rubio,et al.  Time-dependent density-functional theory. , 2009, Physical chemistry chemical physics : PCCP.

[32]  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 .

[33]  Kenneth Ruud,et al.  A density matrix-based quasienergy formulation of the Kohn-Sham density functional response theory using perturbation- and time-dependent basis sets. , 2008, The Journal of chemical physics.

[34]  P. Jørgensen,et al.  Efficient elimination of response parameters in molecular property calculations for variational and nonvariational energies. , 2008, The Journal of chemical physics.

[35]  Henrik Koch,et al.  Method specific Cholesky decomposition: coulomb and exchange energies. , 2008, The Journal of chemical physics.

[36]  T. Helgaker,et al.  Variational and robust density fitting of four-center two-electron integrals in local metrics. , 2008, The Journal of chemical physics.

[37]  Trygve Helgaker,et al.  Hartree-Fock and Kohn-Sham time-dependent response theory in a second-quantization atomic-orbital formalism suitable for linear scaling. , 2008, The Journal of chemical physics.

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

[39]  Martin Head-Gordon,et al.  Hartree-Fock exchange computed using the atomic resolution of the identity approximation. , 2008, The Journal of chemical physics.

[40]  A. Kamel,et al.  BSSE effects on the static dipole polarizability and first dipole hyperpolarizability of diclofenac sodium , 2008 .

[41]  Florian Weigend,et al.  Hartree–Fock exchange fitting basis sets for H to Rn † , 2008, J. Comput. Chem..

[42]  Trygve Helgaker,et al.  Excitation energies in density functional theory: an evaluation and a diagnostic test. , 2008, The Journal of chemical physics.

[43]  Jörg Kussmann,et al.  A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels. , 2007, The Journal of chemical physics.

[44]  E. Schlodder,et al.  Steady-state and transient polarized absorption spectroscopy of photosystem I complexes from the cyanobacteria Arthrospira platensis and Thermosynechococcus elongatus. , 2007, Biochimica et biophysica acta.

[45]  R. Lindh,et al.  Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals. , 2007, The Journal of chemical physics.

[46]  Paweł Sałek,et al.  Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory. , 2007, The Journal of chemical physics.

[47]  Joseph E. Subotnik,et al.  Linear scaling density fitting. , 2006, The Journal of chemical physics.

[48]  F. Manby,et al.  Explicitly correlated second-order perturbation theory using density fitting and local approximations. , 2006, The Journal of chemical physics.

[49]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[50]  Dmitrij Rappoport,et al.  Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules. , 2005, The Journal of chemical physics.

[51]  K. Burke,et al.  Time-dependent density functional theory: past, present, and future. , 2004, The Journal of chemical physics.

[52]  Dmitrij Rappoport,et al.  Density functional methods for excited states: equilibrium structure and electronic spectra , 2005 .

[53]  Frederick R. Manby,et al.  Fast Hartree–Fock theory using local density fitting approximations , 2004 .

[54]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[55]  Filipp Furche,et al.  Nuclear second analytical derivative calculations using auxiliary basis set expansions , 2004 .

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

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

[58]  Frederick R. Manby,et al.  Density fitting in second-order linear-r12 Møller–Plesset perturbation theory , 2003 .

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

[60]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

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

[62]  K. Capelle.  A bird's-eye view of density-functional theory , 2002, cond-mat/0211443.

[63]  Paweł Sałek,et al.  Density-functional theory of linear and nonlinear time-dependent molecular properties , 2002 .

[64]  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 .

[65]  Florian Weigend,et al.  A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency , 2002 .

[66]  F. Neese,et al.  Efficient use of the resolution of the identity approximation in time-dependent density functional calculations with hybrid density functionals , 2002 .

[67]  S. Grimme,et al.  An improved method for density functional calculations of the frequency-dependent optical rotation , 2002 .

[68]  Christof Hättig,et al.  Implementation of RI-CC2 triplet excitation energies with an application to trans-azobenzene , 2002 .

[69]  K. Hirao,et al.  A long-range correction scheme for generalized-gradient-approximation exchange functionals , 2001 .

[70]  R. Zwanzig.  Nonequilibrium statistical mechanics , 2001, Physics Subject Headings (PhySH).

[71]  Trygve Helgaker,et al.  Hartree–Fock and Kohn–Sham atomic-orbital based time-dependent response theory , 2000 .

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

[73]  Trygve Helgaker,et al.  Direct optimization of the AO density matrix in Hartree-Fock and Kohn-Sham theories , 2000 .

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

[75]  G. Maroulis.  Static hyperpolarizability of the water dimer and the interaction hyperpolarizability of two water molecules , 2000 .

[76]  Yihan Shao,et al.  An improved J matrix engine for density functional theory calculations , 2000 .

[77]  B. I. Dunlap,et al.  Robust variational fitting: Gáspár's variational exchange can accurately be treated analytically , 2000 .

[78]  M. Ratner.  Molecular electronic-structure theory , 2000 .

[79]  G. Beddard.  Exciton Coupling in the Photosystem I Reaction Center , 1998 .

[80]  Christian Ochsenfeld,et al.  Linear and sublinear scaling formation of Hartree-Fock-type exchange matrices , 1998 .

[81]  Poul Jørgensen,et al.  Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy , 1998 .

[82]  Marco Häser,et al.  CALCULATION OF EXCITATION ENERGIES WITHIN TIME-DEPENDENT DENSITY FUNCTIONAL THEORY USING AUXILIARY BASIS SET EXPANSIONS , 1997 .

[83]  Martin Head-Gordon,et al.  A J matrix engine for density functional theory calculations , 1996 .

[84]  Jan Almlöf,et al.  THE COULOMB OPERATOR IN A GAUSSIAN PRODUCT BASIS , 1995 .

[85]  Jochen Schirmer,et al.  An efficient polarization propagator approach to valence electron excitation spectra , 1995 .

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

[87]  F. Aiga,et al.  Higher‐order response theory based on the quasienergy derivatives: The derivation of the frequency‐dependent polarizabilities and hyperpolarizabilities , 1993 .

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

[89]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

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

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

[92]  Richard A. Friesner,et al.  Solution of the Hartree–Fock equations for polyatomic molecules by a pseudospectral method , 1987 .

[93]  Richard A. Friesner,et al.  Solution of the Hartree–Fock equations by a pseudospectral method: Application to diatomic molecules , 1986 .

[94]  Richard A. Friesner,et al.  Solution of self-consistent field electronic structure equations by a pseudospectral method , 1985 .

[95]  M. Rohmer.  Electronic ground state of iron(II)porphyrin. Ab initio SCF and CI calculations and computed electron deformation densities , 1985 .

[96]  J. Olsen,et al.  Linear and nonlinear response functions for an exact state and for an MCSCF state , 1985 .

[97]  P. Eisenberger,et al.  Direct structural study of Cl on Si {111} and Ge {111} surfaces: New conclusions , 1983 .

[98]  Jochen Schirmer,et al.  Beyond the random-phase approximation: A new approximation scheme for the polarization propagator , 1982 .

[99]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[100]  J. Connolly,et al.  On first‐row diatomic molecules and local density models , 1979 .

[101]  John R. Sabin,et al.  On some approximations in applications of Xα theory , 1979 .

[102]  N. H. Beebe,et al.  Simplifications in the generation and transformation of two‐electron integrals in molecular calculations , 1977 .

[103]  Evert Jan Baerends,et al.  Self-consistent molecular hartree—fock—slater calculations. IV. On electron densities, spectroscopic constants and proton affinities of some small molecules , 1976 .

[104]  J. Whitten,et al.  Electron repulsion integral approximations and error bounds: Molecular applications , 1974 .

[105]  Evert Jan Baerends,et al.  Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure , 1973 .

[106]  J. L. Whitten,et al.  Coulombic potential energy integrals and approximations , 1973 .

[107]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[108]  F. London,et al.  Théorie quantique des courants interatomiques dans les combinaisons aromatiques , 1937 .

[109]  P. Dirac.  Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.